History As fl at as a pancake

Prof. John Parker As flat as a pancake

Prof John Parker discusses how to keep things in good shape.

We often use the word ‘flat’ in a rather derogatory sense, for example the party was a bit flat, or a flat drink. And yet for many purposes - windows and mirrors for example - flat is the pinnacle of perfection.

In the absence of significant external forces liquids tend to form shapes that minimise their surface area. So small fragments of glass when heated to a molten state will naturally form perfect spheres – for example ballotini, used in reflective paints. Similarly bubbles in poorly refined glass are usually spherical (unless stretched during forming).

This natural tendency for wrinkles (in liquids, not skin) to disappear is one aspect of highly transparent glass sheets and bottles and means objects viewed through them are undistorted. It also means that the silica soot particles formed in the gas phase and deposited on the inside of tubes in Chemical Vapour Deposition processing, can easily sinter to create fully dense glass layers and ultimately the preforms from which optical fibres are pulled.

But gravity imposes an additional force. Float glass relies on the natural tendency of a glass melt to spread out under gravity when supported on a denser medium, molten tin.

It does not extend indefinitely because minimising surface energy means minimising surface area. In this scenario the energies associated with the tin-melt, melt-atmosphere and tin-atmosphere interfaces define the optimum layer thickness. Fortunately, this is close to the commercially useful value of 6mm. Extending the range of thicknesses available requires the application of additional forces, created either by edge rollers angled to stretch the sheet or physical dams to increase the thickness.

Another situation where shape matters is in crystal growth. The energy penalty of creating a new surface by crystallisation is one reason why glasses exist.

Historically though opaque (white or milk) glasses have been made by controlled precipitation of crystals within a glassy matrix. Compounds of tin, arsenic, lead and antimony are particularly effective because their refractive indices are much higher than the glass.

Incident light suffered numerous reflections at each crystal-glass boundary so that little is transmitted, and the glass is opaque. The more boundaries and the larger the refractive index change the more effective are these opacifiers.

The additive concentrations are small enough that precipitation takes place just above the glass transition temperature when nucleation rates are high and growth rates low.

However, if the crystals are too small, less than the wavelength of light (0.5 µm), the optical physics changes and scattering falls away for a given quantity of precipitate.

For glass artists a problem arises. When reworking hot white glass, ‘coarsening’ occurs, driven by a reduction in surface energy; smaller particles re-dissolve and larger particles grow at their expense, maintaining the total concentration constant while reducing surface area.

So, opacity decreases and articles become more translucent because there are fewer boundaries.

Glasses coloured by metallic or semiconductor particles are strongly and selectively absorbing. Examples are gold, silver or copper precipitates giving the red (cranberry), yellow/orange, or deep red shades often found in tableware and stained-glass windows. Coarsening though spoils the size distribution and hence colour, particularly in reworked semiconductor doped glasses (Cd(S,Se)).

All those examples have smooth spherical particles because surface effects dominate. However, this changes when kinetic factors control the process.

Thus, at lower temperatures diffusion coefficients fall rapidly and steeper concentration gradients occur. Random variations in surface profile in small particles means that part of the surface experiences a higher concentration than another and consequently grows more quickly. As it ‘runs’ ahead of its neighbours it wins the competition for access to new material and a protuberance on an otherwise flat surface is formed. Kinetics dominate over surface energy.

The result is often the dendritic (treelike) structures often seen in photographs of ice crystals in snow.

It also happens with 1) opal glasses reheated near their liquidus temperature and results in brittle products and 2) with silver halide crystals grown in a silicate matrix and led to an interesting product.

The silver halide dendritic crystal tips when exposed to light are reduced to silver metal nanoparticles whose shape (length to width ratio) depends on the conditions of exposure.

Changing the aspect ratio of these silver particles changed the energy levels for the free electrons and hence their optical absorption. So, strongly coloured images could be developed in glassware, with colours dependent on light exposure. Sadly, the technology proved too expensive for mass production.

Dendritic structures are also seen in glass ‘stones’ arising from AZS refractories. The solution sacs around them have a supersaturated zirconia-rich composition where dendritic zirconia crystals can form. The high refractive index of zirconia results in a characteristic, high contrast image under the microscope.

Cristobalite dendrites are also found in siliceous defects formed when there is insufficient sodium sulphate to fulfil its secondary role as surfactant; dendrites grow from pre-existing crystals.

*Curator of the Turner Museum of Glass, The University of Sheffield, UK www.turnermuseum.group.shef.ac.uk j.m.parker@sheffield.ac.uk