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Debye model
About: Debye model is a research topic. Over the lifetime, 7462 publications have been published within this topic receiving 133987 citations.
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TL;DR: In this article, the adiabatic elastic moduli of hexagonal close-packed lutetium single crystals have been determined by the ultrasonic pulse superposition technique over the temperature range 4.2-300°K.
Abstract: The adiabatic elastic moduli of hexagonal close‐packed lutetium single crystals have been determined by the ultrasonic pulse superposition technique over the temperature range 4.2–300°K. The values at 300°K in units of 1011 dyn/cm2 are C11=8.62, C33=8.09, C44=2.68, C66=2.71, and C13=2.8; the values extrapolated to 0°K are C11=9.10, C33=8.40, C44=2.91, C66=2.96, and C13=2.9. The Debye temperature calculated using the elastic moduli at 0°K is 184.5°K. The bulk elastic properties have also been calculated and they agree favorably with previously predicted polycrystalline values. The linear thermal‐expansion coefficients of the lutetium single crystals have been determined over the same temperature range by using a linear‐variable‐differential‐transformer dilatometer. The room‐temperature coefficients of thermal expansion are α∥=2.0×10−6 and α⊥=4.82×10−6°K−1. A maximum in α⊥ was found at 130°K, which apparently correlates with the maximum found in the γ⊥/γ∥ ratio at 130°K, where γ is the Gruneisen constant.
38 citations
TL;DR: In this paper, the Debye model was used to calculate the energy gap of the first excited electronic states within the 5 D orbital term, both at M1 and M2, and applied-field MS revealed that the principal component of the electric field gradient, V zz, is positive.
Abstract: Transmission 57 Fe Mossbauer measurements were acquired in the temperature range 11–745 K from a suite of nine synthetic Ca-free P 2 1 / c Mg-Fe clinopyroxenes (cpx) along the MgSiO 3 -FeSiO 3 join. The paramagnetic Mossbauer spectra (MS) consist of one doublet produced by Fe 2+ ions at an almost regular octahedral M1 site and a second doublet at a more distorted octahedral M2 site. The temperature dependencies of the Fe 2+ center shifts were fit to equations derived from the Debye model for the lattice vibrations, allowing the determination of the characteristic Mossbauer temperatures for the two Fe sites. The temperature variations of the M1 and M2 quadrupole splitting Δ E Q ( T ) are consistent with the higher distortions of the M2 octahedra. Applied-field MS revealed that the principal component of the electric field gradient, V zz , is positive, implying a tetragonal compression of both octahedral sites. The crystal-field model was used to analyze Δ E Q ( T ) and to calculate the energy gaps Δ 1 and Δ 2 of the first excited electronic states within the 5 D orbital term, both at M1 and M2. The various physical quantities derived from the MS are discussed in terms of the Fe/(Fe + Mg) ratio.
38 citations
TL;DR: In this paper, the size dependent Debye Temperature (θD) and Mean Square Displacements (MSDs) of nanocrystalline Au, Ag and Al are determined.
38 citations
TL;DR: It is argued that this onset temperature corresponds to the emergence of the process as a distinct mode of orientational relaxation and the coupling between rotational and translational diffusion breaks down at a still lower temperature where a change occurs in the temperature dependence of the average inherent structure energy.
Abstract: A significant deviation from the Debye model of rotational diffusion in the dynamics of orientational degrees of freedom in an equimolar mixture of ellipsoids of revolution and spheres is found to begin at a temperature at which the average inherent structure energy of the system starts falling with drop in temperature. We argue that this onset temperature corresponds to the emergence of the $\alpha$ process as a distinct mode of orientational relaxation. Further, we find that the coupling between rotational and translational diffusion breaks down at a still lower temperature where a change occurs in the temperature dependence of the average inherent structure energy.
37 citations
TL;DR: First-principles calculations of the crystal structures, phase transition, and elastic properties of B1-B2 phase calcium sulfide have been carried out with the plane-wave pseudopotential density functional theory method and the normalized elastic constants c(ij)' have been introduced to investigate the elasticity of CaS in detail.
Abstract: First-principles calculations of the crystal structures, phase transition, and elastic properties of B1-B2 phase calcium sulfide (CaS) have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values (for crystal structures and the phase transition) are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c(ij), the aggregate elastic modulus, the deviation from the Cauchy relation, and the elastic anisotropy on pressure have been investigated. The normalized elastic constants c(ij)' have been introduced to investigate the elasticity of CaS in detail. Moreover, the variation of the Poisson ratio, Debye temperature, and longitudinal and transverse elastic wave velocity with pressure P up to 70 GPa at 0 K have been investigated for the first time.
37 citations