Contributions of Debye Functions to Bosons and Its Applications on Some Nd Metals, Part Ii

Abstract

Internal thermal energy in solids contributes to vibrations (phonons) energy; spin waves (magnons) energy if solid has magnetism and fermions energy across very complicated mechanisms. Debye functions, mathematically, was estimated because they are considered a main term which controls in all equations of those contributions.Semi-empirical equation has been obtained to nd (n=3,4,5) transition metals specific heat to calculate some important physical constants.Numerical analyses gives an agreement with experimental results on nd transition metals. Comparison between theoretical and experimental was investigated.

Fermi-Dirac and Bose-Einstein Integrals and Their Applications to Resistivity in Some Magnetic Alloys, Part III

“…Fermi-Dirac and Bose-Einstein integrals are the cornerstones to calculate the thermal energy and its derivative in all materials (2,3,6,8). This part will shed light on the relaxation time ( ) τ and the number of particles (fermions and bosons) in the resistivity by comparing between theoretical and experimental expressions, where as previous works [20]- [23] were concentrated on the general behavior of resistivity, phase diagrams of Kondo and spin glasses, maximum and minimum of resistivity, s-d and RKKY interactions.…”

“…The relaxation time and the number of particles (fermions and bosons), could be calculated from experimental data analysis and compare them with theoretical expressions to get a semi-empirical formula for each parameter. For this reason, it is supposed that the number of particles could be calculated from thermal energy and specific heats of my previous work [2], and crude experimental database for the temperature dependence behavior of resistivity to some magnetic alloys (AuMn alloys) has been collected [24]- [26] and analyzed as in Figure 1, which shows a general diagram of experimental resistivity as a function of low temperatures. Data analysis of the resistivity as a function of temperature by the least-squares method made it possible to determine all temperature coefficients.…”

“…The contributions of the Bloch-Grüneisen and Debye integrals family to phonons, photons, magnons and electrons energy in solids were treated in previous parts [1] [2]. This part will highlight the important part of the integrals, where the authors' interests are mostly concerned with the application of the Fermi-Dirac (FD) and Bose-Einstein (BE) integrals to real physical problems [3]- [10].…”