Applications of the thermodynamics of elastic, crystalline materials

Abstract

The thermodynamic behaviors of multicomponent, elastic, crystalline solids under stress and electro-magnetic fields are developed, including the extension of Euler’s equation, Gibbs equation, Gibbs-Duhem equation, the conditions to be expected at equilibrium, and an extension of the Gibbs phase rule. The predictions of this new phase rule are compared with experimental observations. The stress deformation behaviors of the single martensitic crystal with and without magnetic fields were studied with the stress deformation equation derived by Slattery and Si (2005). One coherent interfacial condition between two martensitic variants was developed and used as one boundary condition of the problem. The dynamic magnetic actuation process of the single crystal actuator was analyzed. The extension velocity and the actuation time of the single crystal actuator are predicted. The relationship between the external stress and the extension velocity and the actuation time with the presence of a large external magnetic field was studied. The extended Gibbs-Duhem equation and Slattery-Lagoudas stress-deformation expression for crystalline solids was used. Interfacial constraints on the elastic portion of stress for crystalline-crystalline interfaces and crystalline-fluids or crystallineamorphous solids interfaces were derived and tested by the oxidation on the exterior of a circular cylinder, one-sided and two-sided oxidation of a plate. An experiment for measuring solid-solid interface surface energies was designed and the silicon-silicon dioxide surface energy was estimated. A new generalized Clausius-Clapeyron equation has been derived for elastic crystalline solids as well as fluids and amorphous solids. Special cases are pertinent to coherent interfaces as well as the latent heat of transformation.