Applications of spring-mass model on crystalline lattices

Abstract

In this work we present a study of different one-dimensional, two-dimensional and three-dimensional arrangements of masses coupled by springs, to which are made to vibrate by small oscillations, achieving a vibration over the entire systeml called “mode of vibration”. To achieve the vibrations, the model Spring-Mass is used, that is a proposed mathematical-physical model by using systems of linear differential equations of second degree with constant coefficients, considering the forces applied to the masses as linear-elastic restitution forces with small displacements. Then the system is discretized and solved numerically by using the Euler-Cromer integration method. In order to experiment, we simulating the vibration of different periodic molecular configurations, where the ions are connected to each other by means of ideal springs. Each ion in the network vibrates as if it were a harmonic oscillator, so it is possible to analyze the dynamic lattice properties, such as the normal modes.