Elastic properties of tantalum over the temperature range 4–300 K

Abstract

The elastic properties of tantalum have been investigated over the temperature range 4.2–300 K. The values of the adiabatic elastic constants C11, C44, and CL=(1/2) (C11+C12+2C44) at 4.2 K in units of 1012 dyn/cm2 are, respectively, 2.70, 0.873, and 3.02. The Debye temperature was calculated from the elastic constants and found to have the value of 265 K at low temperature. The elastic constants become temperature independent at low temperatures and approach linear behavior at high temperatures. In contrast to the normal behavior of the elastic constants, nuclear acoustic resonance experiments show anomalous line broadening.

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

“…For the lattice parameter a, good agreement is obtained within deviations of maximum 1.4% for Pd and Pt, which is acceptable based on the employed exchange-correlation functionals [33]. The calculated elastic properties and thermal expansion coefficients agree reasonably well with experimental data [8,[26][27][28][29][30][31][32] within deviations of 20%, except for the elastic constant c 44 of V and Nb, where a significant underestimation of up to 45% compared to experimental values [28,29] is obtained which is a well-known finding for DFT calcul ations using various basis sets and exchange-correlation functionals [34]. According to Koči et al [34], the theoretical underestimation may be attributed to a van Hove singularity in the electronic DOS close to the Fermi level.…”

“…Table 1 summarizes the calculated lattice parameter a, ground state bulk moduli B and the elastic shear constants c 44 and c of bcc Mo, V, Nb and Ta as well as fcc Cu, Pd and Pt. In addition, measured values from literature are added for comparison [8,[25][26][27][28][29][30][31][32].…”

Radial X-Ray Diffraction Study of Static Strength of Tantalum to 80 GPa

“…Thus we can tilt the DAC to an 𝛼 angle to minimize the contribution of Be diffraction lines to the sample patterns. [17] In this geometry, 𝜓 corresponding to the angle between the diffracting plane normal and the loading axis is calculated by [20] cos 𝜓 ℎ𝑘𝑙 = sin 𝛼 cos 𝛿 cos 𝜃 ℎ𝑘𝑙 + cos 𝛼 sin 𝜃 ℎ𝑘𝑙 , (3) where 𝜃 is the diffraction angle, and 𝛿 is the azimuthal angle in the plane of the detector.…”

Exploring Thermal and Mechanical Properties of Selected Transition Elements under Extreme Conditions: Experiments at High Pressures and High Temperatures

“…The heat capacity (Anderson, 1936;White and Colloco, 1984;Guillermet and Fernandez Guillermet, 1985;Takahashi and Nakamura, 1996), bulk modulus (Bolef and De Klerk, 1962;Featherston and Neighbours, 1963;Lowrie and Gonas, 1967;Bolef et al, 1971;Hubbell and Brotzen, 1972;Leisure et al, 1973;Bujard et al, 1981;Saxena and Zhang, 1990;Gülseren and Cohen, 2002), molar volume and thermal expansion (Nix and MacNair, 1942;Edwards et al, 1951;Amonenko et al, 1963;Dutta and Dayal, 1963a;Ross and Hume-Rothery, 1963;Vasyutinskii et al, 1966;Westlake and Ockers, 1970;Waseda et al, 1975;Touloukian et al, 1979b;Pialoux et al, 1982;Dubrovinsky and Saxena, 1997;Wang and Reeber, 1998) of Group VB and VIB elements have been measured enormously; complete review of thermal expansion experimental data is provided by Wang et al (Wang and Reeber, 1998) and Lu et al (Lu and Chen, 2009). proposed model is the overestimation of the bulk modulus at high temperatures to avoid mechanical instability in high temperature (Brosh et al, 2007).…”