Anomalous temperature dependence of elastic constant c44 in V, Nb, Ta, Pd, and Pt

Abstract

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Temperature-dependent elastic properties of binary and multicomponent high-entropy refractory carbides

“…The monotonic reduction in SOEC with increasing temperature [68][69][70] is also reflected by a corresponding decrease in mechanical strength and hardness [42,71]. Deviations from the typical behavior of SOEC vs. Tsee, e.g., temperature-induced increase in the C44 of some metals [72,73] may arise from strainor thermally-induced modifications of electronic-structures.…”

From qualitative to quantitative description of the anomalous thermoelastic behavior of V, Nb, Ta, Pd and Pt

“…Among these elements, Nb exhibits the largest anomaly of c 44 [9]. The anomalous thermoelastic behavior of these elements and related alloys have thoroughly been examined, both experimentally and theoretically [9][10][11][12]. As suggested, features in the electronic structure, such as a high electronic density of states (DOS) at the Fermi level, are likely to cause the thermoelastic anomaly of the shear elastic constant c 44 .…”

Temperature and Impurity Induced Stabilization of Cubic HfV2 Laves Phase

“…Consequently, the temperature and volume dependency of the Helmholtz free energy is transferred to the elastic constants [50], enabling the calculation of elastic constants as a function of temperature. The approach conducted in this work, introduced by Huang et al [50,51], was to treat these two contributions separately by keeping the other variable constant. Hence, the thermoelastic constants were calculated by…”

“…Thus, the vibrational energy contribution was neglected for the calculation of the thermoelastic constants and the overall temperature dependence of the elastic constant ∆c V (T) was reduced to the electronic free energy F e (T) at equilibrium volume V 0 . Supplementary information about the approach can be found elsewhere [50,51,53,54].…”