LATTICE DYNAMICS OF CRYSTALS HAVING RUTILE STRUCTURE (FeF2, MnF2, MgF2 and TiO2)

Abstract

Using Born's theory the secular equation has been formulated for the dynamics of the rutile structure. Group theoretical method has been used to decompose it into smaller degree equations at the centre of the Brillouin zone. On account of the electrostatic contribution to the elements of the secular equation these elements do not have unique values at the wave vector q = 0, but rather depend on the direction in which the wave vector tends to zero. In order to get the expressions for all the infrared active transverse and longitudinal modes, it is necessary to make the calculations for the wave vector ->O along the two non-equivalent crystallographic axes of the rutile structure. The  frequencies of vibration of iron fluoride,Manganese fluoride,magnesium fluoride and rutile have been calculated using rigid ion model with short range axially symmetric forces and long range Coulomb forces.