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Point Defect Trapping in Crystal Growth
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4.We shall use the customary terms supersaturation ratio α and supersaturation as is appropriate for discussion of growth of a crystal from the ideal gas phase where with the equilibrium vapor pressure of the crystalline substance j and the observed partial pressure of vapor in the growth medium. In more complex cases the free energy change activating crystal growth may be more precisely expressed in terms of the thermodynamic activity where is the chemical potential of species j with respect to the crystal as standard state. See for example, W. W. Webb and E. F. Riebling, J. Chem. Phys. 28, 242 (1958). In an ideal gas by definition.
5.This procedure leads to gross overestimate of the energy of formation of vacancies since relaxation around the vacant site is not taken into account. However, the process is used only for relative values that are then normalized using measurements of formation energies in the crystal interior. Nearly identical relative values result from estimates based on the surface energy of a vacancy; see H. Brooks, Impurities and Imperfections (American Society of Metals, Cleveland, 1955), p. 1.
6.Superscripts i and s are used to designate quantities referring to the crystal interior and surface, respectively.
7.J. Bardeen and C. Herring, Atom Movements (American Society of Metals, Cleveland, 1951), p. 87.
8.Actually depends on the rate of trapping stage (2), but local equilibrium is assumed in this fast stage between the outer lattice layer and the adsorbed layer.
9.Definitions are summarized here for convenience: of point defects actually trapped by growth, of point defects buried under advancing growth ledges so available for trapping; see Eq. (II.7), equilibrium concentration of point defects at the growth temperature as given by Eq. (II.1), coefficient for point defects given by Eq. (II.9) rate surface thickness (cm).
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42.P. E. Doherty (Ph.D. thesis, Harvard University, 1961) has suggested the possibility of vacancy trapping and dislocation nucleation at relatively low growth rates by impingement of growth ledges one of which has nucleated with a stacking fault relation to the underlying layer. The packing error along the line of impingement can be removed only by systematic movement of the whole faulted area which eventually may leave a row of vacancies. Unless slip occurs the annealing process would be extremely slow.
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