Yield Law
Microscopic rate equations define the evolution of plastic deformation in brittle materials through the interaction of dislocation density and effective stress. The alexander-haasen model provides the framework for calculating these changes in covalent crystals such as silicon or germanium. It accounts for the initial scarcity of mobile carriers by linking the multiplication rate to the velocity of existing lines.
Dislocation Multiplication
Internal structural changes during the early stages of deformation drive the sudden drop in observed load. Within the alexander-haasen model, the density of mobile dislocations increases as a function of both the current population and the stress exerted upon them. This growth produces the characteristic yield point phenomenon where the upper yield stress transitions to a lower steady value.
The process follows a specific multiplication law where the rate of change in density remains proportional to the product of the existing density and the local velocity. High purity crystals are particularly susceptible to this effect because the lack of starting carriers requires a massive multiplication event to accommodate the applied strain rate.
Velocity Relation
Mobile line movement follows a power law dependent on temperature and the local force field. The alexander-haasen model treats this velocity as a thermally activated process governed by an activation energy specific to the crystal lattice. Impurities or dopants often alter this movement, shifting the resulting strain rate sensitivity.
Application Boundary
Predictive accuracy remains highest during the initial transition from elastic to plastic behavior. Beyond the lower yield point, the alexander-haasen model requires additional terms to account for work hardening and mutual dislocation interference. The model supports practitioners in the optimization of crystal growth and semiconductor wafer processing.
