Ab initio study of structural, electronic, and thermal properties of Ir₁₋xRhx alloys
The structural, electronic, mechanical and thermal properties of Ir₁₋xRhx alloys was studied systematically using ab initio density functional theory at different concentration (x = 0.00, 0.25, 0.50, 0.75, 1.00). The Special Quasirandom Structure method was used to make the alloys with FCC structure...
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Інститут фізики конденсованих систем НАН України
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irk-123456789-1534472019-06-15T01:29:48Z Ab initio study of structural, electronic, and thermal properties of Ir₁₋xRhx alloys Ahmed, Sh. Zafar, M. Shakil, M. Choudhary, M.A. The structural, electronic, mechanical and thermal properties of Ir₁₋xRhx alloys was studied systematically using ab initio density functional theory at different concentration (x = 0.00, 0.25, 0.50, 0.75, 1.00). The Special Quasirandom Structure method was used to make the alloys with FCC structure with four atoms per unit cell. The ground state properties such as lattice constant and bulk modulus were calculated to find the equilibrium atomic position for stable alloys. The calculated ground state properties are in good agreement with the experimental and previously presented other theoretical data. The electronic band structure and density of states were calculated to study the electronic properties for these alloys at different concentration. The electronic properties substantiate metallic behavior of alloys. The first principle density functional perturbation theory as implemented in quasiharmonic approximation was used for the calculation of thermal properties. We have calculated the thermal properties such the Debye temperatures, vibration energy, entropy, constant-volume specific heat and internal energy. The ab initio linear-response method was used for phonon densities of states calculations. Структурнi, електроннi, механiчнi i тепловi властивостi сплавiв Ir₁₋xRhx систематично дослiджено з використанням ab initio теорiї функцiоналду густини при рiзних концентрацiях (x = 0.00, 0.25, 0.50, 0.75, 1.00). Було використано метод спецiальної квазiвипадкової структури для моделювання сплавiв, що мають структуру FCC з чотирма атомами на одиничну комiрку. Були обчисленi властивостi основного стану, такi як постiйна ґратки та об’ємний модуль пружностi, для того, щоб знайти рiвноважнi положення атомiв для стiйких сплавiв. Обчисленi властивостi основного стану добре узгоджуються з експериментальними та iншими ранiше отриманими теоретичними даними. З метою вивчення електронних властивостей цих сплавiв при рiзних концентрацiях обчислено електронну зонну структуру та густину станiв. Електроннi властивостi обгрунтовують металiчну поведiнку сплавiв. Для обчислення теплових характеристик була використана першопринципна теорiя збурень функцiоналу густини, iмплементована у квазiгармонiчне наближення. Нами обчислено такi тепловi характеристики, як температура Дебая, енергiя коливань, ентропiя, питома теплоємнiсть при постiйному об’ємi та внутрiшня енергiя. Було використано ab initio метод лiнiйного вiдгуку для обчислення густини станiв фононiв. 2015 Article Ab initio study of structural, electronic, and thermal properties of Ir₁₋xRhx alloys / Sh. Ahmed, M. Zafar, M. Shakil, M.A. Choudhary // Condensed Matter Physics. — 2015. — Т. 18, № 2. — С. 23601: 1–12. — Бібліогр.: 62 назв. — англ. 1607-324X DOI:10.5488/CMP.18.26001 arXiv:1506.03966 PACS: 61.50f, 65, 71.15Mb, 71.20Be http://dspace.nbuv.gov.ua/handle/123456789/153447 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
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| description |
The structural, electronic, mechanical and thermal properties of Ir₁₋xRhx alloys was studied systematically using ab initio density functional theory at different concentration (x = 0.00, 0.25, 0.50, 0.75, 1.00). The Special Quasirandom Structure method was used to make the alloys with FCC structure with four atoms per unit cell. The ground state properties such as lattice constant and bulk modulus were calculated to find the equilibrium atomic position for stable alloys. The calculated ground state properties are in good agreement with the experimental and previously presented other theoretical data. The electronic band structure and density of states were calculated to study the electronic properties for these alloys at different concentration. The electronic properties substantiate metallic behavior of alloys. The first principle density functional perturbation theory as implemented in quasiharmonic approximation was used for the calculation of thermal properties. We have calculated the thermal properties such the Debye temperatures, vibration energy, entropy, constant-volume specific heat and internal energy. The ab initio linear-response method was used for phonon densities of states calculations. |
| format |
Article |
| author |
Ahmed, Sh. Zafar, M. Shakil, M. Choudhary, M.A. |
| spellingShingle |
Ahmed, Sh. Zafar, M. Shakil, M. Choudhary, M.A. Ab initio study of structural, electronic, and thermal properties of Ir₁₋xRhx alloys Condensed Matter Physics |
| author_facet |
Ahmed, Sh. Zafar, M. Shakil, M. Choudhary, M.A. |
| author_sort |
Ahmed, Sh. |
| title |
Ab initio study of structural, electronic, and thermal properties of Ir₁₋xRhx alloys |
| title_short |
Ab initio study of structural, electronic, and thermal properties of Ir₁₋xRhx alloys |
| title_full |
Ab initio study of structural, electronic, and thermal properties of Ir₁₋xRhx alloys |
| title_fullStr |
Ab initio study of structural, electronic, and thermal properties of Ir₁₋xRhx alloys |
| title_full_unstemmed |
Ab initio study of structural, electronic, and thermal properties of Ir₁₋xRhx alloys |
| title_sort |
ab initio study of structural, electronic, and thermal properties of ir₁₋xrhx alloys |
| publisher |
Інститут фізики конденсованих систем НАН України |
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2015 |
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http://dspace.nbuv.gov.ua/handle/123456789/153447 |
| citation_txt |
Ab initio study of structural, electronic, and thermal properties of Ir₁₋xRhx alloys / Sh. Ahmed, M. Zafar, M. Shakil, M.A. Choudhary // Condensed Matter Physics. — 2015. — Т. 18, № 2. — С. 23601: 1–12. — Бібліогр.: 62 назв. — англ. |
| series |
Condensed Matter Physics |
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2025-07-14T04:58:38Z |
| last_indexed |
2025-07-14T04:58:38Z |
| _version_ |
1837597058215706624 |
| fulltext |
Condensed Matter Physics, 2015, Vol. 18, No 2, 23601: 1–12
DOI: 10.5488/CMP.18.23601
http://www.icmp.lviv.ua/journal
Ab initio study of structural, electronic, and thermal
properties of Ir1−xRhx alloys
S. Ahmed∗, M. Zafar, M. Shakil, M.A. Choudhary
Simulation Laboratory, Department of Physics, The Islamia University of Bahawalpur, Bahawalpur 63100,
Pakistan
Received August 4, 2014, in final form October 31, 2014
The structural, electronic, mechanical and thermal properties of Ir1−xRhx alloys were studied systematicallyusing ab initio density functional theory at different concentrations (x = 0.00, 0.25, 0.50, 0.75, 1.00). A Special
Quasirandom Structure method was used to make alloys having FCC structure with four atoms per unit cell.
The ground state properties such as lattice constant and bulk modulus were calculated to find the equilibrium
atomic position for stable alloys. The calculated ground state properties are in good agreement with the exper-
imental and previously presented other theoretical data. The electronic band structure and density of states
were calculated to study the electronic properties for these alloys at different concentrations. The electronic
properties substantiate the metallic behavior of alloys. The first principle density functional perturbation theory
as implemented in quasiharmonic approximation was used for the calculation of thermal properties. We have
calculated the thermal properties such as Debye temperatures, vibration energy, entropy, constant-volume spe-
cific heat and internal energy. The ab initio linear-response method was used to calculate phonon densities of
states.
Key words: electronic, structural and thermal properties of Platinum group metals
PACS: 61.50f, 71.15Mb, 71.20Be
1. Introduction
Platinum group metals are promising candidates for a wide range of applications. Iridium (Ir), Rho-
dium (Rh) belong to this group and are the rarest elements found in the earth’s crust. Their incredible
catalysis activity increases research interest in these rare elements [1]. Iridium has high density, high
melting temperature and the highest corrosion resistance. Its thermal stability at high temperatures and
the highest shear modulus at room temperature made it a superior metal [2–4]. It has been investigated
for carbon materials protective coatings [5], heavy-metal-ion sensors [6] and Re-rocket thrusters [7] ap-
plications. It is broadly used in organic chemistry for hydrogenation, hydroformulation, hydroboration,
hydrosilylation, cycloadditions [8, 9] and oxidation reactions for catalytic converters in automobiles. It
remains a metal of high interest due to its unique properties for the scientific community [10, 11] during
the past decades. Binary intermetallic alloys that contain a transition metal display interesting electronic,
structural, optical and thermal properties. Recently, Ir- and Rh-base alloys are known as ultra-high tem-
perature materials due to their high-melting temperatures, good high-temperature strengths and good
oxidation resistances [12–14]. Rh-base alloys have better oxidation resistance, lower density, lower ther-
mal expansion coefficient and higher thermal conductivity than Ir-base alloys. These properties make
Rh-base alloys more promising for ultra-high temperature gas turbine applications. To our knowledge,
theoretical and experimental calculation are performed for Ir, Rh and their alloys with other metals but
neither theoretical nor experimental calculations are available for Ir-Rh alloys. These alloys provide a
class of systems exhibiting unique mechanical properties that make them attractive for structural ap-
plications [15]. In recent years, Ir-base super-alloys with good high-temperature properties have been
∗
E-mail: shabir_sehr@hotmail.com
© Sh. Ahmed, M. Zafar, M. Shakil, M.A. Choudhary, 2015 23601-1
http://dx.doi.org/10.5488/CMP.18.23601
http://www.icmp.lviv.ua/journal
S. Ahmed et al.
developed as promising candidates for ultrahigh-temperature applications to replace the traditional Ni-
base super-alloys, which have limited temperature capabilities due to the rather low melting point of
Ni [16–18]. These alloys are promising materials for high temperature and pressure applications, and
currently they are being examined for use in diesel engine turbocharger rotors, high-temperature die
and molds, hydroturbines, and cutting tools [19]. Due to the improvements in simulation techniques in
material science, it is now possible to study materials from bulk to nano scale devices [20]. The use of
first principles calculations offers one of the most powerful tools for carrying out theoretical studies of a
number of important physical and chemical properties of condensed matter with great accuracy [21, 22].
Electronic structure simulations based on density-functional theory (DFT) [23, 24] have been instrumen-
tal to this revolution, and their application has now spread outside a restricted core of researchers in
condensed-matter theory and quantum chemistry, involving a vast community of end users with very
diverse scientific backgrounds and research interests. The knowledge of thermal properties is essential
for the study of mechanical properties [25]. To the best of our knowledge, there are no experimental and
other theoretical data for comparison, so we consider the present results as a predictive study for the first
time, which still awaits an experimental confirmation.
2. Computational method
Thefirst principles investigationwas performed using a pseudo-potential planewave (PP-PW)method
as implemented in QUANTUMES ESPRESSO [26]. Special Quasirandom Structure method proposed by
Zunger and coworkers [32] was used to make FCC structure with four atoms per unit cell alloys. SQSs
are specially designed for a small supercell that is computationally feasible for DFT calculations. Vander-
bilt ultra soft pseudo-potential parameterized by Perdew and Zunger [27, 28] was used for calculations.
We used ultrasoft Vanderbilt formalism with local density approximation (LDA) [29] for the exchange
correlation energy of electrons. The special k-points were integrated to the sampled Brillouin zone us-
ing the Monkhorst-Pack method [31]. A special k-points mesh of 14× 14× 14 was used to produce an
irreducible Brillouin zone. Pseudo-wave functions were expanded in a plane wave basis set using the
cut-off energy of 25 Ry for all concentrations. The chosen cut-off energy and k-point mesh ensure conver-
gence with an accuracy of 10
−6
Ry. Density Functional Perturbation Theory (DFPT) and Quasi Harmonic
Approximation (QHA) code developed by Baroni et al. [26] were used to investigate the phonon density
of states and thermal properties from optimized structure. The dynamical matrices at arbitrary wave
vectors were obtained using the Fourier transformation-based interpolations to calculate thermal prop-
erties. A 12×12×12 q point meshwas implemented to obtain dynamical matrices of force constants in the
irreducible Brillouin zone at Γ point. The linear response approachmethod was used to obtain the curves
of phonon density of states within the framework of DFPT [26] as implemented in Quantum ESPRESSO.
The parameters such as cell dimension, energy cut-offs and the k-points used in the study were obtained
from their respective convergence tests. These convergence parameters provide a fast way toward an
optimized structure.
3. Results and discussion
3.1. Structural properties
We have found the ground state properties of Ir1−xRhx alloys at x = 0, 0.25, 0.5, 0.75, and 1.00. The
total energy per unit cell was computed at various lattice parameters to find the equilibrium lattice con-
stant. The equilibrium lattice constant was found by minimizing the total energy of system. Murnaghan’s
equation of state was used to evaluate the optimized lattice constants and bulk moduli [33].
The structural parameters i.e., lattice constants and bulkmodulus for pure Ir, Rh and their alloys were
calculated and reported in table 1 along with experimental and other theoretical results. The optimized
lattice curves for Ir1−xRhx alloys at x = 0, 0.25, 0.5, 0.75, and 1.00 are shown in figure 2. Figure 1 shows
the variation of lattice constants and bulk modulus for Ir1−xRhx evaluated using Vegard’s law. It is seen
23601-2
Ab initio study of structural, electronic, and thermal properties of Ir1−xRhx alloys
Table 1. Calculated lattice parameters and bulk modulus of Ir1−xRhx alloys compared with experimental
and other theoretical results at x = 0, 0.25, 0.5, 0.75, and 1.00.
Composition Lattice constant (Angstrom) Bulk modulus (Gpa)
x This work Experimental Other This work Experimental Other
calculation calculation
0.00 3.831 3.84
a
3.88
b
360 355
e
386
g
0.25 3.81394 337.375
0.50 3.80373 315
0.75 3.79589 294.5
1.00 3.792 3.803
c
3.847
d
269.5 268.7
f
259.6
h
a
reference [34],
b
reference [35],
c
reference [36],
d
reference [37],
e
reference [38],
f
reference [39],
h
reference [40],
g
reference [41].
La
tt
ic
e
C
o
ns
ta
nt
/ Å
3.79
3.8
3.81
3.82
3.83
Concent rat ion X
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
Calculated
Vegard's Law
(a)
B
ul
k
M
o
du
lu
s/
G
pa
260
280
300
320
340
360
380
Concent rat ion X
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
Calculated
Vegard's Law(b)
Figure 1. Calculated lattice parameters and bulk modulus in comparison with Vegard’s law at experimen-
tal values for Ir1−xRhx alloys: (a) lattice constant, (b) bulk modulus.
that with the change of Rh concentration in Ir1−xRhx alloys, the lattice constant and bulk modulus show
a considerable change from Vegard’s law which may be due to the lattice mismatch in these alloys.
The calculated results are compared with experimental and other theoretical results for pure Ir and
Rh. However, the experimental or theoretical results for their alloys are not yet available in the literature
for comparison. These calculations may be a prediction for researchers for future. The values of the cal-
culated lattice constant and the bulk modulus for Ir1−xRhx alloys turned out to decrease with an increase
of the Rh concentration.
3.2. Electronic properties
Electronic properties depend on the electronic configuration in materials, particularly on the exis-
tence of prohibited regions of energy and on the magnitude in their electronic excitation spectra. De-
tailed band-structure calculations are needed to understand the electronic properties of any material.
Thus, the band structures for Ir1−xRhx along various high symmetry directions were calculated at equi-
librium lattice constants. The electronic band structures are shown in figure 3. The Fermi level for the
band structure was set to be 0 eV. It can be seen from figure 3 (a)–(e) that electronic bands for all con-
centrations overlap at the Fermi level. The electronic structures calculated for different concentrations
clearly show the metallic nature of the materials since the energy bands intersect at the Fermi level.
Conductivity in Ir metal is dominated by overlapping of s, p and d bands.
For Rh metal, the conductivity is dominated by a narrow d -band with some empty states overlapped
by a broad free electron s-band. Their alloys show a metallic nature due to s, p , d of Ir atoms and s, d of
Rh atoms bands overlapping. So, these alloys lead to archetypical transition metals, in which a narrow d -
23601-3
S. Ahmed et al.
Figure 2. Structural optimization plots for Ir1−xRhx alloys: (a) at x = 0.00, (b) at x = 0.25, (c) at x = 0.50,
(d) at x = 0.75 and (e) at x = 1.00 concentrations.
band containing some empty states was overlapped by a broad free-electron like s-bandwhich dominated
the conductivity [42].
The calculated electronic band structures along the principal symmetry directions are presented in
figure 3 (a)–(e). The overall band structure shows a similar metallic nature. The main hybridization re-
mains between d bands of both Ir and Rh when mixed in order to form their alloys. The Fermi energy
decreases with an increase of Rh percentage in Ir1−xRhx alloys. The calculated electronic band structure
is in good agreement with the previous result for pure Ir and Rh [43, 44]. From the calculated electronic
band structure for Ir1−xRhx alloys, it can be seen that the band overlapping increases with Rh concentra-
tion which causes a decrease of resistivity with Rh concentration [45].
The density of states plays an essential role in studying many physical properties. Total energies of
material can be calculated from the knowledge of the density of states. The number of electrons within
the Fermi surface can be used to determine the nature of materials. The Fermi energy is determined by
the Density of States (DOS) which provides information on the Fermi energy level. To further study the
nature of electronic band structure, we have also calculated the total and partial DOS for these alloys for
different concentrations at an ambient pressure and presented them in figure 4 (a)–(e). In figure 4 (a), for
pure Ir, the lowest lying bands were due to s, p states and the higher energy states were mainly due to
23601-4
Ab initio study of structural, electronic, and thermal properties of Ir1−xRhx alloys
d states, and the conductivity was dominated by s, p and d hybridization states. In case of Ir0.75Rh0.25
in figure 4 (b), the bottom state of the valence band was dominated with s, p states of Ir and Rh s state.
The upper valance band region was dominated with Ir d state with some contribution of other states.
In figure 4 (c), with Ir0.50Rh0.50, the lowest part of the valance band was mostly contributed by s state of
both metals and Ir p state but the higher energy level was dominated by a broad contribution of d -states
of these metals with little part of other states. In figure 4 (d), for Ir0.25Rh0.75, s, p states of Ir and Rh s state
for this alloys dominated the bottom of the valence band. In the upper band, Rh d state was much wider
than the Ir d states. In figure 4 (e), with pure Rh, the bottom valence levels were mostly dominated by s
states but the higher valence band was dominated with d states.
Figure 3. Calculated band structures for Ir1−xRhx alloys: (a) at x = 0.00, (b) at x = 0.25, (c) at x = 0.50, (d)
at x = 0.75 and (e) at x = 1.00 concentrations.
From the analysis of the band structure of Ir1−xRhx alloy, it was observed that, at different concen-
trations of these metals, the band structure shows a similar behavior that differs from each other mainly
by the energy level of each band relative to the Fermi level. In pure Ir, the conductivity was mostly
dominated by s, p and d hybridization but for pure Rh, the conductivity was prominent with s and d
overlapping. The electronic energy density of states are compared with the previously reported result
for cubic Ir and Rh [46, 47]. When these metals were mixed to make alloys, strong hybridization between
23601-5
S. Ahmed et al.
Figure 4. Density of states for Ir1−xRhx alloys: (a) at x = 0.00, (b) at x = 0.25, (c) at x = 0.50, (d) at x = 0.75,
and (e) at x = 1.00 concentrations.
the Ir and Rh d states with small contribution of s states dominated the conductivity. Ir has a lower elec-
tronic DOS than Rh at the Fermi level and it increases with an increase of Rh concentration in the alloy.
The material having a lower electronic DOS at the Fermi level often characterizes a more stable structure
[48, 49]. Thus, Ir is a more stable structure than Rh and it decreases with Rh concentration.
23601-6
Ab initio study of structural, electronic, and thermal properties of Ir1−xRhx alloys
3.3. Thermal properties
Thermal properties of metals are of interest below the melting temperature. We have used a quasi-
harmonic approximation and phonon density of states to obtain thermal properties. Helmholtz free en-
ergy ∆F , internal energy ∆E , entropy S and constant-volume specific heat Cv , at zero pressure are calcu-
lated. Phonon DOS has a strong impact on thermodynamic properties. The electron excitation becomes
P
ho
no
n
D
O
S/
c
m
-1
−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
ω/ cm-1
−50 0 50 100 150 200 250
Ir Phonon DOS
(a)
0
0.1
0.2
0.3
−50 0 50 100 150 200 250 300
Ir0.75Rh0.25PDOS
Ir DOS
Rh DOS
Ph
on
on
D
O
S/
S
ta
te
s.
cm
-1
0
0.05
0.1
0.15
0.2
ω/ cm-1
0 100 200 300 400 500
Ir0.75Rh0.25 Total DOS
(b)
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0 100 200 300
Ir0.50Rh0.50 Total PDOS
Ir DOS
Rh DOS
Ph
on
on
D
O
S/
S
ta
te
s.
cm
-1
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
ω/ cm-1
0 100 200 300 400 500
Ir0.50Rh0.50 Total DOS
(c)
−0.05
0
0.05
0.1
0.15
0.2
0.25
−50 0 50 100 150 200 250
Ir0.25Rh0.75 PDOS
Ir DOS
Rh DOS
Ph
on
on
D
O
S/
S
ta
te
s.
cm
-1
0
0.05
0.1
0.15
0.2
ω/ cm-1
0 100 200 300 400 500
Ir0.25Rh0.75 Total DOS
(d)
P
ho
no
n
D
O
S/
c
m
-1
−0.05
0
0.05
0.1
0.15
0.2
0.25
ω/ cm-1
0 50 100 150 200 250
Rh Phonon DOS
(e)
Figure 5. Phonon density of states for Ir1−xRhx alloys: (a) at x = 0.00, (b) at x = 0.25, (c) at x = 0.50, (d) at
x = 0.75, and (e) at x = 1.00 concentrations.
easier with higher phonon DOS [50]. Figure 5 depicts the phonon density of states of Ir1−xRhx alloys with
different concentrations. The total phonon DOS for pure Ir was shown in figure 5 (a) and has a maximum
DOS at frequency 112.5 cm
−1
. In figure 5 (b), two higher peaks in phonon DOS occur, first peak is dom-
inated by Rh at frequency of 115.5 cm
−1
and the second was due to Ir atoms at 162 cm
−1
frequency. In
figure 5 (c), three high peaks for phonon density of states occurs at a frequency of 103.5 cm
−1
, 126 cm
−1
,
164.25 cm
−1
which are due to movements of Rh, Ir and Rh and Ir atoms, respectively. In figure 5 (d), the
contribution of total phonon DOS was dominated by Ir and Rh atoms at low frequency of 108 cm
−1
. Con-
23601-7
S. Ahmed et al.
versely, phonon density of states is mainly dominated by Rh atoms after this frequency. In figure 5 (e),
for pure Rh, two higher peaks occur in phonon DOS, the first peak is dominated mainly at 155.25 cm
−1
frequency and the second peak with frequency 166.5 cm
−1
.
Figure 6. Debye temperature variation with tem-
perature for Ir1−xRhx alloys at x = 0.00, 0.25, 0.50,
0.75, 1.00.
Figure 7. Vibration energy variation with temper-
ature for Ir1−xRhx alloys at x = 0.00, 0.25, 0.50,
0.75, and 1.00.
Figure 8. Entropy variation with temperature for
Ir1−xRhxalloys at x = 0.00, 0.25, 0.5, 0.75, and 1.00.
Figure 9. Specific heat at a constant volume vari-
ation with temperature for Ir1−xRhx alloys at x =
0.00, 0.25, 0.50, 0.75, and 1.00.
To further study the thermal properties, the Debye temperatures, vibration energy, entropy, constant-
volume specific heat and internal energy are plotted in figures 6–10 for this alloy. Debye temperature
determines the thermal characteristics of materials and it is closely related to many physical properties
such as specific heat [51]. The materials with high Debye temperature are associated with higher thermal
conductivity. The knowledge of thermal conductivity and melting temperature is essential for develop-
ing and manufacturing electronic devices [52, 53]. The Debye temperature plays an important role in
the field of thermo-physical properties of materials. Debye temperature was maximum at 0–20 K, then
it decreases rapidly and approaches a constant for higher temperature values. Entropy, constant-volume
specific heat and internal energy values increase quickly at a lower temperature and becomes converged
to constant values with high temperature as in figure 9. Vibration energy remains constant for low tem-
perature and decreases inversely as temperature increases. Entropy, constant-volume specific heat de-
23601-8
Ab initio study of structural, electronic, and thermal properties of Ir1−xRhx alloys
creases with Rh concentration but increases for Ir0.50Rh0.50, then continues the decreasing behavior for
further Rh concentration. The increasing behavior may be due to the maximum lattice mismatch at 50
percent concentration and these quantities decrease with the further increase in Rh amount. It is seen
that the internal energy and vibration energy increases slightly with Rh concentration but decreases for
Ir0.50Rh0.50 concentration and then continues to progress. From figure 7, it can also be seen that Rh has
a greater vibration energy compared to Ir. However, entropy, constant-volume specific heat , internal
energy, vibration energy and Debye temperature show a different behavior at 50 percent concentration
which may be due to a greater lattice mismatch. High entropy possesses many attractive properties, such
as high hardness [54], outstanding wear resistance [55], good fatigue resistance characteristics [56], ex-
cellent high-temperature strength [57], good thermal stability [58] and, in general, good oxidation and
corrosion resistance [59]. These properties suggest a great potential in a wide variety of applications.
Figure 10. Internal energy variation with temperature for Ir1−xRhx alloys at x = 0.00, 0.25, 0.50, 0.75, and
1.00.
Our calculated results of thermal properties for pure Ir and Rh are in good agreement with the pre-
viously published data [60–62]. There were no experimental or theoretical results for their alloys. There-
fore, the results reported in this work will be predictive for future. From the above investigations of
thermodynamics properties, it can be demonstrated that Ir1−xRhx with x = 0.5 has a larger entropy and
constant-volume specific heat due to a maximum lattice mismatch within the considered range of tem-
peratures but the vibration energy and the Debye temperature were minimum for x = 0.5.
4. Conclusions
The first principle method was employed to analyze the structural, electronic, mechanical, and ther-
mal properties of the Ir1−xRhx alloys with a four atom unit cell. The pseudopotential scheme was used
to study the alloys at different concentrations (x = 0.00, 0.25, 0.50, 0.75, 1.00). The following conclusions
were drawn:
1. For the Ir1−xRhx alloys, by increasing Rh concentration, the lattice constant and the bulk modu-
lus decrease. The variations in the calculated lattice constant and the bulk modulus are slightly
different from Vegard’s law.
2. In electronic properties, the electronic bands overlap at the Fermi level, and the Fermi energy
decreases with an increase in Rh concentration but the band overlap increases. This is because
Rh has a larger electronic conductivity than Ir. In pure Ir, a narrow d state was overlapped by a
broad free-electron s and p but pure Rh has an overlap between s and d only which dominates the
conductivity in these metals. When Ir and Rh were mixed to form alloys, the main hybridization
was between d states with some contribution from other states.
23601-9
S. Ahmed et al.
3. Thermodynamic properties such as phonon density of states, the Helmholtz free energy, the phonon
contribution to the internal energy, the constant-volume specific heat, and entropy were calculated
using the quasi-harmonic approximation. The minimum value of phonon density of states is for
the alloy having Ir0.50Rh0.50 concentration. Debye temperature was maximum at 0–20 K, then it
decreases rapidly and approaches a constant for higher temperature values. Entropy, constant-
volume specific heat and internal energy values increase quickly at a lower temperature and be-
come converged to constant values with high temperature. Entropy, constant-volume specific heat
decreases with Rh concentration but increases for Ir0.50Rh0.50, then continues a decreasing behav-
ior for further Rh concentration. Vibration energy remains constant for low temperature and de-
creases inversely as temperature increases. It is seen that the internal energy and the vibration
energy increase slightly with Rh concentration but decrease for Ir0.50Rh0.50 concentration and then
continue to progress.
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S. Ahmed et al.
Ab initio дослiдження структурних електронних i теплових
властивостей сплавiв Ir1−xRhx alloys
Ш. Ахмед ,М. Зафар,М.Шакiл,М.А. Чоуджарi
Лабораторiя комп’ютерного моделювання, фiзичний факультет, Iсламський унiверситет м. Бахавалпур,
м. Бахавалпур 63100, Пакистан
Структурнi, електроннi, механiчнi i тепловi властивостi сплавiв Ir1−xRhx систематично дослiджено з ви-
користанням ab initio теорiї функцiоналду густини при рiзних концентрацiях (x = 0.00, 0.25, 0.50, 0.75,
1.00). Було використано метод спецiальної квазiвипадкової структури для моделювання сплавiв, що ма-
ють структуру FCC з чотирма атомами на одиничну комiрку. Були обчисленi властивостi основного стану,
такi як постiйна ґратки та об’ємний модуль пружностi, для того,щоб знайти рiвноважнi положення атомiв
для стiйких сплавiв. Обчисленi властивостi основного стану добре узгоджуються з експериментальними
та iншими ранiше отриманими теоретичними даними. З метою вивчення електронних властивостей цих
сплавiв при рiзних концентрацiях обчислено електронну зонну структуру та густину станiв. Електроннi
властивостi обгрунтовують металiчну поведiнку сплавiв. Для обчислення теплових характеристик була
використана першопринципна теорiя збурень функцiоналу густини, iмплементована у квазiгармонiчне
наближення. Нами обчислено такi тепловi характеристики, як температура Дебая, енергiя коливань, ен-
тропiя, питома теплоємнiсть при постiйному об’ємi та внутрiшня енергiя. Було використано ab initioметод
лiнiйного вiдгуку для обчислення густини станiв фононiв.
Ключовi слова: електроннi, стактурнi i тепловi властивостi металiв платинової групи
23601-12
Introduction
Computational method
Results and discussion
Structural properties
Electronic properties
Thermal properties
Conclusions
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