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Extra resources for Comprehensive Nuclear Materials, Volume 1: Basic Aspects of Radiation Effects in Solids / Basic Aspects of Multi-Scale Modeling
The vacancy chemical potentials for ½127 FC(R(N)) replaces now the surface free energy FS(N) used in eqn  to arrive at the cavity surface tension 2g0/R. The latter is now given by FC(N þ 1) – FC(N). It will be evaluated in the next section and compared with 2g0/R. 35 1 10 100 1000 Number of vacancies in void 104 Figure 23 The relaxation volume of voids in Cu according to atomistic simulations by Shimamura48 and according to the surface stress model. 5 Ni Vacancy chemical potential (eV) 2 r Á j ¼ P À recombination Capillary approx.
To circumvent this complication, one considers an ensemble of identical systems, all having identical microstructures, and identical internal and external stress fields. The ensemble average of the defect concentration at each site, denoted simply as C(r,t) without a subscript, is now assumed to be the thermodynamic average such that expðÀbEmf Þ Cm ðr; t Þ ¼ Cðr; t ÞP expðÀbEnf Þ n ¼ Cðr; t ÞexpðÀbEmf Þ=N ðrÞ r r + R/2 r+R Figure 18 Schematic of the potential energy profile for a migrating defect.
Matching it for fcc Cu indicates that the dilated region reaches out to third nearest neighbors, and hence NG ¼ 44. However, the best match for bcc Mo is obtained with NG ¼ 10, a region that only includes the dumbbell and its first nearest neighbors. These respective values for NG are also adopted for the other fcc and bcc elements in Table 11, and the shear polarizabilities so obtained are listed in the fifth column. To compare these estimates with experimental results, the approximation given in eqn  is used with the data in Table 9 for the shear polarizabilities of Frenkel pairs.
Comprehensive Nuclear Materials, Volume 1: Basic Aspects of Radiation Effects in Solids / Basic Aspects of Multi-Scale Modeling by R.J.M. Konings (editor)