Profile Fitting

While the normal peak searching algorithm is relatively fast and produces peak data appropriate for many "routine" problems, there may nevertheless be cases in which a more accurate determination of the peak parameters (d-value/2theta and intensity) is required, e.g. if a diffraction pattern contains "shoulder" peaks. In these cases, profile fitting may be applied.

During the profile fitting calculation, Match! tries to optimize the peak parameters (intensity, FWHM (="Full Width at Half Maximum"), and optionally 2theta) in order to obtain a reasonably good agreement between calculated and experimental diffraction pattern (profile data). This is achieved by using the peak data as parameters in a constrained least-squares refinement.

Profile fitting requires the presence of peak parameters (2theta, I, FWHM). If no peaks are currently present when the profile fitting command is executed, a special variant of the peak searching algorithm will first be applied. There are two major differences to the normal peak searching algorithm:

If no peaks are currently marked/selected, the parameters of all peaks will be fitted, otherwise only the parameters of the marked peaks. Besides this, the user can select which parameter(s) (2theta, I, FWHM) shall be varied in the profile fitting. This can be achieved by clicking the corresponding buttons in the toolbar, by pressing the corresponding function keys, or alternatively be selecting the corresponding options in the "Pattern/Profile fitting" submenu:

Parameter to be fitted

Toolbar button

Keyboard Shortcut

2theta

F6

Intensity

F7

FWHM

F8

In other words: It is not only possible to perform a peak search followed by profile fitting for all peaks, but you can also fit individual parameters of individually selected peaks.

The actual profile fitting calculation can be executed once the peaks and/or the parameters which shall be fitted have been selected. This is achieved simply by pressing the "F5" key on your keyboard, by pressing the corresponding button in the main toolbar, or by selecting the corresponding command in the "Pattern/Profile fitting" submenu. When the calculation is finished, the success is announced in the status bar at the bottom. Besides this, the Rp-factor which has been reached is given.

Profile fitting of the complete pattern (i.e. for all peaks) is implemented in Match! as an iterative process, where peaks are modified or eliminated in each so-called "pass" of the profile fitting. The profile fitting will stop either if convergence has reached (Rp-factor could not be reduced compared to the last pass), or if a maximum number of passes (currently 10) has been carried out.

When a combined peak searching/profile fitting calculation is carried out for the first time, a default sensitivity is used which takes the "noise" found in the raw diffraction data into account. This default sensitivity has been chosen to obtain good results with a large variety of diffraction patterns. However, If you have the impression that the calculation either yielded too many or too few peaks, you might want to adjust the peak search sensitivity for your special data.

Normally, the intensity values resulting from the profile fitting procedure are integrated intensities, taking into account both the height as well as the FWHM of each peak. You can view the integrated intensity values in the peak list on the upper right-hand side. An exception to this is the relative intensity scaling of the vertical axis, in which case the integrated intensity values are scaled to a maximum value of 1000.0.

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