A Modified Valence Force Field Approach to Lattice Dynamics of Trigonal Selenium

A modified valence-force-field (VFF) model is applied to the lattice dynamics of trigonal selenium. Five adjustable parameters, four valence-force-constants ( K r , K θ , K r r ' , K r θ ) within intra-chain couplings and one inter-chain force constant ( K R ), are determined from the observed six elastic constants by mans of the least squares method. By using these fore constants, comparable fits to the \(\)-point optical frequencies for the A 1 , E 1 and E 2 modes are obtained except that for the A 2 mode. However, the last can be also accounted for well if the contribution of about 50 cm -1 from the long-range electrostatic interaction is taken into account. The estimation of the above contribution seems reasonable from the view-point of the shell-model analysis due to Chen and Zallen [Phys. Rev. 173 (1968) 833]. In conclusion, the modified VFF employed here reflects the bonding in trigonal Se fairly well.