Structure factor - Revision history

KevinYager at 18:07, 20 January 2015

2015-01-20T18:07:36Z

KevinYager: /* Mathematics */

2015-01-14T21:55:58Z

‎Mathematics

KevinYager: /* Mathematics */

2015-01-14T21:55:02Z

‎Mathematics

KevinYager: /* Mathematics */

2015-01-14T21:54:39Z

‎Mathematics

KevinYager at 14:00, 29 October 2014

2014-10-29T14:00:25Z

KevinYager at 19:08, 15 October 2014

2014-10-15T19:08:31Z

KevinYager at 18:41, 15 October 2014

2014-10-15T18:41:52Z

KevinYager: Created page with "The '''structure factor''' is an contribution to measured scattering. The structure factor, $\scriptstyle S(q)$ can be thought of as encoding the structural inf..."

2014-10-15T18:39:54Z

Created page with "The '''structure factor''' is an contribution to measured scattering. The structure factor, <math>\scriptstyle S(q)</math> can be thought of as encoding the structural inf..."

New page

The '''structure factor''' is an contribution to measured [[scattering]]. The structure factor, <math>\scriptstyle S(q)</math> can be thought of as encoding the structural information about the same: how the constituents are organized, in relation to one another. This can be contrasted with the [[form factor]], which is the scattering coming from the constituents themselves (i.e. their size, shape, and composition).

==Example Structure Factors==
* [http://en.wikipedia.org/wiki/Structure_factor Wikipedia]:
** [http://en.wikipedia.org/wiki/Structure_factor#Structure_factors_for_specific_lattice_types BCC]
** [http://en.wikipedia.org/wiki/Structure_factor#Structure_factors_for_specific_lattice_types FCC]
** [http://en.wikipedia.org/wiki/Structure_factor#Structure_factors_for_specific_lattice_types Diamond Crystal Structure]
* [http://www.ncnr.nist.gov/resources/old_applets/index.html NCNR SANS Resources]:
** [http://www.ncnr.nist.gov/resources/old_applets/sansmodels/SquareWellStruct.html SquareWell Model]
** [http://www.ncnr.nist.gov/resources/old_applets/sansmodels/HardSphereStruct.html HardSphere Model]
* Pedersen Review: [http://linkinghub.elsevier.com/retrieve/pii/S0001868697003126 Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting] Jan Skov Pedersen, Advances in Colloid and Interface Science 1997, 70, 171. [http://dx.doi.org/10.1016/S0001-8686(97)00312-6 doi: 10.1016/S0001-8686(97)00312-6]
*# Hard-sphere potential
*# Sticky hard-sphere potential
*# Screened Coulomb potential
*# Hard-sphere potential, polydisperse system
*# Sticky hard-sphere potential, polydisperse system
*# Screened Coulomb potential, polydisperse system
*# Cylinders
*# Solutions of polymers

← Older revision		Revision as of 18:07, 20 January 2015
Line 1:		Line 1:
−	The '''structure factor''' is a contribution to measured [[scattering]]. The structure factor, <math>\scriptstyle S(q)</math> can be thought of as encoding the ''structural'' information about the sample: how the constituents are organized, in relation to one another. This can be contrasted with the [[form factor]], which is the scattering coming from the constituents themselves (i.e. their size, shape, and composition).	+	The '''structure factor''' is a contribution to measured [[scattering]]. The structure factor, <math>\scriptstyle S(q)</math> can be thought of as encoding the ''structural'' information about the sample: how the constituents are organized, in relation to one another. This can be contrasted with the [[form factor]], which is the scattering coming from the constituents themselves (i.e. their size, shape, and composition). The structure factor may also be called the '''interference function''', since it describes how the scattering from different objects interferes.

	Different structure factors describe different spatial arrangements. Random or disordered materials have diffuse structure factors. Well-ordered materials, such as atomic crystals or nanoscale [[superlattices]], have structure factors with well-defined peaks, which encode the layer-spacing of repeating structures (i.e. <math>\scriptstyle S(q)</math> reflects the [[Fourier transform]] of the crystallographic symmetry).		Different structure factors describe different spatial arrangements. Random or disordered materials have diffuse structure factors. Well-ordered materials, such as atomic crystals or nanoscale [[superlattices]], have structure factors with well-defined peaks, which encode the layer-spacing of repeating structures (i.e. <math>\scriptstyle S(q)</math> reflects the [[Fourier transform]] of the crystallographic symmetry).

@@ Line 4: / Line 4: @@
 ==Mathematics==
-The [[scattering intensity]] is frequently divided into the contribution from the [[form factor]] (''F'') and structure factor (''S''):
+The [[scattering intensity]] is frequently divided into the contribution from the [[form factor]] (''F'' or ''P'') and structure factor (''S''):
 :<math>
 \begin{alignat}{2}
@@ Line 12: / Line 12: @@
 \end{alignat}
 </math>
-Thus, the structure factor can be obtained by dividing the measured intensity by an independently-measured (or predicted/assumed) form-factor:
+Thus, the structure factor can be obtained by dividing the measured intensity (<math>\scriptstyle I(q)</math>) by an independently-measured (or predicted/assumed) isotropic form-factor intensity (<math>\scriptstyle P(q)</math>):
 :<math>
 \begin{alignat}{2}

@@ Line 16: / Line 16: @@
 :<math>
 \begin{alignat}{2}
-S(q) & = \frac{I(q){P(q)}
+S(q) & = \frac{I(q)}{P(q)}
 \end{alignat}
 </math>

@@ Line 12: / Line 12: @@
 \end{alignat}
 </math>
 ==Example Structure Factors==

← Older revision		Revision as of 14:00, 29 October 2014
Line 1:		Line 1:
−	The '''structure factor''' is an contribution to measured [[scattering]]. The structure factor, <math>\scriptstyle S(q)</math> can be thought of as encoding the structural information about the ~~same~~: how the constituents are organized, in relation to one another. This can be contrasted with the [[form factor]], which is the scattering coming from the constituents themselves (i.e. their size, shape, and composition).	+	The '''structure factor''' is a contribution to measured [[scattering]]. The structure factor, <math>\scriptstyle S(q)</math> can be thought of as encoding the ''structural'' information about the sample: how the constituents are organized, in relation to one another. This can be contrasted with the [[form factor]], which is the scattering coming from the constituents themselves (i.e. their size, shape, and composition).

	Different structure factors describe different spatial arrangements. Random or disordered materials have diffuse structure factors. Well-ordered materials, such as atomic crystals or nanoscale [[superlattices]], have structure factors with well-defined peaks, which encode the layer-spacing of repeating structures (i.e. <math>\scriptstyle S(q)</math> reflects the [[Fourier transform]] of the crystallographic symmetry).		Different structure factors describe different spatial arrangements. Random or disordered materials have diffuse structure factors. Well-ordered materials, such as atomic crystals or nanoscale [[superlattices]], have structure factors with well-defined peaks, which encode the layer-spacing of repeating structures (i.e. <math>\scriptstyle S(q)</math> reflects the [[Fourier transform]] of the crystallographic symmetry).

← Older revision		Revision as of 19:08, 15 October 2014
Line 2:		Line 2:

	Different structure factors describe different spatial arrangements. Random or disordered materials have diffuse structure factors. Well-ordered materials, such as atomic crystals or nanoscale [[superlattices]], have structure factors with well-defined peaks, which encode the layer-spacing of repeating structures (i.e. <math>\scriptstyle S(q)</math> reflects the [[Fourier transform]] of the crystallographic symmetry).		Different structure factors describe different spatial arrangements. Random or disordered materials have diffuse structure factors. Well-ordered materials, such as atomic crystals or nanoscale [[superlattices]], have structure factors with well-defined peaks, which encode the layer-spacing of repeating structures (i.e. <math>\scriptstyle S(q)</math> reflects the [[Fourier transform]] of the crystallographic symmetry).
		+
		+	==Mathematics==
		+	The [[scattering intensity]] is frequently divided into the contribution from the [[form factor]] (''F'') and structure factor (''S''):
		+	:<math>
		+	\begin{alignat}{2}
		+	I(q) & = \langle \|F(\mathbf{q})\|^2 S(\mathbf{q}) \rangle \\
		+	& = P(q) \left\langle \frac{\|F(\mathbf{q})\|^2}{P(q)} S(\mathbf{q}) \right\rangle \\
		+	& = P(q)S(q)
		+	\end{alignat}
		+	</math>

	==Example Structure Factors==		==Example Structure Factors==

← Older revision		Revision as of 18:41, 15 October 2014
Line 1:		Line 1:
	The '''structure factor''' is an contribution to measured [[scattering]]. The structure factor, <math>\scriptstyle S(q)</math> can be thought of as encoding the structural information about the same: how the constituents are organized, in relation to one another. This can be contrasted with the [[form factor]], which is the scattering coming from the constituents themselves (i.e. their size, shape, and composition).		The '''structure factor''' is an contribution to measured [[scattering]]. The structure factor, <math>\scriptstyle S(q)</math> can be thought of as encoding the structural information about the same: how the constituents are organized, in relation to one another. This can be contrasted with the [[form factor]], which is the scattering coming from the constituents themselves (i.e. their size, shape, and composition).
		+
		+	Different structure factors describe different spatial arrangements. Random or disordered materials have diffuse structure factors. Well-ordered materials, such as atomic crystals or nanoscale [[superlattices]], have structure factors with well-defined peaks, which encode the layer-spacing of repeating structures (i.e. <math>\scriptstyle S(q)</math> reflects the [[Fourier transform]] of the crystallographic symmetry).

	==Example Structure Factors==		==Example Structure Factors==

Structure factor - Revision history

KevinYager at 18:07, 20 January 2015

KevinYager: /* Mathematics */

KevinYager: /* Mathematics */

KevinYager: /* Mathematics */

KevinYager at 14:00, 29 October 2014

KevinYager at 19:08, 15 October 2014

KevinYager at 18:41, 15 October 2014

KevinYager: Created page with "The '''structure factor''' is an contribution to measured scattering. The structure factor, \scriptstyle S(q) can be thought of as encoding the structural inf..."

KevinYager: Created page with "The '''structure factor''' is an contribution to measured scattering. The structure factor, $\scriptstyle S(q)$ can be thought of as encoding the structural inf..."