Following on from my primary studies, the rest of my time will be divided between two areas : the simulation and classification of spheres in a close packed arrangement and the modelling of percolation within these structures.
1. Simulation and classification
Synthetic opals (SiO2) can be easily made in the laboratory, however, the physical size of the spheres cannot be made so sphere 1 = sphere 2. This gives rise to a number of problems, such as settling, distortions, pore unevenness (which has it's own subset of problems) and most of all, accurate determination of how liquid settle within these structures. They can be made within a reasonable level of accuracy (around 3% difference in sphere size).
A good approximation of these can be made with table tennis balls (the size and tolerance of which are laid down by the Table Tennis association). The close packing arrangement can be made by placing the balls into a suitable contained and placing the balls on top of each other.
Under standard conditions (STP), the balls will settle in the box (diagram 18) with the forces on opposing balls (diagram 19). It is important to note that the effect of gravity (G0 and G1) will be the same for each row of balls and the forces between the balls (van der Waals, W0, W1 and W2) will be the same. There is an effective zero deformation and constitutes the crystal in a zero energy (defect) condition.
Deformation of the lattice
The lattice deformation is achieved by placing a plateau of varied height (up to a
maximum of
).
Any change in the distance from the base of the box to that of the first layer of
balls will affect the surrounding sphere (diagrams 20 and 21). The effect of
gravity on the raised spheres will change by
.
There will also be a deformation angle, a.
a varies with the height of the plateau. With the
change in the internal lattice structure, there will also be a net change of
internal energy and a strain will be placed on the nearest neighbours not affected
by the plateau.
Diagram 20.
Diagram 21.
Diagrams 20 and 21 do not take into account the small cohesive forces (such as van der Waals) between the spheres and their nearest neighbours. For very small defects, it is seen in nature that given enough layers, over a large enough distance, this defect is removed (an example would be a piece of coal in a bucket with sand poured over. After a certain point, the surface will be flat). A larger scale version (and exaggerated) is given in diagram 22. By the time the balls have reached the 5th layer, the interaction between the balls is enough to straighten the surface.
By performing a series of experiments with differing plateau heights, it should be possible to predict how the FCC lattice corrects for defects and from there, determine how the crystal will infill with liquid vapours.
Diagram 22.
Gravity will also have a bearing on how the spheres settle. The spheres will always settle in the lowest possible energy state (in this case, conformation). In the case of the box, they will try and fill as much space at the bottom before having to form the next layer. With the introduction of the defects, "gap space" appears which will mean a further unevenness in the layering. This can be largely avoided by filling in the gaps with appropriate sized fillers.
The exact depth of the layer difference between the flat and defected flat will need to be measured. As this is a critical measurement and the gaps in some cases too small for a weighted string, a different method will need to be devised.
Percolation.
The results from the microbalance experiments at Hiden and Salford (combined with the neutron scattering results at Rutherford Appleton Labs) show that infill of opals is possible and is reversible. The Kelvin equation also shows that altering the surface tension will alter the contact angle, and effect how the opal will fill and drain. By studying different solvents and both their hysterisis loops and neutron scattering patterns, an overall series can be built up on how these effect the percolative abilities.
Given the definition of the vapour being that of any gas below the critical point (see Modelling and Practice), by knowing the surface tension of any vapour, it should possible to predict how this will move within an opal.
With the current research into infilling opals with various substrates (such as gallium arsenide), the ability to predict the degree of infill can be used to refine the process and also be used for the creation of cheap lasers by filling the opal with a suitable dyestuff (one with the correct photonic properties).