It is shown that the theory of elasticity under hydrostatic pressure p at zero temperature is unified and simplified by the use of the Gibbs free energy G, rather than the energy E. The minima of G, but not of E, give the equilibrium structure; the second derivatives of G, but not of E, with respect to strains at the equilibrium structure give the zero-temperature elastic constants; the stability of a phase at p is then determined by the same Born stability conditions used at p = 0 when applied to the elastic constants from G. Examples are noted of mistakes due to use of E rather than G.

A low phase turning temperature of 35°C has been observed in the semiconductor-to-metal transition of nanoscale vanadium dioxide (VO2) thin films. The thin films are prepared by reactive ion beam sputtering deposition and subsequent thermal annealing. Both scanning electron microscopy and transmission electron microscopy measurements show that the grain size of the fabricated VO2 thin films are several tens of nanometers. The average height of the crystallite is 20nm and the grain diameter is between 20 and 100nm. The low-temperature phase transition is accompanied by a significant change in the thin film’s infrared transmission property.

First-principles total-energy calculations with WIEN97 on ferromagnetic iron in body-centered tetragonal structure under hydrostatic pressure have shown that the body-centered cubic ͑bcc͒ phase exists up to 1500 kbar of pressure. At that pressure a shear constant vanishes and the phase becomes unstable. A body-centered tetragonal ͑bct͒ phase is shown to come into existence at 1300 kbar and becomes stable at 1825 kbar and above. The minima of a free energy evaluated along the epitaxial Bain path generalized to finite pressure give the tetragonal phases of iron under pressure. Second derivatives of the free energy at the minima define elastic constants of both the bcc and bct phases as functions of pressure, which are appropriate to determine stability. These elastic constants are the same functions of pressure as the usual elastic constants computed from stress-strain relations under pressure. Minima of tetragonal energies calculated at constant volume are shown to be unreliable for determining stability of a phase.

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Line 7 from bottom on the left side of page 104431-3: Wrong correct c 66 ϭϪ65.41 Mbar c 66 ϭϪ0.232 MbarThe numerical error does not affect the other five elastic constants and any conclusion made in the paper.

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