• Select Open from the main menu. The program displays an open-file dialogue.
• Use the item list "Which file type?" to select the file format"ILL TAS file".
• Select the edit text "Directory name" and type the pathname of the directory Tutorial Examples
• Hold down the Tab key to select the edit text "filename" and enter enscan.tas
• Type a carriage return to end the edit session and click the button "OK".

When the data file has been successfully read, PkFit opens a graphic window and displays the spectrum. The window is divided into three parts: the plot region (top left), the message region (bottom) and the parameter region (top right) of which the latter two are presently empty.

Select item "Param" from the menu "ResCal" to check the settings of the sample, scan and instrument parameters.

Since, in this example, the incoherent signal (centered at 0 meV) is much stronger than the inelastic signal, the Y scale must be changed to make the inelastic peaks visible.

Select the item "Chg_Scales" from the menu "Plot". Select the edit-text YMax and type a new value, e.g. 100. Then click the button OK. The graphic window is updated.

The model PkFit uses to fit TAS spectra is a linear background plus a series of peak functions. In addition this model may include the Bose factor, a kf or ki correction, an absorption correction and a convolution of the signal with a one-dimensional or four-dimensional resolution function. In the following we will start with the simplest model and then introduce some corrections and the 1D resolution function.

Because PkFit automatically sets:

• the starting background position to a flat background at the position of the lowest point (blue line by default),
• the peak widths by performing a preliminary fit on the widths alone,

initializing the model is dead simple:

• set the number of peaks,
• locate the top of each peak,
• set the peak type.

Number of peaks

Although three excitations are expected, this energy scan seems to show only two excitations right to the strong incoherent peak at zero energy. Never mind, let us build a model with only three peaks and then let us fit it.

Select the menu Fit. A dialogue box allows you to set the number of peaks (in the range 0 to 6) of the fit model. Select 3 from the item list or type 3 in the edit text and then click the button OK.

Setting the three peaks

PkFit is now ready to set the starting peak position(s) and height(s) interactively. To initialize the peak parameters, first position the cross cursor at peak maximum and then either click the mouse button for a Gaussian peak shape or hit one of the following keys. Keys I, G, L, O, B, D or X (case insensitive) respectively stand for an Incoherent, Gaussian, Lorentzian, Harmonic oscillator, Bragg peak, Delta function or a user-defined peak shape.

As an exercise, we will initialize the peak parameters using both methods, i.e. using a mouse click and a keystroke.

Since the top of the incoherent peak (centered at zero energy) is not visible, click anywhere on the vertical line EN=0. The true height value will be set later on. PkFit displays a cross mark at the selected position and draws a horizontal line which indicates the starting peak width at half maximum. Then move the cursor successively to the top of the two inelastic peaks and type a "L" (case insensitive). The full widths at half maximum (FWHM) are (arbitrarily) initialized to one third of the plot width divided by the number of peaks. As soon as the three peaks have been defined, a preliminary fit on the widths alone is performed to better estimate the starting peak widths.

Then a dialogue is automatically displayed, which allows you to change the peak types and the non-fitting peak-parameters. Note that this dialogue box can be opened at any time by means of the item "PeakType" of the menu "Fit".

Convoluting peak shapes with the instrument resolution

The observed peak shapes are generally substantially deformed due to the effect of the instrument resolution. This can be computed as a convolution of the expected profile with the resolution-function of the instrument. In the case of three-axis spectrometers, the latter is a four-dimensional Gaussian, with axes the energy and either the direct or reciprocal space axes.

The incoherent signal being Q independent, the four-dimensional convolution becomes one-dimensional (in energy) once the 4D resolution function has been integrated in Q. Furthermore, since the incoherent scattering can be modeled by a delta function in energy, it can be finally modeled by a 1D Gaussian with a width equal to the Q-integrated resolution width (GW).

For the magnon excitations, the convolution is theoretically a 4D one. However for excitations with flat or slightly dispersive dispersion, the Q-independent approximation can be made. In other words, we can model a magnon peak shape by a Lorentzian function convoluted with a 1D Gaussian resolution-function, the width of which is equal to the Q-integrated resolution width (GW).

These assumptions mean that three different resolution-widths (GW) must be computed since the peaks are at different energies. Thus, ask the program to compute the Gaussian resolution widths (GW) by checking the three "CalcGW" check box.

As soon as the first check box is clicked the dialogue "Instrument configuration" is shown which let you select the method to be used to compute the instrument resolution-function. This dialogue is displayed automatically only the first time a resolution calculation is requested but it can be accessed at any time via item "Resol. calc." of the menu "ResCal".

For the present test run, click the radio button "Cooper-Nathans method" and then click the button OK. We are back to the previous dialogue and the computed value of the GW parameter of the first peak is shown in the corresponding GW edit field.

Finally note that we will not check the check boxes "Equicenter" since the equivalent peaks at negative energies can be neglected due to the Bose factor.

The image below gives the aspect of the dialogue window once all the settings have been made.

We can check that the values in the three edit texts "GW" do correspond to the Q-independent case. Click the button "Set dimensionality". A dialogue is shown which displays the GW status and allows you to set the type of the Q-dependence of the peak function.

Since the three item lists are set to "Q independent" as expected, simply click the button OK.

We are back again to the "Non fitting peak parameters" dialogue. Click the button OK to exit the dialogue. The background line and the different peak(s) are drawn in the graphic window. Note that a message is written in the message region (bottom part) and that the fit-parameter list is shown in the parameter region (right part). For each peak, the first line (same color as the peak curve) gives the peak number plus the type and the dimension of the convolution into parenthesis.

Adjusting the incoherent peak height

The current initialization of the incoherent-peak parameters is not yet correct. As stated in section "Initializing fit parameters", since the top of the peak is out of the window frame, the interactive initialization process made it possible to set the peak location but not the peak height. Thus we will now adjust the height parameter manually.

Select item "FitPar" from menu "Fit". A dialogue is shown. Set the height field of the incoherent peak to 3200, and click the button OK.

Select item "Fit" from the menu "Fit". The iterative minimization process is performed and the plot region now displays the fitted spectrum. The parameter region displays the final parameter values together with there e.s.d's in parentheses. The comment region shows the linear expression defining the background, the value of the refinement agreement-factor "CHISQR" and the correction factors for three points (the axis extrema and center).

Because the fit gives a width of the lower energy Lorentzian peak (here W2=.68 meV) much larger than the resolution width (GW=0.254 meV) and larger than the width of the second Lorentzian peak (W3=.49 meV), we can suspect that the expected third excitation does exist. Thus, let us try adding a new peak centered around 1.3 meV with a height of 20 counts.

Select the item "Peak+" from the menu "Fit" and initialize the new peak with the mouse as explained before. The dialogue "Set non-fitting parameters" is automatically displayed. Set the peak 4 type as the Lorentzian and check the boxe "CalcGW" as we did before for the first two excitations.

Click the button OK. The window contents is updated accordingly.

Select the item "FitPar" from the menu "Fit". A dialogue is displayed. Type "W2" in the width field of peak 4. Thus the fit will be performed keeping the widths of peaks 2 and 4 (W2=W4) equal.

Click the button OK and perform a new fit (item "Fit" from the menu "Fit"). The window contents display the new fitted curves and parameter values.

Because the enscan.tas data set comes from a highly absorbing sample, an absorption correction must be added to the model. Furthermore this correction will be applied on the sample contribution to the background which is called "sample background" in PkFit.

Select the item "AbsCor" from the menu "Options". A dialogue is displayed which allows for the initialization of the absorption parameters. The latter are the sample shape, the cross sections (in barns), the sample dimensions (in cm) and the relevant axes (in rlu).

To help you check the given absorption parameters, PkFit gives a graphical and numerical summary of the absorption-correction calculations. It draws the reciprocal lattice in the scattering plan. The latter are defined by the two axes (AX,AY,AZ) and (BX,BY,BZ) which can be set in the dialogue "Resolution parameters" (item "Param" from the menu "ResCal").

Click the item "Menu1" to go back to the main menu and then perform again a fit (item "Fit" from the menu "Fit"). The graphic window displays the final results as shown below.

Each time you have successfully processed a spectrum it is a good practice to save both the data and the results to a log file. The latter may be understood as an output file which can be used for subsequent post-processing with other programs. For example, Kaleidagraph can be used to produce documents with publishing quality from these log files.

Select the item "Save" from the main menu. A new menu bar allows the choice of the file or the window to be saved.

Click the item "LogFile". A dialogue allows to change the file name of the log file. The default name is the data-file name with the extension ".LOG".