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Multicaloric effect in Pb(Mn1/3Nb2/3)O3-32PbTiO3 single crystals

Aditya Chauhan,1 Satyanarayan Patel1 and Rahul Vaish⇑

School of Engineering, Indian Institute of Technology Mandi, 175 001 Himachal Pradesh, India

Received 17 November 2014; revised 6 January 2015; accepted 27 January 2015

Abstract—Enhanced electrocaloric response has been obtained for Pb(Mn1/3Nb2/3)O3-32PbTiO3�(PMN-32PT) single crystal by the application ofuniaxial compressive pre-stresses. It was observed that an improvement of the electrocaloric effect (DT elec = 0.62 K) to the tune of 200% can beobtained for an applied compressive of 28 MPa against a conventional unstressed peak electrocaloric effect (DT elec = 0.27 K). Furthermore, theaccompanying large strain variations and second order structural transition of the single crystal can be used to obtain significantly large valuesof elastocaloric effect (DT elas 0.36 K) for an operating temperature of 323 K and applied compressive stress of 2–28 MPa (at 1.5 MV m�1). The mag-nitude of elastocaloric response is even larger than the conventional unstressed DT elec of 0.27 K for the same operating temperature. The results indi-cate that ferroelectric materials possess significant multicaloric potential and can yield better cooling when employed as elastocaloric materials asopposed to conventional electrocaloric effect. Additionally, the two individual caloric effects can be suitably combined to obtain a further enhancedmulticaloric DT of �0.63 K using a novel electro-mechanical thermodynamic cycle for an optimized operating temperature of 323 K and appliedcompressive stress of 2–14 MPa. The results of this study are expected to largely benefit the field of ferroelectric solid-state refrigeration and opennew horizon for future exploration of multicaloric potential in ferroelectric materials.� 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Multicaloric; Coupled caloric; Elastocaloric; Electrocaloric; Ferroelectric

1. Introduction

Last decade has witnessed quantum advances in the fieldof non-conventional refrigeration technology. Much of thisdevelopment is centred on the idea of obtaining high perfor-mance cooling systems for specialized applications which arecapable of replacing the traditional vapour-compressiontechnology [1–5]. As a result, research in the field of a suc-cessful and practically viable solid-state refrigerator is beingbacked by vested commercial interests. The caloric effectsare being projected as an environmental-friendly alternativefor reducing greenhouse emission and improved efficiencyfor small to medium load cooling requirements [6]. Caloriceffects in ferroic solids are best described as a reversibleisothermal entropy change or adiabatic temperature changeobtained upon the application of a suitable external stimulus[7,8]. Any material system when acted upon by an adiabaticstimulus can possibly generate a non-dissipative tem-perature change [9]. However, it is different from caloriceffects in ferroic materials which are characterized by largeand reversible, entropy ordered phase transitions. Thus, lar-gest caloric effects are obtained in the vicinity of phase tran-sition which represents the tipping point between two states

http://dx.doi.org/10.1016/j.actamat.2015.01.0701359-6462/� 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights

⇑Corresponding author. Tel.: +91 1905 237921; fax: +91 1905237945; e-mail: rahul@iitmandi.ac.in

1 These authors have contributed equally to this work.

of large entropy difference [8]. Furthermore, dependingupon the origin of entropy change and the nature of stimulusapplied, the caloric effects can be classified as electrocaloric(electric field), elastocaloric (stress), magnetocaloric (mag-netic field) and barocaloric (volumetric strain) [6–8,10,11].From among these, electrocaloric (EC) effect in particularhas shown good potential for practical solid-state refrig-eration systems [3,8,9,12–30]. It stems from the fact thatlarge EC effect can be obtained by a relatively small valueof applied electric potential when thin film geometries areemployed. Finally, minimization of moving parts increasesthe reliability of operation and reduces the risk of failure.All these factors contribute towards economizing the opera-tion of a system based on EC cooling technology and hence,it is favoured over other caloric effects.

However, one of the main drawbacks associated withpractical implementation of EC effect is the low adiabatictemperature change (DT elec) associated with the conven-tional ferroelectric material set. In order to produce a largeDT elec the application of electric field must be accompaniedby a correspondingly large change in entropy of the system.For ferroelectric materials, the change in entropy is gov-erned by the degree of polarization of the material[11,15–19,22–24]. Therefore, a large change in polarizationis required in order to obtain significant DT elec. Maxwell’srelations for entropy change in ferroelectric materials pre-dict that a higher DT elec can be obtained from a material

reserved.

A. Chauhan et al. / Acta Materialia 89 (2015) 384–395 385

which can withstand a larger intensity of electric field [8].Since, for a given material the bulk ceramic possesses theleast dielectric breakdown strength followed by single crys-tals and thin films, the magnitude of EC effect increases inthe same order. However, the use of thin film morphologyseverely limits the heat extraction ability per cycle. Whilethe use of bulk ferroelectrics are plagued by low adiabatictemperature changes and restrictions on the upper boundof EC effect [31]. These drawbacks have long prevented suc-cessful commercialization of ferroelectric refrigerators.

Several methodologies can be adopted to overcome theassociated disadvantages. The foremost solution suggestsincorporation of anhysteretic second order phase transitionthrough strain engineering in ferroelectric materials [2,8].Second order phase transitions can be driven over a widerange of temperatures and are associated with large entropyordered structural transformations. Additionally, nothreshold field is required to achieve a second order transi-tion and hence, a material’s performance can be substan-tially enhanced when EC effect is obtained by driving itthrough a crossover between first and second order transi-tions. A second approach towards enhancing the DT of aferroelectric based cooling system would be to couple mul-tiple caloric effects within the same material. This approachis classified as multicaloric and significant improvement inperformance is expected as coupling of the caloric effectsare bound to increase the magnitude of temperature changethat is obtainable [5,32]. However, coupled caloric effectshave not yet been demonstrated experimentally and it israre to find materials which are capable of demonstratingappreciable multiple caloric effects.

This study is an attempt towards investigating the stress-mediated tuning and enhancement of the EC effect anddemonstration of elastocaloric effect in bulk ferroelectricmaterials. It is an established fact that ferroelectric materi-als are a subclass of piezoelectric materials which impliesthat polarization in ferroelectric materials is a function ofexternally applied stress. Thus, stress-mediation can beeffectively utilized to fine tune the magnitude of EC effector produce elastocaloric effect in bulk ferroelectric materi-als. In this study, the same has been demonstrated forPb(Mn1/3Nb2/3)O3-32PbTiO3�(PMN-32PT) single crystals.Indirect measurements using Maxwell’s relations revealenhanced electrocaloric effect for a certain range of applied

Fig. 1. Methodology of producing solid-state r

compressive stresses, and significant elastocaloric effectwhich rival the conventional unstressed EC effect. Finally,a novel cycle has been proposed for effective coupling ofthe two caloric effects to obtain enhanced multicaloric cool-ing capacity in bulk ferroelectric materials. The study isexpected to have a positive bearing on the field of ferroelec-tric solid-state refrigeration technology and provide insightinto the multicaloric ability of ferroelectric materials.

2. Materials and methods

2.1. Electrocaloric effect

When an adiabatically applied external stimulus pro-duces a large change in entropy of the material, the effectis termed as caloric effect. The corresponding change in tem-perature can be calculated using the following equation [8]:

DT ¼ � TC

Z xf

xi

@X@T

� �x

dx ð1Þ

Eq. (1) has been derived on the basis of Maxwell’s relationfor first order entropy change in a material system underthe application of an external stimulus. Here, T representsthe initial temperature of the material, x the applied exter-nal field, X the corresponding change in dependent para-meter and C the heat capacity of the material. Caloriceffect forms the basis of many solid-state refrigeration sys-tems. The mode of operation of a system employing solid-state refrigeration has been graphically depicted in Fig. 1.In electrocaloric effect, x represents the applied electric field(E) and corresponding change is produced in electric dis-placement (D). Since for ferroelectric materials,D ¼ 20E þ P � P (20 being the dielectric permittivity offree space), Eq. (1) can be rewritten as [8]:

DT elec ¼TC

Z Ef

Ei

@P@T

� �E

dE ð2Þ

It is evident from Eq. (2) that in order for a material tomanifest a large EC effect, it must possess a high pyroelectricconstant @P

@T

� �over a wide range of temperature and electric

field values. Thin films tend to perform comparativelybetter than bulk ceramics owing to their higher dielectric

efrigeration effect using ferroic materials.

386 A. Chauhan et al. / Acta Materialia 89 (2015) 384–395

breakdown strength and enhanced polarizability. However,the major drawback with thin films is their lower thermalinertia. The total enthalpy change Q for a thermodynamiccycle is given by the relation:

Q ¼ m � C � DT ð3ÞHere C is the specific heat capacity at constant electric field.Judging from Eq. (3), it is evident that thin films will ulti-mately suffer from low enthalpy change. This puts themat a disadvantage when compared to bulk ceramics; eventhough the magnitude of DT elec is higher for thin films,the advantage will be offset by the reduced bulk of the sys-tem. Therefore, it would be highly beneficial if a relativelylarge temperature change can be induced in bulk ceramics.This can be achieved by coupling the conventional ECeffect with additional entropy-ordered ferroelectric–ferro-electric (f–f) phase transition as discussed in the nextsection.

2.2. Stress-mediated tuning of electrocaloric effect and originof elastocaloric effect

Phenomenological theory developed for ferroelectricmaterials can be used as an alternate approach for under-standing and improving the EC response. According tothe theory, the general form of Gibbs free energy due topolarization can be described using [33]:

G ¼ 1

2aD2 þ 1

2nD4 þ 1

2cD6 ð4Þ

Here, a ¼ bðT 1 � T Þ , T being the initial temperature, b is atemperature dependent material constant while n and c aretemperature independent material constants. Generally, theterm ðT 1 � T Þ is dependent upon temperature T 1 in theform of Curie–Weiss law which changes its sign at T [34].Additionally, b and c are the positive constants, while nassumes a negative value for the first order transition andpositive value for second order transition [34]. Using Eq.(4), the change in entropy DT of a ferroelectric materialcan be represented as [33]:

@G@T

� �D

¼ �DS ¼ 1

2bD2 ð5Þ

Thus, adiabatic temperature change DT for a ferroelec-tric material can be determined using the new relation [33]:

DT ¼ 1

2cEbTD2 ð6Þ

The nature of Eq. (6) indicates that electric displacement(or polarization) is the most important factor governing theadiabatic temperature change. Additionally, it is also to benoted that a material possessing a higher b would also dis-play a higher EC effect. It is for the same reason that ferro-electric polymers, specially P(VDF-TrFE) have beencredited with the highest electrocaloric effects. The valueof b for ferroelectric polymers is generally an order of mag-nitude higher than those obtained for either ceramics orsingle crystals.

However, recent observations have been reported wherethe degree of polarization in a ferroelectric material hasbeen altered by the application of compressive pre-stresses.This in turn is expected to have a direct bearing on theextent of EC effect demonstrated by the material underthe stressed conditions. The phenomenon is particularly

large for materials in the compositional vicinity of theirmorphotropic phase boundary (MPB). In ferroelectricmaterials, MPB signifies the co-existence of multiple phaseswithin a homogeneous solid solution. These phases areseparated by only a small difference in their free energies.Therefore, a reversible transformation can be drivenbetween two corresponding phases by suitable applicationof external stimulus. Most of these transitions are ferroelec-tric-ferroelectric (f–f) in nature and are accompanied bystructural transformations. Additionally, these structuraltransformations are followed by large volumetric strains,which are preferably oriented in the direction of appliedexternal electric and mechanical actuations. These areindicative of a second order phase transformation and arecaused by structural transformations. This effect is directlyreflected in the ferroelectric response of the material and isaccompanied by considerable change in polarization. Thisphenomenon has been extensively reviewed in the literaturefor a number of materials and has been employed for tun-ing of ferroelectric response [35,36], energy harvesting [37]and energy storage applications [38].

Coupling the change in free energy of the system, due tostress applications, with the change in energy due to polar-ization can be used to enhance and even control the extentof EC effect in ferroelectric materials [39,40]. Furthermore,the large changes in strain energy alone can be used to drivethe material through considerable amount of elastocaloriceffect, which can be quantified by using Maxwell’s relationfor elastocaloric effect as follows:

DT elas ¼ �TC

Z r2

r1

@e@T

� �r

dr ð7Þ

In Eq. (7) the symbols are used to denote the conven-tional quantities of stress (r) and strain (e). In order todemonstrate the applicability of our hypothesis, we illus-trate these effects using data obtained from PMN-32PT sin-gle crystal. The necessary data have been adapted fromsources published in the literature [41,42]. Some of thedetails of measurements and observations are discussed inthe following sections.

2.3. Pb(Mn1/3Nb2/3)O3-32PbTiO3 (PMN-32PT) singlecrystal

The (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3�(PMN-xPT) com-position is representative of a binary solid solution of indi-vidual PMN and PT phases [43]. The single crystalsbelonging to this family have been extensively exploredand documented over the last decade, owing to their excel-lent piezoelectric attributes. Like any binary composition,PMN-xPT exhibits a morphotropic phase boundary fromx = 30–38 mol.% PT [35]. PMN-xPT single crystals havebeen observed to possess a rhombohedral phase fromx = 30–32 mol.% PT and a tetragonal phase is manifestedwith increasing PT content. Both these phases have beendocumented to exist at room temperature, co-existing witha small amount of monoclinic phase. However, the presenceof external stimulus in the form of stress, electric field andtemperature can give rise to a host of intermediate phasesincluding several variants of the monoclinic phase and anorthorhombic phase. Detailed documentation has been pre-sented by various authors regarding the structural transfor-mation and changing response of PMN-32PT single crystalsnear their MPB compositions [44]. Most notably, the work

A. Chauhan et al. / Acta Materialia 89 (2015) 384–395 387

by McLaughlin et al. [41,42] and Webber et al. [45] is recom-mended for a detailed review on the behaviour of PMN-32PT single crystals under combined loading.

PMN-32PT single crystals propose to offer the bestinsight into structural phase transformation as 32 mol.%PT marks the boundary between the dominant rhombohe-dral and tetragonal phases. All the other phases can beobserved between these two independent states, subjectedto varying degrees of external loading. Hence, this compo-sition was selected for the study. P-E loops (used in the pre-sent study) were adopted from McLaughlin et al. [41,42].

3. Results and discussion

PMN-32PT single crystals poled along the h001i direc-tions were exposed to varying degrees of directional com-pressive stress and temperatures using a modified SawyerTower circuit [41,42]. Unipolar electric field was used toobtain saturated polarization versus electric field P–E loops

Fig. 2. Unipolar polarization versus electric field (P–E) hysteresis loops for Pstress (x33) and operating temperature of (a) 278 K, (b) 293 K, (c) 313 K, (d

for the crystals. An example of the loops generated for dif-ferent magnitudes of applied stress and temperature isgiven in Fig. 2. Additionally, the corresponding strain val-ues for the crystal under different loading conditions werealso obtained for the purpose of evaluating its elastocaloricresponse. The same has been displayed in Fig. 3. Severalinstances of experimental demonstration and direct mea-surement of caloric effects have been reported in the lit-erature. However, the number of such investigations islimited owing to the fact that only a few calorie-metres existwhich allow real time analysis of thermodynamic propertiesof materials under the application of multiple external sti-mulus. Hence, in majority of the studies the predictionsare derived through an indirect measurement of materialdata and use of Maxwell’s relations. Using these data inconjunction with Eqs. (2) and (7) the magnitude of DT elec

and DT elas has been calculated and displayed in Figs. 4and 5 respectively.

While calculating the results for PMN-32PT singlecrystals, Maxwell’s relations were used extensively. At this

MN-32PT single crystals as a function of applied uniaxial compressive) 323 K, (e) 333 K and (f) 353 K.

388 A. Chauhan et al. / Acta Materialia 89 (2015) 384–395

point, it is imperative to mention that Maxwell’s relationsonly hold true for non-ergodic systems undergoing firstorder phase transitions [40,46,47]. The PMN-32PT compo-sition being used in this study is a relaxor ferroelectric bynature. It implies that polarization in PMN-32PT resultsfrom changes observed in nano-domains which do not dis-play any significant long range coupling. As such PMN-32PT is classified as an ergodic system which requires theuse of free energy evaluation or mean-field theory such asthat proposed by Landau, to produce accurate results.However, Maxwell’s theory can be used to predict the gen-eral behaviour of the system with sufficient accuracy andhas been used previously to predict caloric effects in relaxorcompositions [40,46,47]. Thus, we proceed on the assump-tion that Maxwell’s theory can be used to generalize andpredict the caloric trends of the PMN-32PT compositionunderstudy. Fig. 4 gives a graphical representation of theresults obtained for EC effect in PMN-32PT single crystal.Fig. 4 (a through d) represents the change in peak polariza-tion, adiabatic temperature change, entropy and enthalpyrespectively, as a function of applied stress and initial tem-perature. Uniaxial compressive loading has been used alongthe axis of applied external electric field (x33). It can beobserved that the value of peak polarization, as a functionof temperature, increases with the applied stress andremains higher than that of unstressed material even upto the application of 28 MPa. The corresponding change

Fig. 3. Uniaxial compressive strains for PMN-32PT single crystal as afunction of applied uniaxial compressive stress (x33) and operatingtemperature for (a) 0 MV m�1 and (b) 1.5 MV m�1 applied electricfields respectively.

in adiabatic temperature of the material also increases inaccordance to the induced pyroelectric coefficient of thematerial. A highest DT elec of 0.35 K is observed at a tem-perature of 323 K for an applied compressive stress of14 MPa. This value represents a 30% improvement overthe DT elec of 0.27 K for unstressed material while the elec-tric field normalized value of EC effect obtained for stressedmaterial is 0.0247 K cm kV�1. Upon a further increment(P21 MPa) in the value of applied stress, the peak shiftstowards lower temperature regime (�300 K) signifying astructural transition that is intermediate to the dominatingrhombohedral and tetragonal phases. It is for the appliedcompressive stresses of 21 MPa or greater that anotherstructural transition can be observed in the vicinity of330 K. This is marked by a sudden increase in the valueof pyroelectric coefficient. The phenomenon is reciprocatedby the adiabatic temperature change and a new maximumDT elec of 0.62 K is predicted at 28 MPa and 350 K. The

ig. 4. Variation of thermodynamic attributes (a) peak polarizationdPm/dT), (b) electrocaloric effect (DT), (c) entropy (DS) and (d) heatarrying capacity (DQ) as a function of applied stress and initialemperature for PMN-32PT single crystal.

F

(ct

A. Chauhan et al. / Acta Materialia 89 (2015) 384–395 389

value obtained at this point is 100% improvement overunstressed material. Fig. 4 illustrates the effect of appliedcompressive stress on EC effect in PMN-32PT for varyinginitial temperatures. The field assisted (f–f) phase transi-tions can be clearly identified by the sudden change in slopeof the attributes. Further, electrocaloric effect in variouscompositions of (1-x)Pb(Mg1/2Nb2/3)O3-xPbTiO3�(PMN-xPT) is given in Table 1. It can be easily concluded thatthe PMN-32PT has very small electrocaloric effect 0.27 K(at 2 MPa) as compared to other compositions. However,application of stress can drastically enhance the elec-trocaloric cooling capacity from 0.27 K to 0.62 K (at28 MPa) which is double to initial one. This stress mediatedelectrocaloric effect is comparable with most of the otherPMN-32PT compositions. Therefore, this finding opens anew window for tuning of electrocaloric cooling withoutaffecting the chemistry of the materials.

A corresponding trend can be observed in valuesobtained during uniaxial strain measurement of thePMN-32PT crystal. Fig. 3 (a and b) represents the valuesof uniaxial strain produced in PMN-32PT single crystalas a function of applied stress and operating temperature,for 0 and 1.5 MV m�1 applied electric fields respectively.These data have been further used in conjunction withMaxwell’s relation as described in Eq. (7) to calculateDT elas for the two electromechanical loading conditionsrespectively. Results for the same have been presented in

Fig. 5. Elastocaloric effect in PMN-32PT single crystals as a functionof applied stress and temperature for (a) 0 MV m�1 and (b)1.5 MV m�1.

Fig. 5. A highest DT elas of 0.36 K is observed in the vicinityof 320 K for an applied compressive stress of 28 MPa.When compared to the conventional unstressed DT elec of0.27 K (at 323 K) this value again represents an improve-ment of 80% in the caloric capacity of the material and iscomparable to the enhanced DT elec of 0.35 K which isobtained under a compressive pre-stress of 14 MPa. Thisis where the peak DT elec is observed for all values of com-pressive stress applied. At this point it becomes importantto mention that the elastocaloric effect obtained here isinverse in nature. It implies that the material cools downupon the application of compressive stress and heats upupon its removal. Such behaviour is expected due to thepositive strain rate observed in the crystal as a function

of increasing temperatures @e@T

� �r> 0

� �. However, a slight

anomaly is observed near 310 K where the value of strainobserved in the crystal suddenly increases. This can be cred-ited to the onset of monoclinic phase under the combinedelectromechanical loading (at 1.5 MV m�1) and a tem-perature of 310 K. The transformation is seemingly invari-ant to the magnitude of applied compressive stress andseems to be only dependent on temperature. However,the value of strain obtained during the phase transforma-tion is significantly enhanced under the application ofexternal electric field which also results in larger DT elas.

3.1. Ferroelectric-ferroelectric (f–f) structural phase transi-tion; tuning of electrocaloric effect and origin of elastocaloriceffect

The highest EC effect in ferroelectric materials has beenpredicted near ferro-para (f–p) phase transition tem-peratures. This is due to the strong coupling that existsbetween structural transition and polarization at this point.We now proceed on the assumption that a similar couplingexists between structural transition and polarization abilityin (f–f) phase change that is exhibited by the ferroelectricmaterials at MPB. It has been well reported in the literaturethat enhanced piezoelectric and pyroelectric properties areobtained for materials in the compositional vicinity of theirMPB. Thus, the composition in this study has been selectedclose to its MPBs such that upon a field induced structuraltransition the net entropy change DSnet of the system is givenby:

DSnet ¼ DSpol þ DSstr ð8ÞHere, DSpol is contribution due to change in polarization,while DSstr is the contribution due to change in lattice para-meters. Based on these inputs, the values of various ther-modynamic attributes, observed as a function ofoperating temperature and compressive stress, have beenpresented in Fig. 4 for PMN-32PT, respectively.

It was earlier hypothesized that (f–f) transition can beused to enhance the ECE by increasing the net entropychange for the material system. However, another impor-tant observation that can be made from these results is thatthe shift in the EC response with the applied stress is rathergradual in nature. The only exception to this rule isobserved near the point of transition where the rate ofchange of thermodynamic attributes is high. Thus, properapplication of mechanical confinement/compressive pre-stresses can be used to tune the EC response of the materialconcerned. This can be explained on the basis of drivingenergy required for the (f–f) structural transition in

Table 1. Comparison of EC properties in PbMg1/2Nb2/3O3 (PMN) and (1-x)Pb(Mg1/2Nb2/3)O3-xPbTiO3 (PMN-xPT).

Material Bulk or film SC or PC* T (K) DT (K) DE (MV.m�1) DT/DE (10�6 mKV�1) References

PMN Bulk SC 226 0.15 1.5 0.1 [48]PMN Bulk PC 340 2.5 9 0.28 [49]PMN-8PT Bulk PC 296 1.35 1.5 0.9 [50]PMN-10PT Bulk PC 301 1.25 1.5 0.83 [50]PMN-10PT Bulk PC 323 0.45 2.91 0.15 [51]PMN-10PT Bulk PC 328 1 4 0.25 [52]PMN-10PT Bulk SC[111] 283 1 1.6 0.625 [47]PMN-13PT Bulk PC 343 0.56 2.4 0.23 [53]PMN-15PT Bulk PC 291 1.71 1.6 1.07 [47]PMN-25PT Bulk PC 305 0.4 1.5 0.267 [50]PMN-25PT Bulk SC[100] 393 0.56 2.5 0.22 [15]PMN-25PT Bulk SC[110] 373 0.89 2.5 0.37 [15]PMN-25PT Bulk SC[111] 373 1.1 2.5 0.44 [15]PMN-25PT Bulk PC 383 0.9 2.5 0.36 [15]PMN-28PT Bulk SC[110] 404 0.53 0.9 0.59 [54]PMN-29PT Bulk SC[100] 444 2.3 5 0.46 [55]PMN-29PT Bulk SC[111] 440 2 5 0.4 [55]PMN-30PT Bulk PC 430 2.7 9 0.3 [56]PMN-30PT Bulk SC[111] 400 2.7 1.2 2.25 [57]PMN-30PT Bulk SC[100] 408 0.65 1 0.65 [58]PMN-7PT Thin film PC 298 9 72.3 0.12 [59]PMN-10PT Thin film PC 348 5 89.5 0.056 [60]PMN-32PT Thin film [001] 418 13.4 60 0.22 [61]PMN-33PT Thin film [001] 418 14.5 60 0.24 [62]PMN-33PT Thin film PC 508 4.25 11.6 0.36 [63]PMN-35PT Thin film PC 413 31 74.7 0.41 [64]PMN-32PT# at 2 MPa Bulk SC[001] 318 0.27 1.5 0.19 Present workPMN-32PT# at 28 MPa Bulk SC[001] 353 0.62 1.5 0.41 Present work

* single crystal (SC) or polycrystalline (PC).# Pb(Mn1/2Nb2/3)O3-32PbTiO3 (PMN-32PT).

390 A. Chauhan et al. / Acta Materialia 89 (2015) 384–395

ferroelectric materials. The Helmholtz free energy density Ain a ferroelectric material is defined as [37]:

dA ¼ rdeþ EdD� TdS ð9ÞIn Eq. (9), the symbols are used to denote the conven-

tional quantities of stress (r), strain (e), electric field (E),electric displacement (D), temperature (T) and entropy(S). It can be deduced from Eq. (9) that the free energyof the material can be suitably altered by the applicationof stress (resulting strain), electric field (resulting electricdisplacement) or temperature (resulting change in entropy).Some finite amount of coupling is expected to exist betweenthe three phenomena, but it is negligibly small compared todirect effects and thus can be safely discounted from consid-eration. Further expanding upon this knowledge, it can bededuced that carefully controlling the nature and magni-tude of external impetus, a preferred free energy densityand phase can be attained. Thus, for transition betweentwo different phases, Eq. (9) can be rewritten as [65]:

dA1!2 ¼ rde1!2 þ EdD1!2 � TdS1!2 ð10ÞIn Eq. (10) the superscripts 1 and 2 indicate the initial

and final phases respectively. These Eqs. (9) and (10) arevalid for reversible transformation. It implies that oncethe external actuation is removed, the material reverts toits original state.

For the crystals discussed in this study, the initial phaseis predominantly rhombohedral while the second phase isdominated by the presence of tetragonal structure. Bothof these co-exist with traces of other phases in minoramounts. Application of compressive pre-stresses provides

part of the energy required for achieving the phase transi-tion and the rest is provided by the effect of temperature.At this point it is imperative to mention that the effect ofelectric field is to counter the domain switching producedby the application of stress and temperature and restorepolarization. Thus, the combined work of electric field,stress and temperature is being utilized to drive the struc-tural transition in a desired direction. Fig. 6 describes thecombined effect of electro-mechanical (x33) loading on thestructural transitions for PMN-32PT single crystal. Thisappends to the net entropy change and boosts the magni-tude of DT elec. Additionally so, if one of the external fields(stress or temperature) becomes dominating in nature, thematerial stays frozen in its preferred structure. This isbecause of the incomplete energy provided by the compet-ing electric field required to drive the phase transformation.This is evident by the observable shift in the pyroelectriccoefficient and peak entropy change towards a lower mag-nitude of temperature, as depicted in Fig. 4 (a and c).

Furthermore, it is expected that ferroelectric materialsare also capable of producing significant amount of elas-tocaloric effect. It stems from the fact that ferroelectricmaterials form a subclass of piezoelectric and pyroelectricmaterials [66]. This implies that their polarization changeswith respect to applied external stimulus in the form ofstress and temperature. This is represented by a change inthe remnant polarization of the material [66]. Such beha-viour is intensified greatly under the application of externalelectric field due to the inherent non-linear response of fer-roelectric materials under high field actuation. Since thechange in polarization of a ferroelectric material is closely

Fig. 6. Role of combined electro-mechanical (x33) loading on the ferroelectric–ferroelectric structural transition in PMN-32PT single crystal.

A. Chauhan et al. / Acta Materialia 89 (2015) 384–395 391

related to the change in entropy of the material itself, it is tobe expected that ferroelectric materials are capable of dis-playing both EC and elastocaloric response [46]. However,an important concern is the suitable prediction and mea-surement of stress-induced temperature change in ferroelec-tric materials. One of the methods of doing this is tomeasure the polarization change in such materials withrespect to applied stress and then use modified Maxwell’srelationship to determine the ‘piezocaloric’ response.However, such predictions represent an indirect assessmentof the elastocaloric ability of the ferroelectric materials andmay not be a true indicator of the prime cooling capacity.The other method of investigation involves a directmeasurement of strain values as a function of temperatureand applied stress and to calculate the elastocaloric effectdirectly using the original Maxwell’s relationship. Thelatter approach forms the basis of this investigation.Since large measureable strains are required to predict, withconsiderable accuracy, the full extent of elastocaloriceffect; it becomes a prerequisite to select a suitableferroelectric material capable of displaying large recover-able strain response. PMN-32PT single crystals have beenlargely reported in the literature for their excellent piezo-electric and pyroelectric properties. Hence, it forms an idealcandidate for investigation of ferroelectric elastocaloriceffect.

Under the application of a compressive stress, up toelastic limit, the energy is stored in the material by suitablestretching and compression of molecular bonds with theanalogy of a complex spring system. This energy is releasedupon the removal of external load and material regains itsshape. The finite change in entropy that is observed in thematerial’s structure, between loaded and unloaded states,gives rise to the linear elastocaloric effect inherent to mostmaterial classes. However, in a poled ferroelectric materialthis response is modified. Here, an unloaded sampleconsists of oriented dipoles most of which are aligned in

a particular direction forming the polar vector of the bulkmaterial. When large external compressive stress is appliedalong the poling direction, non-180� ferroelastic domainswitching is observed in the material; accompanied by acorrespondingly large strain response. This is known aspiezoelectric effect and indicates how ferroelectric materialsconvert mechanical input into electric potential. This phe-nomenon has been previously reported by our group forenhanced electro-mechanical and electro-thermal energyconversion [67,68]. Under the application of an externalelectric field, the magnitude of stress required to causedepolarization is increased and the ferroelastic switchingoptions available for dipolar rotation are limited due toemergence of electric potential minima favouring a par-ticular direction [67,68].However, during the process, thematerial undergoes large entropy variation which can giverise to significant elastocaloric effects.

3.2. Multicaloric coupling for enhanced cooling capacity

This knowledge alone can be used to arrive at the consen-sus that appreciable elastocaloric effect can be obtained inferroelectric materials and the same has been demonstratedin this study using PMN-32PT single crystals. Since fromthe present results it can now be inferred that two types ofcaloric effects exist within the same material itself. Suitablecoupling of these two individual caloric effects could beemployed to produce multicaloric cooling and substantiallyimprove the thermodynamic efficiency of the material. Inorder to achieve this, a new electro-mechanical thermody-namic cycle has been proposed. The suggested methodologyresembles the Ericsson cycle, previously employed by ourgroup for enhanced electromechanical energy conversion[67,68]. Fig. 7 indicates typical electro-mechanical cyclebetween 2–28 MPa stress and 0–1.5 MV m�1 electric field(at 293 K). Various processes of this cycle are describedbelow:

Fig. 7. Proposed electromechanical cycle over unipolar P–E hysteresisloops of PMN-32PT single crystal (at 293 K and 2–28 MPa stressinterval) for multicaloric cooling.

392 A. Chauhan et al. / Acta Materialia 89 (2015) 384–395

3.2.1. Process 1–2 (Adiabatic electric field application)In this process the electric field is applied adiabatically to

an unpoled ferroelectric material. This produces elec-trocaloric heating of the material under zero stress condi-tions. The heat produced during the process is rejected tothe environment (sink) as sensible heat and the material isallowed to cool down.

3.2.2. Process 2–3 (Adiabatic stress application underconstant electric field)

The second step involves the application of adiabaticcompressive stress to the material. This produces cooling

Fig. 8. Schematic of the proposed methodology for obtaini

of the material due to inverse elastocaloric effect. Thus,the material’s temperature is lowered below sinktemperature.

3.2.3. Process 3–4 (Adiabatic electric field removal)Once the cycle reaches the end point of process 2–3, the

electric field applied to the material is shut off in an adiabat-ic fashion. This results in an additional EC cooling effect,the magnitude of which is dependent on the degree of con-finement (applied stress). Thus, if processes 2–3 and 3–4 areexecuted in rapid succession, the individual caloric effectscan be coupled to yield an enhanced cooling capacity usingthe same material. This material can now be used to absorbheat from the source to produce the necessary refrigeration.

3.2.4. Process 4–1 (Adiabatic stress removal under constantelectric field)

The final step of the cycle involves removal of the com-pressive stress which restores the material to its innate formand thus completes the process.

Schematic of the above mentioned cycle is depicted inFig. 8. The proposed methodology has two variables whichcan be further optimized to tune the total caloric response ofthe material. The first is the initial operating temperature ofthe material which decides the magnitude of DT for both ECand elastocaloric effects. The second is the magnitude ofapplied compressive stress which also affects both the elas-tocaloric cooling capacity and the EC cooling obtained atthe end of process 3–4. In order to further elaborate onthe topic, Fig. 9 has been used to formulate the multicaloriccooling capacity of PMN-32PT single crystal as a functionof operating temperature and applied stress. The last curverepresents the combined DT obtainable at the end of process3–4. It can be observed from the Fig. 9 that optimization of

ng combined caloric cooling in ferroelectric materials.

Fig. 9. Elastocaloric, electrocaloric and multicaloric temperature changes at compressive stress of (a) 7 MPa (b) 14 MPa (c) 21 MPa and (d) 28 MPaas a function of temperature.

A. Chauhan et al. / Acta Materialia 89 (2015) 384–395 393

cooling capacity can be achieved by a careful selection of theoperating temperature and applied compressive stress.Additionally, the same methodology can be used to createboth heating and cooling effects of various magnitudes. Fur-thermore, the presence of anomalous (inversion) caloriceffects can also be used to obtain cooling effects at the termi-nus of other processes. For example, when the applicationof external electric field causes inverse EC effect, the coupledcaloric cooling can be obtained at the end of process 2–3instead of the previously suggested process 3–4. An analysisof the presented data also reveals that a maximum com-bined DT of �0.63 K can be obtained for an initial tem-perature of 323 K with the operating parameters of (0–1.5 MV m�1 and 2–14 MPa). This value represents a sig-nificant 100% increment over the conventional unstressedDT elec of 0.31 K. Even when compared to the mechanicallytuned (14 MPa) DT elec of 0.35 K it still indicates an incre-ment of over 80% in the cooling capacity of the material.Another maxima of combined caloric effect is observed foran operating temperature of 353 K where a total DT of�0.76 K is observed for cycle parameters of (0–1.5 MV m�1

and 2–28 MPa).

According to the inference derived from the observa-tions made, it can be safely concluded that suitable cou-pling of (f–f) phase transition with conventional EC effectcan be used to significantly enhance the adiabatic tem-perature change. Furthermore, the knowledge of stress-me-diated tuning of EC response can be applied to a host ofother ferroelectric materials to avail increased efficiency.Additionally, wherever possible, suitable coupling of elas-tocaloric effect can be further used to increase the produc-tivity of ferroelectric based solid-state refrigeration systems.Thus, increment in output can be obtained from the samematerial without the need to alter either its chemistry ormorphology. These results are bound to have far reachingconsequences in the field of ferroelectric solid-state refrig-eration and can provide the much needed technologicalbreakthrough to make bulk ferroelectric materials employ-able as suitable caloric candidates. This study is also aimedto trigger extensive research in the field of mechanical tun-ing of EC effect and multicaloric potential of other ferro-electric materials. This is one of the first instances wherean enhanced multicaloric response has been experimentallydemonstrated in a ferroelectric material and much yet

394 A. Chauhan et al. / Acta Materialia 89 (2015) 384–395

remains to be explored. Research in this field needs to beexpanded to other materials and morphologies as the find-ings indicate towards a potential technological break-through that can revolutionize the field of ferroelectricsolid-state refrigeration.

4. Conclusion

Ferroelectric materials respond to externally appliedcompressive stress by producing a change in their polariza-tion. Furthermore, this effect is substantially enhancedwhen the material is fabricated in the compositional vicinityof its morphotropic phase boundary and is accompanied bya corresponding structural change and large strainresponse. The objective of this study was to investigatethe effect of compressive stress on the electrocaloriceffect and to explore the elastocaloric potential ofbulk Pb(Mn1/3Nb2/3)O3-32PbTiO3 single crystal. It wasobserved that application of compressive pre-stress can beused to suitably enhance and even tune the electrocaloricresponse of the PMN-32PT single crystal. A maximumDT elec of 0.62 K can be obtained for an applied compressivestress of 28 MPa which represents a remarkable 200%improvement over the peak unstressed DT elec of 0.27 K.Furthermore, the accompanying large strain variationsand second order structural transition can be used to obtainsignificantly large values of DT elas 0.36 K for an operatingtemperature of 323 K and applied compressive stress of2–28 MPa (at 1.5 MV m�1). The large elastocaloric respon-se trumps the conventional unstressed DT elec of 0.27 K andcan be achieved through ferroelastic domain switchingalone. The results indicate that ferroelectric materials pos-sess significant multicaloric potential and can yield bettercooling when employed as elastocaloric materials asopposed to conventional electrocaloric effect. Finally, thetwo individual caloric effects were coupled using a novelelectro-mechanical thermodynamic cycle to obtain a fur-ther enhanced multicaloric DT of �0.63 K for an optimizedoperating temperature of 323 K and applied compressivestress of 2–14 MPa. The results of this study are expectedto benefit greatly the field of ferroelectric solid-state refrig-eration and open new horizon for future exploration of theregime of multicaloric effects in ferroelectric materials.

Acknowledgments

One of the authors (Rahul Vaish) acknowledges support fromthe Indian National Science Academy (INSA), New Delhi, India,through a Grant by the Department of Science and Technology(DST), New Delhi, under INSPIRE faculty award-2011 (ENG-01) and INSA Young Scientists Medal-2013.

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