Characterization of fluorine-doped magnesium oxide: A computer simulation study

1. Phys. Printed

Chew.

Solids

Vol.

51.

No.

8, pp.

92%931.

1990

0022-3697/90

53.00

Q 1990 Pergmoll

in Great Britain.

+ 0.00 F?ess

plc

CHARACTERIZATION OF FLUORINE-DOPED MAGNESIUM OXIDE: A COMPUTER SIMULATION STUDY RAVINDRAPANDEY and A. BARRYKUNZ Department of Physics, Michigan Technological University, Houghton, MI 49931, U.S.A. (Received

30 October

1989; accepted 24 January

1990)

Abstract-A computer simulation study is performed to characterize F--doped MgO. The impurity potentials, namely F--Mg2+ and F--O*- are derived using ICECAP and are then used to study Fdiffusion in MgO. The activation energy by vacancy mechanism comes out to be 1.53 eV. The excitonic state associated with the F- ion is also studied. Furthermore, the excess electron associated with the F- ion is predicted to be unbound in the lattice. Keywords:

Magnesium oxide, computer simulation, diffusion, charge states.

environment as a Coulomb potential and also by means of short-range interactions of the cluster ions with the shell model ions. The harmonic distortion and polarization of the embedding lattice are then determined by simulating the defect cluster by a set of point charges whose low-order electrostatic multipole moments match those of the defect cluster. ICECAP therefore combines electronic-structure calculations with the shell model treatment of lattice polarization and distortion in a mathematically and physically consistent way. (For a detailed discussion, we refer to Harding ef al. [2] and Pandey and Vail [4].) In the shell model, each point ion consists of a core of charge x and a shell of charge y, such that the total ionic charge is the sum of core and shell charges. The ionic polarization is described by the displacement of a shell from a massive core; the two being connected by a harmonic spring with a force constant k. ICECAP applies the minimum energy principle to an infinite crystal of MgO containing the defect. The total defect crystal energy is minimized with respect to all shell and core positions and simultaneously with respect to variational parameters in the defect cluster wave function. This minimization is updated while the nuclear positions of the defect cluster are varied to give overall minimization of the total defect crystal energy. That is,

1. INTRODUCTION Fluorine ions are found to be effective in promoting densification of MgO during hot-pressing or sintering [I]. Furthermore, an F- ion substituting O*- in MgO can be considered as an analog of the fission product, I- in nuclear fuel oxides such as UO,. Thus there is a significant interest in characterizing fluorine-doped MgO and in this paper we intend to achieve this objective by studying optical and transport properties of fluorine ion along with its different charge states in MgO. Our simulation procedure is based on the embedded cluster model using the program package ICECAP (ionic crystals with electronic cluster, automatic program) (21.The ICECAP procedure with its long-range lattice relaxation capability is ideal for such a study. In Section 2 we give a brief description of our computational model simulating the impurity, F- in MgO. The results are presented and discussed in Section 3, and summarized in Section 4.

2. COMPUTATIONAL

MODEL

The impurity, fluorine, in MgO is considered to occupy the on-center position as F- substituting in the lattice for the O*- ion. Since MgO has rock-salt structure with octahedral site symmetry, F--doped MgO is modeled in ICECAP as a defect cluster of F- ions at the cluster center, six nearest-neighbor MgrC ions at the sites (a, o, o) and/or 12 next-nearestneighbor O’- ions at the sites (a, o, o) where u is the nearest-neighbor spacing. In this way, the electronic structure of the F- ion and all the neighboring ions that are assumed to be significantly affected by the F- ion are described quantum-mechanically. The defect cluster is embedded in the classical shell model lattice [3]. The cluster is therefore seen by its

dE -=aft

dE aa

s-z

dE aR,

0.

This results in obtaining lattice (R), electronic (a), and cluster (R,) configurations and the total defect crystal energy E. To describe the electronic structure of the defect cluster, we use the unrestricted Hartree-Fock selfconsistent field (UHF-SCF) approximation obtaining 929

RAVINDRA

930

the Fock equation (Ys):

for the one-electron

PANDEYand A. BARRY KUNZ

functions

Table 1. Impurity-near-neighbor short-range potentials in MgOderivedfromquantumcluster, V = A exp(-r/p) --CT-~ A (W

F(r)tik(r) = rttilr(r),

k = 1,2, . . . J,

(2)

where the Fock operator F is F(r)=

-V2-2~zj~r-Rj~-‘+2

j

x

(3)

and p(r’, y) = ? +&‘)$li+.(y), k’-I

2

2467.24 20483.20 1275.20 22764.30

C (ev.A6)

0.2515 0.2862 0.3012 0.1490

0.0 14.4t 0.0 20.37

t Calculated from the Slater-Kirkwood formula, Ref. 10. $ Empirically fitted, Ref. 7.

dr’lr-r’l-l

dvSCY- r’)[l - f’(r, y)lp(r’, Y),

F--M$+ F--0202--Mg*+ 02--0*-$

1 (A)

(4)

where r’ = (r, s), r is position and s is spin, Rj and Zj are nuclear positions and charges, and P(r, y) is the electron pairwise interchange operator. In the unrestricted Hartree-Fock approximation (UHF), $k is a spin eigenstate only, and not an eigenstate of symmetry. In eqn (4) p is the Fock-Dirac, oneparticle density. We solve the Fock equation using the linear combination of atomic orbitals (LCAO) technique as described by Roothaan [5]. In the defect cluster the atomic orbital basis sets for M$+ and 02- are taken from the work of Pandey and Vail [4]. These basis sets are Gaussians of the form (7, 7/4) and are obtained from the embedded (perfect-lattice) cluster [i.e. either M$+ (0*-J or (Mg’+& 02-] calculations using ICECAP. The basis set associated with the F- ion is based on Huzinaga’s (4 3/4) set for negative fluorine [6]. [It is to be noted here that the cluster 95 basic functions F(Mg’+)b (O*-),2 contains associated with 190 electrons.] The shell model parameters for the embedding lattice, MgO, is taken from Sangster and Stoneham [7j. 3. RESULTS AND DISCUSSION 3.1. Impurity potential and diffusion The ionic interactions can be represented as the sum of long-range Coulomb interactions and shortrange non-Coulombic interactions caused by the overlap of the electron cloud of the two ions. A pair potential description of short-range interactions is generally of the Born-Mayer type: V(r) = A exp( - r/p) which may be supplemented by the so-called dispersive terms in rb6. In the present work, impurity short-range are derived potentials, i.e. F--Mg2+ and F--02from the embedded quantum cluster method [4] developed by us. Our approach has been to dilate and compress the quantum-mechanical cluster by as much as 20%. Impurity potentials are then

determined such that the same sequence of distortions, applied to the F--doped shell model lattice, produces the same energy dependence. In all cases, the embedding lattice is fully relaxed. The parameters for the derived potentials are given in Table 1 along with those for host-lattice ions that were empirically fitted to bulk properties of MgO. The diffusion process is known to provide an important and sensitive test of the quality of the derived potentials. We now use the derived impurity potentials to calculate the thermal activation energy for the F- diffusion in MgO using HADES [8]. We note here that ICECAP may be used to analyze the impurity diffusion process. However, HADES calculations require less computational time than ICECAP calculations providing a very efficient extension of a single defect analysis to a large number of processes. The activation energy by vacancy mechanism is taken to be the difference between the initial and so-called saddle point configurations. The initial configuration has a F- ion substitutional at an O?site, the origin, with a second neighbor O*- vacancy at (110) a. The saddle-point configuration is taken to consist of the F- ion at (0.5,0.5,0.0) a with the O*vacancies at (0, 0,O) and (1, 1,O) a sites. The calculated activation energy by vacancy mechanism comes out to be 1.53 eV. For the diffusion by interstitial mechanism, in the initial configuration, the F- ion is at the center of a cube with alternating anions and cations at its comers. In the activated configuration it is at the center of a face of that cube. The calculated activation energy by interstitial mechanism is found to be 1.64 eV. No experimental study has so far been made for the diffusion of the F- ion in MgO. However, we note that the activation energy either by vacancy or interstitial mechanism is lower than that for oxygen self-diffusion (_ 3 eV) in MgO. Hence, the faster makes of F- ions in the lattice diffusion rearrangement of ions possible, contributing towards densification of F--doped MgO. 3.2. Excitonic-like state We describe the local excitonic process associated with F- in MgO as the excitation of an electron from a 2~” state to a localized 2ps 3s’ state, with the excited electron and its hole resonating at the F- site. An electron-hole pair in the triplet spin state therefore

Characterization

of fluorine-doped

the low-lying excited state of the F- ion. Excitation energy is obtained by calculating ground and excited-state configurations separately and then taking the difference in energy of these two configurations. Therefore, spectroscopy will not be obtained by using Koopman’s theorem, but rather by evaluation of total system energies and their differences. Our defect cluster consists of the F- ion and the nearest-neighbor Mg-‘+ ions. s-Type primitives are added to the F- basis set to describe the 2ps 3s’ excited state of the F-. The calculated transition energy associated with 2p6-+2p5 3s’ excitation comes out to be 15.2 eV. This is in contrast to what has been

defines

calculated for isovalent impurities like S’- in MgO where the excitation energy is predicted to be in the bandgap of MgO. (For S2-, the excitation energy is found to be 7.09 eV [9].)

magnesium oxide

931

Mg’+ ions or localized on one of the M8+ ions in a lower symmetry than the octahedral symmetry about the F site. This has been achieved by adding a 13s) type orbital to the minimal basis set (I Is), 12s) and 12~)) of Mg?+ while associating only the minimal basis set with F in the defect cluster. Both the cases are referred to as symmetrical and asymmetrical configurations, respectively, in Table 2. For completeness, Table 2 also includes the energies for F’- in MgO as well. In all cases, the excess electron is predicted to be unbound to the F- ion in MgO. However, the magnitude of the energy involved (-0.8 eV) indicates that the F’- ion might become stabilized in the presence of defects in the lattice. For example, the F’- ion may like the F- ion with an electron localized into a second-neighbor oxygen vacancy.

3.3. Charge states In nuclear fuel oxides, it has been suggested that the fission product, iodine, may exist in different charge states, namely I-, 12- and I’-, substituting 02- in the lattice. In the present work we have investigated this suggestion by studying the charge states of fluorine in MgO. The defect cluster now consists of fluorine substituting O’- ion and six nearest-neighbor Mg” ions only. The fluorine in monovalent charge state

(i.e. F-) has a net positive charge in the lattice. It is therefore expected to bind an additional electron becoming F2- ion in the lattice. To facilitate the localization of an excess electron at the F site, we add a 13s) type orbital taken from Huginaga to the minima1 basis set (I Is), 12s) and 12~)) of F- in the defect cluster. The calculated ICECAP energies are given in Table 2. We have also considered the alternative possibility of localization of an excess electron at Mg?+ sites. In this case, the F?- ion may be like the F- ion with an excess electron either shared by six near-neighbor Table 2. ICECAP energies for the Pwhere n = 1,2,3

(Mg?+), cluster

Defect cluster energies (eV) F- basis Added (3s) Minimal

Mg?+ basis

F-

F*-

F’-

Minimal Added 13s) Symmetrical Asymmetrical

0

0.8

3.63

3.44 3.96

5.17 6.02

t The F- (Mg”), to be zero.

cluster energy -35105.77 eV is taken

4. CONCLUSION We have calculated the F--near-neighbor potentials and have obtained reasonable values for the diffusion of F- ion in MgO predicting the lower

activation energy (- 1.5 eV) for the vacancy mechanism. The excitation energy associated with the 2p6-2ps 3s transition of the F- ion is found to be 15.2 eV. The excess electron associated with the F- ion is predicted to be unbound in the lattice. Acknorcledgements-This work is supported by the Office of Naval Research 0014-89-H-160. We are grateful to Dr A. M. Stoneham for suggesting this study.

REFERENCES 1. Ikegami T., Kobaynshi M., Moriyoshi Y. and Shiraski

S., J. Am. &ram. Sot. 63, 640 (1980). 2. Harding J. H., Harker A. H., Keegstra P. B., Pandey R., Vail J. M. and Woodward C., Physica. (B, C) 131, 151 (1985). 3. Dick B. G. and Overhauser A. W., Whys. Rec. 112, 90 (1958). 4. Pandey R. and Vail J. M., J. Phys: Condens. Mutter 1, 2801 (1989). 5. Roothaan C. C. J., Rev. mod. Phys. 23, 69 (1951). 6. Huzinaga S. (Editor) Gaussian B&c Sers fir &folecu[ar Calculations. Elsevier. New York (1984). 7. Sangster M. J. and Stoneham A. h., Phil. Msg. B43, 597 (1981).

8. Norgett M. J., AERE Harwell Report R7650 (1974). 9. Pandey R., Zuo J. and Kunz A. B., Phys. Rev. B39, (1989).

10. Fowler P. W., Knowles P. J. and Pyper N. C., Molec. Phys. 56, 83 (1985) and references therein.