<i>Ab-Initio</i> Structural Study of SrMoO<sub>3</sub> Perovskite

doi:10.4236/jmp.2012.312238

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Journal of Modern Physics, 2012, 3, 1891-1894

http://dx.doi.org/10.4236/jmp.2012.312238 Published Online December 2012 (http://www.SciRP.org/journal/jmp)

Ab-Initio Structural Study of SrMoO3 Perovskite

Avinash Daga, Smita Sharma

Government Dungar College, Bikaner, India

Email: avinashdaga2009@gmail.com, [email protected]

Received August 10, 2012; revised September 27, 2012; accepted October 10, 2012

ABSTRACT

The equilibrium crystal structure parameter and bulk modulus of the SrMoO3 perovskite has been calculated with

ab-initio method based on density functional theory (DFT) using both local density approximation (LDA) and general-

ized gradient approximation (GGA). The corresponding total free energy along with its various components for SrMoO3

was obtained. The lattice parameter and bulk modulus calculated for SrMoO3 within LDA are 3.99 Å and 143.025 GPa

respectively whereas within GGA are 4.04 Å and 146.14 GPa respectively, both agree well with the available experi-

mental data. The total energy calculated within LDA and GGA is almost the same however lower results are obtained

for GGA. All calculations have been carried out using ABINIT computer code.

Keywords: Perovskite; DFT; LDA; GGA; ABINIT

1. Introduction

Crystal and electronic structures of solid materials are

crucial to understand and improve properties. Many

technological applications, including catalysis, micro-

electronics, substrates for growth of high Tc supercon-

ductors, etc., are based on thin films of ABO3 perovskite.

Until recently, 4d transition metal oxides (TMO) have

attracted less attention because they had the crystalline

defects and having more extended d-orbitals compared to

3d TMO. Yet, numerous studies have shown that this is

no longer the case for some promising TMO such as

molybdates. These oxides are observed to exhibit un-

conventional superconductivity [1] and research is going

on to understand the mechanism [2] of this new quantum

order due to strong electron-electron interaction. Pseudo

gap formation [3], metal-insulator transitions [4,5] and

high-voltage applications are the other significant prop-

erties which draw a considerable attention to 4d TMO.

Some related data were reported by daga et al. [6].

The density functional theory (DFT) is a good ap-

proach for the description of ground state properties of

metals, semiconductors, and insulators. The success of

this technique is that it has allowed us to better under-

stand materials and processes. It has deepened the inter-

pretation of experimental findings. We have used AB-

INIT computer code in order to perform first-principles

DFT calculations. This code is open source ab initio elec-

tronic structure calculation software and has been under

continuous development.

In the present study we calculated lattice constant,

bulk modulus and total energy along with its components

for SrMoO3 perovskite. The chosen perovskite has sim-

ple, cubic Pm3m symmetry.

2. Calculation Method

There are some approximations existing which permit the

calculation of certain physical quantities quite accurately.

In physics the most widely used and the simplest ap-

proximation is the local-density approximation (LDA). It

is based upon exact exchange energy for a uniform elec-

tron gas. The unknown part is exchange-correlation part

of the total-energy functional and it must be approxi-

mated. The functional depends only on the density at the

coordinate. Generalized gradient approximations (GGA)

are still local but also take into account the gradient of

the density at the same coordinate.

In this work, LDA and GGA density functionals are

considered for computation of lattice parameter, bulk

modulus and the total energy. The calculations are carried

out using numerical implementation of the formulation of

DFT; the ABINIT code, based on the DFT using plane

waves and pseudopotentials. Plane waves are used as a

basis set for the electronic wave functions. Many input

variables are needed to run the ABINIT code for the cal-

culations. The main input variables have been listed in

Table 1. “Spgroup” defines space group number of the

perovskite in the input file. “acell” parameter gives the

length scales by which dimensionless primitive transla-

tions are to be multiplied and is specified in Bohr atomic

units. We include input variables “ntypat” and “znucl”,

where “ntypat” gives the number of types of atoms and

“znucl” gives nuclear charge Z of the elements in order

A. DAGA, S. SHARMA

1892

Table 1. Main input variables used for calculation for

SrMoO3.

Input Variables LDA GGA

spgroup 221 221

acell (Bohr) 7.55 7.652

ntypat 3 3

znucl 38 42 8 38 42 8

natom 5 5

typat 1 2 3 3 3 1 2 3 3 3

xred 0.5 0.5 0.5 0.5 0.5 0.5

0.0 0.0 0.0 0.0 0.0 0.0

0.5 0.0 0.0 0.5 0.0 0.0

0.0 0.5 0.0 0.0 0.5 0.0

0.0 0.0 0.5 0.0 0.0 0.5

ixc 1 11

ecut (Hartree) 45 69.57

ntime 10 50

nstep 10 60

toldfe (Hartree) 1.0d-6 1.0d-6

to define the atom types.

Atoms in the unit cell can be described by using vari-

ables “natom” which gives the total number of atoms in

the unit cell; “typat” which is an array that gives an inte-

ger label to every atom in the unit cell to denote its type;

“xred” which gives the atomic locations within unit cell

in coordinates relative to real space primitive translations.

The array “typat” must agree with “xred” and “natom”.

Exchange correlation functional can be included in our

calculation by using “ixc” which has a different integer

value for LDA and GGA. The plane wave basis set can

be defined by “ecut” which is used for kinetic energy

cutoff which controls number of plane waves at given

k-points. We get a good convergence for the bulk total

energy calculation with the choice of cut-off energies at

45 Ha for LDA calculations and 69.57 Ha for GGA for

SrMoO3 4 × 4 × 4 Monkhorst-Pack mesh grid.

The number of self-consistent field cycles (SCF) are

defined by variables “nstep” which gives the maximum

number of SCF iterations and “toldfe” which sets a tol-

erance for absolute differences of total energy that reached

twice successively, will cause one SCF cycle to stop.

Apart from these variables input files also include vari-

ables for optimization of the lattice parameters and vari-

ables defining k-points grids.

3. Results & Discussions

This work analyses the overall performance of the local

density approximation and generalized gradient approxi-

mation in describing the structural properties of SrMoO3

perovskite. The overall accuracy of the calculated values

depends on both the accuracy of the potentials associated

with the exchange correlation and non additive kinetic

functionals as well as on these functionals themselves.

The computed values of total free energy and the differ-

ent components of the total energy for this perovskite

have been assembled in Table 2. The different compo-

nents of total energy are kinetic energy, Hartree energy,

exchange and correlation (XC) energy, Local pseudopo-

tential energy, Non-local pseudopotential energy, local

pseudopotential “core correction” (PspCore) energy and

Ewald energy. On average, LDA total free energy and its

components are similar to the GGA ones. But viewing

precisely both the LDA total energy and its components

are all smaller in absolute magnitude than the corre-

sponding calculated values in GGA.

In Table 3, it is observed that, near the nucleus, the

LDA density is too small while GGA gives an increased

charge density due to the lower value at short distances.

This increase in the GGA density results in an increase in

the magnitude of all the components of the total energy.

Consequently, the GGA yields improvements not only in

Exc but also in other components of the total energy be-

cause of the exchange-correlation at the nucleus.

Lattice constant of the perovskite is calculated using a

series of total energy calculations. Energy versus lattice

constant curve is obtained from this calculation. The cor-

responding “acell” parameter for which minima of en-

ergy occurs is the lattice parameter for the perovskite.

The curves obtained using LDA and GGA are shown in

the Figures 1 and 2 respectively. The value of lattice

parameter within LDA is 3.9897 Å and within GGA is

4.0423 Å. Both the values calculated are in good agree-

ment with the experimental value 3.98 Å [6].

Figure 1. Total energy versus acell using LDA.

Figure 2. Total energy versus acell using GGA.

A. DAGA, S. SHARMA

1893

Table 2. Eight components of total free energy of SrMoO3.

Energy Components (Hartree) LDA GGA

Kinetic energy 4.320E+01 4.558E+01

Hartree energy 1.913E+01 2.022E+01

XC energy –1.278E+01 –1.310E+01

Loc.psp. energy –6.732E+01 –7.123E+01

NL psp. energy –2.060E+00 –2.352E+00

PspCore energy 5.007E+00 4.813E+00

Ewald energy –4.162E+01 –4.108E+01

Etotal (ev) –1.536E+03 –1.555E+03

Figure 3. B.E. versus atomic Vol. using LDA.

Figure 4. B.E. versus atomic Vol. using GGA.

Table 3. Maximum & minimum values of charge density along with their reduced coordinates for SrMoO3.

SrMO3 Max. I

[el/Bohr^3] Red.

Coord Max. II

[el/Bohr^3] Red.

Coord Min. I

[el/Bohr^3] Red.

Coord Min. II

[el/Bohr^3] Red.

Coord

SrMoO3 9.9498E−01 0.5185 9.9498E−01 0.4815 1.2087E−06 0.5000 4.1731E−06 0.000

(LDA) 0.9444 0.9444 0.5000 0.000

0.9815 0.9815 0.5000 0.000

SrMoO3 1.08 0.5000 1.08 0.9556 3.9706E−07 0.5000 4.7765E−07 0.000

(GGA) 0.9556 0.5000 0.5000 0.000

0.9667 0.9667 0.5000 0.000

Bulk modulus for SrMoO3 perovskite can be obtained

by binding energy per atom versus atomic volume curves.

A quadratic polynomial fitting of the curves is then ob-

tained. From this polynomial, “c2” which is the coeffi-

cient of x2 in the quadratic equation is obtained. By using

the atomic volume and the calculated value of c2, we

obtained the bulk modulus for the perovskite. Binding

energy per atom versus atomic volume curves forSrMoO3

perovskite using LDA & GGA are shown in the Figures

3 and 4.

The computed value of Bulk modulus within LDA is

143.025 GPa and within GGA is 146.1381 GPa which is

in accordance with the reported value calculated by oth-

ers [7]. The maximum and minimum values of the charge

density for this perovskite along with their reduced coor-

dinates have been assembled in Table 3. The values are

slightly greater in case of GGA.

4. Conclusion

The structural properties of transition metal oxide,

SrMoO3, with cubic perovskite structure are studied us-

ing an ab-initio pseudopotential method using ABINIT

code using LDA & GGA. A detailed description of its

total free energy and its different components are given.

Maximum and minimum value of charge density has also

been provided which is helpful in knowledge of charge

accumulation in the unit cell of the considered perovskite.

It is found that both GGA and LDA functionals lead to a

reasonable description of the key parameters of the total

energy of SrMoO3 perovskite. The calculated energies

depend on both the accuracy of the potentials associated

with the exchange correlation and non additive kinetic

functionals as well as on these functionals themselves.

Both the total energy and its components have larger

values in GGA than in LDA, which is associated with the

calculated values of charge density that show the LDA

density is too small while GGA has an increased charge

density. This increase in the GGA density results in an

increase in the magnitude of all the components of the

total energy. Consequently, the GGA yields improve-

ments not only in Exc but also in other components of

A. DAGA, S. SHARMA

1894

the total energy.

On the other hand, quantities related to the single-par-

ticle eigenvalues are not improved in GGA relative to

LDA. On average, LDA lattice parameters and bulk

modulus agree better than the GGA ones. The LDA lat-

tice parameter is almost exactly similar to the experi-

mental data, whereas the GGA lattice parameter is some-

what overestimated. Similarly LDA bulk modulus is closer

to the reported values of bulk modulus for SrMoO3

perovskite as compared to GGA bulk modulus. This in-

dicates that the errors in the non additive kinetic energy

and exchange-correlation energy functionals and poten-

tials compensate better at the LDA than GGA level. Such

compensation can be explained in the LDA case by the

fact that the exchange and kinetic functionals use the

same approximation to one-particle density matrix. Un-

fortunately, a similar construction of a pair of functionals

based on the same approximation to one-particle density

matrix is not unique for gradient-dependent functional.

Lattice parameters and bulk modulus are found to com-

pare well with the available data in the literature also

show the relevance of this approach for the SrMoO3

perovskite.

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