Experimental and theoretical studies on the elasticity of tungsten to 13 GPa

Abstract

Compressional (VP) and shear wave (VS) velocities of polycrystalline tungsten have been measured up to ∼13 GPa at room temperature using ultrasonic interferometry in a multi-anvil apparatus. Using finite strain equation of state approaches, the elastic bulk and shear moduli and their pressure dependences are derived yielding KS0=325.9±4.8 GPa, G0=164.1±2.5 GPa, KS0′=3.65±0.05, and G0′=1.28±0.02. On the basis of the current experimental data, the high-pressure behavior of Young's modulus, Poisson's ratio, and ductility/brittleness for tungsten are also investigated. Complementary to the experimental data, the single crystal elastic constants, as well as the elastic anisotropy of tungsten are computed using density functional theory (DFT). The Voigt-Reuss-Hill average of the bulk and shear moduli calculated using the single crystal elastic constants from DFT are found comparable to the current experimental results within about 5%. The present study offers a dataset for the elasticity of polycrystalline bcc tungsten to a maximum pressure more than 25-fold higher than other previous ultrasonic studies, which can further our understanding about the elastic, mechanical, and electronic properties of tungsten under extreme conditions as well as thermodynamic modelling of its alloys.

Pressure Dependence of Structural and Mechanical Properties of Single-Crystal Tungsten: A Molecular Dynamics Study

“…Using linear regression analysis approaches, the elastic moduli of the single-crystal tungsten were calculated. It was found that the Young's modulus, shear modulus, and bulk modulus, as well as Poisson's ratio, show a clear increasing trend with the increase in pressure, which is in good agreement with the experimental results [15]. In addition, the Pugh's modulus ratio of the single-crystal tungsten increases with the increase in pressure, implying that hydrostatic compression can effectively improve the ductility of BCC tungsten.…”

“…Figure 5c illustrates that the bulk modulus B varied in the range of 300-374 GPa, rising almost linearly with the increase in applied pressure. The predicted trends and values of Young's, shear, and bulk moduli agree well with the experimental work of Qi et al [15], who observed that the shear and bulk moduli of polycrystalline tungsten both increase monotonically with an increase in pressure. Obviously, the higher the external pressure, the closer the distance between atoms (see Figure 4) and the more densely compacted the lattice structure.…”

“…It is shown that the Poisson's ratio of the single-crystal tungsten increased from 0.284 to 0.325 at the highest applied pressure of 16 GPa. The computed Poisson's ratio was within the normal range (from 0.27 to 0.42 [26]) of metal materials and showed a clear increase with an increase in pressure, which agrees reasonably with previous experiments [15]. Pugh's modulus ratio B/G is a useful parameter to describe the ductility/brittleness of a solid material.…”

“…In this work, a supercell with a size of 20 a × 20 a × 20 a was constructed by repeating the BCC unit cell along the [001], [010], and [100] directions of the crystal (see the right panel of Figure 1). Periodic boundary conditions were applied in all three directions to determine the bulk properties compared with experimental data in the literature [15]. The quality of the interatomic potential is of vital importance for modeling in MD simulations.…”

“…The first effort may have been made by Katahara et al [14], who measured the elastic moduli of tungsten at pressures up to 0.5 GPa. With the development of measurement techniques, Qi et al [15] recently studied the elastic constants and Poisson's ratio of tungsten and their pressure dependence under pressures up to 13 GPa. Simultaneously, the high-pressure elastic moduli of tungsten were also predicted by using first-principles calculations with the assumption that the temperature of the system approaches absolute zero [16,17].…”