Convolved peak shape with offset peak position

ChrisRidley

Is it possible to define a custom peak_type pv, where the peak is convolved of two gaussians with a user-specified offset between the two peak centres away from the nominal 'centre'? Something like peak_type pv split. I can do this with single peak fitting easily, but I am looking to do this for all the peaks from a specified crystal structure.

johnsoevans

Almost certainly yes! This is basically similar to e.g. having an emission profile with kalpha1/kalpha2 components for lab data so should be possible. If nothing built-in works you can try a user_defined_convolution.
I don't know what data you're trying to fit (so sorry if the following is patronising): with powder diffraction split peaks often means 2 phases with similar cell parameters, or two different effective sample positions. Would just adding a second str with the same contents but different cell parameters solve your problem? Of if you have a peak position difference that's linear in X you could have two strs with different zero point corrections (or heights). If your peak offsets change with X for different reasons you could write a bespoke "th2_offset = ....;" type equation for one of the strs.

ChrisRidley

Thanks John - I have some TOF neutron data from a guide with two distinct primary flight paths - this results in data from a single phase having peakshapes which cannot be accounted for with any number of additional gaussians/lorentzians/exponentials/broadenings shape terms, but can be accounted for with offset additional reflections, which scale linearly with d-spacing/TOF. As you say, this is analagous to alpha1/alpha2 like behaviour, but I have TOF neutron data. Ideally I would treat this with the peakshape rather than multiple strs, so I will play around with the user_defined_convolution

ChrisRidley

I'm not having much luck with this. I've tried th2_offset with some D_spacing parameterisation, but this seems not to capture the observed split - I don't think it is doing what I think it is doing. For the user_defined_convolution, how do I specify that I want to convolve the exact same peakshape with an X-offset?

rowlesmr

ChrisRidley

I don't think you can parameterise th2_offset (which is really x_offset) in terms of d-spacing, as if we think of two beams + one specimen being one beam with two displaced specimens, then the displacement needs to be modelled in some real-space coordinates of some type, not in d-space. You need to think about the geometry of what is going on and parameterise it in those terms.

Maybe do it in time?

Now, I have essentially zero experience in TOF, so I don't know if I'm going to be much more help.

rowlesmr

ChrisRidley

Proof of concept


macro add_d_pk(posn) {
	d_Is
		d posn           
		I 1
		peak_type pv
		pv_lor 0
		pv_fwhm 0.001
}

yobs_eqn row119.xy = 0; min 30000 max 110000 del 10 
	bkg 0
	
	prm !t0 -16.50480
	prm !t1 48262.6018
	prm !t2 -8.35418
	
   lam
   	ymin_on_ymax 0.0001
   	la 1  lo 0	lh 0.0001
   pk_xo = t0 + t1 D_spacing + t2 D_spacing^2;

   prm !bb = 500 Sin(D_spacing);
   prm !cc = 100;
   prm !rng = 5000;
   'Can be a function of H, K, L, M, Xo, Th, and D_spacing
   ' convolving a gaussian
   user_defined_convolution = Exp(-(X-bb)^2 / (2 cc^2)) +  'the offset peak 
                              Exp(-(X   )^2 / (2 cc^2));   ' at the peak posn
   	min =-rng; max =rng;
   	
	add_d_pk(0.7)
	add_d_pk(0.8)
	add_d_pk(0.9)
	add_d_pk(1.0)
	add_d_pk(1.1)
	add_d_pk(1.2)
	add_d_pk(1.3)
	add_d_pk(1.4)
	add_d_pk(1.5)
	add_d_pk(1.6)
	add_d_pk(1.7)
	add_d_pk(1.8)

rowlesmr

Two flight paths and one specimen sounds like it could be modelled with one flight path and two specimens.

Do your data look like this: https://onlinelibrary.wiley.com/doi/abs/10.1107/S0021889810047461?

Just need to link the two strs together, so that cell prms and the like stay at the same value. Maybe even scale factor? but I would leave them free to begin with. This is basically different specimen displacements applied to the to different instantiations of the same structure.

Also I'm interested in a diffractogram with two sources. Why are there two? Everything I've heard of until now has had only one source.

ChrisRidley

Thank you for this. I think I can get this to work - will continue to play with it.