Evidence for mechanical softening-hardening dual anomaly in transition metals from shock-compressed vanadium

Solids usually become harder and tougher under compression and turn softer at elevated temperature. Recently, the compression-induced softening and heating-induced hardening dual anomaly was predicted in group VB elements such as vanadium. Here, the evidence for this counterintuitive phenomenon is reported. By using accurate high-temperature, high-pressure (HP) sound velocities measured at Hugoniot states generated by shockwaves, together with first-principles calculations, we observe not only the prominent compression-induced sound velocity reduction but also strong heating-induced sound velocity enhancement in shocked vanadium. The former corresponds to the softening in the shear modulus by compression, whereas the latter reflects the reverse hardening by heat. These experiments also unveil another anomaly in Young's modulus. Based on the experimental and theoretical data, we infer that vanadium might transition from body-centered cubic into two different rhombohedral phases at ∼79 and 116 GPa along the Hugoniot, respectively, which implies a dramatic difference in static and dynamic loading, as well as the significance of deviatoric stress and rate-relevant effects in HP phase transition dynamics.

Figure 1

Calculated high-pressure (HP) and high-temperature (HT) elastic constants of polycrystalline body-centered cubic (BCC) vanadium: (a) $B$ and $C_b$, (b) $E$, and (c) $G$.

Figure 2

Calculated variation of polycrystalline elastic constants and sound velocities of two different rhombohedral (RH1 and RH2) phases as a function of pressure at different temperatures, respectively. Notice the strong compression-induced softening and heating-induced hardening (CISHIH) in RH1 phase and the heating-induced softening to heating-induced hardening (HIS-HIH) crossover in RH2 phase (as indicated by the arrows). In both phases, bulk sound velocity $C_b$ is almost temperature independent.

Figure 3

Calculated high-pressure, high-temperature sound velocity of polycrystalline vanadium. (a) Comparison of Hugoniot with isotherms of 0 and 3000 K in body-centered cubic (BCC) phase. (b) Comparison of Hugoniot with isotherms of 0 and 2000 K in rhombohedral (RH) phases, along with the Hugoniot of the BCC phase.

Figure 4

Calculated and experimental sound velocity of shocked polycrystalline vanadium along the Hugoniot. The shock experimental data of Dai et al. [27], Yu et al. [28], and our two sets of experiments are shown (solid points for $C_l$, half-filled points for $C_s$. The open crossed points are for $C_b$ as reported by Yu et al. [28]), respectively. The isothermal curve of the body-centered cubic (BCC) phase at 0 and 3000 K and that of rhombohedral 2 (RH2) at 0 K are also displayed for comparison. The Hugoniot sound velocity given by the Steinberg-Guinan (SG) model are also presented [49, 52]. The phase boundaries at 0 K as estimated by Wang et al. [4] are given as vertical dotted lines.

Figure 5

Comparison of the shock experimental and theoretical shear sound velocity at high pressure and high temperature with respect to those values of (a) the Steinberg-Guinan (SG) model with the same temperature along the shock path, and (b) along the 3000 K isotherm of the body-centered cubic (BCC) phase at the same pressure. The shaded bands contain the scattering and uncertainty of the experimental data and represent an overall variation trend of the experimental data along the compression and heating path. The colormap in (b) indicates the shock pressure of each experimental or theoretical data.