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Acta Materialia 74 (2014) 66–84

The effect of heat treatments on Ni43Mn42Co4Sn11 meta-magneticshape memory alloys for magnetic refrigeration

Nickolaus M. Bruno a, Cengiz Yegin b, Ibrahim Karaman a,b,⇑, Jing-Han Chen c,Joseph H. Ross Jr. b,c, Jian Liu d, Jianguo Li e

a Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USAb Department of Materials Science and Engineering, Texas A&M University, College Station, TX 77843, USA

c Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843, USAd Key Laboratory of Magnetic Materials and Devices, Ningbo Institute of Material Technology and Engineering, Chinese

Academy of Sciences, Ningbo 315201, Chinae School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Received 21 December 2013; received in revised form 5 March 2014; accepted 6 March 2014Available online 8 May 2014

Abstract

The inverse magnetocaloric effect (MCE) in bulk polycrystalline and melt-spun ribbons of the Ni43Mn42Co4Sn11 meta-magnetic shapememory alloy (MSMA) is investigated. The influence of several material properties on the MCE and relative cooling power (RCP) arediscussed and the property combinations for optimum MCE and RCP identified for a given thermodynamic framework. These include asmall slope of magnetic field vs. martensitic transformation temperature phase diagram, a narrow transformation range, low transfor-mation thermal hysteresis and a large change in magnetization on martensitic transformation, which results in low levels of appliedmagnetic fields desired for repeated MCE on field cycling. The thermo-magnetic responses of the samples were measured before and afterheat treatments. The heat-treated ribbons produced the most favorable MCE by exhibiting the highest magnetization change and small-est elastic energy storage through the transformation. This was attributed to the specific microstructural features, including grain size tothickness ratio and degree of L21 ordering. In addition, issues in the literature in determining RCP for MSMAs are discussed, and a newmethod to find RCP is proposed and implemented. Completely reversible magnetic-field-induced martensitic transformation cycles wereused to investigate hysteresis losses relative to actual refrigeration cycles, whereby the RCP was calculated using the defined thermody-namic framework and indirectly measured entropy changes. The annealed ribbons exhibited the high RCP level of 242 J kg�1 under theapplied field of 7 T compared with a theoretical maximum of 343 J kg�1. Similar values of RCP in other MSMAs can be achievable ifmicrostructural elastic energy storage and hysteresis loss are minimized during the transformation with the help of annealing treatments.� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Magnetocaloric effect; Magnetic refrigeration; Magnetic entropy change; Magnetic shape memory alloys; Relative cooling power

1. Introduction

Over the last decade, there has been increased interest inthe thermal behavior of Heusler-type meta-magnetic shapememory alloys (MSMAs) because of their potential for dem-

http://dx.doi.org/10.1016/j.actamat.2014.03.020

1359-6454/� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights r

⇑ Corresponding author at: Department of Materials Science andEngineering, Texas A&M University, College Station, TX 77843, USA.

E-mail address: ikaraman@tamu.edu (I. Karaman).

onstrating a giant magnetocaloric effect (MCE). These mate-rials offer a viable solution for environmentally friendlyrefrigeration, as their magnetic response may be tailored toprovide relative cooling powers (RCP) comparable to thoseof expensive rare-earth-containing MCE materials. Giantisothermal entropy, or adiabatic temperature, changes asso-ciated with MCE have been measured for a variety ofMSMAs such as Ni–Mn–X (X = In, Sn, Sb) [1,2].

eserved.

N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84 67

MSMAs exhibit a change in magnetic order near a first-order structural phase (martensitic) transformation [3,4].Often, the material changes from low temperature martens-ite, which exhibits small magnetic susceptibility, to a ferro-magnetic (FM) austenite, resulting in the so-called inverseMCE, with the application of a magnetic field when thematerial is in its martensitic state. Conventional MCE ischaracterized by the cooling of a sample during the unload-ing of a magnetic field, while in common MSMAs, coolingoccurs on the field loading on martensite and thereby sta-bilizing austenite.

MSMAs can be modified using simple heat treatmentsand conventional fabrication methods to control latticeparameters, atomic ordering and microstructure, resultingin various Curie temperatures, martensitic transformation(MT) temperatures, transformation hysteresis and mag-netic responses across MT, affecting refrigeration perfor-mance parameters [5–12]. Heat treatments were reportedto change atomic ordering, resulting in large changes inmagnetic response [13–15] due to variations in Mn–Mnspacing and magnetic spin interactions [16]. Wu et al. [9]showed that the magnetic responses in Ni50Mn37Sn13 rib-bons differed between samples solutionized at 1273 K for15 min and those solutionized for 4 h. The increase in mag-netization resulting from the shorter annealing treatmentwas attributed to Mn ordering corresponding to anincrease in the L21 order parameter. However, an increasein magnetization difference across MT has been reportedfor increasing B2 disorder (decreasing L21 order) [17] inNiMnIn systems. Clearly, the type of ternary addition inNi–Mn systems plays a major role in the influence ofatomic ordering on the magnetic response of thesematerials.

Most studies aimed at quantifying the MCE in MSMAshave focused on entropy changes related to magnetizationincreases across MT [1–10,13–18]. However, most of themhave not properly identified other key parameters thatshould play a role in dictating how well MSMAs wouldperform as refrigerants or explained how manipulatingthe material’s microstructure will affect refrigeration cycles,as is attempted in the present work. The key performanceparameters studied here include the entropy change acrossMT, the RCP, calculated using a simplified method devel-oped specifically for MSMAs, and the magnetic fieldsrequired to induce and complete the MT. Furthermore, aclear distinction between the proper analysis that shouldbe conducted to quantify the MCE in MSMAs and thatwhich is typically conducted using archaic conventionalmethods for non-SMAs without significant hysteresis [19]has been made. Improper analysis poses problems in ana-lyzing MSMAs, especially when determining the RCP.

The RCP is useful for comparing MSMA refrigerantsand conventional MCE materials, when used properly.The RCP is a metric used for quantifying the maximumthermal energy that can be transferred between hot andcold reservoirs under application of a given external mag-netic field [19]. Since some conventional MCE materials

are capable of producing nearly reversible refrigerationcycles around their Curie point [20], the comparable RCPvalues in MSMAs can only be determined accurately whenproper operating temperatures are defined and the thermo-dynamic irreversibility from transformation hysteresis isdetermined and subtracted from the apparent RCP values.

Thus, in the present work, a thermodynamic cycle forthe inverse MCE in MSMA is defined and used to showhow the RCP is quantified using simple magneto-thermalexperimental loading paths. In addition, the influence ofthe types of experimental protocols [21] on reported RCPvalues is investigated, and it is shown how these affectthe RCP measurements for MSMAs, which arises fromthe effect of the transformation hysteresis on thesemeasurements.

Furthermore, the influence of the microstructuralchanges on MCE and RCP in Ni43Mn42Co4Sn11 was stud-ied in bulk and melt-spun ribbon samples after heat treat-ments near the reported order–disorder transition (920 K)[9]. A homogeneous microstructure was achieved in solu-tion heat-treated (SHT) ribbon samples, which resulted inlow thermal hysteresis, small transformation ranges andlarge magnetization changes across MT. These materialcharacteristics were further improved with secondary heattreatments, which in turn enhanced the refrigeration per-formance parameters. The peak entropy change valuesreported here for the present composition are greater thanthose reported for NiMnCoIn alloys in the literature [13].

The RCP for selected heat treatment cases was deter-mined using the thermodynamic framework developedhere, where the entropy change vs. temperature (DS � T)diagrams were used to aid understanding. The appliedfields below and above those capable of inducing a com-plete isothermal MT were determined, thus permittingthe thermodynamic irreversibility to be subtracted easilyfrom the apparent RCP values. The influence of micro-structural factors and structural transformation character-istics, such as the transformation range and thermalhysteresis, on the refrigeration performance parameters isdiscussed in detail.

2. Determination of performance parameters for the inverse

MCE in MSMAs

In general, the focus of MCE studies on MSMAs hasbeen to determine magnetic field-induced temperaturechange or indirectly measured entropy change. However,these are not the only parameters that define the perfor-mance of MSMA refrigerants. Other important perfor-mance and critical materials parameters include the RCP,which is a fundamental property indicative of how muchuseful work can theoretically be performed by the refriger-ant within some operating temperature range, the magneticfield required to induce, or complete, MT at a given tem-perature, MT characteristics such as transformation rangeand hysteresis and, ultimately, the sample microstructurethat governs some of the aforementioned parameters.

68 N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84

To illustrate the importance of each of these parameters, asimple MCE refrigeration cycle is outlined in Fig. 1.

2.1. Example Brayton cycle for MCE in MSMAs

Fig. 1 demonstrates the idealized entropy vs. tempera-ture (S–T) diagrams around a first-order thermoelasticmartensitic transformation on cooling and subsequentheating, with (blue curve) and without (green curve) anapplied magnetic field H. The S–T curve shifts to lowertemperatures on application of the field. The field reducesthe transformation temperatures of the MSMA and stabi-lizes the austenite where the austenite is FM, and the mag-netic ordering of martensite is defined by short-rangefrustrated anti-ferromagnetism [22,23]. For the sake of sim-plicity and ease of understanding the thermodynamic cycle,these idealized responses neglect the contribution of mag-netic entropy to the total entropy in austenite and martens-ite phase regions, and thus the conventional MCE behaviorof martensite and austenite phases. In addition, the dia-grams assume that the difference between the martensitestart Ms and martensite finish Mf temperatures is equiva-lent to the difference between the austenite finish Af andaustenite start As temperatures. The difference betweenstart and finish temperatures is commonly known as thetransformation range and, for the rest of the paper, theaverage of the transformation ranges (for forward andreverse MT) is defined as DT elas ¼ ½ðAf � AsÞþ

Fig. 1. Example MCE Brayton cycle discussed in the text. The sample starts un(region 2) and cools the sample to point 3. The sample absorbs energy to poinrefrigerated volume and adiabatic demagnetization occurs in region 5 to pointregion indicates the work performed by the Brayton cycle. The schematics undeor region.

ðMs �Mf Þ�=2. The transformation range is controlled bymicrostructurally stored elastic energy, and therefore thetransformation range is denoted by the subscript “elas”.

As shown in Fig. 1, the MSMA initially begins thedepicted Brayton cycle [24] at Mf (point 1 in the figure),or the hot reservoir of the cycle Thot. The schematicsunder the S–T plot in Fig. 1 represent microstructures ofthe material at specified points or regions in the S–T

diagram. Upon the field application Hadcomp, sufficient to

induce a complete adiabatic reverse MT at Mf

(M : Martensite! A : Austenite), the sample exhibitsendothermic behavior and cools to Tcold (point 3) if insu-lated from external heat sources. This temperature changeis shown in the figure by the line Thot! Tcold (region 2)and is directly related to the transformation entropychange. Next, the sample is exposed to the refrigerated vol-ume and allowed to absorb energy, thus heating the samplecomposed of field-induced austenite (see Tcold! Trefrigerator,point 4 in the figure). The sample is then removed from therefrigerated volume, and the field is released under insu-lated conditions, warming up the sample because of theforward MT (A!M), which is an exothermic process(Trefrigerator! Tend, region 5). At this point (point 6 inthe figure), the sample is exposed to ambient temperatureand releases heat from the temperature Tend to Thot, return-ing the sample to a temperature 6Mf, which allows theprocess to be repeated. As shown on the abscissa inFig. 1, the operating temperatures that define the Brayton

der zero magnetic field at Mf at point 1. An applied field nucleates austenitet 4 within the refrigerated volume. The sample is then removed from the6. At point 6, the sample is allowed to cool to Mf from Tend. The hatchedrneath the S–T plot show the representative microstructure at a given point

N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84 69

cycle are T hot 6 Mf and Tcold = Thot � DTad, where Tcold isthe temperature that is achieved as a result of adiabaticmagnetization of the sample, and DTad is the adiabatictemperature change on the field application (is DT max

ad ifthe transformation is complete [25]).

As discussed in Ref. [19], the maximum work that can beperformed by a magnetic refrigerant (RCP) has beendefined in the past for non-SMA materials as the integralof the entropy change DS across the operating temperature

range, orR T hot

T coldDSdT, where Thot and Tcold correspond to

the operating temperature limits. However, using the Bray-ton cycle in Fig. 1, the maximum amount of work that canbe performed by the MSMA is represented by the hatchedregion. Clearly, the Brayton cycle offers less work than thematerial is theoretically capable of performing, and thecycle is limited (bound) by the martensitic transformationtemperatures.

MSMAs should theoretically be able to perform morework than that specified by the Brayton cycle in Fig. 1. Thisis illustrated in Fig. 2 for a given applied magnetic fieldcapable of inducing a complete adiabatic structural trans-

formation, Hadcomp. The theoretical maximum work, the

RCP, that a MSMA can perform is independent of thermo-dynamic cycles and is defined as the area of the shadedregion in the DS vs. T plot in Fig. 2b. However, it is limitedby the transformation temperatures. Fig. 2b is constructedbased on the ideal S–T diagrams shown in Fig. 2a: at a given

Fig. 2. (a) Entropy vs. temperature plot for a MSMA under zero andH ad

comp magnetic fields near the thermoelastic transformation. (b) Entropychange vs. temperature plot where the shaded region indicates RCP. Therectangular shaded region between MH¼0

f and AH¼Had

comp

f indicate the RCP inthe temperature range where the total entropy change is reversible. Theareas of the transformation hysteresis indicate the operating temperatureranges where the forward and reverse entropy changes during isothermalmagnetization experiments are not the same, and are therefore cyclicallyirreversible.

temperature, DS ¼ SAustenite at H¼Hadcomp� SMartensite at H¼0, where

SMartensite at H¼0 is the entropy of martensite at H = 0, which

fully transforms to austenite under H ¼ H adcomp, and

SAustenite at H¼Hadcomp is the entropy of the austenite under

H ¼ Hadcomp, which transforms back to martensite under

H = 0. The temperatures limiting the shaded region wereextended down from Fig. 2a, and areas of thermal transfor-mation hysteresis, i.e. two-phase regions, were not consid-ered to contribute to reversible work on field cycling.

It is clear from Fig. 2b that the transformation temper-atures and DS dictate the size of the shaded region that isused to determine the useful work, or RCP. Upon closerinspection of Fig. 2b, the elastic transformation ranges

(AH¼Had

comp

f � AH¼Had

comps and MH¼0

s �MH¼0f ) also contribute to

the shaded region by amount DS � DTelas, but these operat-ing temperatures can only be accessed if special thermody-namic processes are used that allow martensite to form atthe start of each cycle. In addition, it can be seen that,

within the operating temperature range of MH¼0f and

AH¼Had

comp

f , the maximum entropy change of the MSMA

can be achieved, and thus is capable of contributing tothe RCP by the amount DS � DT max

ad . For the Brayton cycleabove, only part of this value was captured, and it isbelieved that special thermodynamic cycles, possiblyinvolving mechanical stress or regenerative cycles, can beused to access the entire theoretical values.

The example cycle in Fig. 1 and depiction of RCP inFig. 2 clearly indicate the importance of studying the crit-ical materials parameters mentioned above. It is shown inFig. 2 that a large RCP can be achieved if samples exhibitlarge adiabatic temperature changes, have large entropychanges across transformation, and have broad elastictransformation ranges. However, it will be shown later thatdecreasing the transformation ranges with annealing treat-

ments affects the difference between MH¼0f and A

H¼Hadcomp

f in

Fig. 2, and thus presents the possibility of increasing thesize of the shaded region and RCP. In addition, small elas-

tic transformation ranges decrease Hadcomp and improve

refrigeration performance. The following sections definehow to calculate each performance parameter.

2.2. Calculating the magnetic field-induced entropy change

The first performance parameter that should be definedis the entropy change across MT. Traditionally, this valueis measured indirectly using an integral form of the Max-well relation linking experimental magnetic responses toentropy changes. This method has been used to quantifysecond-order magnetic entropy changes for most non-SMA MCE materials [19], and has been adopted by theSMA community to quantify entropy changes across thefirst-order MT. However, owing to the singular behaviorof a first-order phase transformation, using derivatives tocalculate entropy changes from the differential form of

70 N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84

the Maxwell relation may result in large discrepancies [20].Maxwell relations are derived from a single energy poten-tial, but SMAs have free energy equivalence in two phases,namely martensite and austenite, and thus require theequivalence of two free energy potentials. This manifestsas the Clausius–Clapeyron (CC) relation, which looks verysimilar to the Maxwell relation. These two relations areoften used interchangeably, but this is not valid.

Here, the magnetic field-induced entropy changes arecalculated from the experimental isothermal magnetizationresponses following two experimental schemes, namely, thecontinuous and discontinuous heating protocols [21,25],using the traditional integral form of the CC relation inEq. (1) and determine how each protocol affects the con-structed DS � T diagram like that shown in Fig. 2. Entropychanges determined from the continuous heating scheme(whereby the sample temperature is increased a constantamount between the isothermal magnetization measure-ments) are denoted as the effective entropy changes, DSeff,and those predicted from the discontinuous heating(whereby the sample is cooled between each magnetizationmeasurement below Mf [25]) are simply denoted as theentropy change, DS. To populate the DS � T diagram, likethat shown in Fig. 2b, the magnetostatic energy density orarea under M vs. H curves (Fig. 3) was found at discretetemperatures, and then DS was calculated using

DSðT K ; 0! HÞ ¼ 1

DT k

Z H

0

MT kþ1dH �

Z H

0

MT k dH� �

ð1Þ

where Tk+1 and Tk are test temperatures, Tk+1 > Tk,DTk = (Tk+1 � Tk) and TK = (Tk+1 + Tk)/2. According toEq. (1), the entropy change caused by the field-inducedtransformation can be quantified by finding the differencein the magnetostatic energy density between two differentmagnetic responses at different temperatures (with smalltemperature increments), divided by the temperature incre-ment [19]. A schematic representation of how to determineDS is shown in Fig. 3.

Fig. 3 depicts the isothermal magnetic response (M–H)of a MSMA during field-induced M! A transformationat five different temperatures, T1, Mf, As, T2 and T3. Here,T1 < Mf < As < T2 < T3 and, as the sample resides at hottertemperatures, the FM austenite phase is more stable, thus

Fig. 3. Example magnetic response of the reverse magnetic field-inducedmartensitic transformation for the discontinuous heating protocol attemperatures T1 < Mf < As < T2 < T3.

requiring less magnetic field to transform the sample frommartensite to austenite, as indicated by Hreq. The entropychange is then quantified by finding the area (hatchedregions) between two reverse MT M–H curves and dividingby the temperature increment responsible for the change(see area ‘A’). Area ‘A’ in Fig. 3 is related to a single pointin Fig. 2b below the Mf temperature. Clearly, if the mag-netic field is not ramped to a level high enough to inducecomplete transformation, the total transformation entropycannot be determined easily.

Fig. 3 also demonstrates the magnetic responses ofMSMAs when their initial microstructural state is mixed,i.e. containing both martensite and austenite phases, shownby the curves labeled T2 and T3. It can be seen from the M–H curves labeled T2 and T3 that, when the material is at atemperature in the two-phase region, small temperaturechanges may result in predicted entropy changes (shadedregions) at magnetic fields smaller than Hreq (see area Bfor small fields), which should not be confused with trans-formation entropy change.

The continuous heating protocol used to find magneti-zation curves like that in Fig. 3 is defined by heating thesample through small increments after loading and unload-ing the magnetic field. Thus, some of the austenite thatforms on field loading may still be present in the micro-structure after field unloading, especially if the temperatureis > MH¼0

f . Owing to the mixed microstructure, the M–H

area measured from the differences in magnetostatic energydensity is larger in regions of small applied field similar tothose labeled T2 and T3 in Fig. 3 and yields incorrect valuesfor entropy change related to the magnetic field-inducedphase change. Therefore, the continuous heating protocolover-predicts entropy changes and RCP, as discussed insubsequent sections.

In the discontinuous heating protocol, in contrast, anextra step is added to cool the sample below Mf after thefield is ramped [25]. Ultimately, this results in magneticresponses like those shown by T1, Mf and As in Fig. 3,and little to no entropy contribution is captured at mag-netic fields smaller than that required to transform theMSMA below As. The entropy change captured from thediscontinuous heating protocol is nearly representative ofthe transformation entropy change comparable to thatmeasured with differential scanning calorimetry (DSC) asdiscussed in Section 5.

2.3. Calculating the RCP of MSMAs

Once the DS � T diagrams are constructed for a givenmaterial, the RCP is calculated as the area of the shadedregion in Fig. 2b. The RCP is dependent not only on mag-netic field, but also on the martensitic transformation tem-peratures and its maximum is defined here as

RCPmaxðH ;T Þ¼DS �DT maxad þDS �DT elas�

Sirr

2�ðDT max

ad þDT elasÞ

ð2Þ

Fig. 4. Schematic of M–H response of a MSMA. The adiabatic conditionsshown in Fig. 1 result in a larger required magnetic field to induce acomplete transformation.

N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84 71

where DT maxad is the maximum adiabatic temperature change,

DT elas is the average of the forward and reverse elastic trans-formation ranges mentioned earlier, and Sirr � ðDT max

ad þDT elasÞ is the thermodynamic loss on the forward and reversephase front motion associated with the transformationhysteresis. It is important to include this entropy productionto avoid violating the second law of thermodynamics asdefined by the Clausius inequality [2,26].

Compared with the conventional method of calculatingRCP, or

R T hot

T coldDSdT from Ref. [19], the present authors

have added terms to include work obtained within the elas-tic transformation ranges, losses due to transformationhysteresis, and have set limitations on Thot and Tcold tocorrespond to the MT temperatures. Note that the adia-batic temperature change can be approximated using thetraditional method [2,19], i.e. �DT ad � T 0DS=Cp, whereT0 is the equilibrium MT temperature [27], and Cp is theisobaric heat capacity, assumed to be independent of mag-netic field and equivalent in both austenite and martensite.

The third term in Eq. (2) approximates the coolingpower losses from the entropy production during the trans-formation process. The entropy production from the trans-formation hysteresis is approximated as the hysteresis lossdefined in Ref. [28] divided by the temperature of theisothermal magnetization tests [2] as

Sirr ¼nðHÞ � DStr � DT hys

Tð3Þ

which if n(H) = 1, approximates entropy production for acomplete transformation cycle. For magnetic fields thatinduce only partial transformation, the percentage trans-formation n(H) is 0 < n(H) < 1. In Eq. (3), Sirr can beroughly determined by multiplying the transformationentropy from DSC, DStr, by the thermal hysteresis of trans-formation DThys under zero magnetic field and dividing bythe temperature of the isothermal field-induced transfor-mation. Only half the Sirr is considered in Eq. (2) because,in the refrigeration cycle like that shown in Fig. 1, thetransformation front propagates only once during the cool-ing step (Thot! Tcold), but Sirr takes into account both for-ward and reverse phase front motion. Upon releasing themagnetic field outside the refrigerated volume, the otherhalf of frictional dissipation associated with the completetransformation is produced. This second half does notaffect how much the sample will cool on field rampingbut, as shown in Fig. 2b, the hysteresis does limit the oper-ating temperatures and thus reduces RCP. Lastly, it isimportant to note that the approximation of entropy pro-duction from the MT is assumed to be independent of rate.This, however, is not true in general, and suggests that amore accurate model must be developed in future studiesto account for the rate dependence of entropy production.

2.4. Calculating critical magnetic fields for MCE in MSMAs

The final two performance parameters that are essentialto quantify the MCE of MSMAs are the magnetic fields

required to induce and complete transformation, Hreq

and Hcomp, respectively. These parameters are dependenton the cycle in which the MSMA is to be analyzed. Theirmagnitude is dependent on the MT temperatures. Definingthermal hysteresis as DThys = [(Af + As) � (Ms + Mf)]/2,the magnetic field required to induce the transformationwhen Thot = Mf is defined as

Hreq ¼ ðAs �Mf Þ � dH As=dT ð4Þwhere dH As=dT is the austenite start temperature’s sensitiv-ity to external magnetic field. The field required to induce acomplete structural transformation under isothermal con-ditions is defined as

Hisocomp ¼ ðDT hys þ DT elasÞ � dH Af =dT

¼ DT comp � dH Af =dT ð5Þ

where (DThys + DTelas) = DTcomp, which reduces to Af �Mf

(i.e. the difference between the Af and Thot temperatures

when Thot = Mf), and dH Af =dT is the austenite finish temper-ature’s sensitivity to the applied field. However, for the pro-cess described in Fig. 1, the magnetic field is increased anddecreased under adiabatic conditions. This implies that thelatent heat of the transformation will affect the field required

to complete transformation. H adcomp is then defined as

Hadcomp ¼ ðDT comp þ DT adÞdH Af =dT ð6Þ

where DTad is the field-dependent temperature change.Fig. 4 depicts the magnetic responses of a MSMA at dif-

ferent states in Fig. 1. The magnetic response at Mf showsthe magnetic field Hreq needed to start the transformation.If the sample is to transform under isothermal conditions,the field required to complete the transformation would bedefined by the same magnetization curve, and is labeledHiso

comp. However, the sample is insulated while the field is

applied, and an endothermic reaction occurs, as shown inFig. 1, thus the magnetic response is shifted to the right,

while the sample cools and ultimately requires H adcomp to

complete the transformation. From Figs. 1 and 4, it can

be deduced that T hot 6 Mf and T cold P AH¼Had

comp

f .

When considering that the latent heat of transformationaffects the required magnetic field to complete transforma-

72 N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84

tion, a MSMA will require the least amount of magneticfield to transform when DThys and DTelas are the smallestand the Af field sensitivity is the highest, as shown byEqs. (5) and (6). These imply that MSMAs with small

Hadcomp will have large RCP, because Sirr will be small, and

the temperature range MH¼0f ! A

H¼Hadcomp

f in Fig. 2b will

increase at the expense of the elastic transformation ranges,thus increasing the area of the shaded region. Unfortu-nately, large adiabatic temperature changes, althoughseeming to be desired at first, increase the required mag-netic field to complete transformation. This emphasizesthe need to determine heat treatments and processingtechniques that yield optimum meta-magnetic behaviorfor inverse MCE refrigeration.

Using Eqs. (4)–(6), the percentage of transformingvolume is defined (when Thot = Mf) as

nðHÞ ¼ H � H req

Hadcomp � Hreq

� 100 where Hreq < H < H adcomp ð7Þ

where H is constrained between the minimum field requiredto induce transformation and the field required to attaincomplete transformation. For H < Hreq and H > Hcomp,n(H) obviously equals 0 and 1, respectively, when consider-ing only the reverse transformation. The fraction of trans-formation can then be used to determine RCP, and Sirr

under any given field or transformed volume fraction.The thermodynamic framework discussed above sug-

gests that the entropy and magnetization changes acrossMT are not the only parameters required to quantify theMCE performance in MSMAs. The hot and cold tempera-ture reservoirs used to determine RCP are limited by thetransformation temperatures. Thot must be less than orequal to Mf in order for the refrigeration cycle to be repeat-able through fully reversible complete transformation [25].Alternatively, Thot could be a temperature between Ms andMf to use only partial phase transformation for refrigera-tion. In order to use the elastic transformation ranges forbetter RCP levels, special thermodynamic cycles need tobe implemented to capture the entire useful work regime,like that shown by the path from point 6 to point 1 inFig. 1. Therefore, processing and fabrication methods thataffect the sample microstructure and the transformationcharacteristics can be used to improve the performanceparameters for MSMAs so that they may be used as refrig-erants at maximum capacity. The following demonstrateshow simple heat treatments can change the refrigerationperformance parameters of MSMAs by modifying themicrostructure, and how the reported values for entropychange in the literature across MT can be misleading inevaluating the real refrigeration capacity of these alloys.

3. Experimental procedures

Bulk polycrystalline Ni43Mn42Co4Sn11 (at.%) alloyswere prepared using vacuum induction melting. Someinduction melted samples were then homogenized in argon

at 1173 K (above the reported L21 ordering temperature[9]) for 24 h and quenched in ice water. The melt-spun rib-bon samples were prepared by re-induction melting thebulk samples. Once melted, the alloy was ejected onto acopper wheel rotating with a surface velocity of 30 m s�1.The melt-spun ribbons were heat treated in an argon atmo-sphere at 1173 K for 2 h and then quenched in ice water.Secondary heat treatments were then conducted on theSHT ribbons. They were conducted for 1 h at 673 K,773 K and 873 K, and the ribbons were either rapidlyquenched (RQ) in water or furnace cooled (FC). All theseheat treatments were conducted below the reported B2/L21

order temperature [9].Microstructural analysis of the samples was conducted

using optical microscopy and a Cameca SX-50 electronprobe microanalyzer. Compositional analysis was per-formed using wavelength dispersive spectrometry (WDS).Thermo-magnetic measurements were carried out using aQuantum Design SQUID-VSM magnetometer at a heat-ing–cooling rate of 5 K min�1 under constant magneticfields. These measurements were used in determining MTtemperatures and transformation hysteresis. All thermo-magnetic measurements began with zero field heating to400 K, whereby the field was ramped to a constant levelafter stabilizing at 400 K. The temperature was thenreduced to 10 K, stabilized, and ramped back up to400 K. For qualitative comparison of the effect of thesecondary heat treatments, the change in magnetizationacross MT, DM, was determined from the difference ofthe magnetization levels at Af and As from the thermo-magnetization curves 0.05 T or Hreq (defined in Eq. (4)).

Isothermal M–H data were obtained using experimentalschemes referred to as continuous and discontinuous heat-ing protocols [21], as described in Section 2. The discontin-uous heating scheme was carried out as follows.

1. The samples were cooled to a temperature <Mf underzero magnetic field, resulting in a fully martensitic state.

2. The samples were then heated under zero magnetic fieldto a temperature just below the austenite start tempera-ture, without overshooting the target temperature.

3. Holding the temperature constant, the magnetic fieldwas ramped from zero to 7 T and then back down tozero at a rate of 25 Oe s�1; meanwhile, the magnetiza-tion was measured.

4. The temperature was then decreased to <Mf.5. Next, the temperature was increased to the previous

temperature plus 3 K (without overshoot), and then step3 was repeated.

6. Step 4 and 5 were repeated until the test temperaturewas very close to the austenite finish temperature.

The continuous heating protocol was conducted asfollows.

1. The samples were cooled to a temperature <Mf underzero magnetic field.

N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84 73

2. They were then heated under zero magnetic field to atemperature just below the austenite start temperature,without overshoot.

3. Holding temperature constant, the magnetic field wasramped from zero to 7 T and then back down to zeroat a rate of 25 Oe s�1, meanwhile, the magnetizationwas measured.

4. The temperature was increased by 3 K without over-shoot, and then step 3 was repeated.

5. Step 4 was repeated until the test temperature was veryclose to the austenite finish temperature.

Once the isothermal magnetization responses had beenmeasured at small temperature intervals, the forward(A!M) and reverse (M! A) paths were separated sothat Eq. (1) could be applied to construct a diagram likethat in Fig. 2b. Only the reverse transformation wasconsidered here, because the M! A transformation wasassociated with the endothermic response responsible forthe cooling, as shown in Fig. 1. In these experiments, sincethe applied field was ramped at 25 Oe s�1, the magneticresponses were considered as isothermal, because this rateis sufficiently low to prevent temperature changes fromthe latent heat of the transformation. Eventually, Eq. (1)yielded DSeff (the entropy change from the continuousheating protocol) and DS (from the discontinuous heatingprotocol) over a range of temperatures from the isothermalmagnetization curves, which then allowed RCP to be calcu-lated using Eq. (2). Isothermal magnetization measure-ments also provided information for finding the criticalfields Hiso

comp, H adcomp and Hreq using Eqs. (4)–(6).

Thermo-magnetic MT temperatures measured under0.05 T were then compared with the MT temperatures mea-sured by DSC. For DSC analysis, the temperature wasramped at 2 K min�1. In order to determine DT max

ad in Eq.(2), approximate heat capacity measurements wereconducted using a Quantum Design Physical PropertyMeasurement System (PPMS) from 10 K to 250 K by apulsed-relaxation method employing the continuous heat-ing scheme.

4. Results

This section presents the results obtained from theexperiments described in Section 3. Here, the basis forselecting the most favorable ribbons for further MCE studyis presented. Most importantly, DTelas, DThys, DTcomp,DTad, H ad

comp, H isocomp, Hreq, dH/dT and the RCP, defined using

Eqs. (2)–(6), were determined for all samples studied in thiswork.

4.1. Magnetic and martensitic transformation characteristics

Magnetic characterization of the Ni43Mn42Co4Sn11

samples was performed, and the results are compared inFig. 5a. The figure shows the thermo-magnetization curvesof the solutionized bulk, and as-spun and solutionized

ribbon samples under 0.05 T. The as-cast bulk specimendid not exhibit a notable meta-magnetic phase transition,thus the results are not shown here. The austenite phaseof the bulk sample is FM for a narrow temperature intervalon heating until its Curie temperature Tc is reached. The Tc

of the austenite was found to be �365 K. The martensiteexhibits a small magnetic susceptibility, which in past stud-ies was attributed to short-range frustrated antiferromag-netic interactions by neutron polarization measurements[22,23]. The frustrated antiferromagnetic response is shownby the low magnitude of magnetization values from 4.2 Kto 160 K. Around 200 K, the sample started transformingto highly magnetic austenite during the reverse transforma-tion. Both as-spun and solutionized ribbons exhibited goodmeta-magnetic shape memory characteristics, with a sharptransition between the austenite and martensite. Thechanges in magnetization across MT (DM), transformationranges (DTelas), temperature hysteresis (DThys) and theirsum (DTcomp) were extracted from Fig. 5a, as defined bythe schematic in Fig. 5b, and tabulated in Table 1. The dataindicate that the solutionized bulk sample exhibits thesmallest thermal hysteresis, but the ribbon samples exhibitthe smallest transformation range.

To find out whether the aforementioned performanceparameters, such as H iso

comp and Hreq, are dependent on sam-ple microstructure, they need to be determined using theequations in Section 2 and the data in Table 1. In addition,the CC slopes (the slope of the critical field for the transfor-mation vs. temperature phase diagram) should be foundusing the thermo-magnetization results like those seen inFig. 5c for the solutionized ribbon samples. The corre-sponding phase diagrams are shown for the solutionizedbulk and ribbon samples in Fig. 5d. These results will laterbe used to discuss the effect of microstructure on theperformance parameters summarized in Section 2.

4.2. Microstructure

Since DM, DTelas and DThys are quite different in thebulk and ribbon samples, WDS analysis was conductedto check for compositional differences. Table 2 containsthe average content (in at.%) for each component measuredover eight different locations and their standard deviationsfor the solutionized samples. Clearly, the composition wasrelatively homogeneous throughout the samples, as indi-cated by the low standard deviations, and therefore, theobserved differences in the transformation characteristicsmust be largely due to factors other than compositionalinhomogeneity. The bulk sample, however, was found tocontain �0.5 at.% more Co than the solutionized ribbon.It has been reported that a small substitution of Co foreither Mn or Ni reduces the MT temperatures andincreases the Tc of austenite [1,29], which is consistent withthe magnetic responses of the present samples.

Fig. 6 shows the SEM images of the SHT bulk andribbon samples. The average grain size of the solutionizedribbons is �15 lm. The ribbons are �50 lm thick.

120

100

80

60

40

20

0

Mag

netiz

atio

n (e

mu/

g)

300200100

Temperature (K)

340KSHT Ribbon

As-SpunRibbon

365K

Ni43Mn42Co4Sn11

H=0.05T

SHTBulk

120

100

80

60

40

20

0

Mag

netiz

atio

n (e

mu/

g)

300200100

Temperature (K)

0.05T

7T

Ni43Mn42Co4Sn11 SHT Ribbons10

8

6

4

2

0

Hcr

(T

)

280260240220200180

Temperature (K)

-0.26 (T/K)-0.22 (T/K)

Af AfBulk

AsBulkAs

Ni43Mn42Co4Sn11

(a) (b)

(c) (d)

Fig. 5. (a) 0.05 T thermomagnetization curves of Ni43Mn42Co4Sn11 polycrystalline samples in as-spun ribbon, bulk, solutionized at 1173 K for 1 day, andribbon, solutionized at 1173 K for 2 h, forms. (b) Schematic showing how some of the parameters in Table 1 were determined using the results in (a). (c)Thermo-magnetization curves of the solutionized ribbon samples under 0.05 T and 7 T, which were used to construct the critical field-temperature phasediagram in (d). (d) Includes the critical field–temperature phase diagrams for the solutionized bulk and ribbon samples.

Table 1Martensitic transformation characteristics of the Ni43Mn42Co4Sn11 sam-ples determined using the thermo-magnetization results under 0.05Tshown in Fig. 5(a).

Sample DM (emu/g) DTelas (K) DThys (K) DTcomp (K)

As-Melted Bulk 6.1 182 39 221Solutionized Bulk 56 94 16 110As-spun ribbon 83 25 30 55.0Solutionized ribbon 90 13.5 21 34.5

Table 2WDS results for the solution heat treated Ni43Mn42Co4Sn11 bulk andribbon samples averaged from 8 different grains.

Sample Ni(avg. ± std.)

Co(avg. ± std.)

Mn(avg. ± std.)

Sn(avg. ± std.)

Ni43Co4Mn42Sn11 (at.%, nominal)

Bulk Heattreated

42.9 ± 0.2 4.56 ± 0.04 40.9 ± 0.3 11.5 ± 0.2

Heat treatedRibbon

43.1 ± 0.1 4.05 ± 0.04 41.2 ± 0.1 11.6 ± 0.1

74 N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84

Solutionized bulk samples have an average grain diameterof 140 lm. The differences in grain size and specimen thick-ness, and thus grain size to thickness ratio, are believed tobe some of the main reasons for the observed differences in

MT characteristics between the bulk and ribbon samples.

This will be discussed further in the subsequent sections.

4.3. Secondary heat treatments

Differing from the samples in the bulk form, the ribbonsexhibit a large DM with the application of very low mag-netic fields. In addition, the ribbons show the smallestDTcomp that is desired for efficient refrigeration perfor-mance per Eqs. (4)–(6). In contrast, the solutionized bulksample exhibits the smallest DThys. Since the refrigerationperformance parameters can be improved by decreasingDThys, the solutionized Ni43Mn42Co4Sn11 ribbons wereexposed to secondary heat treatments in attempts tofurther reduce their DThys, as can typically be done forNiMnIn alloys [17].

In Ref. [17], it was shown that DThys is related to L21

ordering, and therefore secondary heat treatments wereconducted at temperatures (673 K, 773 K, 873 K) belowthe reported B2/L21 ordering temperature for 1 h topromote L21 ordering as observed in NiMnIn alloys. Ateach temperature, ribbons were RQ or FC. Characteristicfeatures of the MT after secondary heat treatments aredetermined directly from the experiments or calculatedusing the equations in Section 2 and tabulated in Table 3.

(a) (b)

Fig. 6. Backscattered electron images of Ni43Mn42Co4Sn11 samples at room temperature: (a) solutionized bulk sample (white areas indicate room-temperature martensite); and (b) solutionized ribbon.

Table 3Martensitic transformation (MT) characteristics of the secondary heat treated ribbons. FC indicates furnace cooling ; RQ indicates rapid quenching andthe MT temperature is determined as T0=(Ms+Af)/2 [24].

AnnealingTreatment

dHAs

dT (T/K) dHAf

dT (T/K) Mf(K) Ms(K) As (K) Af (K) T0 (K) DThys (K) DTelas (K) Hisocomp (T) H ad

comp (T) Hreq (T) Tc(K)

673K FC �0.14 �0.23 193 208 217 225 217 21 11.5 7.56 9.6 3.4 368773K FC �0.17 �0.23 185 217 214 230 223 23 26 11.2 13.3 4.9 367873K FC �0.19 �0.26 189 225 216 243 234 22 31.5 13.9 17.0 5.0 366673K RQ �0.16 �0.25 210 222 229 238 230 17 10 6.9 9.5 3.1 361773K RQ �0.18 �0.27 209 227 230 240 233 17 14 8.2 11 3.8 360873K RQ �0.22 �0.24 213 233 232 246 240 16 17 8.0 10.1 4.3 3601173K SHT �0.19 �0.22 198 216 224 233 224 21 13.5 7.6 9.6 5 340

N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84 75

The critical field vs. temperature phase diagrams for thecompletion of the martensite to austenite transformationin the secondary heat-treated ribbons are shown in Fig. 7a,which are extracted from the thermo-magnetization curves.Later, these phase diagrams will be used to find the H iso

comp

parameter.As shown in Table 3, secondary heat treatments resulted

in slight changes in transformation temperatures, thermalhysteresis and magnetic field sensitivity of As and Af, buton average, the DM across MT remained approximatelythe same and therefore was not included in the table. TheRQ samples exhibited an increase in transformation tem-peratures, whereas the FC samples showed a decrease intransformation temperatures compared with the SHT rib-bons. This suggests that slight changes in atomic orderingwere dependent on the cooling rate of the secondaryheat-treated ribbons.

The product of the slopes of the CC lines in Fig. 7a andthe DTcomp tabulated in Table 3 yielded H iso

comp following Eq.

(5), which is also tabulated in Table 3. The solutionized

ribbon that was heat treated at 673 K for 1 h and thenRQ was found to exhibit the smallest H iso

comp of 6.9 T,

whereas the solutionized ribbon sample originally had aHiso

comp of 7.6 T.

4.4. Meta-magnetic response of heat-treated ribbons

Fig. 7b shows the 7 T thermo-magnetization curves ofthe Ni43Mn42Co4Sn11 as-spun, solutionized (SHT), andsolutionized plus 673 K 1 h RQ ribbons (SHT+673K(RQ)). The 0.05 T thermo-magnetization curve forthe SHT+673K(RQ) sample is shown in the inset. Theinset shows that the 7 T field does not lead to a largechange in the magnetization of austenite, and the largeapplied field reduces DM across MT, as the magnetizationof martensite increased more than that of the austenite.This is attributed to the short-range antiferromagneticinteractions of martensite [22,23,30], making magneticsaturation of martensite difficult. Large fields decrease the

MT temperatures, as expected. The CC slopes, dHAs=dT

(a)

(b) (c)

250240230220210200190180

Temperature (K)

10

8

6

4

2

0

H A

f (T

)

673K FC773K FC

873K FC

673K RQ

773K RQ873K RQ

As-Spun

Ni43Mn42Co4Sn11 Ribbons

160

140

120

100

80

60

40

20

Mag

netiz

atio

n (e

mu/

g)

300250200150100500

Temperature (K)

120

80

40

0Mag

neti

zatio

n (e

mu/

g)

400300200100Temperature (K)

7T

0.05T

SHT

SHT+673K (RQ)

As-Spun

Ni43Mn42Co4Sn11

Ribbons

SHT+673K (RQ)

H=7T

120

100

80

60

40

20

0M

agne

tizat

ion

(em

u/g)

86420

Applied Field (T)

T =Mf =210K

Ni43Mn42Co4Sn11

SHT + 673K (RQ) Ribbons

T =190K

T =245KAustenite

Martensite

Fig. 7. (a) The critical field-temperature phase diagram for the completion of the martensite to austenite phase transformation for the secondary heat-treated ribbons. (b) Thermo-magnetization curves of the Ni43Mn42Co4Sn11 as-spun, SHT and SHT+673K(RQ) ribbons in the field of 7 T. Inset: 0.05 Tand 7 T thermo-magnetization curves of SHT+673K(RQ) ribbons, (c) Isothermal magnetization curves of the SHT+673K(RQ) ribbons. Magnetizationisotherms were measured at temperatures (=190 K) much less than Mf, at Mf = 210 K and > Af = 245 K.

76 N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84

and dH Af =dT , for the SHT+673K(RQ) ribbons were deter-mined as �0.16 T K�1 and �0.25 T K�1, respectively, fromthermo-magnetization curves.

To verify the validity of Eqs. (4) and (5), the isothermalmagnetic response of the Ni43Mn42Co4Sn11 SHT+673K(RQ) ribbons was measured under applied magneticfields up to 7 T at a temperature (=190 K) much below Mf,at Mf (=210 K), and at a temperature >Af (=245 K), usingmartensite as the initial phase in the former two cases. Theresponse is shown in Fig. 7c. The magnetization values atlow temperatures are small. Small magnetic hysteresis isobserved at T = 190 K, since the field is not sufficient toinduce a large structural transformation, and the sample iscomposed mainly of short-range frustrated antiferromag-netic martensite. The small hysteresis may be attributed toa low concentration of magnetic domains rotating at lowapplied fields or a small volume fraction of phase transfor-mation. The response near Mf shows magnetic hysteresison unloading the field, indicating that structural transforma-tion has taken place. At temperatures >Af, no magnetic hys-teresis is observed, indicating that the field does not induce atransformation from austenite to another phase, and austen-ite is purely FM.

More importantly, the isothermal magnetization curvesin Fig. 7c verify the validity of Eqs. (4) and (5) for theSHT+673K(RQ) ribbons. In Table 3, H iso

comp and Hreq werepredicted to be 6.9 T and 3.1 T, respectively, using thethermo-magnetization results. As can be seen from the

isothermal magnetization curve at T = Mf in Fig. 7c, thesemagnetic fields reasonably match those experimentallyobserved in the figure for the M!A transformation.

4.5. Entropy of transformation, heat capacity and RCP

The latent heat and heat capacity were determined forthe SHT ribbon samples using DSC and the PPMS men-tioned in Section 3. As shown in Fig. 8a, DStr was foundto be 18 J kg K�1 from the area of the endothermic peak(DStr ¼

RðCp=T ÞdT ). In addition, the transformation

temperatures match those obtained from 0.05 T thermo-magnetic measurements for the SHT ribbons.

The CC relation can also be used to find DStr. The CCrelation is defined as [31]

DStr ¼ DMM!A dH Af

dTð8Þ

where DMM!A is the magnetization change across MT. Tofurther verify that the DStr was �18 J kg K�1, the aboveequation was used, where DM was found, from magneticdata like that shown in Fig. 7c, at T = Mf, to be 84.1emu g�1 and dH Af =dT was found to be �0.22 T K�1 fromthermo-magnetic measurements. The CC relation predictedthe transformation entropy of 18.6 J kg K�1, which is ingood agreement with the DSC measurements. This indi-cates that either Eq. (8) or the experimental results shownin Fig. 8 can be used to determine DStr.

Hea

t Flo

w (

W/k

g)

260240220200180

Temperature (K)

Ni43Mn42Co4Sn11

SHT Ribbons

Exo

Up

ΔStr ~ 18 (J/kgK)

600

500

400

300

200

100

0

Hea

t Cap

acity

(J/

kgK

)

250200150100500

Temperature (K)

Ni43Mn42Co4Sn11

SHT Ribbons

(a) (b)

Fig. 8. (a) DSC curve of the SHT ribbons and (b) heat capacity measurements of SHT ribbons on cooling.

N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84 77

In Fig. 8b, the heat capacity data are shown. The dataprovide an accurate measure of the heat capacity bracket-ing the hysteresis region, although the first-order transitionregion itself is not reproduced by the pulse-relaxation tech-nique. These values are used to determine the adiabatictemperature change near T0, as required in Eq. (2) to calcu-late the RCP. At higher temperatures, the data approachthe classical 3NkB per mole, as expected, plus a small elec-tronic term. Using DStr of 18 J kg K�1 and a Cp of434 J kg K�1 at 190 K (near Mf), and a T0 of 224 K fromTable 3, DT max

ad is calculated to be 9.3 K. This implies that,if Thot is considered to be equal to Mf = 198 K as in Fig. 1,Tcold would be 188.6 K (i.e. T hot � DT ad). The RCP contri-bution within the temperature range permitting the com-

plete field-induced entropy change (AH¼Had

comp

f to MH¼0f ) is

defined as DStr � DT maxad � ðSirr � DT max

ad Þ=2. Here Sirr equals1.9 J kg K�1 when T = Mf in Eq. (3). This leads to theRCP of 159 J kg�1 for the SHT ribbons in this temperaturerange. However, when considering the entropy changes inthe elastic regions of transformation, the total reversibleRCP is calculated as DStr � DT max

ad þ DStr � DT elas � Sirr

ðDT maxad þ DT elasÞ=2 (Eq. (2)). For the SHT ribbons, this

total reversible RCP is 389 J kg�1.In the SHT+673K(RQ) ribbon samples, the entropy

change across transformation was calculated using the CCequation (Eq. (8)) as explained for the SHT sample above.The DM was measured at T = (Af + As)/2 to be 79 emu

g�1, and the CC slope (dH Af =dT ) to be �0.25 T K�1. Eq.(8) then results in DStr of 19.7 J kg K�1. Assuming the heatcapacity does not significantly change after the secondaryheat treatments, DT max

ad is found to be 10.4 K, and thus

theHadcomp (from Eq. (6)) then equals 9.5 T for the

SHT+673K(RQ) ribbon, which is slightly lower than thatof the SHT ribbons. The RCP contribution within thetemperature range permitting the complete entropy change

(AH¼Had

comp

f to MH¼0f ) is calculated to be 196 J kg�1, with Sirr

being equal to 1.5 J kg K�1 when T = Mf in Eq. (3). Includ-ing the entropy changes in the elastic regions of transforma-tion, the total reversible RCP is calculated to be 385 J kg�1

for the SHT+673K(RQ) ribbon.Comparing the SHT ribbons with those exposed to

secondary heat treatments, it was found that the

transformation entropy change increases as a result ofthese heat treatments, H iso

comp decreases for the RQ samples,

and AH¼Had

comp

f ! MH¼0f (temperature region where the com-

plete reversible entropy change can be achieved) grows atthe expense of the elastic transformation regions

AH¼Had

compf � A

H¼Hadcomp

s and MH¼0s �MH¼0

f . These findings

suggest that the material can easily be tailored for a givencycle with simple heat treatments to permit not only acertain cooling capacity under a given field, but also thatthe field levels required to achieve refrigeration and theiroperating temperatures can be modified.

5. Analysis and discussion

So far, this work has presented an accurate characteriza-tion framework describing the magnetic refrigeration per-formance in MSMAs. An example Brayton refrigerationcycle was used to show how important materials propertyparameters will affect the refrigeration performance of asolid-state refrigerant exhibiting a first-order phase trans-formation and latent heat. The parameters affecting therefrigeration performance in this work have been identifiedas the entropy change across the MT, the magnetic fieldsrequired to initiate and complete the MT both adiabati-cally and isothermally, and the RCP. Each parameterwas described and discussed in detail. Finally, a NiCoMnSn SMA alloy composition was selected to demonstratehow simple heat treatments can influence these refrigera-tion performance parameters explained in Section 2. Thefollowing sections discuss what heat treatments change inthe microstructures and how these changes influence theMT characteristics and performance parameters in thesame alloy composition.

5.1. Effect of fabrication method on martensitic and magnetic

transformation characteristics

As shown in Table 1, the responses of the SHT samplesin Fig. 5a under 0.05 T vary significantly owing to thefabrication technique. After the SHT, no second phaseswere observed in the backscattered electron images inFig. 6 or from the WDS analysis. This indicates that second

78 N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84

phases are not the cause of the differences in DT elas betweenthe SHT bulk and ribbon samples like that reported forNiMnCoIn alloys [13]. Instead, the present authors believethat other stress non-uniformities developing during thereversible martensitic transformation, such as those causedby a large degree of grain constraints, affect the transfor-mation range. In conventional SMAs, elastic energy stor-age has been linked to grain size to thickness ratio [32,33]during superelastic loading and, thus, thermally or magnet-ically induced martensitic transformation ranges shouldalso be affected by this microstructural parameter as dis-cussed below.

5.2. Effect of grain size constraint on elastic energy storageduring martensitic transformation

In conventional SMAs, Wert et al. [32,33] showed that theratio of grain size (GS) to specimen thickness (t) is inverselyproportional to the elastic energy storage, or DT elas. The lar-ger transformation range was an indication of the difficultyfor transformation phase front motion, which required fur-ther undercooling or superheating (or higher stress levels inthe case of superelasticity), and resulted in more nucleationevents and higher stored elastic energy in CuZnSn and CuZ-nAl alloys [32,33]. For example, superelastic loading onCuZnSn [32] alloys showed a transformation stress rangeof <4.7 MPa with a GS/t ratio of 2.5. However, the samecomposition transformed under the stress range of7.4 MPa with a GS/t ratio of 0.55 [32]. The larger transfor-mation stress ranges indicate more elastic energy stored dur-ing transformation, owing to small GS/t ratios. Similarly,the GS/t ratio affects the amount of stored elastic energy inthe Ni43Mn42Co4Sn11 alloy and, thus, the transformationranges Ms–Mf and Af–As. Apparently, samples with largeGS/t ratios require less thermal or mechanical (or magnetic)driving force to achieve the same response than samples withsmall GS/t ratios.

Table 4 shows average grain sizes for the SHT samplesand their corresponding GS/t ratios. The solutionized rib-bon exhibits �1.7 times larger GS/t than the solutionizedbulk sample, and thus less elastic energy is stored in themicrostructure on transformation, owing to the relaxationof the strain energy on the free surface. Moreover, less driv-ing force is required to complete the transformation, hencethe smaller DT elas and DT comp in the ribbon samples, asshown in Table 1.

The reduction in DT elas will, in turn, decrease the secondterm in Eq. (2). Decreasing this term may seem undesirable,

Table 4Average grain size to thickness ratio (GS/t) for heat treated samples ofNi43Mn42Co4Sn11 and the corresponding percent elastic energy storage ofthe heat of transition [25].

Sample AverageGS (lm)

Thickness(lm)

GS/t(lm/lm)

Eelas(%)

Solutionized Bulk 137 ± 24 860 ± 10 0.16 16Solutionized Ribbon 13 ± 1 50 ± 10 0.26 3

since it would reduce the reversible RCP levels, but mini-mizing DT elas should also drop DT comp and Hcomp. A reduc-tion in Hcomp is desired to make the field requirements formagnetic refrigeration more practical. In addition, in orderto take advantage of reversible RCP in the temperatureranges Ms–Mf and Af–As, one needs special refrigerationcycles to access the energy in those regions, which maybring about practical challenges.

Therefore, minimizing stored elastic energy within theSMA microstructure is beneficial to magnetic refrigerationapplications, and it should be consistently analyzed tocompare SMA performance in different compositions andmicrostructures. A relative measure of the elastic energystored in the MSMA across MT has been shown in Ref.[28] to be the ratio of the elastic free energy to the latentheat of the MT. Using this framework, the ratio can bedetermined as Eelas=DH tr ¼ DT elas=ð2MsÞ where DHtr isthe latent heat of the MT. Eelas is dependent on the GS/tratio and, therefore, these values are listed in Table 4. Here,DT elas was determined as explained earlier, and Ms wasdetermined as shown in Fig. 5b. The difference in theGS/t ratio for the samples is a result of the fabricationmethod, and the ribbon samples demonstrated more favor-able parameters for MCE, such as small DT elas (Table 3)and large DM (Table 1), because they would require lessenergy for the cyclic response, as outlined in Fig. 1.

5.3. Effect of solution heat treatment on martensitic and

magnetic transformation characteristics

In addition to DT elas, the role of transformation hyster-esis DT hys on the refrigeration performance parameters wasinvestigated in the Ni43Mn42Co4Sn11 samples. As shown inEqs. (4)–(6), thermal hysteresis is directly related to themagnetic fields required to induce and complete the trans-formation. Also, it can be seen in Fig. 2b that decreasingDT hys will result in a wider temperature range that willallow a fully reversible field-induced transformation,

AH¼Had

comp

f ! MH¼0f . Increasing the shaded area in Fig. 2b

ultimately increases the achievable thermal work producedby the SMA. Heat treatments provide a means for chang-ing DT hys, because they influence the atomic order inMSMAs.

The atomic order and thermal hysteresis in SMAs arelinked by the compatibility between austenite and martens-ite phases [34]. Some ordered Heusler alloy compositionsmay exhibit good compatibility between the transformingphases and therefore, produce small thermal hysteresis[17]. In addition, atomic order influences the Mn–Mn dis-tances for Mn-containing Heusler alloys and this signifi-cantly affects the magnetic response of the MSMA [9]. Inthe present materials, DM increases after the SHT, asshown in Fig. 5a, which indicates that there may have beena slight change in atomic order. This increase in DM coin-cides with the information reported in Ref. [9]. In addition,DT hys and DT elas are smaller in the SHT ribbons compared

N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84 79

with the as-spun ones. Clearly, a decrease in DT hys isobserved after SHT with an apparent grain growth andhomogenization of the as-spun ribbons. Since the SHThas such a large effect on the transformation characteris-tics, the Ni43Mn42Co4Sn11 alloy could potentially exhibiteven smaller Hcomp and larger RCP, if tailored properlywith secondary heat treatments, as in NiMnIn systems [17].

5.4. Effect of secondary heat treatments

In attempts to further change the atomic order inNi43Mn42Co4Sn11, secondary annealing treatments wereconducted in 100 K increments followed by two differentcooling procedures. As a result, small but notable changesin the magnetic response and MT characteristics wererecorded, as presented in Table 3. The differences betweenthe samples with different cooling procedures may beexplained by point defect concentration within the crystallattice. After RQ, point defects, such as vacancies, resultin slightly higher lattice strain, thus martensite is stabilized,and MT temperatures increase [35].

To check whether atomic order was influenced by sec-ondary heat treatments, thermal hysteresis and As field sen-sitivity were plotted in Fig. 9 against the parameterðT c � T 0Þ=T c [17,36], or the ratio between the differencein the austenite Curie temperature and the MT tempera-tures and the austenite Curie temperature (see Table 3).

-0.22

-0.20

-0.18

-0.16

-0.14

dHA

s /dT

(T

/K)

0.420.400.380.360.34

(Tc - T0 )/ Tc

Ni43Mn42Co4Sn11

Annealed Ribbons

1173K 2hrs + 673K 1hr RQ

L21 Ordering

SHT

26

24

22

20

18

16

14

ΔThy

s (K

)

0.360.340.32

(Tc -

L21 Ordering

RQ

Poin

t Def

ect C

once

ntra

tion

SHT

(a)

(c)

Fig. 9. (a) As field sensitivity, (b) secondary heat treatment temperature and (c)secondary heat-treated ribbon samples of Ni43Mn42Co4Sn11 alloys.

This parameter has been shown to be related to the L21

order in NiMnIn and NiMnSn alloys [17,36] whereby, asðT c � T 0Þ=T c increases, the L21 order also increases. Inter-estingly, the trends observed from the secondary heat treat-ments in Ni43Mn42Co4Sn11 match the trends observed inother MSMAs, only their changes are on a much smallerscale owing to the high L21 stability [37].

As shown in Fig. 9b, the FC samples tend to ordertoward L21 more than the RQ samples, and the RQ processseems to retain more disorder. In Fig. 9c, the L21 orderingalso results in larger temperature hysteresis, which is linkedto the changing lattice coherency between austenite andmartensite phases. Clearly, in the present NiMnCoSn alloycomposition, atomic disorder improves lattice coherencebetween martensite and austenite phases.

Fig. 10a and b shows the transformation range as afunction of the parameter ðT c � T 0Þ=T c and heat treatmenttemperatures for the RQ and FC cases. It can be seen thatthe FC procedure results in broader temperature ranges. Itis observed that the lowest temperature heat treatment cor-responds to the smallest transformation range, even smallerthan the solutionized ribbon. The results in Fig. 10 indicatethat the cooling process greatly affects the transformationrange. Since FC and RQ procedures result in the sameðT c � T 0Þ=T c parameter with different DT elas, the evolvedmicrostructure must be responsible for this difference.Since FC samples were held at an elevated temperature

950

900

850

800

750

700

650

Seco

ndar

y H

eat T

reat

men

t Tem

pera

ture

(K

)

0.440.400.360.32

(Tc - T0 )/ Tc

Poin

t Def

ect C

once

ntra

tion

L21 Ordering

FC

RQ

Ni43Mn42Co4Sn11

Annealed RibbonsSHT

0.420.400.38

T0 )/ Tc

Ni43Mn42Co4Sn11

Annealed Ribbons

FC

(b)

DThys as a function of the normalized difference between Tc and T0 for the

50

40

30

20

10

0

ΔTel

as (

K)

0.440.400.360.32

(Tc - T0 )/ Tc

RQ

FC

Ni43Mn42Co4Sn11

Annealed Ribbons

Poin

t Def

ect C

once

ntra

tion

L21 Ordering

SHT

40

35

30

25

20

15

10

5

ΔTel

as (

K)

950900850800750700650

Secondary Heat treatment Temperature (K)

Ni43Mn42Co4Sn11

Annealed Ribbons

FC

RQ

SHT

(a) (b)

Fig. 10. Thermoelastic transformation range as a function of (a) normalized distance between Tc and T0 indicating the level of L21 ordering and (b)secondary heat treatment temperature for the Ni43Mn42Co4Sn11 ribbon samples.

Fig. 11. Effective entropy change (DSeff) in the solutionizedNi43Mn42Co4Sn11 polycrystalline ribbon as a function of temperaturearound the martensitic transformation from the continuous heatingprotocol. The theoretical DS � T diagram from Fig. 2b has been drawnover the experimentally collected data as a black trapezoid defined byEq. (2).

80 N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84

for a longer period of time, it is possible that some phasedecomposition may have occurred [38], but on a scale smallenough not to be observed with BSE imaging (<1 lm). Inthe FC samples, the transformation may have been“pinned” by the presence of anti-phase boundaries, asobserved in Ni2Mn(Ga0.5Al05) alloys [39–41]. Further stud-ies, however, are needed to verify the existence of theseanti-phase boundaries in NiMnCoSn alloys.

Nevertheless, the parameters measured from theSHT+673K(RQ) sample indicate that thermal hysteresishad further decreased compared with that of the SHTribbon, the As field sensitivity remained about the same,and the transformation range had also decreased. There-fore, since the SHT+673K(RQ) ribbons showed the largestDM and smallest DT comp, they were selected for furtherMCE study and are compared with the SHT samples.

5.5. Calculated performance parameters for magnetic

refrigeration

The main goal of the following section is to discuss theinfluence of experimental protocol and MT characteristicson the DS � T curves as in Fig. 2. As mentioned earlier,RCP can be directly calculated using Eq. (2), and integrat-ing the DS � T diagram is not needed when considering thelatent heat of a first-order transition. However, since muchof the SMA community has published results that includethe DS � T diagrams, correctly interpreting these resultsis important. These diagrams can still serve as an indicationof how well a SMA would perform as a refrigerant, as longas the experimental protocol is declared, the MT tempera-tures are given, and the alloy’s heat capacity is known.Below, the DS � T diagrams are compared for two experi-mental protocols on the same sample. Furthermore, theDS � T diagrams are presented for the SHT+673K(RQ)and SHT samples, to show how improving the samplemicrostructure (and MT characteristics) affects thesediagrams.

Fig. 11 displays the DSeff values (discussed in Section 3)deduced for the Ni43Mn42Co4Sn11 SHT ribbon using thecontinuous heating protocol for which all the values were

calculated from the reverse (M!A) transformation magne-tization curves such as those in Fig. 7c, and using Eq. (1). Aschematic of the DS � T diagram using the same thermody-namic assumptions in Fig. 2b has also been drawn over thedata to indicate how the DS � T diagram should look tocalculate the maximum theoretical thermal work (RCP).This DS � T schematic shows the maximum theoreticalreversible entropy change expected from this sample as aresult of the reverse martensitic transformation assumingthat the applied field is not limited to 7 T, but is sufficientto complete the adiabatic transformation. Clearly, there area few discrepancies between the theoretical and measuredcurves. At first glance, the most obvious discrepancy is thatEq. (1) combined with the continuous heating protocolover-predicts the transformation entropy change, DStr, i.e.the maximum DSeff value in the figure. DSeff values weregenerated for different field changes between 0 and 7 T.

The maximum DSeff value (DSpkeff ) obtained for the SHT

ribbons was 28 J kg K�1 at 219 K for 4 T, 5 T, 6 T and7 T in the continuous heating scheme. This entropy changeis comparable with other reports on Ni45Mn35Co8In12

(15.3 J kg K�1, 5 T) [13], Ni43Mn43Co3Sn11 (33 J kg K�1,5 T) [29], Ni50Mn34In16 (20 J kg K�1, 5 T) [42] and Ni45

Co5Mn37.5In12.5 (30 J kg K�1, 7 T) [43]. However, DSpkeff is

larger than DStr calculated from Eq. (8), indicating that a

Fig. 12. Entropy change (DS) in the solutionized Ni43Mn42Co4Sn11

polycrystalline ribbon as a function of temperature around the martensitictransformation from the discontinuous heating protocol. The theoreticalDS � T diagram from Fig. 2b has been drawn over the experimentallycollected data as a black trapezoid defined by Eq. (2).

N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84 81

discrepancy is present from the experimental scheme. Thiscould also mean that the transformation entropy changeincreases with applied field, but this is not the case, asshown by the discontinuous heating protocol discussednext. For smaller applied fields, the DSeff values in Ni43-

Mn42Co4Sn11 SHT ribbons are larger than those typicallyreported. For example, under 2 T and 3 T, solutionized rib-bons seem to produce 14.6 J kg K�1 and 20.8 J kg K�1,respectively, whereas Ni50Mn37Sn13 (10 J kg K�1, 1.8 T)[9] and Ni50Mn35.5In14.5 (13 J kg K�1, 3 T) [14] alloys pro-duce smaller entropy changes under similar fields. This maybe due to the fact that the continuous heating scheme per-mits an initially mixed microstructural state to be analyzedwith Eq. (1).

The next notable discrepancy is that most of the con-structed DS � T diagram is outside the temperature rangerequired to find the reversible RCP. This is due to the factthat Hreq is relatively large (Table 3). In order to achieve afield-induced transformation under applied fields <7 T, the

temperature of the SHT ribbon must reside near AH¼0s .

Comparing Fig. 2b with Fig. 11, it can be seen that mostof the DS � T diagram has been found in the area of ther-

mal hysteresis, MH¼0s ! AH¼0

f . MH¼0s is labeled in Fig. 11 for

clarity. This indicates that the SHT ribbon sample cannotbe used as a refrigerant in the Brayton cycle depicted inFig. 1 under the applied field of 7 T, because the entropychange will not be repeatable with field cycling. Lastly, aclose comparison between Fig. 2b and Fig. 11 shows that

AH¼0f , represented on the DS � T diagram in Fig. 11, is

under-predicted by �6 K. In Table 3, AH¼0f is listed as

233 K, whereas in Fig. 11 it is shown to be 227.5 K. Thisdiscrepancy is a product of the continuous heatingprotocol.

Fig. 12 shows the DS curves from the discontinuousheating protocol for the SHT ribbons. Note that, previ-ously, DSeff was used to describe entropy changes fromthe continuous heating protocol. Here, DS from the field-induced transformation, over the entire temperature range,seemed to plateau at a value (18 J kg K�1), which nearlymatches that measured in DSC. This indicates that thetransformation entropy change is not largely a functionof magnetic field, and entropy production from hysteresisis relatively small compared with the entropy change ofthe MT. In addition, a clear growth of the DS � T diagramto lower temperatures is observed as the fields becomelarger. This is due to the negative CC slope shown inFigs. 5d, 7a and 9a. In addition, the AH¼0

f in Fig. 12 nowagrees with the data in Table 3.

Again, a schematic of the DS � T diagram derived fromFig. 2b has been drawn over the data to indicate how theDS � T diagram should look to experimentally verify thecalculated RCP from the first two terms of Eq. (2). Clearly,the magnitude of the entropy change is now consistent withthe theoretical diagram, but a majority of measurementsstill reside outside the temperatures of interest, enclosedby the black trapezoid in Fig. 12. Again, this is due to

the large DT elas, DThys and H isocomp (or H ad

comp) exhibited by

the SHT ribbons. This can also be viewed as the inabilityto sufficiently decrease the transformation temperatureswith the applied field of 7 T. Reducing DT elas and DThys

would effectively overlap theoretical DS � T and experi-mentally captured DS � T curves with small appliedmagnetic fields.

The RCP is determined from the data in Fig. 12 by thearea of the overlapping theoretical and experimentalDS � T curves (shaded area) with the hysteresis losses sub-tracted as defined in Eq. (3). The applied fields, in this case,will produce very small RCP values, as only a fraction ofthe theoretical curve overlaps the experimentally capturedone up to 7 T. The maximum measured RCP value (over-lapping of two curves) was found to be 74 J kg�1 under theapplied field of 7 T. However, the projected RCP of 389 Jkg�1 was found using Eq. (2).

Finally, the discontinuous heating protocol was per-formed for the SHT+673K(RQ) ribbons, and the DS � T

diagram is shown in Fig. 13a. The theoretical DS � T curvefrom the thermodynamic framework in Fig. 2b has alsobeen drawn over the data. Hreq, Hiso

comp and Hadcomp for the

SHT+673K(RQ) ribbons were calculated to be 3.1 T, 6.9T and 9.5 T, respectively, as shown in Table 3. The DS

value saturates near 19.7 J kg K�1 as calculated from Eq.(8). It is important to note that the SHT+673K(RQ)ribbons show a Hiso

comp of 6.9 T. According to Eq. (5) inSection 2, this means that an isothermal test at temperatureMf will produce a complete field-induced structural trans-formation with the application of 6.9 T. This predictionis verified in Fig 13a, because the 7 T DS � T curve showsan entropy change of �19 J kg K�1 at temperature MH¼0

f asindicated by point 1 in the figure.

Furthermore, the RCP for the SHT+673K(RQ) ribbonswas calculated as the overlapping areas of the theoreticaland experimental DS � T curves for each applied field level(shaded area) with hysteresis losses subtracted as defined inEq. (3). Fig. 13b shows Sirr/2 � T diagrams, which werecalculated using Eq. (3). Since the DS � T curves saturateat DStr measured by DSC, the diagram in Fig. 13a canbe used at every temperature and field level to yield a value

Fig. 13. (a) Entropy change (DS) in the SHT+673K(RQ) ribbon as afunction of temperature around the martensitic transformation from thediscontinuous heating scheme. The theoretical DS � T diagram fromFig. 2b has been drawn over the experimentally collected data as a blacktrapezoid defined by Eq. (2). (b) Half the entropy production from thereverse MT for the same temperatures and field levels as shown in (a). Ablack curve defined from Eq. (3) has been drawn in over the data.

300

250

200

150

100

50

0

RC

P (J

/kg)

86420

Magnetic Field (T)

Ni43Mn42Co4Sn11 RibbonsHeat Treated at 1173K 2hrs + 673K 1hr RQ

isocompH

reqH

Fig. 14. RCP of the SHT+673K(RQ) ribbons as a function of appliedmagnetic field. Values were calculated from the data in Fig. 13a and busing the discontinuous heating protocol.

82 N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84

for nðHÞ � DStr in Eq. (3). In other words, the DS � T

curves in Fig. 13a were multiplied by DThys and dividedby the temperature at each data point in which the isother-mal test was conducted to produce the Sirr/2 � T diagrams.

To determine the RCP in this and the SHT ribbon casesdiscussed earlier, the area of overlapping theoretical andmeasured DS � T curves was first determined, and thenthe overlapping area of the theoretical and measuredSirr � T curves were subtracted at each field level. Thisassumes that the entropy production is a function of trans-formation volume fraction. The RCP results are plotted inFig. 14 for the SHT+673K(RQ) ribbons. The measuredRCP value was found to be 234 J kg�1 at Hiso

comp, as shownin Fig. 14. The maximum projected RCP, however, shouldreach 385 J kg�1 under Had

comp, considering all the terms inEq. (2). Although this projected RCP of theSHT+673K(RQ) ribbons is almost the same as that ofthe SHT ribbons (389 J kg�1), the secondary heat treat-ment allows this high RCP to be reached under a smallermagnetic field than that of the SHT ribbons as shown byHad

comp values in Table 3. This improvement is attributedto the larger GS/t ratio and beneficial degree of L21 order-ing, which yields desired MCE properties.

The RCP of Ni43Mn42Co4Sn11 heat-treated ribbons isgreater than other MSMAs that have been reported inthe literature since a very simple parameter optimizationapproach was used to select a favorable microstructureand resulting desirable properties to maximize MCE. How-ever, it is difficult to compare the results directly, because

most results in the literature calculate the RCP in theconventional way, which defines Thot and Tcold arbitrarilyat full width at half maximum of the DS � T curve [19].These temperatures are often inside the thermal hysteresisrange shown in Fig 2b, and the values do not reflect revers-ible DS and RCP values. It has been shown here that, forthe framework given in Fig. 2, the conventional way of cal-culating RCP is not correct for MSMAs.

Ni43Mn42Co4Sn11 SHT ribbons exhibit a RCP of389 J kg�1 and, from the isothermal tests, only 74 J kg�1

was accessible experimentally under 7 T. The MCE perfor-mance of the solutionized ribbons was improved with sec-ondary heat treatments, whereby a RCP of 385 J kg�1 isachievable under an applied field of 9.5 T. The SHT rib-bons allow for a slightly larger RCP using special thermo-dynamic cycles, because they also have a larger elastictemperature range. This, in turn, requires higher appliedfields to transform the ribbon. The alloys in the literature,such as Ni50Mn37Sn13 (39 J kg K�1, 1.8 T) [9] and NiMnIn(130 J kg�1, 3 T) [14], have been reported to exhibit smallerRCP under smaller fields, but neither their measurementprotocol nor their heat capacity were reported.

6. Conclusions

In the present work, to demonstrate how MSMAs canbe used as solid-state refrigerants in a refrigeration cycle,an example Brayton cycle was introduced and discussedin detail. From this cycle, the key material parameters,important for controlling MCE and refrigeration perfor-mance, such as the magnetic fields required to induce andcomplete the martensitic transformation, magnetizationchange across the transformation, transformation tempera-ture range and thermal hysteresis, were identified. Theperformance parameter RCP was used to compare therefrigeration capability of MSMAs with different composi-tions and microstructures. It was shown that the conven-tional method of finding the RCP for non-SMAs is not a

N.M. Bruno et al. / Acta Materialia 74 (2014) 66–84 83

valid approach for materials that exhibit a latent heatacross a first-order transformation.

In attempt to validate the selection of the above materi-als parameters, a case study was conducted on a specificNiMnCoSn composition. The results indicated that theseparameters can be optimized using simple heat treatmentseven in the compositions of MSMAs that show high L21

atomic stability. The grain size to thickness ratio was foundto influence the size of the transformation range. Atomicordering was shown to change the transformation thermalhysteresis. The best performance parameters were achievedin Ni43Mn42Co4Sn11 polycrystalline ribbons when theywere homogenized at 1173 K and then annealed at 673 Kfor 1 h, followed by RQ in water. Furthermore, the coolingmethod after the secondary heat treatments was shown toaffect the meta-magnetic response and ultimately controlthe transformation range and thermal hysteresis.

More precisely, the effects of secondary heat treatmentson the aforementioned materials parameters were studiedin Ni43Mn42Co4Sn11 melt-spun ribbons. Promoting atomicdisorder decreased the thermal hysteresis. The elasticenergy storage on martensitic transformation was reducedby increasing the grain size to thickness ratio, whichreduced the transformation range from 25 K in the as-spunribbons to only 10 K in the heat-treated ribbons. This effec-tively reduced the magnetic fields required to transform thematerials and increased the operating temperature range ofthe refrigerant.

Finally, the relationships between the magneto-thermalloading protocol, sample microstructure and entropychange vs. temperature diagrams were discussed. It wasshown that the continuous heating protocol over-predictsthe entropy change on the phase transformation. In addi-tion, the comparison between theoretical and experimentalentropy change vs. temperature curves showed how thesample responses were improved by the optimization heattreatments. Ultimately, it was found that past reports onthe MCE in MSMAs can still yield valuable informationas long as the experimental protocol, martensitic transfor-mation temperatures and heat capacity are also presentedso that the RCP can be calculated accurately.

The key materials parameters proposed in the presentwork provide a powerful tool for analyzing MSMA refrig-erants. The alloy composition and responses presented inthis study indicate MSMAs can be used as solid staterefrigerants. Moreover, further composition and micro-structural optimization through thermal treatments canimprove the transformation characteristics and thus therefrigeration performance parameters for them to competewith conventional rare-earth-based MCE materials such asGd alloys.

Acknowledgments

This work was supported by the U.S. National ScienceFoundation, Division of Materials Research, Metals andMetallic Nanostructures Program, Grant No. 1108396,

under the umbrella of the Materials World Network Initia-tive. In addition, partial support from the National ScienceFoundation, under Grant No. DMR 08-44082 is acknowl-edged, which funds research in the International MaterialsInstitute for Multi-functional Materials for Energy Conver-sion (IIMEC) at Texas A&M University. This work is alsopartially supported by the National Natural Science Foun-dation of China under Grant No. 51371184. JHR acknowl-edges partial support from the Robert A. Welch Foundationunder Grant No. A-1526, and finally, NMB acknowledgesDr. Patrick Shamberger for fruitful discussions.

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