Inte rnational Journal of Engineering Technology, Manage ment and Applied Sciences
www.ijetmas.com September 2015, Volume 3, Special Issue, ISSN 2349-4476
Structural Study of ScP at Room Temperature
Purvee Bhardwaj and Sadhna Singh
High Pressure Research Lab., Department of Physics, Barkatullah University, Bhopal-462026, India
Abstract
We report calculations of pressure-induced structural phase transition and elastic properties of the NaCl -type ScP at
room temperature. For the present study a Realistic Interaction Potential Approach (RIPA) model (including the
covalency and temperature effect) has been developed. It is observed that the present compound is more stable in NaClphase. It is predicted that at high pressures these compounds undergo a structural phase transition from the NaCl (B1)
structure into the CsCl (B2) structure. The phase transition pressures and associated volume collapses obtained from
present potential model show a generally good agreement with available experimental data and others.
PACS No: 62.20.de, 62.20.dq, 62.50.-p, 64.00.00
Key words: Rare earth pnictide, Phase transition, High pressure, Volume collapse.
1.
Introduction
Among the III-V compounds the scandium pnictides (ScX, X=N, P, As, Sb) are a new class of materials
having the uses in devices application. At ambient temperature and pressure these pnictides exhibit six fold
coordinated NaCl (B1) structure. However under pressure they show a first order structural phase transition
from NaCl (B1) to CsCl (B2) structure. The full potential linear augmented plane wave (FPLAPW) method
had been used to study the structural and elastic properties of III-V scandium compounds by Maachou et. al.
[1]. Electronic and geometric structure of diatomics ScN, ScP and ScAs has been studied by Tientega et. al.
[2]. The ground-state properties and high-pressure structural phase transition (B1–B2) of ScX (X= N, P, As,
Sb) compounds have been studied by Tebboune et al. [3], emphasizing the metallic behavior of these
compounds. The structural, electronic, and elastic properties of ScN and ScP in NaCl (B1 phase) and CsCl
(B2 phase) structures and the phonon dispersion at ambient and high pressure, close to phase transition, have
been investigated by using first-principles pseudopotential method in the framework of density functional
theory with the generalized gradient approximation by Pandit et. al. [ 4].
Since the present compound shows the ionic as well as covalent nature we thought it pertinent to apply a
Realistic Interaction Potential Approach (RIPA) model which includes the covalency effect in the potential
model. Furthermore, the available literature is reported at T=0K for the present compound. While
experimental measurements are performed at room temperature. To make the study realistic, it should be
performed by taking temperature effects. Seeing as the previous calculations ignored the covalency effect in
their calculations, we thought it pertinent to apply a Realistic Interaction Potential Approach (RIPA) model
which includes the covalency and temperature effect as well in the potential model. The model consists of
Coulomb interaction, three body interactions modified by covalency effect, van der Waal interaction, overlap
repulsive interaction and temperature effect. In the present paper, we use the model theory to calculate the
high pressure structural and elastic properties of ScP at room temperature and compare them with available
theoretical and experimental data to judge the suitability of the potential and our predictions for these
properties. The organization of this paper is as follows: the method of calculation of structural phase transition
pressure and model theory are given in Section 2, while in Section 3, we present interesting results on
structural and elastic properties of ScP.
2. Potential Model and Method of Calculations
The natural consequence of application of pressure on the crystals is the compression, which in turn leads to
an increased charge transfer (or three-body interaction effects) [6] due to the existence of the deformed (or
exchanged) charge between the overlapping electron shells of the adjacent ions.
303
Purvee Bhardwaj and Sadhna Singh
Inte rnational Journal of Engineering Technology, Manage ment and Applied Sciences
www.ijetmas.com September 2015, Volume 3, Special Issue, ISSN 2349-4476
These effects have been incorporated in the Gibbs free energy (G = U+PV-TS) as a function of pressure and
three body interactions (TBI), which are the most dominant among the many body interactions. Here, U is the
internal energy of the system equivalent to the lattice energy at temperature near zero and S is the entropy. At
temperature T=300K and pressure (P) the
  M Z 2 e 2 12 M Ze 2 f m (r ) C X D X
G BX (r ) 

[ 6  8 ]
rX
rX
rX
rX
 6b ij exp[(ri  r j  r X ) /  ]  6b ii exp[(2ri  YX r X ) /  ]
X
X
 6b jj exp[(2r j  YX r X ) /  ]  PVBX (r X )  TS BX
Where X= 1 (Phase 1=B1), 2(Phase 2=B2), and Y x= 1.414, 1.154, for NaCl and CsCl structures respectively.
With α mX as the Madelung constant. C and D are the overall van der Waal coefficients for NaCl and CsCl
structure respectively, β ij (i,j=1,2) are the Pauling coefficients defined as β ij =1+(Zi /ni )+(Zj /nj ) with Zi (Zj ) and
ni (nj ) as the valence and the number of electrons of the i(j) th ion. Ze is the ionic charge and b (ρ) are the
hardness (range) parameters, r is the nearest neighbour separations f m (r) is the modified three body force
parameter which includes the covalency effect with three body interaction, r i (rj ) are the ionic radii of ions i
(j). S1 and S2 are the entropies for NaCl (CsCl) structure [7].
These lattice energies consist of long range Coulomb energy (first term), three body interactions
corresponding to the nearest neighbour separation r (second term), vdW (van der Waal) interaction (third
term), energy due to the overlap repulsion represented by Hafemeister and Flygare (HF) type potential and
extended up to the second neighbor ions (fourth, fifth and sixth term).
Covalency effects have been included in three-body interaction in the second terms of lattice energies given
by Eq. (1). Now modified three body parameter fm (r) becomes
f m (r )  fTBI (r )  f cov (r )
(2)
The relevant expressions of fTBI (r) and fcov (r) are given in our earlier work [6].
3. Results and Discussion
The parameters are calculated by using equilibrium conditions [6]. The input and model parameter are given
in Table 1. We have followed the technique of minimization of U B1 (r) and UB2 (r’) at different pressures in
order to obtain inter ionic separation r and r’ for B3 and B1 phases respectively associated with minimum
energies. We have evaluated the corresponding GB1 (r) and GB2 (r’) and their respective differences 
G=GB1 (r)–GB2 (r’). As the pressure is increased, the values of  G decreases and approaches zero at the
transition pressure. Beyond this pressure  G becomes negative as the phase B2 become more stable. The
variation of  G with pressure for ScP has been plotted in Fig 1. The phase transition pressure obtained from
this calculation is presented in Table 2 and compared with the available results. Fig 1 shows the phase
transition from NaCl to CsCl structure in ScP at 246.5 GPa which is comparable with other values.
Table-1 Input parameters and generated model parameters for ScP.
Solid
ScP
Input Parameters
r0 (Å)
B (GPa)
2.25a
97.6a
a-ref [4]
304
Purvee Bhardwaj and Sadhna Singh
Model Parameters
b(10-12
ρ(Å)
ergs)
147.36
0.337
fm (r)
0.05673
Inte rnational Journal of Engineering Technology, Manage ment and Applied Sciences
www.ijetmas.com September 2015, Volume 3, Special Issue, ISSN 2349-4476
Table-2 Phase transition and volume change of ScP.
Solid
Transition Volumes (Å 3 )
Phase Transition Pressure
(GPa)
Present Others
ScP
246.5
a
Present
VB1
22.47
b
245.61 , 247.56
VB2
23.71a
Others
VB1
20.38
VB2
21.87a
a-ref [1], b–ref [4]
100
ScP
80
G (KJ/mole)
60
NaCl-Phase
40
20
0
CsCl-Phase
-20
0
50
100
150
200
250
Pressure (GPa)
Fig. 1. Variation of ∆G (KJ/mole) with pressure for ScP
ScP
1.00
Relative volume change
0.96
NaCl-Phase
0.92
0.88
0.84
0.80
0.76
CsCl-Phase
0.72
0
50
100
150
200
250
300
Pressure (GPa)
Fig. 2. Relative volume change with the variation of pressure for ScP
The relative volumes,
𝑉 (𝑃)
𝑉 (0)
(Here, V (P) is the volume of the material at applied pressure P in NaCl phase and
V (0) is the volume at P = 0 i.e. in NaCl phase) have been computed and plotted against the pressure in Fig 2.
The values of transition volumes along with others results are listed in Table 2 for ScP. It is clear from Table 2
305
Purvee Bhardwaj and Sadhna Singh
Inte rnational Journal of Engineering Technology, Manage ment and Applied Sciences
www.ijetmas.com September 2015, Volume 3, Special Issue, ISSN 2349-4476
and Fig. 2 that the magnitude of transition volumes of B1 phase is 22.47 and for B2-phase is 20.38 for ScP
which are in good agreement with others.
4. Conclusion
On the basis of above work we conclude that the inclusion of covalency effect in potential model is
adequately suitable for the prediction of B1 → B2 phase transition pressure and associated volume collapse in
ScP. This approach may be applied to other II-IV and III-V semiconducting compounds for the study of phase
transition phenomenon.
Acknowledgments
Authors are thankful to Department of Science & Technology (DST), New Delhi for the financial support to
this work. One of the authors (PB) is grateful to Department of Science & Technology (DST), New Delhi for,
awarding WOS-‘A’ (Grant no. SR/WOS-A/PS-17/2013).
References
1.
2.
3.
A. Maachou, B. A mrani and M. Driz, Physica B 388(2007) 384-389.
F. Tientega and J. F. Harrison, Chem. Phys. Lett. 223 (1994) 202-206.
A. Tebboune, D. Rached, A. Ben zair, N. Sekkal, and A. H. Belbachir, Phys. Status Solidi B 243, 2788 (2006).
4.
5.
6.
Premlata Pandit, Bipul Rakshit, and Sankar P. Sanyal, Phys. Status Solidi B (2010) 1–7.
M P Tosi and F G Fu mi J. Phys. Chem. So lids 23 (1962) 359-366; M P Tosi Solid State Physics 16 (1964) 1-120.
P. Bhardwaj and S. Singh, phys. status solidi b, 249 (2012) 38-49.
7.
Purvee Bhard waj and Sadhna Singh Current Applied Phys. 14 (2014) 496-507.
306
Purvee Bhardwaj and Sadhna Singh