2013 INTERNATIONAL CONFERENCE ON COMPUTING, ELECTRICAL AND ELECTRONIC ENGINEERING (ICCEEE)

437

Ab initio Method Study of Ionic Conductor CaF2

Nahed Osman

Dept. of Physics, Alzaim Alazhari University

Khartoum, Sudan nahedosman@yahoo.com

Nodar Osman

Physics department, Sudan University of Science and Tech.

Khartoum, Sudan

Alwaleed Adllan

Afriac City of Technology

Khartoum, Sudan

Gamar Alanbia Bilal

Physics department, Sudan University of Science and Tech.

Khartoum, Sudan qamar2008@yahoo.com

Karlo Ayuel

College of Applied Science, Juba University

Juba, South Sudan

Abstract— CaF2, fluorite, is a prime candidate for solid state

electrolytes used in batteries could replaced of SiO2 in metal-oxide

semiconductor (MOS) technology. Using Ab initio density

functional theory (DFT) method corrected by plane augmented

waves (PAW) and ultra soft pseudopotential, the structural,

electronic, lattice constant, band gab, density of states in addition to

thermal and optical properties have been investigated. The results

have a good agreement with the experimental data.

Keywords: Abinitio, DFT, CaF2, lattice constant, thermal

property, optical property

I. INTRODUCTION

The alkaline-earth fluorides XF2 (X= Ca, Sr, Ba) generally

crystallize to a cubic fluorite structure (Fm3m) consisting of a

close-packed cubic alkali ( X ) lattice with fluorine ( F )

occupying the tetrahedral sites [1].The aim of the present work

is to add to the general understanding of the ionic conduction

through the knowledge of electronic and phonon properties

using the abinitio pseudo potential method based on the

density functional theory (DFT). Generalized gradient

approximation (GGA) and the local density approximation

(LDA) using plane augmented waves (PAW) and ultra soft

(US) were implemented [2,3]. The choice of (GGA) lies with

the fact that the GGAs are intended to be an improvement on

the conventional local density approximation and indeed

perform better in certain situations [4].Ionic conductors are

promising candidates for solid state electrolytes used in

batteries [5]. The fluorite CaF2 is a proto type ionic conductor

showing a strong increase of conductivity with variation of

external parameters such as temperature that saturates

at1420K, where it becomes comparable to that of a molten

salt; the melting temperature is near 1690K [6]. In addition it

possesses intrinsic optical properties, superior character at

high temperature and is the subject of several experimental

and theoretical studies in the recent past [7–10]. In order to

add to the general understanding of ionic conduction we have

investigated the static and dynamic lattice properties of CaF2

both theoretically by means of abinitio calculations as well as

experimentally by coherent inelastic neutron scattering. As the

process of ionic conduction involves hopping over potential

barriers, ionic motion is an intrinsically anharmonic and

strongly temperature dependent process. Even at temperatures

below the onset of ionic conductivity, the ions will experience

the anharmonic potential. [11].

Fig.1 Crystal structure for CaF2

Phonons are the primary excitations, which influence the

thermodynamic behavior. Therefore, a systematic

characterization of the phonon density of states (PDOS) and

dispersion relations of alkaline-earth fluorides is highly

desirable. There are many experimental and theoretical

characterizations about the phonon characteristic of CaF2

[11−15] as early as 1970, Elcombe and Pryor [11] obtained

the phonon spectrum from the inelastic neutron scattering on a

triple-axis spectrometer experiment. Merawa et al [12]

evaluated the IR and Raman central zone phonon frequencies

of CaF2 by using the periodic abinitio linear combination of

atomic orbital method in several different approximations.

Schmalzl et al [11] reported the phonon frequencies

(dispersion and density of state) both experimentally and

theoretically. Later, Verstraete and Gonze[14] studied the

dielectric, and vibrational properties of CaF2 from first

principles using density functional theory. Recently, Ricci et

al [15] showed that the phonon confinement has been pointed

as the main cause of the broadening and the blue-shift of the

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Raman peak in CaF2 which is a prime candidate for a

replacement of SiO2 in metal-oxide-semiconductor (MOS)

technology, due to its excellent lattice matching to silicon,

with only 0.6% mismatch at room temperature [16]. In this

paper, we focus on the phonon properties, including the

phonon density of state and phonon dispersion curves, of

fluorite. Since the phonon properties of solids provide an

important link with thermodynamic behaviors of crystals, thus

we have also obtained some thermodynamic properties of

CaF2. All calculations are implemented through the Quantum

ESPRESSO code [3], by which we have successfully

investigated the elastic properties of CaF2; the results obtained

are well consistent with the available experimental data and

other theoretical results [17].

Furthermore, phonon dispersion curves are an essential key

ingredient for the calculation of specific heat, thermal

expansion and vibrational entropy. In addition the phonons

play an important role not only in the formation of various

defects, hopping over potential barriers and disorder but also

in several mechanical and optical properties. Hence, a

comprehensive theoretical study is not only essential to verify

the observed experimental data but also to find a correlation

between the alkaline compounds and to establish stability of

their structures [1].

Ground state Properties

The ground-state properties of CaF2 are obtained from

Density functional theory in the local-density approximation

of Ceperley and Alder. In LDA, one needs to solve the Kohn-

Sham equation

(1)(r),LDA

nk

ψLDA

nk

E=(r)LDA

nk

ψ(r)

xc

V+(r)

H

V+(r)

ps

V+2

2m

2

Where Vps and VH are the pseudopotential (PP) of the ions

and the Hartree potentials, respectively. Vxc is the exchange

correlation potential.

C. Thermal properties

Heat capacities are fundamental quantities characterizing

thermal properties of solids, their systematic experimental

investigations, appropriate theoretical interpretations, and

detailed numerical descriptions are permanent topics of solid

state physics.

The calculation of thermal expansion coefficient has been

carried out in the quasi harmonic approximation (QHA). In

QHA thermal expansion coefficient CVh(T) is related to the

Grüneisen parameter by the following relation:

,

1

)(1)(3)(

n

nTnATpkTpnRkTpC (2)

the coefficients of which, A1, A2, A3,. . ., are accounting for

lattice expansion and anharmonicity effects.

II. METHODOLOGY

DFT calculations are carried out either within the local

density approximation (LDA) or within the PBE form of the

generalized gradient approximation (GGA) using the

Quantum ESPRESSO package [3]. Several ultrasoft

pseudopotentials (US-PPs) and projector augmented-wave

(PAW) have been tested, calculating the band structure,

density of state, thermal and optical properties. The US-PPs

and the PAW pseudopotentials are constructed with the

same recipe and using the local density approximation or the

generalized gradient approximation for the exchange and

correlation energies.

III. RESULTES

A. Structural and electronic properties

CaF2 has fcc structure with one Ca and two F atoms in the unit

cell situate at (0, 0, 0), ± ( 1/4a, 1/4a, 1/4a,)Å as shown in

(Fig.1). Structure optimization in LDA gives a lattice constant

of 5.318 Å while in GGA gives 5.503 Å. In this work the band

structure and density of states (DOS) for CaF2 crystal has

been obtained by Quantum ESPRESSO code. As a starting

point of our calculations, we have tested how different

methods reproduce the lattice constant (a), where in the first

step; the equilibrium lattice parameter has been computed by

minimizing the total energy calculated for different

pseudpotintials and it found that the calculated result for the

lattice constant has good agreement with the experimental

values. Table1 has comparison with the available experimental

and theoretical values. TABLE I LATTICE PARAMETER IN (ANGSTROME)

Present work

Other calculations

Pz-PAW

Pz-US

Pbe-PAW

Pbe-US

Theoretical

Experimental

5.318

5.318

5.503

5.503

5.501a

5.466b

The self-consistent band structures along with the electronic

density of states (DOS) for CaF2 are presented in Fig. 2, in

which the DFT calculations have been performed in order to

improve the band gap along the high symmetry directions.

439

Fig.2 CaF2Band Structure and density of states (DOS) using

different pseudo-potentials (a) pz-US, (b)pbe-PAW, (c) pz-

PAW, (d) pbe-US

Fig.3 The phonon dispersion curves and corresponding

PDOS using different pseudo-potentials (a) pbe-PAW,(b)pbe-

US, (c) pz-PAW, (d) pz-US

B. Phonon dispersion

In order to investigate the thermal and optical properties of

CaF2 a series of self consistent calculations were carried out

and revealed a good agreement with the theoretical and

experimental available values as in table 1. Refer to Fig.3 at

the Γ point; there is an extra complication in the calculation

of the phonons. In crystals the degeneracy of the transverse

optical (TO) and longitudinal optical (LO) modes is broken

due to the electric field that is generated during vibration.

CaF2 is a typically ionic compound, so the polarity causes the

intensive LO/TO splitting.

C. Specific heat

Fig.4 shows the Calculated heat capacity CV(JK-1

MOL-1

)versus temperature T(K) using equation 2, it is obvious that

the PAW psedos are overlapping as well as US pseudo.

Fig.4 Calculated heat capacity CV(JK

-1MOL

-1 )versus

temperature T(K)

440

TABLE I. CALCULATED FREQUENCY OF THE PHONON MODES AT SOME

MAIN SYMMETRY POINTS OF THE BRILLOUIN ZONE FOR 2CaF

Pseudo-potential

Parameter

Present

calculation

Other

calculation

Experimental

Pbe-paw LO(cm-1) TO(cm-1)

436.91 229.81

453.82a 225.96a

466.35d

257.18f

Pbe-us LO(cm-1)

TO(cm-1)

433.00

228.96

447.75c

227.08c

466.35d

257.16e

Pz-paw LO(cm-1) TO(cm-1)

494.18 280.93

486.56b 286.95c

473.01b

260.34b

Pz-us LO(cm-1)

TO(cm-1)

485.82

281.46

473.13c

289.00h,i

473.01b

269.98k aRef[1], bRef[11], cRef[17], dRef[18], eRef[12], fRef[19], gRef[20], h,iRef[21,22], kRef[23]

IV. CONCLUSION

Both the electronic and phonon properties calculations suggest

that this compound has superionic nature and the ionic

bonding is in the direction of Ca and F

ion. The LO –TO

splitting is maximum for CaF2, which suggests that CaF2 is

most ionic. To the best of our knowledge, this is the first

report using of the mentioned pseudo potentials (constructed

by [24] to calculate the electronic and phonon properties of

CaF2 using quantum espresso code. This work has been done

in Sudan High Performs Computing.

ACKNOWLEDGMENT

The authors would like to express their thanks to the

following: Sudan cluster at Sudan university of Sience and

Technology, HAKEEM HPC Africa City of Technology,and

to Mr. Anas Omer for their continuous supporting during

manuscript.

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