Light scattering in transparent glass ceramics

Abstract

Transparent glass ceramic materials, with microstructures comprised of dispersed nanocrystallites in a residual glass matrix, offer the prospect of nonlinear optical properties. However, good transparency requires low optical scattering and low atomic absorption. The attenuation of light due to scattering (turbidity) will depend upon the difference in refractive index of the two phases and the size and distribution of crystals in the glass. Here, we model the glass ceramic as a late-stage phase-separated structure, and compute scattering in this model. We find that the turbidity follows a k 8 R 7 relationship, where k is the wavevector of light in the glass ceramic and R is the average radius of the crystals in the glass.Glass ceramics are glasses containing nanometer to micron sized crystals embedded in a glass matrix. Glass ceramics are easier to manufacture into complex shapes than traditional ceramics, utilizing standard techniques developed for the glass industry [1]. In addition, the embedded crystalline phase can enhance existing, or offer entirely new, properties from that of the parent glass. Recently, much attention has been paid to optically transparent glass ceramics [2,3,4], which have greater thermal stability than their parent glasses. Transparent oxyflouride glass ceramics, for example, can be doped with optically active rare-earth cations, offering the possibility of numerous applications in nonlinear optics [3]. However, the understanding of the transparency of these nanophase glass ceramics is still relatively poor. Transparency has been found to occur in glasses with large volume fractions of crystals (∼ 30-35 %) and nanoscale crystal sizes (1-15 nm). Application of the Mie theory of scattering to such a material, leads to an over-estimate of the attenuation due to scattering (turbidity) by many orders of magnitude [2].A more sophisticated approach is to use RayleighDebye theory, which allows for the possibility of coherence and interference between scatterers. To describe the scattering, this theory requires a structure factor which depends on the distribution of scatterers in the medium. For example, Hopper [5] has developed an approximate structure factor for glasses which have undergone latestage microstructural phase separation via spinodal decomposition. Hopper's structure factor has been used to describe the scattering in transparent glass ceramics [3,4] and gives a turbidity ofwhere k is the wavevector of the incident light propagating in a medium with refractive indexn, ∆n is the difference in refractive index between the glass and crystal phases, and L is the mean distance between phases. This model improves on Mie theory, predicting turbidities that are somewhat closer to those measured for transparent glass ceramics.Subsequent to Hopper's work, there has been a considerable improvement in the understanding of late-stage structure factors in phase-separated media [6,7,8,9]. In particular, the small wave-number limit of the late-stage structure factor is now well characterized. We w...

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