Experimental and first-principles studies on the elastic properties of α-hafnium metal under pressure

Compressional and shear wave velocities of the α phase of hafnium have been measured up to 10.4GPa at room temperature using ultrasonic interferometry in a multi-anvil apparatus. A finite strain equation of state analysis yielded Ks0=110.4(5)GPa,G0=54.7(5)GPa,Ks0′=3.7,andG0′=0.6 for the elastic bulk and shear moduli and their pressure derivatives at ambient conditions. Complementary to the experimental data, the single crystal elastic constants, the elastic anisotropy, and the unit cell axial ratio c/a of α-hafnium at high pressures were investigated by Density Functional Theory (DFT) based first principles calculations. A c/a value of 1.605 is predicted for α-Hf at 40GPa, which is in excellent agreement with previous experimental results. The low-pressure derivative of the shear modulus observed in our experimental data up to 10GPa was found to originate from the elastic constant C₄₄, which exhibits negligible pressure dependence within the current experimental pressure range. At higher pressures (>10GPa), C₄₄ was predicted to soften and the shear wave velocity ν_S trended to decrease with pressure, which can be interpreted as a precursor to the α-ω transition similar to that observed in other group IV elements (titanium and zirconium). The acoustic velocities, the bulk and shear moduli, and the acoustic Debye temperature (θD=240.1K) determined from the current experiments were all compared well with those predicted by our theoretical DFT calculations.