Temperature and Impurity Induced Stabilization of Cubic HfV2 Laves Phase

Abstract

The stability of cubic HfV2 (Fd3m) was investigated as a function of temperature as well as interstitially solved oxygen and hydrogen using density functional theory. Mechanical and energetic instability of pristine cubic HfV2 is obtained in the ground state at 0 K, which is unexpected as it can readily be synthesized. Combined Debye–Grüneisen and electronic entropy calculations indicate that HfV2 is stabilized with increasing temperature primarily as a result of lattice vibrations. In contrast, temperature-induced mechanical stabilization, considering the Born stability criteria, is achieved due to the electronic entropy. Interstitial incorporation of hydrogen and oxygen into the cubic structure contributes to the energetic and mechanical stabilization in the ground state for impurity concentrations as low as 1 at%, owing to strong ionic/covalent bond formation with the matrix atoms.

A Proposal for a Composite with Temperature-Independent Thermophysical Properties: HfV2–HfV2O7

“…Consequently, the high temperature of 700 • C required to form crystalline HfV 2 is attributed to the kinetically limited formation of the Laves phase structure and not to an energetic instability of the cubic structure up to these temperatures. This notion is supported by theoretical predictions suggesting the energetic stabilization of cubic HfV 2 at temperatures as low as −120 • C due to lattice vibrations [29]. For ZrV 2 , due to the considerably higher energy of formation in the ground state [71], its energetic stabilization is expected at higher temperatures, potentially explaining the discussed phase formation differences between Hf-V and Zr-V thin films.…”

“…Materials 2020, 13, x FOR PEER REVIEW 7 of 17 notion is supported by theoretical predictions suggesting the energetic stabilization of cubic HfV2 at temperatures as low as −120 °C due to lattice vibrations [29]. For ZrV2, due to the considerably higher energy of formation in the ground state [71], its energetic stabilization is expected at higher temperatures, potentially explaining the discussed phase formation differences between Hf-V and Zr-V thin films.…”

“…However, it may also be explained by the thermodynamic instability of cubic ZrV2, as predicted by DFT in the ground state [71][72][73], exhibiting an energy of formation of 150 meV atom −1 [71], which persists at elevated temperatures. In comparison, several theoretical studies also predict cubic HfV2 to be energetically unstable in the ground state, reporting energies of formation between 20 and 35 meV per atom [29,74,75]. Furthermore, experiments show a transformation of cubic HfV2 upon cooling into an orthorhombic structure at around −160 °C [76,77] possibly due to kinetically limited decomposition into elemental V and Hf, since orthorhombic HfV2 also exhibits positive energy of formation [29,75].…”

“…In comparison, several theoretical studies also predict cubic HfV2 to be energetically unstable in the ground state, reporting energies of formation between 20 and 35 meV per atom [29,74,75]. Furthermore, experiments show a transformation of cubic HfV2 upon cooling into an orthorhombic structure at around −160 °C [76,77] possibly due to kinetically limited decomposition into elemental V and Hf, since orthorhombic HfV2 also exhibits positive energy of formation [29,75]. However, for sputtered HfV2 at 500 °C (see Figure 2), the change in shape of the main peak at around 38° suggests the first formation of nanocrystals, and the emerging hump around 20° points towards intermetallic HfV2 nanocrystals, since their presence cannot be explained by hcp Hf or bcc V.…”

“…Furthermore, binary Nb-Zr, Nb-Mo, Pd-Ag, and Pd-Rh solid solutions behave anomalously within well-defined concentration ranges [24][25][26]. Experimental and theoretical studies revealed the combination of a high density of states and electronic reallocation upon lattice distortion in the vicinity of the Fermi level to be the physical origin of the anomalous thermoelastic behavior [27][28][29][30][31]. However, the anomaly in these systems is mostly limited to the shear elastic constant c 44 , whereas the remaining elastic constants (there are three independent elastic constants for cubic symmetries, i.e., c 11 , c 12 , and c 44 ) behave normally.…”