An equilibrium crystal simulated by Gerard Barkema and Mark Holzer, here at Cornell (unpublished). |
This is not the reason diamond rings and salt grains have facets! The salt crystals on your table have facets because they break that way: diamonds have facets because jewellers grind them with great patience. It takes careful experiments to see these shapes: they've been seen in salt (NaCl), gold, lead, and in the blue phases of chiral nematic liquid crystals.
Rock crystals like quartz aren't showing equilibrium facets either: they develop facets because of the way they grow (rather than because it's the shape they like the best).
A simulated copper cluster. |
Heating up to the roughening transition.
(Perversely, it's called the roughening temperature because the nice, flat face becomes all bumpy and rugged above that temperature. Of course, the microscopic bumpy, rugged face with the wiggly and jiggly atoms makes the nice smooth, round shapes you see in the experiments: the ``rough'' phase has round faces and the ``smooth'' phase has facets.)
A salt (NaCl) crystal in equilibrium at a cooler temperature of 620 C. (Heyraud and Métois, J. Cryst. Growth 84, 503 (1987)). |
It's been really hard for experimentalists to see these corners. They tell us that the crystals get really slow and sluggish just around where the corners would form. Joel Shore studied this problem in our group, when we were trying to understand why glasses get sluggish just before they freeze. The way the crystal finds the right shape is a lot like the way coarsening occurs when a material (like a metal) with lots of small crystalline regions is annealed to let the big regions grow at the expense of small ones. Joel showed that coarsening looks completely different if the regions have sharp corners!
More Information
Much of the information here is derived from Michael Wortis, in ``Chemistry and Physics of Solid Surfaces VII,'' Springer Series in Surface Science 10, ed. R. Vanselow and R. Howe, pp. 367 (1988).
Last modified: February 11, 1995