Rigid-Ion Model of Ionic Crystal

To investigate the possibility of a 3-D intrinsic gap mode in ionic crystals we use the tabulated rigid ion potential for NaI from Table's 2 and 4 of Ref.[1]. The potential has the following form
The lattice constant for the fcc structure is chosen to be 6.35A, within 1% of the experimental value [2]. The calculated TO frequency is WTO=2.51*1013rad/s, within 5% of the experimental value of 2.39*1013rad/s [2]. The gap between the optic and acoustic branches extends from W+=2.41*1013rad/s to W-=1.46*1013rad/s.

In carrying out the MD calculations on a 216-ion cube with periodic boundary conditions the method of Sangster and Dixon [3] has been used to evaluate the Ewald sum. For this method the cut-off distance in real space is approximately half the length, L/2, of the cube (the interaction of sixth neighboring shell is counted), and the reciprocal lattice is summed with the convergence parameter of 5.6/L.

In order to investigate the role of point group symmetry on the intrinsic gap mode parameters the zinc blende structure has also been tested with the same potential. A local minimum of the lattice energy occurs at the slightly larger lattice constant, 7.00A.

[1] J.Michielsen, P.Woerlee, F.V.D.Graaf, and J.A.A.Ketelaar, J. Chem. Soc. Faraday Trans. II 71, 1730 (1975).
[2] M.J.L.Sangster, U.Schrooder, and R.M.Atwood, J. Phys. C: Solid State Phys. 11, 1523 (1978).
[3] M.J.L.Sangster and M.Dixon, Adv. Phys. 25, 247 (1976).

Last modified: April 3, 1997