emission_profile_modelling
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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: | ||
+ | >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: | ||
+ | |||
+ | 1) 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. | ||
+ | |||
+ | 2) 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' | ||
+ | |||
+ | 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 | ||
+ | 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 | ||
+ | lh 0.52 | ||
+ | la = alpha2_intensity 0.0871; | ||
+ | lo = 1.544721 (1 - (al_in_degrees | ||
+ | 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 ' | ||
+ | |||
+ | <code topas> | ||
+ | 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</ | ||
+ | |||
+ | 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. | ||
+ | |||
+ | |||