Limiting low temperature value of the grüneisen parameter for metals

Physical Review Letters, 1987

If electrons in a metal are heated to a temperature T, greater than the lattice temperature TI, the electron-phonon interaction causes temperature relaxation dT, /dt = yr(Tt-T,) which is rapid for TL) Oo. A formula yr =3hZ(co')/nkaT, is derived, where k(ro') =q/M is an important parameter in the theory of superconductivity. Quantitative agreement with recent experiments is good.

Physical review, 2017

The electronic thermoelectric coefficients are analyzed in the vicinity of one and two Anderson localization thresholds in three dimensions. For a single mobility edge, we correct and extend previous studies and find universal approximants which allow us to deduce the critical exponent for the zero-temperature conductivity from thermoelectric measurements. In particular, we find that at nonzero low temperatures the Seebeck coefficient and the thermoelectric efficiency can be very large on the "insulating" side, for chemical potentials below the (zero-temperature) localization threshold. Corrections to the leading power-law singularity in the zero-temperature conductivity are shown to introduce nonuniversal temperature-dependent corrections to the otherwise universal functions which describe the Seebeck coefficient, the figure of merit and the Wiedemann-Franz ratio. Next, the thermoelectric coefficients are shown to have interesting dependences on the system size. While the Seebeck coefficient decreases with decreasing size, the figure of merit, first decreases but then increases, while the Wiedemann-Franz ratio first increases but then decreases as the size decreases. Small (but finite) samples may thus have larger thermoelectric efficiencies. In the last part we study thermoelectricity in systems with a pair of localization edges, the ubiquitous situation in random systems near the centers of electronic energy bands. As the disorder increases, the two thresholds approach each other, and then the Seebeck coefficient and the figure of merit increase significantly, as expected from the general arguments of Mahan and Sofo [J. D. Mahan and J. O. Sofo, Proc. Natl. Acad. Sci. U.S. A. 93, 7436 (1996)] for a narrow energy range of the zero-temperature metallic behavior.

As is common knowledge, the experimentally measured and theoretically deduced values of the γ-coefficient of the electronic heat capacity of metals exhibit a clear discrepancy. This discrepancy is usually attributed to the neglected effects such as the electron self-interaction and the electron interaction with phonons and the Coulomb potential. Despite the said pointers to the possible cause in the obtaining theoretical and experimental dichotomy, no dedicated effort has been put in order to come up with a theory to explain this. An effort is here made to come-up with an alternative theoretical framework whose endeavour is to proffer a theory that may explain why there is this theoretical and experimental dichotomy by invoking the hypothesis that the temperature of electrons and the lattice may be different. We argue that the different electron and lattice temperatures canin-principle-give an alternative explanation as to the said theoretical and experimental dichotomy in the γ-coefficient of the electronic heat capacity of metals without the need to invoke the effective mass theory as currently obtains. "Thermodynamics is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, it doesn't bother you anymore."

Physical Review Letters, 2006

We report the first accurate measurement of the electronic Gru ¨neisen constant e using a novel method employing the new technique of femtosecond electron diffraction. The contributions of the conduction electrons and the lattice to thermal expansion are differentiated in the time domain through transiently heating the electronic temperature well above that of the lattice with femtosecond optical pulses. By directly probing the associated thermal expansion dynamics in real time using femtosecond electron diffraction, we are able to separate the contributions of hot electrons from that of lattice heating, and make an accurate measurement of e of aluminum at room temperature. This new approach opens the possibility of distinguishing electronic from magnetic contributions to thermal expansion in magnetic materials at low temperature.

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Journal of Physics and Chemistry of Solids, 2001

The temperature dependence of the Gru Èneisen parameter of MgSiN 2 (80±1600 K), AlN (90±1600 K), and b-Si 3 N 4 (300± 1300 K) was evaluated from thermal expansion, elastic constants and heat capacity data of these materials. For all compounds the Gru Èneisen parameter increases as a function of the reduced temperature approaching a constant value at high temperatures (T/u $ 0.8). The high temperature limit of the Gru Èneisen parameter of the wurtzite type materials MgSiN 2 and AlN is about the same (0.98 and 0.95, respectively) whereas these are much higher than that of the phenacite b-Si 3 N 4 (0.63). This behaviour can be understood quantitatively from the relation between the Gru Èneisen parameter and the bond parameter W as established by Slack. q

International Journal of Pure and Apllied Mathematics, 2015

Internal thermal energy in solids contributes to all kinds of bosons and fermions energy across very complicated mechanisms. Bloch-Grüneisen (BG) function is considered a main term which controls in phonons resistivity. Mathematical treatment had been applied on BG resistivity equation, which gave a Semi-empirical relationship between integral constant and Debye temperature in noble metals as a function of temperature. Comparison between theoretical and experimental was examined.

Using previous results and general thermodynamical formalism,an expression is obtained for the specific heat per particle under constant volume of a degenerate non-relativistic electron gas on a 1D lattice.The result is a non-linear function of the temperature,and it could have applications in studies of quasi one-dimensional organic metals.

Journal of Non-Crystalline Solids, 2006

A simple theoretical approach to investigate the low-temperature behavior of the specific heat of a non-crystalline solid is proposed. We discuss the possibility that this behavior can be explained in analogy to what is done in the physics of superfluid helium. We assume that the low-temperature excitation spectrum of the system is formed by two ideal gases of boson quasiparticles. One of them is a phonon gas that is always present in the spectrum, leading to the Debye contribution; the other one, which is very important for very low temperature, is an ideal gas of another boson quasiparticles, whose dispersion relation is similar to the one proposed for the liquid helium. To explore in more details this analogy, we discuss the possibility to build a simple, but general framework to understand the temperature behavior of the specific heat at very low temperatures, by following a programme similar to the one developed by Bogoliubov for a system of interacting bosons.

Journal of Physics: Conference Series, 2015

Data on thermal conductivity in states with hot electrons are necessary for the calculation of ultrashort laser exposure and the behavior of matter near the tracks of fast particles penetrating the condensed phase. The paper presents new analytical expressions describing the state of gold with the extra-high heat conductivity within a broad range of two-temperature phase diagram including the melting curve. This is a region in the threedimensional space defined by the electron temperature Te, ion temperature Ti and the density ρ, at which the thermal conductivity κ is one order of magnitude larger than the value related to the room temperature. The growth of heat transfer is due to a sharp increase in the heat capacity of carriers (electrons) when they are heated and, accordingly, the gradual loss of the degeneracy. The developed model is based on an exact solution of the kinetic equation, involving experimental data and calculations of the electronic spectrum by the density functional method. The model works well also at low temperatures Te that allows describing the crystallization of the melt as it cools down.