Advanced materials for solid-state refrigeration
aa r X i v : . [ c ond - m a t . m t r l - s c i ] M a r
51 INTRODUCTION
Advanced Materials for Solid-State Refrigeration.
Llu´ıs Ma ˜nosa, ∗ a Antoni Planes, a and Mehmet Acet b Received Xth XXXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XXFirst published on the web Xth XXXXXXXXXX 200X
DOI: 10.1039/b000000x
Recent progress on caloric effects are reviewed. The application of external stimuli such as magnetic field, hydrostatic pressure,uniaxial stress and electric field give rise respectively to magnetocaloric, barocaloric, elastocaloric and electrocaloric effects.The values of the relevant quantities such as isothermal entropy and adiabatic temperature-changes are compiled for selectedmaterials. Large values for these quantities are found when the material is in the vicinity of a phase transition. Quite oftenthere is coupling between different degrees of freedom, and the material can exhibit cross-response to different external fields.In this case, the material can exhibit either conventional or inverse caloric effects when a field is applied. The values reportedfor the many caloric effects at moderate fields are large enough to envisage future application of these materials in efficient andenvironmental friendly refrigeration.
Every material changes its temperature when subjected to asudden change of an external field (electric, mechanical, mag-netic...). This property is generally known as the caloric effectand is related to a change in the material’s entropy when theexternal field is isothermally modified. Generally, around roomtemperature, the magnitude of such a caloric effect is smalland the temperature-change only becomes relatively large atvery low-temperatures when the specific heat of the material islow. For this reason, refrigeration based on sweeping an ex-ternal field adiabatically has been limited to low-temperaturesfor very long. The typical example is the attainment of cryo-genic temperatures by making use of the magnetocaloric effectin paramagnetic salts when adiabatically demagnetized .The efficient use of the magnetocaloric effect for refrigera-tion around ambient temperature was proposed by Brown in thelate seventies, and a major breakthrough took place at the endof the nineties with the discovery by Pecharsky and Gschnei-dner of a material exhibiting large magnetic-field-induced en-tropy and temperature-changes around room temperature; theintermetallic Gd-Si-Ge compound, which was denoted as a gi-ant magnetocaloric material . This discovery boosted the re-search in the field, and nowadays there is a large variety ofmaterials which have been reported to exhibit the giant magne-tocaloric effect. The key feature for the effect to be giant is thepresence of a first-order phase transition that most of these ma- a Departament Estructura i Constituents de la Mat`eria, Facultat de F´ısica.Universitat de Barcelona. Diagonal 645. 08028 Barcelona. Catalo-nia. Fax: 34 934037063; Tel: 34 934039181; E-mail: [email protected];[email protected] b Experimentalphysik. Universit¨at Duisburg-Essen D-47048 Duisburg. Ger-many. E-mail: [email protected]. terials undergo. It is the transition entropy-change (associatedwith the latent heat of a first-order phase transition) that makesthe major contribution to the field-induced entropy-change ofthe magnetocaloric effect. As a consequence of strong inter-play between magnetic and structural degrees of freedom, thephase transition also involves typically a change in the crystal-lographic structure.While most of the efforts are nowadays devoted to investi-gating the magnetocaloric effect, the possibility of inducing thephase transition in the solid state by fields other than magneticopens up new routes for solid-state refrigeration using manydifferent external stimuli. Indeed, materials showing signifi-cant changes in a certain thermodynamic quantity at the phasetransition − such as volume, strain or polarization − will be ex-tremely sensitive to the application of the corresponding ther-modynamically conjugated field − pressure, stress and electricfield, respectively. Hence, the possibility of inducing the transi-tion by means of pressure, uniaxial stress and electric field willgive rise to the barocaloric, elastocaloric and electrocaloric ef-fects, respectively. A solid-state cooling cycle is illustrated inFig. 1 based on a giant caloric effect attained by applying ageneric external field.Usually the material’s entropy decreases when an externalfield is applied isothermally, and its temperature increases whena field is applied adiabatically. Since this is the most frequentsituation, the caloric effect is known as ’conventional’. How-ever, there are some cases for which the situation is reversed:the entropy increases on applying a field isothermally, and thematerial cools. This effect is known as the ’inverse’ caloric ef-fect. Inverse caloric effects are possible in those systems witha strong coupling between different degrees of freedom, with across-response to the external fields, and for which the entropycontains contributions from all these degrees of freedom.1.1 Experimentaldeterminationofthecaloriceffects 2 THERMODYNAMICSOFCALORICEFFECTS. Fig. 1
Refrigerating cycle. Schematic diagram for a solid-state basedrefrigerating cycle based on a conventional giant caloric effect. Onthe first stage the field is adiabatically applyied resulting in atemperature temperature increase of the material (a forward phasetransition occurs in this stage). On the second stage the material isallowed to cool down at constant field by transferring heat to a heatsink. On the third stage the field is adiabatically removed and thematerial cools further (the reverse phase transition occurs in thisstage). In the fourth stage, the cool material absorbs heat from thecold reservoir (which becomes colder) and recovers the initial state.The images to illustrate the cycle correspond to a magnetic shapememory alloy which undergoes a martensitic phase transition. Thefield can be either magnetic field, hysdrostatic pressure or uniaxialstress.
There have been detailed and comprehensive reviews deal-ing with magnetocaloric materials and other caloric ef-fects . Also, details on the chemistry of the different ma-terials illustrated in the present paper can be found in ,and references therein. It is not intended to duplicate that ef-fort here. The present paper is aimed at presenting the differentcaloric effects reported so far. For each of them, we select aparticular material which conveniently illustrates the case.
Let a generic system in thermodynamic equilibrium be de-scribed in terms of the generalized displacements, x i , forces Y i (fields) and temperature T . Both displacements and forceshave the same tensorial character. However, a scalar approachis appropriate to describe most cases of interest (where onlythe magnitude of the external field is varied), and this will be considered in the following. The change in entropy reads: dS = CT dT + (cid:229) i (cid:18) ¶ x i ¶ T (cid:19) Y j dY i , (1)where we have made use of the Maxwell relations (cid:16) ¶ S ¶ Y i (cid:17) T , Y j = i = (cid:16) ¶ x i ¶ T (cid:17) Y j , and C is the heat capacity.For an isothermal change of a given field from 0 to Y , thefield-induced entropy-change accounting for the caloric effectis given by: S ( T , Y ) − S ( T , Y = ) = D S ( T , Y ) = Z Y (cid:18) ¶ x ¶ T (cid:19) Y dY . (2)When the field is applied adiabatically, the correspondingchange in temperature is given by: D T = − Z Y TC (cid:18) ¶ x ¶ T (cid:19) Y dY (3)The above expressions quantify the magnetocaloric ( Y = H and x = M ), barocaloric ( Y = − p and x = V ), elastocaloric( Y = s and x = e ) and electrocaloric ( Y = E and x = P ) effects,where H is the magnetic field, M , magnetization, p , hydrostaticpressure, V volume, s , uniaxial stress, e , uniaxial strain, E ,electric field and P , polarization. The most commonly used method for the determination of theentropy-change makes use of isothermal x vs Y curves to nu-merically integrate eq. 2: D S ( Y , T ( k )) = D T k (cid:20) Z Y x ( T k + ) dY − Z Y x ( T k ) dY (cid:21) (4)where T ( k ) = ( T k + + T k ) / D T k = T k + − T k . While thisprovides a fast and easy procedure to quantify a caloric ef-fect, there has been considerable controversy on whether or notthe method can be applied to first-order phase transitions .Large spurious values were shown to arise from inappropri-ate experimental protocols . The major issue associated withthis problem is the existence of a hysteresis at the first-orderphase transition. However, at present, it is clear that the methodgives reliable data for D S , provided that the experimental proto-col is the appropriate one which correctly takes into account thehysteresis of the transition (details can be found in refs. ).Alternatively, D S can also be obtained by numerically integrat-ing the derivatives (cid:16) ¶ x ¶ T (cid:17) Y computed from measured isofield x ( T ) curves. The latter method ensures that the sample com-pletes the full phase transformation and consequently is freefrom giving spurious values.2 GD-SI-GECOMPOUNDS.THEGIANTPROTOTYPEMAGNETOCALORICMATERIAL.An alternative way to obtain D S is from calorimetric mea-surements of the temperature dependence of the specific heat ofthe material for different constant values of the external field Y (see equation 1). As previously mentioned, most giant caloricmaterials undergo a first-order phase transition, and the bestsuited calorimetric technique for first-order phase transitionsis differential scanning calorimetry (DSC). Purpose-built DSCoperating under different external fields have been developed tostudy several caloric effects . These devices provide heatflux as a function of temperature, from which the entropy (ref-erenced to a given state at T ) is obtained as: S ( T , Y ) − S ( T , Y ) = Z TT T ˙ Q ( Y ) ˙ T dT (5)where ˙ Q and ˙ T are the heat flux and cooling (or heating) rate,respectively. The field-induced entropy-change (accounting forthe caloric effect) is readily obtained by subtracting the inte-grated curves resulting from equation 5.Some of these devices can also operate at constant temper-ature and sweeping the external field. This method provides adirect determination of the field-induced entropy-change whichis given by: S ( T , Y ) − S ( T , ) = T Z Y ˙ Q ( T ) ˙ Y dY (6)where ˙ Y is the field rate.For a first-order phase transition, the shift in the transitiontemperature with field is governed by the Clausius-Clapeyronequation: dTdY = − D x D S (7)Since D S is negative (lower entropy of the low-temperaturephase), the shift in the transition is determined by the sign ofthe generalized displacement discontinuity, D x .Finally, a direct determination of a caloric effect is alsoachieved by measuring the temperature of the sample (usingan appropriate thermometer) while the external field is adia-batically modified. Although this is a quite direct method toquantify a caloric effect, adiabatic temperature-change exper-iments are usually difficult to implement, and the majority ofstudies are devoted to field-induced entropy-changes. At room temperature Gd Si Ge is paramagnetic and exhibitsa monoclinic structure (space group P / a ). On coolingit undergoes a magnetostructural transition to an orthorhom-bic (space group Pnma ) structure which is ferromagneticallyordered. Since Gd Ge is antiferromagnetic and Gd Si is ferromagnetic, the phase diagram for off-stoichiometricGd (Ge − x Si x ) is very rich. For all x , the ground state is ferro-magnetic with an orthorhombic structure (space group Pnma ),but different structural and magnetic phases can be found de-pending on x . A detailed phase diagram is described in .The giant magnetocaloric effect is observed for alloys with0 . ≤ x ≤ .
5. It is within this composition region that thealloy undergoes the paramagnetic to ferromagnetic first-ordermagnetostructural transition with a transition temperature thatlinearly increases with increasing Si concentration.The structural transition involves shear displacements ofatomic layers in which (Si,Ge)-(Si,Ge) dimers that are richer inGe increase their distances. This modifies the spin-dependenthybridization between Ge 4 p and Gd 5 d conduction states re-ducing the net Gd 5 d moment and the strength of the ferromag-netic RKKY exchange coupling across sheared layers . Inaddition to the giant magnetocaloric effect, the magnetostruc-tural transition is also at the origin of other technologicallyimportant properties of this alloy, such as giant magnetoresis-tance and magnetostriction .
100 200 300 T t (K) - S ( Jk g - K - ) Fig. 2
Magnetocaloric effect in Gd-Si-Ge. Transition entropy-changeas a function of the transition temperature for Gd (Ge − x Si x ) alloys.Figure adapted from ref. The magnetocaloric effect in the Gd (Ge − x Si x ) family hasbeen investigated by numerous researchers by means of sev-eral experimental techniques. Depending on composition andpurity of the samples, the reported entropy values range from10 Jkg − K − up to 50 Jkg − K − . The highest values corre-spond to those compositions for which the magnetostructuraltransition is close to the Neel temperature of the orthorhombicphase. Interestingly, the whole entropy-change has been foundto scale with the transition temperature, no matter if the latter istuned by composition or magnetic field . This result is illus-3 LA-FE-SIFAMILYANDTHEINVERSEBAROCALORICEFFECT.trated in fig. 2 and proves that magnetovolume effects due tothe magnetic field are of the same nature as the volume effectscaused by substitution. Such a statement has been corrobo-rated by later studies showing the equivalence of temperature,magnetic field, and chemical and hydrostatic pressures on thepolymorphism of Gd (Ge − x Si x ) .
240 250 260 270 280 290-12-8-40 S ( Jk g - K - ) p (kbar) T (K)
Fig. 3
Barocaloric effect in Gd-Si-Ge. Temperature dependence ofthe pressure induced entropy-change for Gd Si Ge . Figure adaptedfrom ref. . The magnetostructural transition involves a change in vol-ume of the unit cell: the volume of the low-temperature mono-clinic phase is larger than that of the ferromagnetic orthorhom-bic one. Owing to such a volume change, the transition issensitive to external hydrostatic pressure, and therefore, it isprone to exhibit a giant barocaloric effect. Such a possibilitywas theoretically predicted within the framework of band the-ory , and experimentally demonstrated by differential scan-ning calorimetry under hydrostatic pressure . Figure 3 showsthe pressure-induced entropy-change as a function of temper-ature for selected values of hydrostatic pressure for stoichio-metric Gd Si Ge . The values found for moderate pressuresaround 3 kbar are comparable to those corresponding to themagnetocaloric effect for fields around 2 T for this compound.For Gd Si Ge , both magnetocaloric and barocaloric effectsare found to be conventional, i.e. the entropy decreases withincreasing field and pressure. This is associated to the largermagnetization and lower volume of the low-temperature ferro-magnetic orthorhombic phase. The total entropy of the alloydecreases at the paramagnetic-monoclinic to ferromagnetic-orthorhombic transition, and such a decrease is due to a de-crease in both magnetic and structural contributions to the en-tropy. The La(Fe − x Si x ) compounds have a cubic NaZn structure(space group Fm ¯3 c ) in the concentration range 1.2 ≤ x ≤ . On cooling,the alloy orders ferromagnetically at a Curie temperature ( T C )that increases from 198 K for x = . x = .
5. Thesaturation magnetic moment decreases from 2.08 m B to 1.85 m B in this range . Above T C , an itinerant-electron metage-netic (IEM) transition can be induced by an external magneticfield . The transition has a marked first-order character forlow x , but for x ≥ Si Ge , the phase transition does not in-volve structural symmetry breaking, and the material keeps thecubic Fm ¯3 c structure above and below the transition temper-ature. However, a strong coupling between magnetism andstructure is evidenced by the change in the unit cell volume: thevolume of the low-temperature ferromagnetic phase is ∼ .These large magnetization and volume changes at the phasetransition suggests that this alloy might have interesting mag-netocaloric and barocaloric properties.The IEM trasition originates from a magnetic-field-inducedchange in the density of states of the 3d electrons at the Fermilevel . A strong magnetovolume effect originates from the ex-istence of a peak in the electronic density of states close to theFermi level that yields a negative contribution from spin fluc-tuations to the magnetostriction, resulting in a volume increaseon cooling from the paramagnetic to the ferromagnetic state.From the point of view of potential applications,La(Fe − x Si x ) is an attractive material due to its reducedhysteresis at the first-order phase transition (irreversibilitiesrelated to hysteresis reduce the cooling capacity of the alloy).It only has the drawback that the transition temperature isbelow room temperature. Two alternative methods have beenreported to bring the transition temperature to values close toroom temperature . One method is to add interstitial elements(H is the most successful one) that expand the crystalline latticeand modify the exchange interaction between iron atoms. Theelectron band-structure is not modified but the tri-critical pointis shifted to higher temperatures as a consequence of thechange in the lattice parameter. Another method is to replacesome Fe atoms by other magnetic transition metals (Co hasbeen found to be the best suited element). Such a substitutiondoes modify the electron band-structure and consequentlythe relative phase stability. As the amount of Co increases,the first-order character of the transition weakens; and forhigh enough Co content, the phase transition turns to secondorder. The study of the magnetocaloric effect in La(Fe − x Si x ) has4 LA-FE-SIFAMILYANDTHEINVERSEBAROCALORICEFFECT. S ( Jk g - K - ) Concentration of Si, x
Fig. 4
Magnetocaloric effect in La-Fe-Si. Magnetic-fieldentropy-change as a function of the Si concentration forLa(Fe − x Si x ). Figure adapted from ref. . An average density of7229 kgm has been used for all data. The line is a guide to the eyes. received considerable interest . Figure 4 shows reported valuesfor the isothermal entropy-change as a function of Si concentra-tion. A marked decrease is observed as x increases: The first-order character of the transition diminishes and approaches asecond order character. Such a decrease is overcome by tai-loring the transition temperature by the concentration of inter-stitial hydrogen in hydrogenated La(Fe − x Si x )H y compounds.While T c linearly rises with increasing y , the entropy-changeonly exhibits a very weak dependence on the hydrogen con-tent .
180 210 240 2700246810 p(kbar) 0 0.8 1 1.2 1.4 1.7 2.1 S ( Jk g - K - ) T(K)
Fig. 5
Barocaloric effect in La-Fe-Si. Temperature dependence ofthe pressure-induced entropy-change for LaFe . Co . Si . .Figure adapted from ref. . The pressure dependence of the magnetic and magne-tocaloric properties of La-Fe-Si and doped compounds hasbeen reported by several experimental techniques, and it hasalso been theoretically modeled . The barocaloric effectin LaFe . Co . Si . was measured by means of differen-tial scanning calorimetry under applied hydrostatic pressure .Figure 5 shows the values obtained for the pressure-inducedentropy-change as a function of temperature for selected valuesof the hydrostatic pressure. The barocaloric effect increaseswith pressure, and for pressures ∼ ∼
5T for the same compound. The most strikingfeature in fig. 5 is the positive value for the entropy-changewhich indicates that the barocaloric effect in this material isinverse: the entropy increases with increasing pressure. Thisfinding is consistent with the decrease in the temperature of themagnetostructural transition with increasing pressure.
200 220 240 260 2800.00.51.01.52.02.5 T ad ( K ) T(K)
Fig. 6
Barocaloric effect in La-Fe-Si. Temperature dependence ofthe adiabatic temperature-change for decompression of 2 kbar(circles) an 1kbar (diamonds) for LaFe . Co . Si . . Figureadapted from ref. . A material exhibiting the inverse barocaloric effect will havethe unusual property of cooling when adiabatically compressedand warming when decompressed. Such a feature is illus-trated in figure 6 which shows measurements of the adiabatictemperature-change when a LaFe . Co . Si . is rapidly de-compressed. The positive values are direct evidence of the in-verse nature for the barocaloric effect in this compound.In systems with coupling between different degrees of free-dom, the dominant change in entropy at the transition should beassociated with a conventional caloric effect, whereas the sec-ondary property may provide conventional or inverse effect de-pending of the specific feature of the coupling. In La-Fe-Si themagnetocaloric effect is conventional while the barocaloric is5 MAGNETICHEUSLERALLOYSANDTHEINVERSEMAGNETOCALORICEFFECT.inverse, which reflects that the transition is essentially of mag-netic nature. Indeed the major contribution to the entropy inthese compounds is due to the magnetic contribution from itin-erant 3 d electrons. Spin fluctuations induce a larger volume ofthe ferromagnetic phase, and as a consequence, the barocaloriceffect in this material is inverse. Shape memory materials have received considerable attentionboth from the fundamental point of view and from the view-point of technological applications of the shape memory ef-fect. They are cubic intermetallics with an open structure (typ-ically Fm m or Pm m ) at high-temperature which upon cool-ing transform martensitically to a more compact structure withlower symmetry. They are capable of recovering from verylarge deformations ( ∼ .In non-magnetic shape memory alloys, there is negligibledifference in the volume of the unit cell of the martensiticand cubic phases. Nevertheless, the transformation involvesa large shear distortion (typically shearing { } planes alongthe h i directions), and therefore, it is very sensitive to theapplication of uniaxial stresses. Indeed the possibility of in-ducing martensitic transitions by mechanical stress has beenknown since decades, and many of the mechanical applicationsof these alloys rely on such a possibility.The entropy-change associated with the latent heat of thefirst-order martensitic transition gives rise to a large caloriceffect when the transition is induced by uniaxial stress: Thisis the elastocaloric effect. A giant elastocaloric effect was re-ported for a Cu-Zn-Al single crystal and for Ti-Ni polycrys-tals . It is also worth mentioning that the elastocaloric effectwas earlier reported for non martensitic Fe-Rh alloys . Thetemperature-dependence of the stress-induced entropy-change(elastocaloric effect) for Cu-Zn-Al is illustrated in figure 7 forselected values of applied stress. There are a few salient fea-tures in comparison to the other caloric effects referred in theprevious sections. First of all, since the sample is ductile andthe transition temperature is very sensitive to stress, it is possi- ble to induce the full transformation in the whole sample, andconsequently, the stress-induced entropy values coincide withthe total transition entropy-change. A second feature is that thetransition can be shifted to temperatures well above the zero-stress transition temperatures. This results in a large plateau in D S (fig. 7) which reflects that such a giant caloric effect spansover a broad temperature range giving rise to a very large re-frigerant capacity in these materials. We note here that the datashown in fig. 7 correspond to an alloy with a transition tem-perature (in absence of stress) well below room temperature(T M =234K), and experiments carried out close to this temper-ature show that stresses as low as 5 MPa are enough to inducethe transformation in the whole sample.
296 300 304 308 =105MPa =110MPa =115MPa =120MPa =125MPa =130MPa =135MPa =140MPa =143MPa
T (K)05101520 - S ( Jk g - K - ) Fig. 7
Elastocaloric effect in Cu-Zn-Al. Temperature dependence ofthe stress-induced entropy-change for Cu . Zn . Al . . Figureadapted from ref. . The elastocaloric effect in shape memory alloys is conven-tional, and this is also corroborated by direct measurementsof the adiabatic temperature-change . Significant cooling ofthe sample was measured when the stress was rapidly released.Values around 10 K for Cu-based alloys and around 20 K forTi-Ni based alloys have been reported .In contrast to all other giant caloric materials, the transitionentropy change is solely related to the change in structure atthe transition (contributions from other degrees of freedom arenegligeable). Indeed such an entropy-change is mostly vibra-tional and originates from low-lying transverse phonons in theTA branch of the open cubic high-temperature phase (detailscan be found in ). Heusler alloys are X Y Z intermetallics with a Fm m structurewhere X atoms occupy the 8c Wyckoff positions and Y and Z which wasfurther promoted with the report that Ni MnGa could exhibitlarge deformations by the application of a moderate magneticfield . At present, strains as large as 10 % have been reportedin off-stoichiometric compounds for fields below 1 T . Thelarge strains are related to the martensitic transition taking placein these magnetic alloys. As a consequence of its lower symme-try, the martensitic phase exhibits a heterostructure formed bytwin-related structural domains (variants) and magnetic do-mains. There is strong interplay between structural and mag-netic degrees of freedom at the mesoscale of these domains.Owing to the high mobility of the twin boundaries and a highmagnetic anisotropy, applying a magnetic field causes twinboundary motion that gives rise to these large field-induced de-formations. Alloys exhibiting this property are known as mag-netic shape memory alloys .In the Ni-Mn-based Heusler family, Ni MnGa is the only fer-romagnetic alloy that undergoes a martensitic transition at thestoichiometric composition, but almost any alloy of this fam-ily undergoes a martensitic transformation at appropriate off-stoichiometric compositions . Among them, the particularlyinteresting ones are those exhibiting magnetic superelastic be-haviour . They also exhibit large magnetic-field-inducedstrains. But in this case, the strains are not due to a rearrange-ment of structural domains but rather to the possibility of induc-ing the reverse martensitic transition on applying a magneticfield. In this case, large magnetocrystalline anisotropy is notrequired, but there must be a significant change in the magneticmoment between the high-temperature phase and the marten-sitic phase.In general, Ni-Mn-based Heusler materials show a rich va-riety of magnetic behaviour with associated multifunctionalproperties, which include, in addition to the aforementionedmagnetic shape memory, giant magneto-resistance, exchangebias, and giant caloric effects which will be discussed in thefollowing.The magnetocaloric effect in Ni-Mn-Ga was first reported byHu et al. who observed an increase in the entropy by apply-ing a 1 T magnetic field. Soon after, the same authors reportedin a sample with a slightly different composition an entropydecrease for fields above 1 T . Such puzzling behaviour wasexplained by Marcos et al. who showed that it arises fromthe different length scales of the magnetostructural coupling.The inverse effect at low fields (entropy increase with magneticfield) is related to a magnetostructural coupling on the lengthscale of magnetic domains and martensitic variants: The stronguniaxial magnetocrystalline anisotropy of the martensitic phaseresults in a magnetic domain configuration with a lower mag-netization than that of the high-temperature cubic phase, thusgiving rise to an inverse magnetocaloric effect. At high fields,the coupling at a microscopic scale becomes dominant. Since S ( Jk g - K - ) Ni Mn Ga Ni Mn Ga Ni Mn Ga Ni Mn Ga Ni Mn Ga H (kOe) -6-4-202
Fig. 8
Magnetocaloric effect in Ni-Mn-Ga. Average magnetic fieldinduced entropy-change as a function of magnetic field for a familyof composition related Ni-Mn-Ga alloys. Figure adapted from ref. . for Ni-Mn-Ga the intrinsic magnetic moment in the martensiteis larger than in the cubic phase, the magnetization increases atthe transition and the magnetocaloric effect becomes conven-tional. Interestingly, when the composition is varied in sucha way that the martensitic transition temperature approachesthe Curie point, the magnetic anisotropy weakens with a cor-responding decrease of the inverse contribution, and the con-ventional magnetocaloric effect becomes dominant. Actually,for Ni-Mn-Ga alloys, optimum magnetocaloric properties oc-cur when both the martensitic and ferromagnetic transitionstake place close to one another . This behaviour is illustratedin fig. 8 which shows the magnetocaloric effect as a functionof magnetic field for a series of Ni-Mn-Ga alloys in which themartensitic transition temperature approaches the Curie pointas the Mn concentration decreases.Ni-Mn-Z alloys with Z different from Ga behave signifi-cantly different from Ni-Mn-Ga. On the one hand, the mag-netocrystalline anisotropy is low in both martensitic and cu-bic phases. On the other hand, the intrinsic magnetic momentof martensite is smaller than in the cubic phase. Such a de-crease in the magnetic moment is a consequence of an enhance-ment of the antiferromagnetic correlations between Mn-atomslocated at the 4b positions . Such a decrease is illustrated infig. 9 for Ni-Mn-Sn and Ni-Mn-In alloys. Consistent with thedecrease in the magnetization, the martensitic transition shiftsto lower temperatures with applied magnetic field, and conse-quently, the magnetocaloric effect is inverse in the vicinity ofthe martensitic transition, as firstly reported for Ni-Mn-Sn .Later, other alloys from the Ni-Mn-Z family (with Z as In andSb, and related quaternary alloys) were also reported to exhibit7 MAGNETICHEUSLERALLOYSANDTHEINVERSEMAGNETOCALORICEFFECT.
160 170 180 190 2000246 180 200 220 2400246 T(K) M ( e m u / m o l ) T(K) M ( e m u / m o l ) Fig. 9
Magnetization in Ni-Mn-Z magnetic shape memory alloys.Temperature dependence of the magnetization for Ni Mn Sn (left panel) and Ni Mn In (right panel) for selected magneticfields. From bottom to top: H=0.1,0.2,0.5,1,2,10,50 kOe (left panel)and H=0.1,0.5,2,5,10,20,30,40,50 kOe (right panel). Figure adaptedfrom an inverse magnetocaloric effect . At the Curie point, thealloys exhibit a conventional magnetocaloric effect where theentropy-change is solely due to a magnetic contribution. Theinverse character of the magnetocaloric effect was confirmed bydirect measurements of the adiabatic temperature-change .An example is shown in figure 10, which displays the measuredadiabatic temperature change for Ni-Mn-In around the marten-sitic and magnetic transitions.
200 250 300-3-2-101234
T (K) T ( K ) Fig. 10
Magnetocaloric effect in Ni-Mn-In. Temperature dependenceof the adiabatic temperature-change for Ni Mn In . Figureadapted from . It is worth remarking that in Ni-Mn based Heusler alloys, thephysical mechanism of the magnetocaloric effect is the same asthat leading to their unique magnetic-field induced strain. Onthe one hand, the magnetostructural coupling at the mesoscaleis responsible for the magnetic-shape memory and the low fieldinverse magnetocaloric effect in Ni-Mn-Ga alloys. Both effects require a large magnetocrystalline anisotropy in the martensiticstate. On the other hand, the magnetostructural coupling at amicroscopic scale gives rise to magnetic superelasticity and theinverse magnetocaloric effect. In this case a significant differ-ence in the magnetic moment of the two phases is necessary insuch a way that the martensitic transition can be driven by ap-plying a magnetic field. The decresase in the magnetic momentis a consequence of a decrease in the distance between excessMn-atoms in the martensitic unit cell compared to the cubicone which results in an enhancement of antiferromagnetic ex-change .
100 200 300-0.4-0.20 M s M s T (K) l/l ( % ) Ni Mn Ga Ni Mn Sn Ni Mn In M s Fig. 11
Length change in magnetic shape memory alloys.Temperature dependence of the relative length change forNi Mn In , Ni Mn . Sn . and Ni Mn Ga polycrystallinealloys. Figure adapted from . Typically, the volume change at the martensitic transition inshape memory alloys is negligibly small. Nevertheless, forsome alloys of the Ni-Mn-Z family (Z different from Ga), aconsequence of the strong interaction between magnetic andstructural degrees of freedom is a difference between the unitcell volume of the martensitic phase and that of the cubic one.A first indication for such a volume change is evidenced bythe relative length change at the temperature-induced marten-sitic transition (in the absence of any external magnetic field orstress) shown in figure 11 for several polycrystalline alloys .To a good approximation, the relative volume-change amountsto three times the relative length-change. While for Ni-Mn-Gathe coupling at a microscopic level is small, and consequentlythe volume change at the transition is negligible, there is a no-ticeable volume change for the rest of alloys of the family withstrong coupling. The martensitic transition in these alloys willbe influenced by hydrostatic pressure and they will be proneto exhibit a giant barocaloric effect.8 BATIO ANDTHEELECTROCALORICEFFECT.
285 290 295 300-30-20-100 S ( Jk g K ) p (kbar) Fig. 12
Barocaloric effect in Ni-Mn-In. Temperature dependence ofthe pressure-induced entropy-change for Ni . Mn . In . .Figure adapted from ref. . The giant barocaloric effect was first reported for a Ni-Mn-In sample from calorimetric measurements under hydrostaticpressure. Results are illustrated in figure 12, which showsthe temperature-dependence of the pressure-induced entropy-change for selected values of hydrostatic pressures. It is foundthat the barocaloric effect in this compound is conventional.It is slightly larger than that found for Gd Si Ge and signif-icantly larger than the effect found for La-Fe-Co-Si. Further-more, the values measured for moderated pressures are largerthan the corresponding magnetocaloric values for fields around1T.As previously mentioned, the martensitic transition is mainlyaccomplished by a shear distortion, and consequently, it isvery sensitive to applied uniaxial strain. A stress-induced first-order transition gives rise to an associated elastocaloric effect.Conventional elastocaloric effect has been found in magneticshape-memory alloys . Nevertheless the strong brittlenessof these alloys precludes the application of large stresses, andconsequently, the associated elastocaloric effect remains atlower values.Ni-Mn-based magnetic shape memory alloys exhibit con-ventional barocaloric and elastocaloric effects while the mag-netocaloric effect is inverse (with the exception of Ni-Mn-Ga). This indicates that the main contribution to the transi-tion entropy-change in these alloys is associated to the struc-tural degrees of freedom. Actually, the origins are the sameas in nonmagnetic martensitic materials: the cubic high-temperature phase has a larger vibrational entropy than theclose-packed phase as a consequence of the low energy TA phonon branch . On the other hand, the total transition en-tropy, which contains a structural and a magnetic contribu-tion, decreases as the martensitic transition is pushed below the Curie point either by tuning composition or by applying amagnetic field . This reflects that the magnetic contributionbecomes more and more important and eventually can com-pensate the structural contribution resulting in a vanishing totalentropy-change. This has been suggested to be at the origin ofthe interesting phenomenon of kinetic arrest in magneticshape memory alloys. and the electrocaloric effect. The electrocaloric effect refers to the temperature and entropy-changes occurring in polar materials when an electric field isapplied. The effect has been known for many decades but itreceived little attention due to its small magnitude. Parallelingthe development in other caloric effects, the research was trig-gered on realizing that giant effects were expected close to aparaelectric-ferroelectric phase transition. This was shown tooccur in ceramic films and later in ferroelectric copolymersand ferroelectric relaxors .Although thin films exhibit large electrocaloric effects sincethey can support large driving fields, their performances are sig-nificantly lower than those of bulk oxides for which the temper-ature and entropy-changes per unit of applied field are an orderof magnitude higher .The prototype ferroelectric material is BaTiO . At high-temperatures, it crystallizes in a cubic (perovskite) structure(space group Pm m ). On cooling, it undergoes a structural tran-sition to a tetragonal structure (space group P / mmm ). On fur-ther cooling, the material transforms to an orthorhombic phase(space group Amm
2) at around T= 270 K and to a rhombo-hedral phase (space group R m ) around T=200 K . At thecubic to tetragonal transition, the Ti + ions move relatively tothe O − octahedra resulting in spontaneous polarization alongthe c -axis. Such an electrosturctural paraelectric-ferroelectricphase transition is responsible for the significant electrocaloriceffect in this oxide.The electrocaloric effect measured using calorimetry underelectric field in a BaTiO single crystal is illustrated in figure13 for an electric field of 3 kV cm . The peak value of theentropy-change coincides within experimental errors with thetransition entropy-change which indicates that for this samplelow values of the applied field are enough to achieve the to-tal transition entropy-change. The electrocaloric effect is con-ventional, which is in agreement with the larger polarizationof the tetragonal phase. Direct measurements of the adiabatictemperature-change, shown in figure 14, confirm this issue: thesample heats on applying an electric field. It is interesting tonote that above a certain temperature (labeled T h in the fig-ure), the measured adiabatic temperature-change values are re-versible. This behaviour is intimately related to the hysteresisof the first-order electrostructural transition in this sample .9 CONCLUSIONSANDFUTUREPROSPECTS.
394 396 398 400012 T (K) - S ( J k g - K - ) Fig. 13
Electrocaloric effect in BaTiO . Temperature dependence ofthe electric field induced entropy-change for BaTiO . Figure adaptedfrom ref. . The cubic to tetragonal phase transition encompasses achange in the volume of the unit cell of around 0.037cm mol − . The volume of the low-temperature tetragonalferroelectric phase is larger than that of the cubic phase andtherefore an inverse barocaloric effect is expected for this com-pound. Preliminary calorimetric measurements under hydro-static pressure do evidence such an inverse barocaloric ef-fect. Interestingly, the maximum value for the entropy-change(around 2.5 J kg − K − ) is already obtained for pressures as lowas 1kbar. In general, the different thermodynamic degrees of freedomcan lead to several caloric effects. The key point for these ef-fects to be large enough for potential practical applications isthe occurrence of a phase transition. We have illustrated theeffects reported so far in a variety of materials. The relevantquantities for fields readily accessible in practical applicationsare summarized in table 1.The magnitude of all these caloric effects open new perspec-tives for designing solid-state refrigeration devices as alterna-tives to the presently existing technologies.In most materials, the hysteresis associated with the first-order phase transition represents a drawback because it reducesthe refrigerant capacity. Most effort is devoted at finding mate-rials where the hysteresis is small in comparison with the shiftof the transition with field. The detrimental effect of hysteresis -1
12 kV cm -1
390 400 410 42000.51.0 E o ff | T | ( K ) T (K) E on T h2 Fig. 14
Electrocaloric effect in BaTiO . Temperature dependence ofthe adiabatic temperature-change for electric fields of 8kVcm − (circles) and 12 kVcm − (triangles). Solid symbols correspond to theapplication of the field and open symbols, to the removal of the field.Figure adapted from ref. . can also be reduced by taking advantage of the cross-responseof several materials which enables using simultaneously morethan one field.The existence of the inverse caloric effects can also representan added value, since devices with an appropriate combinationof both conventional and inverse effects can enhance the refrig-erant efficiency of a given device.Recently efforts have been undertaken in order to deal withcaloric properties from first principle calculation. These calcu-lations are expected to give hints for the development of newmaterials with desired caloric properties or simply for optimiz-ing caloric properties of already known materials. The valid-ity of this point of view is supported by the fact that they haveproved to be able to nicely reproduce caloric behaviour of givenmaterials . These investigations are approached with the ideaof finding materials undergoing a phase transition involvinga large change of the properties giving rise to the caloric ef-fects of interest. There are, however, still few works with pre-dictive character. By combining density functional modellingand Monte Carlo simulations Siewert et al suggested thatPt-doping in Ni-Mn-based Heusler alloys improves the perfor-mances of these alloys, in particular their magnetocaloric prop-erties . Furthermore, in recent works, models based on firstprinciples have been used to predict a giant electrocaloric ef-fect in LiNbO and both, electrocaloric and elastocaloric effects in Ba . Sr . TiO . Computational discovery of new10EFERENCES REFERENCES Table 1
Transition entropy change ( D S t ), measured field-induced isothermal entropy ( D S ) and adiabatic temperature ( D T ) changes for severalcaloric effects obtained for the indicated values of the corresponding field. All data are in absolute value. (a) ref. , (b) ref. , (c) ref. , (d)ref , (e) ref , (f) ref. and (g) ref. .Gd Si Ge LaFe . Co . Si . Cu . Zn . Al . Ni . Mn . In . BaTiO D S t (Jkg − K − ) 21.0 11.4 21.0 27.0 2.2 m H (T) 1 1 - 1 - D S (Jkg − K − ) 8 2 - 10 - D T (K) 4 1 - 0.5 - p (kbar) 1 1 - 1 - D S (Jkg − K − ) 8 5 - 11 - D T (K) ∼ s (MPa) - - 5 - - D S (Jkg − K − ) - - 21 - - D T (K) - - 10 - - E (kVcm − ) - - - - ∼ D S (Jkg − K − ) - - - - 2.2 D T (K) - - - - 1Ref. a,b c,d e f g caloric and multicaloric materials not only represents an im-portant step towards the understanding of these properties butalso opens a new route in relation to the development of thisclass of materials. While this certainly could yield to more effi-cient solid-state refrigeration devices, care must be taken sinceby using these numerical techniques it is not easy to have a rea-sonable estimation of hysteresis effects related to dissipativenon-equilibrium aspects which reduce the refrigerant capacity.Prototype refrigerators are, to a larger extent, based on thethermodynamic Brayton cycle, and the degree of field matu-rity is different for the several caloric effects: a significantnumber of prototypes using permanent magnets have alreadybeen developed in the case of the magnetocaloric effect (a goodcompilation can be found in ), and very recently a refrig-erator based on the electrocaloric effect has been reported which uses multilayer capacitors of BaTiO . With regardsto barocaloric and elastocaloric effects the research is still onthe early stages.While recent progress in the development and understandingof multicaloric materials have resulted in significant advancesthat suggest that solid-state refrigeration can become a realityin a near future, there are still important challenges to overcomeboth in the basic understanding and design of new materials andalso on the engineering of prototypes before these technologiesbecome commercially competitive. We are grateful to our recent PhD students and post-docs J.Marcos, E. Bonnot, X. Moya, T. Krenke, E. Duman, S. Aksoy,D. Gonz´alez-Comas, I. Titov, E. Stern-Taulats, D. Soto-Parra,S. Y¨uce and B. Emre for their collaboration on the topics cov- ered in this paper. Financial support is acknowledged to CI-CyT (Spain) under project MAT2010-15114 and to DeutscheForschungsgemeinschaft, Project SPP1239.
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