MATHEMATICAL AND COMPUTER MODELING OF INTERPHASE INTERACTION IN HETEROGENEOUS SOLID STRUCTURES

Abstract

The aim of this work was to develop a mathematical model and computer modelling of interphase interaction, mechanical stresses and adhesion mechanisms between mechanically inhomogeneous media (different phases). Methodology. For the system "metal – dielectric" we use a macroscopic approach, which corresponds to the ratio of non-equilibrium thermodynamics and physics of solid surfaces. Let’s consider the system of equations and boundary conditions for describing the change of energy parameters (σh, γ), which characterize the thermodynamic state of the system of contacting bodies. Method for calculating the main energy parameters (interfacial energy – γm, interfacial tension – σm, work of adhesion – Aadand energy of adhesive bonds – γad) in complex solid-state structures containing boundary phases is proposed. Based on the basic equations of nonequilibrium thermodynamics and surface physics a mathematical model of the interphase boundary is designed. A comparative analysis of the features of interphase interaction in the systems "metal-metal", "metal-semiconductor" and "metal-dielectric" on the example of interacting systems "Cu – Zn", "Cu – Si" and "Cu – quartz". It is established that the most sensitive parameter in the analysis of interphase interactions is the interphase energy γm.A model of mechanical stress formation in the "condensate-substrate" system is proposed. In particular, internal stresses in metal condensates are caused by changes in the value of interphase energy parameters (primarily interfacial tension) in the substrate-nanocondensate system and due to phase-forming processes accompanied by changes in surface energy in the condensate volume during its formation. The resulting internal stresses in metal condensates are an integral result of the action of statistically distributed on the plane of the film local stresses. Such phenomena are due to the anisotropy of the energy parameters of the interphase interaction in the condensate plane. Behavior analysis of energy and adhesion parameters can be used to predict the results of interphase interaction in order to select contact pairs to create thermodynamically stable structures with predicted values of energy parameters of interphase interaction, a certain type of chemical bond and a given level of mechanical stresses.