Debye model

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

Temperature and pressure dependence of intrinsic anharmonic and quantum corrections to the equation of state

Abstract: Results of detailed calculations of the anharmonic and the quantum corrections to the equation of state and to Gruneisen's parameter γ are given for pressures P from zero to 2B0 (where B0 is the bulk modulus at P = 0 and T = 0) and for temperatures T from zero to (0.6) Te (where Te = ∈/k,∈ is the depth of the potential well and k is Boltzmann's constant). Interionic potentials of the form A/r+ϕR with ϕR proportional to r−12, r−8, and e−αr were used. It was found, for example, that at T = (0.2) T∈ the anharmonic corrections to P for the potentials in the order just given were approximately 7, 6, and 4% at P = (0.1)B0, while they were approximately 1, 1, and ½% at P = (0.5)B0. Quantum corrections to P were found to depend very weakly on P and to be about 1% or less for (0.2)B0 < P < 2B0 for temperatures above the zero-pressure Debye temperature. Anharmonic corrections decreased the values of γ and of P, while quantum corrections decreased the value of γ but increased the value of P.

The Low-Temperature (2 to 4$\cdot $2 degrees K) Specific Heats of Palladium-Silver Alloys

Abstract: The low-temperature, 2 to 4$\cdot $2 degrees K specific heats of a series of nine palladium-silver alloys and the pure metals have been measured. From the results the variation with concentration of $\theta _{D}$, the Debye temperature, and $\gamma $, the electronic heat coefficient, have been determined. According to the collective electron approach the height of the band at the Fermi level is proportional to $\gamma $. This enables an approximate band shape to be deduced on the assumption that alloying leaves the shape substantially unchanged. The band obtained in this way is considered in relation to earlier work on the magnetic susceptibilities of this alloy series.

Raman spectroscopic determination of the length, strength, compressibility, Debye temperature, elasticity, and force constant of the C-C bond in graphene

Abstract: From the perspective of bond relaxation and bond vibration, we have formulated the Raman phonon relaxation of graphene, under the stimuli of the number-of-layers, the uni-axial strain, the pressure, and the temperature, in terms of the response of the length and strength of the representative bond of the entire specimen to the applied stimuli. Theoretical unification of the measurements clarifies that: (i) the opposite trends of the Raman shifts, which are due to the number-of-layers reduction, of the G-peak shift and arises from the vibration of a pair of atoms, while the D- and the 2D-peak shifts involve the z-neighbor of a specific atom; (ii) the tensile strain-induced phonon softening and phonon-band splitting arise from the asymmetric response of the C3v bond geometry to the C2v uni-axial bond elongation; (iii) the thermal softening of the phonons originates from bond expansion and weakening; and (iv) the pressure stiffening of the phonons results from bond compression and work hardening. Reproduction of the measurements has led to quantitative information about the referential frequencies from which the Raman frequencies shift as well as the length, energy, force constant, Debye temperature, compressibility and elastic modulus of the C‐C bond in graphene, which is of instrumental importance in the understanding of the unusual behavior of graphene.

Ab initio study of mechanical and thermo-acoustic properties of tough ceramics: applications to HfO 2 in its cubic and orthorhombic phase

Abstract: By means of the ab initio all-electron new full-potential linear-muffin-tin orbitals method, calculations were made for elastic constants C11, C12 and C44 for Si, ZrO2 and HfO2 in their cubic phase, and constants C11, C22, C33, C12, C13, C23, C44, C55 and C66 for HfO2 in its orthorhombic phase. Using the Voigt and Reuss theory, estimations were made for polycrystals of their bulk, shear and Young moduli, and Poisson coefficients. The speed of elastic wave propagations and Debye temperatures were estimated for polycrystals built from Si and the above mentioned compounds. The semicore 4f 14 electrons should be included in the valence set of Hf atom in this all-electron approach if accurate results for elastic properties under pressures are looked for.