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0987-PP05-08

Lattice Dynamics and Thermodynamics of bcc Vanadium at High Pressures Xianwei Sha and R. E. Cohen Carnegie Institution of Washington, 5251 Broad Branch Road, NW, Washington, DC, 20015

We investigate the lattice dynamics and thermodynamics of nonmagnetic bcc vanadium as a function of temperature and pressure, using the first principles linear response linear-muffin-tinorbital method.

The calculated phonon density of states (DOS) show strong temperature

dependence, different from inelastic neutron scattering measurements where the phonon DOS show little change from room temperature up to 1273 K. We obtain the Helmholtz free energy including both electronic and phonon contributions and calculate various equation of state properties such as the bulk modulus and the thermal expansion coefficient. comparison has been made with available experimental measurements.

PACS number(s): 63.20.-e, 05.70.Ce, 65.40.De, 71.20.Be

A detailed

I.

Introduction It has been long known that the phonon-dispersion relations of bcc vanadium could

not be determined by conventional inelastic neutron scattering techniques since its cross section for neutron scattering is almost totally incoherent. Instead, people use the thermal diffuse scattering of x-rays to measure the phonon frequencies along principle symmetry directions.1 During the past decade, inelastic neutron scattering techniques have been applied to measure the phonon density of states (DOS) of elemental vanadium as well as its temperature and volume dependence.2, 3 The phonon DOS of bcc vanadium showed little change from room temperature up to 1273 K and a large softening at 1673 K, which might be attributed to the phonon-phonon scattering.3 We examined the phonon dispersion and phonon density of states of ferromagnetic bcc Fe using the first-principles linear response linear-muffin-tin-orbital (LMTO) method in the generalized-gradient approximation (GGA), and the theoretical results at both ambient and high pressures show excellent agreements with inelastic neutron scattering data.4 Applying the same theoretical techniques to bcc vanadium might provide important information to understand the interesting temperature dependence of the phonon DOS. When using the quasi-harmonic first-principles linear response method to examine various thermal equation of state properties for ferromagnetic bcc Fe, we find that the calculated thermal expansion coefficients agree well with experiment at low temperatures, but the discrepancies increase at high temperatures.4 One possible reason for the large differences might be magnetic fluctuations at high temperatures, which have not been included in our firstprinciples calculations yet. We would like to apply the same theoretical techniques to examine the thermal properties of nonmagnetic bcc vanadium where such magnetic fluctuations are absent, to see how the theoretical predictions compare to the experiment at high temperatures.

II.

Theoretical methods The Helmholtz free energy F for many metals has three major contributions