Grain boundary chemical potential

For a specified shape of the surface S and a prescribed chemical potential field X over S, this functional is maximum when the trial velocity field n is in fact that actual velocity field Vn defined by (9.9). The variational approach in terms of surface flux was introduced in a numerical study of grain boundary transport and cavitation by Needleman and Rice (1980), for which the grain boundary chemical potential is given by (8.14). It was introduced in the way as described here by Suo (1997) and Zhang et al. (1999) as a basis for study of surface evolution. 

Under the assumptions adopted, the chemical potentials are spatially uniform over both the free surface and the grain boundary. The free surface chemical potential is denoted by Xh x,t) and is determined according to (8.8), while the grain boundary chemical potential is denoted by Xh y,t) and is determined according to (8.14). In terms of instantaneous grain dimensions, these are... 

Fig. 19.15 Schematic representation of range of corrosion potentials expected from various chemical tests for sensitisation in relation to the anodic dissolution kinetics of the matrix (Fe-l8Cr-IONi stainless steel) and grain boundary alloy (assumed to be Fe-lOCr-lONi) owing to depletion of Cr by precipitation of Cr carbides of a sensitised steel in a hot reducing acid (after Cowan and Tedmon )...

Figure 3-7. Fraction of point defects in a-Ag2S adsorbed on grain boundaries and dislocations as a function of the chemical potential of Ag (T = I68°C).

At the grain boundaries, the condition Fv = 0 should also hold. The boundaries will be under a traction, ann = hT -tr-n, and when an atom is inserted, the tractions will be displaced as the grain expands by the volume For the case in Fig. 3.10, the boundary is oriented so that its normal is parallel to the z-axis and therefore (7nn = zz- This displacement contributes work, oyiuFIa = o zz a, and reduces the potential energy of the system by a corresponding amount. This term must be added to the chemical term, fi°A, and therefore the diffusion potential along the... 

Electron-hole recombination velocities at semiconductor interfaces vary from 102 cm/sec for Ge3 to 106 cm/sec for GaAs.4 Our first purpose is to explain this variation in chemical terms. In physical terms, the velocities are determined by the surface (or grain boundary) density of trapped electrons and holes and by the cross section of their recombination reaction. The surface density of the carriers depends on the density of surface donor and acceptor states and the (potential dependent) population of these. If the states are outside the band gap of the semiconductor, or are not populated because of their location or because they are inaccessible by either thermal or tunneling processes, they do not contribute to the recombination process. Thus, chemical processes that substantially reduce the number of states within the band gap, or shift these, so that they are less populated or make these inaccessible, reduce recombination velocities. Processes which increase the surface state density or their population or make these states accessible, increase the recombination velocity. 

The initial sintering stress is dependent upon only the dihedral an e. The application of stress on a string of particles will affect the chemical potential at the grain boundary and, more important, determine the sintering rate. The chemical potential of a surface atom is given by [9]... 

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