Add Instrumental Standard for Crystallite Size Estimation

Basics and Background

In this dialog you can create or edit an instrumental peak broadening standard that is required for a crystallite size analysis using Scherrer's formula:

Crystallite size (average in Å) = K λ / (FWHM * cos θ)

where K is the so-called "Scherrer constant" (typically =0.94 for FWHM of spherical crystals with cubic symmetry), λ is the wavelength of the radiation and θ is the diffraction angle of the peak. As you can see, the formula is based on the FWHM values (FWHM = Full Width at Half Maximum) of the peaks.

For obtaining these FWHM values from the diffraction pattern it is necessary to separate the contribution of the instrument to the peak broadening (FWHM) from the contribution of the sample. The FWHM values of the latter are then used in the Scherrer formula to calculate an estimate for the crystallite size of the corresponding phase/compound.

In order to separate the instrument contribution to the FWHM of the experimental peaks from the sample contribution, it is necessary to first record a powder diffraction pattern from a sample/compound for which it is known that it does not contribute to the diffraction peak profile (so that the peak broadening is almost entirely caused by the instrument). For this, the crystallite size should be larger than 500 nm while the particle size should be less than 10 μm. In addition, the standard material should be defect and strain free. Finally, the standard should have a similar mass absorption coefficient than the nanocrystalline specimen as well as a similar atomic weight and packing density [1].

A standard as it is used in Match! consists of a list of peaks from the diffraction pattern of a suitable standard compound (e.g. LaB6, CeO2, Si, etc.) that has been recorded using the same instrument and setting than the compound for which you would like to determine the crystallite size. The most important data are the peak positions and their FWHM values, both of which should have been obtained from a profile fit calculation of the peak data to the standard's diffraction pattern. At least one peak position and FWHM value must be entered in order to create a valid standard.


In order to create a standard for crystallite size estimation in Match!, the first thing you have to do is to import the powder diffraction pattern of a suitable standard (see above). Afterwards, run the peak searching (if it is not performed automatically), then mark click on the individual peaks and run a profile fitting calculation for them until the agreement between the experimental diffraction profile and the one calculated from the experimental peak is fairly good. You can display the resulting peak parameters in the peak list if you like.

Now you are ready to add these peak data as a new instrumental standard for crystallite size estimation: Run the "Crystallite size estimation..." command from the "Tools" menu. If you do so for the very first time (no standards are present up to now), a dialog displaying some background information will be displayed, asking if you are ready to add/enter the peak data of your new standard now. Please accept by clicking on "Yes".

Afterwards, Match! will detect that experimental peak data are currently present, so it will ask if you would like to add these peak data as a new instrumental standard. Again, click on "Yes" to do so. The "Add/edit instrumental broadening standard" dialog will be displayed, providing a variety of commands and options to handle instrumental standards:

By pressing the New button you can delete all current peak data and start from scratch. If peak data are already present (e.g. if you have copied them from the current experimental pattern), you will be asked if you would like to save the current data/standard. If you click "Yes", you can enter a reasonable name (e.g. the formula sum) for the new standard. Afterwards, the peak data table in the dialog will be erased.

Using the Save button you can save the current peak data as a new standard, or update the standard currently given as "Preset" (see below). Please enter a reasonable name (e.g. the formula sum) for the new standard if you do not want to overwrite the current standard ("Preset").

If you press the Default button, the standard currently given as "Preset" (see below) will be made the default instrumental standard for future crystallite size estimation calculations.

By pressing the Delete button you can remove the standard currently given as "Preset" (see below) from the settings, so it won't be available in the future anymore.

In the Preset line the instrumental standard for which the peak data are currently displayed is given. If you press the "drop down" arrow on the right-hand side, a list of all instrumental standards that are currently available in the settings is provided, so that you can select the standard for which you would like to see or modify the peak data, or which you would like to make the new default standard.

Below, you can define the radiation type and the wavelength for the current standard.

The peak positions in the table can either be displayed as d-values or 2theta, depending on the corresponding selection.

In the lower half of the dialog, the peak data table is given, where you can view or edit the peak data for the current instrumental standard given in the "Preset" line.

Below the peak data table you can use the Add or Delete buttons to either add a new peak or delete the peaks (lines) that are currently marked in the peak data table.

By pressing the button Copy from exp. you can copy the experimental peak data from the current Match! document, in order to add them as a new standard. It is also possible to Import peak data from 3-column peak list files (2theta/d intensity FWHM) or Stoe peak list files (*.pks), by pressing the corresponding button.

Once you have finished editing your instrumental standard peak data, please press OK in order to close this dialog. You may be asked to save your current standard data if you have not already done so. Help will display this page in the online help.


[1] Scott A Speakman, "Estimating Crystallite Size Using XRD",