ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
Disorder resulting in a Gaussian distribution of lattice points around their average positions is investigated according to a bead-and-spring harmonic model of thermal fluctuations, which may also be approximately extended to defective lattices with structural inhomogeneities. Using both the monoatomic simple-cubic lattice model and a more sophisticated model with crossing bonds, exact results are obtained in both cases for the infinite crystal. Conversely, finite crystals are exactly treated within the first model only, whereas the second one is investigated through Monte Carlo simulations in the phase space of the phonon modes. The less accurate Monte Carlo results appear to support the analytical ones. Unlike Hosemann's model of the paracrystal, fluctuations of the lattice points cannot be described according to the convolution rule. In qualitative agreement with Hosemann's suggestions, disorder increases with decreasing crystal size. The half-peak width δS(S=2 sin θ/λ) of the diffraction lines varies as A/N+(BS)2/α, where A and B are suitable constants and N is the number of lattice points per cubic crystal edge. In the most significant S range comprised between two limits Smin and Smax, α=1 and B∝N−1, whereas α〉1 and α〈1 for S〈Smin and S〉Smax, respectively. While Smin vanishes for large N, Smax is slowly increasing with N.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.453312
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