Structure determination - Revision history

ShigeruOhba at 14:08, 26 March 2019

2019-03-26T14:08:03Z

BrianMcMahon: Added German and Spanish translations (U. Mueller)

2017-11-20T08:53:26Z

Added German and Spanish translations (U. Mueller)

MassimoNespolo: /* Experimental techniques */ why "polymer' ?

2017-10-12T14:03:21Z

‎Experimental techniques: why "polymer' ?

BrianMcMahon: Style edits to align with printed edition

2017-05-17T11:15:01Z

Style edits to align with printed edition

MassimoNespolo: /* Methodology */ internal link

2016-04-15T09:06:11Z

‎Methodology: internal link

BrianMcMahon at 16:31, 1 April 2008

2008-04-01T16:31:51Z

BrianMcMahon: /* Methodology */

2008-03-29T13:18:45Z

‎Methodology

BrianMcMahon at 13:17, 29 March 2008

2008-03-29T13:17:03Z

BrianMcMahon at 12:05, 29 March 2008

2008-03-29T12:05:00Z

New page

== Definition ==

'''Structure determination''' in crystallography refers to the process of elaborating the three-dimensional positional coordinates (and also, usually, the three-dimensional anisotropic displacement parameters) of the scattering centres in an ordered crystal lattice. Where a crystal is composed of a molecular compound, the term generally includes the three-dimensional description of the ''chemical'' structures of each molecular compound present.

== Experimental techniques ==

Owing to the highly ordered arrangement of atoms as scattering centres in a crystal lattice, most structure determination techniques involve the diffraction of electromagnetic or matter waves of wavelengths comparable to atomic dimensions. [[Bragg's Law]] specifies the condition for plane waves to be diffracted from lattice planes. The diffracted radiation passing through a crystal emerges with intensity varying as a function of scattering angle. This variation arises from constructive and destructive interference of scattered beams from the planes associated with the different atoms present in the lattice. The result is seen by an imaging detector as a pattern of diffraction spots or rings.

Among diffraction-based techniques are:

* single-crystal X-ray diffraction
* X-ray powder diffraction
* X-ray fibre diffraction
* neutron powder diffraction (occasionally neutron single-crystal diffraction)
* polymer electron diffraction

Other techniques for three-dimensional structure determination that are complementary to diffraction methods include

* electron microscopy
* nuclear magnetic resonance spectroscopy (used largely for biological macromolecules in solution)

== Methodology ==

The following summary applies to single-crystal X-ray diffraction. A crystal, mounted on a goniometer, is illuminated by a collimated monochromatic X-ray beam, and the positions and intensities of diffracted beams are measured. The measured intensities <math>I_{hkl}</math> (corresponding to scattering from a lattice plane with [[Miller indices]] <math>h, k, l</math> are reduced to structure amplitudes <math>F_{hkl}</math> by the application of a number of experimental corrections:

<math>F^2_{hkl} = I_{hkl}(k \mathrm{Lp} A)^{-1}</math>

where <math>k</math> is a scale factor, Lp the [[Lorentz--polarization correction]], and <math>A</math> the transmission factor representing the absorption of X-rays by the crystal. The structure amplitude represents the amplitude of the diffracted wave measured relative to the scattering amplitude of a single electron.

== See also ==

Dynamical theory of X-ray diffraction
A. Authier. ''International Tables for Crystallography'' (2006). Vol. B, ch. 5.1, pp. 534-551 [http://dx.doi.org/10.1107/97809553602060000569 doi:10.1107/97809553602060000569]

Dynamical theory of electron diffraction
A. F. Moodie, J. M. Cowley and P. Goodman. ''International Tables for Crystallography'' (2006). Vol. B, ch. 5.2, pp. 552-556 [http://dx.doi.org/10.1107/97809553602060000570 doi:10.1107/97809553602060000570]

Dynamical theory of neutron diffraction
M. Schlenker and J.-P. Guigay. ''International Tables for Crystallography'' (2006). Vol. B, ch. 5.3, pp. 557-569 [http://dx.doi.org/10.1107/97809553602060000571 doi:10.1107/97809553602060000571]

[[Category:Structure determination]]

← Older revision		Revision as of 14:08, 26 March 2019
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−	<font color="red">Strukturbestimmung</font> (''Ge''). <font color="green">Determinación estructural</font> (''Sp'').	+	<font color="red">Strukturbestimmung</font> (''Ge''). <font color="purple">構造決定</font> (''Ja''). <font color="green">Determinación estructural</font> (''Sp'').

← Older revision		Revision as of 08:53, 20 November 2017
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		+	<font color="red">Strukturbestimmung</font> (''Ge''). <font color="green">Determinación estructural</font> (''Sp'').
		+
		+
	== Definition ==		== Definition ==

@@ Line 44: / Line 44: @@
 The atomic scattering factor can be worked out from the physical properties of the atom species, but the phase cannot be determined by direct experimental observation. If the phases can be derived in some way, then the positional coordinates can be calculated from the expression above. The [[phase problem]] represents the major obstacle to constructing an initial structural model, and is addressed through a number of techniques, such as [[direct methods]], Patterson synthesis, heavy-atom method, isomorphous replacement ''etc.''
-Once an initial structural model has been calculated, it is usually necessary to conduct an iterative [[refinement]] procedure to improve the agreement between the structural model and the experimental diffraction intensities. The most common approach is to perform a least-squares minimization between the experimental structure factors and those calculated by varying the adjustable parameters of the structural model. These normally include atomic positions, anisotropic displacement parameters, occupancies, chemical bond lengths and angles, and other geometric characteristics of a molecule. Some metric, such as the residual [[R factor]]
+Once an initial structural model has been calculated, it is usually necessary to conduct an iterative [[refinement]] procedure to improve the agreement between the structural model and the experimental diffraction intensities. The most common approach is to perform a least-squares minimization between the experimental structure factors and those calculated by varying the adjustable parameters of the structural model. These normally include atomic positions, anisotropic displacement parameters, occupancies, chemical bond lengths and angles, and other geometric characteristics of a molecule. Some metric, such as the residual [[R factor|''R'' factor]]
 <math>R = {{\sum | F_{obs} - F_{calc} | } \over {\sum |F_{obs} |}}</math>,
-is used to indicate improvements or reductions in the quality of fit between model and observation. In the expression above (the 'conventional' R factor), <math>F_{obs}</math> and <math>F_{calc}</math> are the observed and calculated structure amplitudes, and the deviations are summed over all experimentally recorded intensities. There is considerable discussion on the most appropriate statistical metric to use for this purpose.
+is used to indicate improvements or reductions in the quality of fit between model and observation. In the expression above (the 'conventional' ''R'' factor), <math>F_{obs}</math> and <math>F_{calc}</math> are the observed and calculated structure amplitudes, and the deviations are summed over all experimentally recorded intensities. There is considerable discussion on the most appropriate statistical metric to use for this purpose.
 Other refinement techniques, such as [[maximum likelihood]] and maximum entropy, are also used.
@@ Line 54: / Line 54: @@
 == See also ==
-Dynamical theory of X-ray diffraction.
+*Dynamical theory of X-ray diffraction. A. Authier. ''International Tables for Crystallography'' (2006). ''Vol. B'', [https://doi.org/10.1107/97809553602060000569 ch. 5.1, pp. 534-551]
-Dynamical theory of electron diffraction.
+*Dynamical theory of electron diffraction. A. F. Moodie, J. M. Cowley and P. Goodman. ''International Tables for Crystallography'' (2006). ''Vol. B'', [https://doi.org/10.1107/97809553602060000570 ch. 5.2, pp. 552-556]
-Dynamical theory of neutron diffraction.
+*Dynamical theory of neutron diffraction. M. Schlenker and J.-P. Guigay. ''International Tables for Crystallography'' (2006). ''Vol. B'',  [https://doi.org/10.1107/97809553602060000571 ch. 5.3, pp. 557-569]
-Least squares.
+*Least squares. E. Prince and P. T. Boggs. ''International Tables for Crystallography'' (2006). ''Vol. C'', [https://doi.org/10.1107/97809553602060000609 ch. 8.1, pp. 678-688]
-Other refinement methods.
+*Other refinement methods. E. Prince and D. M. Collins. ''International Tables for Crystallography '' (2006). ''Vol. C'', [https://doi.org/10.1107/97809553602060000610 ch. 8.2, pp. 689-692]
 [[Category:Structure determination]]

@@ Line 50: / Line 50: @@
 is used to indicate improvements or reductions in the quality of fit between model and observation. In the expression above (the 'conventional' R factor), <math>F_{obs}</math> and <math>F_{calc}</math> are the observed and calculated structure amplitudes, and the deviations are summed over all experimentally recorded intensities. There is considerable discussion on the most appropriate statistical metric to use for this purpose.
-Other refinement techniques, such as maximum likelihood and maximum entropy, are also used.
+Other refinement techniques, such as [[maximum likelihood]] and maximum entropy, are also used.
 == See also ==

@@ Line 27: / Line 27: @@
 <math>F^2_{hkl} = I_{hkl}(k \mathrm{Lp} A)^{-1}</math>
-where <math>k</math> is a scale factor, Lp the [[Lorentz--polarization correction]], and <math>A</math> the transmission factor representing the absorption of X-rays by the crystal. The structure amplitude represents the amplitude of the diffracted wave measured relative to the scattering amplitude of a single electron.
+where <math>k</math> is a scale factor, Lp the [[Lorentz&ndash;polarization correction]], and <math>A</math> the transmission factor representing the absorption of X-rays by the crystal. The structure amplitude represents the amplitude of the diffracted wave measured relative to the scattering amplitude of a single electron.
 However, the diffracted wave is completely described by the [[structure factor]] <math>\mathbf{F}_{hkl}</math>:

@@ Line 9: / Line 9: @@
 Among diffraction-based techniques are:
-* single-crystal X-ray diffraction
+* X-ray diffraction (single-crystal, fibre, powder)
-* X-ray powder diffraction
+* neutron diffraction  (single-crystal, powder)
-* X-ray fibre diffraction
+* electron diffraction (Selected Area, Convergent Beam, Precession)
-* neutron powder diffraction
+* gamma-ray diffraction
 Other techniques for three-dimensional structure determination that are complementary to diffraction methods include
-* electron microscopy
+* transmission electron microscopy
 * nuclear magnetic resonance spectroscopy (used largely for biological macromolecules in solution)

@@ Line 5: / Line 5: @@
 == Experimental techniques ==
-Owing to the highly ordered arrangement of atoms as scattering centres in a crystal lattice, most structure determination techniques involve the diffraction of electromagnetic or matter waves of wavelengths comparable to atomic dimensions. [[Bragg's Law]] specifies the condition for plane waves to be diffracted from lattice planes. The diffracted radiation passing through a crystal emerges with intensity varying as a function of scattering angle. This variation arises from constructive and destructive interference of scattered beams from the planes associated with the different atoms present in the lattice. The result is seen by an imaging detector as a pattern of diffraction spots or rings.
+Owing to the highly ordered arrangement of atoms as scattering centres in a crystal lattice, most structure determination techniques involve the diffraction of electromagnetic or matter waves of wavelengths comparable to atomic dimensions. [[Bragg's law]] specifies the condition for plane waves to be diffracted from lattice planes. The diffracted radiation passing through a crystal emerges with intensity varying as a function of scattering angle. This variation arises from constructive and destructive interference of scattered beams from the planes associated with the different atoms present in the lattice. The result is seen by an imaging detector as a pattern of diffraction spots or rings.
 Among diffraction-based techniques are:
@@ Line 12: / Line 12: @@
   * X-ray powder diffraction
   * X-ray fibre diffraction
-  * neutron powder diffraction (occasionally neutron single-crystal diffraction)
+  * neutron powder diffraction
   * polymer electron diffraction
@@ Line 22: / Line 23: @@
 == Methodology ==
-The following summary applies to single-crystal X-ray diffraction. A crystal, mounted on a goniometer, is illuminated by a collimated monochromatic X-ray beam, and the positions and intensities of diffracted beams are measured. The measured intensities <math>I_{hkl}</math> (corresponding to scattering from a lattice plane with [[Miller indices]] <math>h, k, l</math> are reduced to structure amplitudes <math>F_{hkl}</math> by the application of a number of experimental corrections:
+The following summary applies to single-crystal X-ray diffraction. A crystal, mounted on a goniometer, is illuminated by a collimated monochromatic X-ray beam, and the positions and intensities of diffracted beams are measured. The measured intensities <math>I_{hkl}</math> (corresponding to scattering from a lattice plane with [[Miller indices]] <math>h, k, l</math>) are reduced to structure amplitudes <math>F_{hkl}</math> by the application of a number of experimental corrections:
 <math>F^2_{hkl} = I_{hkl}(k \mathrm{Lp} A)^{-1}</math>
@@ Line 28: / Line 29: @@
 where <math>k</math> is a scale factor, Lp the [[Lorentz--polarization correction]], and <math>A</math> the transmission factor representing the absorption of X-rays by the crystal. The structure amplitude represents the amplitude of the diffracted wave measured relative to the scattering amplitude of a single electron.
 == See also ==
-Dynamical theory of X-ray diffraction
+Dynamical theory of X-ray diffraction.
 A. Authier. ''International Tables for Crystallography'' (2006). Vol. B, ch. 5.1, pp. 534-551  [http://dx.doi.org/10.1107/97809553602060000569 doi:10.1107/97809553602060000569]
-Dynamical theory of electron diffraction
+Dynamical theory of electron diffraction.
 A. F. Moodie, J. M. Cowley and P. Goodman. ''International Tables for Crystallography'' (2006). Vol. B, ch. 5.2, pp. 552-556  [http://dx.doi.org/10.1107/97809553602060000570 doi:10.1107/97809553602060000570]
-Dynamical theory of neutron diffraction
+Dynamical theory of neutron diffraction.
 M. Schlenker and J.-P. Guigay. ''International Tables for Crystallography'' (2006). Vol. B, ch. 5.3, pp. 557-569  [http://dx.doi.org/10.1107/97809553602060000571 doi:10.1107/97809553602060000571]
 [[Category:Structure determination]]