Debye model

About: Debye model is a research topic. Over the lifetime, 7462 publications have been published within this topic receiving 133987 citations.

Enhanced cooperative interactions at the nanoscale in spin-crossover materials with a first-order phase transition.

Abstract: We analyzed the size effect on a first-order spin transition governed by elastic interactions. This study was performed in the framework of a nonextensive thermodynamic core-shell model. When decreasing the particle size, differences in surface energies between the two phases lead to the shrinking of the thermal hysteresis width, the lowering of the transition temperature, and the increase of residual fractions at low temperature, in good agreement with recent experimental observations on spin transition nanomaterials. On the other hand, a modification of the particle-matrix interface may allow for the existence of the hysteresis loop even at very low sizes. In addition, an unexpected reopening of the hysteresis, when the size decreases, is also possible due to the hardening of the nanoparticles at very small sizes, which we deduced from the size dependence of the Debye temperature of a series of coordination nanoparticles.

The thermal conductivity of metals at low temperatures

Abstract: The thermal conductivity of high-purity samples of thirty-two metals has been measured. These were Ag, Al, Au, Be, Cb, Cd, Ce, Co, Cu, Fe, Ga, In, Ir, La, Mg, Mn, Mo, Ni, Pb, Pd, Pt, Rh, Sb, Sn, Ta, Ti, Tl, U, V, W, Zn and Zr. For most metals measurements were taken from 2 to 40°K, but where necessary they were extended to 90°K. For superconductors they were taken in both the superconducting and normal states. The conductivity was found to be entirely electronic except for Sb and U. Most of the specimens were polycrystalline, but single crystals of Zn, Cd, Sn, Pb, Ga and Ti were measured. For Zn and Ga, specimens of different orientations with respect to the rod axis were obtained, and in both these metals the thermal conductivity was found to be anisotropic. The thermal resistance, W, at low temperatures of nearly all the metals is of the form W — a T 2 + gjT, and the constants a and /? have been calculated. If is the limiting thermal conductivity at high temperatures and 6 is the Debye temperature, then the value of aK^d2 is the same for the metals in any one chemical group. For some metals the electrical resistance was measured at the same time as the thermal conductivity over the full temperature range and hence the Lorenz number, L, was calculated. The limiting value of L at low temperatures for several metals was found to be considerably higher than the theoretical value, in particular for Ti and Zr. A corresponding effect to the minimum in the electrical resistance of Mg has been found in the thermal resistance. A large increase in the thermal conductivity of Fe after a period of time has been ascribed to the precipitation of impurities in the metal. A method is given for estimating the thermal conductivity of a metal at low temperatures.

Pressure dependence of the elastic constants of nonmetamict zircon

Abstract: The single crystal elastic constants of nonmetamict zircons have been measured as a function of pressure to 12 kb at room temperature and also as a function of temperature between 25 and 300° C at atmospheric pressure. The pressure derivatives of the elastic constants are: C 11=10.78, C 33=5.88, C 44=0.99, C 66=−0.31, C 12=3.24, C 13=6.20. The anomalous negative behaviour of C 66 versus pressure could be associated with a high pressure phase transition. The pressure and temperature derivatives of the isotropic elastic wave velocities and elastic moduli for nonmetamict zircon are calculated from the present single crystal data by the Voigt, Ruess, and Hill approximations and compared with the values of some other oxides and silicates. The pressure derivative of the isotropic adiabatic bulk modulus is relatively high (dK S/dP=6.50), and the pressure derivative of the shear modulus is relatively low, (dG/dP=0.78), compared to the corresponding values for some other oxides and silicates. The Debye temperature, ϑD, and the high temperature limit of the Gruneisen parameter, γHt, calculated from the elastic constants and their pressure derivatives, agrees well with the Debye temperature and the thermal Gruneisen parameter, γth, calculated from the thermal expansion, heat capacity, and compressibility data.

Extended x-ray absorption fine structure determination of thermal disorder in Cu: Comparison of theory and experiment

Abstract: The extended x-ray absorption fine structure (EXAFS) of Cu at temperatures from 10 to 683K has been used to evaluate the EXAFS disorder term and compare it with theory. The change in disorder for different temperatures was extracted from the slopes of $\mathrm{ln}(\frac{{\ensuremath{\chi}}_{1}}{{\ensuremath{\chi}}_{2}})$ plots and by using a least-squares curve-fitting program. The values of the disorder parameter vs temperature are compared to a pure Debye model without correlation, a Debye model with correlation, and a model incorporating the measured phonon spectrum of Cu. The pure Debye model predicts too large an effect, whereas there is good agreement between the experimental data and either of the other two theories. This indicates that models which account for the correlated motion of the absorbing and scattering atom can give $\ensuremath{\sigma}$ values which are in good agreement with those determined experimentally.