Phonon and elastic instabilities in MoC and MoN

We present several results related to the instability of MoC and MoN in the B1 ~sodium chloride! structure. These compounds were proposed as potential superconductors with moderately high transition temperatures. We show that the elastic instability in B1-structure MoN, demonstrated several years ago, persists at elevated pressures, thus offering little hope of stabilizing this material without chemical doping. For MoC, another material for which stoichiometric fabrication in the B1 structure has not proven possible, we find that all of the cubic elastic constants are positive, indicating elastic stability. Instead, we find X-point phonon instabilities in MoC ~and in MoN as well!, further illustrating the rich behavior of carbo-nitride materials. The early transition metal carbides and nitrides represent a technologically important series of materials, often revealing an interplay between their interesting properties and the incipient instabilities that seem to drive those properties. 1 The important features of these materials include extreme hardness and high melting temperatures, as well as superconductivity in many cases. In some of these materials, the atomistic properties ~e.g., bonding properties! that drive particular macroscopic behaviors can also lead to instabilities that inhibit the stoichiometric B1 ~sodium chloride! structure from forming. MoC and MoN are good examples of this circumstance. In this paper, we report theoretical results related to the stability of B1 MoC and MoN. We show that the elastic instability in MoN is not mitigated, but rather enhanced, by the application of pressure, and that the difficulty in fabricating B1 MoC is due to a phonon instability at the X point in the Brillouin zone ~BZ!. All the calculations reported here were performed with the linear-augmented