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