On the coarsening of gas-filled pores in solids
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An analytical study is presented of the asymptotic coarsening kinetics of both monatomicand diatomic-gas-filled pores in solids, the rate-controlling p r o c e s s being assumed to be the volume diffusion of gas atoms within the host solid. It is shown that the asymptotic size-distribution functions can be expressed in t e r m s of appropriate similarity t r a n s f o r mations, and exact expressions are derived for both the frequency and cumulative distributions for each of the two cases considered. The fact that the order in size between pores is maintained as coarsening proceeds is used, together with the cumulative distribution functions, to derive expressions which describe the temporal evolution of individual pores. The behavior of g r o s s properties of the pore distributions, such as pore concentration, mean radius, and volume fraction is also evaluated.
INtheir
analytical treatment of the theory of sintering, Lifshitz and Slyozov ~ discussed the importance of interphase boundaries, at which the supersaturation of vacancies is zero, upon pore-growth kinetics. In particular, they pointed out that at asymptotic times, three rather sharply defined regions would exist in a supersaturated half-space: 1) that situated closest to a boundary, within which no pores exist, but over which vacancy flow to the boundary occurs; 2) the middle region, which contains cavities that generally tend to dissolve; 3) the region farthest from the boundary, within which the influence of the boundary is negligible. Their analysis of precipitate coarsening (i.e., Ostwald ripening) in the same work 1 is also applicable to the lattice-diffusioncontrolled coarsening of a void population existing within this third region. In the present work, we shall quantitatively evaluate the effects of contained gas on the kinetics of pore coarsening in this region, and in particular, under the assumption that the rate-controlling p r o cess is the volume diffusion of gas atoms through the solid. Two cases will be considered, corresponding to the gas contained within pores being monatomic and diatomic. Special attention will be paid to asymptotic properties of the pore size distribution for each of these two cases. I. P O R E - C O A R S E N I N G
We assume that the pores are spherical and are stationary with respect to their surroundings, and that the pore distribution is relatively disperse in coordinate space, such that each pore lies at the center of a v i r tually spherically s y m m e t r i c 2 concentration field of dissolved gas. Then, assuming quasistationary diffusion kinetics, it follows that the rate at which the number of gas molecules, N, in a pore of radius R, is changing with time t, is given by [1]
where m is a dimensionless numerical p a r a m e t e r , having, for example, unit magnitude for a monatomic gas and magnitude one-half for a diatomic gas which must dissociate before undergoing dissolution in the solid, D is the temperature-dependent volume-diffusion coeffiALANJ. MARKWORTHis a Principal Physicist with the Metal Scien
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