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![[Figure 2]](to5146fig2mag.jpg)
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Figure 2
Phonons in periodic crystals. Envelope functions of the diffraction peaks for a periodic crystal with phononic disorder obtained by three different shapes of atomic distributions around ideal positions: Gaussian (black circles, curve A), Bessel function (red crosses, curve B) and cardinal sine function sin(x)/x (blue triangles, curve C). The diffraction pattern is periodic with a discrete set of peaks – note the equidistantly distributed peaks. The corresponding probability distributions P(u) for a periodic structure given by (a) Gaussian, (b) harmonic and (c) uniform distributions are shown in insets. For ideal positions the Dirac delta function applies (marked with dashed vertical lines in each inset). The periodic cell parameter is denoted as a. The envelope function is the square of the Fourier transform of the corresponding distribution function P(u). |
![[Figure 2]](to5146fig2.jpg)
 | JOURNAL OF APPLIED CRYSTALLOGRAPHY |
ISSN: 1600-5767
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