Prediction of ion-exchange process in glass by using multi-component diffusion theory for making of gradient index glasses

玻璃中的离子交换技术被应用于制造梯度折射率透镜、波导等微光学元件。该技术的关键是找出离子交换过程中的处理条件，以形成预期的指数分布，即玻璃中的浓度分布。这是可靠地模拟离子交换过程中的浓度分布，并通过虚拟实验找出离子交换条件的最好方法。遗憾的是，目前的发展阶段，在梯度折射率玻璃不是如上所述。本研究采用多组分扩散方程来描述玻璃中的离子交换过程，该方程由移动阳离子的通量密度和电化学电位梯度推导而来，由于方程是非线性的，因此采用有限差分法对理论浓度分布进行了数值求解。另一方面，离子交换实验确定了其浓度分布。该计划是在开发含银离子多的玻璃和研究三种移动阳离子之间的离子交换动力学的基础上提出的。因此，选择含有Na、K、Ag离子且具有化学耐久性的磷酸盐玻璃作为样品。利用放射性同位素示踪技术测定了可移动阳离子的自扩散系数，以便于数值计算。理论分布可以用依赖于组分的自扩散系数来严格描述。进行了玻璃与熔盐、玻璃-玻璃偶的离子交换实验。离子交换后的实验分布用EPMA定量测定。当离子交换实验中处理条件与计算条件相同时，模拟曲线与实验曲线吻合较好。浓度分布被转换成折射率。通过对扩散理论的计算机模拟，得出了令人信服的结论，并对一些剖面进行了论证，为梯度折射率玻璃的研制提供了依据。少

The ion-exchange technique in glass is applied to produce the micro-optic components such as gradient index lens, waveguide, and so on. The key point on the technique is to find out the treated conditions in the ion-exchange process in order to form an intended index distribution, namely concentration distributions in a glass. It is the best way to reliably simulate the concentration profiles during ion-exchange and to find out the conditions by a virtual experiment. Unfortunately, the present stage in the development of gradient index glasses is not as mentioned above.In this study ion-exchange process in glass is described by multi-component diffusion equations, which are derived from the flux densities of mobile cations and the gradient of electrochemical potential, and the numerical solution to obtain the theoretical concentration distributions has been programmed with a finite difference method because the equations are nonlinear. On the other hand, the concentration distributions … More are determined by ion-exchange experiments. The plan is put on the basis which contains a development of glasses with much silver ion and a deal with ion-exchange kinetics among three kinds of mobile cations for practical merits. As the results, bonrphosphate glasses are chosen as the samples which contain Na, K, and Ag ions for mobile ones and have chemical durability. The selfdiffusion coefficients of mobile cations have been determined by means of a radio-isotope tracer technique for the sake of use in the numerical calculation. The theoretical distributions can be rigorously described by using the selfdiffusion coefficients which depend on the composition. The ion-exchange experiments are carried out between glass and molten salt, and glass-glass couples. The experimental distributions after ion-exchange were quantitatively determined by means of an EPMA. When the treated conditions in an ion-exchange experiment were same as the calculation conditions, the simulation profiles coincided closely with the experimental ones. The concentration distributions are transformed into refractive indexes. As we have obtained the convincing condusion that the computer simulation on the diffusion theory is effective, some profiles bompulncl were demonstrated for the purpose of support to the development of gradient index glasses. Less