Papers by Keyword: Debye Function

Abstract: In the induction heating, in the calculation of the electric machines losses, in the mechanical engineering, in the calculation of the thermal field distribution, the equations of Maxwell and heat equation are required. Those utilize the magnetic permeability and the calorific capacity at constant volume which strongly depends on the temperature and the temperature of Debye, which is a constant for each metal.The Physics of the Solid State,through the study of the acoustic and thermal properties of metals, establishes a formula giving the calorific capacity at constant volume by an integral which one can calculate only numerically.That is due to the form even of the function of distribution of Debye. The purpose of this work is to propose an analytical formulation of the calorific capacity at constant volume by analogy with the Brillouin's function largely used in ferromagnetism.This formulation has the advantage to put at the disposal of the Engineer specific concepts to the Physicist. Another advantage is the facility of ‘’to keep’’ this new formulation by functions which come under the domain of Numerical Analysis, such spline function or other.This same formulation will also allow finding an analytical formulation of internal energy whereas it was given by an integral which one can calculate only numerically.

Abstract: Patterns calculated by applying the Debye function to faulted spherical nanoparticles are used to test the accuracy of modern Line Profile Analysis theory of faulting for small crystallites. The relative deviation of the determined fault density is found to be dependent on the fault position, and on the particle size. The study of the average pattern from systems of 100 particles (D = 9.8nm) shows an overestimated deviation of the determined fault density by as much as 30%.