ENTROPY DIFFERENCE BETWEEN THE FACE-CENTERED-CUBIC AND HEXAGONAL CLOSE-PACKED CRYSTAL-STRUCTURES

SPHERES can be stacked into two close-packed crystalline arrangements, face-centred cubic (f.c.c.) and hexagonal closed-packed (h.c.p.), whi ch have identical close-packed volumes' and very similar equations of state(2). But they are structurally distinct, implying that they might have different thermodynamic properties and stabilities. Finding a di fference in free energy between the two structures has been the object ive of much theoretical(3,4) and computational(5-7) effort, but withou t a conclusive resolution, Here I report that a significant difference in the pressure-volume (P-V) behaviour can be detected in the vicinit y of a mechanical instability point within a single-occupancy cell mod el(8) of these packings, This model provides an exact thermodynamicall y reversible path between the two structures, and sa, the P-V isotherm s can be integrated to obtain the Gibbs free-energy difference. I find that the f.c.c. phase is more stable by around 0.005RT per mol (where R is the universal gas constant); as the enthalpy difference is negli gible, this implies that the entropy difference is of the order of 0.0 05R for all temperatures up to the melting point.