In the abstract of his 1970 paper, Eshelby stated: "The force on a dislocation or point defect, as understood in solid-state physics, and the crack extension force of fracture mechanics are examples of quantities which measure the rate at which the total energy of a physical system varies as some kind of departure from uniformity within it changes its configuration." He then went on to demonstrate that the elastic energy-momentum tensor proves to be a useful tool in calculating such forces. The 'forces' turn out to be the appropriate traction vectors associated with the energy-momentum (stress) tensor. It is therefore natural and perhaps even fundamental to look for the 'strain tensor' that can be paired with the 'stress tensor' to form work. The 'strain rate' would then be that some kind of departure from uniformity within a physical system. In this paper, we examine the configurational changes brought about by atomic diffusion in a nonuniform alloy crystal. The transformation from a reference, single-parameter simple cubic cell to a six-parameter alloy crystal cell, called the eigentransformation, is identified as the needed kinematic tensor.

Electromigration (EM) in a metal line is the phenomenon of flow of the metal atoms along the line. The flow is driven by the current of electrons and is also affected by the variation of chemical potential along the line. The replacement of atoms leads to a change in eigenstrain, which, in turn, alters the chemical potential. Since the chemical potential is very often dominated by a stress term, this back flow is very often attributed to the presence of a stress gradient. In microelectronic applications metal lines are usually subjected to the actions of large thermally induced eigenstrain even before the current is turned on. This large eigenstrain, together with the EM-induced eigenstrain, may lead to a nonlinear back flow, which is the subject of investigation of this paper.

The chemical potential used in interdiffusion analysis was derived by Li, Oriani and Darken (1966), and Larche and Cahn (1982). It contains the trace of the stress tensor as the essential elasticity contribution to the configurational force conjugate to the material composition. As a result, the underlying diffusion equation is totally independent of any accompanying elastic field. In particular, when an alloy epifilm is annealed, the theory implies that the rather large lattice mismatch has no effect on the ensuing diffusion process. However, it is perhaps intuitively clear by now--almost fifty years since Eshelby published his first paper on energy momentum tensor in 1951--that the trace of the (canonical) Eshelby stress tensor should be the total elasticity contribution to the desired configurational force. This conjecture is formally established in this paper for an n-component substitutional solid. Since the elastic energy is now a part of the chemical potential, the interplay between a composition-generated deformation and another elastic field may become important via the interaction energy.

ABSTRACT

The mismatch strain of a thin alloy film deposited on a uniform substrate may be obtained as the sum of a large constant mismatch and an infinitesimal, periodic perturbation. The large coherent strain is a function of a uniform alloy composition, while the amplitude of the perturbation is the result of a non-uniform perturbation in composition about the uniform state. The possibility of the existence of a lower energy state brought about by a perturbation is an indication that the uniform state is unstable. For the case where the stress-free molar Gibbs energy is described by a regular solution, this instability condition may be expressed in terms of a critical temperature, which is commonly assumed to be independent of the large but constant mismatch. It is shown in this paper that the critical temperatures are very much affected by the sign and magnitude of a large mismatch strain. The critical temperatures for several III-V ternary alloys are calculated to demonstrate the significance.

ABSTRACT

The placement of a point load at a crack tip does not contribute to the magnitude of the stress intensity factors (SIF) at that tip. It nevertheless can couple with other SIF-producing loads and lead to a change in the potential energy of the system. As a result, the configurational equilibrium condition or the fracture criterion of linear elastic fracture mechanics is altered. The inclusion of surface stress leads to yet another point load with similar effect. In the context of linear elasticity, however, the change produced by surface stress is of second order, while that affected by a point force is of first order in that the surface tension is actually reduced by an amount equal to the applied force. This is another one of those situations where the applied mechanical force actually combines with the so-called fictitious force in bringing about configurational changes. The splitting of a double-cantilever-beam by a wedging force, which is not the same as a crack-tip point load, is used to demonstrate that the wedging force at fracture is of the order of magnitude of the surface tension.