Debye model

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

Invar model for δ-phase Pu: thermal expansion, elastic and magnetic properties

Abstract: We present a statistical mechanical model for the anomalous thermodynamic properties of fcc δ-phase Pu and Pu–Ga alloys. The model is based on the addition of a two-level ‘Invar’-like electronic energy structure to the ordinary Debye model for the lattice, there is no assumption of magnetic character of these electronic levels. Together with the usual Debye temperature Θ and lattice Gruneisen constant γ the model includes two additional parameters, the energy spacing ΔE and an electronic Gruneisen constant Γ. ΔE is 1400 K, and Γ is negative and depends strongly on the Ga content. The model accounts satisfactorily for thermal expansion, and it accounts for the anomalous decrease in the bulk modulus with temperature provided that one assumes zero elastic stiffness for the excited electronic state. This assumption is consistent with the results of the dynamic mean-field theory for Pu. We found some evidence for the hypothetical two-level structure using inelastic neutron scattering.

Acoustic investigations on PbO-Al2O3-B2O3 glasses doped with certain rare earth ions

Abstract: Elastic moduli (Y, η), Poisson’s ratio (σ), microhardness (H) and some thermodynamical parameters such as Debye temperature (θD), diffusion constant (D i),latent heat of melting (ΔH m) etc of PbO-Al2O3-B2O3 glasses doped with rare earth ions viz. Pr3+, Nd3+, Sm3+, Eu3+, Tb3+, Dy3+, Ho3+, Er3+ and Yb3+, are studied as functions of temperatures (in the temperature range 30–200°C) by ultrasonic techniques. All these parameters are found to increase with increasing atomic numberZ of the rare earth ions and found to decrease with increasing temperature of measurement. From these results (together with IR spectra of these glasses), an attempt is made to throw some light on the mechanical strength of these glasses.

First Principles Investigation of the Elastic, Optoelectronic and Thermal Properties of XRuSb: (X = V, Nb, Ta) Semi-Heusler Compounds Using the mBJ Exchange Potential

Abstract: Semi-Heusler materials are intensively investigated due to their potential use in diverse applications, such as in spintronics and green energy applications. In this work, we employ the density functional theory to calculate the structural, electronic, elastic, thermal and optical properties of the VRuSb, NbRuSb and TaRuSb semi-Heusler compounds. The calculated results for the lattice constants, bulk moduli and their corresponding pressure derivative values are in fairly good agreement with previous works. In addition, besides the local density approximation, the modified Becke–Johnson exchange potential is also used to improve the value of the band gaps. The bonding nature reveals a mixture of covalent and ionic bonding character of the VRuSb, NbRuSb and TaRuSb compounds. Furthermore, the elastic constants (Cij) and the related elastic moduli confirm their stability in the cubic phase and demonstrate their ductile nature. We also analyze the influence of the pressure and temperature on the primitive cell volume, heat capacity, volume expansion coefficient, and Debye temperature of the semi-Heusler compounds. Additionally, we investigate the optical properties, such as the complex dielectric function, refractive index, reflectivity, and the energy loss function.

Thermal equation of state and thermodynamic properties of molybdenum at high pressures

Abstract: A comprehensive P-V-T dataset for bcc-Mo was obtained at pressures up to 31 GPa and temperatures from 300 to 1673 K using MgO and Au pressure calibrants. The thermodynamic analysis of these data was performed using high-temperature Birch-Murnaghan (HTBM) equations of state (EOS), Mie-Gruneisen-Debye (MGD) relation combined with the room-temperature Vinet EOS, and newly proposed Kunc-Einstein (KE) approach. The analysis of room-temperature compression data with the Vinet EOS yields V0 = 31.14 ± 0.02 A3, KT = 260 ± 1 GPa, and KT′ = 4.21 ± 0.05. The derived thermoelastic parameters for the HTBM include (∂KT/∂T)P = −0.019 ± 0.001 GPa/K and thermal expansion α = a0 + a1T with a0 = 1.55 ( ± 0.05) × 10−5 K−1 and a1 = 0.68 ( ± 0.07) × 10−8 K−2. Fitting to the MGD relation yields γ0 = 2.03 ± 0.02 and q = 0.24 ± 0.02 with the Debye temperature (θ0) fixed at 455-470 K. Two models are proposed for the KE EOS. The model 1 (Mo-1) is the best fit to our P-V-T data, whereas the second model (Mo-2) is derived by including the shock compression and other experimental measurements. Nevertheless, both models provide similar thermoelastic parameters. Parameters used on Mo-1 include two Einstein temperatures ΘE10 = 366 K and ΘE20 = 208 K; Gruneisen parameter at ambient condition γ0 = 1.64 and infinite compression γ∞ = 0.358 with β = 0.323; and additional fitting parameters m = 0.195, e0 = 0.9 × 10−6 K−1, and g = 5.6. Fixed parameters include k = 2 in Kunc EOS, mE1 = mE2 = 1.5 in expression for Einstein temperature, and a0 = 0 (an intrinsic anharmonicity parameter). These parameters are the best representation of the experimental data for Mo and can be used for variety of thermodynamic calculations for Mo and Mo-containing systems including phase diagrams, chemical reactions, and electronic structure.

Elastic constants of Pd39Ni10Cu30P21 bulk metallic glass under high pressure

Abstract: The pressure-dependent acoustic velocities of a Pd39Ni10Cu30P21 bulk metallic glass (BMG) have been measured up to 0.5 GPa by using an ultrasonic technique with the pulse echo overlap method. The elastic constants, the Debye temperature, and their pressure dependence are obtained. The isothermal equation of state (EOS) of the BMG is established in terms of the Murnaghan form. The atomic configurations of the BMG are discussed by comparing the elastic constants and the EOS with those of its metallic component and of other amorphous materials.The pressure-dependent acoustic velocities of a Pd39Ni10Cu30P21 bulk metallic glass (BMG) have been measured up to 0.5 GPa by using an ultrasonic technique with the pulse echo overlap method. The elastic constants, the Debye temperature, and their pressure dependence are obtained. The isothermal equation of state (EOS) of the BMG is established in terms of the Murnaghan form. The atomic configurations of the BMG are discussed by comparing the elastic constants and the EOS with those of its metallic component and of other amorphous materials.