[GSAS-II] Questions on secondary extinction of TOF neutron scattering

[Yi Luo]

Dear Developers, Colleagues, and Friends,

Hi, I am a Ph.D. student working on neutron scattering at Johns Hopkins Univerisity. This is my first post concerning a question that has confused me for a while, and would really appreciate any thoughts and advice about it.

Concerning the secondary extinction correction of Type I, I have read the code in "SCExtinction(ref,im,phfx,hfx,pfx,calcControls,parmDict,varyList)" starting at line 2275 of the script "GSASIIstrMath.py"  to understand how GSAS-II evaluate the extinction correction and found that the treatment for neutron scatterings with constant wavelength (SNC) and time of flight neutron scatterings (SNT)  are quite different:

In lines 2292-2295 (for SNT), we have the definition "PL=SQ ", SQ is defined in the line 2282 so it means PL=1/4 ref[4]^2=1/(4D^2);

In lines 2296-2299 (for SNC), we instead have the definition "PL=np.sqrt(1.0-cos2T**2)/parmDict[hfx+'Lam']", which means "PL=sin(2*theta)/lambda".

For both cases, AV and PLZ are defined in a similar fashion. The variable PL appears later in the line 2316 for the secondary extinction of type I, as "PSIG = parmDict[phfx+'Eg']/PL". For the case of SNC, the following equation of extinctions seem to agree with those in Becker & Coppens (1973). However, I do not understand how the PL defined for SNT can also be correct. PL defined for SNT (1/(4D^2)) even has a different dimension compared to PL defined for SNC (sin(2*theta)/lambda). Is there any crucial difference between the extinction correction of these two cases (eg: dimensions of F^2, Eg, other factors) other than that the fact that for SNT we have different neutron wavelengths for different peaks?

Another question I have is why we need a 1e7 in lines 2293 and 2297 for the definition of AV? Is that for some unit transformation, I am under the impression that if we have FcTsq in unit of barn, volume of unit cell in unit of Ang^3 , wavelength and D in units of Ang and tbar in unit of cm we do not need any unit conversion in the evaluation of extinction.

I apologize in advance if this is a silly question, any clarification you can provide will be much appreciated.

Best regards,
Yi Luo

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