Ion-exchange processing of glasses under non-isothermal conditions

The general solution of the diffusion equation with a diffusion coefficient depending on time is found. The solution is applied in describing ion exchange diffusion in glasses at arbitrarily varying temperatures in processing. It is shown that the processing yields identical concentration profiles if the integral, integral(0)(t) D(xi)d xi, taken over the processing time, t, is the same, where D(xi) is the time-dependent interdiffusion coefficient, which is determined from the real temperature schedule during the process. The range of applicability of the formulated criterion is discussed. Applying that criterion to the technology of graded-index (GRIN) optics the results of the simulation of isothermal ion exchange can be used for processing at non-isothermal conditions. (C) 1999 Published by Elsevier Science B.V. All rights reserved.