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--- emission_profile_modelling [2012/10/12 20:40] – johnsoevans
+++ emission_profile_modelling [2022/11/03 15:08] (current) – external edit 127.0.0.1
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+====== Ge Monochromator Emission Profile ======
+[From the Rietveld mailing list 18/6/2012]
+>A question to the specialists: In case of an asymmetric monochromator
+>like typical Ge, can we expect an homogeneous distribution of intensity
+>within the beam bunch?
+I agree with your assessment; I have also sometimes observed alpha 1 and alpha 2 separation that is different to what is expected when a pre-monochromator is used. Like you suggest it is due to an inhomogeneous wavelength spread across the beam in the equatorial plane. For a flat pre-monochromator then it would be expected as physically the alpha 1 and alpha 2 would be spatially separated in the equatorial plane. A bent crystal attempts to fix this but of course misalignment could change matters.
+Thus there are two problems when using a Ge pre-monochromator:
+) The emission profile changes due to the filter of the crystal; this can be modelled by fitting enough Voigts to fit the emission profile shape; the Tan(Th) broadening dependence of the emission profile allows for such refinement.
+) The non-standard change in alpha 1 and alpha 2 separation as a function of 2Th can be modelled as follows:
+The alpha 1 and alpha 2 components of the primary beam hits the sample off axis. For a off axis ray the change in 2Th measured as:
+      Delta_2Th =  (1/2) divergence^2 / Tan(Th)
+where divergence is the angle primary ray makes with the axis in the axial plane (small angle approximations used). Alpha 1 and alpha 2 would both have different Delta_2Th's but it's the difference we are interested in. We can change the wavelength of alpha 2 to reflect this change and the correction becomes:
+      Aplha_2_wavelength_new = Aplha_2_wavelength (1 - (Pi/360)^2 divergence^2 / Tan(Th)^2)
+Implementing this into an emission profile, using TOPAS for example, is as follows:
+      lam
+            ymin_on_ymax  0.0001
+            la  0.0159 lo  1.534753 lh  3.6854
+            la  0.5791 lo  1.540596 lh  0.437
+            la  0.0762 lo  1.541058 lh  0.6
+            prm al_in_degrees 0 min 0 max = 2 Val + .1;
+            prm alpha2_intensity 1 min 1e-6 max 2
+            la = alpha2_intensity 0.32417;
+                  lo  = 1.5444493 (1 - (al_in_degrees  (Pi / 360)  / Tan(Th))^2 );
+                  lh  0.52
+            la  = alpha2_intensity 0.0871;
+                  lo  = 1.544721 (1 - (al_in_degrees  (Pi / 360)  / Tan(Th))^2 );
+                  lh  0.62
+The two parameters of al_in_degrees and alpha2_intensity are refined to change the emission profile.
+Alpha 1 will also be shifted but that is taken up by lattice parameters, zero error, specimen displacement etc... and would be difficult to refine in the presence of the others.
+The above seems to work but there may well be other affects not taken into consideration and IMO it would be difficult to discern other effects.
+Cheers
+Alan
+====== Empirical Profile Modelling: Split Peaks in LaB6 ======
+ ======
+From the Rietveld mailing list 5/10/2012:
+Yaroslav
+Thank you for the MYTHEN data.
+And thank you Lubo for also sending the data and for pointing out that the splitting increases at high angles and hence the opposite effect to a capillary.
+I took the liberty of trying to fit to the data in a purely empirical manner; it's a little naive of course as many have no doubt spent a lot of time looking at the MYTHEN detector in detail. I myself would favour alignment such that splitting does not occur as Francois explained.
+FWIW however and when desperate a 'perfect' empirical fit is possible with four Gaussians for an emission profile with an Rwp of 3.52% for a structural fit and 3.80% for a Pawley fit. It also seems that a Gaussian convolution that is constant with 2Th is also necessary. The main components of the peak shape are:
+<code topas>macro LL { min 1e-5 max 1 val_on_continue = Rand(.001, .1); } prm xx  0.58476` min .3 max 1.5 macro Fn(x) { / Tan(x)^xx }
+prm w1  0.00017`	min -.01 max .01	val_on_continue = Val + Rand(-1, 1) 0.0001;
+prm w2 -0.00047`	val_on_continue = Val + Rand(-1, 1) 0.0001;
+prm w3 -0.00038`	min -.01 max .01	val_on_continue = Val + Rand(-1, 1) 0.0001;
+prm w4  0.00040`	val_on_continue = Val + Rand(-1, 1) 0.0001;
+prm w5  0.00000`	min -.01 max .01	val_on_continue = Val + Rand(-1, 1) 0.0001;
+prm w6 -0.00022`	val_on_continue = Val + Rand(-1, 1) 0.0001;
+lam
+	ymin_on_ymax 0.001
+	la 1
+		lo  0.82257
+		lg @  0.21693` LL
+		lo_ref
+	la  @  0.17840` min .1 max 10
+		lo =  0.82257 + w1 + w2 Fn(Th);
+		lg @  0.19588` LL
+	la  @  0.28193` min .1 max 10
+		lo =  0.82257 + w3 + w4 Fn(Th);
+		lg @  0.07650` LL
+	la  @  1.24781` min .1 max 10
+		lo =  0.82257 + w5 + w6 Fn(Th);
+		lg @  0.17791` LL
+gauss_fwhm @  0.0150418688` min 1e-5</code>
+I apologize if the TOPAS script is not understandable to some. The w2, w4 and w6 parameters offsets emission profile lines as a function of 1/Tan(Th) which then offsets the emission profile lines in 2Th space proportional to 2Th. The xx parameter if set to 1 increases Rwp by around 1%.
+In any case if desperate then an empirical fit is possible using an emission profile comprising 4 Gaussians.