Suppose we have two structures and one of them is just uniformly expanded as compared to the other, then if we select a window along the r-axis in the PDF pattern corresponding to the two structures and compare the two, we will have the relative shift in between the two patterns linearly increase as the window move from the low-r to the high-r part. The slope gives us an idea about how the unit cell is expanded. Beyond that, any non-linear behavior of the relative shift as the function of the moving box position will give us some idea about the structural variation beyond the uniform expansion/shrinking between the two.

Current tool was created for performing such an analysis in between two PDF patterns, without any input of structure model, i. e.. model free. One can select a PDF pattern as the reference and select multiple PDF files to compare with the reference pattern one by one. For each PDF data file, we have four main parameters controlling the analysis. The first one is the `Residual type` which controls how we are going to calculate the difference between the two PDF patterns. The default option is to use the absolute value of the difference (and sum over all involved points within the window), and the alternative way is to use the squared value of the difference. Then we have a boxcar window defined with a certain size (default as 250 data points), and we will compare the difference between the two PDF patterns within the window. We will try to minimize the residual versus the relative shift. Therefore, for a certain window location, we have a single value representing the relative shift between the two PDF patterns that is minimizing the difference. Then we will move the boxcar with a certain step size (default as 25 data points) an repeat the same minimization process. The last parameter is the maximum shift to be considered.

One can upload the reference PDF file using the `PDF reference file` button and multiple PDF data files with the `PDF data file(s)` button. All the input boxes should already present the default value for each input. One can feel free to change them as needed. They also can be left blank and the default value will be used. However, as long as the box contains some input value, it has to be a valid input and we will be performing checking initially. Once we are happy with the input parameters, we can hit the `Submit` button which will bring us to the next page where we can drag & drop to re-order the PDF data files in case the default uploaded order of files does not make any meaningful sense. Once we are happy with the order, we can hit the `Submit` button again to start the analysis, and when the analysis is done, the result page will be presented and one can view & download the results.