silveira
Greetings,
I am analyzing some martensite/austenite in-situ phase transformation data with Topas academic 6, and I am currently having some troubles with the crystallite size (CS) and microstrain (MS). The results for these parameters either vary drastically, or the obtained error is very large. This is more evident in the austenite results.
As far as I understood, the double-Voigt approach assumes that both CS and MS can be obtained by the peak's deconvolution using a Gaussian and Lorentzian component.
However, in some old Topas 4.2 templates in my department, I found that the CS is evaluated only with the Lorentzian component, and the MS is evaluated only with the Gaussian part.
Therefore, I try to apply this approach, and I observed much more stable results than the Double Voigt. However, I never found any information supporting this kind of approach.
My question are:
-Does it make sense to evaluate each parameter with one deconvolution component?
Lorentzian -> CS
Gaussian -> MS
-If it does not make any sense to use a single component for each parameter, is there anything that I can do to reduce this instability in the CS and MS results?
To further evaluate these differences, I batch-process one set of data using three different templates.
1st Template (double Voigt approach -> CS and MS)
'e0MA=microstrain
prm maxStr_a = 1;
Strain_G(GS_a, 0.50000`_0.27653 min 1e-6 max=maxStr_a;) 'Lorentzian component
Strain_L(LS_a, 0.50000`_0.33755 min 1e-6 max=maxStr_a;) 'Gaussian Component
prm e0Ma = Voigt_FWHM_GL((GS_a), (LS_a)) 0.25(Pi/360); : 0.00179`_0.00077
'cry_MA=crystallite size
CS_L(CS_La, 82.81536`_113.12992 min 5 max 2000) 'Lorentzian component
CS_G(CS_Ga, 1921.96712`_2425283.23754 min 5 max 2000) 'Gaussian Component
prm cry_Ma = (1) / Voigt_Integral_Breadth_GL(1/(CS_Ga), 1/(CS_La)); : 52.87025`_326.26019
2nd Template (Lorentzian ->CS and Gaussian-> MS)
'e0MA_G = microstrain
prm maxStr_a = 1;
Strain_G(GS_a, 0.50000`_0.09516 min 1e-6 max=maxStr_a;)
'Strain_L(LS_a, 0.1 min 1e-6 max=maxStr_a;)
prm e0Ma_G = Voigt_FWHM_GL((GS_a), ) 0.25(Pi/360); : 0.00109`_0.00021
'cry_MA_L = crystallite size
CS_L(CS_La, 29.37136`_3.01216 min 5 max 2000)
'CS_G(CS_Ga, 20 min 5 max 2000)
prm cry_Ma_L = 1 / IB_from_CS( ,CS_Lt); : 66.39920`_2.34188
3rd Template (Gaussian -> CS and Lorentzian -> MS)
'e0Ma_L = microstrain only with Lorentzian
prm maxStr_a = 1;
'Strain_G(GS_a, 0.1 min 1e-6 max=maxStr_a;)
Strain_L(LS_a, 0.50000`_0.08756 min 1e-6 max=maxStr_a;)
prm e0Ma_L = Voigt_FWHM_GL( 0 , (LS_a)) 0.25(Pi/360); : 0.00109`_0.00019
'cry_Ma_G = crystallite size only with Gaussian
'CS_L(CS_La, 20 min 5 max 2000)
CS_G(CS_Ga, 30.05365`_4.68249 min 5 max 2000)
prm cry_Ma_G = 1 / IB_from_CS(CS_Ga, ); : 28.23352`_4.39891
Here is a comparison of the obtained results for crystallite size and microstrain. (I tried to upload an image)
I am a beginner with Topas and would appreciate any suggestions and comments. (sorry for the long post)
Best regards,
Antonio Silveira
rowlesmr
Hi Antonio
Could you show us what your data looks like? And also the different models with that data?
It does sometimes make sense to use only a single component in the convolution, as sometimes the peakshape can be described with only a gaussian or lorentzian shape.
Matthew
silveira
Hello Matthew,
Sure!
I am analyzing some in situ data with many heating and cooling cycles. So it goes from liquid austenite to solid austenite and then martensitic transformation.
I am sure what is the best way to show you the data, so I am attaching a small graph of a part of the diffraction data plotted over time, some diffraction patterns from it, and the templates that I use.
" It does sometimes make sense to use only a single component in the convolution, as sometimes the peakshape can be described with only a gaussian or lorentzian shape."
I could not find any discussion about using a single component in the convolution here. Is there any paper that could help me with this matter?
Let me know if it's not possible to open my attachment. (I hope it was possible to open the image that I attached in the first post)
Antonio
rowlesmr
It's basically a data scarcity issue.
You've only got 5 peaks (and one overlap) per phase over 5°. There isn't enough information to support gaussian and lorentzian size and strain.
With regards to references:
[1] - "...it appears justified to assume that the 'size' profile in general may be described by the 'corresponding' Lorentzian component, and that the 'strain' profile in general may be described by the 'corresponding' Gaussian component."
[2] - "These approaches have led to the common practice of ascribing the Lorentzian profile shape to crystallite size and the Gaussian shape to strain. A good discussion can be found in [1]."
With the unstable values and large errors, that usually points to a parameter that is very dependent on starting conditions, and whose refinement isn't really supported by the data. It should either be fixed at a previously determined value, or not included in the refinement.
Combining these two, I wouldn't find it too hard to just use CS_L and MS_G.
[1] Delhez, Robert, Thomas H. de Keijser, J. Ian Langford, Daniel Louër, Eric J. Mittemeijer, and Eduard J. Sonneveld. 1995. "Crystal Imperfection Broadening and Peak Shape in the Rietveld Method." In The Rietveld Method, edited by R.A. Young. New York: Oxford University Press. (chapter 8, appendix 8B)
[2] Honkimäki, V., and P. Suortii. 2002. "Effects of Instrument Function, Crystallite Size, and Strain on Reflection Profiles." In Defect and Microstructure Analysis by Diffraction, edited by Robert L. Snyder, Jaroslav Fiala and Hans J. Bunge. Oxford: Oxford University Press, p. 53.
silveira
Thank you for your comments and references Matthew!!