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Response to the “comments on fourier transforms of truncated quasilattices”

Indian Academy of Sciences
Publication Date
  • Molecular Biophysics Unit
  • Physics


Response to the “comments on fourier transforms of truncated quasilattices” Pramana - J. Phys., Vol. 36, No. 4, April 1991, pp. C443-C444. © Printed in India. Response to the "comments on Fourier transforms of truncated quasilattices" V S K BALAGURUSAMY, S BARANIDHARAN, E S R GOPAL and V SASISEKHARAN* Department of Physics, *Molecular Biophysics Unit, Indian Institute of Science, Bangalore 560012, India It has been suggested by Srinivasan (1990) that the intensity fluctuations observed by us in the diffraction pattern of finite-size quasilattices are due to the effect of the window function which is well-known. It is shown that, in the present case, the window-function effect is quite negligible, contrary to the suggestion made by Srinivasan. It is also shown that several other features cannot be explained by the window-function whereas these are relevant to the present calculation. The contribution of the window-funGtion to the intensity fluctuations and the half-widths of the peaks in the diffraction from finite-size quasilattice have been estimated. The details are given below for the peak closest to the origin (x* ~ 2) which will be affected maximum by the window-function. The intensity fluctuations observed with the change in the size of the l-dimensional quasilattice cannot be quantitatively accounted for by the conventional finite-size effect known in the periodic lattice. The intensity distribution due to the slit-function (width L) is given by l(k)= (L(sin (kL/2)/(kL/2))) 2. The positions of the secondary maxima are approximately given by x*= n/2L; n:odd(k = 2nx*) (Sommerfeld 1954). At these positions, the intensity is given approximately by l(x* sec. max.) ~ LZ/2n 2. For the peak closest to the origin (x* .,~ 2"341), l(x* ,~, 2)/N 2 ~ 1/32N 2 where the number of scatterers, N ,~. L. For N = 20, l(x* .~ 2)/N 2 ~ 1/(32,400) ~ 0-8 x 10 -4. For N = 30, it comes to 0-4 x 10 -4. This gives the intensity fluctuation 0-4 x 10 -4 whereas t

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