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- Crystal growth (1)
- Crystal morphology (1)
- Crystal orientation (1)
- Crystallization (1)
- EBSD (1)
- Fresnoite (1)
- Growth kinetics (1)
- Growth rate (1)
- JMAK model (1)
- Supersaturation (1)
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- 5 Werkstofftechnik (2)
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Controlled oriented crystallization of glass surfaces is desired for high precision applications, since the uppermost crystal layer significantly influences the properties of the material. In contrast to previous studies, the data presented here deal with separated crystals growing at defect-free surfaces in four atmospheres with different degrees of humidity (ambient/dry air, argon and vacuum). A glass with the composition 2 BaO–TiO2–2.75 SiO2 was heat-treated at 825 °C until fresnoite (Ba2TiSi2O8) grew to a significant size. The crystal growth rate is found to increase with increasing humidity. The morphology of the crystals changes from highly distorted dendrites in the driest atmosphere (vacuum) to circular/spear-head-shaped crystals in the wettest atmosphere (ambient air), which we attribute to a decrease in viscosity of the glass surface due to water uptake. The least distorted crystals appear in the form of depressions of up to 6 µm. This has an influence on the observed crystal orientation, as measured by electron backscatter diffraction (EBSD). The pulled-in crystals change the orientation during growth relative to the flat glass surface due to an enrichment in SiO2 at the crystal fronts. This confirms that the orientation of crystals is not fixed following nucleation.
The crystallization proceeds by the advance of the crystal faces into the disordered phase at the expense of the material excess, the supersaturation. Using a conservation constraint for the transformation ratio α∈[0,1] as complementing the rescaled supersaturation to 1 and a kinetic law for the normal growth velocity as function of the supersaturation raised to power g, the growth order, we derive an equation for the rate of transformation dα/dt. We integrate it for the six combinations of the three spatial dimensions D = 1, 2, 3 and the two canonical values of g = 1, 2 towards obtaining expressions for αDg. The same equation, with g = 1 and D = n (n is the so called Avrami exponent) is obtained when taking only the linear in α term from the Taylor’s expansion around α = 0 of the model equation of Johnson-Mehl-Avrami-Kolmogorov (JMAK). We verify our model by fitting datasets of α21 and α31 (from α = 0 to αupper = 0.999) with JMAK to obtain from the fit n = 1.725, 2.43, resp. We show
further how the values of n depend on the value of αupper to which the fit is performed starting always from 0. Towards building a validation protocol, we start with validating α21 with published results.