Multi-Phase Fitting of Core/Shell Nanostructure into an Alloy

Andrew_Crossman

Hi All,

I am trying to fit several hundred sequential pXRD patterns of a bi-metallic Core/Shell powder as it diffuses into a spherical alloy. The diffusion was facilitated by heating the sample and pXRD patterns were taken every 1 second courtesy of the synchrotron beamline facility at BNL. What I would like to do is measure/qualify the diffusion as a function of temp/time by using TOPAS to output the percent_weight parameter for each phase that contributes to each pXRD pattern. So, for example, the available phases for TOPAS to determine the percent_weights of for each pattern could be:
100%Metal_A
90%Metal_A/10%Metal_B
80%Metal_A/20%Metal_B
.
.
.
20%Metal_A/80%Metal_B
10%Metal_A/90%Metal_B
100%Metal_B
Currently I have managed to get TOPAS to try and fit each pXRD pattern and output the percent_weight for each of the listed phases above while controlling the elemental_composition variables to their measured XRF values and phases to their temperature dependent lattice parameter, . However, I am having two main issues:
1) The percent_weight_errors are huge (often by several orders of magnitude) even though the percent_weights are mostly reasonable.
2) The room temperature fits are quite poor compared to the high temperature fits.

In regards to (1), my first thought is that there may be a syntax issue. Is there anything about the following that could make the error accidentally 1000 instead of .1000?

Out(wt_A90B10, " %11.5f", " %11.5f")

In regards to (2), I have tried several different solutions without success so any advice would be appreciated.

Thank-you.

rowlesmr

weight fractions are determined by the scale factors, unit cell masses, and unit cell volumes. If any of those are being refined, then they will influence the errors in the weight fraction.

Cell parameters - volume
occupancies - mass
beq, element_weight_by_XRF constraints, intensity corrections, sometimes crystallite size,... - scale factor

Try not using your XRF constraints and see how it goes. Are you refining thermal parameters? (you need to be v. cautious if you are).

Try everything you can on a single pattern, just for expedititiousness, and then roll it our to the entire dataset.

Andrew_Crossman

@rowlesmr Thank-you for your response.

I tested your suggestions with some success. Removing refinements for the cell masses, unit cell volumes, and thermal parameters certainly improved the fit somewhat. However, removing the XRD constraints pretty much ruined the fit so I kept that part at least. The main issue at this point is that the first peak (111 FCC) is not intense enough to match the data and the second peak (200 FCC) is much more intense than the data at low temperatures. All of the other peaks match fairly well.

I tried introducing various combinations of instrumental and sample effects to resolve this such as:
Zero_error, One_on_X, Capillary Correction, Strain, etc.
but nothing really seemed to improve the fit further. Any ideas on how to address this issue?

johnsoevans

None of those factors will significantly affect relative peak intensities. Is there a chance of texture in the sample? You could try a preferred orientation correction, but be careful this isn’t artificially mopping up some other error.

Andrew_Crossman

@johnsoevans Thank-you for your response.

Yes, there is a chance that the intensity mismatch is due to texture and/or preferred orientation effects because the sample was gently packed into a quartz capillary tube. I have dabbled with the Spherical Harmonics command in conjunction with individual phase peak_types:

`str
phase_name Cu9Ni1
space_group "Fm-3m"
Cubic( = lp_Cu9Ni1; )
scale Cu9Ni1_scale 0.00001
r_bragg 0
site Cu9Ni1_site x 0 y 0 z 0 occ Cu 0.9 beq = Cu_beq; occ Ni 0.1 beq = Ni_beq;
weight_percent wt_Cu9Ni1 5
TCHZ_Peak_Type(pku1, 0.00039,pkv1, -0.00221,pkw1, -0.00146,!pkz1, 0.0000,pkx1, 0.00957, pky1, 0.0001)
str
phase_name Cu8Ni2
space_group "Fm-3m"
Cubic( = lp_Cu8Ni2; )
scale Cu8Ni2_scale 0.00001
r_bragg 0
site Cu8Ni2_site x 0 y 0 z 0 occ Cu 0.8 beq = Cu_beq; occ Ni 0.2 beq = Ni_beq;
weight_percent wt_Cu8Ni2 5
TCHZ_Peak_Type(pku2, 0.00039,pkv2, -0.00221,pkw2, -0.00146,!pkz2, 0.0000,pkx2, 0.00957, pky2, 0.0001)
...

for strs {
PO_Spherical_Harmonics(sh,8)
scale_pks = Max(sh,0);
}
`
where lp_Cu9Ni1, lp_Cu8Ni2, Cu_beq and Ni_beq are all fixed values.

In combination, these commands fix the intensity mismatches for the (111) and (200) peaks (see here) but don't rectify other smaller mismatches highlighted here .

This leaves me with a few questions. Is there something I am fundamentally missing in the analysis? If not, is it worth trying out some of the other preferred orientation commands such as March-Dollase? Or is this about as good of a fit as I can expect using several phase_groups as opposed to fitting individual peaks, etc.?!

alan-coelho

The PO_Spherical_Harmonics macro contains scale_pks; thus remove the "scale_pks = Max(sh,0)" line.

Also, the sh in "spherical_harmonics_hkl sh" is local to the str. Place the macro outside of the for strs loop and view the coefficients; ie.

str...
    spherical_harmonics_hkl sh
    ....
str...
    spherical_harmonics_hkl sh
    ....

If you want the same coefficients then give them a similar name across the structures.

Andrew_Crossman

Hi @alan-coelho ,

Thank you for the suggestion it helped a lot! And just to clarify, if I want to try different coefficients for each phase I could do the following:

str...
   spherical_harmonics_hkl sh1
      sh_order = 8;
   scale_pks = sh1;
   scale_pks = Max(sh1,0);

str...
   spherical_harmonics_hkl sh2
      sh_order = 8;
   scale_pks = sh2;
   scale_pks = Max(sh2,0);

rowlesmr

Yes