A Simple Approach to Compute Interatomic Force Constant for Mono and Diatomic Semiconductors

In this paper, a mathematical relation was found between interatomic Hooke’s force constant and both the bulk modulus and interatomic distance in solid crystals, considering that the forces which have effect on an atom are only those resulted from the neighboring atoms, and the forces are subject to Hooke’s law as the deflections of atoms from their equilibrium positions are very small. This work has been applied on some solid semiconducting crystals of diatomic primitive cell, including crystals of mono-atomic primitive cell automatically, by using linear statistical fitting with computer programming and, then, using mathematical analysis, proceeding from the vibrational dispersion relation of solid linear lattice, these two methods have been used in the process in order to support each other and for the result to be satisfying and reasonable. This is a contribution to the process of using computer programming in physics to facilitate mathematical analyses and obtain the required relations and functions by designing and developing appropriate computer programs in line with the macro and micro natures of materials. The importance of this is in enhancing our understanding of the interatomic actions in cells and of the crystal structure of materials in general and semiconductors in particular, as it is a step of the initial steps to facilitate the process of calculating energies and extracting mathematical relations between correlation energy and temperature as well as between sub-fusion and fusion energies with temperature.

Dynamic characterization of a stochastic SIR infectious disease model with dual perturbation

Environmental perturbations are unavoidable in the propagation of infectious diseases.In this paper,we introduce the stochasticity into the susceptible-infected recovered(SIR)model via thc^parameter perturbation method.The stochastic disturbances associated with the disease transmission coefficient and the mortality rate are presented with two perturbations:Gaussian white noise and Levy jumps,respectively.This idea provides an overview of disease dynamics under different random perturbation scenarios.By using new techniques and methods,we study certain interesting asymptotic properties of our perturbed model,namely:persistence in the mean,ergodicity and extinction of the disease.For illustrative purposes,numerical examples are presented for checking the theoretical study.

Structural and dielectric properties of sol-gel processed Ce-doped BaTi_(0.97)Y_(0.03)O_(3)ceramics

Structural and dielectric properties of Ce-doped BaTi_(0.97)Y_(0.03)O_(3)powders,with the chemical formulation(Ba_(1−x)Ce_(x))(Ti(_(0.97−x/4))-Y_(0.03))O_(3)such as x=0%,1%,3%,5%,7%and 9%,produced by the sol-gel method,have been investigated.X-ray diffraction analysis showed that Ce^(3+)ions incorporated Ba sites until x=7%indicating that this concentration represents a solubility limit of Ce^(3+)ions in BaTi_(0.97)Y_(0.03)O_(3)matrix.Scanning electron microscopy(SEM)analysis showed a decrease in grain size down to the same concentration of 7%.Raman spectroscopy analysis showed the appearance of A_(1g) mode,which we attributed to the effect of incorporation of Ce^(3+)and Y^(3+)in BaTiO_(3)matrix.Dielectric measurements revealed that doping with cerium lowers the temperature of permittivity maximum at the ferroelectric-to-paraelectric transition(FPT)of the BaTi_(0.97)Y_(0.03)O_(3)sample,and reaches a value that should be below 40℃ for x=9%.Moreover,the phenomenon of dielectric resonance was observed on all Ce-doped samples,which was not the case with other dopants as reported in the literature.