Anomalous Diffraction Project Status Update

Completed So Far Incorporating Daniel Haskel’s solid-state effects into the model Incorporating experimental uncertainties into the data and fits Inverting the ratios taken, so I fit S1/F instead of F/S1 Creating and testing a full model of the Bragg reflections and slit function Systematically fitting the data, varying the Debye- Waller factor

Solid State Effects So far, I’ve used only the theoretical scattering factors because of the absence of measured factors for Ge.

Uncertainties Since we originally took the data with DAFS in mind, the uncertainty from the amplitudes are fairly low The larger source of uncertainty comes from the L-scan intensities, which were used to scale all the amplitudes – the superlattice peaks were relatively weak and a peak shape suffered – Could have been avoided if I wasn’t trying to get more compositions than I had time for Of note is that some data sets lack the (111) amplitude data. – Again, could have been avoided if I hadn’t tried to get too many compositions (took lots of data at the Fundamental)

Inverting the Data Since one reason for fitting intensity ratios rather than intensity is to ‘normalize’ to the fundamental, Yong suggested fitting S1/F and S2/F rather than the reverse. As expected, this did not noticeably affect the fits or results.

Slit Function Correction Several models were attempted taking various short-cuts and making various assumptions None gave a correction even close to that of the Full Model: – 3D Lorentian Bragg Reflection – 2D Slit Window in 3-space, sectioning the Ewald Sphere – Correct reflection widths confirmed by comparing modeled scans to various data sets (see next slides)

Detecor L-direction Ewald Sphere Bragg Reflection q kiki kfkf Another Bragg Reflection kfkf Blending Lab with Reciprocal Space Whatever intersects the Ewald sphere in reciprocal space will become scattered photons in lab space. Sample Slits

This is only a 2D representation. The Bragg reflection is really a 3D volume and the Ewald sphere is a surface. The slits limit the amount of the Ewald sphere for the detector to see. L-direction Ewald Sphere Slits limit how much solid angle of the Ewald Sphere the detector can see. The diffractometer manipulates the Ewald Sphere so that it travels through the Bragg reflection along L. Bragg Reflection Illustrating an L-Scan

The Model Right: A 2D representation of the final Lorentian used for all three reflections and four compositions Below: an example of the modeled slit window and the intensity it captured from the Ewald Sphere. This was summed as one data point in a diffractometer scan such as an L-scan.

Confirming Model Accuracy With known slit sizes, all I had to do was model the three reflection widths. I had all three directions (L, In-Plane, and Phi) scanned for the Fundamental and the (111)-type to test the model One set of widths clearly work for all three directions, both reflections and most compositions. L-scan’s tails are off due to interface fringes

Final Correction The same model also worked for a data series with varying slit sizes. Right: The final Corrections used in the anomalous diffraction fits.

Systematic Fitting The Debye-Waller factor measured (including the latest Slit correction) gave a value of σ=0.13 → I measured = I 0 exp(- σq i 2 ), where i represents different reflections This value is still probably not accurate because σ is actually different for different directions The measured value allows a range, which are systematically set and fit. The proper value is determined based on the fit outputting the measured composition.

Fits with All Corrections but Sold State Next slide shows results from these fits We desire for an acceptable fit: – low nchisq value (first param) – Co-Mn ratio near 2 (panel 2, blue) – Ge comp near 30, 35, 40 and 45 respectively (panel 2, red) – Co-Mn swapping = 0 (panel 3, red)

Compositions Fit Parameters

Adding Solid State Effects Problem: I don’t get compositions that are correct for the Ge-level It seems as though the spike in the Ge scattering factor is the cause as residuals go down everywhere else when adding solid state effects.

Compositions Fit Parameters

Chosen Fits (no SS): Ge30 Data

Chosen Fits (no SS): Ge35 Data

Chosen Fits (no SS): Ge40 Data

Chosen Fits (no SS): Ge45 Data