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Many X-ray diffraction patterns show overlapping bands, and the aim here was to find a method to dissociate these bands. This method is based on the fact that a diffraction band can be accurately described by a mathematical formula of the type:
Thus, the overlapping of the two bands can be treated by using the relation: 
where each of the two bands is described by the above expression. The validity of the results can be checked by the variance range function and Fourier analysis. These profile-analysis methods can be applied both to separate bands and to bands from the superimposed profiles. A second application of the method concerns the problem of side bands which appear in the spinodal decomposition of certain alloys such as Cu-Ni-Fe. These side bands, which are very broad when compared to the diffraction peaks, can be described by a pure Lorentzian function:
. The smoothing of the experimental profile using the sum of the functions which satisfy the two types of equations gives good results even when the side bands have weak intensity and when experimentally no other direct measurement of their position can be made. This method can be applied to all structural transformations.
![I(x)= A \Big[ {\rm cos}\pi \Big( {x-x_{0}-\delta \over a} \Big)\Big]^{n} {K^{2} \over K^{2} + (x-x_0)^{2}}.](http://journals.iucr.org/j/issues/1977/02/00/a15329//teximages/a15329fd1.gif){kind=small}
where each of the two bands is described by the above expression. The validity of the results can be checked by the variance range function and Fourier analysis. These profile-analysis methods can be applied both to separate bands and to bands from the superimposed profiles. A second application of the method concerns the problem of side bands which appear in the spinodal decomposition of certain alloys such as Cu-Ni-Fe. These side bands, which are very broad when compared to the diffraction peaks, can be described by a pure Lorentzian function:
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