On evaluating the standard deviation of<i>U</i><sub>eq</sub>

Schomaker, Verner; Marsh, R. E.

doi:10.1107/s0108767383001622

Cited by 50 publications

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“…The calculation of this estimate is described in detail by Schomaker & Marsh (1983). A useful measure of the anisotropy of the mean-square displacement tensor is the ratio of its minimum and maximum eigenvalues.…”

Section: Equivalent Isotropic Displacement Parametersmentioning

confidence: 99%

Atomic Dispacement Parameter Nomenclature. Report of a Subcommittee on Atomic Displacement Parameter Nomenclature

Trueblood¹,

Bürgi²,

Burzlaff³

et al. 1996

Acta Crystallogr A Found Crystallogr

356

242

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Modern X-ray and neutron diffraction techniques can give precise parameters that describe dynamic or static displacements of atoms in crystals. However, confusing and inconsistent terms and symbols for these quantities occur in the crystallographic literature. This report discusses various forms of these quantities, derived from probability density functions and based on Bragg diffraction data, both when the Gaussian approximation is appropriate and when it is not. The focus is especially on individual atomic anisotropic displacement parameters (ADPs), which may represent atomic motion and possible static displacive disorder. The first of the four sections gives background information, including definitions. The second concerns the kinds of parameter describing atomic displacements that have most often been used in crystal structure analysis and hence are most commonly found in the literature on the subject. It includes a discussion of graphical representations of the Gaussian mean-square displacement matrix. The third section considers the expressions used when the GaussJan approximation is not adequate. The final section gives recommendations for symbols and nomenclature.

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Section: Equivalent Isotropic Displacement Parametersmentioning

confidence: 99%

Atomic Dispacement Parameter Nomenclature. Report of a Subcommittee on Atomic Displacement Parameter Nomenclature

Trueblood¹,

Bürgi²,

Burzlaff³

et al. 1996

Acta Crystallogr A Found Crystallogr

356

242

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“…Absorption corrections, varying from 0.69 to 0.81, were applied (g= 117.8 cm-]). Wells ' (1949) coordinates of non-H atoms were refined anisotropically, and used to phase a Ap map which revealed Schomaker & Marsh (1983). (2) 1906 (1 Discussion.…”

mentioning

confidence: 99%

The structure of atacamite and its relationship to spinel

Parise¹,

Hyde²

1986

Acta Crystallogr C Cryst Struct Commun

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“…The calculation of these standard uncertainties is not straightforward, because it can involve the transformation to an orthogonal coordinate system (Fischer & Tillmanns, 1988). Therefore, in many instances approximations are used for the calculation (Schomaker & Marsh, 1983;Watkin, 2000). …”

Section: Practical Application 4: Equivalent Isotropic Adpsmentioning

confidence: 99%

Linear transformations of variance/covariance matrices

Parois

Lutz

2011

Acta Cryst Sect A

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Many applications in crystallography require the use of linear transformations on parameters and their standard uncertainties. While the transformation of the parameters is textbook knowledge, the transformation of the standard uncertainties is more complicated and needs the full variance/covariance matrix. For the transformation of second-rank tensors it is suggested that the 3 Â 3 matrix is re-written into a 9 Â 1 vector. The transformation of the corresponding variance/covariance matrix is then straightforward and easily implemented into computer software. This method is applied in the transformation of anisotropic displacement parameters, the calculation of equivalent isotropic displacement parameters, the comparison of refinements in different space-group settings and the calculation of standard uncertainties of eigenvalues.

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On evaluating the standard deviation ofU_eq

Cited by 50 publications

References 0 publications

Atomic Dispacement Parameter Nomenclature. Report of a Subcommittee on Atomic Displacement Parameter Nomenclature

Atomic Dispacement Parameter Nomenclature. Report of a Subcommittee on Atomic Displacement Parameter Nomenclature

The structure of atacamite and its relationship to spinel

Linear transformations of variance/covariance matrices

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On evaluating the standard deviation ofUeq

Cited by 50 publications

References 0 publications

Atomic Dispacement Parameter Nomenclature. Report of a Subcommittee on Atomic Displacement Parameter Nomenclature

Atomic Dispacement Parameter Nomenclature. Report of a Subcommittee on Atomic Displacement Parameter Nomenclature

The structure of atacamite and its relationship to spinel

Linear transformations of variance/covariance matrices

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Product

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About

On evaluating the standard deviation ofU_eq