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 exch ange diffusion in glasses at arbitrarily varying temperatures in processing . It is shown that the processing yields identical concentration profiles i f 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. Appl ying that criterion to the technology of graded-index (GRIN) optics the res ults of the simulation of isothermal ion exchange can be used for processin g at non-isothermal conditions. (C) 1999 Published by Elsevier Science B.V. All rights reserved.