Elasto-Caloric Effect Review: Solid-State Refrigeration

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A review and analysis of the elasto-caloric effect
for solid-state refrigeration devices: Challenges
and opportunities
Article in MRS Energy & Sustainability--A Review Journal · January 2015
DOI: 10.1557/mre.2015.17
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MRS Energy & Sustainability: A Review Journal
page 1 of 18
© Materials Research Society, 2015
doi:10.1557/mre.2015.17
REVIEW
A review and analysis of the
elasto-caloric effect for solidstate refrigeration devices:
Challenges and opportunities
Aditya Chauhan and Satyanarayan Patel, Rahul Vaish, School of
Engineering, Indian Institute of Technology Mandi, Mandi, Himachal pradesh,
175 001, India
Chris R. Bowen, Department of Mechanical Engineering, University of
Bath, Bath, Somerset, BA2 7AY, United Kingdom
Address all correspondence to Rahul Vaish at [email protected]
These authors contributed equally to this work.
(Received 22 August 2014; accepted 30 October 2015)
ABSTRACT
This review article deals with the current state-of-art research and developments in the field of elasto-caloric effect as applicable for
solid-state refrigeration devices. Furthermore, the current challenges and future prospects in the field of elasto-caloric refrigeration
technology have also been discussed.
Solid-state refrigeration is of interest since it has the potential to be a light-weight and environmentally-friendly alternative for small scale
cooling. Much research is currently being undertaken to develop solid-state cooling technologies which is primarily achieved by utilizing the
significant caloric effect exhibited by particular classes of materials. A variety of caloric effects exist including: electro-caloric, magnetocaloric, baro-caloric, and elasto-caloric. Among these, the elasto-caloric effect has shown potential within the field of mechanical refrigeration
with shape-memory alloys being potential materials for producing significant levels of elasto-caloric cooling. This article explains the elasto-caloric effect in shape memory alloys, polymers, and ferroelectric materials. Technical parameters associated with the elasto-caloric performance of these materials are discussed. A discussion regarding existing functional shortcomings and future prospects in the field of mechanical
refrigeration is covered. Aspects related to the long term environmental impact of solid-state cooling technology are also discussed. This study
is aimed at promoting the understanding and commercial investigation of the elasto-caloric effect in the field of solid state refrigeration.
Keywords: elasto-caloric; solid-state refrigeration; shape memory alloy; ferroelectric
DISCUSSION QUESTIONS
• Solid-state caloric effects propose to offer a high efficiency and
cleaner alternative to conventional vapor-compression
technology for electronic cooling applications.
• Large entropy change associated with phase transformation in
ferroic materials can be exploited for giant caloric effects.
• Elasto-caloric effect offers a bulk, high refrigeration capacity
alternative for efficient cooling under low load conditions.
Introduction
Solid-state refrigeration is generally associated with small
scale cooling applications. For example, it is often necessary
to install an on-board refrigeration system to maintain the
temperature of electronic systems,1 where it is essential to
remove unwanted heat which is generated during operation.
With modern advances in solid-state technologies, electronic
devices are shrinking in size while simultaneously increasing
in efficiency. The amount of heat generated by such devices
often exceeds their capacity to dispel it, thereby creating a
thermal imbalance resulting in a temperature increase. This
in turn could lead to a decrease in performance or increased
degradation. Hence, there is a need to develop new generation of cooling technology capable of on-board installation
and rapid heat extraction. Such refrigeration systems are
required to be compact, effective, responsive, and highly efficient. Vapor compression technology presently forms the
backbone of current refrigeration architecture. However, the
successful application of a vapor compression system for small
scale cooling has some inherent drawbacks: (i) the system can
be large and therefore does not facilitate on-board installation,
(ii) the system is relatively slow and requires several cycles to be
fully operational and (iii) for intermittent cooling requirements, the system can be inefficient and uneconomical.2 Therefore, research has focused on the successful development of
small, energy efficient, and robust cooling systems.3–5 In this
context solid-state refrigeration is of relevance6,7 since it offers
a solution for small scale and on-board cooling. A solid-state
refrigerator thus offers the following advantages: (i) the
material itself is the major part of the refrigeration system,
thus, the volume of the installation is reduced, (ii) a rapid
response, (iii) it is potentially efficient and requires less
power compared to other systems, (iv) the number of moving
parts is minimal, allowing for less wear and extended operational life and (v) many of the materials used in solid-state
refrigeration are environmental friendly.8 These advantages
in terms of energy usage and sustainability indicate that solidstate refrigeration is an attractive route for future small scale
cooling technology.
Ferroic materials are the prime contender for solid-state
refrigeration through suitable application of their associated
caloric effects. A caloric effect is described as the thermal
response of a material when it is subjected to an external
stimulus. All forms of matter display some level of caloric
effect. However, ferroic materials are capable of exhibiting
large entropy ordered variations when subjected to a suitable
external stimulus and when accomplished adiabatically, this
gives rise to large temperature changes which forms the basis
of solid-state refrigeration. Depending upon the change in
material parameter and the nature of external field applied,
the various caloric effects can be classified as: magneto-caloric
(ferromagnetic materials),9,10 electro-caloric (ferroelectric
materials),11,12 thermo-electric or Peltier (metallic heterojunction), baro-caloric,13,14 and elasto-caloric (ferroelastic
materials).6 In addition, a thermo-acoustic effect has also
been reported.15,16 A detailed discussion of the major solidstate cooling technologies has recently been made.6,17 Among
these, the thermo-electric (Peltier) effect is the only approach
to be successfully commercialized for solid-state refrigeration. While prototyping has begun for the commercialization
of magneto-caloric effect devices, other effects are either
in the developmental stage or pilot testing is being undertaken.18,19 The scientific and technological importance of
this field is evident from the large number of papers being
published annually in this domain. Further, recent reviews
have presented the development and technological advances
achieved to date. However, a dedicated review in the field of
elasto-caloric refrigeration is still lacking due to its lower
exposure compared to both electro-caloric and magnetocaloric effects. Thus, in this paper, we review and highlight
the underlying parameters that affect the performance of
elasto-caloric materials. Recently, a number of studies have
reported a “giant” elasto-caloric effect in shape memory alloys
(SMAs) which can be utilized for solid-state refrigeration.20–23
This has renewed interest in the field of elasto-caloric cooling24
and a potential advantage of elasto-caloric systems would be
their ease of design owing to minimal part movement and
operation under only unidirectional forces. This review will
present a description of the elasto-caloric effect, its underlying mechanism, the variety of classes of materials exhibiting
this effect and the parameters which ultimately decide the
material's performance along with the present challenges
and prospects in this field.
Elasto-caloric effect
It has been widely observed that specific materials undergo a
change in temperature when subjected to a sudden change of an
external field (such as electric, magnetic or mechanical stress
fields). This effect is known as the caloric effect6 and is demonstrated by most materials to some extent. In materials systems
where this effect is prominent it has the potential to be successfully utilised for solid-state refrigeration. The caloric effect
involves either a change in entropy of the material when the
change in the external field is isothermal or a change in temperature if the material is excited under adiabatic conditions. The
adiabatic change in the material attribute leads to an increase or
decrease of temperature depending upon the nature of change
induced. The resulting temperature difference (ΔT) with applied
field is an indicator of the extent of the caloric effect. Consequently, the larger the change in the entropy with applied field
the greater will be the change in temperature. The nature of
external field required to produce an apparent caloric effect
varies for different classes of materials. For the electro-caloric
effect, the polarization of the material changes upon application
of an electric field, and this effect is confined to ferroelectric
materials. In the magneto-caloric effect, the magnetization of
the material changes due to a change in magnetic field applied
(ferromagnetic material). However, in case of elasto-caloric
effect, a change in strain of the material is observed upon application of suitable compressive/tensile or hydrostatic stress; the
details of which shall now be discussed.
Force-elasticity and entropy-elasticity
To understand elasto-caloric effect, the difference between
elastic deformation mechanisms between conventional and ferroelastic materials needs to be understood. Two types of elastic
responses exist; these are force-elasticity and entropy-elasticity.
Most metals, ceramics, and glasses are categorized under
force-elasticity which has two associated attributes which distinguish it from entropy-elasticity. Force-elasticity is primarily
characterized by an initial linear relationship between stress
and strain up to the elastic limit of the material and subsequent
permanent plastic deformation, or fracture, when stressed
beyond the elastic limit. It should be noted that the magnitude
of the elastic modulus is a material characteristic and is inversely
dependent on temperature. Figure 1 shows a typical stress–
strain response of a ductile force-elastic metal at different
temperatures; the elastic modulus (the gradient of the stress–
strain curve in the elastic region) decreases with increasing
temperature.
In entropy-elastic materials, elastic deformation is highly
correlated to the change in lattice structure of the material
which is often a function of temperature and applied stress.25,26
These materials display a hysteresis loop in their stress–strain
response which is illustrated in Fig. 2; in this case the material
is a SMA. The relationship between the stress and strain is
nonlinear and the loading and unloading paths are different.
The area of the hysteresis loop represents the difference in
the energy required to load the material and the work done by
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equivalent or even exceeds the conventional electro-caloric effect
for which these materials are traditionally investigated.29,32,33
Additional details will be provided later in the article to explain
the mechanism behind such behavior.
Entropy-elastic stress–strain behavior for solid-state cooling
Figure 1. Stress–strain behavior of typical force-elastic material (ductile
metals).
In order for a practical device to produce cooling using a
thermodynamic cycle, some specific conditions must be met. The
coolant or material must be able to reduce its entropy (reject
heat) at a higher temperature and then increase its entropy
(absorb heat) at a lower temperature, when subjected to an
applied external stimulus. This is necessary to establish a system
which is capable of extracting heat from the source and expel it
to the sink. This is the primary requirement that limits the type of
materials which can be used for such cooling applications.
Force-elastic materials are unable to provide any cooling since
from Fig. 1 it can be seen that they lack hysteresis; the loading
and unloading response is fully reversible up to the elastic limit
with negligible hysteresis. Thus, little or no difference in energy
exchange occurs between the material and its surrounding,
during the loading and unloading processes. Additionally, the
amount of stress required to produce the same amount of
strain (entropy change) reduces with increasing temperature.
In contrast, entropy-elastic materials possess the required
characteristics to produce solid-state cooling. The nonlinear
stress–strain relation leads to a hysteresis loop and the increase
of the elastic modulus with increasing temperature enables the
material to be used in a refrigeration cycle. Entropy-elasticity is
primarily displayed by three types of materials, namely crosslinked elastomeric polymers (elastomers),26,34,35 SMAs,36–39
and ferroelectric materials.6,13,14,29–32,40 It is to be noted that
the mechanism for a strain driven entropy change is different in
cross-linked polymers, SMA, and ferroelectric systems and will
now be described.
Cross-linked elastomeric polymers
Figure 2. Stress–strain behavior of entropy-elastic materials (SMA).
the system during unloading. From Fig. 2 it can be established
that the material associated with entropy-elastic behavior has a
modulus of elasticity that increases with temperature,27,28
unlike the force-elastic material in Fig. 1. However, this is not
the sole criteria to define candidate ferroelastic materials for
elasto-caloric applications. It has recently been established that
some ferroelectric materials29–33 are also capable of exhibiting a
perceptible change in temperature when subjected to an applied
stress in an adiabatic manner. This category of “ferroelastic”
materials is often able to exhibit an elasto-caloric effect which is
Most metallic and ceramic materials exhibit a limited region
of elastic deformation. The degree of elastic deformation is generally less than 1% since the strain is achieved as a result of the
displacement of atoms from their equilibrium position. However, elastomers are unique in that they can be easily stretched
to several hundred percent of their original size without any
appreciable permanent deformation.41 Polymer materials can
be classified into two types: cross-linked and straight-chained.
Among them the cross-linked materials can be further classified
as heavily-linked, medium-linked, and low-linked. Elastomers
are classified as polymers with a medium number of cross-links
along the polymer chains.34 Natural rubber (NR) has been
widely studied as an elastomer that exhibits the elasto-caloric
effect.25,26,34,35 Several studies have been undertaken regarding
the thermodynamic and elasto-caloric effect associated with
NR and a detailed thermodynamic analysis of NR has been
reported.35 The ability to deform to large levels and corresponding giant strain is the result of polymer chains that are
able to reversibly rotate around the chain bonds (cross-links).
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A schematic of the mechanism is shown in Fig. 3. In an
unstressed state, the polymer chains are randomly aligned and
the cross-links are evenly distributed [Fig. 3(a)]. However, as
the material is stretched the polymer chains are aligned and the
molecular segments are separated from each other in the direction of deformation. Thus, on a molecular level the entropy is
said to have decreased as the state of order has increased.
According to the second law of thermodynamics, if the volume
and internal energy of a system remains constant, the entropy of
that system will remain constant. Thus, when an external stress
is applied to an entropy-elastic material it increases the level of
order and decreases the molecular entropy; this results in the
deformed state being metastable. To compensate for the
decrease in entropy, heat can be released during deformation
[Fig. 3(b)]. Upon the removal of external stress, the material
will tend to revert to its higher entropy state and will return to
its un-stretched state, while absorbing heat from the surrounding environment [Fig. 3(c)].
If the application of the load is instantaneous/adiabatic
no exchange of heat takes place between the system and surroundings: the temperature of the material increases in accordance to the Helmholtz equation for free energy (A)34:
2 § F − ED
(1)
here, U represents the internal energy (J) of the material, T
denotes temperature of the material (K), and S signifies its
entropy (J/K). For a constant temperature and volume, the differential form of Eq. (1) is:
S 2 §SF − E S D − D SE 
SF § SB ¥SH
Here, dW is the work done by the system and dQ is the energy
change in terms of heat added. For an isothermally varied load,
the right hand terms in Eq. (3) can be represented by34:
SB § E ⋅ S D
(4)
SH § 7 ⋅ S [ 
(5)
In Eq. (5), the work done is in terms of energy spent in
stretching the material through an additional length dl, using a
force of magnitude F. In addition, the change in entropy of the
NR under constant volume can be calculated as35:
=  δD ¬
S D E G § ¨ žžž ­­­ S =
={ Ÿ δ= ®
EG
(6)
Here, L0 represents original length and L represents the final
length after the application of force. From Maxwell's relation35
we know that
 δD ¬­
 ¬
žž ­ § −žž δτ ­­
Ÿž δ= ®­E G
Ÿž δE ®­= G
(7)
where, δτ represents the change in mechanical force. It has been
δτ
is positive for elastomers such as NR,42
established that
δE
thus dS is negative and indicates that the entropy of rubber
decreases upon stretching. Again from Maxwell's relation:
 δE ¬­
žž ­ § E
Ÿž δ= ®­D G 4
(2)
We now proceed with the assumption that NR is not an ideal
elastomer since a finite amount of energy is required to rotate
the polymer chains about the cross-links. In such condition, the
change in internal energy dU is given by:
(3)
=G
 δτ ¬­
ž ­
Ÿžž δE ®­= G
(8)
Here, CL,V (J/kg K) is the heat capacity of NR at constant length
and volume. Since, all terms to the right in Eq. (8) are positive,
this indicates that NR will heat up when stretched.
From the Clausius equality34:
SD §
SB

E
(9)
Therefore, the higher the entropy change, higher will be the
heat content. Thermodynamic analysis of elasto-caloric effect
associated with NR has been discussed in detail34 and it has
been reported that for a 400% increase in elongation, a temperature increase of 3 K can be achieved for NR.34
Shape memory alloys
Figure 3. Thermo-elastic behavior of NR under the application of uniaxial
strain. The figure illustrates the orientation of polymer chains and
respective cross links under the application of tensile stress and its release.
The related entropy and caloric effect with different states have also been
represented.
SMAs have the ability to return to their original shape after
being subjected to a permanent deformation38 and are typically
used in various actuation applications. Upon being subjected to
a sufficiently high mechanical load, SMAs are able to undergo a
stable plastic deformation by a process of twinning; this is in
contrast to the plastic deformation of a conventional metal (as
in Fig. 1) where there are changes at the atomic order due to
dislocation motion. Upon heating of the deformed martensite
phase a diffusionless structural transition from the martensitic
to the austenite phase takes place, this can be seen as the
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austenite start, As, and finish, Af temperatures, in Fig. 4. This
phase change leads to the original shape of the SMA being
recovered. The austenite phase has a very high degree of compactness and thus, offers higher yield strength compared to the
martensite phase.43–45 As the metal is cooled down to its original temperature the phase reverts back to the martensite phase
and a typical temperature-phase transition is shown in Fig. 4
by the martensite start, Ms, and finish, Mf, temperatures. This
cycle can be repeated a number of times.37,46
The austenite phase of SMA as a higher state of order compared to martensite and therefore has lower entropy. This results
in austenite phase being less stable than the martensitic phase
and hence, upon cooling the martensitic phase is restored.44,45,47
Since the phase transformation is diffusionless, it is reversible
in nature, much like the rotation of polymer chains in the case
of elastomers. Such transformations are known as first-order
transformations48 and are responsible for producing the elastocaloric effect in these materials.
SMAs display hysteresis during loading and unloading paths
in stress–strain plots as shown in Fig. 2. The phase transition in
the material is not sharply defined and occurs over a range of
temperatures, see Fig. 4, which can vary with the material composition.44 This difference in phase formation (start) and completion (finish) temperatures creates a transition zone and in
this region SMA displays typical pseudoelasticity45,49,50; implying that a stress-induced phase transformation can be achieved
in the transition zone.51 This phenomenon has been depicted in
Fig. 5. Figure 5(a) shows the crystal structures of martensite
and austenite phases associated with NiTi SMA, while Fig. 5(b)
shows the pseudoelastic phase transformation undertaken by
NiTi SMA. The dependence of pseudoelasticity on various factors such as crystallographic orientation, temperature, and
strain rate has been described.45 Reports regarding the thermomechanical aspects of transformation pseudoelasticity have
been discussed in detail49 along with the thermo-mechanical
equations and kinetics governing transformation pseudoelasticity for uniaxial stress states.49 A study expanding upon the
thermodynamic theory of pseudoelasticity to include the
observed effects in isotropic materials has also been undertaken.50 Theoretical and experimental results have been
compared and these properties can be effectively utilized to
achieve refrigeration.6,20–23,36,52,53
Based on the previously described applied theory for elastomers, the change in entropy of an SMA can be described by:
σ  δε ¬
S D § − ¨ žžž ­­­ Sσ.
{ Ÿ δE ®
σ
(10)
Equation (10) is based on Maxwell's relation for entropy
change in ferroic materials, where the dependent material
property is the rate of strain change with respect to temperature
 δε ¬­
žž ­ while stress (σ) is the driving force. Equation (10) is valid
žŸ δE ®­
for cases where the variation in stress is isothermal.36 A major
part of the entropy change occurs from the stress-induced phase
transformation at a predefined transition temperature Tt. In the
vicinity of transition temperature, the strain is expected to follow a predescribed relationship35:
ε E σ § ε { ¥ Δε ¸ 7 ¢¡ Ec σ − E ΔE ¯°±
(11)
Here, ε0 is the initial strain outside the (pseudoelastic) transition zone. F is a shape dependent function and ΔT is the range of
temperature over which the transition is spread. Under the
assumption that Δε and ε0 are constant and using Eq. (11) in
Eq. (10) we arrive at:
£¦ Δε
¦−
E ∈¢Ec { Ec σ ¯±
Δ D { → σ = ¦¤ α
¦¦
¯
¦¦¥ 0 E ∉¢Ec { Ec σ ±
(12)
Here, α = dTt/dσ and is considered constant.35 It can be inferred
from Eq. (12) that a stress induced entropy change remains
constant over a broad range of temperatures. The major part
of entropy change results from the phase transformation, which
is best described as the latent heat of transformation associated
with the martensite to austenite phase change. This latent heat
is responsible for producing the significantly large elastocaloric effect in SMAs.
Ferroelectric materials
Figure 4. Phase transition diagram for shape-memory alloys.
A number of other phase-ordered materials have also been
associated with entropy-ordered elastic states including ferroelectric materials,21,54,55 phase separated manganite,56 and
ferromagnetic materials.57 Detailed explanations have been
published in the literature relating to the origin and nature of
elasto-caloric effects (or baro-caloric/mechano-caloric) in ferroic materials.40,58 The elasto-caloric effect associated with
ferroic (electronic/dipolar) materials does not originate from
martensitic transformation or pseudoelasticity, it originates
from the distinctive difference in the entropy states of these
materials under high intensity mechanical stresses.
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Figure 5. (a) Martensite and austenite crystal structures for NiTi SMA and (b) pseudoelastic behavior as observed in NiTi SMAs.
In ferroelectric and ferromagnetic materials, there exists
a long range order of structural arrangements; these are
referred to as domains. The domains represent a unidirectional arrangement of dipolar or magnetic moments for a
given volume of the material. Within a single domain, the
material properties are anisotropic and the polarization or
magnetization states are perfectly ordered. However, throughout the material the domains exist in random orientations
within the total volume of the material and are separated by
domain walls. Therefore, on a macroscopic level, a state of
disorder is maintained and a high entropy level is exhibited
in the virgin material.
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When these materials are subjected to an adiabatic application of electric or magnetic field, for ferroelectric and ferromagnetic materials respectively, the moments are aligned along
the direction of the externally applied field. Consequently, the
domains are rotated simultaneously in a unidirectional manner
and a higher state of order is established within the material.
Since the application of field is of an adiabatic nature, the reduction of entropy is followed by an increase in the temperature
of the material. These phenomena are known as the electrocaloric12 and magneto-caloric59 effects for ferroelectric and
ferromagnetic materials, respectively. It has been reported40
that a coupling may exist between ordered states which can
predict and explain many giant multi-caloric phenomena
which have been reported.9,13,14,22,53–56,58
Recent developments have been made with regards to quantifying stress-driven caloric effects in ferroelectric materials.
Relations developed in Ref. 40 can be used to explain the underlying theory of the origin of elasto-caloric effect in ferroelectric
materials. Due to the coupling that exists between moment order
in ferroelectric materials and mechanical load, when these materials are subjected to mechanical stress, they undergo a reversible
transition between a lower entropy state (alignment) to a higher
entropy state (randomization/dispersion). This can be explained
by considering ferroelectric materials as an example. Ferroelectric materials, being a sub-class of piezoelectric materials, are
able to exhibit a change in their polarization when subjected to an
external stress. This effect is easily observed for poled/activated
ferroelectric materials in the form of the conventional piezoelectric effect. However, it has also been established that an entropy
change in ferroelectric materials is primarily governed by polarization ordering. Thus, a simple deduction points to the fact that
ferroelectric materials should possess some form of stress-driven
caloric component. This has long been speculated and has been
the subject of many theoretical (first principle) investigations,
where predictions were made for large stress-driven caloric effects
in ferroelectric materials.21,54,60 Recent developments in this
regard have been able to successfully confirm this effect using a
variety of lead-free ferroelectric ceramics of different compositions and morphologies.61,62 Most notably, Liu et al. recently
demonstrated a giant room-temperature (300 K) elasto-caloric
effect in ultra-thin films of barium titanate (BaTiO3).61 Liu et al.
achieved a maximum temperature change of 5.5 K upon application of a uniaxial compressive stress in thin-films with a thickness
of 6 nm. In addition, they also successfully demonstrated that
depending upon loading conditions both positive and negative
elasto-caloric effects can be obtained within the same material. A
continuing study by Liu et al. further confirmed the baro-caloric
potential in BaTiO3 single crystals where the application of a
hydrostatic pressure was reported to produce a maximum temperature change of 3 K63; this phenomenon was corroborated
using mean-field theory. However, in both studies the authors
used the polarization change as a function of temperature to
interpret the net change in entropy of the system and this formed
the basis of predicting the elasto-caloric effect. However, it is
thought that such an approach cannot help to quantify the true
elasto-caloric potential of ferroelectric materials.
In ferroelectric materials, the relationship between strain
and polarization is not essentially linear. Even for discontinuous strain gradients, the polarization change may vary as a function of applied stress and temperature. Thus, the stress–strain
response of the ferroelectric is required to fully assess the
true elasto-caloric potential of ferroelectric materials. In
this regards, our group has been able to successfully demonstrate the same for bulk-ferroelectric materials. Utilizing the
actual stress–strain response for BaxCa1−xZr0.1Ti0.9O3 (BCZTO)32
and Pb(Mn1/3Nb2/3)O3–32PbTiO3 (PMN–32PT)29,30 we were
able to demonstrate that bulk ferroelectric materials possessed
a strong potential for enhanced stress-driven caloric effects.
This is represented by Fig. 6, where Fig. 6(a) demonstrates the
actual stress–strain graphs for BCZTO as a function of temperature; while the corresponding elasto-caloric effect is shown in
Fig. 6(b). It can be observed from Fig. 6 that bulk ferroelectric
materials possess two distinct regions within their stress–strain
behavior. Initially the increase in strain energy is compensated
by ferroelastic switching, as observed by the nonlinear zone.
However, upon complete domain rotation, a linear stress–strain
behavior is observed, akin to normal ceramics. It can also be
observed that the intensity of ferroelastic switching decreases
with an increase in temperature. This behavior is expected since
an increase in temperature leads to thermal relaxation of the
domain structure, which is also responsible for affecting the
polarization, pyroelectric, and piezoelectric properties in
such materials. However, the most intriguing fact is that
stress-driven caloric effects, as observed for bulk materials,
could easily match or exceed conventional electro-caloric
effects for which these materials are traditionally investigated.
For example, in BCZTO bulk ceramics a peak elasto-caloric
temperature change of 1.55 K was observed, which is twice as
large as the previously reported peak electro-caloric effect
for bulk material of the same composition. A similar phenomenon was observed for PMN–32PT single crystals where a
maximum elasto-caloric temperature change of 0.36 K was
observed as opposed to a previously reported peak electro-caloric effect of 0.27 K. In addition, the same study also
discussed the possibility of combining the individual caloric
effects for further cooling. Thus, these studies constitute
what can be stated as the first step toward establishing a new
field of caloric effects in ferroelectric materials. The most
redeeming quality of ferroelectric materials lies in the fact
that relatively small strains are required to produce relatively
large temperature changes, as opposed to conventional ferroelastic materials. These materials are capable of displaying
elasto-caloric effect to a significant extent.58
This effect can manifest itself in a positive or negative caloric
effect depending on the initial state of the material. In a “poled”
ferroelectric sample a significant number of domains are already
aligned in a specific direction (low entropy state) and this lends
the material its activity (piezoelectric or pyroelectric). However,
when a suitable uniaxial compressive stress is applied to the
material, the domains experience a stress induced rotation
which increases the overall entropy of the system, as shown in
Fig. 7(a). This behavior can be attributed to non-180° domain
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Figure 6. (a) Stress–strain behavior of bulk BCZTO polycrystalline (poled) ceramic under uniaxial compressive loading and (b) corresponding elasto-caloric
effect observed in the material, represented as a function of operating temperature.
rotation that is associated with ferroelastic switching.64–69 Consequently, the resulting effect is an overall decrease of temperature to compensate for the entropy increase, resulting in a
negative caloric effect.
However, if the direction and magnitude of the applied stress
is appropriately selected, it can result in an overall decrease in
the entropy of the system. Upon the application of radial stress,
additional domains are aligned along the material's net moment
due to ferroelastic domain rotation.70,71 This increases the
overall polarization of the system and consequently, the state of
order is increased, as shown in Fig. 7(b). Hence, the effective
decrease in entropy can result in a positive caloric effect. Thus,
both positive and inverse caloric effects can be obtained13 and
an attempt in this direction has been recently reported where
ultra-thin ferroelectric films have been reportedly used to
obtain both negative and positive giant elasto-caloric effect
near room temperature.61
Performance parameters
During the selection of a suitable elasto-caloric material, such
as the NRs, SMAs or ferroelectrics for a solid-state refrigeration
system, several parameters have to be considered. These enable
us to compare the performance of the potential materials when
used as coolants for employing the elasto-caloric effect.
Elasto-caloric effect (ΔT)
The elasto-caloric effect is used to refer to the maximum
achievable change in temperature through the application of a
mechanical force. Thermodynamically, the temperature change
in an adiabatic process can be evaluated as:
E ¬
ΔD = 4 ⋅ [] žžž r ­­­
žŸE{ ®­
(13)
Equation (13) can be rewritten as
ΔD
Er
=T 4
E{
(14)
here, C (J/kg K) is the heat capacity at constant pressure, and T1
and T0 are final and initial temperatures. It is clear from Eq. (14)
that the higher the change in entropy of the material due to a
phase change, the higher the Er ratio. It is expected from this
E{
E
r
expression that the
ratio will increase exponentially with ΔS.
E{
This is observed in the case of NR where ΔTNR is 2–3 K when the
strain is low, but increases to 10 K for strain levels of 500%.34,35
It has been reported that a temperature variation ΔTNR between
5 and 10 K has been achieved experimentally.35 A similar observation was reported where the refrigeration capacity of NR
increased exponentially with strain.34 An experiment reporting
a ΔTNR of 7 K has been reported, taking the initial and lowest
temperature as Ref. 34. Thus, to achieve a high ΔT, the entropy
change should be as high as possible. In elastomers the entropy
change is expected to be higher in materials with a larger number of cross-links. However, as the number of cross links increases,
the polymer tends to lose its super-elastic property and behave
more like thermosets. Conversely, a lower number of links leads
to a higher elastic limit, but an increased tendency for the material to flow like a viscous liquid under load, due to relative
motion of molecular chains. Therefore, an optimization of the
number of cross-links is desired.34
In SMAs the entropy change occurs during the phase transformation between the austenite and martensite phase. A higher
ΔTSMA would then be expected when there is a high entropy
change between the two states. A study of the change of entropy
with temperature and applied stress has been undertaken36
8 Q MRS ENERGY & SUSTAINABILITY // V O L U M E 2 // e 1 6 // www.mrs.org/energy-sustainability-journal
Figure 7. Ferroelastic domain switching in poled ferroelectric materials under the application of (a)uni-axial stress and (b) radial stress.
where the entropy change associated with the phase transition
is relatively independent of temperature. This can be explained
in terms of latent energy of transformation, which is essentially
isothermal in nature and is only dependent on the nature of
the phase change. The higher the energy of transformation, the
greater the heat extracted and associated temperature change
(ΔTSMA). For some SMAs the transformation energy can be as
high as 31 J/g.43 A recent study by Xiao and co-workers demonstrated that elasto-caloric behavior in SMAs is also dependent
on crystallographic orientation.72 Using Ni50Fe19Ga27Co4 single crystals it was demonstrated that a temperature change of
9–10 K was obtained for single crystals oriented in [001] direction (328–398 K). However, this value was reduced to 3 K for a
sample orientated in the [111] direction.
An experimental study regarding the elasto-caloric effect in
NiTi polycrystalline samples has been made20 and a ΔTSMA of 17
K was measured for an applied tensile stress of 580 MPa on a
3 mm × 1.780 m cylindrical sample. The extrapolated data predicted a ΔTSMA of 20.8 K under adiabatic loading and unloading
conditions. Additionally, the study reported that the elastocaloric effect increases with an increase of the cross-section of
the material. This is a result of the cylindrical nature of the
material used in the study; the heat loss is inversely proportional to the surface area of the cylindrical material used. Thus,
the thickness of the material and heat transfer characteristics
of the material become an important factor.20 A recent study by
Tušek et al. reported a maximum ΔTSMA of 21 K (unloading) for
NiTi wires that were trained at different temperatures.73 The
training procedure involves monitored thermal and mechanical
loading and unloading cycles for a pristine SMA so as to stabilize
its thermo-mechanical actuation behavior. This process enables
the material to “remember” its shape and to reacquire it after
deformation. A ΔTSMA of 16 K has been measured for magnetron
sputtered Ni50.4Ti49.6 20 μm thick films.74 It was reported that
compared to bulk samples, larger strain rates and reduced heat
transfer times were obtained due to the larger surface area to
volume ratio that is achievable for a thin-film morphology.
While for ferroelectric materials the peak adiabatic temperature change is governed by the strain gradient (with respect to
temperature) and the accompanying polarization change. In some
classes of ferroelectric materials, the strain response is large32;
this is primarily dependent on the lattice geometry of the sample at the time of loading. It is possible for a ferroelectric material to under-go first and second order phase transitions when
subjected to a specific magnitude and nature of external stimulus.
This effect is especially pronounced for ferroelectric materials
fabricated near their morphotropic phase boundary (MPB).29,30
A MPB in a ferroelectric indicates the presence of two or more
phases separated by only a small difference in their free energy.
The phenomenon of phase transition in the vicinity of ferroelectric MPB has been discussed in detail in relevant literature.75,76
Thus, upon selection and application of suitable external impetus
MRS ENERGY & SUSTAINABILITY // V O L U M E 2 // e 1 6 // www.mrs.org/energy-sustainability-journal Q 9
a desired phase change can be achieved. This is often accompanied by a large strain and polarization change. Hence, the adiabatic temperature change in ferroelectric materials is dependent
on the quality and quantity of entropy change that is exhibited
by the material.
The upper and lower limits of the elasto-caloric effect also
define the range of working temperatures of the refrigeration
cycle.39 Essentially, a higher elasto-caloric effect means that the
cycle can be operated between wider ranges of operating temperatures, being able to extract heat from lower temperature
sources and rejecting it at a higher temperature sink; thus
becoming more efficient in terms of the Carnot parameters.
Previously, theoretical predictions have been made for an
achievable elasto-caloric ΔT for ferroelectric materials. A maximum ΔT of 9 K obtained for a Ba0.5Sr0.5TiO3 ferroelectric material near its Curie temperature has been reported.21 Additional
data showing the dependence of ΔT on initial temperature have
also been provided. The study reports that a ΔT of 4 K can be
obtained in the vicinity (±50 K) of the Curie temperature which
is attributed to a stress induced ferroelectric–paraelectric phase
change near the Curie point. Additionally, a recent study54
details the possibility of a giant elasto-caloric effect, for example in PbTiO3 ferroelectric material, through a first principle
approach. For ferro-magnetic materials, a elasto-caloric ΔT of
5.17 K has been reported in a Fe49Rh51 alloy when exposed to a
tensile stress of 529 MN/m2.22 The observed negative caloric
effect was attributed to a stress induced antiferromagnetic to
ferromagnetic phase transformation.
Specific heat capacity
A higher specific heat capacity essentially means that a
higher amount of heat can be extracted per cycle. This indirectly
affects the overall refrigeration as it reduces the number of
cycles required to produce the necessary cooling. Therefore,
it is also an important parameter to consider while selecting
materials for solid-state refrigeration. For elastomers such as
NR, the specific heat capacity is a direct measurement of the
amount of heat that can be extracted by the material [Eq. (13)]
and a large specific heat capacity is desirable. For a phase change
material, such as SMAs, the maximum ΔTSMA = L/Cp (Ref. 20);
therefore, a lower Cp would be preferred for a particular value of
L. However, it does not affect the refrigeration capacity of SMAs
as no sensible heat is involved. The best example of this phenomenon can be observed in a study which reported a giant
refrigeration capacity in a Fe–31.2Pd (at.%) single crystal SMA.23
Even though the observed ΔTSMA was low at approximately 2 K
(compared to a ΔTSMA of 15 K for NiTi alloy) a high cooling
capacity of 2 MJ/m3 was observed under an applied stress of
100 MPa. The high cooling capacity can be attributed to the
large latent heat associated with the martensitic transformation
in Fe-31.2Pd single crystal. A similar trend is also expected in
ferroelectric materials, where the temperature change is determined by quantification of entropy change within the material.
A higher value of specific heat capacity may reduce the adiabatic
ΔT. However, it does not affect the heat extraction capacity, nor
does it affect the overall performance. Nevertheless, published
literature77–80 indicates that a material with lower specific heat
capacity would ultimately benefit from a higher caloric effect
which would increase its versatility in terms of operating and
temperature range.
Endurance limit
The performance of a material often degrades as the number
of working cycles is increased. This effect is known as fatigue
and can eventually lead to degradation of properties and material failure. In this regard, the endurance limit is defined as the
maximum magnitude of load which can be applied repeatedly
for a sufficiently large number of cycles without any appreciable
reduction in the performance of the materials. Clearly a high
endurance limit is vital for the materials as they are expected to
go under a large number of loading cycles to achieve long term
cooling. Elasto-caloric materials suffer from two major types of
fatigue, namely structural and functional. Structural (mechanical)
fatigue is a result of cyclic loading and functional fatigue is due
to reversible thermal stresses. A literature survey regarding
the fatigue analysis approaches for rubber has been reported81
where two approaches, namely crack nucleation and crack
propagation, have been discussed for fatigue life analysis of rubber components. The failure of polymers due to the application
of alternating loads has been discussed82 such as the effects
of important material parameters including polymer structure,
molecular weight, and crosslinking; and the effect of external
parameters such as stress intensity, frequency, temperature, and
environment. The study also included a description of methods
to improve the fatigue life of polymers. The addition of fillers,
such as short glass fibers, has shown to significantly increase the
fatigue life of polymers. Shorter fibers were shown to inhibit
fatigue crack initiation and micro-voids introduced during the
kneading process help to inhibit crack growth. Additionally,
it was also observed that reducing the amount of diluents or
plasticizers during the polymerization process decreases the
fatigue crack growth rate. For SMA materials, thermo-mechanical
fatigue has been reviewed83 with a discussion of thermo-mechanical treatments to improve the endurance limit. Another
study discussing structural and functional fatigue of NiTi SMA
reports that satisfactory performance can be achieved for up
to 106 loading cycles84 with a small change in performance. The
material can be subjected to a high number of recoverable cycles
provided the stress required for pseudoelastic phase change
is smaller than the yield stress of the austenite phase.84 A recent
study by Xu et al. reported that dual phase alloys are expected to
exhibit a better endurance limit as opposed to single phase alloys.85
Their study demonstrated that while mechanical fatigue in
Ni–Fe–Ga alloys begins at only 10 cycles for single phase samples while a dual phase sample can readily remain insensitive to
fatigue after 100 cycles. This makes a valuable contribution
toward considering the material phase while evaluating its suitability for elasto-caloric applications. A recent study by Tušek
et al. established the functional integrity of NiTi wires for over
400 cycles,73 while a study by Schmidt et al. discussed in detail
the effect of thermal training on the functional and mechanical
fatigue in NiTiCuV magnetic SMA ribbons.86 It was observed
10 Q MRS ENERGY & SUSTAINABILITY // V O L U M E 2 // e 1 6 // www.mrs.org/energy-sustainability-journal
that the nature of applied training leads to evolution of peculiar
temperature profiles, with thermal behavior displaying local
temperature peaks and distribution pattern which is highly
dependent on the number of cycles.86 The NiTiCuV ribbons
exhibited promising resistance against functional fatigue, indicating their promise for practical applications; while the endurance limit can be high (>1000 cycles) for SMA single crystals72
its applicability is severely limited due to its high cost. While a
high endurance limit is an important factor for a long lifetime
a high strength is also desirable since the magnitude of load
applied to achieve the desired cooling can be high; for example the applied stresses can be up to 700 MPa (Ref. 20) and
thus, possibility of mechanical failure exists.84 In addition,
since the material experiences additional fatigue in the form
of thermal cycles, repeated use can degrade the shape-memory
and elasto-caloric effects.84 Although SMAs and NR seem to
have a sufficiently high Mean Time Between Failures,34,52 a
higher endurance limit is clearly beneficial in terms of economy
and reliability.
In the case of ferroelectric materials there is significant data
present in the literature to indicate that they would make excellent candidates for stress driven solid-state refrigeration. A number of articles are present which describe the fatigue behavior
of various classes of ferroelectric materials.87–92 Ferroelectric
materials possess good functional stability over extended periods of operation time93,94 and they also possess good functional
and mechanical endurance.93,94 Finally, since the required actuation strain (typically 0–0.4%) and stress (typically 0–200 MPa)
is small,30,31,33 it is possible to employ them for applications
where neither polymers nor SMAs would work. As an additional advantage, when the size of a ferroelectric is reduced
their efficiency and performance increases rapidly; for example in thin-films.61 This is in contrast to the degradation in
performance of conventional ferroelastic materials when subjected to similar downscaling to either micro or nano levels.58
Thus, ferroelectrics can be used for diverse applications and is
a topic of interest for future research.
Transition/inversion temperature
The transition temperature in the context of SMA materials,
the inversion temperature for elastomers such as NR and the
Curie or Néel temperature for ferroic materials will now be
described. In SMAs, the entropy change originates from the
phase change between the austenite (A) and martensite (M)
phases. This change is not sharply defined and occurs over a
range of temperature (as in Fig. 4) and there are two temperatures, namely start (s) and finish (f), associated with each phase
which represent the start and completion of the phase formation respectively. A reference temperature known as the transition temperature is used to indicate a point in the phase diagram
that represents a 50% concentration of austenite and martensite phases. This is important since if the transition temperature
of the material is too high with respect to the working temperature, then the heat extracted would be low. Ideally, the transition temperature should be close to the working temperature so
that maximum heat can be extracted. If the heat input is not able
to achieve a phase transition to the austenite phase then clearly
no heat extraction would occur and similarly if the transition
temperature to the martensite phase is too low the material
would remain in the austenite phase.
In elastomeric materials, the inversion temperature (thermoelastic inversion) refers to the point where the inversion in the
slope of linear (thermal) expansion coefficient takes place.35
For low strains (up to 10%), the dependence of thermal expansion coefficient on temperature is positive. However, beyond
the inversion temperature thermo-elastic inversion takes place
on the temperature–strain graph35 where there is a negative
coefficient of linear thermal expansion defined by:
α t{ =
r + sλ {E
Tg_ ¢tλ { EX − E{ ¯±
r − λ {EX
(15)
here, α0 = L/L0(T0) represents the strain of the elastomer associated with its original length at a reference temperature; λ0
is the coefficient of linear expansion of an elastomer in
unloaded condition; T0 is the reference temperature, and Ti is
the inversion temperature. Using Eq. (15) we can observe that
for λ0 = 2.2 × 10−4 K−1 (NR) and T0 = 298.15 K = Ti (isothermal
stretching) the required value of α0 = 1.067. This signifies that a
thermo-elastic inversion can be obtained at room temperature
with a strain of 6.7% or higher. Therefore, such a level of strain
is required for cooling to the desired inversion temperature,
and this represents a lower limit. Thus, the inversion temperature and the corresponding strain are to be considered carefully.
The inversion temperature for ferroic materials is their Curie or
Néel temperatures, for ferroelectric, ferromagnetic, and antiferromagnetic, ferrimagnetic materials, respectively. Beyond
this temperature, the ferroelectric/ferromagnetic property disappears completely due to induction of a paraelectric/paramagnetic phase. Since beyond this point there is no possibility to
attain entropy ordered state, this forms the upper working limit
(temperature) for ferroic materials. The Curie or Néel temperature differs with material composition, structure,95 and applied
external impetus.96 However, relaxor ferroelectric materials
have been reported which display a broad transition temperature range due to presence of nano-domains.97 Recent advances
in ferroelectric elasto-caloric phenomenon have also revealed
that stress driven adiabatic temperature change in ferroelectric
materials is also a function of material temperature.29,30,32 A
maximum caloric effect is observed in the vicinity of phase transition temperature, whether ferroelectric–ferroelectric or ferroelectric–paraelectric29,30,32; as observed from reported studies on
PMN–32PT single crystals29,30 and Ba0.85Ca0.15Zr0.1Ti0.9O3 bulk
ceramics.32
Coefficient of performance (COP)
The COP for a cooling cycle is defined as:
4@A R^^[X]V =
BR
ER^[S
=
H EW^c − ER^[S
(16)
here, Qc is the amount of heat extracted from the cold reservoir
and W is the work done on the system. The second term in Eq. (16)
is used when the cycle in question is a Carnot cycle. Since it is a
MRS ENERGY & SUSTAINABILITY // V O L U M E 2 // e 1 6 // www.mrs.org/energy-sustainability-journal Q 11
measure of heat extracted per unit work done, it can be used as a
performance measurement criterion. A high COP indicates an
efficient process and recent reports on elasto-caloric studies of
SMAs have reported a COP up to 3.07 (COPrelative = 21.6%)20
where;
can even exceed that of a magnetic refrigerator and electro-caloric
effect, at higher temperatures.99 This makes mechanical refrigeration a versatile option to be used in remote conditions.
4@ARhR[T
Other important selection criteria for considering the performance of a material based on its volumetric and material efficiency involves three additional parameters namely (i) isothermal
 ¬
entropy change žž ∂ε ­­ , (ii) wide operation range near room temžŸ ∂E ®­
E
perature (temperature invariant performance), and (iii) field

¬
normalized caloric effect žž ΔE ­­, also known as material efficiency.
žŸ Δσ ®­
4@A aT[PcXeT =
4@ARPa]^c

(17)
In this case the material is mechanically loaded up to its elastic limit; if the unloading part of the cycle can be used to recover
mechanical work, such as pumping, the COP can potentially be
improved to a value of 11.8 which corresponds to a COPrelative =
83.7%.20 Thus, if care can be taken to utilize the unloading
energy to do mechanical work for the refrigeration system, high
efficiencies can be achieved. The only disadvantage of this route
would be an increase of the lower temperature reached upon
unloading. This would arise due to the finite amount of time
required for the material to do mechanical work and could
result in the unloading curve deviating from the adiabatic path
and a finite amount of heat being exchanged with the surrounding environment. Moya et al. have recently published an excellent article discussing the fundamental principle of the required
and recoverable work for caloric effects in ferroic materials.98
Information relating to the magnitude and nature of the actual
work required to drive the material parameter/phase transition
has been discussed. To assess the relative efficiency of materials
with respect to different caloric effects and within the same
caloric effect, a (dimensionless) figure of merit was used termed

¬
the material efficiency žžη = B ­­­.98 To justify the approach,
žŸ
H ®­
a comparison was made for the situation involving similar
amount of heat flow/extraction (Q). Even though it was concluded that the relative efficiency of stress driven caloric effects
is low, this statement was made on the assumption that high
grade electric work is recoverable for re-use in electro-caloric
materials. However, when this assumption is ignored it is
observable that elasto-caloric effects have the ability to reach
efficiencies higher than electro-caloric effect. Further, this data
is only limited to conventional ferroelastic shape-memory alloys
requiring high strains and fails to consider the recently reported
values for elasto-caloric effects in ferroelectric materials. In addition, the generation of high intensity electric fields and magnetic fields require special apparatus while mechanical strains,
if need be, can also be driven manually. This theory has been
corroborated by Tušek et al.99 who describes in detail the working mechanism and performance evaluation of a practical solid
state refrigeration system employing elasto-caloric effects. Two
different SMAs, NiTi and Cu–Zn–Al, were evaluated for their
cooling capacity using a novel regenerative cycle. The performance was evaluated with respect to various operational parameters such as frequency of operation, loading conditions, and
operating temperatures. Further, the performance was evaluated
with respect to a magneto-caloric cooler employing Gd. It was
observed that not only do the SMAs provide the necessary progressive temperature change capacity required for room temperature
cooling applications (30 K or more); but the cooling performance
Other important parameters
The isothermal entropy change, as represented here, is a means
of quantifying the heat extraction capacity of the material of
interest per unit volume. A higher number also contributes
indirectly toward the adiabatic temperature change; however
its main significance is being able to determine the thermal
inertia. Hence a material possessing higher volume specific
entropy change will be able to extract more heat per cycle than
the competing material.
A wider operation range or temperature invariant performance helps the material to perform the temperature uplift
required to provide a consistent performance under varying
heat loads. An adiabatic temperature change assumes a parabolic
shape when plotted against the operating/material temperature;
this implies that the cooling capacity first increases, assumes a
maximum value and then decreases. This is true for all materials; however, the shape or slope of this parabolic behavior can
help to assess the performance of the material. A sharper slope
would indicate that the material performance/cooling capacity
degrades rapidly upon departure from the inversion temperature. Thus, under varying thermal loads such a material would
perform poorly, since a change in heat load causes the sink
temperature to rise or fall from the inversion temperature. Conversely, if this slope is lower the material would respond better
to fluctuating heat loads, making it more suitable for practical
cooling applications.
Finally, the material should also possess good field normalized performance. This translates to having a caloric effect for
reduced input (stress). From the nature of Maxwell's relations
used for predicting caloric effects [Eq. (10)], it can be easily
determined that the elasto-caloric effect is expected to scale linearly with the intensity of applied stress. In this regard, a material which is able to demonstrate a larger ΔT a reduced input
(stress) would be beneficial to enhance the overall performance
and efficiency of the system. Thus, these criteria should also be
considered while selecting a suitable material for elasto-caloric
solid-state refrigeration.
Challenges and future prospects
Apart from the material parameters discussed above, materials for elasto-caloric applications present ample scope for
development before they can be successfully formulated into
competitive technologies. Table 1 provides a list of potential
12 Q MRS ENERGY & SUSTAINABILITY // V O L U M E 2 // e 1 6 // www.mrs.org/energy-sustainability-journal
Table 1. Elastocaloric properties of various SMA and ferroelectric materials.
Material
T (K)
|ΔT | (K)
|ΔS | (J/K kg)
|Q | (kJ/kg)
|Δσ| (GPa)
References
Cu69.6Al27.7Ni2.7
308
14
22
6.8
0.15
100DM
Cu68.1Zn15.8Al16.1
300
15
21
6.2
0.13
36DSC
Cu64.6Zn33.7Sn1.7
296
12
15
4.5
0.20
101DM
NiTi
295
17
32
9.3
0.65
20DM
Ni50.1Ti49.9
343
28
45
15
0.90
102DM
Ni50.2Ti49.8
296
40
74
22
0.80
103DM
Ni50.7Ti49.3
295
11
8.5
2.5
0.03
104DM
Fe68.8 Pd31.2
240
1.5
2.18
…
0.10
105DM
Fe49Rh51
311
5.2
7.8
2.4
0.53
106DM
NiTiCuV
280
…
…
…
0.5
86
Ni50.375Ti49.625
245.5
14.2
50.96
…
…
107DSC
Ni54Fe19Ga27
281
8.4
16.05
…
…
107DSC
Co40Ni33.17Al26.83
303.5
3.1
8.84
…
…
107DSC
Ni54Fe19Ga27
298
4
…
…
0.17
85DM
Ni48.4Mn34.8In16.8
313
4
5.9
…
0.3
108DM
Ni50Fe19Ga27Co4
348
10.2
…
…
0.3
72IM
Ni45.7Mn36.6In13.3Co5.1
300
3.5
5.4
…
0.1
63TA
Ni46Mn38Sb12Co4
296
15
21
…
0.1
109
Ba0.5 Sr0.5TiO3
250
9
…
…
1
21TA
Ba0.85Ca0.15Zr0.1Ti0.9O3
340
1.55
…
…
0.25
32IM
Ba0.865Ca0.135Zr0.1089
298
1.4
…
…
0.20
32IM
298
1.17
…
…
0.20
31IM
640
25
…
…
0.5
60TA
Ti0.8811Fe0.01O3
Ba0.865Ca0.135Zr0.1078
Ti0.8722Fe0.01Nb0.01O3
PbTiO3
Continued
MRS ENERGY & SUSTAINABILITY // V O L U M E 2 // e 1 6 // www.mrs.org/energy-sustainability-journal Q 13
Table 1. Continued
Material
T (K)
|ΔT | (K)
|ΔS | (J/K kg)
|Q | (kJ/kg)
|Δσ| (GPa)
PbTiO3
640
44
…
…
2
60TA
PMN–32PT
323
0.36
…
…
0.028
29IM
BaTiO3
401
3.2
…
…
0.2
61TA
PbTiO3
750
20
…
…
1
55TA
References
DM—direct measurement, IM—indirect measurement, TA—theoretical analysis.
ferroelastic materials reported in the literature for elasto-caloric cooling applications along with their thermodynamic performance parameters. The table is not exhaustive but represents
some of the best reported materials to date. However there
remains a lack of materials for tapping into successful association between two or more caloric effects. The main challenge
lies with the development of suitable materials for coupled
caloric effects. A simultaneous coupling of multiple caloric
effects within the same material could yield large amounts of
heat transfers utilizing co-existing “electric,” “magnetic,” and
“elastic” entropy transitions.
Finding a suitable material chemistry that is able to successfully couple multi-ferroic ordered phase transitions is already
underway. A giant electro-caloric effect has already been reported
for thin film PbTiO3–PbZrO3 (PZT) ferroelectric pervoskite
material.11 PZT is a solid solution of two independent ferroelectric phases of lead-titanate and lead-zirconate. Its properties
can be easily tailored to move between the extremes of these two
individual phases by varying the concentration of constituent
materials and doping of additional elements such as lanthanum.
Additionally, recent studies54,60 have identified the existence of
the elasto-caloric effect in lead-titanate through a first principles
approach. By controlling the chemical composition of the material, the two effects of elasto-caloric and electro-caloric effects
can be made to coincide at the same temperature. This will result
in a transition between states of very high and low entropy and
thereby lead to a giant coupled caloric effect.
A similar phenomenon has been reported for magnetic
SMAs. A large number of Ni–Mn and other magnetic SMAs have
been reported to exhibit a baro-caloric (or elasto-caloric) effect
apart from magnetically ordered phase transformation.6,9,14,53,55
Since the elasto-caloric effect in SMAs is purely stress driven, it
can be made to coincide with the magnetic ordered phase transition to produce giant entropy variations. Furthermore, the
magnetic phase order transition can be controlled by varying
the ratio of Ni and Mn with respect to other constituent elements.53 The maximum entropy change for ferroic materials is
expected to appear near their ferroelectric-paraelectric transition. When a ferroic material is heated past its Curie or Néel
temperature, the material transforms into a paraelectric/
paramagnetic phase accompanied by complete loss of functional
attributes. Thus, the Curie/Néel temperature should ideally be
close to the required operating temperature to achieve the maximum material efficiency and COP for any practical application.
However, such an operation (beyond Curie/Néel temperature)
should only be accomplished within the presence of an external
electric/magnetic field to reorient the domains once the material is cooled back to its initial temperature. In this regard,
we have proposed an electro-thermo-mechanical cycle to successfully combine the elasto-caloric and electro-caloric effects
in ferroelectric single crystals.29 Similar phenomena are also
expected in other ferroelectric compositions and research in
this direction is under progress.
However, the availability of multi-ferroic materials capable
of pseudoelastic phase transition is currently limited. The fabrication of composite multi-ferroic materials may therefore prove
to be highly beneficial. Such composites are ideally expected to
contain at least two individual phases capable of entropy transition in the vicinity of the required operating temperature. Even
though no direct coupling is expected to exist in such materials,
the caloric effect to be obtained in such situations can be larger
than its individual components.40
Apart from coupled caloric effects, any refrigeration working on elasto-caloric effect still has disadvantages associated
with its practical implementations. The primary concern is to
reduce the magnitude of actuation field and work done on the
system by the applied stimulus. While the electro-caloric and
magneto-caloric effects operates with no moving parts, the
elasto-caloric effect requires the development of a suitable load
cell to apply the necessary forces (and accommodate associated
strains); for example the elastic deformation can be up to several
100% for elastomers. Additionally, the design of heat pumps
and circulation devices for such technologies is still under
development. Many alternatives such as heat switches, thermal
diodes,110 Peltier units111 and convection through liquid crystals112 have been proposed to this effect but require further
investigation. However, efforts are being made to overcome the
associated limitations and prototyping is under development.
Most notably, the efforts by Schmidt et al.86,113 and Tušek et al.73,99
must be noted who have designed and analyzed the performance of a practical refrigeration system employing the
elasto-caloric effect. It is expected that reliable and efficient
14 Q MRS ENERGY & SUSTAINABILITY // V O L U M E 2 // e 1 6 // www.mrs.org/energy-sustainability-journal
systems would be realized within the next decade that are ready
for mass deployment.
Sustainability and environmental impact
The last century has witnessed a global temperature increase
of about 0.6 K and a study by the UN Intergovernmental Panel
on Climate Change has projected an increase of the average
global temperature by 1.4–4.5 K by 2100.114 An increase of this
magnitude has the potential to have an impact on the shift in
rainfall seasons, migration patterns of various life forms115 and
increase in the frequency of extreme weather effects among others.114,116–118 These factors have triggered efforts toward reducing activities and emissions that are responsible for climate
change. The foremost effort in this direction has been the initiative in the form of Kyoto Protocol.119 Among the main agendas, the protocol has made it legally binding for industrialized
countries to reduce the collective emission of greenhouse gases
and outlawed the use of various chlorofluorocabons (CFCs)
used in the refrigeration industry.
Refrigeration is one of the main energy sinks in the industrialized world and forms a major part of the European electricity
consumption.17 Thus it is also one of the largest producers of
carbon footprints and contributes greatly to greenhouse emission; the low operational efficiencies and the use of halofluorocarbons (HFCs)120 in vapor compression systems is one potential
concern. The maximum theoretical limit for efficiency of a vapor
compression system peaks at 60% of Carnot efficiency. However,
most of the refrigeration systems employ compressors with substantially reduced performances and an overall efficiency of
40–55% is practically obtainable.121 Secondly, even though the
harmful CFCs have been phased out, commercially available
refrigeration systems still employ HFCs. These gases are less
toxic and do not contribute to ozone depletions. However,
these are classified as super-greenhouse gases and contribute
greatly to the global warming.120 One possible alternative is
to employ low boiling point organic refrigerants like pentane122
or ammonia.123 Nonetheless, the limited range of operating
temperatures hinders wide scale applicability.
In the light of these circumstances solid-state refrigeration
provides a route to offer high reduction potentials in medium to
small scale refrigeration and cryogenic requirements.17,58 The
high order phase transitions associated with ferroic materials
allow for large entropy changes and corresponding giant caloric
effects.58 The thermal inertia of such systems is low which limits their applicability to low load regimes but the associated benefits of solid-state refrigeration can be their high efficiency and
COP. Theoretical values of COP close to 83.7% of Carnot has
been reported for polycrystalline Ni–Ti SMA.20 This represents
a substantial improvement over conventional vapor compression
systems.7,17 Additionally, solid-state cooling essentially operates
without the requirement of a refrigerant as the material itself
forms the source of heat exchange and the need for HFCs is
eliminated. Apart from their nonpolluting and environmentalfriendly application, minimization of moving parts can lead to
enhanced operational life, less failures and safer operation.
Long term life cycle assessment for ferroelectric materials124
has been proposed which would help to develop sustainable solid-state technologies. One of the first steps in this direction has
been the development of lead-free ferroelectric materials.125
The matter is even more simplified for alloy and polymer based
elasto-caloric materials as these can benefit from established
reutilization and recycling. Therefore, further research is warranted into the field of solid-state cooling materials and technologies. Such systems will not only prove to be economically
beneficial but will have a lesser environmental impact than
existing conventional devices.
Conclusions
This paper has explained the underlying characteristics
responsible for the elasto-caloric effect in SMAs, polymeric
materials, and ferroic materials. The two types of elasticity,
namely force-elasticity and entropy-elasticity have been discussed
with the underlying mechanisms explained. The thermodynamic
equations governing the behavior of entropy-elastic materials
were used to derive the respective expressions for the elastocaloric effect. Parameters associated with the performance of
the materials for elasto-caloric cooling were discussed. These
parameters include the elasto-caloric magnitude, specific heat
capacity, endurance limit, transition temperature, and COP.
Some additional background relating to coupled caloric effects
in multi-ferroic materials and its potential applicability to practical realization of mechanical refrigeration has been discussed.
A brief insight has also been provided into the current technological limitations to the successful application of elasto-caloric
effect for commercial applications. Additionally, the long term
sustainability and environmental impact of solid-state cooling
technologies has also been discussed. The presented study is
expected to promote interest and research in the field for efficient and practical use of the elasto-caloric effect for environmentally-friendly solid state refrigeration.
Acknowledgments
One of the authors (Rahul Vaish) acknowledges support
from the 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). Bowen acknowledges funding from the European
Research Council under the European Union's Seventh Framework Program (FP/2007–2013)/ERC Grant Agreement No.
320963 on Novel Energy Materials, Engineering Science and
Integrated Systems (NEMESIS).
REFERENCES :
1.
2.
3.
4.
Ju Y.S.: Solid-state refrigeration based on the electrocaloric effect for
electronics cooling. J. Electron. Packag. 132(4), 041004 (2010).
Chen Z-J. and Lin W-h.: Dynamic simulation and optimal matching of a
small-scale refrigeration system. Int. J. Refrig. 14(6), 329–335 (1991).
Eames I., Aphornratana S., and Haider H.: A theoretical and experimental
study of a small-scale steam jet refrigerator. Int. J. Refrig. 18(6), 378–386
(1995).
Mongia R., Masahiro K., DiStefano E., Barry J., Chen W., Izenson M.,
Possamai F., Zimmermann A., and Mochizuki M.: Small scale refrigeration
MRS ENERGY & SUSTAINABILITY // V O L U M E 2 // e 1 6 // www.mrs.org/energy-sustainability-journal Q 15
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
system for electronics cooling within a notebook computer. In The Tenth
Intersociety Conference on Thermal and Thermomechanical Phenomena in
Electronics Systems, 2006. ITHERM’06, IEEE: San Diego, California, USA,
2006; pp. 751–758.
Phelan P.E., Swanson J., Chiriac F., and Chiriac V.: Designing a mesoscale
vapor-compression refrigerator for cooling high-power microelectronics.
In Thermal and Thermomechanical Phenomena in Electronic
Systems, 2004. ITHERM’04, IEEE: Las Vegas, Nevada, USA , 2004;
pp. 218–223.
Manosa L., Planes A., and Acet M.: Advanced materials for solid-state
refrigeration. J. Mater. Chem. A 1(16), 4925–4936 (2013).
Lu S-G. and Zhang Q.: Electrocaloric materials for solid-state refrigeration.
Adv. Mater. 21(19), 1983–1987 (2009).
Brück E.: Developments in magnetocaloric refrigeration. J. Phys. D: Appl.
Phys. 38(23), R381 (2005).
Krenke T., Duman E., Acet M., Wassermann E.F., Moya X., Mañosa L., and
Planes A.: Inverse magnetocaloric effect in ferromagnetic Ni–Mn–Sn alloys.
Nat. Mater. 4(6), 450–454 (2005).
Gschneidner K.A. and Pecharsky V.K.: Magnetocaloric materials. Annu. Rev.
Mater. Sci. 30(1), 387–429 (2000).
Mischenko A., Zhang Q., Scott J., Whatmore R., and Mathur N.: Giant
electrocaloric effect in thin-film PbZr0.95Ti0.05O3. Science 311(5765),
1270–1271 (2006).
Neese B., Chu B., Lu S-G., Wang Y., Furman E., and Zhang Q.: Large
electrocaloric effect in ferroelectric polymers near room temperature.
Science 321(5890), 821–823 (2008).
Mañosa L., González-Alonso D., Planes A., Barrio M., Tamarit J-L.,
Titov I.S., Acet M., Bhattacharyya A., and Majumdar S.: Inverse barocaloric
effect in the giant magnetocaloric La–Fe–Si–Co compound. Nat. Commun.
2, 595 (2011).
Mañosa L., González-Alonso D., Planes A., Bonnot E., Barrio M.,
Tamarit J-L., Aksoy S., and Acet M.: Giant solid-state barocaloric
effect in the Ni-Mn-In magnetic shape-memory alloy. Nat. Mater. 9(6),
478–481 (2010).
Imamura Y., Sakamoto S-i., and Watanabe Y.: Modulation of sound field in
looped-tube thermoacoustic cooling system with membrane. Jpn. J. Appl.
Phys 46, 4417 (2007).
Paek I., Braun J.E., and Mongeau L.: Evaluation of standing-wave
thermoacoustic cycles for cooling applications. Int. J. Refrig. 30(6),
1059–1071 (2007).
Fähler S., Rößler U.K., Kastner O., Eckert J., Eggeler G., Emmerich H.,
Entel P., Müller S., Quandt E., and Albe K.: Caloric effects in ferroic
materials: New concepts for cooling. Adv. Eng. Mater. 14(1–2), 10–19 (2012).
Gaskill H.V.: Method of using the peltier effect for cooling equipment. U.S.
Patent No. 2984077, 1961.
Abramov V.S., Shishov A.V., Scherbakov N.V., Sushkov V.P., and Ivanov
A.A.: Peltier cooling systems with high aspect ratio. U.S. Patent No.
7823393 B2, 2010.
Cui J., Wu Y., Muehlbauer J., Hwang Y., Radermacher R., Fackler S.,
Wuttig M., and Takeuchi I.: Demonstration of high efficiency elastocaloric
cooling with large ΔT using NiTi wires. Appl. Phys. Lett. 101(7), 073904
(2012).
Lisenkov S. and Ponomareva I.: Giant elastocaloric effect in ferroelectric
Ba0.5Sr0.5TiO3 alloys from first-principles. Phys. Rev. B 86(10), 104103
(2012).
Nikitin S.A., Myalikgulyev G., Annaorazov M.P., Tyurin A.L., Myndyev
R.W., and Akopyan S.A.: Giant elastocaloric effect in FeRh alloy. Phys.
Lett. A 171(3–4), 234–236 (1992).
Xiao F., Fukuda T., and Kakeshita T.: Significant elastocaloric effect in a
Fe-31.2Pd (at. %) single crystal. Appl. Phys. Lett. 102(16), 161914 (2013).
Castillo-Villa P.O., Soto-Parra D.E., Matutes-Aquino J.A., Ochoa-Gamboa
R.A., Planes A., Mañosa L., González-Alonso D., Stipcich M., Romero R.,
Ríos-Jara D., and Flores-Zúñiga H.: Caloric effects induced by magnetic
and mechanical fields in a Ni50Mn25-xGa25Cox magnetic shape memory
alloy. Phys. Rev. B 83(17), 174109 (2011).
Fukuhara M., Inoue A., and Nishiyama N.: Rubberlike entropy elasticity of
a glassy alloy. Appl. Phys. Lett. 89(10), 101903 (2006).
26. Holzapfel G.A. and Simo J.C.: Entropy elasticity of isotropic rubber-like
solids at finite strains. Comput. Methods Appl. Mech. Eng. 132(1–2), 17–44
(1996).
27. Kim H.Y., Satoru H., Kim J.I., Hosoda H., and Miyazaki S.: Mechanical
properties and shape memory behavior of Ti-Nb alloys. Mater. Trans.
45(7), 2443–2448 (2004).
28. Melton K.N. and Mercier O.: The mechanical properties of NiTi-based
shape memory alloys. Acta Metall. 29(2), 393–398 (1981).
29. Chauhan A., Patel S., and Vaish R.: Multicaloric effect in Pb(Mn1/3Nb2/3)
O3-32PbTiO3 single crystals. Acta Mater. 89, 384–395 (2015).
30. Chauhan A., Patel S., and Vaish R.: Multicaloric effect in Pb(Mn1/3Nb2/3)
O3-32PbTiO3 single crystals: Modes of measurement. Acta Mater. 97,
17–28 (2015).
31. Patel S., Chauhan A., and Vaish R.: Caloric effects in bulk lead-free
ferroelectric ceramics for solid-state refrigeration. Energy Technol.
(2015). doi: 10.1002/ente.201500205.
32. Patel S., Chauhan A., and Vaish R.: Multiple caloric effects in
(Ba0.865Ca0.135Zr0.1089Ti0.8811Fe0.01)O3 ferroelectric ceramic. Appl. Phys.
Lett. 107(4), 042902 (2015).
33. Chauhan A., Patel S., and Vaish R.: Elastocaloric effect in ferroelectric
ceramics. Appl. Phys. Lett. 106(17), 172901 (2015).
34. Guyomar D., Li Y., Sebald G., Cottinet P-J., Ducharne B., and Capsal
J-F.: Elastocaloric modeling of natural rubber. Appl. Therm. Eng.
57(1–2), 33–38 (2013).
35. Pellicer J., Manzanares J.A., Zúñiga J., Utrillas P., and Fernández J.:
Thermodynamics of rubber elasticity. J. Chem. Educ. 78(2), 263 (2001).
36. Bonnot E., Romero R., Mañosa L., Vives E., and Planes A.: Elastocaloric
effect associated with the martensitic transition in shape-memory alloys.
Phys. Rev. Lett. 100(12), 125901 (2008).
37. Huang W.: On the selection of shape memory alloys for actuators. Mater. Des.
23(1), 11–19 (2002).
38. Schetky L.M.: Shape-memory alloys. In Kirk-Othmer Encyclopedia of
Chemical Technology, John Wiley & Sons, Inc.: New York, USA , 2000.
doi: 10.1002/0471238961.1908011619030805.a01.
39. Schmidt M., Schütze A., and Seelecke S.: Cooling efficiencies of a NiTi-based
cooling process. In Conference on Smart Materials, Adaptive Structures
and Intelligent Systems, 2013, ASME: Snowbird, Utah, USA , September
16–18, 2013; p. V001T04A014.
40. Melvin M.V.: Theory of giant-caloric effects in multiferroic materials.
J. Phys. D: Appl. Phys. 46(34), 345304 (2013).
41. Boonstra B.B.S.T.: Stress-strain properties of natural rubber under biaxial
strain. J. Appl. Phys. 21(11), 1098–1104 (1950).
42. Cottinet P-J., Guyomar D., Galineau J., and Sebald G.: Electro-thermoelastomers for artificial muscles. Sens. Actuators, A 180, 105–112 (2012).
43. Otubo J., Rigo O.D., Coelho A.A., Neto C.M., and Mei P.R.: The influence
of carbon and oxygen content on the martensitic transformation temperatures
and enthalpies of NiTi shape memory alloy. Mater. Sci. Eng., A 481–482,
639–642 (2008).
44. Wu S.K. and Wayman C.M.: Martensitic transformations and the shape
memory effect in Ti50Ni10Au40 and Ti50Au50 alloys. Metallography 20(3),
359–376 (1987).
45. Otsuka K. and Shimizu K.: Pseudoelasticity and shape memory effects in
alloys. Int. Met. Rev. 31(1), 93–114 (1986).
46. Manosa L., Planes A., Vives E., Bonnot E., and Romero R.: The use of
shape-memory alloys for mechanical refrigeration. Funct. Mater. Lett.
02(02), 73–78 (2009).
47. Orgéas L. and Favier D.: Stress-induced martensitic transformation of a
NiTi alloy in isothermal shear, tension and compression. Acta Mater.
46(15), 5579–5591 (1998).
48. Boyd J.G. and Lagoudas D.C.: A thermodynamical constitutive model
for shape memory materials. Part I. The monolithic shape memory
alloy. Int. J. Plast. 12(6), 805–842 (1996).
49. Tanaka K., Kobayashi S., and Sato Y.: Thermomechanics of transformation
pseudoelasticity and shape memory effect in alloys. Int. J. Plast. 2(1),
59–72 (1986).
50. Raniecki B. and Lexcellent C.: Thermodynamics of isotropic pseudoelasticity
in shape memory alloys. Eur. J. Mech. A-Solid 17(2), 185–205 (1998).
16 Q MRS ENERGY & SUSTAINABILITY // V O L U M E 2 // e 1 6 // www.mrs.org/energy-sustainability-journal
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
McKelvey A.L. and Ritchie R.O.: On the temperature dependence of the
superelastic strength and the prediction of the theoretical uniaxial
transformation strain in nitinol. Philos. Mag. 80(8), 1759–1768 (2000).
Bechtold C., Chluba C., Lima de Miranda R., and Quandt E.: High cyclic
stability of the elastocaloric effect in sputtered TiNiCu shape memory films.
Appl. Phys. Lett. 101(9), 091903 (2012).
Castillo-Villa P.O., Manosa L., Planes A., Soto-Parra D.E., SanchezLlamazares J.L., Flores-Zuniga H., and Frontera C.: Elastocaloric and
magnetocaloric effects in Ni-Mn-Sn(Cu) shape-memory alloy. J. Appl.
Phys. 113(5), 053506 (2013).
Lisenkov S., Mani B.K., Chang C.M., Almand J., and Ponomareva I.:
Multicaloric effect in ferroelectric PbTiO3 from first principles. Phys.
Rev. B 87(22), 224101 (2013).
Entel P., Sahoo S., Siewert M., Gruner M.E., Herper H.C., Comtesse D.,
Acet M., Buchelnikov V.D., and Sokolovskiy V.V.: First-principles
investigations of caloric effects in ferroic materials. AIP Conf. Proc.
1461(1), 11–23 (2012).
Choi Y., Fisher T., Lima Sharma A., Qin Z., Zhou T., and Cheong S-W.:
Competition between magnetocaloric and elastocaloric effect in phase
separated manganites under pressure. APS March Meeting Abstracts,
2010; p. 1037.
Annaorazov M.P., Nikitin S.A., Tyurin A.L., Akopyan S.A., and
Myndyev R.W.: Cooling scheme based on the AF–F transition in Fe–Rh alloys
induced by tensile stress. Phys. Status Solidi A 194(1), 304–314 (2002).
Moya X., Kar-Narayan S., and Mathur N.: Caloric materials near ferroic
phase transitions. Nat. Mater. 13(5), 439–450 (2014).
de Oliveira N.A. and von Ranke P.J.: Theoretical aspects of the magnetocaloric
effect. Phys. Rep. 489(4–5), 89–159 (2010).
Barr J.A., Beckman S.P., and Nishimatsu T.: Elastocaloric response of
PbTiO3 predicted from a first-principles effective hamiltonian. J. Phys. Soc.
Jpn. 84(2), 024716 (2015).
Liu Y., Infante I.C., Lou X., Bellaiche L., Scott J.F., and Dkhil B.: Giant
room-temperature elastocaloric effect in ferroelectric ultrathin films.
Adv. Mater. 26(35), 6132–6137 (2014).
Liu Y., Wei J., Janolin P-E., Infante I.C., Kreisel J., Lou X., and Dkhil B.:
Prediction of giant elastocaloric strength and stress-mediated electrocaloric
effect in BaTiO3 single crystals. Phys. Rev. B 90(10), 104107 (2014).
Lu B., Xiao F., Yan A., and Liu J.: Elastocaloric effect in a textured
polycrystalline Ni-Mn-In-Co metamagnetic shape memory alloy.
Appl. Phys. Lett. 105(16), 161905 (2014).
Patel S., Chauhan A., and Vaish R.: A technique for giant mechanical
energy harvesting using ferroelectric/antiferroelectric materials. J. Appl.
Phys. 115(8), 084908 (2014).
Hwang S.C., Lynch C.S., and McMeeking R.M.: Ferroelectric/ferroelastic
interactions and a polarization switching model. Acta Metall. 43(5),
2073–2084 (1995).
Dong W.D., Finkel P., Amin A., and Lynch C.S.: Giant electro-mechanical
energy conversion in [011] cut ferroelectric single crystals. Appl. Phys.
Lett. 100(4), 042903 (2012).
Chen W. and Lynch C.S.: A micro-electro-mechanical model for polarization
switching of ferroelectric materials. Acta Mater. 46(15), 5303–5311 (1998).
Patel S., Chauhan A., and Vaish R.: Enhanced energy harvesting in commercial
ferroelectric materials. Mater. Res. Express 1(2), 025504 (2014).
Patel S., Chauhan A., and Vaish R.: Analysis of high-field energy harvesting
using ferroelectric materials. Energy Technol. 2(5), 480–485 (2014).
Valadez J., Sahul R., Alberta E., Hackenberger W., and Lynch C.: The effect
of a hydrostatic pressure induced phase transformation on the unipolar
electrical response of Nb modified 95/5 lead zirconate titanate. J. Appl.
Phys. 111(2), 024109 (2012).
Marsilius M., Frederick J., Hu W., Tan X., Granzow T., and Han P.:
Mechanical confinement: An effective way of tuning properties of
piezoelectric crystals. Adv. Funct. Mater. 22(4), 797–802 (2012).
Xiao F., Jin M., Liu J., and Jin X.: Elastocaloric effect in Ni50Fe19Ga27Co4
single crystals. Acta Mater. 96, 292–300 (2015).
Tušek J., Engelbrecht K., Mikkelsen L.P., and Pryds N.: Elastocaloric
effect of Ni-Ti wire for application in a cooling device. J. Appl. Phys.
117(12), 124901 (2015).
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
Ossmer H., Chluba C., Krevet B., Quandt E., Rohde M., and Kohl M.:
Elastocaloric cooling using shape memory alloy films. J. Phys.: Conf. Ser.
476(1), 012138 (2013).
McLaughlin E.A., Liu T., and Lynch C.S.: Relaxor ferroelectric PMN32%PT crystals under stress, electric field and temperature loading:
II-33-mode measurements. Acta Mater. 53(14), 4001–4008 (2005).
McLaughlin E.A., Liu T., and Lynch C.S.: Relaxor ferroelectric PMN32%PT crystals under stress and electric field loading: I-32 mode
measurements. Acta Materialia 52(13), 3849–3857 (2004).
Thacher P.: Electrocaloric effects in some ferroelectric and
antiferroelectric Pb(Zr,Ti)O3 compounds. J. Appl. Phys. 39(4),
1996–2002 (1968).
Wunderlich B. and Baur H.: Heat Capacities of Linear High Polymers
(Springer-Verlag Berlin Heidelberg, Germany, 1970).
Alam K.A., Saha B., Kang Y., Akisawa A., and Kashiwagi T.: Heat exchanger
design effect on the system performance of silica gel adsorption refrigeration
systems. Int. J. Heat Mass Transfer 43(24), 4419–4431 (2000).
Valant M.: Electrocaloric materials for future solid-state refrigeration
technologies. Prog. Mater. Sci. 57(6), 980–1009 (2012).
Mars W.V. and Fatemi A.: A literature survey on fatigue analysis approaches
for rubber. Int. J. Fatigue 24(9), 949–961 (2002).
Sauer J.A. and Richardson G.C.: Fatigue of polymers. Int. J. Fract. 16(6),
499–532 (1980).
Hornbogen E.: Review thermo-mechanical fatigue of shape memory alloys.
J. Mater. Sci. 39(2), 385–399 (2004).
Eggeler G., Hornbogen E., Yawny A., Heckmann A., and Wagner M.:
Structural and functional fatigue of NiTi shape memory alloys. Mater. Sci.
Eng., A 378(1–2), 24–33 (2004).
Xu Y., Lu B., Sun W., Yan A., and Liu J.: Large and reversible elastocaloric
effect in dual-phase Ni54Fe19Ga27 superelastic alloys. Appl. Phys. Lett.
106(20), 201903 (2015).
Schmidt M., Ullrich J., Wieczorek A., Frenzel J., Schütze A., Eggeler G.,
and Seelecke S.: Thermal stabilization of NiTiCuV shape memory alloys:
Observations during elastocaloric training. Shap. Mem. Superelasticity 1,
132–141 (2015).
Chon U., Kim K-B., Jang H.M., and Yi G-C.: Fatigue-free samariummodified bismuth titanate (Bi4−xSmxTi3O12) film capacitors having large
spontaneous polarizations. Appl. Phys. Lett. 79(19), 3137–3139 (2001).
Schäufele A.B. and Heinz Härdtl K.: Ferroelastic properties of lead
zirconate titanate ceramics. J. Am. Ceram. Soc. 79(10), 2637–2640
(1996).
Moazzami R., Hu C., and Shepherd W.H.: Endurance properties of
ferroelectric PZT thin films. In International Technical Digest on Electron
Devices Meeting, 1990. IEDM’90, 1990; pp. 417–420.
Warren W.L., Tuttle B.A., and Dimos D.: Ferroelectric fatigue in perovskite
oxides. Appl. Phys. Lett. 67(10), 1426–1428 (1995).
Brennan C.: Model of ferroelectric fatigue due to defect/domain
interactions. Ferroelectrics 150(1), 199–208 (1993).
Pan W., Yue C-F., and Tosyali O.: Fatigue of ferroelectric polarization and
the electric field induced strain in lead lanthanum zirconate titanate
ceramics. J. Am. Ceram. Soc. 75(6), 1534–1540 (1992).
Gerber P., Kügeler C., Ellerkmann U., Schorn P., Böttger U., and Waser R.:
Effects of ferroelectric fatigue on the piezoelectric properties (d33) of
tetragonal lead zirconate titanate thin films. Appl. Phys. Lett. 86(11),
112908 (2005).
Chen J., Harmer M.P., and Smyth D.M.: Compositional control of
ferroelectric fatigue in perovskite ferroelectric ceramics and thin films.
J. Appl. Phys. 76(9), 5394–5398 (1994).
Tang Z.X., Sorensen C.M., Klabunde K.J., and Hadjipanayis G.C.:
Size-dependent curie temperature in nanoscale MnFe2O4 particles.
Phys. Rev. Lett. 67(25), 3602–3605 (1991).
Brouha M. and Buschow K.: Pressure dependence of the Curie temperature
of intermetallic compounds of iron and rare-earth elements, Th, and Zr.
J. Appl. Phys. 44(4), 1813–1816 (1973).
Cross L.E.: Relaxor ferroelectrics. Ferroelectrics 76(1), 241–267 (1987).
Moya X., Defay E., Heine V., and Mathur N.D.: Too cool to work. Nat. Phys.
11(3), 202–205 (2015).
MRS ENERGY & SUSTAINABILITY // V O L U M E 2 // e 1 6 // www.mrs.org/energy-sustainability-journal Q 17
99. Tušek J., Engelbrecht K., Millán-Solsona R., Mañosa L., Vives E.,
Mikkelsen L.P., and Pryds N.: The elastocaloric effect: A way to cool
efficiently. Adv. Energy Mater. 5(13), 1500361 (2015).
100. Rodriguez C. and Brown L.: The thermal effect due to stress-induced
martensite formation in Β-CuAlNi single crystals. Metall. Mater. Trans. A
11(1), 147–150 (1980).
101. Brown L.: The thermal effect in pseudoelastic single crystals of β-CuZnSn.
Metall. Trans. A 12(8), 1491–1494 (1981).
102. Shaw J.A. and Kyriakides S.: Thermomechanical aspects of NiTi. J. Mech.
Phys. Solids 43(8), 1243–1281 (1995).
103. Pieczyska E., Gadaj S., Nowacki W., and Tobushi H.: Phase-transformation
fronts evolution for stress-and strain-controlled tension tests in TiNi shape
memory alloy. Exp. Mech. 46(4), 531–542 (2006).
104. Quarini J. and Prince A.: Solid state refrigeration: Cooling and refrigeration
using crystalline phase changes in metal alloys. Proc. Inst. Mech. Eng., Part C
218(10), 1175–1179 (2004).
105. Xiao F., Takashi F., Tomoyuki K., and Xuejun J.: Elastocaloric effect by a
weak first-order transformation associated with lattice softening in an
Fe-31.2 Pd (at.%) alloy. Acta Materialia 87, 8–14 (2015).
106. Annaorazov M., Nikitin S., Tyurin A., Asatryan K., and Dovletov A.K.:
Anomalously high entropy change in FeRh alloy. J. Appl. Phys. 79(3),
1689–1695 (1996).
107. Pataky G.J., Ertekin E., and Sehitoglu H.: Elastocaloric cooling potential of
NiTi, Ni2FeGa, and CoNiAl. Acta Mater. 96, 420–427 (2015).
108. Huang Y.J., Hu Q.D., Bruno N.M., Chen J-H., Karaman I., Ross J.H. Jr., and
Li J.G.: Giant elastocaloric effect in directionally solidified Ni–Mn–In
magnetic shape memory alloy. Scr. Mater. 105, 42–45 (2015).
109. Millán-Solsona R., Stern-Taulats E., Vives E., Planes A., Sharma J., Nayak
A.K., Suresh K.G., and Mañosa L.: Large entropy change associated with
the elastocaloric effect in polycrystalline Ni-Mn-Sb-Co magnetic shape
memory alloys. Appl. Phys. Lett. 105(24), 241901 (2014).
110. Li B., Wang L., and Casati G.: Thermal diode: Rectification of heat flux.
Phys. Rev. Lett. 93(18), 184301 (2004).
111. Mathur N. and Mishchenko A.: Solid state electrocaloric cooling devices
and methods. U.S. Patent No. WO2006056809A1, 2006.
112. Hwalek J. and Carr E.: A liquid crystal “heat switch”. Heat Transfer Eng.
8(1), 36–38 (1987).
113. Schmidt M., Schütze A., and Seelecke S.: Scientific test setup for investigation
of shape memory alloy based elastocaloric cooling processes. Int. J. Refrig.
54, 88–97 (2015).
114. Houghton J.T., Ding Y., Griggs D.J., Noguer M., van der Linden P.J., Dai X.,
Maskell K., and Johnson C.: Climate Change 2001: The Scientific Basis,
Vol. 881 (Cambridge University Press, Cambridge, 2001).
115. Root T.L., Price J.T., Hall K.R., Schneider S.H., Rosenzweig C., and
Pounds J.A.: Fingerprints of global warming on wild animals and plants.
Nature 421(6918), 57–60 (2003).
116. Mendelsohn R., Nordhaus W.D., and Shaw D.: The impact of global warming
on agriculture: A Ricardian analysis. Am. Econ. Rev. 84, 753–771 (1994).
117. Collins M., An S.-I., Cai W., Ganachaud A., Guilyardi E., Jin F.-F., Jochum M.,
Lengaigne M., Power S., and Timmermann A.: The impact of global
warming on the tropical Pacific Ocean and El Niño. Nat. Geosci. 3(6),
391–397 (2010).
118. Miller J.R. and Russell G.L.: The impact of global warming on river runoff.
J. Geophys. Res.: Atmos. 97(D3), 2757–2764 (1992).
119. Kyoto Protocol: United Nations Framework Convention on Climate Change
(Kyoto Protocol, Kyoto, 1997).
120. U.N.E.P.O. Secretariat: Handbook for the Montreal Protocol on Substances
that Deplete the Ozone Layer (UNEP/Earthprint: Nairobi, Kenya, 2006).
121. Ashare Handbook: HVAC Systems and Equipment (ASHRAE Eng.:
American Society of Heating Atlanta, Georgia, USA, 1996).
122. Powell R.L., Poole J.E., Capper J.D., and Thomas J.V.: R 22 replacement
refrigerant. U.S. Patent No. 6606868 B1, 2003.
123. Wong K.K., Yudin B., Bonaquist D.P., and Rashad M.A-A.: Multicomponent
refrigeration fluid refrigeration system with auxiliary ammonia cascade
circuit. U.S. Patent No. 6494054, 2002.
124. Dingquan X.: Environmentally conscious ferroelectrics research—present
and prospect. Ferroelectrics 231(1), 133–141 (1999).
125. Saito Y., Takao H., Tani T., Nonoyama T., Takatori K., Homma T.,
Nagaya T., and Nakamura M.: Lead-free piezoceramics. Nature
432(7013), 84–87 (2004).
18 Q MRS ENERGY & SUSTAINABILITY // V O L U M E 2 // e 1 6 // www.mrs.org/energy-sustainability-journal