The three-dimensional pair distribution function analysis of disordered single crystals: basic concepts

Weber, Thomas; Simonov, Arkadiy

doi:10.1524/zkri.2012.1504

Cited by 100 publications

(143 citation statements)

References 17 publications

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“…Looking forward, one particular challenge for the PDF community is the development of a more complete understanding of which problems are definitively solvable using PDF analysis and which are not. Recent developments such as (i) the 3D-∆PDF approach, 85 (ii) "dynamic" PDF measurements which can in principle separate static and vibrational contributions to G(r) peak broadening, 86,87 and/or (iii) the ability to incorporate additional data from a variety of experimental techniques during PDF analysis [88][89][90][91] offer a particular sense of optimism in this regard.…”

Section: Discussionmentioning

confidence: 99%

Local structure study of the orbital order/disorder transition inLaMnO3

et al. 2017

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We use a combination of neutron and X-ray total scattering measurements together with pair distribution function (PDF) analysis to characterise the variation in local structure across the orbital order-disorder transition in LaMnO3. Our experimental data are inconsistent with a conventional order-disorder description of the transition, and reflect instead the existence of a discontinuous change in local structure between ordered and disordered states. Within the orbital-ordered regime, the neutron and X-ray PDFs are best described by a local structure model with the same local orbital arrangements as those observed in the average (long-range) crystal structure. We show that a variety of meaningfully-different local orbital arrangement models can give fits of comparable quality to the experimental PDFs collected within the disordered regime; nevertheless, our data show a subtle but consistent preference for the anisotropic Potts model proposed in Phys Rev. B 79, 174106 (2009). The key implications of this model are electronic and magnetic isotropy together with the loss of local inversion symmetry at the Mn site. We conclude with a critical assessment of the interpretation of PDF measurements when characterising local symmetry breaking in functional materials.

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Section: Discussionmentioning

confidence: 99%

Local structure study of the orbital order/disorder transition inLaMnO3

et al. 2017

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“…As the hightemperature phase is cubic, the low-temperature phase can easily become twinned. We analyze these diffuse-scattering data using the threedimensional difference pair distribution function (3D-ÁPDF) method (Canut-Amoró s, 1967;Schaub et al, 2007;Weber et al, 2007;Weber & Simonov, 2012), which makes it possible to directly construct the two-dimensional superstructure of the layers as well as identify the one-dimensional disorder of the layer stacking. In 2017, Eikeland et al showed that the diffraction pattern of a very high quality single crystal of -Cu 2Àx Se can be divided into strong main reflections and weak superstructure reflections and was able to solve the average structure from the main peak intensities only (Eikeland et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

“…However, this difficulty is not enough to explain the problem of solving the structure. The 3D-ÁPDF is defined as the inverse Fourier transform of the scattered diffuse intensity, which is equal to the autocorrelation of the difference between the total electron density and the average periodic electron density (Weber & Simonov, 2012): This average structure contains ordered Se sites and Cu on disordered sites.…”

Section: Introductionmentioning

confidence: 99%

Solving the disordered structure of β-Cu_2−xSe using the three-dimensional difference pair distribution function

Roth

Iversen

2019

Acta Crystallogr A Found Adv

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High-performing thermoelectric materials such as Zn 4 Sb 3 and clathrates have atomic disorder as the root to their favorable properties. This makes it extremely difficult to understand and model their properties at a quantitative level, and thus effective structure-property relations are challenging to obtain. Cu 2Àx Se is an intensely studied, cheap and non-toxic high performance thermoelectric, which exhibits highly peculiar transport properties, especially near the -tophase transition around 400 K, which must be related to the detailed nature of the crystal structure. Attempts to solve the crystal structure of the lowtemperature phase, -Cu 2Àx Se, have been unsuccessful since 1936. So far, all studies have assumed that -Cu 2Àx Se has a three-dimensional periodic structure, but here we show that the structure is ordered only in two dimensions while it is disordered in the third dimension. Using the three-dimensional difference pair distribution function (3D-ÁPDF) analysis method for diffuse single-crystal X-ray scattering, the structure of the ordered layer is solved and it is shown that there are two modes of stacking disorder present which give rise to an average structure with higher symmetry. The present approach allows for a direct solution of structures with disorder in some dimensions and order in others, and can be thought of as a generalization of the crystallographic Patterson method. The local and extended structure of a solid determines its properties and Cu 2Àx Se represents an example of a high-performing thermoelectric material where the local atomic structure differs significantly from the average periodic structure observed from Bragg crystallography.

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“…The calculation of the diffuse intensities could be further optimized by using GPU processors to Fourier transform the scattering density of the disordered crystals as shown by Gutmann (2010). In addition, they may be combined with other modeling techniques, MC modeling (Proffen & Welberry, 1998) and three-dimensional PDF techniques (Weber & Simonov, 2012) in particular. The resulting local structure variations may then provide a basis for explaining structure-property relationships of disordered materials.…”

Section: Discussionmentioning

confidence: 99%

Analyzing diffuse scattering with supercomputers

et al. 2013

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Two new approaches to quantitatively analyze diffuse diffraction intensities from faulted layer stacking are reported. The parameters of a probability-based growth model are determined with two iterative global optimization methods: a genetic algorithm (GA) and particle swarm optimization (PSO). The results are compared with those from a third global optimization method, a differential evolution (DE) algorithm [Storn & Price (1997). J. Global Optim. 11, 341-359]. The algorithm efficiencies in the early and late stages of iteration are compared. The accuracy of the optimized parameters improves with increasing size of the simulated crystal volume. The wall clock time for computing quite large crystal volumes can be kept within reasonable limits by the parallel calculation of many crystals (clones) generated for each model parameter set on a super-or grid computer. The faulted layer stacking in single crystals of trigonal three-pointedstar-shaped tris(bicylco[2.1.1]hexeno)benzene molecules serves as an example for the numerical computations. Based on numerical values of seven model parameters (reference parameters), nearly noise-free reference intensities of 14 diffuse streaks were simulated from 1280 clones, each consisting of 96 000 layers (reference crystal). The parameters derived from the reference intensities with GA, PSO and DE were compared with the original reference parameters as a function of the simulated total crystal volume. The statistical distribution of structural motifs in the simulated crystals is in good agreement with that in the reference crystal. The results found with the growth model for layer stacking disorder are applicable to other disorder types and modeling techniques, Monte Carlo in particular.

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The three-dimensional pair distribution function analysis of disordered single crystals: basic concepts

Cited by 100 publications

References 17 publications

Local structure study of the orbital order/disorder transition inLaMnO3

Local structure study of the orbital order/disorder transition inLaMnO3

Solving the disordered structure of β-Cu_2−xSe using the three-dimensional difference pair distribution function

Analyzing diffuse scattering with supercomputers

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The three-dimensional pair distribution function analysis of disordered single crystals: basic concepts

Cited by 100 publications

References 17 publications

Local structure study of the orbital order/disorder transition inLaMnO3

Local structure study of the orbital order/disorder transition inLaMnO3

Solving the disordered structure of β-Cu2−xSe using the three-dimensional difference pair distribution function

Analyzing diffuse scattering with supercomputers

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Product

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Solving the disordered structure of β-Cu_2−xSe using the three-dimensional difference pair distribution function