Valence force field treatment of the rutile structure at zero-wave vector

Abstract

The lattice vibrational frequencies at zero-wave vector of 10 MX 2-type rutile structures (X = O, F) are analyzed using a valence bond force field which includes parameters to accommodate the two types of M-X bonds and the forces associated with the two types of nearest neighbor X…X interactions. The two different M-X force constants are constrained to a single adjustable parameter by applying the relationship K mx = K ′ mx( r mx r ′ mx ) 6 . This simplified force field with three adjustable paramete and one constraining relationship reproduces the Raman active phonon frequencies of all 10 rutile compounds with an average error of ⩽ 5% in almost all cases. The agreement between observation and calculation is not as good for the infrared active phonons—a result which is attributed in part to discrepancies in the measurement and analysis of infrared reflectivity spectra and in part to the absence in the simplified valence bond force field of a term to account for forces along the c-axis of the rutile structure.