First-Principles Study of Superconducting ScRhP and ScIrP
Pnictides
Author
Nasir, MT, Hadi, MA, Rayhan, MA, Ali, MA, Hossain, MM, Roknuzzaman, M, Naqib, SH, Islam,
AKMA, Uddin, MM, Ostrikov, K
Published
2017
Journal Title
physica status solidi (b)
Version
Accepted Manuscript (AM)
DOI
https://doi.org/10.1002/pssb.201700336
Copyright Statement
© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. This is the peer reviewed version
of the following article: First#Principles Study of Superconducting ScRhP and ScIrP pnictides,
physica status solidi (b), 2017, 254 (11), pp. 1700336, which has been published in final form at
https://doi.org/10.1002/pssb.201700336. This article may be used for non-commercial purposes
in accordance with Wiley Terms and Conditions for Self-Archiving (http://olabout.wiley.com/
WileyCDA/Section/id-828039.html)
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1
First-principles study of superconducting ScRhP and ScIrP pnictides
M. T. Nasir
a
, M. A. Hadi
b*
, M. A. Rayhan
a
, M. A. Ali
c
, M. M. Hossain
c
, M. Roknuzzaman
d
,
S. H. Naqib
b*
, A. K. M. A. Islam
b*,e
, M. M. Uddin
c
, K. Ostrikov
d
a
Department of Arts & Science, Bangladesh Army University of Science and Technology, Saidpur-5310, Nilphamari, Bangladesh.
b
Department of Physics, University of Rajshahi, Rajshahi-6205, Bangladesh.
c
Department of Physics, Chittagong University of Engineering and Technology, Chittagong-4349, Bangladesh.
d
School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, QLD 4000, Australia
e
International Islamic University Chittagong, 154/A College Road, Chittagong, Bangladesh
Abstract
For the first time, we have reported in this study an ab initio investigation on elastic properties,
Debye temperature, Mulliken population, Vickers hardness, and charge density of superconducting
ScRhP and ScIrP phosphides. The optimized cell parameters show fair agreement with the
experimental results. The elastic constants and moduli, Poisson’s as well as Pugh’s ratio and elastic
anisotropy factors have also been calculated to understand the mechanical behaviors of these ternary
compounds. Their mechanical stability is confirmed via the calculated elastic constants. The
calculated values for Poisson’s and Pugh’s ratio indicate the ductile nature of these compounds. ScIrP
is expected to be elastically more anisotropic than ScRhP. The estimated value of Debye temperature
predicts that ScRhP is thermally more conductive than ScIrP and the phonon frequency in ScRhP is
higher than that in ScIrP. The hardness of ScRhP is lower due to the presence of antibonding Rh-Rh
in ScRhP. The investigated electronic structures predict that the metallic conductivity of ScRhP
reduces significantly when Rh is replaced with Ir. The main contribution to the total density of states
(TDOS) at Fermi-level (E
F
) comes from the d-electrons of Sc and Rh/Ir in both compounds. These
two ternary compounds are characterized mainly by metallic and covalent bonding with little ionic
contribution. As far as superconductivity is concerned, the matrix elements of electron-phonon
interaction are noticeably enhanced in ScIrP compared to that in ScRhP.
Keywords: Superconducting phosphides; elastic tensors; electronic structures; electron-phonon
coupling
1. Introduction
There are many ternary pnictides that crystallize in the ordered hexagonal Fe
2
P-type structure with a
chemical formula of MM
X (X = P and As) and a space group of 6
2 [1]. In their chemical formula,
M stands for early transition metals including Ca and M
is commonly a late transition metal.
A large number of pnictides with this structure exhibit superconducting behaviors with relatively
high transition temperature T
c
. The most well known members in this family ZrRuP, ZrRuAs and
HfRuP exhibit superconductivity with an onset transition temperature T
c
~ 12 K [2–7]. Another member
in this family, MoNiP is observed to show a bulk superconducting transition at 15.5 K [8,9]. In fact, the
superconductivity in MM
X raised the attention of the scientific community to this family. Very
recently, Okamoto et al. [10] synthesized the ternary phosphide ScIrP and confirmed its
superconducting transition temperature of 3.4 K. Following this study, Inohara et al. reported the
discovery of ScRhP, which shows superconductivity with T
c
~ of 2 K [11]. They also discuss the
distinguishing features of superconducting state in ScRhP by means of comparison with its
isoelectronic and isostructural ScIrP. The comparison shows that T
c
of ScRhP is nearly half that of
ScIrP, whereas the upper critical field H
c2
(0) of ScRhP is found to be only ~1/10 of that ScIrP. The low
H
c2
(0) of ScRhP indicates the weaker spin–orbit interaction of the Rh 4d electrons in ScRhP compared
to the Ir 5d electrons in ScIrP. In addition, the upper critical field H
c2
(0) in ScIrP is considerably
increased by the antisymmetric spin–orbit interaction of the Ir 5d electrons in the noncentrosymmetric
crystal structure. Additionally, the electron–phonon couplings in both ternary phosphides are
recommended to be weak or moderate from the fact that the experimentally measured Sommerfeld
*
Corresponding author: email: hadipab@gmail.com, azi46@ru.ac.bd, salehnaqib@yahoo.com
2
coefficients, i.e., γ
expt
values are nearly the same as γ
cal
calculated using the first principles methods. If
the conventional phonon-mediated superconductivity is understood in both phosphides, the larger
density of states N(E
F
), the higher phonon frequency
p
, and the stronger electron–phonon interaction
will lead to a higher T
c
. Except superconducting properties, there is hardly any study on other physical
properties of these phosphide superconductors. The elastic properties, Mulliken population, Vickers
hardness of these ternaries are still unexplored. Only band structure and density of states (DOS) among
electronic properties are calculated for both the compounds [10–12].
So, here we plan to conduct first-principles study of various physical properties mentioned above of
these ternary phosphide pnictides. The previous study [11] shows that the DOSs at the Fermi level
calculated with and without spin-orbit coupling (SOC) are almost same for both superconductors
ScRhP (9.58 and 9.61 states per eV, respectively) and ScIrP (5.16 and 4.99 states per eV, respectively).
Moreover, the inclusion of SOC has only a minor effect on structural, elastic and bonding properties of
transition metal based compounds such as MAX phases, namely, M
2
AlC (M = Ti, V, and Cr) and
Mo
2
AC (A = Al, Si, P, Ga, Ge, As, and In) [13,14]. For these reasons, SOC has not been taken into
consideration in the present study.
2. Computational Methods
The calculations are carried out using the Cambridge Serial Total Energy Package (CASTEP) code [15]
based on the first-principles density-functional theory (DFT) [16]. The generalized gradient
approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) [17] is used to evaluate the electronic
exchange and correlation potentials. The electrostatic interaction between valence electron and ionic
core is represented by the Vanderbilt-type ultrasoft pseudopotentials [18]. The cutoff energy for the
plane wave expansion is chosen as 440 eV. A k-point mesh of 8 × 8 × 12, according to Monkhorst-Pack
[19] scheme, is used for integration over the first Brillouin zone. The Broyden–Fletcher–Goldfarb–
Shanno (BFGS) algorithm [20] is applied to optimize the atomic configuration and density mixing is
used to optimize the electronic structure. Convergence tolerance for energy, maximum force, maximum
displacement, and maximum stress are chosen as 5.0×10
-6
eV/atom, 0.01 eV/Å, 5.0×10
-4
Å, and 0.02
GPa, respectively.
3. Results and Discussion
3.1. Structural properties
The ternary phosphides ScRhP and ScIrP crystallize in a hexagonal structure with space group of
6
2. (No 187). The structures are fully relaxed by optimizing the geometry with the lattice
parameters and internal coordinates. In optimized structure, the Sc atom resides on the 3g Wyckoff
position with fractional coordinates (0.5831, 0, 0.5) and (0.5805, 0, 0.5) in ScRhP and ScIrP,
respectively. In ScRhP and ScIrP, the Rh and Ir atoms occupy 3f Wyckoff site with fractional
coordinates (0.2508, 0, 0) and (0.2512, 0, 0), respectively. The P atoms occupy two Wyckoff positions
1b and 2c with fractional coordinates (0, 0, 0.5) and (1/3, 2/3, 0), respectively in both compounds. The
unit cell of ScRhP as a structural model of hexagonal MM
X crystals is shown in Fig. 1 and the unit cell
properties are given in Table 1. The calculated lattice constants a and c and unit cell volume V are
found to be consistent with the experimental values [10,11,21]. It is observed that the replacement of
Rh by Ir atom affects the lattice constants; the unit cell volume remains almost unchanged. The lattice
constant a is found to decrease by 2.14%, whereas the lattice parameter c increases by 3.27% when Rh
is substituted by Ir atom. Consequently, c/a ratio increases in ScIrP by 5.47% compared to that in
3
ScRhP, which is indicative of highly compressive in crystal structure of ScRhP in the c-direction in
comparison with that in ScIrP.
Fig. 1: Optimized unit cell of ScRhP (left) with its two dimensional view in ab plane (right). ScIrP is iso-
structural with Ir atoms on place of Rh.
Table 1. Optimized lattice parameters (a and c, in Å), hexagonal ratio c/a, and unit
cell volume (V in Å
3
) of ScRhP and ScIrP along with experimental values.
Phase a
c
c/a
V Remarks
ScRhP 6.481 3.790 0.585 137.857 This calc.
6.453 3.727 0.578 134.404
Expt. [11]
ScIrP 6.342 3.914 0.617 136.326 This calc.
6.331 3.885 0.614 134.855
Expt. [10]
6.372 3.892 0.611 136.853
Expt. [21]
3.2. Mechanical properties
To be mechanically stable, the hexagonal crystals should fulfill the Born criteria [22]: C
11
> 0, C
11
– C
12
> 0, C
44
> 0, (C
11
+ C
12
)C
33
–2C
13
C
13
> 0. The calculated five independent elastic tensors, shown in
Table 2, completely satisfy the above conditions, which indicate that the hexagonal ScRhP and ScIrP
are mechanically stable. Unfortunately, there is no experimental data for elastic constants to compare
with. It is observed that the unidirectional elastic tensors C
11
and C
33
are higher than the pure shear
elastic constant C
44
for both ternaries. It means that the shear deformation is easier than the linear
compression along the crystallographic a- and c-axes. Again, C
11
is greater than C
33
, which implies that
the two ternary pnictides are more incompressible along a-axis compared to that along c-axis. The
substitution of Rh by Ir causes a significant increase of C
11
and C
33
and reduction of C
44
. The
comparatively large value of C
44
for ScRhP indicates that the ability of resisting the shear deformation
in (100) plane is significant in ScRhP compared to ScIrP. The elastic tensor C
12
together with C
13
combines a functional stress component in the crystallographic a-direction in the presence of a uniaxial
strain along the crystallographic b- and c-axes, respectively. The reasonable values of these tensors
imply that the ternary phosphides ScRhP and ScIrP are capable of resisting the shear deformation along
the crystallographic b- and c-axes, while a large force is applied to the crystallographic a-axis. Though
the elastic constant C
12
increases, the elastic tensor C
13
decreases when Rh is replaced with Ir.
The polycrystalline elastic properties, namely bulk modulus and shear modulus are calculated
using single crystal elastic constants, C
ij
in the Voigt-Reuss-Hill approximations [23–25] and listed in
Table 2. So, the compound ScIrP, with a higher G, should be more rigid compared to ScRhP. It is
evident from Table 2 that both the novel phosphide superconductors should behave as ductile materials
4
as their Pugh’s ratios, B/G > 1.75 [26]. The comparison of the values of Y (= 9BG/(3B + G)) given in
Table 2 shows that substitution of Rh with Ir increases the stiffness. In fact, the replacement of Rh with
Ir increases all the moduli (B, G, and Y) of ScIrP including Pugh’s ratio. Thus, the mechanical
properties are enhanced significantly when Rh is substituted with Ir. The thermal shock resistance,
which varies inversely with Y [27] is an essential factor for selecting a material as a thermal barrier
coating (TBC) substance. We observe that as Y increases due to substitution of Ir, R decreases
considerably in ScIrP. Accordingly, ScRhP should be more resistant to thermal shock than ScIrP.
Table 2. The single crystal elastic constants (C
ij
in GPa), polycrystalline
bulk, shear, and Young’s modulus, (B, G and Y in GPa), Pugh’s ratio G/B,
Poisson’s ratio ν and elastic anisotropy factors (A
1
, A
2
, A
3
, A
B
and A
G
) of
ScRhP and ScIrP.
Compound
Single crystal elastic constants
C
11
C
12
C
13
C
33
C
44
ScRhP
277 105 138 228 87
ScIrP
351 124 115 303 53
Compound
Polycrystalline bulk elastic properties
B G Y B/G ν
ScRhP
171 76 199 2.25 0.30
ScIrP
190 82 215 2.32 0.31
Compound
Elastic anisotropy factors
A
1
A
2
A
3
A
B
A
G
ScRhP
0.55 1.01 0.55 0.05 2.9
ScIrP
1.95 0.47 0.91 0.31 6.4
Poisson’s ratio v is calculated via the equation, v = (3B – 2G)/(6B + 2G) and presented in Table 2.
Frantsevich et al. [28] predicted that a material behaves in brittle manner if its Poisson’s ratio does not
exceed the value of 0.26 and if exceeds this critical value the material will show ductility. This criterion
indicates that both the ternary pnictides are ductile in nature.
To identify the interatomic forces that stabilize the crystal systems, Poisson’s ratio serves as a good
predictor. There are two types of interatomic forces for stabilizing the crystal solids. Firstly, the central
forces among the nearest neighbors are responsible for the stability of fcc and almost all bcc crystals.
Secondly, the stability of the diamond structures assumes the non-central forces [29]. The structural
stability will be established with central forces if the crystals have Poisson’s ratio ranging from 0.25 to
0.50. The non-central forces will be active to stabilize the crystal structure when the systems have
Poisson’s ratio either less than 0.25 or greater than 0.50 [30]. The calculated value of v for ScRhP and
ScIrP lies within 0.25 and 0.50, indicating that the interatomic forces in the two ternary phosphides are
basically central forces.
There are three types of shear anisotropy factors for hexagonal crystals due to having three
independent shear elastic constants. These factors for {100}, {010} and {001} shear planes can be
defined successively as [31]:
=
(
+
+ 2
−4
)
6
=
2
−
=
(
+
+ 2
−4
)
3(
−
)
