— Dr. Xiaodong (Tony) Wang 2025/09/17 02:13

The application of Molecular Scattering Power (MSP) method (Wang & Spratt, 2025) on a phase of unknown crystal structure requires its total diffraction intensity to be accurately extracted from the measured sample pattern. This may not be easy when the target unknown phase is of low concentration in the sample mixture, or when the diffraction peaks of one unknown phase overlap with those from another unknown phase.

The PONKCS method is able to record the full diffraction pattern for an unknown phase and be saved in user-database for re-use (Scarlett & Madsen, 2006). Yet the ZM (unit cell mass) calibration step of PONKCS method requires an experimental synthesis of a standard mixture of the unknown phase with known amount of internal standard. This step is limited to the scenarios that a pure unknown phase sample is available or the unknown phase can be purify or enriched.

The joint PONKCS-MSP method combines the idea of diffraction pattern recording in PONKCS method and the ZM calculation equation in MSP method. Essentially PONKCS-MSP method is a PONKCS method free from experimental calibration of ZM factor. Same as the MSP method, to use the PONKCS-MSP method, the 2θ range of data collection should be as wide as possible.

This tutorial is mainly designed for TOPAS V7 GUI mode, using the IUCr CPD Round Robin dataset (three-phase mixtures of Corundum, Zincite, and Fluorite, samples CPD-1A to CPD-1H) as follows:

• Corundum is designated as the unknown
• Crystal structures for Fluorite and Zincite are known

All required diffraction data, weighed phase ratios of the synthetic mixtures, and the crystal structure files can be download from: https://www.iucr.org/__data/iucr/powder/QARR/intro.htm

For easy calculation of molecular weight, it is recommended to download the TOPAS macro “AW” from either the supporting document of (Wang & Spratt, 2025), or copy from Macro to generate Atomic Weight from Atomic Symbol. To use a new macro, save the macro in the “local.inc” file in the C:/TOPAS7 folder on your computer, and restart TOPAS.

To build a “PONKCS-MSP model” for Corundum we will distinguish two cases:

• Pure specimen available
• Pure specimen unavailable

Step 1: Perform a Pawley refinement on the Corundum data.

1. Start a fresh TOPAS in GUI mode and load the data Corundum.raw, from which a “PONKCS-MSP model” will be build.

2. Switch to the Parameters Window and define the refinement model. Expand the Corundum.raw range and perform the following tasks:

• Select the Emission Profile item and load the emission profile CuKa5_Berger.lam. By default, this file is located in C:\Topas7\Lam.
• Select the Background item and use a Chebyshev Polynomial of 1st order.
• Select the Instrument item and define the instrument settings according to below:

Goniometer Radius Primary: 173 mm; Secondary: 173 mm; Receiving Slit Width: 0.3mm; Fixed Divergence Slit Angle: 1°; Soller Slits Primary: 4.6°; Secondary: 4.6°;

• Select the Corrections item. Check Sample Displacement and set its code to “Refine”.
• Since a secondary graphite monochromator was used to collect the CPD-1 series data, we need to account for the polarization effects coming from it. Check the LP factor and set its value to 26.4, which is the 2θ degree value of a graphite monochromator to monochromatize the CuKα photons. Finally check Absorption and set its code to “Refine” in order to account for the profile shape distortion caused by the low mass absorption of the sample.
• Select Miscellaneous. Check Start X and set its value to 22. Check Finish X and set its value to 150.

3. Right click the Corundum.raw data, choose Add hkl phase. Select the generated hkl_Phase item and rename it to “hkl_Corundum”. Input the crystallographic data given below in the Phase Details page. Set the lattice parameters to “Refine”, enable the Scale factor but fix its value to 1. Switch to the Microstructure page and make sure to refine Cry Size L and Strain L.

Crystallographic Data for Corundum: Space group: Trigonal R_-3_C (167); Cell parameters a (Å): 4.7592; c (Å): 12.992

4. Start the refinement, then press “Yes” to accept the extracted corundum peak intensities.

Step 2: Calculate the ZM factor using MSP equation

5. In the GUI Text page of hkl_Corundum item, type in “prm !mol_f2_cor 825.609” to create a user defined parameter of a fixed value. The number is the “mol_f2” value calculated for the molecule of Al2O3 from Section I of the MSP Tutorial: Quantitative Phase Analysis Tutorial: Joint PONKCS-MSP method.

6. Calculate the total LP factor-removed intensity. In the hkls Is page, summing up all the “I” values of reflections within the scan range of 150 °2θ. In the GUI Text page, create a user defined parameter “prm !S_cor” followed by the value of total intensity (should be close to 2500.426).

7. Create another user defined parameter “prm !M_cor = 2*AW(“Al”)+3*AW(“O”);:1” to store the relative molecular weight for Al2O3. The value can be calculated either manually or through an equation using the assisting “AW” macro installed at the beginning of this tutorial.

8. In the GUI Text page, type in “prm =M_cor S_cor / mol_f2_cor/ Get(cell_volume);:1”. The last value represents the value of this MSP equation, which will be updated after refinement.

9. Start the refinement, press “Yes” to update the values of above parameters. Use the updated value as the “ZM” calibration constant (should be close to 1.212) in the Cell Mass box in the Phase Details page of the “hkl_Corundum” phase.

10. Select the the Phase Details page of the “hkl_Corundum” item. Make sure the Delete hkls on Refinement box is not checked and set Scale factor to “Refine”. Switch to the hkls Is page and fix all the “I” intensities.

11. Save a PONKCS-MSP phase for re-use: Right click the “hkl_Corundum” phase and select Save Phase. It is suggested to use the *.STR extension, this allows easy re-loading together with other crystal structure data.

12. Continue the Tutorial about using this PONKCS-MSP phase in Section III.

The procedure is mostly identical to that described in Section I. In this example the diffraction pattern of the unknown, Corundum, needs to be determined from a mixture, not from a pure specimen. In reality, It is preferred to build a PONKCS(-MSP) model for an unknown phase from a mixture data of a high concentration of it (sample of purified or enriched unknown phase), to minimize the risk of erroneously accounting for some of the intensity from other impurities (specifically in peak overlapping regions). In this sense the CPD-1B.raw data with 94.31 wt.% of Corundum would be most suitable for the current case. But to show the robustness of the PONKCS-MSP method, below tutorial builds a PONKCS-MSP phase for corundum from the CPD-1E.raw data which contains just 55.12 wt.% of corundum. The calibration constant (unit cell mass) will be calculated from the MSP equation.

Step 1: Perform a Pawley refinement on the Corundum phase.

1. Start a fresh TOPAS in GUI mode and load the data CPD-1E.raw, from which a PONKCS-MSP model for corundum will be build.

2. Switch to the Parameters Window and define the refinement model. Expand the CPD-1E.raw data and perform the following tasks:

• Select the Emission Profile item and load the emission profile CuKa5_Berger.lam. By default, this file is located in C:\Topas7\Lam.
• Select the Background item and use a Chebyshev Polynomial of 1st order.
• Select the Instrument item and define the instrument settings according to below:

Goniometer Radius Primary: 173 mm; Secondary: 173 mm; Receiving Slit Width: 0.3mm; Fixed Divergence Slit Angle: 1°; Soller Slits Primary: 4.6°; Secondary: 4.6°;

• Select the Corrections item. Check Sample Displacement and set its code to “Refine”.
• Since a secondary graphite monochromator was used to collect the CPD-1 series data, we need to account for the polarization effects coming from it. Check the LP factor and set its value to 26.4, which is the 2θ degree value of a graphite monochromator to monochromatize the CuKα photons. Finally check Absorption and set its code to “Refine” in order to account for the profile shape distortion caused by the low mass absorption of the sample.
• Select Miscellaneous. Check Start X and set its value to 22. Check Finish X and set its value to 150.

3. Right click the CPD-1E.raw data and select Add hkl phase. Rename the newly generated hkl_Phase item to “hkl_Corundum”. Input the unit cell information given below to the Phase Details page. Set the lattice parameters to “Refine”, enable the Scale factor but fix its value to 1. Switch to the Microstructure page and refine Cry Size L and Strain L.

Crystallographic Data for Corundum: Space group: Trigonal R_-3_C (167); Cell parameters a(Å): 4.7592; c(Å): 12.992;

4. Right click the CPD-1E.raw data, select Load STR(s) to import the crystal structure data for Fluorite.str and Zincite.str. Make sure to refine their lattice parameters, Scale factor, and Cry Size L and Strain L.

5. Start the refinement, then press “Yes” to accept the extracted corundum peak intensities.

Step 2: Calculate the ZM factor using MSP equation

6. In the GUI Text page of hkl_Corundum item, type in “prm !mol_f2_cor 825.609” to create a user defined parameter of a fixed value. The number is the “mol_f2” value calculated for the molecule of Al2O3 from Section I of the MSP Tutorial: Quantitative Phase Analysis Tutorial: Molecular Scattering Power (MSP) method.

7. Calculate the total LP factor-removed intensity. In the hkls Is page, summing up all the “I” values of reflections within the scan range of 150 °2θ. In the GUI Text page, create a user defined parameter “prm !S_cor” to record the value of total intensity (should be close to 851.091).

8. Create another user defined parameter “prm !M_cor = 2*AW(“Al”)+3*AW(“O”);:1” to store the relative molecular weight for Al2O3. The value can be calculated either manually or through an equation using the assisting “AW” macro installed at the beginning of this tutorial.

9. In the GUI Text page, type in “prm =M_cor S_cor / mol_f2_cor/ Get(cell_volume);:1”. The last value represents the value of this MSP equation, which will be updated after refinement.

10. Start the refinement, then press “Yes” to update the values of above equation. Use the updated value of above equation as the “ZM” calibration constant (should be close to 0.413) in the Cell Mass box in the Phase Details page of the “hkl_Corundum” phase.

11. Select the the Phase Details page of the “hkl_Corundum” item. Make sure the Delete hkls on Refinement box is not checked and set Scale factor to “Refine”. Switch to the hkls Is page and fix all the “I” intensities.

12. Save a PONKCS-MSP phase for re-use: Right click the “hkl_Corundum” phase and select Save Phase. It is suggested to use the *.STR extension, this allows easy re-loading together with other crystal structure data.

13. Continue the Tutorial about using this PONKCS-MSP phase in Section III.

Refine the remaining CPD-1 patterns using the calibrated PONKCS-MSP model for corundum.

1. Right click the data range and choose Replace Scan data with other CPD-1 series data. For real application of PONKCS-MSP method, you will need to load the previously saved PONKCS-MSP.str model(s) through Load STR(s) option of the real sample data.

2. Load crystal structure of other phases (fluorite.str and zincite.str for CPD-1 series data). Make sure the PONKCS-MSP phase for Corundum as defined in the previous two sections (I or II) is used.

3. Avoid below frequent user-errors related to working with PONKCS phases:

• Delete hkls on Refinement must be unchecked
• The Scale factor must be refined
• All intensities “I” in the hkls Is page must be fixed

4. Start the refinement and note the results. The accuracy of your results should be within ± 3 wt.% absolute deviation from the real weighed phase fractions of CPD-1 series sample.

Ideas for further practices:

• Repeat the same exercise designating Fluorite or Zincite as unknowns
• Repeat the same exercise designating all three phases as unknowns