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hkl_dependent_peak_shapes [2009/08/27 17:56]
johnsoevans
hkl_dependent_peak_shapes [2020/07/16 11:29]
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-====== hkl-dependent Peak Shapes ====== 
  
- 
-There are lots of ways of doing this. 
- 
-One excellent approach (sometimes with fewer parameters than a spherical harmonic function) is to use the Stephens approach (P.W. Stephens, J. Appl. Cryst. (1999) 32, 281-9) as coded in gsas. Peter, Robert Dinnebier and Andreas Leineweber have worked out the macros for this. eta term allows mixture of Gauss/​Lorentz broadening: 
- 
-<code topas>​prm s400 11769.84126` 
-prm s004 153.55044` 
-prm s220 28029.32854` 
-prm s202 -1067.03124` 
-........ 
-prm eta 0.52180` min 0 max 1 
-Stephens_tetragonal(s400,​ s004, s220, s202, eta) 
-</​code>​ 
- 
-The macros you'll need are below. ​ You need to define the correct parameters to refine for each macro. ​ Somebody could automate this if they have time! 
- 
-<code topas>​macro Stephens_tetragonal(s400,​ s004, s220, s202, eta) 
-{ 
-prm mhkl = Abs(S400 (H^4+ K^4)+ S004 L^4+ S220 H^2 K^2 + S202 (H^2 L^2 + K^2 L^2) ); 
- 
-prm pp = D_spacing^2 * Sqrt(Max(mhkl,​0)) / 1000; 
-gauss_fwhm = 1.8/​3.1415927 pp (1-eta) Tan(Th) + 0.0001; 
-lor_fwhm = 1.8/​3.1415927 pp eta Tan(Th) + 0.0001; 
-}</​code>​ 
- 
-<code topas>​macro Stephens_monoclinic(s400,​ s040, s004, s220, s202, s022, s301, s121, s103, eta) 
-{ 
-prm mhkl = H^4 s400 + K^4 s040 + L^4 s004 + 
-H^2 K^2 s220 + H^2 L^2 s202 + K^2 L^2 s022 + 
-H K^2 L s121 + 
-H L^3 s103 + H^3 L s301; 
- 
-prm pp = D_spacing^2 * Sqrt(Max(mhkl,​0)) / 1000; 
- 
-gauss_fwhm = 1.8/​3.1415927 pp (1-eta) Tan(Th) + 0.0001; 
-lor_fwhm = 1.8/​3.1415927 pp eta Tan(Th) + 0.0001; 
-}</​code>​ 
- 
-<code topas>​macro Stephens_hexagonal(s400,​ s202, s004, eta) 
-{ 
-prm mhkl = H^4 s400 + K^4 s400 + L^4 s004 + 
-H^2 K^2 3 s400 + H^2 L^2 s202 + K^2 L^2 s202 + 
-H K L^2 s202 + 
-H^3 K 2 s400 + H K^3 2 s400; 
- 
-prm pp = D_spacing^2 * Sqrt(Max(mhkl,​0)) / 1000; 
- 
-gauss_fwhm = 1.8/​3.1415927 pp (1-eta) Tan(Th) + 0.0001; 
-lor_fwhm = 1.8/​3.1415927 pp eta Tan(Th) + 0.0001; 
-}</​code>​ 
- 
-<code topas>​macro Stephens_orthorhombic(s400,​ s040, s004, s220, s202, s022, eta) 
-{ 
-prm mhkl = H^4 s400 + K^4 s040 + L^4 s004 + 
-H^2 K^2 s220 + H^2 L^2 s202 + K^2 L^2 s022; 
- 
-prm pp = D_spacing^2 * Sqrt(Max(mhkl,​0)) / 1000; 
- 
-gauss_fwhm = 1.8/​3.1415927 pp (1-eta) Tan(Th) + 0.0001; 
-lor_fwhm = 1.8/​3.1415927 pp eta Tan(Th) + 0.0001; 
-} 
-</​code>​ 
-  

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