An improved transformation procedure for radial distribution function analysis

Lovell, R.; Mitchell, Geoffrey R.; Windle, A. H.

doi:10.1107/s0567739479001406

Cited by 37 publications

(9 citation statements)

References 11 publications

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“…͑7͒ at R max induces spurious ripples with a period of ⌬ =2 / R max . 40 A number of methods have been proposed to suppress these ripples so that the Fourier ringing dies out more quickly. 35,38,39,41,42 The method that we adopt in this work is to multiply the integrand in Eq.…”

Section: ͑2͒mentioning

confidence: 99%

Time-resolved diffraction profiles and atomic dynamics in short-pulse laser-induced structural transformations: Molecular dynamics study

2006

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The diffraction profiles and density correlation functions are calculated for transient atomic configurations generated in molecular dynamics simulations of a 20 nm Au film irradiated with 200 fs laser pulses of different intensity. The results of the calculations provide an opportunity to directly relate the detailed information on the atomic-level structural rearrangements available from the simulations to the diffraction spectra measured in time-resolved x-ray and electron diffraction experiments. Three processes are found to be responsible for the evolution of the diffraction profiles. During the first several picoseconds after the laser excitation, the decrease of the intensity of the diffraction peaks is largely due to the increasing amplitude of thermal atomic vibrations and can be well described by the Debye-Waller factor. The effect of thermoelastic deformation of the film prior to melting is reflected in shifts and splittings of the diffraction peaks, providing an opportunity for experimental probing of the ultrafast deformations. Finally, the onset of the melting process results in complete disappearance of the crystalline diffraction peaks. The homogeneous nucleation of a large number of liquid regions throughout the film is found to be more effective in reducing long-range correlations in atomic positions and diminishing the diffraction peaks as compared to the heterogeneous melting by melting front propagation. For the same fraction of atoms retaining the local crystalline environment, the diffraction peaks are more pronounced in heterogeneous melting. A detailed analysis of the real space correlations in atomic positions is also performed and the atomic-level picture behind the experimentally observed fast disappearance of the correlation peak corresponding to the second nearest neighbors in the fcc lattice during the laser heating and melting processes is revealed.

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Section: ͑2͒mentioning

confidence: 99%

Time-resolved diffraction profiles and atomic dynamics in short-pulse laser-induced structural transformations: Molecular dynamics study

2006

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“…These effects, combined with the experimental uncertainty in the structure factor, affect the extraction of the three-dimensional liquid structure from the RDF. Several attempts have been made to propose mathematical procedures to reduce this numerical error in the RDF (Yarnell et al, 1973;Waser & Schomaker, 1953;Kaplow et al, 1965;Narayan & Ramaseshan, 1979;Vorob'ev & Yur'ev, 1975;Wei, 1986;Lovell et al, 1979;Sorenson et al, 2000;Peterson et al, 2003;D'Alessandro, 2011;Soper & Barney, 2012) but 'there appear examples in the literature right up to the present where Fourier transform ripples are mistaken for genuine structure' (Soper & Barney, 2012).…”

Section: Introductionmentioning

confidence: 99%

Determination of the structure of liquids: an asymptotic approach

Mayo

Yahel²,

Greenberg³

et al. 2013

J Appl Cryst

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Accurate determination of a liquid structure, especially at high temperatures, remains challenging, as reflected in the scatter between different measurements. The experimental challenge is compounded by the process of the numerical transformation from the structure factor to the radial distribution function. The resulting uncertainty is often greater than that required to resolve issues associated with changes in the short-range order of the liquid, such as the existence of liquid-liquid phase transitions or correlations between thermophysical properties and structure. In the present contribution it is demonstrated for liquid bismuth as a model system that the structure factor can be obtained to high accuracy, by comparing several independent measurements in different setups. A simple method is proposed for improving the accuracy of the radial distribution functions, based on the extension of the finite range of momentum transfer, q, in the measured data by analytical asymptotic expressions. A unified mathematical formalism for the asymptotic dependence of the structure factor is developed and the asymptotic form of the Percus-Yevick hard-sphere solution is obtained as a special limiting case. The multiple expressions in the literature are shown to reflect uncertainty in the nature of the repulsive interatomic interaction at short separation distances. Applying this asymptotic method, it is shown that it enables access to details of the fine structure of the liquid and its temperature dependence. research papers J. Appl. Cryst. (2013). 46, 1582-1591 Martin Mayo et al. Determination of the structure of liquids 1591

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“…Fourier transforms were applied to the interference functions. In some cases, the points were calculated only for r-values that satisfied r = nπ/Q max (n = 1, 2, 3 …), known as sampling [11]. Fourier transformations directly yield the corresponding pair distribution functions G(r) (PDF) and from these, one can calculate the radial distribution functions (J(r), RDF) using an average density of ion implanted a-Ge of 0.0435 at/Å 3 [12].…”

Section: Articlementioning

confidence: 99%