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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, pressure and temperature dependence of isotropic elastic moduli of polycrystalline alumina, noting Gruneisen parameter, equation of state and Debye temperature.
Abstract: Pressure and temperature dependence of isotropic elastic moduli of polycrystalline alumina, noting Gruneisen parameter, equation of state and Debye temperature
129 citations
TL;DR: In this paper, the theory of thermal expansion by Gruneisen is improved and the acquired data are analyzed to derive the harmonic and anharmonic parameters of manganosite MnO.
Abstract: Thermal expansion of manganosite MnO at temperatures between 20°C and 850°C has been carefully determined by a dilatometric technique. The theory of thermal expansion by Gruneisen is improved and the acquired data are analyzed to derive the harmonic and anharmonic parameters of MnO. Gruneisen's parameter γ is 1.56, Debye temperature is 441 K, and pressure derivative of bulk modulus is 7. The volume expansion coefficient is 34.3×10-6/K at 20°C and 47.1×10-6/K at 850°C; almost the same in magnitude to those of MgO and FeO.
129 citations
TL;DR: In this paper, the phonon dispersion curves, the temperature dependence of the Debye temperature, and the static elastic, dielectric, and piezoelectric constants of the Si ion have been calculated from a modified rigid-ion model with an effective charge.
Abstract: The phonon dispersion curves, the temperature dependence of the Debye temperature, and the static elastic, dielectric, and piezoelectric constants of $\ensuremath{\alpha}$-Si${\mathrm{O}}_{2}$ have been calculated from a modified rigid-ion model with an effective charge, with short-range central forces for the two Si-O interactions, for the four nearest-neighbor O-O interactions, for the four second-neighbor O-O interactions, and with three-body type angle-bending forces between nearest-neighbor O ions sharing a common Si-ion, and between Si-ions of adjacent tetrahedra and the linking O ion. The model involves 23 parameters which are reduced to 8 independent parameters by the six equilibrium conditions and by 15 constraints on the first and second derivatives of the interaction potential corresponding to the inner and outer O-O interactions. Using explicit expression for the elastic constants and for the optical modes at zero wave vector, the eight free parameters were determined from a least-squares fit of the six elastic constants and of the 16 Raman and transverse ir frequencies. The effective charge of the Si ion is found to be 0.96 electronic charges, indicating a strong degree of covalency and/or screening. The model gives good over-all agreement for the elastic and optical data, rough agreement for the dielectric constants, and the correct sign and order of magnitude of the peizoelectric constants. The dispersion curves along [001] and the temperature dependence of the Debye temperature agree well with available experimental data, with moderate discrepancies occurring for the two acoustic branches and at low temperatures, respectively.
129 citations
TL;DR: In this article, the structural, electronic, mechanical, thermodynamic properties, and pressure induced structural transition of PuO$2}$ have been systematically studied using first-principles density-functional theory.
Abstract: Plutonium dioxide is of high technological importance in nuclear fuel cycle and is particularly crucial in long-term storage of Pu-based radioactive waste. Using first-principles density-functional theory, in this paper we systematically study the structural, electronic, mechanical, thermodynamic properties, and pressure induced structural transition of PuO$_{2}$. To properly describe the strong correlation in the Pu $5f$ electrons, the local density approximation$+U$ and the generalized gradient approximation$+U$ theoretical formalisms have been employed. We optimize the $U$ parameter in calculating the total energy, lattice parameters, and bulk modulus at the nonmagnetic, ferromagnetic, and antiferromagnetic configurations for both ground state fluorite structure and high pressure cotunnite structure. The best agreement with experiments is obtained by tuning the effective Hubbard parameter $U$ at around 4 eV within the LDA$+U$ approach. After carefully testing the validity of the ground state, we further investigate the bonding nature, elastic constants, various moduli, Debye temperature, hardness, ideal tensile strength, and phonon dispersion for fluorite PuO$_{2}$. Some thermodynamic properties, e.g., the Gibbs free energy, volume thermal expansion, and specific heat, are also calculated. As for cotunnite phase, besides the elastic constants, various moduli, and Debye temperature at 0 GPa, we have further presented our calculated electronic, structural, and magnetic properties for PuO$_{2}$ under pressure up to 280 GPa. A metallic transition at around 133 GPa and an isostructural transition in pressure range of 75-133 GPa are predicted.
128 citations
TL;DR: In this article, the Debye temperature of a cubic element was calculated from the knowledge of all the elastic constants of the system, and the calculated results agree very well with the experimental data, and some empirical relationships have been observed between the high temperature entropy −Debye temperature θD(0) and the low temperature limit of the debye temperature −3.
128 citations