J. Phys. I France
Volume 5, Numéro 9, September 1995
Page(s) 1213 - 1222
DOI: 10.1051/jp1:1995192
J. Phys. I France 5 (1995) 1213-1222

A Diffraction Method of Study of Thermal Quasiorder in a Finite Two-Dimensional Harmonic Lattice

P. Aranda and B. Croset

Groupe de Physique des Solides, URA CNRS 17, Tour 23-13, 2 place Jussieu, 75251 Paris Cedex 05, France

(Received 20 February 1995, revised 8 April 1995, accepted 17 May 1995)

Due to the non-existence of long-range order, the diffraction peaks of 2D-solids are considered to have a power-law shape $g_p^{\eta-2}$. Taking into account the finite size effects and calculating the powder average, we show that this power-law behaviour appears only for high qp and then for very small intensities. It is therefore quite difficult and hazardous to characterise the quasiorder by using this asymptotic behaviour. Although the shape of the central part of the peak cannot be used to characterise the quasiorder, we show that, for a fairly good resolution, it is possible to determine $\eta$ using this central part. This determination can be done irrespectively with the other details of the system by comparing the peak width to its value at low temperature, i.e., at low value of $\eta$. By using two diffraction peaks, we propose the simple relation: $\eta(Q_{B_1})/Q_{B_1}^2=\eta(Q_{B_2})/Q_{B_2}^2$ as a check of the two-dimensional quasiorder.

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