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Cobalt based new quaternary Heusler alloys for
Spintronic and thermoelectric applications: an
Ab-initio study
D. Shobana Priyanka, J. B. Sudharsan, M. Srinivasan & P. Ramasamy
To cite this article: D. Shobana Priyanka, J. B. Sudharsan, M. Srinivasan & P. Ramasamy (2022):
Cobalt based new quaternary Heusler alloys for Spintronic and thermoelectric applications: an
Ab-initio study, Materials Technology, DOI: 10.1080/10667857.2021.2014030
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MATERIALS TECHNOLOGY
https://doi.org/10.1080/10667857.2021.2014030
Cobalt based new quaternary Heusler alloys for Spintronic and thermoelectric
applications: an Ab-initio study
D. Shobana Priyanka, J. B. Sudharsan, M. Srinivasan and P. Ramasamy
SSN Research Centre, SSN College of Engineering, Kalavakkam, Chennai, India
ABSTRACT
ARTICLE HISTORY
In this paper, we employed Density Functional Theory (DFT) to study structural and mechanical
stability, electric, magnetic and electronic properties of cubic Co-based new quaternary halfHeusler alloys CoZrCrZ (Z = Al, Ga, In) using WIEN2k. Volume optimisation suggests that these
alloys are stable in the Y1 structure and show ferromagnetic behavioTAur. Generalised
Gradient approximation calculations confirm the half-metallic nature of the reported alloys,
which show metallic nature, and semiconducting band gaps exist in spin-up and spin-down
channels, respectively. From the calculated cubic elastic constants, the reported Heusler alloys
shows ductile nature. The calculated spin-magnetic moments of CoZrCrZ (Z = Al, Ga, In) are
consistent with the Slater-Pauling rule. The very fine narrow band gap in the spin-down
channel enhances the thermoelectric properties. The reported ferromagnetic half-metals
with good thermoelectric parameters suggests that these alloys have possible applications in
spin-based electronics and green energy technology.
Received 25 August 2021
Accepted 28 November 2021
Introduction
The identification of perfect spin-polarised materials
[1,2] opens new possibilities in the fabrication of solid
state memory devices [3–7]. An electronic device can
use only the charge of the electrons. But the devices
that are made up of spin polarised materials exploit
charge, spin and its associated magnetic momentum.
Such devices are capable of storing and performing
faster processing of a very large amount of nonvolatile data. It is really very challenging to identify
a material with perfect spin polarisation. In other
words, a perfect spin-polarised material can be char­
acterised by half-metal (HM), i.e. metallic character in
one spin channel and semiconducting nature in the
other spin channel [8]. Actually, the magnitude of spin
polarisation is given by the ratio between the density
of states (DOS) of spin-up and spin-down channels
around the Fermi level (EF) [9],
P ¼ N " ðEF ÞnN # ðEF Þ=N " ðEF Þ þ N # ðEF Þ;
where N↑ (EF) and N↓ (EF) are spin-up and spin-down
states of electrons at the Fermi level. Since halfmetallic ferromagnets (HMFs) have 100% spinpolarised current, they can be used in magnetic ran­
dom access memories [10], spin injectors [11], mag­
netic tunnel junction [12], spin valves [13], giant
magnetoresistance, tunnelling magnetoresistance and
storage devices [14–16]. The HMF character is found
in different structural compounds such as perovskites,
CONTACT D. Shobana Priyanka
shobiriya15@gmail.com
© 2022 Informa UK Limited, trading as Taylor & Francis Group
KEYWORDS
Density functional theory;
spin polarised; ductile; halfmetal; thermoelectric
property
double perovskite chalcogenides, rutile structural
CrO2 and transition metal pnictides and also con­
firmed in Heusler Alloys (HA)s [17–19].
In particular, HAs are well known for more than
a century. German chemist Fredrich Heusler for the
first time discovered Cu2MnAl full Heusler alloys in
1903 [20]. Based on the structural composition, they
can be classified as full HAs with structural formula X2
YZ, half-HAs with structural formula XYZ and qua­
ternary HAs having structural formula XX’YZ, where X,
X’ and Y are transition metals and Z is a main group
(sp) element. Full HAs belong to the L21 crystal struc­
ture, come under the Fm-3 m space group having four
FCC interpenetrating structures. Half-HAs belong to
the C1b crystal structure in the F-43 m space group
having three FCC interpenetrating structures [21]. The
new structure quaternary HAs come under the F-43 m
space group having an Y-type crystal structure [22].
HAs have been investigated by many researchers
both experimentally and theoretically for their spin­
tronic properties. First, experimental realisation of
HM in the Heusler compound NiMnSb was made by
Groot et al. [23]. Following that, S. Ouardi et al. [24]
experimentally demonstrated very excellent spintronic
properties in the material Mn2CoAl. Cobalt-based
Heuslar alloy CoFeVSi is synthesised using the epitaxy
technique [25]; using the arc-melting technique,
CoFeTiSn and CoFeVGa are fabricated [26]. All the
above Cobalt-based Heusler alloys are identified as
potential candidates for spintronic applications.
SSN Research Centre, SSN College of Engineering, Kalavakkam 603110, India
2
D. S. PRIYANKA ET AL.
Apart from spintronic applications, the firstprinciples studies explored cobalt-based Heusler alloys
for thermoelectric applications. Thermoelectricity is
a green technology to generate electricity from heat
energy and vice versa without any harmful effects. It is
useful to recycle waste heat energy from various indus­
tries to electric energy so that we can reduce the major
problem (global warming) as much as possible. HAs are
more reliable in thermoelectrics due to being environ­
mentally friendly, easily synthesised, stable structure
and robustness [27–31]. Y. El Krimi et al. investigated
full Heusler Fe2MnSi for spintronic and thermoelectric
applications by using GGA and AMF version of the
GGA+U method [32]. By using different exchangecorrelation functionals, S. Shastri et al. have performed
thermoelectric calculations of Fe2VAl and Fe2TiSn [33].
Recently, M. K. Choudhary et al. determined TiNiSnand TiCoSb-based quaternary half-HAs in the year
2020 [34]. Sonu Sharma and Pradeep Kumar have pre­
sented thermoelectric properties of YNiBi half-HA
using LDA and GGA functionals with and without
spin-orbit coupling [35]. Various researchers have
examined the quaternary HAs such as FeMnTaAl
[36], CoZrMnX (X = Al, Ga, Ge, In) [37], CoFeCrZ
(Z = Si, As, Sb) [38], PdZrTiAl [39], FeRhCrZ (Z = Si,
Ge) [40], CoVRhGe [41], CoXMnAs (X = Ru, Rh) [42],
CoCrScZ (Z = Al, Si, Ge, Ga) [43] and CoScCrZ (Z = Al,
Ga, Ge, In) [44]. In this work, we have reported struc­
tural and mechanical stabilities and electric, magnetic
and thermoelectric properties of new cubic Co-based
quaternary HAs CoZrCrZ (Z = Al, Ga, In).
Methodology
Using WIEN2k package [45–47], we employed density
functional theory to perform the calculations.
WIEN2k code is written in the FORTRAN platform,
which performs quantum mechanical calculations on
periodic solids. The importance of DFT is that it
reduces the many body electron problem to the selfconsistent single-electron problem through the KohnSham equation. WIEN2k strongly uses the full poten­
tial linearised augmented plane wave (FPLA-PW)
[48,49] basis set to solve the Kohn-Sham equation.
The unit cell of CoZrCrZ (Z = Al,Ga, In) is splitted
up into muffin tin spheres and interstitial space. The
radii of muffin tin (RMT) spheres, i.e. the radii of Co,
Zr, Cr, Al, Ga and In atoms, were set as 2.5, 2.4, 2.4,
2.2, 2.3 and 2.5, respectively. The cut-off plane wave
used is KmaxRMT = 7.0. Generalised gradient approx­
imation (GGA) [50–52] is used to investigate band
structure calculations more accurately because GGA
improved local density approximation (LDA) by
including the first derivative of electron density [53].
In fact, GGA splits exchange and correlation functions
separately. To exclude the spin-orbit coupling interac­
tion, the core and valence state electrons are separately
treated and at the same time, potential and charge
density are considered without any shape approxima­
tion. 10−4 eV is used to converge the self-consistent
field. The energy of −6.0 Ry is fixed to separate core
and valence electrons. The mesh of 10 × 10 × 10
k points is used to sample the brillouin zone by follow­
ing the Monkhorst-pack scheme [54]. The elasto-cubic
method is employed to find out elastic properties. The
transport properties have been allayed with the help of
Boltzmann approximation implemented in BoltzTrap,
which is interfaced with WIEN2k package by using
a 20 × 20 × 20 dense mesh. It is also useful to calculate
the thermal power and figure of merit in different
temperature ranges.
Results and discussion
Structural stability
A very meticulous crystal structure study is required to
determine or predict the properties of HAs. The elec­
tronic structure of the crystal purely depends on the
individual atomic positions and it verily determines
physical properties of HAs. A minute disorder in any
atomic position can affect the structural stability. So,
in order to reduce disorderings, we investigated all
possible crystal structures to obtain a stable structure
[38]. In general, the quaternary HAs are adopted in
LiMgPdSn-type crystal structure [55]. The three pos­
sible atomic arrangements in the quaternary HAs,
XX’YZ are of Y1type: X (0, 0, 0), X’ (0.25, 0.25, 0.25),
Y (0.5, 0.5, 0.5) and Z (0.75, 0.75, 0.75); Y2 type: X(0,
0, 0), X’ (0.5, 0.5, 0.5), Y (0.25, 0.25, 0.25) and Z (0.75,
0.75, 0.75) and Y3 type: X (0.5, 0.5, 0.5), X’ (0, 0, 0),
Y (0.25, 0.25, 0.25) and Z (0.75, 0.75, 0.75). From
Figure 1, we can see that all three reported Co-based
cubic quaternary HAs CoZrCrZ (Z = Al, Ga, In) have
minimum energy in the Y1-type structure. Thus,
CoZrCrZ HAs are stable under the Y1-type structure
in the ferromagnetic (FM) phase and belong to the
F-43 m space group. For Y1 structure cubic CoZrCrZ
HAs, we calculated equilibrium energy and lattice
parametres (see Table 1) using volume optimisation
in which calculated energies are used in the
Murnaghan equation of states [56]. The cubic struc­
ture of CoZrCrAl is drawn with the help of VESTA
software as shown in Figure 2 and the structure is
similar for other two alloys.
Mechanical stability
The material’s response to the external stress can be
determined by elastic constants. The relation between
strain (εi) and applied stress (σi) in terms of second-
MATERIALS TECHNOLOGY
3
Figure 1. Optimised curves of CoZrCrAl, CoZrCrGa and CoZrCrIn in the Y1 structure.
order elastic constants Cij is given by the equation σi
= Cijεi [57]. C11, C12 and C44 are the fundamental
elastic constants for a cubic structure [58–60]. For
a cubic system, the conditions for mechanical stability
[61,62] in elastic constant terms are given below
C11
C12 > 0;
C11 > 0;
C11 þ 2C12 > 0 and
C12 < tex ¼00
00
> < =b11 : < >
The reported cubic quaternary HAs CoZrCrZ are stable
by satisfying the above conditions. We have calculated
the elastic moduli such as bulk modulus (B), shear mod­
ulus (G) and Young’s modulus (Y), which are given in
Table 2. The bulk modulus (B) measures the resistance to
change in the volume to the external applied stress.
Young’s modulus (Y) describes the stiffness of the mate­
rial and shear modulus (G) measures the solid deforma­
tion when it experiences the parallel force, whilst its
opposite face experiences opposing force. The bulk and
shear moduli can be written as [63,64]
B¼
G¼
C11 þ 2C12
;
3
C11 þ C12 þ C44
:
5
The Young's modulus in terms of B and G is
Y¼
9GB
:
3B þ G
A material ductility and brittleness relationship can be
indicated by the Cauchy pressure CP [65] and Pugh’s
ratio (B/G ratio). CP is positive for ductile materials
and it is negative for those that have brittle nature.
A material can be ductile if B/G > 1.75; on the other
hand, for brittle nature, B/G < 1.75 [66]. Our reported
HA CoZrCrZ is ductile in nature because the Cauchy
Pressure is positive and B/G < 1.75. The values are
shown in Table 2. The information of covalent and
ionic nature of the materials is given by Poisson’s ratio
(ν). The value of ‘ν’ is of the order of 0.1 for covalent
materials, whereas in the case of ionic materials, it is
0.25 [61]. The value of ‘ν’ > 0.25 (~0.28) for all the
three alloys, which indicates that CoZrCrZ exhibits
ionic characteristics. The isotropic and anisotropic
nature of the materials is determined by means of
the Zener anisotropic factor (A). In general, crystals
have anisotropic character, i.e they exhibit directional
properties. For isotropic material, A should be unity,
whereas in the case of anisotropic materials, A gets
deviated from the value of 1 [67]. The elastic wave in
different directions will travel with different velocities
in anisotropic materials so that the physical phenom­
ena such as refractive index, sound velocity and other
things may change according to orientation in crystals.
From Table 2, we can see that all the three alloys have
A > 1, which suggests that these alloys are anisotropic.
4
D. S. PRIYANKA ET AL.
Table 1. Equilibrium energy and lattice constant of CoZrCrZ (Z = Al, Ga, In).
Alloys
CoZrCrAl
CoZrCrGa
CoZrCrIn
Structure
Energy (Ry)
FM
−12572.86
−12572.7713
−12572.7716
−15975.428
−15975.3567
−15975.3564
−23853.7366
−23853.6457
−23853.6455
Y1
Y2
Y3
Y1
Y2
Y3
Y1
Y2
Y3
NM
−12572.823
−12572.7426
−12572.7416
−15975.3843
−15975.3213
−15975.3215
−23853.6768
−23853.6016
−23853.6015
CoZrCrIn has a high value of A (4.9), which indicates
that it is more anisotropic amongst three. The hard­
ness of the materials is very important in the case of
practical applications and it is deliberated by Vickers
hardness Hv [68]. The value of the Vickers hardness
indicates that CoZrCrGa is harder than CoZrCrAl and
CoZrCrIn,
CP = C12 – C44,
a0 (Å)
FM
6.2586
6.2651
6.2659
6.2348
6.2558
6.2489
6.4388
6.4815
6.4804
Volume
FM
413.58
414.87
415.05
408.89
413.04
411.67
450.35
459.38
459.14
Eformation ¼ECoZrCrZ
Bulk modulus (GPa)
FM
131.99
126.58
123.71
139.31
135.84
130.67
136.87
106.52
107.91
ðECo þEZr þECr þEZ Þ;
A¼
2C44
;
C11 C12
where ECoZrCrZ is the total ground state energy of
CoZrCrZ HAs per formula unit and ECo, EZr, ECr and
EZ are the ground state energy of individual atoms Co,
Zr, Cr and Z (Z = Al, Ga, In) in the alloys CoZrCrZ. In
Table 2, we report the formation energy of the
CoZrCrZ HAs. The negative sign indicates their ther­
mal stability and it can experimentally be synthesised.
The calculated values of Debye and melting tempera­
tures are listed in Table 3.
ν¼
3B 2G
;
2ð3B þ GÞ
Electronic calculation
"� � #0:585
G 2
Hv ¼ 2
G
B
3:
The Debye temperature measures the vibrational
response of the material. Thermophysical properties,
such as vibrational entropy, thermal expansion and
specific heat [63,69], are determined from Debye tem­
perature as follows:
ThetaD ¼
h 3nNA ρ 1=3
½
� Vm ;
kB 4πM
where his the Planck constant, kB is the Boltzmann
constant, n is the number of electrons in the unit cell, ρ
is the density and M is the molar mass of the alloys.
The value of Debye temperature θD is directly propor­
tional to the average sound velocity (vm), which is
obtained from the measured values of transverse (vt)
and longitudinal sound velocity (vl). The melting tem­
perature in terms of elastic constant C11 [70] has been
calculated, which is given by Tm ¼ ½553K þ
ðC11 þ 2C12 ÞC11 � � 300K;
3 �
� 1=3
C11 þ2C12
9GB
Vm ¼
; vt ¼ 3BþG
;
5
v1 ¼ C112C44C12 :
The formation energy determines the thermodyna­
mical stability and used to previse whether the mate­
rial can be synthesised experimentally. The formation
energy is given by [37]
The band gap of the material determines the thermo­
electric properties. To study the electronic structure of
the reported HAs, we precisely calculated the band gap
with spin polarisation using GGA-PBE approximation.
In Figure 3, the band structure for spin-up polarisation
shows the metallic nature, i.e. the valence and conduction
band crosses the Fermi level, whereas in the spin-down
band structure, the Fermi level lies between the two
bands, which indicates the semi-conducting nature of
the material. The minima of the valence band and max­
ima of the conduction band lie at the L symmetry point
in all reported three HAs. Thus, these alloys exhibit direct
band gaps of 0.93 eV, 0.9 eV and 0.85 eV for CoZrCrAl,
CoZrCrGa and CoZrCrIn, respectively.
Furthermore, in Figure 4, we have shown the total
density of states (TDOS) and partial or atom projected
density of states (PDOS) as a function of energy from
which we can understand the structure of the bands and
magnetic properties. From the partial density of states of
Co, Zr, Cr and Z atoms in both spin-up and spin-down
states, we predict the individual contribution of the
atoms in order to create band gaps in the alloys. The
density-of-state plot and band structure resemble each
other. The presence of the band gap in CoZrCrZ is
mainly due to the strong d-d hybridisation of Co, Zr
and Cr of group B atoms, whereas the p-block Z (Al, Ga,
In) atoms have negligible contribution to the band gap.
The difference between the Fermi level and valence band
minima (VBM) determines the half-metallic band gap.
The half-metallic gap (HMG) of CoZrCrAl, CoZrCrGa
and CoZrCrIn is 0.85 eV, 0.72 eV and 0.55 eV,
MATERIALS TECHNOLOGY
5
Figure 2. Structure of CoZrCrAl by using VESTA package.
Table 2. Calculated elastic constants and mechanical para­
meters of CoZrCrZ (Z = Al, Ga, In).
Parameter
Elastic constants (in GPa)
CoZrCrAl
C11
C12
C44
22.6
Bulk modulus (B in GPa)
Young’s modulus (Y in GPa)
Shear modulus (G in GPa)
Pugh’s ratio (B/G)
Poisson’s ratio ( )
Anisotropy factor (A)
Cauchy pressure (Cp)
HV
Formation energy (Eformation in Ry)
CoZrCrGa
148.1
109.8
45.8
128.5
156.4
60.74
2.02
0.287
2.4
64.1
6.7
−1.256
CoZrCrIn
159.8
112.9
60.2
121.8
170.4
66.59
1.93
0.279
2.6
52.8
7.8
−1.222
137.6
113.9
58.3
158.9
61.97
1.97
0.283
4.9
55.7
7.1
−1.075
Table 3. Calculated debye temperature θD and melting tem­
perature Tm of CoZrCrZ (Al, Ga, In).
Alloys
ρ (g/cm3) vt (m/s) vl (m/s) vm (m/s) θD (K) Tm ± 300 K
CoZrCrAl
6.2073
3128
5727
3501
420
1428
CoZrCrGa 7.4499
2990
5402
3343
403
1497
CoZrCrIn
7.8859
2803
5092
3135
365
1366
respectively. As we see in Table 4, the band gap energy
(ECBM – EVBM) decreases from 0.93 to 0.85 eV when we
go down in the periodic table from Al to In and also halfmetallic gap (EF – EVBM) decreases from 0.85 eV to
0.55 eV. Because of the confinement of the charge car­
riers, the band gap decreases with the increase of the
atomic size.
Magnetic property
In this section, using spin magnetic moments, we
analyse the magnetic nature of the alloys. In Table 5,
we show the total magnetic moment of CoZrCrZ and
magnetic moment of individual atoms. From TDOS in
Figure 4, we can understand that all the alloys exhibit
asymmetry spin-up and spin-down states, which
means that the presented alloys are magnetic in nature
(FM). Since the Co atom and Cr atom show perfect
asymmetry (see Figure 4), they play major role in the
total magnetic moments. In all the three studied alloys,
the Co atom has the highest contribution to the
increase of the total magnetic moments. Zr and main
group atoms (Z = Al, Ga, In) have a negligible number
of magnetic moments in reported alloys. CoZrCrAl
Heusler alloy has an integer spin magnetic moment of
4µB; moreover, CoZrCrGa and CoZrCrIn have nearly
integer spin magnetic moments of 3.99µB and 3.98µB,
respectively. Half-metallic nature of the alloys is con­
firmed by the integer spin magnetic moments. Thus,
these materials have potential to be used in spinpolarised devices.
The magnetic moment of alloys is given by the SlaterPauling rule (SPR) [71] as MT = NV – 18, where MT is the
total magnetic moment of the alloys and NV is the total
number of valence electrons in the alloys. Magnetic
moments and outermost electrons in the atoms of the
alloys are related by SPR. Since there are 22 valence
electrons in CoZrCrZ (Z = Al, Ga, In), the total magnetic
moment (MT) using the SPR rule is 4µB. The calculated
total magnetic moments well agreed with the SPR rule.
Thermoelectric calculation
The mechanism of thermoelectric technology is based
on Seebeck and Peltier effects. The TE materials are
used in thermoelectric power generators, coolers and
refrigerators and their efficiency can be measured by
a dimensionless quantity called the figure of merit (zT),
2
given by zT = κSl þκσ e (where S is the Seebeck coefficient, σ
is the electrical conductivity, κl is the lattice thermal
conductivity and κe is the electrical part of thermal
conductivity). It is very clear from the above explana­
tion that the efficiency of a thermoelectric material can
be increased when the values of ‘S’ and ‘σ’ are simulta­
neously high and thermal conductivity ‘κ’ is low.
However, maintaining the values of ‘S’ and ‘σ’ simulta­
neously high is really challenging to have very good ZT.
It is because the effective mass (m*) and the carrier
concentration (n) are directly and inversely propor­
tional to ‘S’, respectively, and vice versa for ‘σ.’ These
contradictory requirements hampering the progress
towards higher ZT for many years pose great
6
D. S. PRIYANKA ET AL.
Figure 3. Band structure of (a) CoZrCrAl, (b) CoZrCrGa and (c) CoZrCrIn in the majority spin channel (↑) and minority spin channel (↓).
challenges to material scientist and researchers to engi­
neer efficient thermoelectric devices for real-time appli­
cations. The resulting average Seebeck coefficient,
electrical conductivity and electronic contribution of
thermal conductivity from both the channels are
weighted by using the following formulae [72–74]:
� " "
�
S σ þ S# σ #
S¼
;
σ" þ σ#
σ ¼ σ" þ σ#;
κe ¼ κ"e þ κ#e ;
where S↑, S↓, σ↑, σ↓, κe↑ and κe↓ are the Seebeck coeffi­
cient (S), electrical conductivity (σ) and electronic part
of thermal conductivity (κe) in spin-up ↑ and spindown ↓ orientations.
In this section, the transport properties such as elec­
trical conductivity (σ/τ), electronic part of thermal con­
ductivity (κe/τ), Seebeck coefficient (S), thermal power
factor (PF) and figure of merit (ZT) have been calculated
using constant relaxation time (τ) approximation.
Generally, metals have the decreasing nature of electrical
conductivity with the increase of temperature where the
state is reverse in semiconducting material because in
metals, there is no gap, so the carriers freely move. If we
apply heat energy, the electrons will gain more energy
and vibrate more, causing an increase in collision of
electrons, and finally slow down the electron flow, but
in the case of semiconductors, the electrons require
external energy to overcome the barrier potential, so
the electrons flow freely with the increase of temperature.
In our study, with respect to time, the value of σ/τ
increases for all the three alloys CoZrCrZ (Z = Al, Ga,
In) and illustrated in Figure 5a. The minimum and
maximum values of σ/τ from total electrical conductivity
MATERIALS TECHNOLOGY
7
Figure 4. Total DOS and partial DOS of (a) CoZrCrAl, (b) CoZrCrGa and (c) CoZrCrIn.
Table 4. Calculated energy values of VBM, CBM, band gap,
half-metallic gap and nature of the band gap.
Alloys
CoZrCrAl
CoZrCrGa
CoZrCrIn
EVBM (eV)
−0.85
−0.72
−0.55
ECBM (eV)
0.08
0.18
0.3
Eg (eV)
0.93
0.9
0.85
EHMG (eV)
0.85
0.72
0.55
Nature
Direct
Direct
Direct
Table 5. Total and atom resolved magnetic moments (in µB) of
CoZrCrZ.
Spin magnetic moments (in µB)
Interstitial
In Co
In Zr
In Cr
In Z (Z = Al, Ga, In)
Total spin magnetic moment
CoZrCrAl
0.13514
0.92064
−0.07789
3.06005
−0.02788
4.0
CoZrCrGa
0.13689
0.89143
−0.08956
3.08908
−0.03287
3.99
CoZrCrIn
0.11008
0.84872
−0.14167
3.19558
−0.03148
3.98
are 0.36 × 1020 (Ωms)−1 and 1.34 × 1020 (Ωms)−1 for
CoZrCrAl, 0.95 × 1020 (Ωms)−1 and 1.28 × 1020 (Ωms)−1
for CoZrCrGa, 0.88 × 1020 (Ωms)−1 and 1.38 × 1020
(Ωms)−1 for CoZrCrIn. The electronic and the lattice
part of thermal conductivities contribute to the total
thermal conductivity (κ). Both have their usual meaning
by means of temperature. In this report, we have calcu­
lated electronic part of thermal conductivity only, which
shows an increasing trend with temperature for all the
three studied alloys CoZrCrZ as shown in Figure 5b. The
value of κe/τ
increases from 0.08 × 1015 W/mKs at 50 K to 2.5
× 1015 W/mKs at 800 K in CoZrCrAl, in the case of
CoZrCrGa, the value increases from 0.09 × 1015 W/
mKs at 50 K to 2.4 × 1015 W/mKs at 800 K and the
case is similar in CoZrCrIn, which varies from 0.1
× 1015 W/mKs at 50 K to 3 × 1015 W/mKs at
800 K.
The Seebeck coefficient (S) describes the ability of
the TE material to produce thermo emf in the given
temperature gradient. The minimum and maximum
values of S are 27.7 (µV/K) at 50 K and 109.5 (µV/K)
at 750 K for CoZrCrAl, 45.8 (µV/K) at 50 K and 96.9
(µV/K) at 800 K for CoZrCrGa and −4.85 (µV/K) at
50 K and 73.57 at 550 K for CoZrCrIn. The positive
values of S indicate the p-type nature of the reported
alloys. The elucidated S values of studied alloys have
better performance compared to CoScCrZ (Z = Al,
Ga, Ge, In) [44], CoZrMnX (X = Al, Ga, Ge, In) [37]
and CoFeCrZ (Z = Si, As, Sb) [38]. The acceptability
of the material for thermoelectric application is
determined by the term power factor (PF), which is
given by PF = S2σ. The value of PF increases from 2.8
× 1010 W/mK2s at 50 K to 1.6 × 1012 W/mK2s at
800 K in CoZrCrAl. The trend is similar in
CoZrCrGa where the value increases from1.98 ×
1011 W/mK2s at 50 K to 1.2 × 1012 W/mK2s at
8
D. S. PRIYANKA ET AL.
Figure 5. Schematic representation of (a) electrical conductivity, (b) electronic thermal conductivity, (c) Seebeck coefficient, (d)
power factor and (e) figure of merit (ZT) of CoZrCrZ (Z = Al, GA, In).
800 K. But in the case of CoZrCrIn, the value
increases from 2.1 × 109 W/mK2s at 50 K to 6.9 ×
1011 W/mK2s at 600 K; above 600 K, the value
decreases as shown in Figure 5d. The efficiency of
the TE materials is directly proportional to the
dimensionless figure of merit (ZT). The variation of
the figure of merit vs temperature is shown in
Figure 5e. We can understand from Figure 5c-e that
the thermal power factor and figure of merit greatly
depend upon the Seebeck coefficient. The maximum
obtained figures of merit in CoZrCrAl and
CoZrCrGa are 0.54 and 0.42 at 700 K; above this
temperature, the value of ZT goes down as shown
in the ZT plot. Similarly, the ZT value goes down
above 500 K in the case of CoZrCrIn. The maximum
value of ZT obtained is 0.23 at 500 K. Some of the
quaternary HAs with calculated ZT at respective
temperature are compared with our study and listed
in Table 6. From Table 6, we can see that LaCoCrAl
obtained high ZT of 0.94 at 600 K. So far, this is the
highest ZT obtained in quaternary HAs. But the fact
is that lanthanum can easily be oxidised when
exposed to air and is easily soluble in water.
Conclusion
We employed first-principles calculations to analyse
the structural, mechanical, electronic, magnetic and
thermoelectric properties of cubic Co-based quaternary
half-HAs CoZrCrZ (Z = Al, Ga, In). The energy of the
reported alloys has been optimised to find the equili­
brium lattice constants and the volume optimised
curves show that CoZrCrZ is stable in the Y1-type
structure with ferromagnetic nature. The values of
MATERIALS TECHNOLOGY
Table 6. Reported values of the Seebeck coefficient (S) and
figure of merit (ZT) with the corresponding temperature of
recent quaternary HAs.
Material
CoZrCrAl
CoZrCrGa
CoZrCrIn
CoZrMnIn [37]
CoFeTiAl [75]
LaCoCrAl [76]
CoZrMnGe [38]
CoRhMnAs [42]
T (K)
700
700
500
900
900
600
600
800
S (µV/K)
109
96
73
~50
2151
−60.8
−106
53.4
ZT
0.54
0.42
0.23
0.1
0.75
0.94
0.1
0.5
elastic constants and their derivatives reveal the ductile
nature of the reported alloys. Half-metallic nature of
studied HAs is calculated from density-of-states and
band structure calculations using GGA-PBE approxi­
mation. As we go down in the periodic table from Al to
In, the band gap of CoZrCrZ decreases from 0.93 eV to
0.85 eV in the spin-down state with a simultaneous
decrease of the half-metallic gap. Thus, 100% spin
polarisation occurs in the minority spin channel. The
calculated magnetic moments indicate that the Cr atom
plays a major role in the observed ferromagnetic char­
acter in CoZrCrZ. The maximum obtained figures of
merit are 0.54 at 700 K, 0.42 at 700 K and 0.23 at 500 K
for CoZrCrAl, CoZrCrGa and CoZrCrIn, respectively.
Besides, these results suggest that the studied HAs are
potential candidates for spintronic and thermoelectric
applications and also promote our interest towards
their experimental realisation.
Acknowledgments
The authors gratefully acknowledge the support of SSN insti­
tution for providing financial assistance to carry out this work.
Disclosure statement
No potential conflict of interest was reported by the author(s).
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