Icosahedral incommensurate crystals
The icosahedral structures can be described by 6d space group symmetries and their stability can be understood from a simple Landau theory. The task of the crystallographer is to determine the basis associated with the 6d Bravais lattice. The elastic properties and the elementary excitations can be discussed in terms of these symmetries. The ideal icosahedral structures have complete long range order, with sharp Bragg peaks; it is certainly incorrect to consider them to be intermediate between crystals and glasses; they are crystals. It is not difficult to show that the structures are stable with respect to thermal fluctuations, which simply give rise to a reduction of the Bragg peak intensity. The melting transition is first order since the free energy includes third order terms. In a sense the icosahedral structures are incommensurate structures with only one length scale 2..pi../tau/sub i/. The incommensurability comes about because of the relative rotations of the 6 fundamental vectors tau/sub i/: it is not possible to write any of the 6 vectors as sums of rational multiples of the remaining 5 vectors.
- Research Organization:
- Brookhaven National Lab., Upton, NY (USA)
- DOE Contract Number:
- AC02-76CH00016
- OSTI ID:
- 5530860
- Report Number(s):
- BNL-36437; CONF-850882-1; ON: DE85012512
- Country of Publication:
- United States
- Language:
- English
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