Direct correlation of observed phonon anomalies and maxima in the generalized susceptibilities of transition metal carbides

The generalized susceptibility, chi(q vector), of both NbC and TaC determined from APW energy band calculations show large maxima to occur at precisely those q vector/sub max/ values at which soft phonon modes were observed by Smith. Maxima in chi (q vector) are predicted for other directions. The locus of these q vector/sub max/ values can be represented by a warped cube of dimension approximately 1.2 (2π/a) in momentum space, in striking agreement with the soft mode surface proposed phenomenologically by Weber. In sharp contrast, the chi(q vector) calculated for both ZrC and HfC (for which no phonon anomalies have been observed) fall off in all symmetry directions away from the zone center. The phonon anomalies in the transition metal carbides are interpreted as due to an ''overscreening'' effect resulting from an anomalous increase of the response function of the conduction electrons. 8 figures, 41 references