Thermal equations of state of the α, β, and ω phases of zirconium

We have conducted synchrotron x-ray diffraction studies on high purity zirconium metal at pressures (P) up to 17 GPa and temperatures (T) up to 973 K. Unit cell volumes (V) were derived from the refinements of x-ray diffraction data for the α, β, and ω phases of zirconium and fitted to a Birch-Murnaghan equation of state with the pressure derivative of the bulk modulus, K0′, fixed at 4.0. The derived thermoelastic parameters for α zirconium are isothermal bulk modulus K0 =92 (3) GPa, temperature derivative of bulk modulus (δK δT)P =-2.3 (8) × 10-2 GPa K, volumetric thermal expansivity αT =a+bT with a=1.5 (±0.8) × 10-5 K-1 and b=1.7 (±1.4) × 10-8 K-2, and the pressure derivative of thermal expansion (δ,α δ,P)T =-2.7 (9) × 10-6 GPa-1 K-1. For the β phase we obtained an isothermal bulk modulus of KT =66 (3) GPa at 973 K and a unit-cell volume of V (973 K) =47.7 (3) Å3 at ambient pressure. For the ω zirconium we obtained K0 =90 (5) GPa. Within the experimental errors, the K0 values we determined for the α and ω phases and volumetric thermal expansion for the α phase are in agreement with previous experimental results, whereas all other thermoelastic parameters represent the first determinations for the three crystalline phases of zirconium metal.