Sayre equation - Revision history

BrianMcMahon: Rendered "pi" in math mode for clearer font and better portability.

2017-12-15T11:06:29Z

Rendered "pi" in math mode for clearer font and better portability.

BrianMcMahon: Tidied translations and added German and Spanish (U. Mueller)

2017-11-20T08:38:00Z

Tidied translations and added German and Spanish (U. Mueller)

MassimoNespolo: Created page with "Équation de Sayre (''Fr''); Equazione di Sayre (''It''). In direct methods, the '''Sayre equation''' is used to calcul..."

2017-09-01T18:33:36Z

Created page with "Équation de Sayre (''Fr''); Equazione di Sayre (''It''). In direct methods, the '''Sayre equation''' is used to calcul..."

New page

Équation de Sayre (''Fr''); Equazione di Sayre (''It'').

In [[direct methods]], the '''Sayre equation''' is used to calculate probable values for the phases of some reflections. Its formulation is the following:
<math>F_{hkl} = \sum_{h'k'l'} F_{h'k'l'}F_{h-h',k-k',l-l'} </math>
and states that the structure factor of a reflection ''hkl'' can be calculated as a function of structure factors whose [[Laue indices]] sum to the desired values of ''hkl''.
In particular, in a centrosymmetric structure, the phases of three reflections satisfying the above relation of Laue indices can only be 0 or π and the Sayre equation reduces to a relation between signs of structure factors:

<math>S_{h} \approx S_{h'} S_{h-h'} </math>

where the signs S are positive if the phase is 0 and negative if it is π and the <math>\approx</math> symbol indicates a certain degree of probability that the relationship is true, which becomes higher the stronger the reflections are.

[[Category: Structure determination]]

← Older revision		Revision as of 08:38, 20 November 2017
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−	<font color="blue">Équation de Sayre</font> (''Fr''); <font color="black">Equazione di Sayre</font> (''It'').	+	<font color="blue">Équation de Sayre</font> (''Fr''). <font color="red">Sayre-Gleichung</font> (''Ge''). <font color="black">Equazione di Sayre</font> (''It''). <font color="green">Ecuación de Sayre</font> (''Sp'').

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 In [[direct methods]], the '''Sayre equation''' is used to calculate probable values for the phases of some reflections. Its formulation is the following:
 <math>F_{hkl} = \sum_{h'k'l'} F_{h'k'l'}F_{h-h',k-k',l-l'} </math>
 and states that the structure factor of a reflection ''hkl'' can be calculated as a function of structure factors whose [[Laue indices]] sum to the desired values of ''hkl''.
-In particular, in a centrosymmetric structure, the phases of three reflections satisfying the above relation of Laue indices can only be 0 or π and the Sayre equation reduces to a relation between signs of structure factors:
+In particular, in a centrosymmetric structure, the phases of three reflections satisfying the above relation of Laue indices can only be 0 or <math>\pi</math> and the Sayre equation reduces to a relation between signs of structure factors:
 <math>S_{h} \approx S_{h'} S_{h-h'} </math>
-where the signs S are positive if the phase is 0 and negative if it is π and the <math>\approx</math> symbol indicates a certain degree of probability that the relationship is true, which becomes higher the stronger the reflections are.
+where the signs S are positive if the phase is 0 and negative if it is <math>\pi</math> and the <math>\approx</math> symbol indicates a certain degree of probability that the relationship is true, which becomes higher the stronger the reflections are.
 [[Category: Structure determination]]