Elastic constants in monocrystalline tungsten under quasi-hydrostatic pressures to 11.3 GPa

Abstract

Compressional (P) and shear (S) wave velocities of tungsten single crystals along the [100] and [110] directions were measured using ultrasonic interferometry at room temperature up to 11.3 GPa. Least-squares fitting of VP[100], VS[100], VP[110], and pressure to finite strain (FS) equations yields the elastic constants: C11 = 523.5(5) GPa, C12 = 205.1(32) GPa, and C44 = 160.8(4) GPa, along with their respective pressure derivatives: C11′=6.20(2), C12′=3.35(1), and C44′=1.65(6). Using the Voigt–Reuss–Hill approximation, the elastic moduli were derived as KS0=311.2(22)GPa and G0=160.2(7)GPa, along with their respective pressure derivatives: KS0′=4.30(4) and G0′=1.56(1). The Debye temperature of tungsten was determined to be 380.7(8) K, showing good agreement with previous calorimetric measurements. The elastic anisotropy increases slightly from 1.01(1) at ambient pressure to 1.03(1) at 11.3 GPa, suggesting that tungsten remains nearly isotropic under compression. Poisson's ratio slightly increased from 0.281(3) to 0.288(3) with pressure. Additionally, Pugh's ratio decreased from 0.512(4) to 0.494(4), while Pettifor's ratio increased from 0.148(10) to 0.175(10) as pressure reached 11.3 GPa. These results suggest that tungsten is weakly ductile compared to the critical thresholds for ductile behavior (i.e., Pugh's ratio <0.6 and Pettifor's ratio >0, indicating ductile behavior), but that its ductility increases marginally under pressure.