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DEVELOPMENT OF NI-MN-BASED FERROMAGNETIC
SHAPE MEMORY ALLOYS
Zhigang Wu
School of Mechanical and Chemical Engineering
The University of Western Australia
This thesis is presented for the degree of Doctor of Philosophy of Engineering of The University of Western Australia
(2011)
i
Abstract ________________________________________________________________________________
Since the discovery of Ni2MnGa ferromagnetic shape memory alloys some 15 years ago,
intensive research has been conducted to search and develop new and more powerful
magnetically activated shape memory alloys. The effort has been severely hampered by the
low magnetic driving force, intrinsically limited by the magnitude of magnetic
crystallographic anisotropy, for mechanical actuation. The discovery of metamagnetic
phase transformation in Ni-Mn-Z (Z=In,Sn,Sb) system in 2004, with their large
magnetization difference across the transformation, made a breakthrough and brought new
promise for creating magnetically activated shape memory alloys. This study is concerned
with the development of Ni-Mn-Z (Z=In,Sn) ternary ferromagnetic martensitic alloys.
Whereas having high promise owing to their large magnetization difference between their
nonmagnetic martensite and ferromagnetic austenite, these alloys face the challenges of
high mechanical resistance to deformation and brittleness. In response to these challenges,
this study is focused on two main objectives: (1) to further enhance the magnetization
difference of the metamagnetic reverse transformation of the alloys, and (2) to improve the
toughness and ductility of the alloys, through alloying.
(1) Enhance the Magnetization Difference
New alloy design is accomplished in order to increase the magnetization difference
between the austenitic and martensitic phases in Ni-Mn-Z (Z=In,Sn) alloys. The first step
of the composition design is to maximise the use of Mn content to provide the potentially
largest magnetization. Then, the proportion between Ni and In/Sn contents is adjusted to
alter the chemical order for obtaining ferromagnetic structure. Lastly, Co addition is
employed to modify the e/a ratio and to enhance the magnetic ordering of these alloys. In
the new compositions of Mn50Ni40-xIn10Cox and Mn50Ni42-xSn8Cox alloys, a martensitic
transformation from an Hg2CuTi-type austenite to body centred tetragonal martensite was
observed. In both systems, the magnetization of the austenite increased significantly,
ii
whereas that of the martensite changed much less prominently with increasing the Co
substitution for Ni, leading to the significantly enhanced magnetization difference across
the transformation. The increased magnetization of the austenite is attributed to (i)
formation of ferromagnetically coupled Mn-Mn atoms due to the new atomic configuration
in off-stoichiometric composition, (ii) higher magnetic moment contribution of Co relative
than Ni, and (iii) widening of temperature window for ferromagnetic austenite. The low
magnetization of the martensite, relative to that of the austenite, is due to the significantly
shortened distance between Mn-Mn, which leads to the disappearance of the local
ferromagnetic structure in a tetragonal martensitic structure.
(2) Improve the Alloy Ductility
Fe is utilised to substitute for Mn in Ni-Mn-Z(Z=In, Sn) alloys to form a phase in the
matrix to increase the ductility of the alloys. Whereas much attention has been given to the
ductility improvement, metallurgical origins of the influences of fourth element addition on
the martensitic and magnetic properties are much less understood. In Ni50Mn38-xIn12Fex and
Ni50Mn40-xSn10Fex alloys, a martensitic transformation from a B2 austenite to an
orthorhombic martensite was realised. Substitution of Fe for Mn at above 3 at% introduced
an fcc phase in the microstructure, the amount of which increased with increasing Fe
addition in both systems. The Curie temperature of the parent phase increased slightly,
whereas the Curie temperature of the martensite increased rapidly with increasing Fe
addition. Changes in the temperatures of the martensitic and magnetic transformations are
confirmed to directly relate to the e/a ratio of the matrix caused by the formation of phase.
Fe addition effectively weakens the antiferromagnetic ordering of the austenite in the
matrix phase, leading to the increase of magnetization difference across the martensitic
transformation. The relative shape memory effect decreased from 94 % to 37 % after 4 at%
Fe addition. These findings clarify the metallurgical origins of the side effects of Fe
addition on martensitic and magnetic properties and provide reference on alloy design for
Ni-Mn-based alloy systems.
iii
Publications arising from this thesis ________________________________________________________________________________
This thesis is written as a series of research publications, and my contribution to each
publication is indicated as following:
1. Wu Z (70%), Liu Z, Yang H, Liu Y, Wu G, “Metamagnetic phase transformation in
Mn50Ni37In10Co3 polycrystalline alloy”, Applied Physics Letters, 2011, 98, pp.
061904(1-3). (1st paper in Chapter 2)
2. Wu Z (80%), Liu Z, Yang H, Liu Y, Wu G, “Effect of Co addition on martensitic
phase transformation and magnetic properties of Mn50Ni40-xIn10Cox polycrystalline
alloys”, Intermetallics, 2011, 19, pp.1839-1848. (2nd paper in Chapter 2)
3. Wu Z (80%), Liu Z, Yang H, Liu Y, Wu G, “Martensitic phase transformation and
magnetic properties of Mn50Ni42-xSn8Cox polycrystalline alloys”, Journal of Physics
D: Applied Physics, 2011, 44, 385403(1-8). (3rd paper in Chapter 2)
4. Wu Z (80%), Liu Z, Yang H, Liu Y, “Effect of Fe addition on the martensitic
transformation behaviour, magnetic properties and mechanical performance of
Ni50Mn38-xIn12Fex polycrystalline alloys”, submitted to Journal of Alloys and
Compounds. (1st paper in Chapter 3)
5. Wu Z (60%), Liu Z, Yang H, Liu Y, Wu G, Woodward RC, “Metallurgical origin of
the effect of Fe doping on the martensitic and magnetic transformation behaviours of
Ni50Mn40-xSn10Fex magnetic shape memory alloys”, Intermetallics, 2011, 19, pp 445-
452. (2nd paper in Chapter 3)
Candidate signature: ……………………………... Coordinating supervisor signature: ……………………………....
iv
Acknowledgements ________________________________________________________________________________
I acknowledge my outstanding supervisor Winthrop Professor Yinong Liu. I received
world-class academic trainings of being a scientist, and enjoyed our many discussions
about scientific issues we had through my PhD study. He has been caring, wise, friendly
and supportive, and my debt to his is enormous. I acknowledge Associate Professor Hong
Yang, who has been a mentor to my research. I appreciate her genuine helps to my wife and
myself to set up our life in Australia when we first arrived in Perth and all the assistances
afterwards through the years.
Colleagues in our research group have had a huge influence on my career, which is
reflected in this thesis. In particular, I acknowledge Dr Zhuhong Liu, Qinglin Meng, Mu
Zhang, Jingyang Li, Xiaoxue Xu, Yimeng Yang, Bashir Samsam, Mazlina Mat Darus, and
Mingliang Wang. Their wisdom, support and friendship over the years have been most
important to me.
I acknowledge Dr Alexandra Suvorova, Dr Martin Saunders and Dr Janet Muhling, who
gave me all possible assistances in using the facilities in CMCA. Their knowledge and
experience on materials characterisation are valuable contribution to my research work. I
acknowledge Dr Robert Woodward in School of Physics, who assisted me to measure
magnetic properties of my samples, which weigh ~50% of the total experimental work, and
helped me a lot with understanding of magnetism in many discussions we had.
I have always valued the contribution of my wife, Meifang Lai, who gave enormous
support to my research. She has been a great listener and a true friend in my life. It is her
company and encouragement that made my PhD research possible. I dedicate this work to
her. I have been also receiving tremendous support from my parents in China, who gave me
best education at that time. They have made huge sacrifices to allow me to pursue my
dreams, and for their unconditional support and love, I will always be so grateful.
v
Table of contents ________________________________________________________________________________
Abstract i
Publications arising from this thesis iii
Acknowledgements iv
Table of Contents v
Chapter 1: Introduction 1
Chapter 2: Increasing magnetic driving force of Ni-Mn-based alloys 37
Chapter 3: Increasing ductility of Ni-Mn-based alloys 97
Chapter 4: Closing Remarks 142
CHAPTER 1 1
CHAPTER 1. Introduction
________________________________________________________________________________
1.1 Magnetomechanicaleffectofmaterials
Transducing materials are becoming increasingly important in modern technologies,
which combine large strain, high specific force output and fast dynamic response during an
actuation event. The functionality of these materials is based on the physical mechanisms
responsible for the thermal, electrical, optical, chemical or magnetic energy transformations
into mechanical work, which produce actuation. For example, conventional shape memory
alloys (NiTi) are widely used as thermal actuators. By heating up a typical NiTi alloy to
above the martensitic transformation temperature, a strain of ~6% can be produced, or
recovered, accompanying a force output of up to ~850 MPa. During such an actuating
event, thermal energy is converted to mechanical work. Magnetic-field-induced mechanical
actuation is another type of energy conversion, which has the advantages of high response
frequency, good cycling stability, and environmentally friendliness compared to
conventional shape memory alloys. The most well known magnetoactuators are the
traditional magnetostrictive materials.
Magnetostriction is a common phenomenon for all solid magnetic materials, but
only in a few the effect is large enough for engineering exploitation. It refers to the
phenomenon in which a material changes its physical dimensions in response of changes in
magnetisation state. The best known magnetostrictive materials are cubic Laves-phase
intermetallics, often in the form of (RE)(TM)2 (TM=Fe, Co, Ni and Mn) [1-3]. The largest
ever measured Laves-phase intermetallic is in TbMn2 (0.6 % at 40 K) and the most
successful in application is TbxDy1-xFe2, the infamous Terfenol-D [4].
CHAPTER 1 2
The magnitude of magnetostrain in magnetostrictive materials (<0.6%) is
considered rather small, which severely hinders their engineering applications in many
aspects. Therefore, development of new types of magnetoactuation materials with large
magnetostrains has become an intensive research interest to widen the application realm of
magnetoactuation.
1.2 Largemagnetostrainbymartensitevariant
reorientation
In 1996, Ni2MnGa alloy was found to generate a strain of ~0.2% under the
influence of an applied magnetic field of 8 kOe [5]. This material combines the properties
of ferromagnetism with those of a thermoelastic martensitic transformation, thus denoted as
a ferromagnetic shape memory alloy (FSMA). With this discovery, tremendous effort has
been made on searching for larger magnetostrains by adjusting the compositions to off-
stoichiometric derivatives in Ni-Mn-Ga alloys. These alloys in their martensite state allow
for a stress- or magnetic-field-induced rearrangement of twin variants, resulting in giant
magnetostrains, 5-10% having been reported in the literature [6-9]. The enhanced
magnetostrains, caused by twin boundary motion in Ni-Mn-Ga single crystals, led to
intensively active research in the interdisciplinary field of ferromagnetic martensite in the
following decade. The aforementioned record-breaking values of magnetostrain and the
extreme magnetocaloric effect rekindled the interest in Ni-Mn-Ga and related
multifunctional materials nowadays. FSMAs have been developed into a new class of
functional materials that are capable of magnetic-field-induced actuation, mechanical
sensing and magnetic refrigeration.
1.2.1 Mechanism of magnetostrain in Ni‐Mn‐Ga via martensite
reorientation
The magnetostrain in Ni-Mn-Ga alloys is associated with the orientation change of
the martensite variants via twin boundaries movement. The change of variant orientation
CHAPTER 1 3
induced by the magnetic field is a process to allow the growth of the martensite variants
with the easy magnetisation axis aligned with the applied magnetic field at the expense of
others. This requires the martensite of Ni-Mn-Ga to have both structural anisotropy and
magnetisation anisotropy.
Structural anisotropy of the martensite
The stoichiometric Ni2MnGa undergoes a martensitic phase transformation at
202 K. The austenite shows a superlattice cubic structure, i.e. Heusler structure or L21
structure at higher temperature, a=0.582 nm, while the martensite exhibits a tetragonal
structure, a=b=0.590 nm, c=0.544 nm [10]. The cubic structure of the austenite contracts
along the c direction by 4.45 % and elongates along the a and b directions by 1.63 % to
complete the structural transformation. The crystal structures of martensite are strongly
sensitive to the chemical composition. With the increase of Mn substitution of Ga, the
martensite structure exhibits 5 M, 7 M and can be also non-modulated martensite, leading
to the transformation from tetragonal to orthorhombic [11]. The tetragonal or orthorhombic
structure of the martensite provides the structural anisotropy for the potential shape change.
Magnetic anisotropy of the martensite
Both the austenitic and martensitic phases are ferromagnetic, although the
magnetisation of martensite is slightly bigger than that of austenite in modified composition
[12]. Within the martensite structure, the easy magnetic axis lies along the tetragonal c-axis,
i.e. the short axis. Figure 1 shows the magnetisation measurement of Ni48Mn30Ga22 single
crystal along the easy magnetisation direction ([001] axis) and the hard magnetisation
direction ([100] axis). The magnetic crystallographic anisotropy energy (Ku), which is the
enclosed area between the magnetisation curves along a and c axes, provides the magnetic
driving force for field-induced deformation in the tetragonal martensite.
CHAPTER 1 4
Figure 1 Magnetisation curves along easy ([001]) and hard ([100]) axes of Ni48Mn30Ga22
constrained in single variant martensite. [13]
High mobility of twin boundary of martensite
To complete the magnetostrain in the martensite, sufficient magnitude of Ku and
good twin boundary mobility are essential. It is important to note that the Ku is orientation
dependent and limited with a saturated field. A typical Ku for Ni-Mn-Ga alloys is between
300-500 kJ/m3 [14-16]. Given the shape change is typically 6%, this yields a magnetically
generated stress of 5-8 MPa. Therefore, to achieve a magnetic-field-induced shape change,
the detwining stress level needs to be lower than the magnetostress.
Figure 2 shows stress-strain curve of a single-variant sample of the
Ni48.8Mn29.7Ga21.5 alloy along the [100] direction by a compression test at 300 K. The
critical stress for martensite reorientation is very small, at around 1-2 MPa. Such conditions
can be satisfied by the alloys which transform from cubic austenite to 5 M and 7 M
martensite mentioned above [7, 17] . The magnetostrain is restricted to the tetragonality or
orthorhombility of martensite, denoted as 1-c/a. So far, giant magnetostrain of 6% for 5 M
and 9.5% for 7 M were successfully obtained in single crystals [6, 7]. Very recently, Straka
et al have successfully lowered the critical stress of initiating the twin boundary motion
CHAPTER 1 5
down to 0.1 MPa [18] by modifying the twins microstructure, which greatly improves the
ease of magnetostrain in Ni-Mn-Ga alloys.
Figure 2 Stress-strain curve for compression of a single-variant sample of the Ni48.8Mn29.7Ga21.5 alloy along the [100] direction at 300 K [7].
As aforementioned, the crystallographic anisotropy, magnetisation anisotropy, the
extremely good mobility of the twin boundaries of the martensite determines the success of
yielding large magnetostrains in Ni-Mn-Ga alloys.
1.2.2 Development of other FSMAs
However, there are some serious concerns with Ni-Mn-Ga alloys for their industrial
applications. One is the brittleness of the material, which is due to its intrinsic nature of an
intermetallic compound. Furthermore, the high cost of pure element Ga impedes its
practical production on a large scale. Last but not least, the mechanical work output of Ni-
Mn-Ga, provided by the intrinsically weak magnetic anisotropy energy, is extremely small
as a driving force for mechanical actuations. Even though the critical stress of twinning can
be modified to as low as 0.1 MPa [19], the force generated is still restricted by the limited
magnitude of Ku, at a few MPa [20]. To overcome these problems and to increase the
fundamental knowledge of this alloy system, other ferromagnetic shape memory alloys
with Heusler structure have been investigated since last years.
CHAPTER 1 6
Ni-Mn-Al has been developed as another candidate of FSMAs. The austenite shows
a B2 or L21 structure, while the martensite shows non-modulated tetragonal phase with low
Al and Mn content and 5M and 7M tetragonal martensite with high Al and Mn content
alloys [21]. The magnetostrain of Ni-Mn-Al is rather small: at about 0.17% in single
crystals and 0.01% in polycrystals. A high magnetic field (7 T) is required to yield the
magnetostrain [22]. The ductility of Ni-Mn-Al alloys is improved by the precipitation of γ
phase particles with the addition of other elements, such as Fe, Co or Cr [23].
Thermoelastic martensitic transformations in the ferromagnetic state were obtained
in a large compositional range of Ni-Fe-Ga alloys. Austenite phases have L21 structures
while martensite phases have 5M and 7M orthorhombic structures [24]. The critical stress
for variants reorientation is very low, at 2-3 MPa [25]. The Ku in single crystals of 7M
martensite is 130-180 kJ/m3 [26]. Nevertheless, the magnetostrain is much smaller in Ni-
Fe-Ga than those in Ni-Mn-Ga alloys. The largest strain reported for Ni54.2Fe19.3Ga26.5
single crystals in single variant state is only 0.02 % at 100 K [26]. The magnetostrain can
be enhanced to 0.7 % by doping Co in Ni-Fe-Ga alloys [27]. The stress-assisted
magnetostrain of 8.5 % was also achieved in Ni-Fe-Ga-Co alloys [28]. The ductility of Ni-
Fe-Ga is improved by the presence of the precipitates of γ phase, and the amount and
distribution of γ phase can be modified by suitable heat treatments [29-31]. Though the
ductility is increased, the transformation strain is reduced due to the presence of γ phase of
the material [32].
Co-Ni-Al is being investigated in the last years as another ferromagnetic shape
memory alloy system. The parent phase has the B2 structure and martensitic phase has the
L10 structure [33-35]. The Ku of Co-Ni-Al is about 320 kJ/m3 at 5 K and 200 kJ/m3 at 300
K for Co41Ni32Al27 alloys in single variants state [36]. However, the values of
magnetostrain reported so far are very low: 0.06% in single crystals [37] or 0.013% in
polycrystals [38]. The reason for the small strain induced by the relative large magnetic
field may be due to the elevated critical stress for variant reorientation of L10 structure.
Similar to Ni-Mn-Al and Ni-Fe-Ga, the ductility of Co-Ni-Al alloys is improved by the γ
phase.
CHAPTER 1 7
Co-Ni-Ga is another promising ferromagnetic shape memory alloy system induced
by Wuttig et al in 2001 [39]. It shows the similar properties as in Co-Ni-Al, like the crystal
structures of the two phases (B2 for austenite and L10 for martensite respectively) and the
martensitic transformation happens around the room temperature [39]. The values of
magnetostrain are still small: 0.011% in melt-spun ribbons and 0.003% in polycrystals [40].
Giant magnetostrain triggered by martensite reorientation have been investigated in
ordered Fe-Pt and disordered Fe-Pd alloys. The parent phase of Fe-based alloys is fcc phase
(γ phase) which can be retained at the room temperature by quenching and the martensite
structures of these two alloys are both fct [41]. In Fe-Pt alloys, the martensite
transformation temperature is always much below the room temperature (85 K for Fe3Pt)
[42]. In Fe-Pd alloys, the transformation temperature is around the room temperature and
decreases sharply with the increment of Pd concentration [43]. In Fe-Pt single crystals, the
amount of magnetostrain is up to 2.3 % measured at 4.2 K [41]. However, very low
martensitic phase transformation temperature restricts its application. For Fe-Pd alloys, the
values of magnetostrain of 3.1 % have been measured in single crystals and 0.01 % to 0.05
% in polycrystals depending on the size and shape of the grains [44, 45].
Clearly, the magnetostrains obtained in the aforementioned FSMAs are significantly
lower than those found in Ni-Mn-Ga alloys. To date, Ni-Mn-Ga shows the best
performance of magnetostrain with the mechanism of martensite reorientation under the
influence of a magnetic field.
1.3 Magnetoactuationviamartensitictransformation
Because of the success of Ni-Mn-Ga magnetic shape memory alloys, Ni-Mn-
Z(Z=In,Sn,Sb) were introduced for In, Sn and Sb are the neighbor elements within the same
or neighbor groups as Ga. This satisfies the requirement of Z position should be taken by sp
element in Heusler structure denoting as X2YZ and then taken as the potentially ideal
substitution for Ga. In 2004, Sutou et al discovered Ni50Mn50-xZx (Z=In,Sn,Sb; x=10-16.5)
alloys system [46], and this new system has attracted much interest due to its distinctive
CHAPTER 1 8
magnetic properties. The stoichiometric composition of Ni2MnZ(Z=In,Sn,Sb), exhibit TC
lower than Ni-Mn-Ga, but can be elevated by increasing the Mn content. In fact, Ni50Mn50-
xZx (Z=In,Sn,Sb; x=10-16.5) alloys show thermoelastic martensitic transformation below
the TC temperature. In this case, the magnetic actuation is possible to be carried out by
magnetic-field-induced martensitic phase transformation. This group of alloys is normally
regarded as Ni-Mn-based FSMAs.
1.3.1 Concurrent structural and magnetic transformation
The charm of Ni-Mn-based FSMAs lies on their concurrent martensitic and
magnetic transformation. Figure 3 shows the thermomagnetisation behaviour of
Ni50Mn34In16, Ni50Mn37Sn13 and Ni50Mn37Sb13 alloys [46]. The TC temperature is defined as
the temperature at which the slope of the magnetisation versus temperature is the largest.
The martensitic transformation can be identified by the abrupt dropping upon cooling and
rising upon heating of the magnetisation curves with the variation of temperature, with an
obvious temperature hysteresis. Similar with other conventional FSMAs, the parent phase
is ferromagnetic at higher temperature, with a L21 structure. However, the martensite phase
performs a much weaker ferromagnetism at lower temperature, with a 4M Orthorhombic
structure [46]. The largest saturation magnetisation difference between the austenite and
martensite (ΔM) among Ni50Mn50-xZx (Z=In,Sn,Sb) alloys is ~60 emu/g, found in
Ni50Mn34In16 alloy [47, 48]. The large ΔM is beneficial for magnetic-field-induced
martensitic transformation. By slightly adjusting the composition, alloy Ni46Mn41In13 has
been found to present an enhanced ΔM of ~100 emu/g, which holds the highest ΔM record
in Ni50Mn50-xZx (Z=In,Sn,Sb) alloys. The crystal structure is still L21 structure even the all
these three element have deviated from their own proper concentration, evidenced by XRD
and TEM results [49]. However, the low phase transformation temperatures at around 200
K still impede the further mechanical study and real applications.
CHAPTER 1 9
Figure 3 Thermomagnetisation curves of (a) Ni50Mn34In16, (b) Ni50Mn37Sn13 and (c) Ni50Mn37Sb13 alloys.
1.3.2 Magnetic driving force for magnetostrain in Ni-Mn-Z (Z=In,Sn,Sb) alloys
Different from the magnetic driving force in Ni-Mn-Ga alloys, which is the
magnetic crystallographic anisotropy constant (Ku), the Zeeman energy (ZE) is responsible
for triggering the actuation of Ni-Mn-based FSMAs. The comparison between the magnetic
driving forces for Ni-Mn-Ga and Ni-Mn-based alloys are illustrated in Figure 4. The
magnitude of Ku is the enclosed area between the magnetisation responses from two
differently oriented variants shown in Figure 4 (a). Once the Ku is larger than the energy
required for the twin boundary motion, the variants with the easy magnetisation direction
CHAPTER 1 10
parallel to the magnetic field will grow at the expense of others, resulting in the
macroscopic shape change. It is obvious that the magnitude of the maximum Ku is limited.
Therefore, the low force output has been proven to be a main limitation for the application
of these materials for mechanical actuation.
(a) (b)
Figure 4 Illustration of the maximum magnetocrystalline energy (Ku) in Ni-Mn-Ga alloys responsible for magnetic-field-induced martensite variant reorientation and Zeeman energy (ZE) in Ni-Mn-based alloys responsible for magnetic-field-induced phase transformation.
An intrinsic solution to this problem is to increase the magnetic driving power for
the martensitic transformation. This mechanism is analogous to stress- or temperature-
induced martensitic transformations in conventional shape memory alloys. Different from
the Ku, the ZE plays an important role in magnetic-field-induced phase transformations,
which stems from the difference in the saturation magnetisations of the phases as shown in
Figure 4 (b). Unlike the Ku, the ZE does not strongly depend on crystal orientation, which
provides an opportunity to utilise polycrystals for actuator applications. With increasing the
applied field, the ZE grows continuously with an open end until the phase transformation
occurs. However, for a realistic point of view, one should always expect to achieve a
magnetostrain at a reasonable magnitude of field. In this case, the ZE should be increased
by enhancing the ΔM, such as when a ferromagnetic phase transforms to a paramagnetic or
antiferromagnetic phase, or vice versa.
1.3.3 Effect of Co addition on increasing ΔM
CHAPTER 1 11
The magnetostrain cannot be achieved in Ni-Mn-Z(Z=In,Sb,Sb) ternary alloys until
the Co substitution for Ni was taken as an effective modification for improving the
distinctive magnetic properties between the austenite and martensite. As a matter of fact,
the ΔM can be significantly increased by substitution Co for Ni in Ni-Mn-
Z(Z=In,Sn,Sb,Al,Ga) alloys [50-55]. The most successful compositions with respect to the
production of magnetostrain are Ni-Co-Mn-In alloys, which have been found to
demonstrate a magnetostress level of 140 MPa/T with 1.2% axial strain under compression
[56]. The magnetostrain and magnetostress levels are both significantly higher than those
from the existing magnetostrictive materials and Ni-Mn-Ga alloys.
Figure 5 shows the thermomagnetisation measurements of the Ni45Co5Mn36.6In13.4
alloy in several magnetic fields. In this alloy, Co was added into Ni-Mn-In alloy to increase
the Curie temperature. The magnetisation of the austenite is increased and that of the
martensite is decreased after Co addition, resulting in an enlarged ΔM of about 100 emu/g
across the martensitic transformation. The martensitic transformation temperatures
decreased with increasing magnetic field. The increase of magnetic field from 0.5 to 70
kOe resulted in a decrease in the transformation temperature of about 30 K.
Figure 5 Thermomagnetisation curves of the Ni45Co5Mn36.6In13.4 alloy measured in several magnetic fields by the sample extraction method.
CHAPTER 1 12
Figure 6 shows that magnetisation curves of the Ni45Co5Mn36.6In13.4 alloy between
200 K and 320 K. The alloy presents non-magnetic and ferromagnetic behaviours at 200
and 320 K, respectively. The field induced reverse martensitic transformation from a non-
magnetic phase to a ferromagnetic phase is achieved at 270 and 290 K with a large
hysteresis. The enlarged ΔM between the phases greatly increases the magnetic driving
force for inducing a magnetic-field-induced reverse phase transformation.
Figure 7 shows large magnetostrain of 2.9% in Ni45Co5Mn36.7In13.3 alloy [51]. The
alloy is of martensite state at the testing temperature of 298 K. A compressive pre-strain of
about 3% was applied to the alloy, with the magnetic field applied in parallel to the
compressive axis of the specimen and the length change parallel to the compressive axis
was measured. The shape recovery is due to magnetic-field-induced reverse transformation,
which is called the “metamagnetic shape memory effect” by the authors.
Figure 6 Magnetisation versus magnetic field curves for the Ni45Co5Mn36.6In13.4 alloy between 200 K and 320 K.
CHAPTER 1 13
Figure 7 Recovery strain at 298K induced by a magnetic field for Ni45Co5Mn36.7In13.3.
This magnetostrain is a true “magnetic shape memory effect”, as it involves the
reverse martensitic transformation. The martensitic transformation temperatures are around
room temperature and TC is 387 K. The parent phase shows L21 Heusler ordered structure
where a=0.5978 nm and martensite phases have the modulated structure of monoclinic
where a=0.4349 nm, b=0.2811 nm, c=2.989 nm and β=93.24°, respectively, confirmed by
XRD.
Wang et al have investigated the magnetic-field-induced martensitic transformation
behaviour in Ni45Co5Mn36.6In13.4 polycrystalline alloy, with or without an imposed stress, at
various temperatures using a high-energy synchrotron X-ray diffraction. The reversible
magnetic-field-induced martensitic transformation was observed with the application of 5 T
under stress, suggesting the potential of the application in the real world [57]. The further
investigation on the mechanical properties of Ni45Co5Mn36.6In13.4 single crystal was
systematically done by Karaca et al in 2008. The effects of temperature and bias stress on
the pseudoelastic response and the shape memory effect were explored. A transformation
strain of 5.4% was obtained by thermal cycling under 125 MPa. Temperature hysteresis
changes from 50 to 75 K depending on the applied stress level. Pseudoelastic response was
CHAPTER 1 14
obtained with a large stress hysteresis of 110 MPa and a Clausius-Clapeyron slope of 2.1
MPa/K [58].
Ni43Co7Mn39Sn11 is another successful alloy which yields large magnetostrain by
magnetic-field-induced martensitic transformation discovered by Kainuma et al later in
2006 [50]. The idea of substitution of Co for Ni is similar to that in Ni-Co-Mn-In alloys.
The martensite and reverse transformations were detected in the temperature range from
300 to 350 K and TC is about 430 K. The crystal structures of parent phase and martensite
phase are as same as in Ni45Co5Mn36.7In13.3 alloy with slightly different lattice parameters.
The recovery strain of 1 % which is 77 % of the pre-stain of 1.3 % was confirmed in a
magnetic field strength of 8 T in polycrystalline samples. Moreover, a length change of 0.3
% after releasing the magnetic field was detected, known as the two-way shape memory
alloy effect [50]. Similarly, the substituent of Co atoms in Ni-Co-Mn-Sb alloys help align
the Mn moments in a ferromagnetic ordering, giving rise to a significantly enhanced
magnetisation in the austenite and a large ΔM across the transformation [52].
Since the effect of Co doping on increasing the magnetisation difference across the
phases in Ni-Mn-Z(Z=In,Sn,Sb) alloys has been well realised, similar effect is then also
expected in early found Ni-Mn-Ga and Ni-Mn-Al alloys. It is found that Co substitution for
Ni in Ni50Mn30Ga20 alloy significantly lowered the martensitic transformation temperature,
and elevated the Curie transition temperature. The magnetisation for the ferromagnetic
austenite has been largely increased, while that of the martensite has been lowered to some
extent. This results in the increase of the ΔM across the phases, leading to successful
magnetic-field-induced phase transformation in Ni33Co13Mn32Ga18 alloys [54] and in
Ni40Mn33Co10Al17 alloy [53].
Co substitution for Ni effectively increases the ΔM across the martensitic
transformation, thus enhancing the magnetic driving force for magnetoactuation. The
positive effects of Co can be summarised to a few aspects [52]: (i) it decreases the
martensitic transformation temperatures and increases the Curie transition temperature of
the austenite, thus guaranteeing the concurrent martensitic and magnetic transformation in a
large temperature window, (ii) Co atoms at Ni site contribute larger magnetic moment
CHAPTER 1 15
(~1.0 µB) compared to that of Ni (~0.3 µB) in the austenite, (iii) it strengthens the
ferromagnetic ordering in the austenite by turning the magnetic moments of Mn atoms into
a ferromagnetic ordering instead of the previous antiferromagnetic one [55].
1.4 Energyevaluationofmagnetostrainassociatedwith
martensitictransformationinNi‐Mn‐basedFSMAs
To evaluate the current FSMAs with regard to their potential for magnetic actuation,
it is essential to consider the energy conversion from magnetic energy to mechanical work
associated with the magnetic-field-induced martensitic transformation. For a complete
magnetomechanical actuation, the magnetic energy must overcome the mechanical
resistance of the matrix to deformation, and the remainder of the magnetic energy
transforms to mechanical work output. To clarify the ability of magnetic actuation of
FSMAs, each energy term involved in a magnetic-field-induced shape change via
martensitic transformation is analysed. These energy terms can be grouped into three
components: (i) the magnetic driving force, (ii) the frictional resistance and (iii) the work
output. It is also a useful tool to draw a common criterion for the present FSMAs for
practical applications.
1.4.1 Thermodynamicsformagnetomartensiticphasetransformations
Owing to its lattice distortion, a martensitic transformation is a mechanical event as
well as a thermodynamic event. The Gibbs free energy change of such an event may
include not only the more familiar internal energy, volume-pressure energy and
temperature-entropy energy, but also all other reversible energies involved, such as the
force-displacement elastic potential energy (FL), magnetic energy (BM), optical energy,
etc. The relations among the multiple energy terms can be expressed as:
G U P V T S F L B M (1)
CHAPTER 1 16
For a normal thermoelastic martensitic transformation, we may consider only the
thermal and the mechanical energies. It gives
G U P V T S F L (2)
Based on F A , L L , 1
AL V
, Equation (2) can be written as
G H T S
(3)
When a martensitic phase transformation occurs, the system is in equilibrium state,
thus 0G and hence
d S
dT
(4)
This is the famous Clausius-Clapeyron Equation. Similarly, for an isothermally
magnetic-field-induced martensitic transformation, we may only consider thermal and
magnetic energies. So the equation (1) is now
G U P V T S B M (5)
Once the magnetic energy term BΔM makes a large contribution to the Gibbs free
energy change, the transformation occurs, and then 0G . It gives
dB S
dT M
(6)
The transformation temperature change (dT) induced by the magnetic field change
(dB) is determined by M
S
. To utilise magnetic field to induce martensitic transformation,
a combination of a large ΔM and small ΔS is required for the martensitic transformation.
CHAPTER 1 17
1.4.2 Energyconversionofmagnetostrainviamartensitictransformation
Magnetic energy input
The magnetic energy input is ZE shown in Figure 4 (b), which is the area between
the magnetisation curves of the austenite and martensite. It can be expressed as
ZE B M , corresponding to the last energy term in equation 5. Obviously, with
increasing the magnitude of the applied field B or magnetisation difference ΔM, the ZE
increases.
Resistances for magnetomartensitic actuation
For actuation via magnetic-field-induced martensitic transformation, the ZE must
overcome two energy barriers: (1) Gibbs free energy deficit for the phase transformation at
the testing temperature and (2) mechanical resistance of the matrix to shape change.
(1) Gibbs free energy deficit for magnetomartensitic
transformation
Figure 8 shows thermal- and magnetic-induced martensitic phase transformations,
in which the elastic energy of the phase transformation is neglected. To is the equilibrium
transformation temperature. Because of the irreversible energy of the structural
transformation, the transformation hysteresis always exists between the forward and reverse
phase transformation. Therefore, the transformation temperatures can be regarded as TM
(the forward transformation temperature) at below To and TA (the reverse transformation
temperature) at above To. To induce a reverse transformation at any given temperature T
below TA, the thermodynamic energy deficit may be estimated to be
( )th AE T T S (7)
CHAPTER 1 18
Figure 8 Schematic diagrams of thermal- and magnetic-field-induced martensitic transformations without elastic energy.
It is seen that the irreversible energy consumption of the transformation can be
given by ( )ir A oE T T S . This energy consumption is due to the friction stemming from
the phase interface movement for the crystallographic transition. However, this irreversible
energy barrier can be avoided by deliberately choosing the testing temperature close to TA,
and then applying the magnetic field. Accordingly, a small ΔS and testing temperature close
to TA are expected for easy magnetic actuations.
In a real situation of structural transition, the elastic energy always accompanies, i.e.
the “elasticity” of the transformation. This leads to the temperature-, stress- and magnetic
field-span between the starting and finishing of the transformation. Therefore, the
transformation temperatures are commonly measured as forward and reverse
transformation starting and finishing temperatures (Ms, Mf, As and Af) shown in Figure 9.
Within the transformation span, there is a frictional energy, as part of Eir. For a complete
transformation being induced at any given temperature T, the total thermal deficit can be
rewritten as
CHAPTER 1 19
fA
th
T
E SdT (8)
Given the testing temperature is chosen at As, the frictional energy to be overcome
is shown as the blue shadow area in Figure 9, which corresponds to the minimum energy
requirement for the completion of a magnetic-field-induced transformation:
min
f
s
A
A
E SdT (9)
Figure 9 Schematic diagrams of thermo- and magnetic-field-induced martensitic transformation with transformation elastic energy.
(2) Mechanical resistance for magnetomartensitic transformation
from pre‐straining
For obtaining a magnetostrain via martensitic transformation, a pre-strain to the
alloy at the martensite state is required before applying the magnetic field. The process of
CHAPTER 1 20
generating a pre-strain is to convert the self-accommodated martensite variants to become
reoriented variants, and thus the recovery from the deformed martensite back to the
austenite requires extra energy due to the pure mechanical resistance from the
crystallographic transition. This energy is denoted as Emech. The magnitude of Emech roughly
equals the mechanical work for obtaining the oriented martensite from a self-
accommodated state near As temperature, which is illustrated in Figure 10. The critical
stress for inducing the martensite variant rearrangement is denoted σo, and the maximum
strain is εmax, thus
Emech σo εmax (10)
Figure 10 Schematic illustration of stress-strain curve for martensite reorientation at As temperature.
In fact, Emech equals to the extra thermal energy requirement for the transformation
from the oriented martensite back to austenite by heating, which is known as the
“martensite stabilisation” behaviour in NiTi alloys [67-69]. Figure 11 shows the illustration
for these extra thermal or magnetic energies for thermal- or magnetic-induced martensitic
reverse transformation. In the S-T relation, it is seen that the transformation temperatures
(As and Af) shift to higher temperature range for inducing the reverse transformation from
the orientated martensite to austenite relative to those from the self-accommodated
martensite to austenite. Similarly, in M-H relation, the magnetic field increase to higher
magnitude to meet the requirement from the transformation between a pre-strained
CHAPTER 1 21
martensite to austenite magnetically. The extra energy corresponding to Emech is caused by
the “martensite stabilisation” given as the red shadow area in Figure 11. In this case, the
mechanical resistance due to the martensite stabilisation can be also converted to the form
of thermodynamic energy deficit (shadow area in Figure 11), which is
'
( ' )f
f
A
mech f f
A
E SdT A A S (11)
Figure 11 Extra thermal and magnetic energy requirement for inducing reverse martensitic transformation caused by pre-strained martensite.
1.4.3 CriteriaofevaluationforFSMAs
Criteria I: completion of magnetic‐field‐induced martensitic
transformation
The resistance for a magnetic-field-induced reverse transformation comes only from the thermodynamic deficit for the reverse transformation. Therefore, the magnetic energy input for driving a martensitic transformation at temperature T is given by:
CHAPTER 1 22
mag thE E
As magE B M , and fA
th
T
E SdT , so the condition is
fA
T
B M SdT (12)
Apparently, the minimum magnetic energy requirement for completion of magnetic-field-
induced martensitic transformation is f
s
A
A
B M SdT .
Criteria II: completion of magnetostrain via martensitic
transformation
In addition to the thermal deficit, to transform the deformed martensite back to austenite magnetically requires extra energy input to overcome the mechanical resistance brought by “martensitic stabilisation”. The magnetic driving force now needs to meet
mag th mechE E E
As magE B M ,fA
th
T
E SdT and' f
f
A
mech
A
E SdT , where 'fA is the martensitic reverse
transformation temperature for an oriented martensite transforming to austenite. ' 'f f f
f
A A A
T A T
B M SdT SdT SdT (13)
The minimum magnetic energy requirement for shape recovery via magnetic-field-induced
martensitic transformation is ' f
s
A
A
B M SdT .
Criteria III: completion of two‐way magnetostrain via
martensitic transformation
To obtain a two-way shape memory effect by a magnetic field, the magnetising
temperature T must be at lower than Mf temperature to have the austenite transforming back
to the martensite after releasing the magnetic field, as seen in Figure 11. The minimum
magnetic energy input can be obtained when T=Mf, that equals
CHAPTER 1 23
' f
f
A
M
B M SdT (14)
Based on the analysis above, the energy barriers for a magnetic-field-induced
martensitic transformation or any event related can be ascribed to a thermodynamic energy
deficit. The magnetic driving force must be larger than this thermodynamic energy deficit
to accomplish the energy conversion from magnetic energy to mechanical work output, i.e.
magnetic actuation.
1.5 Challengesformagnetostrainviamartensitic
transformationinNi‐Mn‐basedFSMAs
Although the magnetostrain has been successfully achieved in Ni45Co5Mn36.7In13.3
single crystal and Ni43Co7Mn39Sn11 polycrystalline alloys, no work output was produced.
For instance, the success for inducing magnetostrain of 2.9% in Ni45Co5Mn36.7In13.3 single
crystal is still significantly smaller than the theoretical transformation strain (5-6% based
on the compression direction shown in ref [51]). This indicates that the magnetic field
(~3T) is not able to accomplish the complete martensitic transformation with full strain
recovery. Based on the analysis on energy conversion in Section 1.4, the best alloy
(Ni45Co5Mn36.7In13.3 single crystal) discovered so far cannot fully satisfy energetic criteria
II. This is because the magnetic driving force (or energy input) is completely consumed
during the reverse transformation process, largely by the mechanical resistance, thus
resulting in nil energy to output. Besides, the brittleness of Ni-Mn-based FSMAs still
impedes their engineering applications. The main challenges for developing FSMAs as
engineering magnetoactuators include three aspects as followings.
1.5.1 To increase the magnetic driving force
Failures to have magnetostrain in Ni-Mn-based FSMAs can be always ascribed to
the limited magnetic driving force for such an actuating event. In fact, since Ni-Mn-
Z(Z=In,Sn,Sb) alloys have distinct magnetic states between the austenite and martensite,
CHAPTER 1 24
the ZE can be infinitely increased by applying larger magnetic field B. However, the
magnetostrain needs to be induced using a reasonable magnitude of magnetic field for a
practical consideration. Therefore, the challenge of increasing the magnetic driving force
becomes to increase the ΔM between the austenite and martensite for FSMAs, which is
illustrated in Figure 12. With this consideration, solutions should be sought to increase the
magnetisation of the austenite or to decrease that of the martensite, or both.
sAM
sMM
Figure 12. Illustration of enhancement of Zeeman energy (ZE) in Ni-Mn-based alloys responsible for magnetic-field-induced phase transformation.
1.5.2 To decrease the mechanical resistance
On the other side of the being a successful FSMA candidate, small resistance during
a magnetic-field-induced shape change is also essential, apart from the required large
magnetic driving force. Based on the discussion in Section 1.4, it is known that the
resistances include thermodynamic barrier (Eth) and mechanical resistance (Emech). The
thermodynamic barrier can be realistically decreased by selecting the testing temperature
close to As, and the minimum energy requirement is min
f
s
A
A
E SdT . However, the pure
mechanical resistance originating from transformation between the prestrained martensite
and the austenite is inevitable. It is known that this part of energy corresponds to the extra
CHAPTER 1 25
thermodynamic energy deficit as the “martensite stabilisation” or roughly equals to
mechanical energy required for turning the self-accommodated martensite to reoriented
martensite. This portion of energy must be overcome by the magnetic energy input to meet
criteria II. It is known that the success of having large magnetostrain in Ni-Mn-Ga alloys is
simply due to the high mobility between the twin boundaries of the martensite variants.
Unlike Ni-Mn-Ga alloys, the twining movement of the martensite variant has been proven
very poor in Ni-Co-Mn-In alloys, with a compressive stress of ~100 MPa to initiate
detwining [51, 56, 58]. Therefore, the ZE is mainly depleted by the mechanical resistance
due to the poor mobility of martensite twin boundaries in Ni-Mn-Co-In alloys. Owing to
this consideration, to lower the mechanical resistance is as equally important as to increase
the magnetic driving force during, as it saves the magnetic driving force in another sense,
thus possibly to yield work output.
1.5.3 Brittleness of FSMAs
From an engineering application point of view, reasonable mechanical properties
are needed to draw attention of FSMAs, such as the ductility, the cyclic stability, the
ambient stability and frequency etc. Among all of these requirements, good ductility is
most crucial for the real engineering applications. It is known that Ni-Mn-Z (Z=Ga, Al, In,
Sn and Sb) alloys are intermetallic compounds, which are intrinsically brittle. For a
polycrystalline, the ductility is even worse, due to the volume change before and after the
martensitic transformation. Consequently, this may easily induce cracking during the
actuation process in polycrystalline alloys. Therefore, one of the most the realistic
challenges is to increase the ductility of Ni-Mn-based FSMAs.
1.6 SolutionstothechallengesofFSMAs
In this thesis, solutions for increasing the magnetic driving force and ductility of Ni-
Mn-based FSMAs are explored. On one hand, new composition design in Mn-Ni-In(Sn)-Co
alloys has been carried out with the aim to increase the magnetic driving force for
actuation. On the other hand, introduction of the phase by substitution of Fe for Mn in Ni-
CHAPTER 1 26
Mn-In(Sn) alloys effectively improves the ductility of FSMAs, however, the research
focuses on the metallurgical origin of the changes in transformation behaviour and
magnetic properties brought by the formation of the second phase in these alloys.
1.6.1 Increasing the magnetic driving force ‐ new compositions
design of Ni‐Mn‐based FSMAs
Step I-maximise the use of Mn
The magnetic moments of the constituents in Ni-Mn-based FSMAs can be
estimated from those in the stoichiometric compositions. The magnetic moments are 3.5-
3.7 µB/Mn, 0.1-0.3 µB/Ni and ~0 µB/Z, and the net magnetic moments are 4.0-4.2 µB/f.u. in
Ni2MnZ(Z=Ga,In,Sn,Sb) alloys [70]. It is seen that the net magnetic moment mainly comes
from the contribution of Mn atoms in the unit cell. For this reason, it is reasonable to
consider that the magnetisation of the austenite may be maximised by increasing the Mn
content up to 50 at% with the assumption of ferromagnetic alignment between Mn atoms.
The first step of alloy design is to employ as much Mn content as possible in the
new composition. Therefore, Mn50Ni25Z25(Z=In,Sn) was chosen as the base alloy
compositions.
Step II-stacking order adjustment
The type of magnetic interaction between the Mn atoms is very sensitive to the
distance between them. Early studies found that the type of magnetic interaction between
Mn atoms changes from antiferromagnetic to ferromagnetic when the Mn-Mn distance is
increased to above a critical value of approximately 0.30 nm and exhibits a maximum
around 0.37 nm [71-73]. In case of Mn2NiIn and Mn2NiSn alloys, which have an Hg2CuTi
superlattice structure, Mn atoms occupy A and B sites, which form the nearest neighbour.
The distance between Mn(A) and Mn(B) is 3 / 4a , which is ~0.26 nm, in case of a=0.6
nm. The short distance between Mn(A)-Mn(B) leads to the antiferromagnetic interaction.
One solution is to substitute Z element by Ni in the nominal composition. In this case, the
composition becomes Mn50Ni25+xZ25-x. It is seen that some portion of Mn atoms at A site
CHAPTER 1 27
have been replaced by Ni atoms, and these new Mn atoms share D site with In atoms. This
hypothesis is based on the rule of preferential site occupation in Mn2YZ (Y: 3d elements;
Z: III-V A group elements) alloys reported by Liu et al [63]. They observed that Y elements
on the right hand side of Mn in the Periodic Table of Elements prefer to occupy (A,C) sites,
whereas Y elements to the left of Mn have strong preference for B site occupancy. In
Mn2YZ (Y = V, Cr, Mn, Fe, Co and Ni; Z =Al, Ga, In, Si, Ge, Sn and Sb) Heusler alloys,
this rule of atomic occupancy has been shown to be well obeyed [61, 63, 66]. According to
this principle, Ni substitution for In will have the priority to take A site in preference to Mn.
The distance between the new Mn atoms at D site and Mn atoms at B site is ~0.3 nm,
which may favor the ferromagnetic exchange interaction between the Mn atoms. Therefore,
the magnitude of antiferromagnetic alignment between Mn(A) and Mn(B) is reduced, and
the new Mn atoms at D site form ferromagnetic interaction with the Mn atoms at B site.
The second step of alloy design is to substitute Ni for Z element to separate Mn(A)-
Mn(B) to become Mn(B)-Mn(D), thus the new composition becomes Mn50Ni25+xZ25-
x(Z=In,Sn).
Step III-Co doping
One main problem with continuous substitution of Ni for Z is that the martensitic
transformation temperature increases rapidly and exceeds the Curie transition temperature
of the austenite at the Ni content of 40 at%, leading to the transformation being from
paramagnetic austenite to paramagnetic martensite. The solution is to utilise Co to
substitute for Ni in the nominal composition, which increases the Curie transition
temperature of the austenite and decreases of the martensitic transformation temperatures in
the meantime time, thus giving rise to more temperature room for a concurrent martensitic
and magnetic transformation.
The third step of alloy design is to substitute Co for Ni element to separate the
Curie transition and martensitic transformation temperature, hence the final composition
becomes Mn50Ni25+x-yZ25-xCoy(Z=In,Sn).
CHAPTER 1 28
1.6.2 Ductility improvement and metallurgical origins of changes
in martensitic and magnetic properties caused by Fe addition
of Ni‐Mn‐based alloys
The only solution to increase the ductility is to introduce a ductile second phase (
phase) into the matrix of Ni-Mn-based alloys. The phase was first found in Co-Ni-Al [23,
38, 74], Co-Ni-Ga [75] and Ni-Fe-Ga [76] alloy. Fe and Co as dopants were also found
effectively to form phase in Ni-Mn-based alloys [77-82]. Whereas the purpose is to
improve ductility, addition of a fourth element to the ternary Ni-Mn-Z alloys inevitably
alters the matrix composition, hence changing the structure, thermal and magnetic
properties. Whereas much attention has been given to the influences of fourth element
addition on ductility improvement and transformation properties of these alloys in the
literature, given the level of complexity associated with the quaternary systems, much less
is understood of the metallurgical origins of these influences. In this thesis, this
fundamental issue was examined by investigating the effects of Fe substitution for Mn in
Ni-Mn-In and Ni-Mn-Sn alloys. Fe bears much resemblance to Mn in these alloy systems,
which provides an opportunity to examine the metallurgical influence of Fe addition to the
properties of the alloys, in addition to being a selected element for ductility improvement
for some common ferromagnetic shape memory alloys.
1.7 Thesisorganisation
This thesis is arranged as a series of 5 papers, including 4 published and 1 submitted
papers. Below is an overview of the structure of the thesis.
1.7.1 Chapter 1 (Introduction)
Chapter 1 has provided a concise literature review on ferromagnetic shape memory
alloys, including the development of FSMAs, survey of magnetostrain in various
compositions of FSMAs, and current knowledge in the mechanisms of magnetostrain. It
CHAPTER 1 29
also includes a detailed analysis on the energy conversion of magnetic actuation associated
with the martensitic transformation. Three energetic criteria are established for evaluating
the feasibility of magnetostrain of FSMAs. Followed by the energy analysis, the problems
are identified of FSMAs, leading to the objectives of this thesis. The objectives of the thesis
can be summarised as following:
1. To increase the magnetic driving force by optimising the composition of Ni-Mn-
based alloys.
2. To investigate the metallurgical origins of Fe addition on martensitic and
magnetic properties of Ni-Mn-based alloys.
1.7.2 Chapter 2 (Paper 1, Paper2 and Paper3)
The martensitic transformation and magnetic behaviour of the newly designed
compositions of Mn-rich Ni-Mn-based alloys are illustrated in Paper 1, Paper 2 and Paper 3
in details with the concern of increasing ΔM across the transformation.
Paper 1: Metamagnetic phase transformation in Mn50Ni37In10Co3 polycrystalline
alloy, Zhigang Wu, Zhuhong Liu, Hong Yang, Yinong Liu, Guangheng Wu, Applied
Physics Letters, 2011, 98, pp. 061904(1-3).
This work reports on a new composition design of Mn50Ni37In10Co3, in which a
large magnetisation difference of 89 emu/g was obtained. The complete magnetic-field-
induced martensitic transformation was achieved. It is well demonstrated that the magnetic
driving force in Mn-rich Ni-Mn-based alloys was successfully increased.
Paper 2: Effect of Co addition on martensitic phase transformation and magnetic
properties of Mn50Ni40-xIn10Cox polycrystalline alloys, Zhigang Wu, Zhuhong Liu, Hong
Yang, Yinong Liu, Guangheng Wu, Intermetallics, 2011, 19, pp.1839-1848.
This work reports a complete alloy series design of Mn50Ni40-xIn10Cox alloys. The
effects of Co addition on the martensitic and magnetic properties were investigated. The
origin of the increase of ΔM across the transformation was well interpreted and the
CHAPTER 1 30
magnetic moment interactions between the constituents were demonstrated in the proposed
model.
Paper 3: Martensitic phase transformation and magnetic properties of Mn50Ni42-
xSn8Cox polycrystalline alloys, Zhigang Wu, Zhuhong Liu, Hong Yang, Yinong Liu,
Guangheng Wu, Journal of Physics D: Applied Physics, 2011, 44, 385403(1-8).
A complete alloy series design of Mn50Ni42-xSn8Cox alloy was carried out aiming to
increase the ΔM for magnetic actuation in this work. Co substitution for Ni was found
effective on increasing the magnetisation of the austenite, while that of the martensite
remained unchanged at a very low level, leading to the continuously gained ΔM across the
martensite transformation.
1.7.3 Chapter 3 (Paper4 and Paper5)
Changes on the martensitic transformation behaviour, magnetic properties,
mechanical properties and shape memory effect caused by the formation of phase with the
original purpose of increasing the ductility are clarified in Ni-Mn-based FSMAs. The
studies are carried out in Ni-Mn-In and Ni-Mn-Sn alloys with Fe addition illustrated in
Paper 4 and Paper 5 respectively.
Paper 4: Effect of Fe addition on the martensitic transformation behaviour,
magnetic properties and mechanical performance of Ni50Mn38-xIn12Fex polycrystalline
alloys, Zhigang Wu, Zhuhong Liu, Hong Yang, Yinong Liu, submitted to Journal of Alloys
and Compounds, September 2011.
This work investigates on the martensitic transformation, magnetic properties and
mechanical behaviour of Ni50Mn38-xIn12Fex alloys. Fe substitution for Mn at above 3 at%
was found to create a phase, which greatly alters the composition of the matrix phase. The
martensitic transformation and magnetic transition temperatures were affected by the
change of composition of the matrix phase. Mechanical behaviour and shape memory effect
were also investigated.
CHAPTER 1 31
Paper 5: Metallurgical origin of the effect of Fe doping on the martensitic and
magnetic transformation behaviours of Ni50Mn40-xSn10Fex magnetic shape memory
alloys, Zhigang Wu, Zhuhong Liu, Hong Yang, Yinong Liu, Guangheng Wu, Robert
Woodward, Intermetallics, 2011, 19, pp 445-452.
The metallurgical origin of the effect of Fe doping on the martensitic transformation
and magnetic properties was investigated in Ni50Mn40-xSn10Fex alloys in this work. The
findings clarify the origin of the effect of Fe addition and provide useful reference on alloy
design in Ni-Mn-Sn alloy system.
1.7.4 Chapter 4 (Closing remarks)
The final chapter presents a short summary of the main findings and the
significance of the work in this thesis. The immediate future works as continuation of the
current work are proposed.
CHAPTER 1 32
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CHAPTER 2 37
CHAPTER 2. Increasing magnetic
driving force of Ni-Mn-based alloys
________________________________________________________________________________
Paper1
Metamagnetic phase transformation in Mn50Ni37In10Co3 polycrystalline alloy
Zhigang Wu 1, Zhuhong Liu 2, Hong Yang 1, Yinong Liu 1, Guangheng Wu 3
1 School of Mechanical and Chemical Engineering, The University of Western Australia,
Crawley, WA 6009, Australia
2 Department of Physics, University of Science and Technology Beijing, Beijing 100083,
China
3 Beijing National Laboratory for Condense Matter Physics, Institute of Physics, Chinese
Academy of Science, Beijing 100080, China
This paper reports on an alloy design of Mn50Ni37In10Co3 based on the principle of
Mn-Mn ferromagnetic coupling via Co doping. The alloy is shown to exhibit a
metamagnetic martensitic transformation and a high saturation magnetization of 118 emu/g
in its austenitic state. The transformation generates a large magnetization difference of
89 emu/g, more than 200% of what reported in the literature for similar alloys. A complete
magnetic field induced martensitic transformation was achieved at 170 K. Such high
magnetization difference provides a strong driving force for magnetic-field-induced
transformation, making this material a promising candidate for magnetic actuation
applications.
CHAPTER 2 38
Since the discovery of the magnetic-field-assisted shape memory effect in Mn2NiGa
single crystal in 2005,1 much effort has been made to develop better Mn-rich ferromagnetic
shape memory alloys (FSMAs). In Mn2NiX (Ga,In,Sn,Sb) system, the alloys hold the
promise for higher saturation magnetisation owning to its higher Mn content. Mn-rich Mn-
Ni-In alloys have been found to exhibit concurrent magnetic and martensitic
transformations, i.e., metamagnetic transformations.2,3 The magnetic driving force for such
metamagnetic phase transformations is provided by the Zeeman energy EZeeman=µ0MH,
where M is the saturation magnetization difference between the austenite and martensite
and H corresponds to the strength of the applied field. This energy is dependent on the M,
which is typically ~40 emu/g for Mn50Ni40In10.2,3 Largely due to the low ΔM, a complete
reversible metamagnetic transformation is yet to be achieved in Mn-rich FSMAs. At the
meantime, Co doping has been reported to have prominent effect on increasing M in
Mn48CoxNi32-xGa20 alloys4, due to its effect on promoting ferromagnetic alignment of the
moments of the nearest neighboring Mn atoms. This paper reports on a Mn50Ni37In10Co3
alloy, which has a significantly increased ΔM for its metamagnetic transformation.
A polycrystalline Mn50Ni37In10Co3 button ingot was prepared using an arc melting
furnace in argon atmosphere from high purity (99.99 %) elemental metals. The ingot (~4 g)
was heat treated at 1073 K for 24 hours in vacuum followed by quenching in water to
ensure composition homogeneity. Phase identification and crystal structures were
determined by means of X-ray powder diffraction (XRD) using Cu-Kα radiation, phase
transformation behavior was measured by means of differential scanning calorimetry
(DSC) with a cooling/heating rate of 10 K/min, and magnetic properties were studied using
a superconducting quantum interference device magnetometer (SQUID).
Figure 1 shows an XRD spectrum of powder sample of Mn50Ni37In10Co3 alloy at
room temperature. The alloy shows a single phase structure with bcc fundamental lattice
reflections of (220), (400), (422) and (440) and superlattice reflections of (111), (200),
(311) and (222). The superlattice structure can be determined by comparing the relative
intensities of (111) and (200).5 It is evident that I111/I200>1, implying that the superlattice is
of the Hg2CuTi-type, consistent with other Mn2NiX (Ga,Sn,Sb) alloys.5-7
CHAPTER 2 39
20 30 40 50 60 70 80 90 100
X-r
ay in
ten
sity
2 (o)
22
0
111
20
0
42
2
40
0
440
222
311
140 160 180 200 220 240
Hea
t flo
w
Temperature (K)
FIG. 1. X-ray diffraction spectrum of powder sample of Mn50Ni37In10Co3 alloy; inset: DSC
curve of the martensitic transformation behavior of the alloy.
In this structure, Mn atoms occupy A (0,0,0) site and B (1/4,1/4,1/4) site, leaving C
(1/2,1/2,1/2) site to Ni atoms and D (3/4,3/4,3/4) site to the third element atoms. Such
structure can be expressed in a stacking order of MnMnNiX ( 43F m space group) along the
diagonal [111] direction of the cubic unit cell. The lattice constant is determined to be
a=0.6013 nm. The inset in the figure shows DSC measurement of the transformation. The
peak transformation temperatures are determined to be 169 K and 195 K and the latent heat
of the transformation is 2.9 J/g.
Figure 2 shows the zero-field cooled (ZFC) and field cooled (FC) M(T) curves with
a cooling/heating rate of 10 K/min of the alloy in magnetic fields of different strengths. At
a low field of 50 Oe, the martensitic and austenitic transformation starting and finishing
temperatures are determined to be 186 KsM , 153 KfM , 179 KsA and 212 KfA ,
respectively.
CHAPTER 2 40
0
50
100
0 50 100 150 200 250 300 350
Mag
net
izat
ion
(em
u/g)
Temperature (K)
5x10-3T5x10-2T
2T5T
7T
FC
ZFH
M=
89
em
u/g
FIG. 2. Zero-filed cooled (ZFC) and field cooled (FC) M(T) curves of Mn50Ni37In10Co3
alloy under various fields measured by SQUID.
The transformation hysteresis is determined to be 26 Kf sA M , which is
consistent with the DSC result. It is also seen that at low field strengths the magnetization
behavior exhibited complete reversible phase transformation, shown as the closed ZFC and
FC pathways. At high field strengths (≥2T) the FC pathway did not overlap with ZFC
pathway at 10 K after a cycle of MAM transformation. It is obviously due to the
kinetic arrest of the martensitic transformation under the influence of high magnetic field,
which has been observed and discussed in the literature for several Ni-Mn-In alloys in the
past few years. 8-10 The same phenomenon has also been observed in a similar
Mn49.5Ni40.4In10.1 ribbon alloy, as reported by Sanchez Llamazares recently.11 The increased
magnetization at the finishing point on the FC curves indicates that the amount of the
arrested austenite increased with higher magnetic field applied. It is worth noting that upon
heating (ZFC curves) ΔM between the austenite and the martensite increased progressively
with increasing the magnetic field. The maximum M AM achieved is 89 emu/g in a field
of 7 T.
CHAPTER 2 41
Recently, Charkrabarti and Barman conducted theoretical calculation on the
ferrimagnetism of Mn50Ni25In25 alloy, and showed that the net magnetic moment is 0.47 µB
per formula unit (f.u.) for the austenite,12 corresponding to 9.27 emu/g. The crystal structure
of the austenite is considered as Hg2CuTi-type superlattice bcc structure, which is the same
structure as the present Mn50Ni37Co3In10 alloy. This calculation is based on the condition
that Mn-Mn atoms within the lattice form antiferromagnetic coupling. The austenite of our
alloy showed a much higher magnetization of ~118 emu/g at 7 T. The drastically increased
magnetization is a strong indication that the Mn-Mn interaction in the lattice of the
Mn50Ni37In10Co3 alloy has changed to ferromagnetic coupling. This is attributed to two
reasons: (i) change of magnetic exchange status due to the composition change of the
lattice, and (ii) doping effect of Co.
The exchange interaction between Mn atoms is known to depend strongly on Mn-
Mn distance in the lattice. Early studies found that the type of magnetic interaction between
Mn atoms changes from antiferromagnetic to ferromagnetic when the Mn-Mn distance is
increased to above a critical value of approximately 0.30 nm.13 For Mn-Mn-Ni-X stacking
order, the distance between A site and B site is 3 / 4AB a =0.2604 nm and the distance
between B site and D site is / 2 0.3007BD a nm for the current alloy with a=0.6013
nm. This implies that Mn(A)-Mn(B) form antiferromagnetic interaction and Mn(B) and
Mn(D) form ferromagnetic interaction. In Mn50Ni25In25 alloy, the calculated spin magnetic
moments for the austenite are -3.08, 3.42, 0.13 and 0 µB/f.u. for Mn (A site), Mn (B site),
Ni (C site), and In (D site), respectively.12 However, in Mn50Ni40In10 alloy, the saturation
magnetization of the austenite is ~75 emu/g, as reported by Sanchez Llamazares etc.2,3 This
suggests the change of antiferromagnetic coupling between Mn-Mn atoms in the
stoichiometric alloy to ferromagnetic coupling in the non-stoichiometric alloy. One
scenario is that in MnMnNiX-type lattice, excess Ni above 25 at% has priority to take A
site, displacing Mn from A site to D site. In this case the magnitude of antiferromagnetic
alignment between Mn(A) and Mn(B) is reduced, and the new Mn at D site
ferromagnetically aligns with the Mn at B site. In Mn50Ni40In10 alloy, the “extra” Ni (15
at%) may displace 15 at% Mn from A site to D site, thus forming domains of NiMnNiMn
stacking structure. In this case, the matrix of the alloy may be considered to contain two
CHAPTER 2 42
mixed domains: Mn-Mn-Ni-In domains (40 % in volume) and Ni-Mn-Ni-Mn domains (60
% in volume). In the MnMnNiIn domain, the Mn(A)-Mn(B) interaction is
antiferromagnetic, as in the case of stoichiometric Mn50Ni25In25. In the NiMnNiMn domain,
the Mn(B)-Mn(D) interaction is ferromagnetic. Liu et al reported that the magnetic moment
of Mn(A) and Mn(C) in MnNiMnGa is 2.99 µB.5 Using this value, and assuming the
magnetic moment of Ni is unchanged at 0.13 µB, the net moment of NiMnNiMn can be
estimated to be 6.24 µB. Combining with the net moment of 0.47 µB for the MnMnNiIn
domain, the total magnetic moment of the alloy can be calculated to be
6.240.6+0.470.4=3.94 µB, corresponding to 76 emu/g, as summarized in Table I. This is
in excellent agreement with the experimental evidences reported in the literature.2,3
TABLE I. Magnetization calculation of Ni50Mn25In25, Mn50Ni40In10, and Mn50Ni37In10Co3 alloys at room temperature.
alloy stacking couple
Mn(A)
(µB)
Mn(B)
(µB)
Mn(D)
(µB)
Ni
(µB)
In
(µB)
f.u.
(µB)
total
(emu/g)
Mn50Ni25In25 Mn-Mn-Ni-In anti -3.08 3.42 - 0.13 0 0.47 9.27
Mn50Ni40In10 Mn-Mn-Ni-In (40%) anti -3.08 3.42 - 0.13 0 0.47 76
Ni-Mn-Ni-Mn (60%) ferro - 2.99 2.99 0.13 - 6.24
Mn50Ni37In10Co3
Mn-Mn-(Ni,Co)-In (40%)
ferro 3.08 3.42 - 0.13 0 6.63 123
Ni-Mn-Ni-Mn (60%) ferro - 2.99 2.99 0.13 - 6.24
However, the magnetization of the present alloy is still significantly higher than
thus predicted. This is believed to be related to the effect of Co doping in the crystal
structure of the austenite. There have been evidences that Co doping enhances
ferromagnetic ordering of the austentie.14,15 In Mn48Ni32-xCoxGa20 alloys Co doping
converts the coupling between the nearest neighboring Mn-Mn atoms from
antiferromagnetic into ferromagnetic.4 Assuming the same effect in our alloy, neglecting
the net moment of the 3 at% Co, and converting the moment for Mn(A) from -3.08 µB to
3.08 µB, the lattice magnetization of the Mn-Mn-(Ni,Co)-In (40%) domain may be
estimated to be 6.63 µB. In this case, the total magnetic moment for the alloy is expected to
be 6.630.4+6.240.6=6.39 µB, which corresponds to 123 emu/g. This is a good agreement
CHAPTER 2 43
with the value determined experimentally (118 emu/g). It has been suggested that the
presence of Co in the matrix alters the states of Mn 3d electrons, which leads to the
enhanced ferromagnetic exchange in the austenite.16 This argument is also expected to
apply to the Mn50Ni37In10Co3 alloy.
Figure 3 shows isothermal magnetization loops of the alloy at different
temperatures. The sample showed typical soft magnetic behavior in martensitic state at 5 K
with a saturation magnetization of 29 emu/g under 7 T, which is consistent with previous
findings.2,3 At 200 K, the austenite magnetized in a similar way to saturation at 113 emu/g.
At 170 K, which is 42 K below fA , the sample quickly magnetized at below 0.5 T,
corresponding to the magnetization of the martensite, and then magnetized again at above 2
T, corresponding to the reverse MA transformation. The magnetization reached
saturation level (~118 emu/g) of the austenite at 6 T, indicating the completion of the
metamagnetic transformation. Similar behavior is also observed at 165 K (47 K below fA ),
but the transformation occurred at moderately increased field strength. Consequently, the
transformation was not complete at the maximum field applied (7 T) and the maximum
magnetization reached (~108 emu/g) was slightly below the saturation magnetization of the
austenite.
CHAPTER 2 44
0
20
40
60
80
100
120
0 1 2 3 4 5 6 7
Mag
net
izat
ion
(em
u/g
)
Magnetic field (T)
5 K
165 K
170 K
200 K
FIG. 3. Isothermal magnetization loops of Mn50Ni37In10Co3 alloy at different temperatures.
In Summary, the Mn50Ni37In10Co3 alloy shows a martensitic transformation at
186 KsM .
The crystal structure of the austenite is Hg2CuTi-type superlattice bcc
structure with lattice constant of a=0.6013 nm. The saturation magnetization of the
austenite is 118 emu/g and that of the martensite is 29 emu/g at 7 T, resulting in a large ΔM
of 89 emu/g across the martensitic transformation. The largely improved magnetization for
the austenite is attributed to (i) change of magnetic exchange status due to the composition
change of the lattice, and (ii) doping effect of Co. The calculations for the magnetization of
the austenite show excellent agreement with the experimental measurements. Co doping of
3 at% has increased the magnetization of the austenite by 42 emu/g. A complete
metamagnetic transformation is induced isothermally at 170 K in a magnetic field up to 7
T, indicating this alloy a promising candidate for magnetic actuation applications.
The authors wish to acknowledge the financial supports by the Department of
Innovation Industry, Science and Research of the Australian Government in ISL Grant
CHAPTER 2 45
CH070136, by the National Natural Science Foundation of China in Grant No. 10774178
and by the Fundamental Research Funds for the central universities.
Reference 1 G. D. Liu, J. L. Chen, Z. H. Liu, X. F. Dai, and G. H. Wu, Appl. Phys. Lett. 87, 262504
(2005). 2 J. L. Sanchez Llamazares, T. Sanchez, J. D. Santos, M. J. Perez, M. L. Sanchez, B.
Hernando, L. Escoda, J. J. Sunol, and R. Varga, Appl. Phys. Lett. 92, 012513 (2008). 3 J. L. Sanchez Llamazares, B. Hernando, V. M. Prida, C. Garcia, J. Gonzalez, R. Varga,
and C. A. Ross, J. Appl. Phys. 105, 07A945 (2009). 4 L. Ma, H. W. Zhang, S. Y. Yu, Z. Y. Zhu, J. L. Chen, G. H. Wu, H. Y. Liu, J. P. Qu, and
Y. X. Li, Appl. Phys. Lett. 92, 032509 (2008). 5 G. D. Liu, X. F. Dai, S. Y. Yu, Z. Y. Zhu, J. L. Chen, G. H. Wu, H. Zhu, and J. Q. Xiao,
Phys. Rev. B: Condens. Matter 74, 054435 (2006). 6 R. B. Helmholdt and K. H. J. Buschow, Journal of the Less-Common Metals 128, 167
(1987). 7 H. Luo, G. Liu, Z. Feng, Y. Li, L. Ma, G. Wu, X. Zhu, C. Jiang, and H. Xu, J. Magn.
Magn. Mater. 321, 4063 (2009). 8 W. Ito, K. Ito, R. Y. Umetsu, R. Kainuma, K. Koyama, K. Watanabe, A. Fujita, K.
Oikawa, K. Ishida, and T. Kanomata, Appl. Phys. Lett. 92, 021908 (2008). 9 R. Y. Umetsu, W. Ito, K. Ito, K. Koyama, A. Fujita, K. Oikawa, T. Kanomata, R.
Kainuma, and K. Ishida, Scripta Mater. 60, 25 (2009). 10 V. K. Sharma, M. K. Chattopadhyay, and S. B. Roy, Phys. Rev. B 76, 140401 (2007). 11 J. L. Sanchez Llamazares, B. Hernando, J. J. Sunol, C. Garcia, and C. A. Ross, J. Appl.
Phys. 107, 09A956 (2010). 12 A. Chakrabarti and S. R. Barman, Appl. Phys. Lett. 94, 161908 (2009). 13 T. Yamada, N. Kunitomi, Y. Nakai, D. E. Cox, and G. Shirane, J. Phys. Soc. Jpn. 28, 615
(1970). 14 S. Y. Yu, Z. X. Cao, L. Ma, G. D. Liu, J. L. Chen, G. H. Wu, B. Zhang, and X. X. Zhang,
Appl. Phys. Lett. 91, 102507 (2007).
CHAPTER 2 46
15 S. Y. Yu, L. Ma, G. D. Liu, Z. H. Liu, J. L. Chen, Z. X. Cao, G. H. Wu, B. Zhang, and X.
X. Zhang, Appl. Phys. Lett. 90, 242501 (2007). 16 B. Gao, F. X. Hu, J. Shen, J. Wang, J. R. Sun, and B. G. Shen, J. Magn. Magn. Mater.
321, 2571 (2009).
CHAPTER 2 47
Paper2
Effect of Co addition on martensitic phase transformation and magnetic
properties of Mn50Ni40-xIn10Cox polycrystalline alloys
Zhigang Wu a, Zhuhong Liu b, Hong Yang a, Yinong Liu a,*, Guangheng Wu c
a School of Mechanical and Chemical Engineering, The University of Western Australia,
Crawley, WA 6009, Australia
b Department of Physics, University of Science and Technology Beijing, Beijing 100083,
China
c Beijing National Laboratory for Condense Matter Physics, Institute of Physics, Chinese
Academy of Science, Beijing 100080, China
Keywords:A:magneticintermetallics;B:alloydesign;B:shape‐memoryeffects;B:
martensitictransformations;B:magneticproperties.
Abstract
This study investigated the use of Co to enhance the magnetic driving force for
inducing the martensitic transformation of Mn50Ni40-xIn10Cox alloys. These alloys present a
martensitic transformation from a Hg2CuTi-type austenite to a body centered tetragonal
martensite, with a large lattice distortion of 15.7% elongation along the c direction and
8.2% contraction along a and b directions. The martensitic transformation temperatures,
transformation enthalpy and entropy changes decreased with increasing the Co content in
these alloys. The maximum magnetization of the austenite increased significantly, whereas
that of the martensite changed much less prominently with increasing the Co substitution
CHAPTER 2 48
for Ni, leading to increase of the magnetic driving force for the transformation. The
magnetization increase of the austenite is found to be due to (i) formation of
ferromagnetically coupled Mn-Mn due to new atomic configuration in off-stoichiometric
composition, (ii) magnetic moment contribution of Co and (iii) widening of the temperature
window for magnetization of the austenite. These findings clarify the effect of Co addition
on martensitic transformation and magnetic properties in Mn-rich ferromagnetic shape
memory alloys, and provide useful understanding for alloy design for magnetoactuation
applications.
1.Introduction
Ternary Ni-Mn-Z(Z=In,Sn,Sb) alloys have attracted much attention in the past few
years as a new type of ferromagnetic shape memory alloys (FSMAs) since their discovery
in 2004 [1]. Unlike Ni2MnGa alloy [2], which relies on magnetic crystallographic
anisotropy of the martensite, these Ni-Mn-Z(Z=In,Sn,Sb) alloys exhibit a martensitic
transformation between a ferromagnetic austenite and a paramagnetic martensite. The
different magnetic states between the two phases provide a much greater magnetic driving
force, thus the possibility for a magnetic-field-induced martensitic transformation. Such
transformations are referred to as metamagnetic transformations in recognition of their
concurrent metallurgical and magnetic changes. The magnetic driving force for a
metamagnetic transformation is provided by the Zeeman Energy EZeeman=µ0MH, where
µ0 is the permeability of a vacuum, M is the saturation magnetization difference between
the austenite and martensite and H corresponds to the strength of the applied field. The M
between the ferromagnetic austenite and the paramagnetic martensite, as in the case of Ni-
Mn-Z(Z=In,Sn,Sb), is much greater than the M between the easy and hard magnetization
directions of the same crystal structure, as in the case of Ni-Mn-Ga alloys, thus giving
possibility for much more powerful magnetic-field-induced martensitic phase
transformation and mechanical actuation.
In Ni2MnZ(Z=In,Sn,Sb) alloys, the net magnetic moment mainly comes from the
contribution of Mn [3]. By substituting Mn for X, ΔM has been found to increase in
Ni2Mn1+xIn1-x alloys but to decrease in Ni2Mn1+xSn1-x alloys [4, 5]. At the meantime,
CHAPTER 2 49
increasing Mn content also causes rapid increase of the martensitic transformation
temperatures, to above the Curie temperature of the austenite [6, 7]. This results in the
transformation being between a paramagnetic austenite to a paramagnetic martensite, thus
losing the advantage of large magnetic driving force for transformation and jeopardizing
the possibility for magnetic actuation. This limits the range of Mn content feasible in
Ni2MnX(In,Sn,Sb) alloys.
A new approach is to develop Mn2NiZ(Z=Ga,In,Sn,Sb) alloys. These alloys have
the obvious advantage by having more Mn in the matrix, which has the highest
magnetization contribution among the three constituents [3]. A magnetic-field-assisted
shape change of ~4 % has been achieved in single crystalline Mn2NiGa [8]. However, the
magnetic driving force in this alloy is small due to the limited magnetization difference (~9
emu/g) between the austenite and martensite [8, 9]. A progress has been made recently with
off-stoichiometric Mn50Ni40In10 [10, 11] and Mn48CoxNi32-xGa20 [12] alloys, which showed
a relative large ΔM of about 40 emu/g and 30 emu/g respectively, making these alloys valid
candidates for ferromagnetic shape memory actuation. To further improve ΔM, we have
recently reported our study on a Mn50Ni37In10Co3 polycrystalline alloy. This alloy exhibited
a large ΔM of ~89 emu/g and a complete reversible metamagnetic transformation [13].
These limited early findings indicate a possible solution to challenge of enhancing magnetic
driving force for inducing metamagnetic transformation, a prerequisite for magnetically
actuated shape memory alloys.
The saturation magnetization of the alloys depends greatly on the magnetic moment
distribution from Mn atoms. However, the study on the magnetic moment distribution of
Mn in the off-stoichiometric alloys is much lacking. Very recently, Lazpita et al. proposed
a model of magnetic interaction between Mn atoms in the off-stoichiometric Ni-Mn-Ga
alloys [14]. In their model, the excess of Mn atoms at Ga sites couple antiferromagnetically
with the Mn at Mn sites when Ni atoms are at their proper sties, while the Mn at Ga sites
couple ferromagnetically with the Mn at Mn sites when Mn excess occupies Ni sites.
However, the systematic analysis on atomic configuration in Mn-rich off-stoichiometric
Mn-Ni-Z(Z=In,Sn,Sb) alloys is still missing. Moreover, the magnetic interactions between
the constituents may rise up to another level of complexity after Co doping in these ternary
CHAPTER 2 50
alloys, since Co doping in Ni-Mn-Z(Ga,Al,In,Sn,Sb) has been found to be effective in
inducing its metamagnetic transformation [15-19]. These findings all indicate that Co
doping in Ni-Mn-Z alloys greatly enhances the ferromagnetic interaction of the austenite,
resulting in the significantly increased the magnetic driving for metamagnetic
transformation. A popular argument is that when Co enters the Ni-Mn-Z Heusler lattice, it
has the effect of turning the antiferromagnetically coupled Mn-Mn atoms into
ferromagnetically couples ones [12, 19]. However, detailed explanation of this effect is yet
to be established. In this study, we further expand our investigation on a series of Mn50Ni40-
xIn10Cox alloys, with an emphasis on analyzing the magnetic moment interactions between
Mn-Mn and Mn-Co atoms in our proposed model.
2.ExperimentalProcedures
Polycrystalline Mn50Ni40-xIn10Cox (x=0, 1, 2 and 3) alloy ingots were prepared by
means of arc melting in argon atmosphere using high purity (99.99 at.%) elemental metals.
The samples are referred to as Co0, Co1, Co2, and Co3, respectively. The button shaped
ingots were heat treated at 1173 K for 24 hours in vacuum followed by quenching into
water for homogenization. Transformation behaviour of the alloys was studied by means of
differential scanning calorimetry (DSC) using a TA Q10 DSC instrument with a
cooling/heating rate of 10 K/min. Phase identification and crystal structures were
determined by means of X-ray powder diffraction using Cu-Kα radiation. The compositions
were determined by means of quantitative X-ray energy dispersive spectrometry (EDS)
equipped on a Zeiss 1555 field-emission scanning electron microscope (FESEM). The
magnetic properties were studied using a superconducting quantum interference device
magnetometer (SQUID).
CHAPTER 2 51
3.ExperimentalResults
3.1 Crystal structure
Fig. 1 shows XRD spectra of powder samples of Mn50Ni40-xIn10Cox alloys measured
at room temperature.
20 30 40 50 60 70 80 90 100
Co0
2 (o)
X-r
ay I
nten
sity
(044
) M
(022
) M
(220
) M
(004
) M
(400
) M
(224
) M
(422
) M
(044
) M
Co1
(022
) M
(220
) M
(004
) M
(400
) M
(224
) M
(422
) M
(044
) M
(422
) A
(400
) A
(220
) A Co2
(022
) M
(220
) M
(004
) M
(400
) M
(224
) M
(422
) M
(440
) A
(222
) A
(422
) A
(400
) A(220
) A
24 28 32
(111)
(200)
Co3
Fig. 1. X-ray diffraction spectra of Mn50Ni40-xIn10Cox alloys.
The diffraction peaks of Co0 and Co1 alloys are indexed to body-centered
tetragonal non-modulated martensite structure, which is also observed in Mn2NiGa alloys
[8]. The Co2 alloy has a mixed structure of body-centered cubic austenite and tetragonal
martensite. This indicates that the addition of 2 at.% of Co lowers the martensitic
CHAPTER 2 52
transformation temperatures to below the room temperature. The Co3 alloy shows a pure
austenite structure with bcc fundamental lattice reflections of (220), (400), (422) and (440)
and superlattice reflections of (111), (200), (311) and (222). The superlattice structure can
be determined by comparing the relative intensities of (111) and (200). It is evident that
I111/I200>1, as shown in the inset of Fig. 1, implying that the superlattice is of the Hg2CuTi-
type, consistent with other Mn2NiZ(Z=Ga,Sn,Sb) alloys [20-22].
Fig. 2 shows the effect of Co addition on the lattice parameters and unit cell
volumes for the austenite and martensite at room temperature. It is seen that the
transformation from the cubic austenite to tetragonal martensite is realized by an expansion
in the c direction and equal contractions in the a and b directions (a=b), which is consistent
with Mn2NiGa alloy [8].
0 1 2 30.52
0.56
0.60
0.64
0.68
0.72
0.76AusteniteMartensite
aA
cM
aM
VM
VA
Co Addition (at%)
Lat
tice
Con
stan
ts (
nm)
V
0.204
0.208
0.212
0.216
0.220
0.224
Unit C
ell Volum
e (nm3)
Fig. 2. Effect of Co addition on lattice parameters and unit cell volume of Mn50Ni40-
xIn10Cox alloys.
The lattice distortion can be estimated to be (cM-aA)/aA=15.7 % along the c direction
and (aM-aA)/aA= -8.2 % for the a and b directions for alloy Co2. Both the expansion in c
direction and contractions in a and b directions are larger than those in Ni2MnGa alloy,
which are 8.4 % and -6.6 % respectively [2]. This large lattice deformation implies higher
frictional resistance to the propagation of transformation interfaces, leading to large
CHAPTER 2 53
transformation hysteresis. The unit cell volumes of both the austenite and martensite are
found to slightly increase with increasing substitution of Co for Ni, obviously related to the
slightly larger size of Co atom relative to Ni. It is also evident that the transformation from
the austenite to martensite is accompanied by a volume contraction, of -2.4%. The large
volume change may induce cracking in the material during transformation cycles.
3.2 Alloy composition
All these alloys show single phase microstructure, as confirmed by SEM
observation. The compositions of these alloys were determined by quantitative EDS
analysis, as summarized in Table 1. The Mn contents for all four alloys are approximately
49 at.%, indicating a volatilization loss of ~1 at.% of Mn during the arc-melting process.
The continuous reduction of Ni is compensated well by the addition of Co, as the designed
nominal compositions. The content of In remained nearly unchanged for all four alloys, at
between 9.9 at.% and 10.5 at.%. The valence electron concentrations of the alloys (e/a
ratio) are calculated using the compositions obtained from the EDS analysis based on the
sum of s, p and d electrons for Mn (7), Ni (10), Co (9) and In (3). It is seen that the e/a ratio
of the alloys decreased from 7.837 to 7.756 with increasing Co substitution for Ni from 0 to
3 at.%, obviously due to the smaller number of valence electrons of Co (9) relative to that
of Ni (10).
Table 1. Composition and e/a ratio of Mn50Ni40-xIn10Cox alloys.
Mn
at.%
Co
at.%
Ni
at.%
In
at.%
e/a
ratio
x=0 49.0 - 41.1 9.9 7.837
x=1 48.8 0.9 40.0 10.3 7.806
x=2 49.3 1.9 38.5 10.3 7.781
x=3 49.3 3.0 37.2 10.5 7.756
CHAPTER 2 54
3.2 Martensitic transformation
Fig. 3 shows DSC curves of the Mn50Ni40-xIn10Cox alloys. It is seen that the
martensitic transformation behaviour evolves progressively, to lower temperatures, with
increasing the Co content of the alloys.
100 150 200 250 300 350 400 450 500
Hea
t Flo
w
Co0
Co1
Co2
Temperature (K)
Co30.
1 w
/g
Fig. 3. DSC curves of the martensitic transformation of Mn50Ni40-xIn10Cox alloys.
The transformation thermal parameters, including starting, finishing and peak
temperatures (Ms, Mf, Mp, As, Af and Ap) for the forward and reverse transformation,
transformation hysteresis (ΔT=Ap-Mp), enthalpy change (ΔH) and entropy change (ΔS), of
the alloys are summarised in Table 2. H is obtained directly from the DSC measurement,
and S is calculated as 0
HS
T
, where 0
1( )
2 p pT M A .
Table 2. The martensitic and austenitic transformation starting, finishing and peak
temperatures (Ms, Mf, Mp ,As, Af, Ap), transformation hysteresis (ΔT= Ap- Mp),
enthalpy change (ΔH) and entropy change (ΔS) of Mn50Ni40-xIn10Cox alloys.
Ms
(K)
Mf
(K)
Mp
(K)
As
(K)
Af
(K)
Ap
(K)
ΔT
(K)
ΔH
(J/g)
ΔS
(J/Kkg)
CHAPTER 2 55
x=0 381 350 373 373 403 396 23 9.7 25.0
x=1 318 302 316 334 348 341 25 6.7 23.4
x=2 262 239 249 257 282 269 20 4.6 17.8
x=3 175 161 169 185 199 195 26 2.9 15.9
Fig. 4 shows the effect of Co substitution for Ni on phase transformation
temperatures (Mp and Ap) and transformation hysteresis (ΔT) of the alloys.
0 1 2 3
150
200
250
300
350
400
450
Ap
Mp
Co Addition (at%)
Tra
nsfo
rmat
ion
Tem
pear
ture
(K
)
T
0
5
10
15
20
25
30
35
40
45
50
Transform
ation Hysteresis (K
)
Fig. 4. Effect of Co addition on phase transformation peak temperatures (Mp and Ap) and
transformation hysteresis (ΔT).
It is seen that the transformation temperatures decreased progressively with
increasing the Co content. This is in good agreement with the effect of Co doping in Ni-
Mn-Ga [23] and Ni-Mn-Sb [24] alloys. This is obviously related to the e/a ratio decrease
with the increase of Co substitution for Ni. The ΔT remained practically unchanged,
between 20 and 26 K for the alloys of different Co content. It is known that the
transformation hysteresis generally corresponds to the frictional resistance to the
martensitic transformation, stemming largely from the lattice mismatch, distortion and
volume change of the transformation. Generally, a larger lattice distortion means the
martensitic transformation requires higher energy to overcome the friction during the
motion of the phase boundaries, thus leading to larger transformation hysteresis. It is seen
CHAPTER 2 56
in Fig. 2 that the lattice distortions and the volume change are practically the same for all
the four alloys, thus resulting in nearly constant transformation hysteresis for the
transformation.
Fig. 5 shows the effects of Co addition on the transformation enthalpy (ΔH) and
entropy (ΔS) changes of the alloys, as functions of transformation temperature To in (a) and
e/a ratio in (b). It is to be noted that for the martensitic transformation both ΔH and ΔS are
negative values and the plot customarily neglects this. It is seen that both the enthalpy and
entropy changes increased continuously with increasing To and with e/a ratio, caused by Co
addition. The influence of e/a ratio on the entropy change of martensitic transformation has
been reported for Ni50+xMn25-xGa25 [25], Ni50Mn50-xInx [7], and Ni50Mn50-xSnx [6] alloys. In
these alloy systems, ΔS increases with increasing transformation temperatures and e/a ratio,
which is in good agreement with the findings of this study. Similar phenomenon has also
been observed in Ni50Mn40-xSn10Fex and Ni50Mn37(In,Sb)13 alloys in our previous studies
[26, 27].
150 200 250 300 350 4000
2
4
6
8
10
increase Co addition
S
To (K)
Ent
halp
y C
hang
e (J
/g)
a
H
16
18
20
22
24
26
Entropy C
hange (J/K-kg)
CHAPTER 2 57
7.74 7.76 7.78 7.80 7.82 7.840
2
4
6
8
10
increase Co addition
bS
e/a Ratio
Ent
halp
y C
hang
e (J
/g)
H
16
18
20
22
24
26
Entropy C
hange (J/K-kg)
Fig. 5. Effect of Co addition on enthalpy and entropy changes, (a) as function of
transformation temperature To=(Mp+Ap)/2, and (b) as function of e/a ratio.
3.3 Thermomagnetization behaviour
Fig. 6 shows the thermomagnetization behaviour of the four alloys. The sample was
first cooled down to 10 K in a zero magnetic field prior to the measurement. A magnetic
field was applied at 10 K and then the measurement was taken upon heating to 395 K at a
rate of 10 K/min and cooling back again to 10 K in the same field. Fig. 6(a) shows the M(T)
curves of the alloys between 10 and 395 K in a field of 50 Oe. It is seen that the Co0 alloy
showed a mild decrease of magnetization at between 320 and 340 K upon heating, owing to
the Curie transition of the alloy. Based on the DSC measurement (Fig. 3), the Ms
temperature of this alloy is 381 K. However, the M(T) data shows that the hysteresis
between the heating and cooling curves prevailed at between 320 and 340 K, and continued
to present down to 100 K, as shown in the inset of Fig.6 (a). This implies that the
martensitic transformation is not complete and the austenite coexists in this alloy at very
low temperature. Therefore, the Curie temperature corresponds to that of the remaining
austenite at below Ms temperature, denoted ACT =322 K of Co0.
CHAPTER 2 58
0 50 100 150 200 250 300 350 400
0
1
2
3
4
5
6
7
8
100 200 300 4000.0
0.4
0.8
TC
ACo0
TC
A
Co3
Co1
Co2
Mag
netiz
atio
n (e
mu/
g)
Temperature (K)
Co0
TC
A
a
H=50 Oe
0 50 100 150 200 250 300 350 400
0
20
40
60
80
100
120
Co0
Co1
Co2
Co3
Mag
netiz
atio
n (e
mu/
g)
Temperature (K)
H=70 kOeb
Fig. 6. Thermomagnetization behaviour of Mn50Ni40-xIn10Cox alloys under a field of (a)
H=50 Oe and (b) H=70 kOe.
In the Co1 alloy, the martensite is antiferromagnetic-like at low temperatures, as
evidenced by the nil magnetization. It is also worth noting the cooling curve retraced the
heating curve at the entire low temperature regime below the martensitic transformation.
Normally a splitting phenomenon between the zero field cooled and field cooled M(T)
curves is observed at low temperatures in Ni-Mn based alloys [6, 7], which indicates the
coexistence of ferromagnetic and antiferromagnetic ordering at the martensitic state.
However, the M(T) data of Co1 suggests that the ferromagnetic structure is vanished and
CHAPTER 2 59
the antiferromagnetic exchange is dominant at the martensitic phase. The antiferromagnetic
martensite started transforming to ferromagnetic austenite at 320 K upon heating, followed
immediately by the Curie transition of the austenite at ACT =345 K. Upon cooling, the
magnetization of the austenite increased rapidly through its Curie transition, followed by a
short magnetization plateau before demagnetization rapidly at 325 K upon further cooling
via the transformation from the ferromagnetic austenite to antiferromagnetic martensite.
The martensitic transformation in Co2 alloy can be clearly observed, shown as the
magnetization change upon both heating and cooling, as evidenced by the obvious
transformation hysteresis. The Curie transition for the austenite occurred at 378 K. Similar
to Co1 alloy, the nil magnetization and superposition of M(T) curves at below the
martensitic transformation suggest that the martensite is mainly antiferromagnetic ordered.
Co3 showed clear martensitic transformation as the abrupt magnetization change
upon heating and cooling in the temperature range between 170 and 195 K. The ACT of Co3
is determined to be 393 K. Unlike Co1 and Co2, the separation between the heating and
cooling curves appeared at below 50 K in Co3, suggesting the coexistence of ferromagnetic
ordering and antiferromagnetic ordering at its martensitic state. It is seen that the
martensitic transformation shifted to lower temperatures whereas the Curie transition
shifted to higher temperatures with increasing Co content in these alloys. The increased ACT
is attributed to the fact that the exchange interaction between Co-Mn is stronger than that
between Ni-Mn [12].
Fig. 6(b) shows the M(T) curves of the four alloys between 10 and 395 K in a field
of 70 kOe. The magnetization of the Co0 alloy did not change much during the heating and
cooling cycle, at between 12 and 17 emu/g. The minor increase of the magnetization from
12.5 to 15.5 emu/g at around 380 K upon heating corresponds to the partial occurrence of
the martensitic transformation. With increasing the Co content, it is clear that the
martensitic transformation shifted to lower temperatures. More notably, for alloys through
Co1 to Co3, the magnetization of the austenite increased steadily with increasing Co
content at given temperatures. For example, the magnetization increased from 52 to 70
CHAPTER 2 60
emu/g with the increase of Co content from 1 to 3 at.% at 350 K, giving rise to an average
increase of 9 emu/g per 1 at.% Co.
It is also seen that the magnetization behaviour of Co1 and Co2 were completely
reversible after a complete transformation cycle under 70 kOe. In contrast, the
magnetization loop of alloy Co3 did not close at 10 K. It is due to the kinetic arrest of the
austenite phase under the influence of high magnetic field. This effect has also been
observed in several Ni-Mn-In alloys [28-30]. The magnetization at the finishing point on
the cooling curve comprises of the contributions of the newly formed martensite and the
retained austenite. The enhanced magnetization of Co3 at the end of the cooling implies
that more austenite has been retained by the high magnetic field. This is reasonable given
the significantly lowered martensitic transformation temperature, i.e., reduced
thermodynamic driving force for the transformation, of this alloy.
3.4 Magnetization
The maximum magnetizations of the austenite and martensite ( AM and MM ) are
taken at fA and sA from the heating M(T) curves under 70 kOe. The magnetization
difference between the austenite and martensite is obtained from A MM M M .
The AM , MM , M , and A
CT are summarized in Table 3.
Table 3. Effect of Co addition on maximum magnetizations of the austenite and
martensite obtained at Af and As ( AM and MM ), magnetization difference of
the transformation ( M ), and Curie temperatures of the austenite ( ACT ).
AM MM M A
CT
Co0 15.5 12.5 3 322
Co1 55 3 52 345
Co2 78 5 73 378
Co3 118 29 89 393
CHAPTER 2 61
Fig. 7 shows AM , MM and M as functions of Co content. It is seen that AM
increased greatly with the increase of Co content, from 15.5 emu/g in Co0 to 118 emu/g in
Co3, meanwhile MM first decreased from 12.5 emu/g in Co0 to 3 emu/g in Co1, and then
it increased to 29 emu/g in Co3 alloy. ΔM shows a steady increasing trend with increasing
Co content in the alloys, giving rise to a maximum value of 89 emu/g in Co3 alloy. The
greatly increased M is beneficial for obtaining large magnetic driving force for
metamagnetic transformation, i.e. Zeeman Energy, in these alloys.
0 1 2 3
0
20
40
60
80
100
120
M
MA
Mag
netiz
atio
n (e
mu/
g)
Co Addition (at%)
MM
Fig. 7. The maximum magnetization of the austenite and martensite (MA and MM) and
magnetization difference between the phases (ΔM) as a function of Co addition.
The giant magnetization difference across the martensitic transformation is
obviously due to the distinct magnetic states between the austenite and martensite. To
further examine the magnetic configurations in the austenitic and martensitic phases, M(H)
curves were carried out at 5 and 350 K for the Co0, Co1, Co2 and Co3 alloys, respectively.
Fig. 8 shows the magnetization of the alloys at (a) 5 K and (b) 350 K. It is known that all
the alloys are at martensitic state at 5 K based on the thermomagnetization measurements
(Fig. 6).
CHAPTER 2 62
0 10 20 30 40 500
5
10
15
20
25
30
Mag
neti
zati
on (
emu/
g)
Magnetic field (kOe)
Co0
Co1
Co2
Co3a T=5 K
0 10 20 30 40 50
0
10
20
30
40
50
60
70
80Co3
Co2
Mag
netiz
atio
n (e
mu/
g)
Magnetic field (kOe)
Co1
b T=350 K
Fig. 8. Magnetization curves at (a) 5 K and (b) 350 K of Mn50Ni40-xIn10Cox alloys.
Fig. 8(a) shows that Co0 has a relatively quick magnetizing behaviour at the
beginning of M(H) curve, indicating the existence of ferromagnetic ordering at its
martensitic state. However, based on the form of M(H) curve and the low magnetisation of
15 emu/g at 50 kOe, the antiferromagnetic exchange is expected to coexist with
ferromagnetic structure at 5 K. Co3 alloy shows a similar M(H) behaviour, but with
stronger magnetic correlations than that in Co0, evidenced by the higher magnetisation of
26 emu/g at 50 kOe. The M(H) curves of Co1 and Co2 are nearly linear, particularly for
Co1, strongly suggesting the existence of long-range antiferromagnetic ordering at the
martensitic state of these alloys.
CHAPTER 2 63
Fig. 8(b) shows the magnetization behaviour of the austenitic phase at 350 K of
Co1, Co2 and Co3 alloys. The absence of M(H) data of Co0 is due to its martensitic state at
350K, which is irrelative for comparison with other alloys at the austenitic state. The
austenite of Co1 showed a gradual magnetization growth and maximized at 42 emu/g upon
magnetizing. It is known that the ACT (345 K) of Co1 is very close to the magnetizing
temperature (350 K), therefore, the shape of the M(H) data indicates the existence of
magnetic short-range correlations in the paramagnetic austenitic state. Co2 and Co3
presented very typical ferromagnetic behaviour due to the rapid increase of magnetization
at the initial portion of M(H) curves and the high magnetization magnitude of 59 and 70
emu/g, respectively.
4.Discussion
4.1 Entropy change
It is seen in Fig. 5 that the value of the entropy change of the transformation
decreased significantly with Co doping, by 36 % reduction with addition of 3 at.% Co.
Entropy change (ΔS) of a martensitic phase transformation is a measure of the difference of
degree of order between the austenite and martensite. In addition to being a function of
temperature itself, ΔS is generally considered to have three contributions, including crystal
structural ordering (ΔSlatt), magnetic structure ordering (ΔSmag) and electronic structure
ordering (ΔSel). In Ni2+xMn1-xGa and X2MnSn (X=Co, Ni, Pd, Cu) alloys, it has been shown
that the electronic contribution ΔSel to ΔS is small [25, 31]. The crystal structural
contribution ΔSlatt to ΔS depends on the crystal structures of the transformation. For the
present four alloys, the structural change is the same and the magnitudes of lattice
distortions of the transformation are similar according to the XRD measurements. Thus, the
crystal structural contribution to the entropy change is also expected to be unchanged for
these alloys. In this regard, the increase of total entropy change ΔS with Co content is
attributed to the magnetic ordering contribution, neglecting the temperature effect.
CHAPTER 2 64
Fig. 9 shows a schematic of the contributions of ΔSlatt, ΔSmag to ΔS as functions of
Co content in the alloys.
Fig. 9. Illustration of the effect of Co addition on entropy change of the alloys.
It is known that A Mlatt lattS S , thus the 0M A
latt latt lattS S S for the forward AM
transformation. In the Figure ΔSlatt remains a constant negative value irrespective of Co
content. On the other hand, it is known that A Mmag magS S , thus 0M A
mag mag magS S S . This
is because of the higher magnetic ordering in the austenite relative to the martensite. The
introduction of Co enhances the ferromagnetic ordering of the austenite [13, 16, 19], thus
decreasing the magnetic entropy of the austenite. Meanwhile, the magnetic interaction
between the atomic constituents in the martensite is not significantly affected, relative to
the austenite, as evident in Fig. 7. This results in positive increase of magnetic entropy
change of the transformation with increasing Co content. Consequently, the total entropy
change for the AM transformation becomes less negative with increasing Co content, as
observed in Fig. 5.
4.2 Magnetic moment interactions
4.2.1. Structure of stoichiometric Mn2NiIn
Co content
ΔS
ΔSlatt
ΔSmag
ΔS=ΔSlatt
+ΔSmag
0
+
- ΔS
CHAPTER 2 65
The crystal structure of the austenite is Hg2CuTi-type super lattice cubic structure.
This structure is commonly observed in Mn-rich Heusler alloys, such as Mn2NiGa [20] and
Mn2CoZ(Z=Al,Ga,Ge,In,Sn,Sb) [32]. In this structure, Mn atoms occupy A (0,0,0) site and
B (1/4,1/4,1/4) site, leaving C (1/2,1/2,1/2) site to Ni atoms and D (3/4,3/4,3/4) site to the
third element atoms. This structure is illustrated in Fig. 10, showing the unit cell models for
both the austenite in (a) and martensite in (b) of a stoichiometric Mn2NiIn alloy. Such
structure can be expressed in a stacking order of Mn-Mn-Ni-X ( 43F m space group) along
the diagonal direction of the unit cell.
Fig. 10. Atomic configuration in the unit cell of Mn2NiIn alloy: (a) unit cell of the
austenite with Mn-Mn-Ni-In stacking order (Hg2CuTi structure) and (b) unit cell of the
martensite with Mn-Mn-Ni-In tetragonal structure.
Based on the calculation by Chakrabarti et al [9], the spin magnetic moments of
Mn(A), Mn(B) and Ni in Mn2NiIn alloy are -3.08, 3.42 and 0.13 µB , respectively. The
magnetic moment of In is very small and is neglected in the present discussion. The spin
magnetic moments of Mn atoms are symbolically depicted using arrows on the atoms
shown in Fig. 10. The length of the arrows roughly represents the magnitude of the
magnetic moment of the atom. The exchange interaction between Mn atoms is known to
CHAPTER 2 66
depend strongly on Mn-Mn distance in the lattice. Early studies have shown that the
magnetic interaction between Mn atoms changes from antiferromagnetic to ferromagnetic
when the Mn-Mn distance is increased to above a critical value of approximately 0.30 nm
[33]. For the austenite with Mn-Mn-Ni-In stacking order in the unit cell (Fig. 10(a)), the
distance between the nearest neighboring Mn at A site and B site is 3 / 4AB a =0.2604
nm and the distance between the second nearest neighboring Mn at two adjacent A sites is
2 / 2AA a =0.4251 nm using the lattice constant of a=0.6013 nm for the Co3 alloy. This
implies that the moments of Mn(A)-Mn(B) form antiparrallel coupling and Mn(A)-Mn(A)
form parallel coupling. It is seen that the spin directions of Mn magnetic moments at A site
are antiparrallel with those of Ni at C site, and they are also opposed to those of Mn at B
site. This forms a ferrimagnetic structure in this atomic configuration, with antiparrallel
aligned magnetic moments between (A,C) and (B,D) sub-lattices.
Assuming that the stoichiometric Mn2NiIn alloy also undergoes the same structural
transformation to a tetragonal martensite as for the present alloys, the distance between A
site and B site changes very little by the transformation, at 3 / 4AB a =0.2612 nm in the
martensite, and the distance between two adjacent A sites is shortened to
2 / 2AA a =0.3899 nm as shown in Fig. 10(b). Therefore, Mn(A)-Mn(B) still forms
antiferromagnetic interaction and Mn(A)-Mn(A) forms ferromagnetic interaction in the
martensite. This implies that the magnetic exchange interactions in the martensite are
similar with those in the austenite, which is ferrimagnetic.
4.2.2. Atomic configuration in off-stoichiometric Mn2Ni1+xIn1-x
In Ni-rich off-stoichiometric Mn2Ni1+xIn1-x alloys, the magnetization has been found
to increase greatly relative to its mother alloy Mn2NiIn, as evidenced by the magnetization
of ~75 emu/g (at 230 K) in Mn50Ni40In10 [10] comparing to 9.27 emu/g in Mn2NiIn [9]. The
drastic increase of the magnetization cannot be solely attributed to the magnetic moment
contribution from the “extra” Ni which substitutes for In, as the magnetic moment of Ni is
small, typically ~0.13 µB. This suggests that the increase may originate from the biggest
magnetic moment contributor Mn atoms. This implies that the atomic configuration must
have changed after the Ni substitution for In.
CHAPTER 2 67
Fig. 11 shows the atomic configuration in the unit cell of the austenite in (a) and the
martensite in (b) of the Co0, with the nominal composition of Mn50Ni40In10.
Fig. 11. Atomic configurations in the unit cell of Co0 alloy (Mn50Ni40In10): (a) unit cell of
the austenite and (b) unit cell of the martensite. The number of displaced atoms does not
represent the actual proportion of substitution, which is only for qualitative interpretation.
It is seen that some portion of Mn atoms at A site have been replaced by Ni atoms,
and these new Mn atoms share D site with In atoms. This hypothesis is based on the rule of
preferential site occupation in Mn2YZ (Y: 3d elements; Z: III-V A group elements) alloys
reported by Liu et al. [32]. They observed that Y elements on the right hand side of Mn in
the Periodic Table of Elements prefer to occupy (A,C) sites, whereas Y elements to the left
of Mn have strong preference for B site occupancy. In Mn2YZ (Y = V, Cr, Mn, Fe, Co and
Ni; Z =Al, Ga, In, Si, Ge, Sn and Sb) Heusler alloys, this rule of atomic occupancy has
been shown to be well obeyed [22, 32, 34-36]. According to this principle, Ni substitution
for In will have the priority to take A site in preference to Mn. The distance between the
new Mn atoms at D site and Mn atoms at B site is 0.3007 nm, which favors ferromagnetic
exchange interaction between the Mn atoms. Therefore, the magnitude of antiferromagnetic
CHAPTER 2 68
alignment between Mn(A) and Mn(B) is reduced, and the new Mn atoms at D site form
ferromagnetic interaction with the Mn atoms at B site.
In Fig. 11(a), the spin magnetic moments of the new Mn(D) align parallel with
those of Mn(B). At the meantime, the new (A,C) sub-lattice after the replacement of Ni for
Mn at A site also forms ferromagnetic interaction with Mn(B) and Mn(D), thus creating a
local ferromagnetic structure of Mn(B)-Ni-Mn(D) in the alloy. This explains the increase of
the magnetization of the austenite in off-stoichiometric Mn2Ni1+xIn1-x alloy after Ni
substitution for In compared to the stoichiometric Mn2NiIn alloy.
In the martensite unit cell (Fig. 11(b)), the distance change between the nearest
Mn(A)-Mn(B) atoms is very small, from 0.2604 to 0.2612 nm, which suggests that the
coupling between Mn(A)-Mn(B) does not change after the transformation, still showing
antiferromagnetic interaction between them. However, along the a and b directions in the
tetragonal unit cell, the distance between A and C sites (same for B and D sites) is
shortened to AC=BD=0.2758 nm, which strongly favours antiferromagnetic coupling
between Mn(B)-Mn(D) [37, 38]. This explains the presence of antiferromagnetic
interaction at the martensitic phase obtained from the M(H) data shown in Fig. 8 (a). In this
regard, it is reasonable to attribute the disappearance of the local ferromagnetic structure of
Mn(B)-Ni-Mn(D) in the martensite to the significant decrease of the Mn(B)-Mn(D)
distance.
4.2.3. Magnetic moment contribution from Co
Fig. 12 shows the atomic configuration in the unit cells for the austenite (a) and the
martensite (b) after Co doping in off-stoichiometric Mn50Ni40In10 alloys. Followed by the
rule of selectivity of atomic configuration in Heusler alloys as aforementioned, Co
substitution for Ni should just replace Ni at either A site or C site, and no new atomic
configuration is formed. By assuming that Co atoms replace the Ni atoms at A site, a
stronger local ferromagnetic structure of Mn(B)-Co-Mn(D) will be formed, shown in Fig.
12(a). Each Co atom at the site of Ni contributes a larger magnetic moment (~1.2 µB)
relative to Ni (0.13 µB), based on the calculation of magnetic moments in Mn2NiCoxGa1-x
CHAPTER 2 69
alloys [37]. This results in the further increment of the magnetization of the austenite due to
the magnetic moment contribution from Co.
Fig. 12. Atomic configurations in the unit cell of Co doped Mn50CoxNi40-xIn10 (x≥1): (a)
unit cell of the austenite and (b) unit cell of the martensite. The number of displaced
atoms does not represent the actual proportion of substitution, which is only for
qualitative interpretation.
4.2.4. Maximum magnetization of ferromagnetic austenite
It is evident in Fig. 6(b) that the magnetization of the ferromagnetic austenite
increased progressively with decreasing temperature. The temperature window for
ferromagnetic austenite is limited by two temperatures, the Curie temperature of the
austenite ( ACT ) as the upper boundary and the (reverse) martensitic transformation
temperature ( fA ) as the lower boundary. The maximum magnetization of the austenite
( AM ) is achieved at fA (upon heating), as seen on the M(T) curves (Fig. 6(b)) of these
alloys. It is also seen in Fig. 3 that the transformation temperatures decreased significantly
with increasing Co content. This means that the AM values were actually taken at different
CHAPTER 2 70
temperatures for these alloys and the increase of AM with increasing Co content, shown in
Fig. 7 is really due to the widening of the temperature window of the ferromagnetic
austenite, instead of purely due to the effect of alloying. The effect of alloying may be
estimated by measuring the magnetization of the alloys at a given temperature. As
aforementioned, the magnetization at 350 K increased from 52 emu/g for Co1 to 70 emu/g
for Co3. On the other hand, the maximum magnetization at fA increased from 55 emu/g
for Co1 to 118 emu/g for Co3, corresponding to the magnetization increase of 31.5 emu/g
per at.% of Co addition. It is evident that widening of the temperature window is the more
prominent factor relative to Co alloying contributing to the large ΔM in these alloys.
4.3 Transformation diagram
Fig. 13 shows the effect of e/a ratio, as a result of Co doping, on the martensitic
transformation temperatures Mp and Ap obtained from the DSC measurement and on the
Curie transition temperature ACT obtained from the magnetization measurements of the
Mn50Ni40-xIn10Cox alloys. It is seen that Mp and Ap decreased linearly with decreasing e/a
ratio and ACT increased. This observation is consistent with the general observation of
positive dependence of martensitic transformation temperatures on e/a ratio reported in the
literature for Ni-Mn-Z(Z=Ga,In,Sn,Sb) alloy systems [6, 7, 39]. The linear coefficient is
estimated to be 25 K per 0.01 change of e/a ratio, which is comparable to the value
determined for Ni50Mn40-xSn10Fex alloys [26].
CHAPTER 2 71
7.68 7.72 7.76 7.80 7.840
100
200
300
400
500
A
M (antiferro)Mp
A (ferro)
Co0
Co1
Co2
Tra
nsfo
rmat
ion
Tem
pera
ture
(K
)
e/a Ratio
Co3
A (para)
Ap
TA
C
Fig. 13. Effect of e/a ratio on Mp, Ap and ACT temperatures of Mn50Ni40-xIn10Cox alloys.
The temperature-e/a ratio space shown in Fig. 13 can be tentatively divided into
three regions representing different crystallographic and magnetic states for the alloys,
including austenite (paramagnetic), austenite (ferromagnetic) and martensite
(antiferromagnetic). Among the three states, two transformation schemes may occur. In the
region to the right of point A, the alloy undergoes a single step transformation between
paramagnetic austenite and antiferromagnetic martensite. This transformation is of low
interest for magnetic actuation. To the left of point A, the alloy undergoes the
transformation sequence from paramagnetic austenite to ferromagnetic austenite and then to
antiferromagnetic martensite upon cooling, expressed as
( ) ( ) ( )A para A ferro M antiferro . In this expression, the single arrow represents
magnetic transition and the double arrow represents the martensitic transformation (in this
case it is also a concurrent magnetic transition). The phase area of the ferromagnetic
austenite opens up with the decrease of e/a ratio, thus providing a wider temperature
window for ( ) ( )A ferro M antiferro transformation.
CHAPTER 2 72
5.Conclusions
The effects of Co substitution for Ni on the martensitic transformation and magnetic
behaviour of Mn50Ni40-xIn10Cox alloys were investigated. The experimental evidences and
the discussions lead to the following conclusions:
(1) Co substitution for Ni up to 3 at.% greatly decreases the martensitic
transformation temperature from 381 K to 175 K in these alloys. The martensite
has a non-modulated tetragonal structure, and the crystal structure of the austenite
is determined to be Hg2CuTi-type superlattice cubic structure.
(2) The decrease of the phase transformation temperatures is attributed to the
decrease of the e/a ratio for the alloys with increasing Co substitution for Ni. The
enthalpy and entropy changes of the transformation are both found to increase
with increasing the e/a ratio of the alloys.
(3) The maximum magnetization of the austenite (under 70 kOe) is significantly
increased from 15.5 emu/g in the Co0 alloy to 118 emu/g in the Co3 alloy,
whereas that of the martensite shows much less significant change from 12.5
emu/g in the Co0 alloy to 29 emu/g in the Co3 alloy. Consequently,
magnetization difference between the austenite and the martensite increases
significantly with increasing Co substitution for Ni. The largest ΔM for the
martensitic transformation obtained is 89 emu/g in alloy Co3.
(4) The increased magnetization of the austenite is attributed to three reasons: (i)
formation of ferromagnetic structure of Mn(B)-Ni-Mn(D) in off-stoichiometric
Mn2Ni1+xIn1-x, due to the readjustment of atomic configuration in the unit cell
caused by Ni substitution for In, (ii) higher magnetic moment contribution of Co
relative to Ni, and (iii) widening of the temperature window for ferromagnetic
austenite.
(5) The low magnetization of the martensite, relative to that of the austenite, is due to
the significantly shortened distance between Mn(B)-Mn(D), which leads to the
disappearance of the local ferromagnetic structure in a tetragonal martensitic
structure.
CHAPTER 2 73
Acknowledgements
The authors wish to acknowledge the financial supports by the Department of
Innovation Industry, Science and Research of the Australian Government in ISL Grant
CH070136, and by National Natural Science Foundation of China in Grant No. 51001010.
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CHAPTER 2 76
Paper 3
Martensitic and magnetic transformation behaviours in Mn50Ni42-xSn8Cox
polycrystalline alloys
Zhigang Wu 1, Zhuhong Liu 2, Hong Yang 1, Yinong Liu 1, Guangheng Wu 3
1 School of Mechanical and Chemical Engineering, The University of Western Australia,
Crawley, WA 6009, Australia
2 Department of Physics, University of Science and Technology Beijing, Beijing 100083,
China
3 Beijing National Laboratory for Condense Matter Physics, Institute of Physics, Chinese
Academy of Science, Beijing 100080, China
Abstract
This study investigated the effect of Co substitution for Ni in Mn50Ni42Sn8 alloy
with the aim to increase the magnetic driving force for inducing its martensitic
transformation. The martensitic transformation temperatures, enthalpy and entropy changes
are found to decrease progressively with increasing the Co content, while the
transformation hysteresis increased. Co substitution for Ni also significantly increased the
magnetization of the austenite, but with negligible effect on that of the martensite. A large
magnetization difference 109 emu/g was achieved across the transformation in a
Mn50Ni34Sn8Co8 alloy. The large magnetization difference between the two phases provides
enhanced thermodynamic driving force for the transformation. Consequently, the
martensitic transformation was induced by the application of a magnetic field in
Mn50Ni36Sn8Co6 and Mn50Ni34Sn8Co8 alloys. The effect of Co substitution for Ni on the
magnetic interaction among the constituents for the austenite and martensite was clarified
in this study, which provides a guide for alloy design for magnetoactuation applications.
CHAPTER 2 77
Keywords: A: magnetic intermetallics; B: alloy design; B: shape-memory effects; B:
martensitic transformations; B: magnetic properties.
1.Introduction
Magnetomartensitic transformations in certain alloys have attracted extensive
research interest in the past 15 years, since the discovery of giant magnetic-field-induced
strains (MFIS) of 5-10 % in near stoichiometric Ni-Mn-Ga alloys in 1996 [1-3]. The large
MFIS is associated with the rearrangement of martensite variants, driven by the
magnetocrystalline anisotropy of these variants. The magnetic driving force for this type of
actuation, which is derived from the magnetic anisotropy of the martensite variant, is
generally small, of the order of 300-400 kJ/m3 [4]. Given that the shape change is typically
6%, this yields a magnetically generated stress of 5-6 MPa. Such stress is barely enough to
overcome the mechanical resistance for martensite variant detwining [2, 4]. The low force
output has been proven to be a main limitation for the application of these materials for
mechanical actuation. An intrinsic solution to this problem is to increase the magnetic
driving power for the martensitic transformation. To increase power density, a new group
of off-stoichiometric Heusler Ni-Mn-Z(Z=In,Sn,Sb) alloys have been developed. These
alloys present concurrent martensitic and magnetic transformation, in which one phase (the
martensite) has much lower magnetization compared to the other (the austenite) [5]. In
Ni50Mn34In16 alloy, the magnetization difference between the two transforming phases is
around 70 emu/g, which gives rise to large magnetic power of 700 kJ/m3 at 1 Tesla field.
This large magnetization difference provides the necessary thermodynamic diving force,
thus the opportunity for obtaining a magnetic-field-induced reverse martensitic
transformation.
In the recent few years, much effort has been put into increasing the magnetic
driving force for martensitic transformation in Ni-Mn-Z(Z=In,Sn,Sb) alloys. This driving
force is the Zeeman Energy EZeeman=µ0MH, where µ0 is the permeability of a vacuum,
M is the saturation magnetization difference between the austenite and martensite and H
corresponds to the strength of the applied field. Co substitution for Ni has been found
CHAPTER 2 78
effective for increasing M between the phases in Ni-Mn-Z(Z=In,Sn,Sb) alloys, leading to
the successful field induced phase transformation in these alloys [6-10]. In these alloys, it is
known that the net magnetic moment mainly comes from the contribution of Mn [11], and
the magnetic moment distribution of Mn is very sensitive to interatomic distance. The
magnetic interaction between the Mn atoms can change from ferromagnetic to
antiferromagnetic alignment when the distance becomes below a critical value, which is
~0.3 nm [12]. With the objective of increasing M for the magnetic-field-induced
transformation, understanding of the magnetic moment contribution of Mn in off-
stoichiometric is essential.
In our previous study on Mn50Ni40-xIn10Cox alloys, we proposed an atomic
configuration model in which the mechanism of magnetic exchange interaction between
Mn-Mn and Mn-Co was explained. For better understanding of the properties of structural
and magnetic transitions in other Mn-rich Mn-Ni-based alloys, it is necessary to extend the
studies to a new series of Mn50Ni42-xSn8Cox alloys, with a focus on the effect of Co
substitution for Ni on the martensitic transformation and magnetic properties.
2.ExperimentalProcedures
Polycrystalline Mn50Ni42-xSn8Cox (x=0, 2, 4, 6 and 8) alloy ingots were prepared by
means of arc melting in argon atmosphere using high purity (99.99 %) elemental metals.
The samples are referred to as Co0, Co2, Co4, Co6 and Co8, respectively. The button
shaped ingots were heat treated at 1173 K for 24 hours in vacuum followed by quenching
into water for homogenization. Transformation behaviour of the alloys was studied by
means of differential scanning calorimetry (DSC) using a TA Q10 DSC instrument with a
cooling/heating rate of 10 K/min. Phase identification and crystal structures were
determined by means of X-ray powder diffraction using Cu-Kα radiation. Microstructures
of the samples were studied with optical microscopy and the compositions were determined
by means of X-ray energy dispersive spectrometry (EDS). The magnetic properties were
studied using a superconducting quantum interference device magnetometer (SQUID).
CHAPTER 2 79
3.Resultsanddiscussion
3.1 Crystal structure
Figure 1 shows XRD spectra of Mn50Ni42-xSn8Cox alloys at room temperature. It is
seen that from Co0 through to Co6, the alloys show nearly identical diffraction patterns of
the martensite with a non-modulated body centered tetragonal structure. The lattice
parameters of the martensite are determined to be a=b=0.545 nm, and c=0.697 nm. Alloy
Co8 shows a single phase structure with bcc fundamental lattice reflections of (220), (400)
and (422) and superlattice reflections of (111), (200) and (311). The superlattice structure
can be determined by comparing the relative intensities of (111) and (200) [13]. It is
evident that I111/I200>1, implying that the superlattice is of the Hg2CuTi-type, shown in the
inset of Figure 1(e). This observation is consistent with those observed in Mn2NiZ (Z=In,
Sn and Sb) alloys [14, 15] and Mn50Ni37In10Co3 alloy [16]. In this structure, one Mn
sublattice occupies A (0, 0, 0) site (referred to as Mn(A)), the other Mn sublattice is at B
site (0.25, 0.25, 0.25) (referred to as Mn(B)), Ni atoms occupy C site (0.5, 0.5, 0.5) and Z
atoms occupy D site (0.75, 0.75, 0.75). Such structure can be expressed in a stacking order
of MnMnNiX ( 43F m space group) along the diagonal [111] direction of the cubic unit
cell. The lattice parameter of the austenite in Co8 is determined to be a=0.602 nm.
CHAPTER 2 80
20 30 40 50 60 70 80 90
Co0(a)
2 (o)
(022
) M
(004
) M
(400
) M
(224
) M
(422
) M
X-r
ay I
nten
sity
Co2
(b)
Co4(c)
Co6
(d)
Co8(e) (2
20) A
(311
) A
(400
) A
(422
) A
Figure 1. X-ray powder diffraction spectra of the Mn50Ni42-xSn8Cox alloys. Inset of (e)
shows the comparison between the relative intensities of (111) and (200) reflections.
3.2 Microstructure and alloy composition
Figure 2 shows optical micrographs of the microstructures of Co6 and Co8 alloys
after homogenization treatment. Both alloys have a single phase throughout the matrix.
Alloy Co6 presents evident martensite plates, indicating the martensite state at room
temperature. Co8 shows a few martensite plates in the austenite matrix, which may be due
to the occurrence of partially stress-induced martensitic transformation. Cracks are visible
along the columned grain boundaries for both alloys, indicating the brittleness of these
materials.
24 26 28 30 32
(200
)
(111
)
CHAPTER 2 81
Figure 2. Optical micrographs for (a) alloy Co6 and (b) alloy Co8.
The composition of these alloys was determined by quantitative EDS analysis. The
results are summarized in Table 1. For all the alloys, the Mn contents are approximately 49
at.%, indicating that the volatilization loss of Mn is ~1 at.% during the arc-melting process.
The continuous reduction of Ni is compensated well by the addition of Co. The Sn content
remained nearly unchanged, at between 8.6 at.% and 8.9 at.%. The valence electron
concentration per atom (e/a ratio) was calculated using the compositions obtained from the
EDS analysis with the sum of s, p and d electrons for Mn (7), Ni (10), Co (9) and Sn (4). It
is seen that the e/a ratio decreased from 8.011 to 7.925 with increasing Co substitution for
Ni from 0 to 8 at.%, obviously due to the smaller number of valence electrons of Co (9)
relative to that of Ni (10).
Table 1. Composition and e/a ratio of the Mn50Ni42-xSn8Cox alloys.
Mn (at%) Co (at%) Ni (at%) Sn (at%) e/a
x=0 49.1 - 42.3 8.6 8.011
x=2 48.8 2.1 40.3 8.8 7.987
x=4 48.6 4.1 38.4 8.9 7.967
x=6 48.6 6.1 36.6 8.7 7.959
x=8 49.1 8.0 34.2 8.7 7.925
CHAPTER 2 82
3.3 Martensitic transformation
Figure 3 shows DSC curves of the Mn50Ni42-xSn8Cox alloys. It is seen that the
martensitic transformation behaviour evolves progressively with increasing the Co addition.
200 240 280 320 360 400 440 480
1 J/
gCo8
Co6
Co4
Co2
Hea
t Flo
w
Temperature (K)
Co0
Figure 3. DSC curves of the Mn50Ni42-xSn8Cox alloys.
Both the transformation temperatures and the enthalpy change decreased. The
transformation temperatures (TM: the forward transformation peak temperature, TA: the
reverse transformation peak temperature and 1
( )2o M AT T T ), transformation hysteresis
(ΔT=TA-TM), enthalpy change (H) and entropy change (S) of the alloys are summarized
in Table 2. The H values were determined directly from the DSC measurements, and S is
estimated based on o
HS
T
.
Table 2. Thermal and thermodynamic parameters of the martensitic transformation of the
Mn50Ni42-xSn8Cox alloys.
TM (K) TA (K) To (K) ΔT (K) ΔH (J/g) ΔS (J/Kkg)
CHAPTER 2 83
x=0 377 391 384 14 16.23 42.27
x=2 369 383 376 14 15.84 42.13
x=4 362 375 369 13 14.30 38.75
x=6 330 348 339 18 11.21 33.07
x=8 278 304 291 26 4.69 16.12
Figure 4 shows the effect of e/a ratio on phase transformation temperatures (TM, TA
and To) and hysteresis (ΔT) of the alloys. It is seen that TM and TA increased with increasing
e/a ratio (decreasing Co content). This is consistent with the general trend of positive
dependence of martensitic transformation temperatures on e/a ratio observed in Ni-Mn-
Z(Z=Ga, In, Sn and Sb) alloys [17]. It appears that there are two linear dependences of the
transformation temperatures on e/a ratio. At below e/a=7.967, corresponding to 4 at.% of
Co, the linear coefficient is 18 K per 0.01 e/a unit for To. At above e/a=7.967, the
coefficient is 3.5 K per 0.01 e/a unit. Similarly, ΔT also shows two distinct dependences on
e/a ratio. It increases with more Co content at below 7.967 and remains independent of e/a
ratio at above.
CHAPTER 2 84
7.92 7.94 7.96 7.98 8.00 8.02260
280
300
320
340
360
380
400
To
TM
TA
e/a Ratio
Tra
nsfo
rmat
ion
Tem
pera
ture
(K
)
T
increasing Co centent10
12
14
16
18
20
22
24
26
28T
ransformation H
ysteresis (K)
Figure 4. Effect of Co addition on phase transformation temperatures and hysteresis
expressed as functions of e/a ratio.
Figure 5 shows the effects of Co addition on the transformation enthalpy and
entropy changes of the alloys, shown as functions of transformation temperature To in (a)
and of e/a ratio in (b). It is seen that both the enthalpy and entropy changes increased
continuously with increasing To and with e/a ratio, caused by Co addition. The influence of
e/a ratio on the entropy change of martensitic transformation has been reported for
Ni50+xMn25-xGa [18, 19], Ni50Mn50-xInx [20], and Ni50Mn50-xSnx [21] alloys. In these alloy
systems, ΔS increases with increasing transformation temperatures and e/a ratio, which is in
good agreement with the findings in the present study. The change of ΔS is mainly
attributed to the change of the magnetic component of the total ΔS caused by increasing the
Co addition. With increasing the Co content, the magnetic entropy change increases in the
alloys. This argument is supported by the evidence that the magnetization of the austenite
increases while that of the martensite remains unchanged with increasing the Co content in
the alloys, as shown in Figure 7(b). For the forward transformation, ΔSA-M, the (positive)
increase of magnetic entropy change reduces the (negative) lattice entropy change, thus
resulting in the decrease of the total (negative) ΔS for these alloys.
CHAPTER 2 85
280 300 320 340 360 380 4000
2
4
6
8
10
12
14
16
18
To (K)
Ent
alpy
Cha
nge
(J/g
) H
S
increasing Co content
a
12
16
20
24
28
32
36
40
44
48
Entropy C
hange (J/K-kg)
7.92 7.94 7.96 7.98 8.00 8.020
2
4
6
8
10
12
14
16
18
e/a Ratio
Ent
alpy
Cha
nge
(J/g
)
H
S
b
increasing Co content12
16
20
24
28
32
36
40
44
48
Entropy C
hange (J/K-kg)
Figure 5. Effect of Co addition on enthalpy and entropy changes of the Mn50Ni42-xSn8Cox
alloys, (a) as function of transformation To=(TM+TA)/2, and (b) as function of e/a ratio.
3.4 Thermomagnetization
Figure 6 shows the magnetization of the alloys during a heating-cooling cycle
between 200 and 395 K in a field of 50 Oe (Figure 6(a)) and 70 kOe in (Figure 6(b)). The
sample was first cooled down to 200 K in a zero magnetic field prior to the measurement. A
magnetic field was applied at 200 K and then the sample was heated at a rate of 10 K/min
up to 395 K and cooled back again to 200 K in the same field.
CHAPTER 2 86
200 250 300 350 400
0.00
0.05
0.10
0.15
0.20
0.25
350 360 370 380 3900.00000.00010.00020.00030.00040.00050.0006
Co8
Co6
Mag
netiz
atio
n (e
mu/
g)
Temperature (K)
Co4
H=50 Oe
a
Magnetization (em
u/g)
Temperature (K)
Co2
Co0
200 250 300 350 4000
20
40
60
80
100
120
Co8
Co6
Co4
Co2
Mag
neti
zatio
n (e
mu/
g)
Temperature (K)
Co0
H=70 kOeb
M=
109
emu/
g
Figure 6. Thermomagnetization curves in a magnetic field of (a) H=50 Oe and (b) H=70
kOe for Mn50Ni42-xSn8Cox.
At a low field of 50 Oe, as shown in Figure 6(a), alloys Co4, Co6 and Co8 undergo
a structural transformation between a ferromagnetic austenite and a ferrimagnetic
martensite with obvious transformation hysteresis between the heating and cooling curves.
For Co4, the magnetization drop of the austenite upon heating to ~380 K is due to the Curie
transition of the austenite, denoted as 380ACT K . The Curie transition was not observed in
Co6 and Co8 within the testing temperature range, suggesting higher Curie transition
CHAPTER 2 87
temperatures at above 400 K for these two alloys. In the inset of Figure 6(a), alloys Co2
and Co4 present similar martensitic transformation, but with much smaller magnitude of
magnetizations of the austenite compared to those of Co4, Co6 and Co8. The Curie
temperatures of the austenite of Co0 and Co2 alloys seem close to 400 K, which are higher
than that of Co4. Normally, with more Co substitution for Ni, the Curie temperature is
expected to increase, due to the stronger exchange interaction between Co-Mn than that
between Ni-Mn [22]. The anomaly of ACT in these alloys is not clear at this stage.
It is evident that the martensitic transformation temperature decreased with
increasing Co content in these alloys, consistent with the observation from DSC
measurement (Figure 3). The Curie temperatures of these alloys are obviously higher than
those in Ni2Mn1+xSn1-x [21, 23, 24] alloys, which are around 320 K. It has been reported
that CT is 588 K in Mn2NiGa alloy [25], suggesting the generally higher CT in Mn-rich
Mn2NiZ alloys relative to Ni-rich Ni2MnZ alloys. It is also worth noting that the
transformation hysteresis is around 40 K for Co8, which is much larger than the value
determined from DSC measurement (26 K). The large hysteresis usually means higher
frictional resistance to the propagation of the transformation interfaces. This may lead to
large difficulty for two-way magnetic-field-induced martensitic transformation in Co8
alloy.
Figure 6(b) shows the thermomagnetization behavior of the five alloys between 200
and 395 K at a field of 70 kOe. The martensitic transformation temperatures were lowered
under the influence of the higher magnetic field. For alloy Co8, the transformation
temperatures are * 255 KMT and * 285 KAT at 70 kOe, which are approximately 30 K
lower than those at 50 Oe.
Figure 7 shows magnetization of the austenite at the martensitic transformation
starting temperature Ms (s
AMM ), magnetization of the martensite at the martensitic
transformation finishing temperature Mf (f
MMM ), magnetization difference across the
transformation (s f
A MM MM M M ), at 70 kOe as functions of Co content in the alloys. It is
CHAPTER 2 88
seen that s
AMM increased rapidly from 13 emu/g in Co0 to 117 emu/g in Co8, while
f
MMM remained almost constant (~5 emu/g), thus resulting in an increasing M across the
martensitic transformation with increasing the Co content. The maximum M is 109 emu/g
in alloy Co8.
0 2 4 6 80
20
40
60
80
100
120
Mag
netiz
atio
n (e
mu/
g)
Co Content (at %)
Figure 7. The magnetization of the austenite at Ms (s
AMM ), the magnetization of the
martensite at Mf (f
MMM ), and the magnetization difference across the martensitic
transformation (s f
A MM MM M M ) at a field of 70 kOe as functions of Co content in
Mn50Ni42-xSn8Cox.
3.5 Magnetic coupling
Figure 8 shows the atomic configuration in the unit cell of Mn50Ni42-xSn8Cox alloys.
Illustration (a) represents the unit cell of the austenite with Mn-Mn-Ni-Sn stacking order
(Hg2CuTi-type structure) and illustration (b) represents the unit cell of the martensite with
Mn-Mn-Ni-Sn tetragonal structure.
s
AMM
M
f
AMM
CHAPTER 2 89
Figure 8. Atomic configuration in the unit cell of Mn50Ni42-xSn8Cox alloys: (a) unit cell of
the austenite with Mn-Mn-Ni-Sn stacking order (Hg2CuTi structure) and (b) unit cell of
the martensite with Mn-Mn-Ni-Sn tetragonal structure.
For Mn2YZ (Y: 3d elements; Z: III-V A group elements) compounds, it has been
observed that Y elements with more valence electrons prefer to occupy A and C sites,
whereas Y elements with fewer valence electrons have preference for B site occupancy
[26]. For the Mn50Ni42-xSn8Cox alloys, Co substitutes Ni at C site, and the excess Ni atoms
prefer to occupy A sites, displacing Mn(A) to Mn(D) site, as illustrated in Figure 8(a).
Based on this rule, the atomic occupation for Mn50Ni42-xSn8Cox alloys can be written as
[Mn(A)Ni(A)]25Mn(B)25[Co(C)Ni(C)]25[Sn(D)Mn(D)]25.
In the austenite (Figure 8(a)), the Mn(A) and Mn (B) are the nearest neighbors with
a distance of 0.26 nm ( 3 / 4a ) in between. The nearest distance between Mn(B) and
Mn(D) atoms is 0.301 nm (a/2). It has been found that the magnetic interaction between Mn
atoms changes from ferromagnetic to antiferromagnetic alignment when the Mn-Mn
CHAPTER 2 90
distance reduces to below a critical value of approximately 0.30 nm [12]. Therefore,
Mn(A)-Mn(B) is expected to form antiferromagnetic alignment, whereas Mn(B)-Mn(D)
forms ferromagnetic alignment in the austenite. After the replacement of Mn(A) by Ni(A),
there will be a significant increase of the net magnetic moment for the austenite, which is
due to the reduction of the antiferromagnetic Mn(A)-Mn(B) coupling and the formation of
the ferromagnetic Mn(B)-Mn(D) coupling. Co substitution for Ni at C site also provides
magnetic moment contribution to some extent due to its larger magnetic moment (~1 µB)
relative to that of Ni (~0.3 µB).
The significant increase of s
AMM can also be attributed to the enlarged temperature
window for the ferromagnetic austenite to develop, caused by Co addition. The s
AMM is
measured at sM (upon cooling), as seen on the M-T curves (Figure 6(b)) of these alloys. It
is also seen in Figure 3 that the transformation temperatures decreased significantly with
increasing Co content. This means that the s
AMM values were actually taken at different
temperatures for these alloys. Therefore, the increase of s
AMM with increasing Co content is
largely due to the widening of the temperature window of the ferromagnetic austenite, in
addition to the effect of Co alloying as aforementioned.
Upon the martensitic transformation, the crystallographic transformation changes
the crystal lattice in the unit cell, consequently altering the exchange coupling of the
magnetic atoms. Upon transforming form the cubic austenite (Figure 8(a)) to the tetragonal
martensite (Figure 8(b)), a and b axes shrink by 9.5% and c axis elongates by 15.7%.
Through the transformation, the nearest distance between Mn(B)-Mn(D) decreases from
0.301 nm (a/2, parent phase) to 0.273 nm (a/2, martensite phase) which is below the critical
distance for ferromagnetic coupling. This leads to the moments of Mn(B) and Mn(D) to
change from in parallel alignment in the austenite to antiparrallel alignment in the
martensite. The distance between Mn(A)-Mn(B) changed from 0.261 nm ( 3 / 4a ) in the
austenite to 0.260 nm in the martensite, which causes no change to the magnetic alignment
between Mn(B) and Mn(D). Exchange interaction between Mn(A) and Mn(B) is still
CHAPTER 2 91
antiparrallel alignment. Therefore, the magnetic coupling of the martensite is expected to be
ferrimagnetic.
3.6 Magnetic‐field‐induced martensitic transformation
The magnetic driving force for a magnetic-field-induced martensitic phase
transformation arises from the Zeeman Energy EZeeman=µ0MH. The M for the present
Mn50Ni42-xSn8Cox alloys has been significantly increased by substituting Co for Ni. To
verify this increased M in regards to benefiting the field induced martensitic
transformation, alloys Co6 and Co8 were magnetized isothermally at different
temperatures, as shown in Figure 9.
0 10 20 30 40 50 60 700
10
20
30
40
50
60
70
80
340 K
335 K
390 K
Mag
netiz
atio
n (e
mu/
g)
Magnetic Field (kOe)
5 K
a
CHAPTER 2 92
0 10 20 30 40 50 60 70
0102030405060708090
100110b
290 K
280 K
390 K
5 K
Mag
netiz
atio
n (e
mu/
g)
Magnetic Field (kOe)
Figure 9. Isothermal magnetization behaviours of (a) alloy Co6 and (b) alloy Co8 at
different temperatures.
Figure 9(a) shows the magnetization behaviour of alloy Co6. At 5 K, the martensite
shows low magnetization of 11 emu/g (at 70 kOe). At 390 K, the austenite shows a typical
soft ferromagnetic behaviour, with a saturation magnetization of 68 emu/g. At 335 K, the
martensite shows a very low saturation magnetization (~2 emu/g) at below 20 kOe. Upon
increasing the magnetic field to above 50 kOe, the magnetization increased rapidly,
signifying the phase transformation from the martensite to the austenite. The maximum
magnetization reached is 30 emu/g at 70 kOe. This magnetization is much lower than the
saturation magnetization of the austenite (~70 emu/g). This is obviously due to the fact that
the transformation is incomplete at 335 K. At 340 K (8 K below TA), the martensite starts to
transform to the austenite at 30 kOe and saturates at 72 emu/g at 7 T, indicating the
completion of the reverse transformation. Upon removal of the external magnetic field, the
magnetization decreases slowly at above 30 kOe, and then quickly drops to 20 emu/g,
indicating the occurrence of the forward martensitic transformation.
Figure 9(b) shows the magnetization behaviour of alloy Co8. The magnetization
behaviours of the martensite at 5 K and the austenite at 390 K are similar to those of Co6.
At 280 K, the martensite starts to transform to austenite at the field of 30 kOe upon
magnetizing. The magnetization maximized at 75 emu/g at 70 kOe, indicating the
CHAPTER 2 93
incomplete magnetic-field-induced transformation. At 290 K (14 K below TA), the
martensite starts to transform to the austenite at 10 kOe and saturates at ~100 emu/g at 70
kOe, indicating the completion of the reverse transformation. Upon removal of the external
magnetic field, the austenite remained saturated and did not transform back to the
martensite. This is due to the large transformation hysteresis in Co8. The testing
temperature of 290 K is well above the forward transformation temperature (TM=278 K),
thus resulting in the retained austenite after demagnetization. It is worth nothing that the
complete field-induced transformation can be achieved at lower temperature below TA in
Co8 (14 K below TA) than that in Co6 (8 K below TA), which is due to the larger ΔM across
the transformation of Co8 relative to that of Co6. This indicates that the magnetic driving
force is increased with increasing the Co content in Mn50Ni42-xSn8Cox alloys in a certain
field, thus easier for obtaining a field-induced transformation.
4.Conclusions
In this study, the effects of Co substitution for Ni on the martensitic transformation
and magnetic behaviour of Mn50Ni42-xSn8Cox alloys were investigated. The experimental
evidences and the discussions lead to the following conclusions:
(1) The Mn50Ni42-xSn8Cox alloys exhibit a martensitic transformation from an
Hg2CuTi-type austenite to a non-modulated tetragonal martensite. The martensitic
transformation temperatures were found to decrease significantly with increasing
Co substitution for Ni, due to the decreasing e/a ratio in the alloys. The enthalpy
and entropy changes of the transformation are both found to decrease with
increasing Co addition.
(2) The magnetization of the austenite is significantly increased from 13 emu/g in the
Co0 alloy to 117 emu/g in the Co8 alloy, whereas that of the martensite remains
unchanged at ~5 emu/g. Consequently, magnetization difference between the
austenite and the martensite increases significantly with increasing Co
substitution for Ni. The largest ΔM for the martensitic transformation obtained is
109 emu/g in alloy Co8.
CHAPTER 2 94
(3) The increased magnetization of the austenite is attributed to two reasons: (i)
higher magnetic moment contribution of Co relative to Ni, and (ii) widening of
the temperature window for ferromagnetic austenite to magnetize.
(4) The low magnetization of the martensite is due to the significantly shortened
distance between Mn(B)-Mn(D), which leads to the antiparallel alignment of the
magnetic moments of neighbouring Mn atoms in the tetragonal martensitic
structure.
(5) The magnetic-field-induced martensitic transformation from ferrimagnetic
martensite to ferromagnetic austenite was successfully induced in alloys Co6 and
Co8 under a field within the range of 30~70 kOe.
Acknowledgements
The authors wish to acknowledge the financial supports by the Department of
Innovation Industry, Science and Research of the Australian Government in ISL Grant
CH070136, and by National Natural Science Foundation of China in Grant No. 51001010.
CHAPTER 2 95
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CHAPTER 3 97
CHAPTER 3. Increasing ductility of Ni-
Mn-based alloys
________________________________________________________________________________
Paper 4
Effect of Fe addition on the martensitic transformation behaviour,
magnetic properties and mechanical performance of Ni50Mn38-xIn12Fex
polycrystalline alloys
Zhigang Wu1, Zhuhong Liu2, Hong Yang1 and Yinong Liu1
1 School of Mechanical and Chemical Engineering, The University of Western Australia,
Crawley, WA 6009, Australia
2 Department of Physics, University of Science and Technology Beijing, Beijing 100083,
China
Abstract
CHAPTER 3 98
This study investigated the effect of Fe substitution for Mn on the transformation,
magnetic and mechanical behaviours of Ni50Mn38-xIn12Fex (x=0, 3, 4, 5, 6) alloys. These
alloys show a martensitic transformation from a B2 austenite to an orthorhombic martensite
at above the room temperature. Substitution of Fe for Mn at above 3 at.% introduced a fcc γ
phase in the microstructure, the amount of which increased with increasing the Fe addition.
The formation of γ phase influenced the composition of the matrix phase, particularly the
Mn and In contents, leading to a series of changes in alloy properties. The e/a ratio of the
matrix phase decreased rapidly with increasing Fe addition, resulting in the decrease of
martensitic transformation temperature and enthalpy change. Fe addition also effectively
weakens the antiferromagnetic ordering of the austenite in the matrix phase, leading to the
increase of magnetisation difference across the martensitic transformation. The
compressive strength and ductility appear to optimise at 4~5 at.% Fe addition, reaching 770
MPa and 14.3 %, respectively. The relative shape memory effect decreased from 94 % to
37 % after 4 at.% Fe addition.
Keywords: Shape memory alloy; martensitic transformation; magnetic properties;
intermetallics
1. Introduction
Ferromagnetic shape memory alloys Ni-Mn-Z (Z=In, Sn, Sb) have been widely
investigated in the past few years as potential candidates for magnetic actuation. The large
difference in magnetic state between the austenite and martensite produces high magnetic
driving force for magnetic-field-induced martensitic transformation [1]. Substitution of Ni
by Co is found to increase the magnetic ordering of the austenite and to decrease that of the
martensite, further increasing the magnetisation difference of the martensitic
transformation in Ni-Mn-Z (Z=Ga, Al, In, Sn, Sn, Sb) alloys [2-8]. As a result, >1% strain
has been realised in Ni45Co5Mn36.7In13.3 and Ni43Co7Mn39Sn11 alloys [2, 3], demonstrating
the promise of the alloys for actuation applications in smart systems.
Unfortunately, the intrinsic brittleness of these intermetallic compounds severely
hinders their engineering application. To date, it has not been possible to process
polycrystalline Ni-Mn-Z (Z=In, Sn, Sb) ferromagnetic shape memory alloys using
CHAPTER 3 99
conventional methods. It is known that the introduction of a ductile second phase is helpful
in improving the ductility of the alloys, as initially discovered in Ni-Fe-Ga [9], Co-Ni-Ga
[10] and Co-Ni-Al [11] alloys. Later, adding Fe and Co was found to form a ductile phase
in Ni-Mn-Z (Z=Ga, In, Sn) [12-17], accordingly increasing the ductility of these alloys.
Apart from the improved ductility, addition of a fourth element to the ternary Ni-
Mn-Z (Z=Ga, In, Sn, Sb) alloys alters the matrix composition, which causes a number of
changes in the structure, thermal and magnetic properties. The effect of Fe substitution for
Mn in Ni-Mn-Sn alloys has been found to decrease the martensitic transformation
temperatures and increase the Curie transition temperatures of both the austenite and the
martensite [18, 19]. In our previous study on Ni50Mn40-xSn10Fex alloys, Fe substitution for
Mn changed the composition of the matrix phase in addition to forming the phase [20]. It
is revealed that changes in Mn and Sn contents in the matrix phase are the actual reasons
for the property changes. This study investigated the effects of the formation of the phase
caused by Fe substitution for Mn in Ni50Mn38-xIn12Fex. The addition of Fe is expected to
alter the composition of the matrix phase, thus affecting the magnetic state and valence
electron number of the alloys. Besides concerning on changes of the physical properties
influenced by the phase, mechanical performance and shape memory effect were also
investigated in Ni50Mn38-xIn12Fex alloys.
2. Experimental procedures
Bulk ingots of polycrystalline Ni50Mn38-xIn12Fex (x=0, 3, 4, 5, 6) alloys were
prepared by means of arc melting in argon atmosphere using high purity Ni (99.99 at.%),
Mn (99.99 at.%), In (99.99 at.%) and Fe (99.95 at.%). The samples are referred to as Fe0,
Fe3, Fe4, Fe5 and Fe6, based on the atomic percentage of Fe addition in the alloys. The
button shaped ingots were heat treated at 1173 K in vacuum for homogenisation followed
by furnace cooling to room temperature. Transformation behaviour of the alloys was
studied by means of differential scanning calorimetry (DSC) using a TA Q10 DSC
instrument with a cooling/heating rate of 10 K/min. Phase identification and crystal
structures were determined by means of X-ray powder diffraction using a Siemens D5000
instrument with Cu-Kα radiation and transmission electron microscopy (TEM) using a Jeol
CHAPTER 3 100
2100 instrument. Microstructures of the samples were studied with TEM and scanning
electron microscopy (SEM) using a Zeiss 1555 instrument. The compositions were
determined by means of X-ray energy dispersive spectrometry (EDS) equipped on SEM.
Magnetic properties were studied using a superconducting quantum interference device
magnetometer (SQUID).
3. Results and discussion
3.1 Microstructure and alloy composition
Figure 1 shows back-scattered electron (BSE) micrographs of the microstructures of
the Ni50Mn38-xIn12Fex (x=0, 3, 4, 5, 6) alloys after homogenisation treatment.
(a) (b)
(c)
grain boundaries
(c)
grain boundaries
CHAPTER 3 101
(e)
Figure 1. Back-scattered electron images of the Ni50Mn38-xIn12Fex alloys: (a) Fe0, (b) Fe3, (c) Fe4, (d) Fe5, and (e) Fe6 alloys.
The BSE microstructures of the alloys were examined without etching. The Fe0 and
Fe3 samples (micrograph (a) and (b)) showed uniform single phase structure, without sign
of a second phase. The black spots are solidification shrinkage pores formed during ingot
casting. The Fe4, Fe5 and Fe6 samples showed a continuous matrix in light contrast and
dispersed γ phase particles in dark contrast. The volume fraction of the γ phase increased
with increasing Fe addition. It is also seen that the γ phase particles tend to form along the
grain boundaries in Fe4 and Fe5 alloys, as shown in micrograph (c) and (d). The alloy Fe6
showed distinctive texture of the γ phase compared to Fe4 and Fe5, with straight and
elongated γ phase grains.
Table 1 shows compositions of the phases in the samples as determined by
quantitative EDS analysis. It is seen that the matrix phase of the Fe-doped alloys contained
about 49 at.% Ni. The content of Mn decreased continuously from 37.8 to 32.5 % with
increasing Fe addition from 2.9 to 3.8 % in the matrix. The content of In was also found to
increase from 12.8 to 14.8 %. The γ phase is effectively a Ni-Mn-Fe alloy containing a
small amount of In (~1.1 at.%). The volume fraction of the γ phase is determined by image
analysis from the SEM micrographs using Image J.
Table 1. Composition, e/a ratio and γ proportion of Ni50Mn38-xIn12Fex (x=0, 3, 4, 5, 6)
alloys.
CHAPTER 3 102
Matrix (at.%) The γ phase (at.%)
Ni Mn In Fe e/a
ratio
Ni Mn In Fe γ (%)
X=0 49.4 37.8 12.8 - 7.970 - - - - -
X=3 48.6 35.3 13.2 2.9 7.962 - - - - -
X=4 49.1 34.0 13.7 3.2 7.958 54.5 31.1 1.1 13.3 6.8
X=5 49.1 33.0 14.4 3.5 7.936 54.0 30.9 1.1 14.0 11.5
X=6 48.9 32.5 14.8 3.8 7.913 52.5 30.2 1.1 16.2 14.0
The increase of In content in the matrix phase is apparently related to the increase of
the fraction of γ phase, which contains very little In. The valence electron concentrations
per atom (e/a ratio) of the matrix phase was calculated using the compositions obtained
from EDS analysis from the sum of s, p and d electrons for Mn (7), Ni (10), Fe (8) and In
(3). It is obvious that the e/a ratio decreases with increasing In and decreasing Mn contents
of the alloys.Figure 2 shows the effect of Fe addition on the matrix phase composition
(graph (a)) and the e/a ratio (graph (b)) of the alloys. With increasing Fe addition, both Fe
and In contents in the matrix phase increased, and the Mn content decreased. The e/a ratio
of the alloy decreased continuously with increasing Fe addition in the alloys, shown in
graph (b). The decrease of the e/a ratio is obviously related to the composition change in
the matrix phase caused by the formation of the phase. More specifically, the decrease of
Mn (7 valence electrons) and increase of In (3 valence electrons) contents are the main
reasons for the decrease of the e/a ratio, though Fe (8 valence electrons) content slightly
increased as well in the matrix phase. It is worth noting that there are two different negative
dependencies of the e/a ratio on Fe addition, which are 0.003 per at.% for Fe≤4 and 0.023
for 4≤Fe≤6. This indicates that the e/a ratio of the matrix phase decreased more rapidly
when Fe addition is above 4 at.% in the alloys.
CHAPTER 3 103
0 1 2 3 4 5 6
12
16
20
24
28
32
36
40
Fe
In
Fe Addition (at.%)
In, M
n C
on
ten
t (a
t.%
)
Mn(a)
0
1
2
3
4
5
Fe
Conten
t (at.%)
0 1 2 3 4 5 6
7.91
7.92
7.93
7.94
7.95
7.96
7.97
e/a
Ra
tio o
f Mat
rix
Ph
ase
Fe Addition (at. %)
(b)
transformationdisappears
Figure 2. Effects of Fe addition on (a) element concentrations and (b) e/a ratio of the matrix
phase of the Ni50Mn38-xIn12Fex alloys.
3.2 Martensitic transformation behaviour
Figure 3 presents DSC curves of the Ni50Mn38-xIn12Fex alloys. It is seen that the
martensitic transformation behaviour evolved progressively with increasing Fe addition in
these alloys.
CHAPTER 3 104
100 150 200 250 300 350 400 450 500 550
TA
Fe6
Fe5
Fe4
Fe3
He
at F
low
Temperature (K)
Fe0
0.2
w/g
TM
Figure 3. DSC measurements of martensitic transformation behaviour of the Ni50Mn38-
xIn12Fex alloys.
The martensitic transformation is clearly observed for Fe0, Fe3 and Fe4 alloys, and
the transformation temperatures decreased with increasing Fe addition in these alloys.
However, no transformation was detected in Fe5 and Fe6.
Figure 4 shows the effect of e/a ratio on transformation temperature To and
transformation enthalpy change ΔH. To is defined as To=1/2(TM+TA), where TM and TA are
the peak temperatures of the forward and the reverse transformations, and ΔH is obtained
from the forward transformation. It is seen that the transformation temperatures of Fe0, Fe3
and Fe4 increased practically linearly with increasing the e/a ratio of the alloys. This
observation is consistent with the findings of the effect of e/a ratio on transformation
temperatures in Ni-Mn-Z (Al, Ga, In, Sn and Sb) alloys [21-23]. It is also evident that the
ΔH increased with increasing e/a ratio of the matrix.
CHAPTER 3 105
7.945 7.950 7.955 7.960 7.965 7.970
280
320
360
400
440
Fe4
Fe3
e/a Ratio
To
(K)
Fe0
To
H
0
2
4
6
8
10
12
14
16
H
(J/g)
Figure 4. Effects of Fe addition on transformation temperature To=(TM+TA)/2 and
transformation enthalpy change ΔH. The arrow pointing to the e/a ratio axis indicates the
threshold e/a ratio value below which the martensitic transformation is expected to vanish.
Extending ΔH curve to zero tentatively defines the threshold value of e/a ratio
below which the martensitic transformation is expected to vanish. The threshold value, as
indicated by the arrow in Figure 4, is estimated to be e/a = 7.948. The e/a ratio value
corresponds to an Fe addition of 4.5 at.% estimated from Figure 2 (b). For Fe addition of
more than 4.5 at.% in the system, no martensitic transformation is expected. This explains
the disappearance of martensitic transformation in Fe5 and Fe6.
3.3 Crystal structure
Figure 5 shows the crystal structures of the Ni50Mn38-xIn12Fex alloys examined by
X-ray diffraction at room temperature. The non-modulated orthorhombic martensite
structure can be observed in Fe0, Fe3 and Fe4 alloys. The observation of martensitic phase
is consistent with the results obtained from DSC (Figure 3), which indicate the martensitic
state at room temperature of these alloys. Apart from the martensite structure, diffraction
peaks of the fcc phase can also be identified in the spectrum of Fe4 alloy, which is
consistent with its microstructure (Figure 1 (c)). Alloy Fe5 exhibits a more complicated
case, showing a mixed structure of the orthorhombic martensite, the bcc austenite and the
CHAPTER 3 106
fcc γ phase. Alloy Fe6 presents a two-phase structure, with the bcc austenite and the fcc γ
phase.
20 30 40 50 60 70 80 90 100
Fe6
Fe5
Fe4
Fe3
X-r
ay
Inte
nsi
ty
2 (o)
A M
Fe0
Figure 5. X-ray spectra of the crystal structure of the Ni50Mn38-xIn12Fex alloys at room
temperature. The phases are identified with labeled symbols: (○) represents phase, A
(▼) represents the austenite phase and M (■) represents the martensite phase.
The lattice parameters of the γ phase in Fe4, Fe5 and Fe6 are very close, with an
average value of a=0.366 nm at room temperature. The lattice parameter of the bcc
austenite is determined to be a=0.2991 nm for Fe5 and Fe6 alloys. The lattice parameter of
the orthorhombic martensite is determined to be a=0.6535 nm, b=0.5928 nm, c=0.5701 nm
for Fe0, Fe3 and Fe4 alloys. Figure 6 shows TEM observation of the microstructure and
crystal structure of Fe4 and Fe5 alloys at room temperature. Micrograph (a) shows a bright
field image of Fe4. Two phases are present in the microstructure, which are the matrix
phase in dark contrast and the phase in light contrast. Selected area diffraction pattern
(SADP) from area A of the matrix phase is shown in Figure 6(b), which can be indexed to
B2 structure along its [001] zone axis. Presence of (010) reflection is the evidence of the
superlattice B2 structure. Figure 6(c) shows the SADP of area B of the phase. The pattern
is indexed to fcc system along [011] zone axis. Fe5 also exhibits two phases in the
microstructure, including the matrix and the phases. The SADPs obtained from area C
CHAPTER 3 107
and D are presented in Figure 6(e) and Figure 6(f), respectively. Similarly, the matrix phase
shows a B2 structure austenite and the phase is confirmed to be fcc structure.
(a) (b)
[001]
000010
110
110_
0.5 μm
A
B
Matrix phase
phase
(c)
[011]
200
200
111
111_ _ _
_
(d)
(f)
[011]
000
200
200
111
111_ _ _
_
0.5 μm
C
D
Matrix phase
phase
000010110
110_
[001]
(e)
Figure 6. Room temperature TEM micrographs and selected area diffraction patterns
(SADPs) of the matrix and phase of Fe4 and Fe5 alloys. (a) bright field image of Fe4, (b)
and (c) SADPs obtained from areas A and B of Fe4, (d) bright field image of Fe5, (e) and
(f) SADPs obtained from areas C and D of Fe5.
3.4 Magnetic properties
CHAPTER 3 108
In Ni50Mn25+xIn25-x alloys, it is known that magnetic moments of the excessive Mn
atoms occupying the In sites align in parallel formation with respect to those of the Mn
atoms at the Mn sites, thus introducing extra ferromagnetic coupling between the two,
leading to increase in the saturation magnetisation with increasing Mn substitution for In
[24]. In Ni50Mn38-xIn12Fex alloys, the concentration of Mn can be up to 38 at.%. That means
13 at.% of Mn occupy the In sites. In this case, it is expected that ferromagnetic interactions
of the off-stoichiometric Ni50Mn38-xIn12Fex are increased compared to the stoichiometric
Ni50Mn25In25 alloy. Figure 7 shows the M(T) curves of the Ni50Mn38-xIn12Fex alloys in a
small magnetic field of 50 Oe. The sample was first cooled down from 390 to 10 K inside
the instrument without applying a magnetic field. A 50 Oe field was applied at 10 K and
then the magnetisation of the sample was measured upon heating to 390 K. Subsequently,
without removing the external field, the measurement was made upon cooling to 10 K.
0 50 100 150 200 250 300 350 400
0.00
0.02
0.04
0.06
0.08
0.10 TC
M
Mag
net
isat
ion
(em
u/g)
Temperature (K)
(a) Fe0
TC
A
0 50 100 150 200 250 300 350 400
0.0
0.5
1.0
1.5
2.0
2.5
TC
M
Mag
net
isat
ion
(em
u/g
)
Temperature (K)
(b) Fe3
TC
A
0 50 100 150 200 250 300 350 400
0
1
2
3
4
5
6
TC
M
Ma
gn
etis
atio
n (
em
u/g
)
Temperature (K)
(c) Fe4
TC
A
0 50 100 150 200 250 300 350 4000
1
2
3
4
5
Mag
netis
atio
n (
emu/
g)
Temperature (K)
(d) Fe5
TC
A
CHAPTER 3 109
0 50 100 150 200 250 300 350 4000
1
2
3
4
5
6
7
Ma
gnet
isa
tion
(em
u/g
)
Temperature (K)
(e) Fe6
TC
A
Figure 7. Thermomagnetisation behaviour of Ni50Mn38-xIn12Fex alloys in a field of 50 Oe.
As seen in Figure 7(a), Fe0 presents a very small magnetisation at 10 K when the 50
Oe field was applied, at 0.05 emu/g. The magnetisation of the heating curve showed a
broad hump at ~70 K. The abrupt decrease of magnetisation upon heating at ~300 K is
attributed to the Curie transition of the austenite, of the small amount of residual austenite
in the matrix [22]. This temperature is denoted ACT . The heating curve did not follow the
cooling curve at below ACT , apparently due to the application of the magnetic field on this
second cooling. The rapid increase of magnetisation at below 70 K upon cooling is
attributed to the Curie transition of the martensite, denoted MCT =70 K.
The magnetisation behaviour of Fe3 is similar to that of Fe0. The TA temperature is
~355 K (Figure 3), and similar to Fe0, the Curie transition at ~315 K corresponds to that of
the remnant austenite in this alloy. The Curie transition of the martensite is determined to
be MCT =100 K. Fe4 showed a similar thermomagnetic behaviour to Fe3. The M
CT and ACT
are determined to be about 155 K and 320 K for Fe4 alloy, respectively. Fe5 and Fe6
showed different magnetisation behaviour to the previous three samples. The magnetisation
was fairly constant at below or above ACT . These two samples showed no martensitic
transformation within the testing temperature range, thus the absence of the Curie transition
of the martensite on the curves.
It is seen that the ACT temperature increased slightly from 300 to 320 K with the
increase of Fe addition from 0 to 6 at.%. However, the MCT temperature was more
CHAPTER 3 110
significantly affected by Fe addition, from 70 to 155 K with increasing Fe addition up to 4
at.%.
For alloy Fe4, the martensitic transformation temperature TM (319 K) is very close
to the Curie transition temperature ACT (320 K). This implies that the martensitic
transformation overlaps with the Curie transition of the austenite, i.e., the phase
transformation is “hidden” on the M(T) curve. To reveal the martensitic transformation via
the M(T) measurement, a higher magnetic field is applied, which lowers TM without
affecting ACT , thus delaying the AM transformation to after the completion of the Curie
transition of the austenite [8].
Figure 8 shows the thermomagnetisation behaviour of alloy Fe4 in a high field of 70
kOe. It is seen that the magnetisation changed abruptly at ~300 K with a hysteresis of 10 K
between the heating and cooling curves. This is obviously due to the martensitic
transformation of this alloy. The forward transformation temperature is estimated to be
*MT =300 K, which is 10 K below that obtained from the DSC measurement, obviously due
to the effect of the applied magnetic field. It is seen that the ferromagnetic interactions in
the austenite are much stronger than that in martensitic phase, which leads to 40 emu/g
magnetisation difference across the transformation.
0 50 100 150 200 250 300 350 400
20
30
40
50
60
70
80
Mag
netis
atio
n (e
mu
/g)
Temperature (K)
Fe4
H=7 T
T*
M
CHAPTER 3 111
Figure 8. Thermomagnetisation behaviour of Fe4 alloy in a field of 70 kOe.
To reveal the magnetic structure of the austenite and martensite, M(H)
measurements were carried out of the Ni50Mn38-xIn12Fex alloys at 5 K. The measurements
are shown in Figure 9. At 5 K, the matrix phase is in martensitic state for Fe0, Fe3 and Fe4,
whereas it is in austenitic state for Fe5 and Fe6. It is seen that Fe5 and Fe6 showed typical
soft ferromagnetic behaviour, with saturation magnetisation of 105 and 108 emu/g,
respectively. The M(H) data of Fe4 also showed the characteristics of ferromagnetic
ordering in its martensitic state, but with a much reduced magnetisation of 47 emu/g. The
initial slope of M(H) curve of Fe3 indicates the short range ferromagnetic correlations
together with antiferromagnetic exchange in the martensitic phase. The coexistence of the
ferromagnetic and antiferromagnetic structures can also be seen as the splitting between the
heating and cooling M(T) curves (Figure 7b). In Ni50Mn38-xIn12Fex alloys, extra Mn atoms
occupy In sites, forming a ferromagnetic coupling between the Mn(Mn site) and Mn(In
site) atoms in the austenitic phase [24]. Through the martensitic transformation, the
distance between the Mn(Mn site)-Mn(In site) decreases and favours antiferromagnetic
interaction in the martensitic phase. However, the Mn atoms at the Mn site still form
ferromagnetic interaction in the martensitic phase. Therefore, the inhomogeneous magnetic
structure is common to observe in the martensitic state of the Mn-rich Ni-Mn-
Z(Z=In,Sn,Sb) alloys [21, 22, 25]. The magnetisation of Fe0 showed nearly linear
dependence on the applied magnetic field up to 40 kOe. The linearity of M(H) data suggests
that it is antiferromagnetic in the martensitic state of this alloy. The saturation
magnetisations are determined to be 13.6 and 27.7 emu/g for Fe0 and Fe3, respectively.
CHAPTER 3 112
0 10 20 30 40 50 60 70 80
0
20
40
60
80
100
120
M
Fe6
Fe5
Fe4
Fe3
Ma
gnet
isat
ion
(em
u/g
)
Magnetic Field (kOe)
Fe0
T=5 KA
Figure 9. Magnetisation measurements of the Ni50Mn38-xIn12Fex alloys at 5 K. A represents
austenitic state and M represents martensitic state.
It is seen that the saturation magnetisation increased with increasing the Fe addition
in these alloys. Based on the composition determination, it is known that the Mn
concentration decreased in the matrix phase with more Fe addition. With high
concentration of Mn, antiferromagnetic exchange is expected to dominate, as the
composition is close to the antiferromagnet Ni50Mn50. This explains the linearity of M(H)
data in the martensitic state of Fe0 which has the highest Mn concentration (37.8 at.% Mn)
among the Ni50Mn38-xIn12Fex alloys. With the decrease of Mn content (increase of Fe
addition), the antiferromagnetic ordering weakens, and gradually the long-range
ferromagnetic ordering forms in the matrix phase.
3.5 Mechanical properties
Figure 10 shows compressive deformation behaviour of the alloys, with (a) showing
the stress-strain curves and (b) showing the effect of Fe content on the maximum stress and
strain.
CHAPTER 3 113
0 2 4 6 8 10 12 14 160
100
200
300
400
500
600
700
800
Fe6
Fe5Fe4
Fe3
Str
ess
(M
Pa
)
Strain (%)
Fe0
0 1 2 3 4 5 6450
500
550
600
650
700
750
800
Fe Content (at.%)
Ma
xim
um
Co
mp
ress
ive
Str
ess
(M
Pa
)
10
11
12
13
14
15 Ma
ximu
m C
om
pre
ssive S
train
(%)
Figure 10. Compressive deformation behaviour of Ni50Mn38-xIn12Fex alloys; (a) stress-strain
curves; (b) maximum compressive stress and strain as functions of Fe content.
Fe0 and Fe3 showed obvious stress plateau corresponding to the reorientation of
martensite variants. However, stress-strain curves for Fe4, Fe5 and Fe6 suggest that the
deformation was mainly due to the dislocation mechanisms rather than the martensite
detwining process, since the stress plateau corresponding to the reorientation of martensite
variants did not appear in the stress-strain curves. It is also seen that the compressive
strength first increased and then decreased with increasing Fe content, reaching a maximum
of 770 MPa at 5 at.% Fe. The compressive strain showed similar tendency with increasing
Fe addition. The maximum strain reached was 14.3 % at 3 at.% Fe.
CHAPTER 3 114
These observations are in contrast to those made in Ni50Mn34In16-yFey and
Ni50Mn34In16-yCoy alloys, which show continuous increase of strength and strain with
increasing the amount of Fe or Co (or the amount of the phase) in the alloys [17, 26]. The
decrease of the compressive strength and strain at high levels of Fe addition in this case is
attributed to the particular morphology of the phase. It is seen in Figure 1 that the phase
in Fe6 exists as thin and elongated grains in parallel arrays in the matrix phase. This
morphology is detrimental for the strength and ductility of this material. More importantly,
the grain boundaries of matrix phase of Fe6 are not covered nicely by phase grains like
those in Fe4 and Fe5 alloys [27], evidenced by the microstructural observations of these
alloys shown in Figure 1. Therefore, Fe6 showed more intergranular cracking under
compression tests (Figure 11(e)), thus presenting relative low strength and ductility
compared to Fe4 and Fe5. It should be noted that the ductility of Fe0 and Fe3 is associated
with the martensite variant reorientation, and there is not much “real plastic deformation”
before failure. Good ductility is actually given by Fe4 and Fe5, which contain 6.8 % and
11.5 % of the phase, respectively.
Figure 11 shows the fracture morphologies of the Ni50Mn38-xIn12Fex alloys after
compressive testing. It is seen from micrographs (a) and (b) that Fe0 and Fe3 fractured via
typical intergranular cracking. With the increase of Fe addition, the fracture becomes a
mixture of intergranular cracking and transgranular cracking. Some pull-out holes are also
evident due to the pulling out of the phase particles, implying improvement of the
ductility of Fe4 and Fe5 alloys, shown in micrographs (c) and (d). The cracks in Fe6 mainly
formed along the elongated grains in the microstructure, as seen in micrograph (e), leading
to the decrease in strength and ductility.
CHAPTER 3 115
(a)
100 µm
(b)
100 µm
(c)
20 µm
(d)
20 µm
(e)
20 µm
Figure 11. SEM micrographs of the fractured surfaces of Ni50Mn38-xIn12Fex alloys after
compressive testing. (a) Fe0, (b) Fe3, (c) Fe4, (d) Fe5 and (e) Fe6.
Figure 12 shows the compressive stress-strain curves at room temperature and the
strain recovery after heating to above the TA temperature of Fe3 and Fe4 alloys. Fe3 was
deformed to 7.3 % strain. It exhibited a spontaneous recovery of 2.5 % upon unloading,
CHAPTER 3 116
leaving a residual strain of 4.8 %. The arrowed curves below the x-axis represent the strain
recoveries upon heating to 500 K for 5 min. The recovered strain is 4.5 % and the recovery
ratio is 94 % for Fe3. Fe4 had a compressive strain of 6.7 %, and generated a residual strain
of 2.4 % after unloading. After heating to 500 K for 5 min, the strain recovery was 0.9 %,
giving the total recovery ratio of 37 % for Fe4. It is also worth noting that the critical stress
to initiate the detwining of the martensite variants is about 130 MPa in Fe3 which is much
lower than that of 330 MPa in Fe4. The disappearance of stress plateau in Fe4 is due to the
strain hardening effect caused by the phase. Accordingly, it can be envisaged that the
shape memory effect of the two-phase Fe4 alloy is poor due to the presence of the phase,
which does not participate in the reversible martensitic transformation.
0 1 2 3 4 5 6 7 80
50
100
150
200
Str
ess
(M
Pa
)
Strain (%)
(a) Fe3
SME
0 1 2 3 4 5 6 70
100
200
300
400
500
Str
ess
(MP
a)
Strain (%)
(b) Fe4
SME
Figure 12. Shape memory effect of Fe3 and Fe4 alloys.
4. Conclusions
This study investigated the effects of Fe addition for Mn on the properties of
Ni50Mn38In12. The main findings may be summarised as following:
(1) Fe substitution for Mn in Ni50Mn38-xIn12Fex alloys at above 3 at.% causes formation
of an fcc phase. The phase is a Ni-Mn-Fe solid solution phase with small amount
of In dissolved. Formation of phase results in the decrease of Mn and increase of
In contents of the matrix phase. Consequently, the e/a ratio of the matrix phase
decreases with increasing Fe addition.
CHAPTER 3 117
(2) The critical temperature (To), the enthalpy change (ΔH) of the martensitic
transformation decreased with increasing Fe addition, due to the decrease of e/a
ratio of the matrix phase caused by the formation of the phase. A threshold value
of e/a ratio is identified at ΔH=0 to be 7.948, below which no martensitic
transformation is expected in Ni50Mn38-xIn12Fex alloys. This value corresponds to Fe
substitution of 4.5 at.% for Mn.
(3) The Curie temperature of the martensite ( MCT ) increased rapidly from 70 to 155 K
with Fe addition to 4 at.%, whereas that of the austenite ( ACT ) increased slightly
from 300 to 320 K with Fe addition to 6 at.%, The austenite shows much stronger
ferromagnetic characteristic relative to that of the martensite. The ferromagnetic
ordering of the martensite was enhanced with increasing Fe addition, due to the
reduced content of antiferromagnetically coupled Mn in the martensitic phase.
(4) Compressive stress and strain did not simply increase with increasing amount of the
phase. Good compressive strength and ductility are exhibited by Fe4 and Fe5
alloys.
(5) The shape memory effect decreased significantly with the introduction of phase.
The alloy without phase in the microstructure (Fe3) showed a shape memory
effect of 94 %, while the alloy containing 6.8 % phase (Fe4) presented a shape
memory effect of 37 %.
Acknowledgement
The authors wish to acknowledge the financial supports by the Department of
Innovation Industry, Science and Research of the Australian Government in ISL Grant
CH070136, and by National Natural Science Foundation of China in Grant No. 51001010.
CHAPTER 3 118
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CHAPTER 3 120
Paper 5
Metallurgical origin of the effect of Fe doping on the martensitic and
magnetic transformation behaviours of Ni50Mn40-xSn10Fex magnetic shape
memory alloys
Zhigang Wu1, Zhuhong Liu1,2 , Hong Yang1, Yinong Liu1, Guangheng Wu3 and Robert
Woodward4
1. School of Mechanical Engineering, The University of Western Australia, Crawley, WA
6009, Australia
2. Department of Physics, University of Science and Technology Beijing, Beijing 100083,
China
3. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese
Academy of Sciences, Beijing 100080, China
4. School of Physics, The University of Western Australia, Crawley, WA 6009, Australia
Abstract
This study investigated the metallurgical origin of the effects of Fe substitution for
Sn on the martensitic and the magnetic transformation behaviours of Ni50Mn40-xSn10Fex
(x=0, 3, 4, 5, 6) alloys. Substitution of Fe for Mn at above 3 at% introduced an fcc γ phase
in the microstructure. Formation of the γ phase influenced the composition of the bcc/B2
matrix, leading to decrease in martensitic transformation temperatures and transformation
entropy change. The Curie temperature of the parent phase increased slightly, whereas the
Curie temperature of the martensite increased rapidly with increasing Fe addition. Changes
in the temperatures of the martensitic and magnetic transformations are confirmed to
directly relate to the e/a ratio of the matrix caused by formation of γ phase. The minimum
e/a ratio value for the occurrence of the martensitic transformation is estimated to be 8.045
for the alloy system studied. A narrow e/a ratio range of 8.113~8.137 is estimated for the
occurrence of metamagnetic transformation ( ) ( )M para A ferro . This metamagnetic
CHAPTER 3 121
reverse transformation was induced by a magnetic field at 225 K within a range of 3~7 T in
the Ni50Mn35Sn10Fe5 alloy. The magnetic work required to induce the transformation is
estimated to be ~176 J/kg, comparable to the thermodynamic energy deficit for the
transformation at the testing temperature estimated from thermal measurement. These
findings clarify the origin of the effects of Fe doping in Ni50Mn40-xSn10 alloys and provides
reference on alloys design for this system.
Keywords: A. magnetic intermetallics; B. alloy design; B. shape-memory effects; B.
martensitic transformations; B. magnetic properties
1.Introduction
Ni-Mn-X (In, Sn and Sb) alloys have attracted much attention since the discovery of
magnetic field induced reverse martensitic transformation by Sutou et al. in 2004 [1]. In
these alloy systems, the martensitic transformation coincides with the magnetic
transformation from a L21 structure ferromagnetic austenite to an orthorhombic
paramagnetic martensite. The difference in magnetisation between the two phases provides
a driving force for the structural transformation under the influence of magnetic field. In
2006, Kainuma et al. achieved shape recovery accompanying the martensitic transformation
in Ni-Co-Mn-In single crystalline and Ni-Co-Mn-Sn polycrystalline alloys [2, 3],
demonstrating the promise of the alloys for actuation applications in smart systems. In
addition to magnetoactuation, these alloy systems also exhibit several other interesting
properties. The electrical resistance of the parent phase exhibits a typical metallic
behaviour, whereas it is semimetal-like for martensite in such alloy systems [4]. Since
magnetic transition coincides with a first order martensitic phase transformation, the giant
magnetoresistance effect [4-6] and giant magnetocaloric effect [7-9] have also been
discovered. Beside the investigation on Ni-Co-Mn-In (Sn) alloys, many other alloys with
similar compositions have also been extensively studied recently in a number of aspects,
including the thermal and stressed induced martensitic transformation behaviours [10, 11],
phase separation and magnetic properties [12, 13] , martensitic transformation
characteristics [14], time effect [15] and aging effect [16].
CHAPTER 3 122
One main hindrance to engineering application of these materials is the intrinsic
brittleness associated with the intermetallic compound nature of the alloys. Similar problem
is also found in Ni-Mn-Ga alloys. To improve ductility, a second ductile γ phase has been
introduced by introducing Co or Fe into Ni-Mn-Ga alloys [17-20]. Recently, Feng et al.
reported that substitution of Fe for In in Ni-Mn-In alloys introduces the γ phase and
enhances the ductility of the alloys [21].
Whereas the purpose is to improve ductility, addition of a fourth element to the
ternary Ni-Mn-X (In, Sn and Sb) alloys inevitably alters the matrix composition, hence the
structure and thermal and magnetic properties. Passamani and Fukushima have recently
investigated the effect of Fe substitution for Mn in Ni-Mn-Sn alloys on their magnetic
properties. They found that the martensitic transformation temperatures decrease rapidly
whereas the Curie transition temperatures of both austenite and martensite increase with the
increasing Fe substitution [22, 23]. It was also found that the addition of Fe leads to the
enhancement of FM exchange interaction in the austenitic and martensitic phases, and the
magnetic exchange bias effect was detected in the samples with Fe substitution below 10
at.% [22]. Whereas much attention has been given to the influences of fourth element
addition on the magnetic and transformation properties of these alloys, given the level of
complexity associated with the quaternary systems, much less is understood of the
metallurgical origins of these influences. This study is concerned with this fundamental
issue by investigating the effects of Fe substitution for Mn in Ni50Mn40-xSn10Fex. Fe bears
much resemblance to Mn in this alloy system, including magnetic state and valence
electron number, thus providing an opportunity to examine the metallurgical influence of
the addition to the properties of the alloys, in addition to being a selected element for
ductility improvement for some common ferromagnetic shape memory alloys.
2.ExperimentalProcedures
Polycrystalline Ni50Mn40-xSn10Fex (x=0, 3, 4, 5, 6) alloy ingots were prepared by
means of arc melting in argon atmosphere using high purity (99.99 %) elemental metals.
The samples are referred to as Fe0, Fe3, Fe4, Fe5 and Fe6, respectively. The button shaped
ingots were heat treated at 1173 K in vacuum for homogenisation followed by furnace
CHAPTER 3 123
cooling to room temperature. Transformation behaviour of the alloys was studied by means
of differential scanning calorimetry (DSC) using a TA Q10 DSC instrument with a
cooling/heating rate of 10 K/min. Phase identification and crystal structures were
determined by means of X-ray powder diffraction using Cu-Kα radiation. Microstructures
of the samples were studied with optical microscopy and scanning electron microscopy
(SEM) and the compositions were determined by means of X-ray energy dispersive
spectrometry (EDS). The magnetic properties were studied using a superconducting
quantum interference device magnetometer (SQUID).
3.Resultsanddiscussion
3.1 Microstructure and crystal structure
Figure 1 shows back-scattered SEM micrographs of the microstructures of the
Ni50Mn40-xSn10Fex (x=3, 4, 5, 6) alloys after homogenization treatment. The Fe3 sample
(micrograph (a)) showed a uniform single phase structure, without any sign of a second
phase. A few black spots presented in alloy Fe3 are solidification shrinkage pores formed
during ingot casting. These pores are also presented in the other alloy samples. The
microstructure of the F0 sample is essentially identical to that of F3, except the actual
chemical composition of the matrix. The Fe4, Fe5 and Fe6 samples showed a continuous
matrix in light contrast and dispersed γ phase particles in dark contrast. The volume
proportion of γ phase obviously increased with more Fe content from alloy Fe4 to Fe6. The
Fe6 alloy showed much smaller γ phase particles and a different texture compared to the
other two alloys.
CHAPTER 3 124
100 µm
100 µm 100 µm
100 µm
(a) (b)
(c) (d)
Figure 1. Back-scattered electron images of Ni50Mn40-xSn10Fex alloys: (a) x=3; (b) x=4; (c)
x=5 and (d) x=6.
Figure 2 shows XRD spectra of the Ni50Mn40-xSn10Fex alloys. Alloys Fe0 and Fe3
showed an orthorhombic martensite crystal structure. Alloy Fe4 exhibited a more
complicated case, showing a mixed structure of the orthorhombic martensite, the bcc
austenite and the γ phase. Alloy Fe5 presented a two-phase structure, with the fcc γ phase
and the bcc austenite. Alloy Fe6 also showed a two-phase structure, but with the fcc γ phase
and a B2 austenite. The lattice parameters of the martensite are similar for Fe0, Fe3 and Fe4
alloys, and the values are listed in Table 1. The lattice parameters of the γ phase in Fe4, Fe5
and Fe6 are very close, with an average value of a=0.365 nm at room temperature. The
lattice parameter of the bcc austenite was determined to be a=0.2982 nm for Fe4 and
0.2988 nm for Fe5. The lattice parameter of the B2 phase in Fe6 was determined to be
a=0.2996 nm. The phases present in the samples are summarised in Table 1. It is evident
that the intensity of the characteristic peaks of the γ phase increased with increasing Fe
content, which is consistent with the microstructure observations presented above.
CHAPTER 3 125
30 40 50 60 70 80 90 100
AM
X-r
ay
Inte
nsi
ty
2 (deg.)
Fe0
Fe3
Fe4
Fe5
Fe6
Figure 2. X-ray diffraction spectra of the Ni50Mn40-xSn10Fex alloys at room temperature.
Table 1. Effect of Fe addition on phase formation at room temperature (lattice parameters
in nm)
Sample Fe0 Fe3 Fe4 Fe5 Fe6
Fe addition
(at.%)
3 4 5 6
Austenite (bcc)
a=0.2982
a=0.2988
(B2)
a=0.2996
phase (fcc)
a=0.365
Martensite
(orthorhombic)
a=0.6526
b=0.5946
c=0.5704
a=0.6530
b=0.5916
c=0.5695
a=0.6522
b=0.5912
c=0.5685
CHAPTER 3 126
3.2 Alloy composition
Table 2 shows compositions of the phases in the samples as determined by
quantitative EDS analysis. It is seen that the matrix phase of the Fe-doped alloys contained
~2.9 at% Fe, regardless of the total amount of Fe added (the lowest amount added is 3 at%),
implying the solubility limit of Fe in the bcc/B2 matrix phase in the Ni-Mn-Sn system. This
is consistent with a previous study [21]. Adding Fe to above 3 at% did not cause further
increase of the Fe content in the matrix, but an obvious reduction of Mn, which is
compensated by the relative increase of Sn. The increase of Sn in the matrix is apparently
related to the increase of the fraction of the γ phase, which contained very low levels of Sn,
as seen in Table 1. The Ni content remained unchanged with the addition of Fe, at ~49 at%.
The γ phase is effectively a Ni-Mn-Fe alloy containing a small amount of Sn (~1.4 at%).
Table 2. Composition, e/a ratio and γ proportion of Ni50Mn40-xSn10Fex (x=0, 3, 4, 5, 6)
alloys.
Matrix γ phase
Ni
(at%)
Mn
(at%)
Sn
(at%)
Fe
(at%)
e/a
ratio
Ni
(at%)
Mn
(at%)
Sn
(at%)
Fe
(at%)
γ
(vol%)
X=0 49.49 39.90 10.61 - 8.166 - - - - -
X=3 49.47 36.99 10.73 2.81 8.190 - - - - -
X=4 49.07 35.84 12.14 2.95 8.137 52.84 34.01 1.36 11.79 11.9
X=5 48.78 34.62 13.69 2.91 8.082 53.05 33.36 1.38 12.21 22.0
X=6 48.70 34.22 14.19 2.89 8.064 51.66 32.36 1.39 14.59 25.5
The volume fractions of the phases in each alloy were obtained by image analysis
using ImageJ, and the volume fraction of the γ phase determined is listed in Table 1. It
shows that the amount of the γ phase increased with increasing Fe addition, with 25.5 % of
the γ phase present in alloy Fe6.
CHAPTER 3 127
The valence electron concentrations per atom (e/a ratio) of the matrix phase was
calculated using the compositions obtained from EDS analysis from the sum of s, p and d
electrons for Mn (7), Ni (10), Fe (8) and Sn (4). It is obvious that the e/a ratio decreases
with increasing Sn and decreasing Mn contents for the Fe-doped alloys. Figure 3 shows the
effect of Fe addition on the matrix phase composition (graph (a)) and the e/a ratio (graph
(b)) of the alloys. It is to be noted that the Fe0 alloy has a lower value of e/a ratio compared
to Fe3, despite that it contained the least Sn. This is obviously related to the absence of Fe,
which has a higher electron concentration than Mn, making its total e/a ratio to appear in
between those of Fe3 and Fe4. It is clear that the e/a ratio of the alloy decreased
continuously with increasing Sn/Mn atomic ratio in the alloys, as expected.
0 1 2 3 4 5 60
2
4
6
8
10
12
14
Sn,
Fe
Con
cent
ratio
n (a
t %
)
(a)
Sn
Fe
Mn
30
32
34
36
38
40
42
44
Mn C
oncentration (at %)
0 1 2 3 4 5 6
8.06
8.08
8.10
8.12
8.14
8.16
8.18
8.20
8.22
Sn/Mne/a
Fe addition (at %)
e/a
(b)
0.26
0.28
0.30
0.32
0.34
0.36
0.38
0.40
0.42
Sn/M
n Ratio
CHAPTER 3 128
Figure 3. Effects of Fe addition on elemental concentrations and e/a ratio of the matrix
phase of the Ni50Mn40-xSn10Fex alloys.
3.3 Martensitic transformation
Figure 4 presents DSC curves of the Ni50Mn40-xSn10Fex alloys. It is seen that the
martensitic transformation behaviour evolved progressively with increasing Fe addition for
these alloys. The transformation behaviour of alloy Fe0, however, appeared in between
those of Fe3 and Fe4, consistent with the relative position of the alloy in terms of e/a ratio.
100 200 300 400 500
TA
TM
Fe6
Fe5
Fe4
Fe3
Hea
t Flo
w
Temperature (K)
Fe0
Figure 4. DSC measurements of martensitic transformation behaviour of the Ni50Mn40-
xSn10Fex alloys.
Figure 5 shows the effect of e/a ratio on the martensitic transformation
temperatures, characterised by the peak temperatures for the forward transformation TM, the
reverse transformation TA and the median temperature To, of the alloys. Also shown in the
figure is the hysteresis of the transformation, MAT TT . It is seen that the
transformation temperatures increased practically linearly with increasing the e/a ratio of
the alloys, with a coefficient of 17 K per 0.01 change of e/a ratio. This observation is
consistent with the findings of the effect of e/a ratio on transformation temperatures in other
CHAPTER 3 129
Ni-Mn-X (Al, Ga, In, Sn and Sb) alloys [24-26]. It is also evident that the transformation
hysteresis increased significantly with decreasing e/a ratio. This is consistent with
expectation for a decreased transformation entropy change S with transformations at
lower temperatures according to thermodynamic principles [27, 28].
8.06 8.08 8.10 8.12 8.14 8.16 8.18 8.20 8.22
150
200
250
300
350
400
T
To
TM
TA
e/a
Tra
nsfo
rmat
ion
Tem
pera
ture
(K
)
10
12
14
16
18
20
22
24
26
28
Transform
ation Hysteresis (K
)
Figure 5. Effect of Fe addition on martensitic transformation temperatures and hysteresis of
Ni50Mn40-xSn10Fex alloys, expressed as functions of the e/a ratio. TM: martensite
transformation peak temperature, TA: austenite transformation peak temperature, To=(TM+
TA)/2.
Figure 6 shows the effects of Fe addition on the transformation enthalpy and
entropy changes of the alloys, shown as functions of transformation temperature To in (a)
and e/a ratio in (b). The enthalpy change is determined from the DSC curves directly, and
the values have been normalised to the volume fractions of the b.c.c/B2 austenite. The
entropy changes are estimated based on 0
HS
T
. It is seen that both H and S
decreased continuously with decreasing To and with e/a ratio, caused by Fe addition.
CHAPTER 3 130
150 200 250 300 350 4000
5
10
15
20
To (K)
Ent
halp
y C
hang
e (J
/g)
(a)
12
16
20
24
28
32
36
40
44
S
H
Entropy C
hange (J/K K
g)
8.04 8.06 8.08 8.10 8.12 8.14 8.16 8.18 8.200
5
10
15
20
S
H
e/a
Ent
hal
py
Cha
nge
(J/g
)
(b)
12
16
20
24
28
32
36
40
44
Entropy C
hange (J/K K
g)
Figure 6. Effects of Fe addition on enthalpy and entropy changes of the Ni50Mn40-xSn10Fex
alloys, (a) as function of transformation temperature To=(TM+ TA)/2, and (b) as function of
e/a ratio. The arrows indicate the threshold values of To and e/a ratio below which the
martensitic transformation is expected to vanish.
CHAPTER 3 131
For a given transformation in a given alloy, 0
HS
T
is expected to be a constant.
In this case, Fe addition has changed the composition (and the e/a ratio) and effectively
created different alloys among the samples, giving rise to the variation of S with Fe
addition. In particular, the continuous decrease of S with increased Fe addition appears to
correlate to the continuous increase of Sn/Mn ratio in the matrix, as shown in Figure 3.
Another possible contribution to the variation of S among the samples is the
change of the magnetic state of the transformation [24, 29]. The martensitic transformation
in Fe0, Fe3 and Fe4 occurred in the paramagnetic state, i.e., it is )()( paraMparaA
transformation, whereas the transformation in Fe5 and Fe6 occurred in ferromagnetic state,
i.e., it is ( ) ( )A ferro M ferro transformation, as shown below in Figure 8. Ito et al. have
shown that S decreases with the change of the transformation from
)()( antiferroMparaA to )()( antiferroMferroA in NiMnIn and NiCoMnIn alloys
[30], which bears resemblance to the current finding. In addition, they also stated that
smaller S can be obtained from specimens with larger ( )AC sT M . Referring to the results
presented in Figure 8 below, it may be stated that S decreases with increasing ( )AC MT T
and with decreasing ( )MM CT T . However, it is our view that both the changes in S and in
transformation temperatures ( MT , AT , MCT , A
CT ) are consequences of the change in chemical
composition of the matrix phase, and are not causes and results of one to another.
It is seen that H diminishes with increased Fe addition. Extending H curve to
zero tentatively defines threshold values of To and e/a ratio below which the martensitic
transformation is expected to vanish. The threshold values, as indicated by the arrows in (a)
and (b), are estimated to be To = 142 K and e/a = 8.045. The e/a ratio value corresponds to
an Fe addition of 7.2 at% estimated from Figure 3. For Fe addition of more than 7.2 at% in
the system, no martensitic transformation is expected. Obviously, these threshold values are
dependent on the concentrations of the other elements in the matrix of the alloy. Feng et al.
detected a martensitic phase transformation at ~320 K in a Ni50Mn27Sn13Fe10 alloy, which
has an e/a ratio of 7.969. This is inconsistent with the findings of the present work [31].
CHAPTER 3 132
This is possibly related to the difference in the Mn content in these two alloys, but the
actual explanation is yet to be established.
3.4 Magnetic properties
In Ni50Mn25+xSn25-x alloys, it is well recognised that magnetic moments of the
excessive Mn atoms occupying the Sn sites align in anti-parallel formation with respect to
the Mn at the Mn sites, thus introducing antiferromagnetic coupling between the two,
leading to reduction in the saturation magnetisation with increasing Mn substitution for Sn
[24, 32, 33]. In Ni50Mn40-xSn10Fex alloys, the concentration of Mn can be up to 40 at%,
which means 15 at% of Mn occupy Sn sites. In this case, it is reasonable to believe that
antiferromagnetic interactions are widespread in the alloys. Consequently, the magnetic
structure of the austenite may be regarded as coexistence of ferromagnetic and
antiferromagnetic structures. The magnetic structure is less clear in martensite , which may
contain ferromagnetic, ferrimagnetic and spin glass state at below TC, as reported by
Umetsu et al based on the Mössbauer study [34]. Given the lack of certainty with regard to
the magnetic states of phases in these alloys, the austenite and the martensite phases are
referred to as ferromagnetic in this discussion, since both phases show spontaneous
magnetisation at below their Curie transition temperatures.
Figure 7 shows the thermomagnetisation behaviour of the alloys under a small
magnetic field of 50 Oe. The sample was first cooled down to 100 K under a zero field
inside the instrument prior to the measurement. A 50 Oe field was applied at 100 K and
then the sample was heated at a rate of 10 K/min up to 390 K and cooled back again to 100
K in the same field.
CHAPTER 3 133
100 150 200 250 300 350
0
2
100 150 200 250 300 350
0
2
4
100 150 200 250 300 350
0
2
100 150 200 250 300 350
0
2
4
6
8
(a) Fe3
(b) Fe4
(c) Fe5
Temperature (K)
Mag
netis
atio
n (e
mu/
g)
(d) Fe6
Figure 7. Thermomagnetisation behaviour of the Ni50Mn40-xSn10Fex alloys in a field of 50
Oe.
As seen in Figure 7(a), alloy Fe3 presented a very small magnetisation at the
starting point at 100 K when the 50 Oe field was applied. The magnetisation gradually
increased with the increasing temperature up to 170 K, then followed by a decrease with
further heating within 175~220 K, due to the Curie transition of the ferromagnetic
martensite. The transition temperature, MCT , is 188 K for alloy Fe3. The sA temperature of
this sample is 370 K (Figure 4). There is no obvious change in magnetisation upon heating
to above this temperature, implying that both M and A are in paramagnetic state.
M
CT
A
CT
fM
A
CT
A
CT
sM
sA
M
CT
sM
sA
sA
CHAPTER 3 134
The cooling curve showed an identical magnetic behaviour with the heating curve at
temperatures above 170 K, going through the Curie transition of the martensite. With
further cooling the magnetisation continued to increase, resulting in a splitting of the
magnetisation state between the cooling and the heating curves of the martensite. This
splitting is attributed to the existence of exchange bias effect in martensite at low
temperatures [24, 25, 35, 36]. As discussed earlier, the distance between Mn at Mn site and
Mn at Sn site is small enough to introduce AFM exchange between each other. The AFM
interaction is strengthened in the martensitic transformation, leading to a reduction of
magnetisation below TM [32]. The AFM interaction can pin the FM domains in various
configurations depending on whether the sample is cooled though TC in an external field or
not, thus separating the heating and cooling curves presented in the studied alloys.
Figure 7(b) shows that the magnetic behaviour of alloy Fe4 was similar to alloy Fe3
at below 270 K upon heating, but higher MCT = 234 K temperatures. The martensite reached
a magnetisation plateau at between 150 and 220 K, followed by the Curie transition at MCT .
The paramagnetic martensite started transforming to ferromagnetic austenite at ~300 K,
followed immediately by the Curie transition of the austenite at ACT (310 K). Upon cooling,
magnetisation of the austenite increased rapidly through its Curie transition, followed
immediately by a decrease associated with the forward transformation from the
ferromagnetic austenite to the paramagnetic martensite. It is seen that the magnetisation
reached is higher than that achieved on cooling (at 300 K). This is apparently due to the
hysteresis of sM relative to fA which gives more room for the austenite to develop. With
further cooling, the Curie transition of the martensite occurred, and the magnetisation of the
martensite continued to increase with decreasing the temperature to 100 K, as in the case of
alloy Fe3.
In Figure 7(c), alloy Fe5 presented the Curie transition of the austenite at 315 K and
sM at 220 K. Curie transition of the martensite was not observed within the temperature
range. The relative magnetisation of the martensite on the cooling curve may indicate that
the martensite was in ferromagnetic state, i.e., MCT is above sM . In figure 7(d), alloy Fe6
CHAPTER 3 135
showed a similar magnetisation behaviour to alloy Fe5, with ACT =320 K and sM =182 K.
The phase transformation hysteresis of Fe5 and Fe6 is determined to be 24 and 27 K,
respectively, which are consistent with the DSC measurements.
Figure 8 shows a phase diagram with the MT and AT obtained from the DSC
measurements and with the MCT and A
CT obtained from the SQUID measurements against
e/a ratio for the Ni50Mn40-xSn10Fex alloys. It is seen that MT and AT showed a positive linear
dependence on the e/a ratio, whereas MCT and A
CT decreased with the increase of the e/a
ratio, with different coefficients of dependencies. These critical temperatures divide the
space into four areas representing four different crystallographic and magnetic states of the
alloys. The transformation behaviour of the alloys among these four states can be divided
into three regions on e/a ratio. In region I, the alloy undergoes
( ) ( ) ( )A para A ferro M ferro transformation upon cooling, in region II the alloy
undergoes a transformation sequence of ( ) ( ) ( ) ( )A para A ferro M para M ferro , and
in region III the alloy undergoes ( ) ( ) ( )A para M para M ferro . In these expressions,
the single arrows represent magnetic transformations and the double arrows represent the
crystallographic transformations. Among these transformations, the ( ) ( )A ferro M para
transformation in region II is a simultaneous magnetic and crystallographic transformation,
offering the possibility for magnetically induced crystallographic transformation. Such
transformations offer high magnetisation difference between the austenite and martensite,
thus the opportunity for magnetic field induced phase transformation and shape memory
effect. For this particular alloy system, the magnetic field induced transformation is the
reverse transformation from the paramagnetic martensite to the ferromagnetic austenite.
The e/a ratio values at the boundaries of region II are estimated to be 8.113 and 8.137.
CHAPTER 3 136
8.06 8.08 8.10 8.12 8.14 8.16 8.18 8.20 8.22
150
200
250
300
350
400
Mferro
Mpara
Aferro
IIIIII
Tra
nsfo
rmat
ion
Tem
pera
ture
(K
)
e/a
Apara
Figure 8. Effects of valence electron concentration on AT , MT , MCT and A
CT temperatures of
the Ni50Mn40-xSn10Fex alloys.
It is seen in Figure 7 that alloys Fe5 and Fe6 exhibited martensitic transformation in
ferromagnetic state with different magnetisations between the parent and the product
phases, giving rise to the possibility to induce the transformation by a magnetic field. To
verify this, alloy Fe5 was magnetized isothermally at three different temperatures of 210 K,
225 K and 240 K. The magnetisation curves are shown in Figure 9. The curves have been
normalised to the volume fractions of the matrix phase in the samples. At 210 K, which is
16 K below the sA temperature, the ferromagnetic martensite showed soft magnetisation
behaviour to saturation at 51 emu/g (at 7 T). At 240 K, which is just above the fA
temperature, the austenite magnetised in a similar way to saturation at 79 emu/g. At 225 K,
which is 1 K below the sA temperature, the sample magnetised to ~44 emu/g at below 3 T,
corresponding to the magnetisation of the martensite. Upon increasing the external field to
above 3 T, the transformation from the martensite to austenite was induced. The
magnetisation reached the saturation magnetisation level of the austenite at 7 T, signalling
the completion of the reverse transformation. The magnetisation curve at 210 K also
MCT
ACT
ATMT
CHAPTER 3 137
demonstrates that field strength of 7 T is not enough to induce the ( ) ( )M ferro A ferro
transformation.
0 1 2 3 4 5 6 70
10
20
30
40
50
60
70
80
90
Ma
gn
etis
atio
n (
em
u/g
)
Magnetic field (T)
210 K 240 K 225 K
Figure 9. Magnetisation curves of Ni50Mn35Sn10Fe5 at 210 K, 225 K and 240 K, showing
the magnetic field induced metamagnetic ( ) ( )M ferro A ferro transformation at 225 K.
In inducing the metamagnetic ( ) ( )M ferro A ferro transformation shown in
Figure 9, the external magnetic field performed a magnetic work, which is estimated to be
79
0
0
magE HdM ≈ 176 J/kg. At this temperature (T*=225 K), the thermodynamic deficit for
inducing the transformation may be estimated as*
fA
th
T
E SdT . Using data determined
from the thermal measurement of the transformation (shown in Figure 4), this energy may
be estimated to be *
fA
th
T
E SdT ≈181 J/kg. The calculated values showed a good
satisfactory comparison between the two, i.e., mag thE E , demonstrating the feasibility of
the magnetically induced martensitic transformation.
CHAPTER 3 138
4.Conclusions
The effects of Fe substitution for Mn on the martensitic transformation and
magnetic behaviours of Ni50Mn40-xSn10Fex alloys were investigated. The experimental
evidences and the discussions lead to the following conclusions:
(1) Fe substitution for Mn in Ni-Mn-Sn alloys at above 3 at% Fe causes formation of an
fcc γ phase. The γ phase is a Ni-Mn-Fe solid solution phase with small amount of
Sn dissolved. Formation of the γ phase leads increase of Sn content without
affecting the Ni and Fe contents of the bcc/B2 matrix phase. Consequently, the
valence electron concentration of the bcc/B2 matrix phase decreases with Fe
addition. The solubility of Fe in the bcc/B2 matrix phase is slightly below 3 at%.
The effects of Fe addition on the transformation and magnetic behaviours are via
the changes of Sn and Mn contents in the matrix bcc/B2 phase.
(2) As a result of Fe addition, or more specifically the decrease of e/a ratio and the
change of the matrix composition, the critical temperature ( oT ), the enthalpy change
( H ) and the entropy change ( S ) of the transformation decreased whilst the
transformation temperature hysteresis ( T ) increased. oT Exhibited a practically
linear dependence on e/a ratio, with a coefficient of 17 K per 0.01 increase of e/a
ratio. The increase of T is attributed to the decrease of S . A threshold value of
e/a is identified at 0H , to be 8.045, below which no martensitic transformation
is expected in the Ni50Mn40-xSn10Fex alloy system. This value corresponds to Fe
addition of 7.2 at% for substitution of Mn.
(3) The Ni50Mn40-xSn10Fex alloys experience several transformation sequences of
different combinations between the structural martensitic transformation and the
magnetic Curie transition, including (on cooling)
( ) ( ) ( )A para A ferro M ferro at e/a ratio range of 8.045~8.113,
( ) ( ) ( ) ( )A para A ferro M para M ferro at 8.113~8.137, and
( ) ( ) ( )A para M para M ferro at above 8.137. At below e/a=8.045 no
CHAPTER 3 139
martensitic transformation is expected. The ( ) ( )A ferro M para and
( ) ( )A ferro M ferro transformations are metamagnetic transformations.
(4) The ( ) ( )M ferro A ferro transformation was induced in alloy Fe5 under a field
within the range of 3~7 T. The magnetic work done by the external field to the
system in inducing the transformation is estimated to be ~176 J/kg. This energy is
comparable to the thermodynamic energy deficit for the transformation at the
testing temperature, estimated to be ~181 J/g based on the DSC measurements.
(5) The saturation of magnetisation of the ferromagnetic bcc austenite is 79 emu/g and
that of the ferromagnetic orthorhombic martensite is 51 emu/g at the ambient
temperature in alloy Fe5.
Acknowledgment
The authors wish to acknowledge the financial supports by the Department of
Innovation Industry, Science and Research of the Australian Government in ISL Grant
CH070136 and by the National Natural Science Foundation of China in Grant No.
10774178.
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CHAPTER 4 142
CHAPTER 4. Closing Remarks
________________________________________________________________________________
4.1Journeyofferromagneticshapememoryalloys
It has been a 15-year journey of exploring and searching for new
magnetomartensitic materials for mechanical actuation since the discovery of magnetic-
field-induced strain of 0.2% in a Ni2MnGa alloy in 1996. Extensive research has been
carried out afterwards in the interdisciplinary field of ferromagnetic shape memory alloys,
as evidenced by over 14,000 publications [Google Scholar] produced to date on this topic.
Within a very short period research has advanced the discovery to achieving a giant
magnetic field induced strain of 10% in this Heusler alloy. This is an unprecedented
historical achievement. Encouraged by such success, extensive effort has been made to
search for other alloys, both within the Heusler family and outside, for example Ni-Mn-Al,
Ni-Fe-Ga, Co-Ni-Al, Co-Ni-Ga, Fe-Pt and Fe-Pd alloys. However, the magnetostrains
obtained in these alloys are all significantly smaller than those found in Ni-Mn-Ga alloys.
With the very limited success in finding other alloys, the attention has remained
strong on Ni2MnGa. Limited by its intrinsic low magnetic driving force from the magnetic
crystallographic anisotropy, the effort has been on reducing the already extremely low
mechanical resistance to deformation, from 1 MPa to 0.1 MPa. This is practically pushing
the theoretical limit to the minimum resistance to deformation in a metallic matrix. This
effort has enabled the nearly complete energy conversion from magnetic driving force to
the mechanical work. However, the magnetostress level is still 100 times lower compared
to that of its thermoelastic counterpart, NiTi.
The discovery of 2.9% of magnetostrain in Ni-Co-Mn-In alloy in 2006 made a
breakthrough. These alloys exhibit metamagnetic martensitic transformations with large
CHAPTER 4 143
magnetisation difference across the transformation as the driving force for mechanical
activation. To develop these alloys into useful and practical magnetoactuation materials, the
strategy has been on two aspects: to fully realise the potential of magnetisation difference
across the martensitic phase transformation and to lower the metallurgical resistance of the
matrix to deformation.
To lower the metallurgical resistance to shape change, it is preferable to have
intermetallic compound matrices with highly mobile twin boundaries and large grains, as
opposed to ductile solid solution matrices prone to plasticity. This inevitably renders the
alloys high brittleness. These problems severely impede the development of ferromagnetic
shape memory alloys from being successful magnetoactuation materials. These are the
challenges we are facing today. In this thesis, some the solutions to these two problems are
explored, and some key findings are of significance to the research community of
ferromagnetic shape memory alloys.
4.2Significanceofthisthesis
This study contributed to the development of ferromagnetic shape memory alloys in
three aspects: (i) energy balance analysis to determine the criteria of magnetoactuation and
limitations of FMSAs, (ii) alloy design to enhance ΔM of the martensitic transformation in
Ni-Mn-based alloys, and (iii) alloy design to reduce brittleness of Ni-Mn-based alloys. The
main achievements of this study are summarised below.
(1) Evaluation criteria were proposed with respect to energy conversion within
magnetic-field-induced martensitic transformation of FSMAs. Based on the analysis, three
criteria need to be met with regard to different requirements: Criteria I (completion of
magnetic-field-induced martensitic transformation):f
s
A
A
B M SdT ; Criteria II (completion
of shape change via magnetic-field-induced martensitic transformation): ' f
s
A
A
B M SdT ;
Criteria III (completion of two-way shape memory via magnetic-field-induced martensitic
CHAPTER 4 144
transformation): ' f
f
A
M
B M SdT . Using these criteria, current FSMAs can be evaluated
regarding their ability or potential as magnetic actuation materials. The challenges for
developing FSMAs are also clarified, which are to further increase the magnetic driving
force or/and to decrease the mechanical resistance of the metallic matrix to shape change.
(2) Exploration on composition design to increase the magnetic driving force was
made, targeting at the maximisation of ΔM between the austenite and martensite of Ni-Mn-
based alloys. The work was conducted on two alloy systems, including Mn-Ni-In-Co and
Mn-Ni-Sn-Co. The findings demonstrate the importance of Mn magnetic moment
contribution and clarify the magnetic interactions between Mn atoms in different
crystallographic structures of the austenitic and martensitic phases. The effect of Co
substitution for Ni on increasing ΔM is clearly interpreted, which is mainly due to the
enlargement of temperature window for ferromagnetic austenite. Large ΔM of 89 emu/g
and 109 emu/g were obtained in Mn50Ni40-xIn10Cox and Mn50Ni42-xSn8Cox alloy systems,
respectively. The increased ΔM greatly assisted the processing of magnetic-field-induced
martensitic transformation.
(3) It has been a common strategy to improve the ductility of the polycrystalline
alloys by introducing a phase into the matrix of Ni-Mn-alloys. This research investigated
the side effects of the phase on the martensitic transformation, magnetic properties and
shape memory effect of Ni-Mn-based alloys. The formation of the phase by Fe addition
alters the composition of the matrix, thus changing the e/a ratio of the transformation phase.
Consequently, the martensitic transformation behaviour and magnetic ordering of the alloys
are both altered significantly. This finding clarifies a common negligence in the effort to
improve ductility by the introduction of the phase. Furthermore, ductility depends not
only on the amount but also the morphology of the phase in the microstructure. Therefore,
the side effects of phase are prominent based on this research and need to be drawn
attention apart from of being an approach of increasing the ductility of Ni-Mn-based alloys.
CHAPTER 4 145
4.3ConcernswithNi‐Mn‐basedalloysandpossiblefuture
researchfocus
One of the biggest challenges of Ni-Mn-based alloys lies in the massive
metallurgical resistance of the matrix to deformation relative to the limited magnetic
driving force for actuation. With using Mn which has the largest magnetic moment to
replace Ni as the main constituent of the Heusler alloys and by optimising the alloy
composition and crystal structure, we have managed to achieve ΔM of the transformation as
high as ~110 emu/g. This is approaching the theoretical limit of ~138 emu/g in
Mn2NiZ(Z=In,Sn) alloys, given all Mn atoms form ferromagnetic coupling in the austenitic
structure and antiferromagnetic coupling in the martensitic structure. At an applied
magnetic field of 1T, this yields 1.1 MJ/m3 energy output, or ~18 MPa force output at 6%
strain. This corresponds to ~10% of the energy output of NiTi and is insufficient in many
practical applications.
The lack of success is intrinsically due to the dilemma between the limited magnetic
driving force associated with Zeeman energy (at moderate magnetic field strengths) and the
relative large mechanical resistance of the metallic matrix to shape change. For all alloy
systems that exhibit such magnetic energy output, it has been found that the magnetic
energy is merely enough to induce the metamagnetic martensitic transformation, and is well
below the mechanical resistance of the matrix to deformation, typically 100 MPa. In this
regard, the main obstacle to developing practical Ni-Mn-based ferromagnetic shape
memory alloys for mechanical actuation is to reduce the mechanical resistance to shape
change, more precisely the critical resolved shear stress for twining of the alloys. This will
most probably be achieved through metallurgical means.
To date, Ni-Mn-Ga system is the only one exhibiting the extraordinary performance
of low twinning stress, at below 1 MPa, which leads to the success of large magnetostrain.
Such phenomenon has not been seen in any other Ni-Mn-based intermetallics. Perfection in
single crystal and modification of modulation of the martensite structure may need to be
pursued. However, this may still not guarantee the same ease of twin boundary movement
CHAPTER 4 146
of martensite variants as in Ni-Mn-Ga. Another option is to search for alloys with a similar
mechanical behaviour as Ni-Mn-Ga, and then try to modify magnetic properties and
martensitic transformation behaviour afterwards.
Overall, the perspective of ferromagnetic shape memory alloys with high work
output still faces high challenges. To date, Ni-Mn-based alloys have not become truly
successful materials carrying the dream of magnetoactuation. However, enormous
knowledge has been established for the understanding of the magnetomartensitic behaviour
in ferromagnetic shape memory alloys in this study. Effort should be kept making to search
for better alloys with a similar mechanical performance of Ni-Mn-Ga alloys and
metamagnetic behaviour of Ni-Mn-based alloys. Continuation of this research will carry on
for achieving this goal in the future.