Available online at www.sciencedirect.com

www.elsevier.com/locate/actamat

Acta Materialia 56 (2008) 4529–4535

Crystal structure of 7M modulated Ni–Mn–Ga martensitic phase

L. Righi a,*, F. Albertini b, E. Villa c, A. Paoluzi b, G. Calestani a, V. Chernenko c,S. Besseghini c, C. Ritter d, F. Passaretti c

a Dipartimento di Chimica Generale ed Inorganica, Chimica Analitica, Chimica Fisica, Universita di Parma, Viale G. Usberti 17/A, I-43100 Parma, Italyb IMEM, Consiglio Nazionale delle Ricerche, Parco Area delle Scienze 37/A, I-43010 Parma, Italy

c IENI, Consiglio Nazionale delle Ricerche, Corso Promessi Sposi, 23900 Lecco, Italyd Intitut Laue-Langevin, BP 156, 38042 Grenoble Cedex 9, France

Received 28 March 2008; received in revised form 16 May 2008; accepted 19 May 2008Available online 21 June 2008

Abstract

For the first time, the 7M modulated structure, frequently observed in ferromagnetic shape memory Ni–Mn–Ga martensitic phases, issolved by powder diffraction analysis. Two polycrystalline samples with composition Ni2Mn1.2Ga0.8 and Ni2.15Mn0.85Ga, respectively,showing a 7M martensitic state stable at room temperature, were studied. The determination of the modulated crystal structure ofNi2Mn1.2Ga0.8 martensite was achieved by refining the X-ray powder diffraction pattern by the Rietveld method. The basic structurebelongs to monoclinic symmetry. The crystal structure, solved within the superspace approach, is found to show an incommensurate7M modulation with q = 0.308c*. The Rietveld refinement for Ni2.15Mn0.85Ga martensite on the basis of neutron powder data surpris-ingly provides a very similar incommensurate 7M structure with the same periodicity and analogous modulation function. The incom-mensurate structure presents typical displacive modulation with several analogies with the Zhdanov (5,�2)2 stacking sequence.� 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Ni2MnGa; Martensitic phase; Diffraction; Structural modulation; Crystal structure

1. Introduction

Ferromagnetic shape memory materials such as Ni–Mn–Ga Heusler alloys attract much attention because theyexhibit the giant magnetic-field-induced-strain (MFIS)effect (see, e.g., Refs. [1,2] and references therein) andremarkable magnetocaloric properties [3,4]. These ferro-magnetic alloys are characterized by a martensitic transfor-mation below or above the Curie temperature TC. They arealso characterized by the unusual combination of strongmagnetoelastic coupling and extremely mechanically softcrystal lattice [1]. The observed MFIS is due to the mag-netic field-induced twin rearrangement in the martensiticphase.

A number of martensitic structures have been found inthe Ni–Mn–Ga system [5,6]. The basic martensitic struc-

1359-6454/$34.00 � 2008 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2008.05.010

* Corresponding author. Tel.: +39 0521 905448; fax: +39 0521 905556.E-mail address: lara.righi@unipr.it (L. Righi).

ture is a result of the spontaneous uniform lattice distortionof the parent cubic phase with a L21 structure type. Thedistorted lattice can be tetragonal, orthorhombic or mono-clinic, depending on the composition of Ni–Mn–Ga alloyand the temperature [5]. In addition, evidenced by the pres-ence of satellites in diffraction experiments, lattice modula-tions (periodic shuffling of nearly close-packed planes) canappear [5,6].

Despite the intense research dedicated to this importantmaterial, the role of the martensitic structure in definingthe MFIS mechanism and the magnetic properties is notcompletely understood. In particular, the giant magneto-strain effect is observed only for Ni–Mn–Ga modulatedmartensites [7,8]. As MFIS is strongly dependent on mag-netostress value and twin boundary mobility [1,2,7], thecrystal structure determination of these modulated mar-tensites is of fundamental importance.

The most frequently observed modulated Ni–Mn–Gamartensitic structures have been indicated as 5M and

rights reserved.

4530 L. Righi et al. / Acta Materialia 56 (2008) 4529–4535

7M, depending on the number of unit cells of basicstructure involved in the related superstructure [6]. Thedescription of the displacive modulation of atomic layersat the basis of these complex structures has been the objectof several structural investigations [5,6,9]. Recently, accu-rate determination of the ‘‘5M” crystal structure of stoichi-ometric martensite Ni2MnGa has been achieved by theapplication of superspace theory on powder diffractiondata [10]. These studies have demonstrated that the‘‘5M” modulation in Ni–Mn–Ga alloys can be commensu-rate or incommensurate [11].

However, the crystal structure of 7M martensite in Ni–Mn–Ga (known also as 14M-type [5]) is still not well estab-lished. The 7M martensitic structure is characterized by adiffraction pattern with six satellites between the mainreflections associated with the distorted basic structure[5,6,12]. The lattice distortion with respect to the originalparent L21 structure has been generally described in termsof the orthorhombic structure with a > b > c [6,8,11,12].The first observation of this type of structure was reportedin an experiment where a stoichiometric Ni2MnGa singlecrystal was subjected to external tensile or compressionloads along the cubic h100i or h110i crystallographicdirections, respectively, at room temperature [6]. Further-more, investigations devoted to the composition depen-dence of structural and magnetic properties evidenced thepresence of temperature-induced 7M modulated martensitein Mn-rich [13,14] and Ni-rich [15] Ni–Mn–Ga alloys. Sucha Ni–Mn–Ga martensite displays some analogies with theNi–Al layered martensitic structure [16]. The Ni-rich bin-ary Ni–Al alloys show a martensitic phase, called 7R or,more recently, 7M [5], with a monoclinic structure withseven-layered modulation. Elastic neutron scattering exper-iments revealed the periodicity of the modulation to beconsistent with a modulation vector q close to 1/7[11 0]c(subscript c indicates the B2-ordered parent cubic lattice)[17]. This structure has been described in terms of a (5,�2)stacking sequence (related to Zhdanov’s notation) of the(110)c nearly close-packed atomic planes. The same modelhas been applied to the Ni-rich Ni–Mn–Ga martensiticphase showing 7M modulation. This composition has beeninvestigated by transmission electron microscopy (TEM)analysis [14], and the reported high resolution electronmicroscopy (HREM) images along [210] and [010] mono-clinic zone axes were compared with a model consisting ofa (5,�2)2 stacking arrangement of (110)c atomic planes.Although this structural model is considered the most sim-ilar to the martensitic structure shown by HREM projec-tions, the authors reported non-perfect periodicity of thestacking sequence.

The main object of the present study is a precise deter-mination of the crystal structure of the 7M-type modu-lated Ni–Mn–Ga martensitic phase. For this purpose, apowdered sample of Mn-rich composition was investi-gated by X-ray diffraction (XRD). The structure wasfound to show an incommensurate ‘‘7M” modulationwhich has been solved by the superspace approach. The

Rietveld refinement achieved the convergence, giving astructure comparable with a (5,�2)2 layers stacking. More-over, the crystal structure obtained by this procedure hasalso been applied to a martensitic phase of Ni-rich com-position investigated in the present work by powder neu-tron diffraction (PND).

2. Experimental

Polycrystalline ingots with nominal composition Ni2Mn1.2-Ga0.8 and Ni2.15Mn0.85Ga were prepared by melting thepure elements of electrolytic Ni 99.97 at.%, electrolyticMn 99.5 at.% and Ga 99.9 at.% in a non-consumable-elec-trode arc furnace in Ar atmosphere. Several re-melts wereperformed to ensure good homogeneity. The samples werethermally treated in Ar flow at 800 �C for 5 h. Energy dis-persion spectrometry (EDS) was used to check the samplecomposition. Both martensitic and Curie transition temper-atures were determined in the 280–420 K range, with a rateof 1 K min�1 by thermomagnetic analysis (TMA). InNi2Mn1.2Ga0.8, magnetic and martensitic transitions werefound to co-occur at T = 370 �C (on heating) [3]. In con-trast, in Ni2.15Mn0.85Ga the two transitions are well sepa-rated: the martensite–austenite transformation is observedat TMA = 320 K (on heating), while the Curie transitionoccurs at TC = 335 K. Thermal hysteresis DT = 15 K isobserved at the martensitic transformation.

Powder X-ray diffraction (PXRD) patterns were col-lected with Cu Ka radiation, using a Thermo ARL X’tradiffractometer equipped with a Thermo Electron solid-statedetector. A PND experiment was carried out on the samplewith composition Ni2.15Mn0.85Ga at the high resolutionD2B beamline of the Institute Laue-Langevin Institute(Grenoble, France). The parameters of the pattern acquisi-tions are summarized in Table 1. The Rietveld structuralrefinement and the analysis of the resulting crystal struc-tures were carried out using JANA2000 software [18].

3. Results

The powder diffraction pattern of Ni2Mn1.2Ga0.8 mar-tensite, collected at room temperature and shown in Fig. 1,was analyzed in order to determine the unit cell parametersof the fundamental lattice. The system is found to belong toa monoclinic symmetry with unit cell parameters: a =4.222 A, b = 5.507 A, c = 4.267 A and b = 93.3�. As alreadyremarked, the 7M martensite is frequently associated with apseudo-orthorhombic lattice based on the parent L21 struc-ture, whose unit cell parameters are derived from the formerlattice with the following relationship:

aL21

bL21

cL21

0B@

1CA ¼

�1 0 1

�1 0 �1

0 �1 0

0B@

1CA

am

bm

cm

0B@

1CA ð3:1Þ

where a = 6.174 A, b = 5.828 A, c = 5.507 A with anglesapproximated to 90� [5]. However, this unit cell is redun-

Table 1Experimental details and refined crystallographic data for the two sampleswith compositions of Ni2Mn1.2Ga0.8 and Ni2.15Mn0.85Ga, respectively

Sample Ni2Mn1.2Ga0.8

(Mn-rich)Ni2.15Mn0.85Ga(Ni-rich)

Radiation type X-ray NeutronWavelength Cu Ka 1.5942h range (�) 10.00–100.00 15.00–150.00Step/degrees 0.050 0.050Temperature (K) RT RTSuperspace group I2/m(a0c)00 I2/m(a0c)00Modulation vector q 0.3081(4)c* 0.307(4)c*

a (A) 4.2672(4) 4.2201(6)b (A) 5.5074(4) 5.5388(4)c (A) 4.2228(6) 4.1974(3)b (�) 93.31(1) 92.74(1)Volume (A3) 99.07(1) 98.00(1)Z 2 2Calculated density (g cm�3) 7.964(3) 8.221(1)Calculated formula Ni2Mn1.28Ga0.72

Agreement factors

RwF (main reflections) 0.0546RwF (first-order satellites) 0.0717RwF (second-order satellites) 0.0808Rp/Rwp 0.1029/0.1513 0.0845/0.1115

L. Righi et al. / Acta Materialia 56 (2008) 4529–4535 4531

dant, and the most appropriate martensitic fundamentalstructure is monoclinic with the I2/m space group (seeTable 2).

Fig. 1. Rietveld refinement of 7M incommensurate modulated structure of Ni2Mto 2h position of the second-order satellite with respect to the �121 main reflec

Table 2Atomic positions (x,y, z), ADP (Uiso), site occupancy factors (s.o.f.), andmodulated structure

Name Wych. x

Mn1 2a 0Ga1 2d 0Mn2 2d 0Ni1 4h ½Modulation function parameters A1 0.090(1)

A2 0.003(1)

Alongside the main reflections, additional peaks indicat-ing the presence of structural modulation are observed(Fig. 1). Commonly, the 7M modulation is representedby a superstructure with seven adjacent unit cells alongone of the crystallographic axes. The structural modulationwas assumed to be commensurate, and the correspondingmodulation vector q was sought from the observed 2hangular positions of satellites. In the commensurate case,the q vector should be, in the monoclinic reference, 2/7a*

or alternatively 2/7c*. This alternative was found not tobe the case, because either of these two options is appropri-ate for indexing the diffraction pattern.

Different authors have suggested that 7M martensitemight show incommensurate modulation. Both single crys-tal [12] and powder XRD [19] investigations have revealed,in Mn-rich compositions, some displacement of satellitesfrom their positions, corresponding to perfect periodic7M modulation. Taking this information as reliable, theauthors considered the structural distortion incommensu-rate and applied the same procedure adopted for the solu-tion of Ni2MnGa martensitic structure [10]. Hence, thesuperspace theory suitably formulated by Janssen and Jan-ner [20] was introduced to solve incommensurately modu-lated structures.

First, the q vector is taken as roughly 2/7c*, correspond-ing to the resultant calculated satellites closest to thoseobserved. The symmetry of the system is supposed to be

n1.2Ga0.8 martensitic phase. The arrow indicates the bump correspondingtion.

first- and second-order amplitudes Ai of the Ni2Mn1.2Ga0.8 martensitic

y z s.o.f. Uiso

0 0 1 0.018(6)½ 0 0.72(4) 0.022(9)½ 0 0.28(4) 0.022(9)1=4 0 1 0.017(7)0 0.033(1)0 �0.002(2)

4532 L. Righi et al. / Acta Materialia 56 (2008) 4529–4535

described by the superspace group I2/m(a0c)00. Followingthe procedure reported by Martinov and Kokorin [6], themodulation function is defined by the expansion

uið�x4Þ ¼X3

n¼1

Ani sinð2pn�x4Þ ð3:2Þ

where ui represents the spatial i component of the modula-tion function, which depends on the additional x4 super-space coordinate, and the n index indicates the order ofthe Fourier series.

To determine the components Ani of the modulation

function, the following assumptions were made:

(1) The lattice modulation in NiMnGa martensitic alloysis related to the shuffling of atomic layers along the[00 1] crystallographic direction of monoclinic setting[4,5]. Therefore, it was imposed that the y componentof the modulation function for all the atomic siteswas zero.

(2) Because the modulation involves the periodic trans-versal shift of the (00 l) atomic layers, the An

i ampli-tudes are constrained to assume the same value forall the atomic sites. This procedure is also supportedby previous results concerning the determination ofincommensurate and commensurate modulated‘‘5M” structures [10]. In this way, the number ofrefined parameters is considerably reduced.

Starting from this (3 + 1)-dimensional model, a structuralrefinement was performed by the Rietveld method (Fig.1) on the PXRD data collected as illustrated in Section 2.

The first important result concerns the modulation vec-tor q with, in the present monoclinic symmetry, compo-nents (a and c in the superspace symbol, see Table 1)along the a* and c* vectors of reciprocal space. Bothparameters were refined, and the resulting vector isq = �0.003a* + 0.3087c*. As a is very close to zero, thisparameter was neglected, and only the c* component ofthe q vector was considered. The c variable significantly dif-fers from 2/7, so the Rietveld refinement confirms that thismodulated structure is not commensurate with a sevenfoldsuperstructure.

The full profile refinement presented some difficultiesrelated to the particular microstructure characterizing suchmartensitic phase. Anisotropic broadening of the peak pro-file related to an hkl dependence of full width at half max-imum (FWHM) was recovered. Reflections with largerFWHM are associated with lattice planes, which are lar-gely distorted during martensitic transition. In particular,a bump corresponding to the 2h position related to thefirst-order satellite of �121 reflection is observed (see Fig.1), indicating, for this specific crystallographic direction,a strong structural disorder. The occurrence of anisotropicbroadening is always associated with the microstructure ofthe sample under investigation. In order to fit the diffrac-tion pattern of Ni2Mn1.2Ga0.8 martensite, it is necessaryto adopt a peak profile function which is able to reproduce

the strain effect. Application of the phenomenological Ste-phens’s function [21] expressly intended for this purposeand implemented into JANA2000 software [18] consider-ably improved the profile fitting.

The crystallographic data related to the final conver-gence of the structural refinement are shown in Table 1.To define the composition of the off-stoichiometricNiMnGa alloy, the occupancy factors of the differentatomic sites were refined. As expected, an excess of Mnwas found in the Ga site, but the amount of Mn obtainedis slightly higher with respect to the nominal composition,and the calculated formula is actually Ni2Mn1.28Ga0.72.This result is in agreement with EDX analysis which con-firmed a composition closely related to the nominal one.Furthermore, the Rietveld refinement involved the firstand second-order of modulation function, whose final val-ues of An

i amplitudes are reported in Table 2.A polycrystalline sample with nominal composition

Ni2.15Mn0.85Ga was also investigated by PND. A first-stepanalysis of the room temperature diffraction data was per-formed, resulting in the determination of the fundamentalstructural characteristics of this second 7M martensiticphase shown in Table 1. Despite this, the analysis was hin-dered by difficulties related to simultaneous nuclear andmagnetic scattering, the most important result was thevalue of the modulation vector which appeared to be verysimilar to that found for Mn-rich 7M martensite (Table 1).Thus, the 7M martensitic phase in Ni-rich alloy composi-tion studied in this work is also incommensurate. Concern-ing the nuclear structure, the Rietveld refinement indicatesa modulation function with the same characteristics(smoothed zigzag shape) found for the first structure.

4. Structural analysis

This section is dedicated to the crystal structure analysisin comparison with the models previously proposed toexplain the structural characteristic of the 7M martensiticphase.

The values of A1i and A2

i parameters shown in Table 2 evi-dence that the major atomic displacement from the basicpositions corresponds to the x-coordinate. Fig. 2 shows agraphical representation of the modulation function super-imposed onto a two-dimensional projection (with y = 0.5and z = 0) of the fourth-dimensional Fourier map calcu-lated on the basis of the observed structure factors Fobs.The modulation function, which is in a good agreementwith the observed electron density, is more similar to a zig-zag chain than to a perfect sinusoidal modulation character-izing ‘‘5M” martensitic structures [11]. Conversely, thestructural determination indicates that the present 7M mod-ulation is not commensurate with a sevenfold superstruc-ture and, consequently, the simple (5,�2)2 sequence cannotbe applied to the present crystal structure. The interatomicdistances (see Supplementary material) are in agreementwith the typical bond lengths encountered in such a typeof intermetallic compounds. The distances are also consis-

Fig. 2. A3–A4 Fourier map representing a two-dimensional section ofelectron density function along the x4-axis, while considering y andz-components to be constant, in comparison with the modulation functiondepicted by a solid black curve.

L. Righi et al. / Acta Materialia 56 (2008) 4529–4535 4533

tent with those recently obtained by extended X-ray absorp-tion fine structure measurements of the off-stoichiometricNiMnGa martensitic phases [22].

In 2002, Brown et al. [23] suggested a structural model,based on PND, for the Ni2MnGa martensitic phase. Thisstructure is based on a sevenfold superstructure and iscalled 7M by the authors, but, as discussed in Ref. [10], thisindication generated confusion. In defining modulatedmartensitic Ni–Mn–Ga phases, it is important to keep inmind the number of satellites appearing between mainreflections. Because Ni2MnGa martensite generates fourand not six satellites, it has been more properly classifiedas 5M incommensurate [10]. The new incommensurate7M crystal structure confirms this formulation and demon-strates that 7M modulation assumes completely differentstructural features with respect Ni2MnGa martensite.

Fig. 3. View of the tenfold superstructure along the b-axis. The numbe

In order to illustrate in a simple way the structural char-acteristics of the incommensurate ‘‘7M” martensite, con-sider the modulation vector q approximately equal to 3/10c*. With this assumption, it is possible to generate a sim-ple 3D model from a (3 + 1)-dimensional structure. It isimportant to bear in mind that this model is an approxima-tion of the real incommensurate structure. If one refines thestructure by taking the q vector exactly equal to 3/10c*, onewould observe a slight shift (0.1� of 2h) of calculated satel-lites. However, the diffraction pattern corresponding to thissuperstructure is characterized by six satellites. This isshown in Fig. 4, where the [h0�2]* row of the calculatedreciprocal space reflects the typical peak sequence associ-ated with 7M modulation [12], confirming the correctnessof the proposed crystal structure.

The new three-dimensional structure, consisting of 10unit cells along the c-axis, belongs to the monoclinic spacegroup P2/m with unit cell parameters a = 4.267 A, b =5.507 A, c = 10*cm = 42.223 A and b = 93.3�. Each atomtype, Ni, Mn and Ga, possesses 11 independent atomicsites (for fractional coordinates, see the Supplementarymaterial). The zigzag-like displacement of the (00 l) layersis clearly visible in the b projection of the present modelshown in Fig. 3. This three-dimensional representationreveals that the periodic shifting of the atomic planes isnot related to ideal zigzag behaviour with a sudden changein the shear direction, but it is rather smoothed. This par-ticular characteristic was also referred to in a structuralstudy devoted to the incommensurate seven-layered struc-ture of the Ni–Al martensitic phase [24]. During analysisof different models with intent to establish the best solutionfor the observed intensities, the authors indicated a ‘‘soft”modulation function, very similar to that determined in thepresent work, as the most appropriate.

However, if the historical Zhdanov’s notation is appliedto this crystal structure, note that the incommensuratemodulation breaks down the ideal periodic stacking(5,�2)2. In the present case, the sequence comprising the ten-fold superstructure is (4�25�24�3) for a total of 20 layers, asschematically shown in Fig. 3.

The actual structure is compared with the earlier struc-tural model supported by HREM investigations on sam-ples with Mn-rich composition [9,15]. The classical (5,�2)2

stacking was interpreted by Pons et al. [5,15] by a sequence

rs on the top of the picture refer to Zhdanov’s sequence of blocks.

4534 L. Righi et al. / Acta Materialia 56 (2008) 4529–4535

of nano-twinned domains (the two blocks with two and fiveatomic planes, respectively) correlated by mirror planes.This original interpretation has been introduced by Kha-chaturyan et al. [25], where a Ni–Al 7M monoclinic mar-tensite was treated as a nano-twinned adaptive phase.

Martensitic transformation is a diffusionless processinvolving large strains. Alongside the invariant plane, inaddition to the Bain strain generating the martensitic lat-tice, a further invariant lattice deformation process involv-ing multivariant twinning takes place [25]. Khachaturyanet al. also extended these processes to the interpretationof the modulated martensitic structures characterizing dif-ferent alloys. In particular for 7M modulation, in order topreserve the structural constraint of the invariant planestrain, the mesoscale martensitic twinning develops intoan adaptive ‘‘nanostructure” where the size of the individ-ual twin variants is comparable with interatomic distances.This interpretation was favoured by the classical (5,�2)2

expansion of the periodic stacking of the crystallographicplanes. The 7M crystal structure determined in the presentstudy suggests further considerations. The monoclinic dis-

Fig. 4. Calculated diffraction pattern based on the tenfold superstructurealong the [h0�2]* row, where the typical sequence of six satellites (three ofthem are related to 20�2; the other three to 40�2 main reflections) is clearlyvisible. The 20�2 intensity has been cut in order to magnify the satellites.

Fig. 5. View of ten adjacent unit cells of the monoclinic basic structure. The total shear of (00 l) atomic planes is evidenced by the dashed line.

tortion, showing a b angle of �93�, implies a systematicshift of the (00 l) planes (see Fig. 5). After ten unit cells,a total shear of �1/2a is noted. The 7M structural modula-tion can therefore be considered a further distortion, whichtends to oppose the progressive layer displacement. Thismechanism possesses many analogies with the latticeinvariant deformation provoking the ‘‘tweed” martensiticmicrostructure. In general, the microstructural propertiesof a material cannot be directly related to the intrinsic crys-tal structure. In the special case of martensite, crystal struc-ture and microstructure are mutually related (see, e.g., Ref.[26]).

5. Concluding remarks

For the first time, a Ni–Mn–Ga 7M modulated struc-ture has been solved by XRD analysis. The crystalstructure presented in this work represents the first crys-tallographic model of this type of modulated Ni–Mn–Ga martensitic phase provided by a structural refinement.Several new insights emerge from the determination of the7M crystal structure found for Ni2Mn1.2Ga0.8 martensitestable at room temperature. The modulation is not com-mensurate with a sevenfold superstructure but, on thecontrary, is incommensurate. The structure solution wasachieved by adopting the superspace theory, as is alreadysuccessfully done for Ni2MnGa martensite [10,11]. Thefirst-step results concerning the structure determinationof Ni2.15Mn0.85Ga martensite by PDN reveal a completecorrespondence of the modulated structure of Ni-richwith respect to Mn-rich martensite, indicating that, inde-pendently from the composition, for polycrystallinesamples the 7M structure seems to be always incommen-surate. It is therefore necessary to remark that the 7Mnotation is not adequate to represent correctly the typeof modulated structure characterized by six satellitesbetween the main reflections. For this reason, the notation‘‘7M”(IC) is introduced, indicating the ‘‘family” of themodulated structure and the incommensurateness of theperiodic length. This new notation follows from whathas already been affirmed for incommensurate Ni2MnGamartensitic structure, known as ‘‘5M”(IC).

L. Righi et al. / Acta Materialia 56 (2008) 4529–4535 4535

Acknowledgements

The authors are grateful to the Institute Laue-Langevin(Grenoble, France) for providing technical and financialsupport. VAC is grateful to Fondazione Cariplo (Project2004.1819-A10.9251) for financial support.

Appendix A. Supplementary material

Supplementary data associated with this article can be found,in the online version, at doi:10.1016/j.actamat.2008. 05.010.

References

[1] Chernenko VA, Besseghini S. Sensor Actuat A 2008;142:42.[2] Ullakko K, Huang JK, Kantner C, O’Handley RC, Kokorin VV.

Appl Phys Lett 1996;69:1966.[3] Albertini F, Kamara J, Arnoldb Z, Pareti L, Villa E, Righi L. J Magn

Magn Mater 2007;316:304.[4] Albertini F, Paoluzi A, Pareti L, Solzi M, Righi L, Villa E, et al. J

Appl Phys 2006;100:023908.[5] Pons J, Chernenko VA, Santamarta R, Cesari E. Acta Mater

2000;48:3027.[6] Martynov VV, Kokorin VV. J de Phys III 1992;2:739.[7] Sozinov A, Likhachev AA, Ullakko K. IEEE Trans Magn

2002;38:2814.[8] Mullner P, Ullakko K. Phys Status Solidi B 1998;208:R1.[9] Pons J, Santamarta R, Chernenko VA, Cesari E. J Appl Phys

2005;97:083516.

[10] Righi L, Albertini F, Calestani G, Pareti L, Paoluzi A, Ritter C, et al.J Solid State Chem 2006;179:3525.

[11] Righi L, Albertini F, Pareti L, Paoluzi A, Calestani G. Acta Mater2007;55:5237.

[12] Sozinov A, Likhachev AA, Lanska N, Ullakko K. Appl Phys Lett2002;80:1746.

[13] Gaizsch U, Potschke M, Roth S, Mattern N, Rellinghaus B, SchultzL. J Alloy Compd 2007;443:99.

[14] Jiang C, Muhammad Y, Deng L, Wu W, Xu H. Acta Mater2004;52:2779.

[15] Pons J, Santamarta R, Chernenko VA, Cesari E. Mater Sci Eng A2006;438–440:931.

[16] Morito S, Otsuka K. Mater Sci Eng A 1996;208:47.[17] Shapiro SM, Yang BX, Shirane G, Noda Y, Tanner LE. Phys Rev

Lett 1989;62:1298.[18] Petrıcek V, Dusek M. Jana 2000. The crystallographic computing

system. Praha: Institute of Physics; 2000.[19] Ge Y, Soderberg O, Lanska N, Sozinov A, Ullakko K, Lindroos VK.

J Phys IV France 2003;112:921.[20] Janssen T, Janner A, Looijenga A, Wolff PM. International tables for

crystallography, vol. C. Kluwer: Dordrecht; 1992 [Section 9.8].[21] Stephens PW. J Appl Cryst 1999;32:281.[22] Bhobe PA, Priolkar KR, Sarode PR. Phys Rev B 2006;74:

224425.[23] Brown PJ, Crangle PJ, Kanomata J, Matsumoto TM, Neumann KU,

Ouladdiaf B, et al. J Phys Condens Mat 2002;14:10159.[24] Noda Y, Shapiro SM, Shirane G, Yamada Y, Tanner LE. Phys Rev B

1990;42:10397.[25] Khachaturyan AG, Shapiro SM, Semenovskaya S. Phys Rev B

1991;43:10832.[26] Wayman CM. Metall Mater Trans A 1994;25A:1787.