Thermodynamics of order-disorder transformations in vanadium carbide

Abstract

Some of the nonstoichiometric carbides of the transition metals (e.g. VCx) undergo transformations to ordered phases at specific values of x. In a thermodynamic study of such order-disorder transformations the latent heats of the reactions VC0.833=V6C5 and VC0.875=V8C7 were measured using differential thermal analysis (DTA) and gave values of 5.7±2.8 cal g−1 and 6.0±2.4 cal g−1 (1 cal=4.1855 J), respectively. For well-annealed specimens intermediate in carbon-to-metal ratio between these two compositions, DTA indicated the coexistence of domains of both ordered phases. The implication is that the nonstoichiometric, disordered, NaCl-structure phase VCx does not represent the lowest energy state of vanadium carbide at room temperature for any value of x. This result may apply to the other isomorphic carbides, i.e. TiCx, ZrCx, HfCx, NbCx and TaCx. The measured temperatures corresponding to the onset of the transformations were 1184±12‡ C for V6C5 and 1112±8‡ C for V8C7, but the centre of the distribution was approximately 50‡ C higher in each case. A rationalization of the existence of first-order transitions and an estimate of the latent heats expected from the measured transition temperatures were attempted using the Bragg-Williams theory of order-disorder transformations. The results are consistent with experiment, though the adequacy of this approximation for such a complex case is questionable.