Journal of Modern Physics Vol.05 No.15(2014), Article ID:50242,5
pages
10.4236/jmp.2014.515155
The Bowing Parameters of
Ternary Alloys
Sinem Erden Gulebaglan1, Emel Kilit Dogan2, Murat Aycibin2, Mehmet Nurullah Secuk2, Bahattin Erdinc2, Harun Akkus2
1Department of Electric Program, Vacational School of Van, Yuzuncu Yıl University, Van, Turkey
2Physics Department, Faculty of Sciences, Yüzüncü Yıl University, Van, Turkey
Email: sinemerden@gmail.com
Copyright © 2014 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
Received 8 May 2014; revised 4 June 2014; accepted 2 July 2014
ABSTRACT
On the basis of first principles calculations using density functional theory, we
explore the struc- tural and electronic properties of two binaries: CaO and MgO
in rock salt structures. Structural properties of the semiconductor
alloys are derived from total-energy minimization within the General Gradient Approximation.
The band gap bowing parameters dependence is very powerful Calcium composition.
The results offer that an average bowing parameter of
alloys is b = ~0.583$ eV. We analyzed the volume deformation, charge transfer and
structural relaxation effects of the
alloys.
Keywords:
Density Functional Theory, Ternary Alloys, Band-Gap Bowing Parameter
1. Introduction
Recently, the binary compounds such as TlAs, AlAs, ScN, GaN and their mixtures such
as TlAlAs, ScGaN have been studied theoretically [1] -[3] , because the wide range
of the band gap is important for microelectronics devices. Generally, monoxide compounds
are known as rock salt structures (B1) at room temperature and under pressure. Y.
Duan et al. [4] have been handled the electronic properties of XO (X = Be, Mg, Ca,
Sr, Ba, Zn and Cd) for wrutzite, zincblende and rock salt structure. Ponce et al.
[5] have analyzed theoreticaly and experimentaly electronic and optic properties
of CaS nad CaO. Albuquerque and Vasconcelos [6] are reported structual, electronic
and optical properties of CaO. Karki et al. [7] [8] have inversigated structual,
dynamic and electronic properties of liquid MgO via density functional theory. Makaremi
and Nourbakhsh have declerated structual, electronic and magnetic properties of
Mgo nanolayers. Nishi et al. [9] have investigated experimentally metastable
solid solutions film ZnO layers. Stolbov and Cohen [10] have studied the electronic
structure for equilibrium MgO-CaO. Miloua et al. [11] have calculated the electronic
properties of
,
theoretically. Besides, A. Srivastava et al. [12] calculated phase translations
in
alloys.
In this paper, we represent the bowing parameter of
alloys by first principles density functional theory. To the best of our knowledge,
no theoretical as well as experimental work has been performed thus far for the
bowing parameter of
.
The aim of this paper is to understand the attitude of the bowing parameters and
contribution to the gap bowing parameters. The paper is methodized as follows: computational
methodology is given in Section 2. Results and discussion are represented in Section
3. The study is concluded in Section 4.
2. Computational Details
The calculations for CaO, MgO and
in the rock salt structure were investigated within the generalized gradient approximation
(GGA) of density functional theory (DFT) using the PWSCF code [13] . In Quantum
Espresso, the examining is performed by utilizing the Kohn-Sham [14] formation established
on the DFT. Total energies have been calculated by using ultrasoft pseudopotentials
and plane-wave basis sets. The exchange- correlation potentials in the GGA [15]
is separately used in the calculations. The electronic configurations used for the
pseudo potentials were Ca(3p64s), Mg(2p63s) and O(2s22p4).
The Khon-Sham [14] orbitals were described using a plane wave basis set. The highest
kinetic energy of a plane wave in the chosen fundamental set is known the cutoff
energy. Specialize assignation of the cutoff energy is important for achieving accurate
results with available computational process. The values of cutoff energies used
in our calculations are summarized in Table 1.
The plane wave energy cut off is selected 90 Ry. Accurate Brillounin zone investigations
are carried out using the standard special k-points technique of Monkhorst and Pack
[16] . The Brillouin zone investigation was performed over a
mesh points. Our calculations involve an 16 atom for
alloys in a supercell. We start at MgO cluster and finish at CaO cluster.
3. Results and Discussion
3.1. Structural Properties of Binary Compounds
The ternary compounds
are bordered by two binary compounds of CaO and MgO. In order to be able to analyze
the energy band gaps and bowing parameters of
ternary alloys, it is wholesome to study the CaO and MgO binary compounds in terms
of their structural and electronic properties. By lessening the total energy with
regards to the atomic positions and lattice parameters we carried out the structural
optimization. Equilibrium lattice parameters are obtained by fitting the total energy
with the different volumes according to the Birch equation of states.
The Birch equation of states [17] can be seen in the Equation (1):
(1)
where
and
are the bulk modulus and its pressure derivative at the equilibrium volume
. The calcu-
Table 1. Ground state energies for equilibrium MgO and CaO with various cutoff energies.
lated values for the equilibrium of CaO and MgO are 4.805 Å and 4.263 Å,
respectively. We represented and compered the equilibrium lattice parameter, bulk
modulus
and bulk modulus derivation
in Table 2.
3.2. Structural Properties of
In this paper, we examined the effectiveness of the Vegard’s law for rocksalt
alloys in its ground states. Ca composition
dependent lattice constant of
compounds is expressed as:
(2)
where,
and
are the lattice constants of the
,
CaO and MgO, respectively. The volve of the deflection from Vegard’s law can be
calculated by Equation (2). The numerical calculations are fulfilled for the different
situations. Seven compositions of
alloys were checked: 0.125, 0.25, 0.375, 0.5, 0.625, 0.75 and 0.875. The calculated
results of lattice parameters with respect to
compositions are itemized in Table 3 from which
we find that the lattice parameter increases with increasing Calcium composition
because these results are due diognosis atomic radius. The atomic radius of Calcium
and Magnesium are 194 and 145 picometers, respectively. We represented and compered
the equilibrium lattice parameter of
ternary alloys in Table 3.
The results also propose that the composition-dependent lattice parameter of the
ternary alloys can be represented by a third-order polynomial equation,
.
The bowing parameter,
,
is significant for investigating the band gap energy ternary alloys. The band gap
energy of ternary alloys describe by the band gap energy of binary compounds, a
quadratic interpolation of
Table 2. Itemized lattice
parameter a, bulk modulus
and bulk modulus derivation
for the binary compounds MgO and CaO in rocksalt structure at equilibrium volume.
Table 3. Itemized lattice
parameter a for the ternary alloys
in rocksalt structure at equilibrium volume. All values are Å.
composition amount
and the bowing parameter.
The band gap energy of ternary alloys
given by
. (3)
Here,
is
the band gap energy of the ternary
compound,
is
the band gap energy of the CaO compound,
is
the band gap energy of the MgO compound and
is the band gap bowing parameter of
.
Bowing parameter is associated with the band gap energy.
Figure 1 shows bowing parameter as a function of
for ternary alloys. We calculated nearly linear variation for
different composition,
,
determinating powerful. Our calculations show that according to the band gap energy
of ternary alloys, bowing parameter decreases. The results are given by Table 4 and our results show that an average bowing parameter
of
is ~0.583 eV.
The combination-dependent bowing parameter function [21]
was
described as
(4)
The band gap of the ternary alloys are correlated with the band gaps of the binary
compounds. The band gap bowing parameters
have three physically contributions [17] .
Finally, the total band gap bowing parameter can be written by resolving into its components as:
. (5)
The effect of volume deformation causes the first term of bowing parameter,
,
in Equation (5). The no-
Figure 1. Composition dependence
of the bowing parameter for
ternary alloys.
Table 4. Itemized bowing
parameter and contribution of the bowing parameter a for the ternary alloys
in rocksalt structure at equilibrium volume.
tional response of MgO(CaO) to hydrostatical pressure states this term via the effect
of the contribution of balanced lattice constant
to the lattice constant of the alloy value
.
(6)
A charge transfer in MgO and CaO at
indicates the second term,
,
of the total band gap bowing parameter,
(7)
The third term,
refers
to the structural relaxation which takes place during the passing from the unrelaxed
to the relaxed alloy
(8)
In Table 4, the values of bowing parameter,
and
its volume deformation component
,
charge exchange component
and structural relaxation component
are expressed for
ternary alloys.
The results also propose that the combination-dependent bowing parameter of the
alloys can be represented by a second-order polynomial equation,
eV.
The results clearly show that
and
are weak and composition dependent. The prime contribution to the gap bowing is
from the
.
The interval of the calculated band gap bowing coefficient for
alloys is from 2.900
to 4.234
.
One can note that for all contributions of
the main addition to the gap bowing is owing to the
effect. This could be correlated to the strong ionicity dissociable of the corresponding
binary compounds (CaO and MgO). The contribution of the volume deformation term
to the bowing parameter
is gradually decreasing with
concentration. Suddenly, in the case of
the addition of the
has increasing. The addition of the other structural relaxation
is weak. Furthermore,
and
is nearly no effect to the bowing parameter. Namely, the
is the only are component which enables the bowing parameter for
alloys.
4. Conclusion
We have examined the electronic properties of the rocksalt
ternary alloys as a function of Calcium composition
by using the GGA method within DFT. The electronic band structures, which are calculated
by using the lattice parameters composed from Vegard’s law. In the GGA, a band gap
bowing parameters are achieved for rock salt
ternary alloys. These results propose the physical condition of a composition dependent
band gap energy for
ternary alloys. Our calculations show that the
ternary alloy’s the bowing parameters are very strong Calcium composition. The average
bowing parameter is 0.583 eV for
ternary alloys. The results clearly show that the
is the only dominant component of the bowing parameter for
alloys. Additionally
and
are weak.
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