Unstable stacking energy

What we have learned is that dislocation nucleation will occur once 4>i np) reaches its maximum allowable value. This idea is depicted graphically in fig. 11.19 where it is seen that instability to dislocation nucleation occurs when (Siip) = Yus, where yus is a material parameter that Rice has christened the unstable stacking energy. This idea is intriguing since it posits that the competition between cleavage and dislocation nucleation has been reduced to consideration of the relative values of two simple material parameters, both of which admit of first-principles determination, and relevant geometrical factors. 

One of the achievements of the PN theory is that it provides a reasonable estimate of the dislocation size. The optimal size of the dislocation core, characterized by the value of is a result of the competition between the two energy terms in Eq. (10.20), as shown schematically in Fig. 10.9 If the unstable stacking energy Yus is high or the elastic moduli K are low, the misfit energy dominates and the dislocation becomes narrow ( is small) in order to minimize the misfit energy. 

To understand ductile-to-brittle transitions, the Rice criterion in which the ratio between the surface energy (Griffith fracture energy) and the unstable stacking fault energy is often... 

Fig. 12(a) further shows that the 110 unstable stacking-fault energy is systematically smaller than the 211 fault energy for all pressures up to 400 GPa in Ta and Mo, and up to 230 GPa in V. This has important implications for the motion of a/2 < 111 > screw dislocations on 110 and 211 slip planes. At all... 

Fig. 12. Unstable stacking-fault energies for Ta, Mo, and V, as calculated with the MGPT method, (a) Energies y and for the 110) and 211) y surfaces, respectively and (b) scaled energy...

In particular, the scaled unstable stacking-fault energy is nearly constant as a function of pressure in the case of Mo, but clearly decreases with pressure for Ta and V. 

For instance, what model should be assumed for the atomic structure of a surface The simplest picture of a surface is a planar terrace, a static array of passive adsorption sites. For a crystal, such terraces are slices through the bulk stacking sequence, a cleavage of the bulk. Is the planar terrace a reasonable model Some unrelaxed bulk terminations are polar and thus inherently unstable (see below). But for non-polar surfaces, planarity is often favoured in order to minimise the surface energy (Section 3). Thus on the timescales of diffraction techniques, such as LEED and XAFS, many surfaces are indeed observed to be... 

At lower temperatures, the y-phase in the 18Cr-10Ni-Ti steel is unstable. This is indicated by a decrease in the stacking fault energy at low temperatures In this material at low temperatures, the e-phase forms during thermal cycling and the a-phase forms under loading. 

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