Peak shape - Revision history

KevinYager at 13:15, 12 October 2016

2016-10-12T13:15:56Z

KevinYager: /* Other */

2015-07-19T15:41:01Z

‎Other

KevinYager at 14:12, 27 June 2015

2015-06-27T14:12:30Z

KevinYager: /* Other */

2015-03-17T17:34:46Z

‎Other

KevinYager: /* See Also */

2014-09-30T14:21:21Z

‎See Also

KevinYager at 14:20, 30 September 2014

2014-09-30T14:20:17Z

KevinYager: /* Fourier Analysis */

2014-09-08T15:34:37Z

‎Fourier Analysis

KevinYager: /* Grain Size Distribution */

2014-09-08T15:27:26Z

‎Grain Size Distribution

KevinYager: /* Literature Examples */

2014-09-08T15:10:51Z

‎Literature Examples

KevinYager: /* Literature Examples */

2014-09-08T15:03:15Z

‎Literature Examples

← Older revision		Revision as of 13:15, 12 October 2016
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	The [[peak width]] observed in x-ray scattering can be related to the grain size of the ordered structure giving rise to the scattering peak. More generally, the peak shape also encodes information about the sample order. Thus, peak shape analysis can be used to extract higher-order information.		The [[peak width]] observed in x-ray scattering can be related to the grain size of the ordered structure giving rise to the scattering peak. More generally, the peak shape also encodes information about the sample order. Thus, peak shape analysis can be used to extract higher-order information.
		+
		+	One interpretation of peak shape is that encodes the average grain ''shape''. That is, the peak shape function is the [[Fourier transform]] of the grain shape. Specific examples:
		+	* Gaussian peak in [[reciprocal-space]] implies a Gaussian-like decorrelation in [[realspace]] (i.e. that the ''average'' of grains/correlation-volumes decays with a Gaussian profile).
		+	* Lorentzian peak in reciprocal-space implies an exponential decorrelation in realspace.
		+	* Sinc function in reciprocal-space implies a top-hat function in realspace (sharp domain boundaries, with little to no variation in size of domains).

	Note also that [[instrumental resolution]] contributes to peak width, and also to peak shape. Scattering peaks are thus sometimes fit using functions that include two contributes (e.g. a Gaussian, representing material [[grain size]], plus a Lorentzian, representing instrumental resolution).		Note also that [[instrumental resolution]] contributes to peak width, and also to peak shape. Scattering peaks are thus sometimes fit using functions that include two contributes (e.g. a Gaussian, representing material [[grain size]], plus a Lorentzian, representing instrumental resolution).

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 * R.J. Hill and C.J. Howard, [http://journals.iucr.org/j/issues/1985/03/00/issconts.html Peak shape variation in fixed-wavelength neutron powder diffraction and its effect on structural parameters obtained by Rietveld analysis] ''J. Appl. Cryst.'' '''1985''', 18, 173-180 [http://dx.doi.org/10.1107/S0021889885010068 doi: 10.1107/S0021889885010068]
 * D. Louer and J.I. Langford [http://scripts.iucr.org/cgi-bin/paper?S002188988800411X Peak Shape and Resolution in Conventional Diffractometry with Monochromatic X-rays] ''J. Appl. Cryst.'' '''1988''', 21, 430-437.
 * Gy. Zilahi, T. Ungár and G. Tichy [http://scripts.iucr.org/cgi-bin/paper?po5024 A common theory of line broadening and rocking curves] ''J. Appl. Cryst.'' '''2015''', 48. [http://dx.doi.org/10.1107/S1600576715001466 doi: 10.1107/S1600576715001466]

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 The [[peak width]] observed in x-ray scattering can be related to the grain size of the ordered structure giving rise to the scattering peak. More generally, the peak shape also encodes information about the sample order. Thus, peak shape analysis can be used to extract higher-order information.
-Note also that [[instrumental resolution]] contributes to peak width, and also to peak shape. Scattering peaks are thus sometimes fit using functions that include two contributes (e.g. a Gaussian, representing material grain size, plus a Lorentzian, representing instrumental resolution).
+Note also that [[instrumental resolution]] contributes to peak width, and also to peak shape. Scattering peaks are thus sometimes fit using functions that include two contributes (e.g. a Gaussian, representing material [[grain size]], plus a Lorentzian, representing instrumental resolution).
 ==Generalized Peak Shape==

@@ Line 89: / Line 89: @@
 * R.J. Hill and C.J. Howard, [http://journals.iucr.org/j/issues/1985/03/00/issconts.html Peak shape variation in fixed-wavelength neutron powder diffraction and its effect on structural parameters obtained by Rietveld analysis] ''J. Appl. Cryst.'' '''1985''', 18, 173-180 [http://dx.doi.org/10.1107/S0021889885010068 doi: 10.1107/S0021889885010068]
 * D. Louer and J.I. Langford [http://scripts.iucr.org/cgi-bin/paper?S002188988800411X Peak Shape and Resolution in Conventional Diffractometry with Monochromatic X-rays] ''J. Appl. Cryst.'' '''1988''', 21, 430-437.
 ==See Also==

@@ Line 91: / Line 91: @@
 ==See Also==
 * [[Scherrer grain size analysis]]: Converting the peak width into a measure of the structural coherence length (grain size)
-* [http://prism.mit.edu/xray/oldsite/CrystalSizeAnalysis.ppt Estimating Crystallite Size Using XRD], Scott A. Speakman, MIT.
+* [[Ring graininess]]: Estimating grain size using the non-uniformity of the scattering ring. (Can be used to compute grain sizes even when the grains are so large that the peak width is instrumental-limited.)

@@ Line 80: / Line 80: @@
 ====Fourier Analysis====
 * C.E. Kril and R. Birringer, [http://www.tandfonline.com/doi/abs/10.1080/01418619808224072#.VA3KbdbgX0M Estimating grain-size distributions in nanocrystalline materials from X-ray diffraction profile analysis] ''Philosophical Magazine A'' '''1998''', 77 (3), 621-640 [http://dx.doi.org/10.1080/01418619808224072 doi: 10.1080/01418619808224072]
 ===Other===

@@ Line 78: / Line 78: @@
 * J. I. Langford, D. Louër and P. Scardi, [http://journals.iucr.org/j/issues/2000/03/02/th0047/index.html Effect of a crystallite size distribution on X-ray diffraction line profiles and whole-powder-pattern fitting] [http://dx.doi.org/10.1107/S002188980000460X doi: 10.1107/S002188980000460X]
 * T. Ungár, J. Gubicza, G. Ribárik and A. Borbély, [http://scripts.iucr.org/cgi-bin/paper?zm0085 Crystallite size distribution and dislocation structure determined by diffraction profile analysis: principles and practical application to cubic and hexagonal crystals] ''J. Appl. Cryst.'' '''2001''', 34, 298-310 [http://dx.doi.org/10.1107/S0021889801003715 doi: 10.1107/S0021889801003715]
 ===Other===

@@ Line 72: / Line 72: @@
 ===Williamson/Hall===
 * G.K. Williamson, W.H. Hall, [http://www.sciencedirect.com/science/article/pii/0001616053900066 X-ray line broadening from filed aluminium and wolfram] ''Acta Metallurgica'' '''1953''', 1 (1), 22-31.
 ===Other===

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 ==Literature Examples==
 ===Warren/Averbach [[paracrystal]]===
-* B. E. Warren [http://www.sciencedirect.com/science/article/pii/0502820559900152 X-RAY STUDIES OF DEFORMED METALS] ''Progress in Metal Physics'' '''1959''', 8, 174-202 [http://dx.doi.org/10.1016/0502-8205(59)90015-2 doi: 10.1016/0502-8205(59)90015-2]
+* B. E. Warren, [http://www.sciencedirect.com/science/article/pii/0502820559900152 X-RAY STUDIES OF DEFORMED METALS] ''Progress in Metal Physics'' '''1959''', 8, 174-202 [http://dx.doi.org/10.1016/0502-8205(59)90015-2 doi: 10.1016/0502-8205(59)90015-2]
-* B.E. Warren, B.L. Averbach [http://scitation.aip.org/content/aip/journal/jap/21/6/10.1063/1.1699713?ver=pdfcov The Effect of Cold‐Work Distortion on X‐Ray Patterns] ''J. Appl. Phys.'' '''1950''', 21, 595 [http://dx.doi.org/10.1063/1.1699713 doi: 10.1063/1.1699713]
+* B.E. Warren, B.L. Averbach, [http://scitation.aip.org/content/aip/journal/jap/21/6/10.1063/1.1699713?ver=pdfcov The Effect of Cold‐Work Distortion on X‐Ray Patterns] ''J. Appl. Phys.'' '''1950''', 21, 595 [http://dx.doi.org/10.1063/1.1699713 doi: 10.1063/1.1699713]
-* B.E. Warren, B.L. Averbach [http://scitation.aip.org/content/aip/journal/jap/23/4/10.1063/1.1702234?ver=pdfcov The Separation of Cold‐Work Distortion and Particle Size Broadening in X‐Ray Patterns] ''J. Appl. Phys.'' '''1952''', 23, 497 [http://dx.doi.org/10.1063/1.1702234 doi: 10.1063/1.1702234]
+* B.E. Warren, B.L. Averbach, [http://scitation.aip.org/content/aip/journal/jap/23/4/10.1063/1.1702234?ver=pdfcov The Separation of Cold‐Work Distortion and Particle Size Broadening in X‐Ray Patterns] ''J. Appl. Phys.'' '''1952''', 23, 497 [http://dx.doi.org/10.1063/1.1702234 doi: 10.1063/1.1702234]
 * B. Crist and J.B. Cohen [http://onlinelibrary.wiley.com/doi/10.1002/pol.1979.180170609/abstract Fourier Analysis of Polymer X-Ray Diffraction Patterns] ''J. Poly. Sci: Poly. Phys.'' '''1979''', 17 (6), 1001-1010 [http://dx.doi.org/10.1002/pol.1979.180170609 doi: 10.1002/pol.1979.180170609]
-* T.J. Prosa , J. Moulton , A.J. Heeger, and M.J. Winokur [http://pubs.acs.org/doi/abs/10.1021/ma981059h Diffraction Line-Shape Analysis of Poly(3-dodecylthiophene):  A Study of Layer Disorder through the Liquid Crystalline Polymer Transition] ''Macromolecules'' '''1999''', 32 (12), 4000-4009 [http://dx.doi.org/10.1021/ma981059h doi: 10.1021/ma981059h]
+* T.J. Prosa , J. Moulton , A.J. Heeger, and M.J. Winokur, [http://pubs.acs.org/doi/abs/10.1021/ma981059h Diffraction Line-Shape Analysis of Poly(3-dodecylthiophene):  A Study of Layer Disorder through the Liquid Crystalline Polymer Transition] ''Macromolecules'' '''1999''', 32 (12), 4000-4009 [http://dx.doi.org/10.1021/ma981059h doi: 10.1021/ma981059h]
-* Rodrigo Noriega, Jonathan Rivnay, Koen Vandewal,	Felix P. V. Koch, Natalie Stingelin, Paul Smith, Michael F. Toney & Alberto Salleo [http://www.nature.com/nmat/journal/v12/n11/full/nmat3722.html#supplementary-information A general relationship between disorder, aggregation and charge transport in conjugated polymers] ''Nature Materials'' '''2013''', 12, 1038-1044 [http://dx.doi.org/10.1038/nmat3722 doi: 10.1038/nmat3722]; see also [http://www.nature.com/nmat/journal/v12/n11/extref/nmat3722-s1.pdf Supplementary Information].
+* Rodrigo Noriega, Jonathan Rivnay, Koen Vandewal, Felix P. V. Koch, Natalie Stingelin, Paul Smith, Michael F. Toney & Alberto Salleo, [http://www.nature.com/nmat/journal/v12/n11/full/nmat3722.html#supplementary-information A general relationship between disorder, aggregation and charge transport in conjugated polymers] ''Nature Materials'' '''2013''', 12, 1038-1044 [http://dx.doi.org/10.1038/nmat3722 doi: 10.1038/nmat3722]; see also [http://www.nature.com/nmat/journal/v12/n11/extref/nmat3722-s1.pdf Supplementary Information].
 * Rodrigo Noriega, Jonatahan Rivnay, Alberto Salleo, Michael Toney [http://www-ssrl.slac.stanford.edu/conferences/workshops/srxas-2012/documents/rodrigonoriega-srxas2012.pdf Warren Averbach analysis of XRD peak shapes: Measuring disorder in soft organic materials]
 ===Williamson/Hall===
-* G.K. Williamson, W.H. Hall [http://www.sciencedirect.com/science/article/pii/0001616053900066 X-ray line broadening from filed aluminium and wolfram] ''Acta Metallurgica'' '''1953''', 1 (1), 22-31.
+* G.K. Williamson, W.H. Hall, [http://www.sciencedirect.com/science/article/pii/0001616053900066 X-ray line broadening from filed aluminium and wolfram] ''Acta Metallurgica'' '''1953''', 1 (1), 22-31.
 ==See Also==
 * [[Scherrer grain size analysis]]: Converting the peak width into a measure of the structural coherence length (grain size)
 * [http://prism.mit.edu/xray/oldsite/CrystalSizeAnalysis.ppt Estimating Crystallite Size Using XRD], Scott A. Speakman, MIT.