Past exam of the materials science course of the University of Cambridge / 2015 / Paper 1 / 2 / b

An unstressed glass is optically isotropic, so it does not split incident light into differently phased in-plane components; it remains dark between crossed polars. A natural explanation of the colored regions after heating is devitrification: anisotropic crystallites have nucleated in the glass. Edges and surfaces provide heterogeneous nucleation sites, making their greater concentration there plausible.

Each approximately uniform crystallite can give a nearly uniform interference colour. Regions with similar thickness and effective birefringence have similar retardation and therefore similar spectral colour, while differing azimuths multiply the intensity by ${\sin }^2(2\alpha )$ and change brightness. Identical hue does not prove identical three-dimensional crystallographic orientation.

Stress-induced birefringence is a possible alternative in a heat-treated glass. The observations alone do not uniquely prove crystallinity; rotating-stage extinction, morphology or diffraction could distinguish the explanations. The crystallite interpretation is the straightforward phase-transformation explanation, without inventing a composition or heat-treatment schedule.

On rotating a fixed crystallite around the microscope axis, the angle $\alpha$ to the fixed polarizer changes. The factor ${\sin }^2(2\alpha )$ repeats every90degrees. Each birefringent region is therefore extinguished four times in a complete revolution and reaches maximum brightness45degrees from its own extinction positions.

Different regions need not extinguish together if their principal in-plane directions differ. For a fixed propagation direction through a uniform region, azimuthal rotation changes brightness more directly than its retardation colour: the underlying index difference and thickness remain the same. The isotropic unstressed matrix remains dark throughout rotation.

The quartz compensator is a birefringent optical compensator: a retarder of known principal directions. With its principal axes at45degrees to the polarizer and analyser, the previously dark isotropic background acquires the compensator's own interference colour. The crystals are now viewed through two retarders.

When a specimen's slow axis is parallel to the compensator's slow axis, the retardations add. A90degree relative principal-axis rotation pairs the specimen's slow axis with the compensator's fast axis, and the signed retardations subtract:Thus different crystallites can shift to higher or lower interference orders even if their original hue was similar. In the subtracting orientation, equal magnitudes can compensate and yield extinction. These shifts identify fast and slow specimen directions.

At a general relative angle the full polarization transformation is required; simple scalar addition is only valid for aligned principal axes. The source does not specify the compensator retardation, so no unique list of resulting named colours can be assigned. The robust predictions are a changed background, orientation-dependent addition or subtraction, and possible compensation.