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Extra info for 52.Reliability
However, if the grain size is increased by one or two orders of magnitude thus enormously reducing the total grain boundary’s cross-sectional area, then electromigration is controlled by the lattice diffusion through the bulk of the grains. Grain boundary width is assumed to be a couple of angstroms. The effective diffusivity Deff can be expressed as Deff = Dv + πδ d Dg (53) where ͳ ϭ Grain boundary width d ϭ Grain diameter Increasing d in Eq. (53) emphasizes bulk diffusivity and accordingly curtails electromigration.
18), if excess vacancies generated by cyclic stress form climb dislocations, plastic deformation is more conducive as the vacancygenerating process is accelerated. 4( f m / f M ) 1/3 ) (32) In Eq. (32), ⑀co is the bump creep without minicycles (just main cycles), and ⑀c is the bump creep in the presence of minicycles. Equation (32) has been validated with the fatigue data produced in the experiments described, with and without minicycles, for the conditions under which the thermal cycle tests have been conducted.
3 kJ/mol) equal to that of lattice diffusion. 6 kJ/mol. For the thermomigration of an interstitial solute in a linear temperature gradient, the stationary state ٌT produces a stationary opposing concentration gradient ٌC, leading to Ji ϭ 0 at steady state. In view of irreversible thermodynamics (51,52), at steady state Q∗ d ln Ci = i d(1/T ) K (62) In a nonstationary state, the initial and final ⌬C conditions must be known accurately, and the flux must be in accordance with J = −D ∇C − C Q∗ ∇T KT 2 (63) Despite the fact that Soret (53) discovered the effect over a century ago, it still is not quite understood.