Model 1 Shrinkage of Pure Element Nanoshells

The boundary conditions for vacancies were formulated by Equation 7.2. 

Internal shell/vacuum (or inert medium) and external surfaces move due to vacancy fluxes as 

Substituting the expression Equation 7.10 into Equations 7.5 and 7.6 for the boundary movement, we obtain the following simple equations for the shrinkage 

Equations 7.11 and 7.12 are not independent and already contain the conservation of matter (and volume) 

Substitution of Equation 7.15 in Equation 7.11 and taking account of Equation 7.13 

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