Abstract:Fundamentally understanding the temperature-dependent modulus is the key issue for materials serving in high temperature environments. This paper proposes a model based on lattice vibration theory to predict the temperature-dependent modulus with respect to isothermal and isentropic assumption. The thermal vibration free energy is expressed as a function of the two independent scalars from the strain tensor and temperature. By using the Einstein theory, we present the analytical expression for the temperature-… Show more
“…Su et al . put Wachtman’s empirical formula on a microscopic basis 37 . Their work shows that can be identified with the Debye or Einstein temperature, .…”
Section: Comparison With Experimental Data and Empirical
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mentioning
It is shown that in the ergodic regime, the temperature dependence of Young’s modulus is solely determined by the magnetic properties of a material. For the large class of materials with paramagnetic or diamagnetic response, simple functional forms of the temperature derivative of Young’s modulus are derived and compared with experimental data and empirical results. Superconducting materials in the Meissner phase are ideal diamagnets. As such, they display remarkable elastic properties. Constant diamagnetic susceptibility gives rise to a temperature independent elastic modulus for ceramic and single crystalline superconductors alike. The thermodynamic approach established in this report, paves the way to tailor elastic material parameters through the design of magnetic properties.
“…Su et al . put Wachtman’s empirical formula on a microscopic basis 37 . Their work shows that can be identified with the Debye or Einstein temperature, .…”
Section: Comparison With Experimental Data and Empirical
T
mentioning
It is shown that in the ergodic regime, the temperature dependence of Young’s modulus is solely determined by the magnetic properties of a material. For the large class of materials with paramagnetic or diamagnetic response, simple functional forms of the temperature derivative of Young’s modulus are derived and compared with experimental data and empirical results. Superconducting materials in the Meissner phase are ideal diamagnets. As such, they display remarkable elastic properties. Constant diamagnetic susceptibility gives rise to a temperature independent elastic modulus for ceramic and single crystalline superconductors alike. The thermodynamic approach established in this report, paves the way to tailor elastic material parameters through the design of magnetic properties.
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