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3.3.2 Strain due to Vacancy Generation/Annihilation

The generation or annihilation of vacancies is accompanied by a change in the concentration of lattice sites, so that $ \Delta\CV = \Delta\CL$ [139]. Thus, the relative volume change of a given test volume due to the addition or removal of lattice sites through a change in the local vacancy concentration $ \Delta\CV$ by means of generation/annihilation processes is [147]

$\displaystyle \frac{\Delta V}{V} = \symVacRelFactor\symAtomVol\Delta\CV,$ (3.36)

where $ \symVacRelFactor\symAtomVol$ accounts for the vacancy volume. Following the same procedure as described above, the strain rate is given by

$\displaystyle \ensuremath{\ensuremath{\frac{\partial \symStrain^g}{\partial t}}...
...cRelFactor\symAtomVol\ensuremath{\ensuremath{\frac{\partial \CV}{\partial t}}},$ (3.37)

where $ \symStrain^g$ refers to the strain produced due to vacancy generation/annihilation processes.

Since the change in vacancy concentration is given by generation or annihilation processes

$\displaystyle \ensuremath{\ensuremath{\frac{\partial \CV}{\partial t}}} = \G,$ (3.38)

which leads to the generation/annihilation strain rate components

$\displaystyle \ensuremath{\ensuremath{\frac{\partial \symVacGenStrain}{\partial t}}} = \left[\frac{1}{3}\symVacRelFactor\symAtomVol\G\right]\symKronecker.$ (3.39)


next up previous contents
Next: 3.3.3 Total Electromigration Strain Up: 3.3 Electromigration Induced Stress Previous: 3.3.1 Strain due to

R. L. de Orio: Electromigration Modeling and Simulation