Anisotropy of piezocaloric effect at ferroelectric phase transitions in ammonium hydrogen sulphate

Article abstract of DOI:10.1016/j.jallcom.2020.155085

The role of anisotropy of the thermal expansion in formation of piezocaloric effect (PCE) near ferroelectric phase transitions in NH₄HSO₄ was studied. Strong difference in linear baric coefficients and as a result in intensive and extensive PCE associated with the different crystallographic axes was found. PCE giving the main contribution to the barocaloric effect were determined at both phase transitions. Rather strong effect of the lattice dilatation on the tuning of PCE was observed. Comparative analysis of PCE at the phase transitions in different materials showed that NH₄HSO₄ can be considered as a promising solid-state refrigerant. A hypothetical cooling cycle based on alternate using uniaxial pressure along two axes was considered.

Full text of DOI:10.1016/j.jallcom.2020.155085

Journal of Alloys and Compounds 839 (2020) 155085
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: http://www.elsevier.com/locate/jalcom
Anisotropy of piezocaloric effect at ferroelectric phase transitions in
ammonium hydrogen sulphate
Ekaterina A. Mikhaleva , Mikhail V. Gorev b, Maxim S. Molokeev a c,
a
a
,
, b,
a,
d
a, b, *
Andrey V. Kartashev , Igor N. Flerov
a
Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036, Krasnoyarsk, Russia
Institute of Engineering Physics and Radioelectronics, Siberian Federal University, 660074, Krasnoyarsk, Russia
Department of Physics, Far Eastern State Transport University, 680021, Khabarovsk, Russia
Astafijev Krasnoyarsk State Pedagogical University, 660049, Krasnoyarsk, Russia
b
c
d
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 8 July 2019
Received in revised form
The role of anisotropy of the thermal expansion in formation of piezocaloric effect (PCE) near ferro-
electric phase transitions in NH HSO was studied. Strong difference in linear baric coefficients and as a
4 4
result in intensive and extensive PCE associated with the different crystallographic axes was found. PCE
giving the main contribution to the barocaloric effect were determined at both phase transitions. Rather
strong effect of the lattice dilatation on the tuning of PCE was observed. Comparative analysis of PCE at
26 February 2020
Accepted 6 April 2020
Available online 8 May 2020
4 4
the phase transitions in different materials showed that NH HSO can be considered as a promising
solid-state refrigerant. A hypothetical cooling cycle based on alternate using uniaxial pressure along two
axes was considered.
Keywords:
Piezocaloric effect
Phase transition
Ferroelectrics
Thermal expansion
High-pressure
Entropy
©
2020 Elsevier B.V. All rights reserved.
1
. Introduction
The main objective of the latter direction is to create solid re-
frigerants that can be used in miniature refrigerators, essential for
modern micro- and nanoelectronic devices with large heat emis-
sion [8]. Obviously, for this purpose, the most suitable are single
crystal or ceramic dielectric materials that do not require bulky
external devices for the implementation of individual or pairing CE:
ECE, PCE (ElCE), FCE. The disadvantages of ECE and FCE are asso-
ciated, first, with the irreversible process of Joule heat generation in
a ferroelectric when high electric field is applied and, second, with
a significant nonlinear deformation of the caloric element which is
not very convenient, for example, when designing combined
working elements of the microcircuiterefrigerator.
Solids exhibiting high caloric effects (CE) attract a great atten-
tion of both researches and engineers due a possibility to use them
as effective solid-state refrigerants at designing alternative cooling
cycles [1e5]. Different CE exist according to their physical nature:
magnetocaloric (MCE), electrocaloric (ECE), barocaloric (BCE),
piezo-(or elasto-)caloric PCE(ElCE), flexocaloric (FCE). All these ef-
fects are associated with a reversible change in the adiabatic tem-
perature (DTAD) or isothermal entropy (DSCE) of the material when
the corresponding external field is applied or removed.
Studies of caloric materials are mainly carried out in two di-
rections. The former is related to the search for solids competitive
in caloric efficiency relative to gas coolants used in traditional
large-scale gas-compressor refrigerators. In such a case, materials
PCE can be considered as a special case of the bulk BCE, coupled
with hydrostatic pressure, and is realized under the influence of
uniaxial mechanical stress s:
with significant intensive,
DTAD, and extensive, DSCE, MCE and BCE
look like the most promising [2,6,7].
*
Corresponding author. Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036, Krasnoyarsk, Russia.
E-mail addresses: katerina@iph.krasn.ru (E.A. Mikhaleva), gorev@iph.krasn.ru (M.V. Gorev), msmolokeev@mail.ru (M.S. Molokeev), akartashev@yandex.ru
A.V. Kartashev), flerov@iph.krasn.ru (I.N. Flerov).
(
https://doi.org/10.1016/j.jallcom.2020.155085
925-8388/© 2020 Elsevier B.V. All rights reserved.
0

2
E.A. Mikhaleva et al. / Journal of Alloys and Compounds 839 (2020) 155085
coefficient of the volume thermal expansion of the crystal lattice,
ð
ꢀ4
ꢀ1
T
b
¼(1.5e2.0),10
K . In accordance with [24], this can signif-
PCE
AD
LAT
D
SPCE ¼ ꢀ V
m
ðT;
s
Þa
ðT;
sÞds
;
DT
¼ ꢀ C
D
SPCE
;
(1)
icantly effects on BCE. However, the question of the influence of
thermal expansion of the crystal lattice on PCE in ferroelectrics
remained open.
p
where V
m
is the molar volume and
thermal expansion coefficient.
a
¼ lꢀ1ðvl=vTÞs is a linear
Taking in mind the points above, we performed detailed
experimental study of linear thermal expansion near both phase
transition in NH HSO as well as hysteretic phenomena around T2.
4 4
For the first time experimental studies of PCE were carried out
by Joule in the 19th century [9]. He performed the measurements at
room temperature and found that the response of the temperature
of the samples under stress depends on the type of material (wood,
metals. etc.) as well as the magnitude of the tensile/compressive
load and is rather small, mainly due to the small values of the co-
2. Experimental
Rather large single crystals of NH
evaporation at 45 from aqueous solution containing equimolar
quantities of (NH SO and H SO
4 4
HSO were grown by slow
efficient
a of the materials studied.
It is known, however, that thermal expansion can significantly
increase in the region of phase transition of various physical origin.
The reason is that linear/volume strain either is itself an order
parameter (ferroelastic and martensitic transformations) or is
strongly related to the principal order parameter of a different
nature (magnetization, polarization). In both cases, a pronounced
anomalous behavior of the coefficient
of the transition point.
In recent years, much attention has been paid to the study of PCE
in shape memory alloys undergoing the martensitic trans-
formations accompanied by large entropy change [10e13]. Rather
low tensile and compressive stresses created in the samples in the
form of wire or ribbon led to significant values of DTAD and DSCE in
some materials [14,15].
However, in the case of alloys, PCE was measured only in one
direction. On the other hand, as can be seen from Eq. (1), it is
obvious that in anisotropic materials, the magnitude and sign of
4
)
2
4
2
4
.
XRD examination of the quality of the sample at room temper-
ature was performed with a Bruker D8 ADVANCE powder diffrac-
tometer (Cu-Ka radiation), TTK 450 Anton Paar heat attachment
and linear VANTEC detector. It revealed, firstly, a monoclinic sym-
metry (sp. gr. P2 =c, Z ¼ 8), consistent with suggested in
1
a is observed in the vicinity
Refs. [23,25,26] and, secondly, the absence of any additional phases.
Fig. 1 shows the results of Rietveld refinement (Rwp¼6.04,
2
R
p
¼ 4.23,
c
¼ 2.06).
A good agreement was found between the unit cell parameters
in the sample under study (a ¼ 14.3954 (7)Å, b ¼ 4.5938 (2)Å,
c ¼ 14.8343 (8)Å, ¼ 120.883 (2) grad) and those determined
earlier in Ref. [25,26].
Further experimental procedure was organized taking in mind
the peculiarities of the phase transitions in NH HSO , Due to a large
b
4
4
volume change in the region of the first order phase transition
Pc4P1, detected when measuring on quasi-ceramic samples pre-
pared using the solution and melt technology [23], we assumed
that single-crystal samples may crack during experiments with
heat treatments around T2.
Therefore, experimental studies were carried out in several
stages. At the first stage, the behavior of linear thermal expansion
was studied on single-crystal specimen in the range from 175 K to
PCE can be different in accordance with the difference in the
a
coefficients along different directions. Recently, we have proved
this assumption studying PCE near ferroelastic phase transitions in
some orthorhombic single crystals [16,17]. It was found that
anisotropy of the crystal lattice allows one to realize conventional
(DTAD > 0, DSCE < 0) and inverse (DTAD < 0, DSCE > 0) PCE in the same
sample using uniaxial stresses applying along different crystallo-
graphic axes. We have also demonstrated that in some case the
values of the uniaxial CE can be comparable with BCE or even
exceed it.
PCE in some ferroelectrics (ceramics, films and single crystals)
was studied experimentally and in the scope of some theoretical
approaches only to a small extent [18e21]. Moreover, in these
materials the effect was also considered only for one direction in
the sample and never the attention was paid to the anisotropy of
PCE.
320 K including the vicinity of the second order phase transition
P2 =c4Pc. The NH HSO sample was cut in the form of rectangular
4
4
1
3
prism with the dimensions of 7.4 ꢁ 8.6 ꢁ 5.9 mm along crystal-
lographic axes a, b, c for the pseudo-orthorhombic cell. Measure-
ments were performed in a vacuum atmosphere (~10 mm Hg)
ꢀ2
Analysis performed recently by U.S. Department of Energy
showed that studies of thermoelastic effects (PCE and BCE) in solids
are the most promising in terms of the development of alternative
cooling technologies [22].
In the present paper, we analyzed the effect of anisotropy of
thermal expansion on the intensive and extensive piezocaloric ef-
4 4
ficiency of ferroelectric NH HSO using method developed by us
earlier [16,17]. Ammonium hydrogen sulphate was chosen as very
convenient model object due to its peculiar and interesting prop-
erties. Firstly, it undergoes the succession of two phase transitions
P2 =c (T ¼271 K)4 Pc (T ¼159 K)4 P1, of the second and first
1
1
2
order, respectively [23]. Secondly, these transformations also differ
greatly from each other by entropy (
D
S ¼1.2 J/mol,K,
D
S2 ¼ 6.7 J/
1
mol,K) and sensitivity to hydrostatic pressure (dT = dp¼þ90± 15 K/
1
GPa and dT =dp ¼ -123±15 K/GPa). Thirdly, strong effect of the
2
4 4
Fig. 1. Rietveld analysis patterns for X-ray powder diffraction of NH HSO at room
hydrostatic pressure on the entropy jump associated with the first
order phase transition at T2 was observed but information on the
temperature hysteresis was absent. Fourthly, far from the phase
temperature. Red dots are experimental data. The blue solid line corresponds to the
calculated intensities. The black line below the profiles stand for the difference be-
tween the observed and calculated intensities. (For interpretation of the references to
colour in this figure legend, the reader is referred to the Web version of this article.)
4 4
transition points, NH HSO is characterized by rather large

E.A. Mikhaleva et al. / Journal of Alloys and Compounds 839 (2020) 155085
3
using a quartz optic-mechanical dilatometer with a sensitivity of
Table 1
ꢀ6
Some parameters of the thermal expansion at the phase transition points T
1
and T
2
=
1
.2 ꢁ 10 cm. Temperature step of discrete heating was ꢂ0.5 K and
in NH
and
shift of the phase transition temperatures under uniaxial and hydrostatic pressure.
4
HSO
4
.
da
i
and db e jumps of the linear and volume expansion coefficients.
d
a
i
ꢃ2 K near and far from T , respectively.
1
a
i
d
V=V e jumps of parameters and volume of the unit cell. dT=d
i
s and (dT=dp) e
At the second stage, the same sample was examined using an a
homemade adiabatic calorimeter [27] in continuous cooling/heat-
ing mode through the phase transition Pc4P1 at a very low tem-
P2
1
=c4Pc
Pc4P1
Ref.
6
ꢀ1
ꢀ1
ꢀ
3
da
a
,10 ,K
þ(25.5±1.0)
þ(64.5±3.0)
-(8.0±0.5)
þ(82.0±4.5)
perature variation rate of about dT=dt ¼ ±10 K/min. It was found
that, indeed, single-crystal sample was cracked after cooling/
heating through the phase transition Pc4P1. Thus, we were unable
6
da ,10 ,K
b
6
ꢀ1
c
,10 ,K
da
6
ꢀ1
db,10 ,K
to measure the linear expansion of the NH
4
HSO
4
single-crystal
d
d
d
d
a=a, %
b=b, %
c=c, %
V=V, %
þ(0.69±0.03)
-(0.52±0.02)
-(1.27±0.06)
-(1.10±0.11)
around T2 using a quartz dilatometer.
Therefore, at the next stage, X-ray studies were performed on a
powder sample to get information on the temperature behavior of
the unit cell parameters. Measurements were carried out in the
temperature range from 155 K to 180 K with the step of about 1 K.
, K,GPa 1
b, K,GPa
c, K,GPa
ꢀ
ꢀ1
þ(33±5)
dT
1
dT
1
=d
=d
s
s
s
a
þ(79±10)
ꢀ1
dT =d
1
-(10±3)
ꢀ
1
ðdT
ðdT
1
=dpÞcalc, K,GPa
þ(10,2±18)
þ(90±15)
ꢀ
1
1
=dpÞ , K,GPa
exp
[23]
[23]
ꢀ
1
1
1
3
. Results and discussion
dT
dT
dT
2
=d
=d
=d
s
s
s
a
, K,GPa
b, K,GPa
, K,GPa
þ(45 ± 4)
-(50±5)
-(122±7)
-(12,7±16)
-(12,3±15)
ꢀ
ꢀ
2
2
c
First of all it is worth to discuss the hysteretic phenomena
ꢀ1
ꢀ1
ðdT
2
=dpÞcalc, K,GPa
observed in calorimetric experiments near T . The hysteresis of the
2
2
ðdT =dpÞexp, K,GPa
phase transition temperature was found of about
d
T2 ¼ 2.5 K. The
entropy jump S2 decreases with pressure increase and is equal to
d
zero at rather low pressure of the tricritical point ptcpz 0:18± 0:02
GPa [23]. The rapid approach of the phase transition under pressure
P
coefficients,
coefficient
da
¼
db, show that jumps in volume strain and
i
to the tricritical point accompanied by
d
T2/0 is an important
b
, at T and T , respectively, have different signs and this
2
1
property of NH HSO and can be considered as very useful for the
4
4
determines the difference of signs of baric coefficients for the phase
implementation of a reliable and stable BCE and PCE [3].
transitions in ammonium hydrogen sulphate (dT =dp¼-123 K/GPa;
2
The temperature dependencies of the linear thermal expansion
dT =dp ¼ 90 K/GPa) [23].
1
coefficients,
a , in the vicinity T and unit cell parameters, a , around
i
1
i
Sensitivity of the phase transition temperatures in NH
4
HSO
i, was determined in the scope of
and ClapeironeClausius,
S, relations using data on the jumps in en-
S, heat capacity [23], linear strain
a =a Þ and coeffi-
4
to
T2 are shown in Fig. 2 (a) and (b). X-ray data are also presented for
the pseudo-orthorhombic cell. It can be seen that far from the
uniaxial stress, dT =ds and dT =ds
1 2
i
the Ehrenfest, dT =d
s
¼
p
T,dai=dC ,
1
i
4 4
phase transition points, NH HSO is characterized by a positive
dT =d
tropy
s
¼
d
ðD
a =a Þ=
d
2
i
i
i
thermal dilatation in all crystallographic directions. The values of
a
i
d
dC
p
d D
ð
i
i
evaluated at 180 K from dependencies of a ðTÞ (
a
a
¼ þ ð7:5 ±0:8Þ,
i
cient of the linear thermals expansion
d
ðDa Þ. The results of
i
ꢀ
5
ꢀ1
ꢀ5 ꢀ1
ꢀ5 ꢀ1
K
1
0
K
;
a
¼ þð3:5 ±0:5Þ,10
K
;
a
c
¼ þð6:4 ±0:7Þ, 10
)
b
calculations are presented in (Table 1). It is evident that in accor-
dance with the strong anisotropy of the thermal dilatation there is a
large difference in the values and signs of the coefficients dT=d
Table 1 also demonstrates that the largest values of dT=d at T and
T2 are, firstly, related to different crystallographic axes, and sec-
ondly, they are the largest contributors to the dT =dp and dT =dp
agree well with coefficients determined in dilatometric experi-
ments (Fig. 2(a)).
si.
A highly anisotropic anomalous behavior of thermal expansion
s
i
1
was found at both T1 and T . The jumps at the phase transition
2
LAT
i
a =a Þ
i
LAT
i
points of the linear expansion coefficients, dai
lattice contribution), and linear strains,
¼
a
i
ꢀ
a
(
a
is a
ꢀ
1
2
d
ðD
a =a Þ ¼ ð
D
i
i
i
T > T2
values. The reliability of the data obtained is confirmed by a good
agreement of the calculated, ðdT=dpÞ and experimentally
ð a =a ÞT < T2, are presented in Table 1.
D
i
i
calc
Different signs of da and
d
ð a =a Þ values associated with
D
i
i
i
determined ðdT=dpÞ
baric coefficients (Table 1).
exp
different axes indicate that in accordance with Eq. 1, PCE can be
In order to determine the intensive and extensive PCE in
NH HSO , we used previously obtained results of the separation of
realized as conventional or inverse. Summation of the jumps of the
P
4
4
unit cell parameters,
dð
D
a =a Þ ¼
d
ð V =VÞ, and linear expansion
D
i
i
4 4
Fig. 2. Temperature dependencies of (a) thermal expansion coefficients ai near T1 and (b,c,d) cell parameters a, b and c for the pseudo-orthorhombic cell near T2 in NH HSO .

4
E.A. Mikhaleva et al. / Journal of Alloys and Compounds 839 (2020) 155085
the anomalous,
D
S ðTÞ and
D
S ðTÞ, and lattice, S , entropies at p ¼
constant entropy SðT;
s
Þ ¼ SðT þ
D
TAD
;s
i
¼ 0Þ. Fig. 4(a)-(d), 5(a)-(d)
1
2
LAT
i
0
[23]. It was mentioned above that at pz0.2 GPa the phase tran-
and 6(a)-(d) show the behavior of PCE associated with the main
crystallographic axes in the region of both phase transitions. In
sition at T2 exhibits a tricritical behavior with
dS2
¼
0. Both
structural units SO 24 and NH4 were defined as disordered and
ꢀ
þ
accordance with the sign of dT =d
s
and dT =ds (Table 1), PCE can
1
i
2
i
totally ordered in the initial P2 =c, and final, P1, phases, respec-
be conventional and inverse.
1
tively [26]. Since we did not find any triple points in the Tꢀ p phase
In the case of the phase transition at T , the maximum possible
value of the extensive PCE equal to the entropy of the phase tran-
1
diagram, the symmetries of all phases in NH
4
HSO
4
are preserved
under pressure. Due to the relationship between symmetry and the
degree of disordering, the latter is also retained and, as a result, the
sition
D
S ¼ 1.2 J/mol K has not been achieved even at
s
¼ 0.4 GPa.
1
i
Due to the most pronounced sensitivity of T to
s
(Table 1),
1
b
entropies
D
S1 and
DS2 remain unchanged, at least under the
4 4
NH HSO shows at all pressures the largest values of PCE under
pressure used in the present studies.
stress along the b axis.
The total entropy as a function of temperature, SðTÞ, at different
The values of the extensive PCE around T for all axes are rather
2
s
> 0 was determined by summation of S
and anomalous con-
close to the maximum value ð
D
SPCE
Þ
¼
D
S2 ¼ 6.7 J/mol,K and
i
LAT
max
tributions
D
S ðTÞ as well as
D
S ðTÞ at
s
¼ 0 shifted along the
can be realized at almost identical very low uniaxial pressures
1
2
i
temperature scale according to the values of dT = d
s
and dT = ds .
i
< 0:05 GPa. However, to achieve the maximum magnitude of the
1
i
2
s
AD
i
intensive PCE, ð
stresses are needed:
saturation of TAD under pressure is due to its strong dependence
on two circumstances: first, on the derivative dSLAT =dT and, second,
on the baric coefficient dT=d
Let us consider now the contribution of the lattice dilatation to
the piezocaloric efficiency of NH HSO . Due to the positive sign of
along all axes, PCELAT is always conventional. Fig. 3 (c), (d)
DT
Þ
maxz10 K, significantly greater mechanical
s zsbz0.3 GPa, s z0.1 GPa, The slower
a c
SðT;
siÞ ¼ SLAT ðTÞ þ
D
S ðT þ ðdT = d
s
iÞsi
Þ þ
D
S ðT þ ðdT = d
s
iÞ
s
iÞ
1
1
2
2
D
(2)
It should be noted that this procedure was carried out at two
different conditions: first, without taking into account, and second,
taking into account the thermal expansion of the crystal lattice. In
the latter case, the lattice entropy change under pressure was
s
.
4
4
ð Þ
a
i
LAT
determined using Maxwell relation ðvSLAT =v
s
iÞ ¼ ðvð a =a Þ=vTÞ .
D
T
i
i
s
i
show that the greatest decrease in SðT;
largest magnitude of ð . At p ¼ 0.1 GPa, the decrease in SðT;
is about 0.5% and 1% near T and T , respectively, and increases with
s
a
Þ is associated with the
a
a
Þ
s
i
Þ
ðꢀvðD
a =a Þ
ꢁ
LAT
PCE
LAT
i
i
1
2
D
S
ðT;
s
iÞ ¼ ꢀ V
m
d
s
z ꢀ V
m
,
a
LAT
ðTÞ,Dsi
:
i
vT
pressure increase. As a result, extensive and intensive PCE undergo
significant changes during both phase transitions.
s
i
(3)
At the transformation P2 =c4Pc, strong increase in both PCE
1
The results of both procedures are shown in Fig. 3 for two
external mechanical stresses, 0.05 and 0.1 GPa.
When lattice expansion was not taken into account, the exten-
sive PCE under stress along different axes was determined as a
was observed: at
ceeds the entropy of the phase transition more than twice and
also becomes very large (>5 K with a). One can also see that taking
s
¼ 0.4 GPa, along all axes. The value
D
SPCE ex-
DTAD
s
into account the lattice dilatation is accompanied by a change in
difference
ature. The temperature dependencies of the intensive PCE were
revealed analyzing plots of SðT; iÞ ¼ SLAT ðT; ¼ 0Þþ SðT; iÞ at
D
SPCEðT;
s
Þ ¼ SðT;
s
Þ ꢀ SðT;
s
¼ 0Þ at constant temper-
PCE along the c axis from the inverse to the conventional (Fig. 6 (e),
(f)).
i
i
i
s
s
D
s
i
Fig. 3. Temperature dependencies of total entropy of NH
4 4
HSO at uniaxial stresses 0.05 (a1,b1,c1) and 0.1 GPa (a2,b2,c2) near (a,b) T1 and (c,d) T2 without taking into account (a,c)
and taking into account (b,d) the thermal expansion of the crystal lattice.

E.A. Mikhaleva et al. / Journal of Alloys and Compounds 839 (2020) 155085
5
Fig. 4. Piezocaloric entropy
DSPCE and adiabatic temperature DTAD changes at different uniaxial stresses sa in temperature regions near T1 and T2 without taking into account
(
a,b,c,d) and taking into account (e,f,g,h) the thermal expansion of the crystal lattice.

6
E.A. Mikhaleva et al. / Journal of Alloys and Compounds 839 (2020) 155085
Fig. 5. Piezocaloric entropy
DSPCE and adiabatic temperature DTAD changes at different uniaxial stresses s in temperature regions near T1 and T2 without taking into account
b
(
a,b,c,d) and taking into account (e,f,g,h) the thermal expansion of the crystal lattice.

E.A. Mikhaleva et al. / Journal of Alloys and Compounds 839 (2020) 155085
7
Fig. 6. Piezocaloric entropy
DSPCE and adiabatic temperature DTAD changes at different uniaxial stresses sc in temperature regions near T1 and T2 without taking into account
(
a,b,c,d) and with taking into account (e,f,g,h) the thermal expansion of the crystal lattice.

8
E.A. Mikhaleva et al. / Journal of Alloys and Compounds 839 (2020) 155085
max
PCE
max
AD
Fig. 7. The dependencies of
DS
and
D
T
on uniaxial stresses along a-axis (a,b), b-axis (c,d) and c-axis (e,f) near T1 without (1) and with (2) taking into account the expansion of
the crystal lattice.
max
PCE
max
Fig. 8. The dependencies of
DS
and
DT
on uniaxial stresses along a-axis (a,b), b-axis (c,d) and c-axis (e,f) near T2 without (1) and with (2) taking into account the expansion of
AD
the crystal lattice.
Similar situation was observed at the phase transition Pc4 P1.
Due to conventional origin of PCE associated with the positive sign
increase in the extensive and intensive effects associated with the a
a
axis: the maximum values are equal to
D
S
¼ -8.8 J/mol,K and
PCE
a
AD
of both
a
a
and ð
a
a
ÞLAT , NH
4
HSO
4
shows the most pronounced
DT
¼ 13 K at
s
a
¼ 0.4 GPa (Fig. 4 (e), (g)). As to PCE along axes b

E.A. Mikhaleva et al. / Journal of Alloys and Compounds 839 (2020) 155085
9
Table 2
Piezocaloric characteristics at phase transitions in materials of different physical origin.
max
PCE
min
i
max
AD
min
i
Sample
D
S
, J/kg,K
s
, GPa
DT
, K
s
, GPa
Ref.
Cu68Zn16Al16
Ni48.9Ti51.1
Ni35Co15Mn35Ti15
Polycr.
Wire
Polycr.
Single cr.
Calculated
Calculated
Thin film
Single cr.
6e7
25
9.0
10
13
20
0.275
0.8
0.6
0.3
0.5
0.8
6
[28]
[29]
[12]
[30]
[20]
[31]
[18]
[17]
46
15
0.8
0.3
Ni50Fe19Ga27Co
4
PbTiO
PbTiO
3
3
BaTiO
NH
3
4.6
(
4
)
2
NbOF
5
c-axis
c-axis
110
ꢀ50
0.9
0.3
ꢀ16
ꢀ7
0.9
0.3
NH
4
HSO
4
(at T
2
)
Single cr.
This work
a-axis
b-axis
c-axis
ꢀ57
þ57
þ57
0.10
0.10
< 0:05
þ10.0
ꢀ10.0
ꢀ10.0
0.30
0.30
0.10
of two extensive effects associated with two temperature-close
phase transitions [17]. When the uniaxial pressure decreases to
the magnitude characteristic of PCE in NH
4
HSO
4
at T2,
s
¼ 0.1e0.3 GPa, extensive effects in both materials become
commensurate with each other. Large intense effect in a number of
other materials was also observed under rather high pressure
(Table 2).
Thus, due to the low pressure necessary for the realization of
max
PCE
max
, ammonium hydrogen sulphate can be considered
AD
DS
and
DT
as a rather efficient solid-state coolant. Moreover, strong anisotropy
of PCE allows the sample of NH HSO to be heated or cooled by
4
4
applying uniaxial pressure along different directions. Obviously this
feature can be used to design a hypothetical combined refrigeration
cycle built on alternate application of pressure along different
crystallographic axes. In the case of the phase transition at T2 in
0
0
Fig. 9. Hypothetical cooling cycle 1-2-3 -4-5-6 -1 built on the combination of the
piezocaloric effect associated with axes a and c. 1e3-4-5-6-1 cycle is the Carnot cycle
with the same changes of entropy.
4 4
NH HSO , the combination of PCE associated with axes a and c
looks the most promising.
Fig. 9 shows how a combined cycle can be organized. At the first
stage, applying uniaxial pressure along the a axis in adiabatic
process 1e2 leads to increase in temperature. During the process
and c, different signs of
lead to decrease in both inverse effects and appearance of con-
ventional contributions that increase with increasing pressure
a
< 0,
a
c
< 0 and ð
a
Þ
> 0, ð
a
c
Þ
> 0
b
b
LAT
LAT
2e3’ (
of
(3e4, S ¼ const) is accompanied by the decrease in temper-
ature. Further cooling (4e5, S ¼ const) is a result of applying
pressure along the c axis, . In the process 5e6’ (
¼ const), heat
transferred from the cooled reservoir to the refrigerant. Removal of
s
a
¼ const) heat transfers out from the refrigerant. Removal
more faster in comparison with the decrease of inverse
D
SPCE and
s
a
DTAD (Figs. 5 and 6).
It is interesting to consider the relation between the de-
s
c
s
c
max
PCE
max
AD
pendences of
DS
ðs
Þ and
DT
ð Þ for all axes at both phase
s
i
i
transitions without and with taking into account the expansion of
s
c
(6’ e 1, S ¼ const) causes the system to return to initial state.
the crystal lattice. At T , the behavior of both maximum effects is
It is obvious that at the same entropy change in individual and
1
close to the linear (Fig. 7). However, it is necessary to be cautious
about this situation, as we suggested that the uniaxial pressure
combined cycles, the efficiency of the latter cycle is much higher
due to a significant expansion of the working temperature range.
Moreover, in this case the filling factor of the Carnot cycle 1-2-3-4-
5-6-1 increases (Fig. 9).
used (
s
ꢂ 0:4 GPa) does not affect the magnitude of the coefficients
a
and
a
LAT
.
Fig. 8 clearly demonstrates that at T , the maximum values of
Considered hypothetical cycle is also more convenient in com-
parison with the cycle based on a combination of two CE of
different nature, ECE and PCE, recently analyzed [20]. One of the
main reasons is that ECE is always accompanied by irreversible
heating of the sample due to the release of Joule heat.
2
D
SPCE associated with each axis are realized at almost the same
max
AD
pressure. As to the values
DT
, they can be achieved at rather
different uniaxial pressure for different axes in accordance with a
large difference in baric coefficients dT=d
s
i. In Fig. 8, the de-
max
PCE
max
s
AD
i
pendencies
DS
ðs
Þ and
DT
ð
Þ for b and c axes with taking
i
into account the lattice contribution are shown only for the part of
inverse PCE. This is the reason why both maximum values decrease
with increasing pressure.
4. Conclusions
The data on PCE in NH
comparison with PCE in some other materials of the different
origin.
One can see that the absolute maximum values of extensive and
intensive effects are characteristic for different materials and can be
4
HSO
4
are summarized in Table 2 in
For the first time the effect of the anisotropy on caloric prop-
erties in ferroelectric material was studied and ammonium
hydrogen sulphate was chosen as model object due to large dif-
ference in origin, type and sensitivity to external pressure of two
structural transformations.
realized with different mechanical stress
s
. Very large value of
Dilatometric and X-ray measurements revealed a strong
anisotropy of thermal expansion in the region of both phase tran-
sitions which led to a significant difference in the signs and values
max
DS
in ferroelastic (NH
4
)
2
NbO
F
2 4
observed under 0.9 GPa is a sum
PCE

10
E.A. Mikhaleva et al. / Journal of Alloys and Compounds 839 (2020) 155085
[7] P. Lloveras, A. Aznar, M. Barrio, P. Negrier, C. Popescu, A. Planes, L. Ma
n~ osa,
of linear baric coefficients and as a result to anisotropy in piezo-
caloric properties. The greatest magnitudes of PCE at T and T are
related to different axes and provide the main contribution to the
barocaloric effect, considered as the sum of linear effects. The
pressure behavior of the intensive and extensive PCE at the P21=
c4Pc phase transition is close to the linear and as a result both of
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DS
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AD
i
[
[
Taking into account the thermal expansion of the crystal lattice
led to the greatest changes in PCE at T . The extensive effect equal
to the entropy of the phase transition was achieved under rather
1
low uniaxial pressure of 0.25e0.30 GPa. At T , the
D
SPCE and
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DTAD
2
s
a
¼ 0.4 GPa. Due to inverse PCE along b
and c axes, these values were decreased.
Comparison of PCE in materials of different physical origin
shows that NH HSO can be considered as competitive solid
4 4
refrigerant. Due to strong anisotropy of PCE, thermodynamic effi-
ciency of the cooling cycle can be improved by alternate using
uniaxial pressure along axes a and c.
[
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Declaration of competing interest
[
[
[
[
[
[
[
17] M. Gorev, E. Bogdanov, I. Flerov, N. Laptash, Thermal expansion, phase dia-
grams and barocaloric effects in (NH4)2NbOF5, J. Phys. Condens. Matter 22
XX The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
The authors declare the following financial interests/personal
relationships which may be considered as potential competing
interests:
(
2010) 185901, doi:0953-8984/22/i¼18/a¼185901.
18] Y. Liu, I.C. Infante, X. Lou, L. Bellaiche, J.F. Scott, B. Dkhil, Giant room-
temperature elastocaloric effect in ferroelectric ultrathin films, Adv. Mater.
26 (2014) 6132e6137, https://doi.org/10.1002/adma.201401935.
19] S. Patel, A. Chauhan, R. Vaish, Elastocaloric and piezocaloric effects in lead
zirconate titanate ceramics, Energy Technol.
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caloric properties of ferroelectrics, J. Appl. Phys. 121 (2017) 144102, https://
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21] G. Bai, Q. Xie, J. Xu, C. Gao, Large negative piezocaloric effect: uniaxial stress
effect, Solid State Commun. 291 (2019) 11e14, https://doi.org/10.1016/
j.ssc.2019.01.002.
22] Energy Savings Potential and RD&D Opportunities for Non-vapor-
compression HVAC Technologies, Report of the U.S. Dpt. Of Energy, March
2014.
23] E. Mikhaleva, I. Flerov, A. Kartashev, M. Gorev, E. Bogdanov, V. Bondarev,
Thermal, dielectric and barocaloric properties of NH4HSO4 crystallized from
an aqueous solution and the melt, Solid State Sci. 67 (2017) 1e7, https://
doi.org/10.1016/j.solidstatesciences.2017.03.004.
CRediT authorship contribution statement
Ekaterina A. Mikhaleva: Formal analysis, Writing - original
draft. Mikhail V. Gorev: Software. Maxim S. Molokeev: Investiga-
tion. Andrey V. Kartashev: Formal analysis, Investigation. Igor N.
Flerov: Formal analysis, Conceptualization, Methodology.
Acknowledgements
[
24] P. Lloveras, E. Stern-Taulats, M. Barrio, J.-L. Tamarit, S. Crossley, W. Li,
The reported study was supported by the Russian Science
Foundation (project no. 19-72-00023). X-ray and dilatometric data
were obtained using the equipment of Krasnoyarsk Regional Center
of Research Equipment of Federal Research Center “Krasnoyarsk
Science Center SB RAS".
V. Pomjakushin, A. Planes, L. Ma n~ osa, N.D. Mathur, X. Moya, Giant barocaloric
effects at low pressure in ferrielectric ammonium sulphate, Nat. Commun. 6
(2015) 8801, https://doi.org/10.1038/ncomms9801.
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26] D. Swain, V.S. Bhadram, P. Chowdhury, C. Narayana, Raman and x-ray in-
vestigations of ferroelectric phase transition in NH4HSO4, J. Phys. Chem. A
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