engleski

The comparison of various methods for extraction of size-strain data from XRD powder pattern of thin films

The structural properties of dc-magnetron sputtered thin W films depend very strongly on deposition conditions. Depending on Ar gas pressure, substrate material, substrate temperature and deposition duration, different relative amount of beta- and alfa-W phase deposits. The appearence of particular tungsten phase might be related to the level of built-in stress in the prepared films. We performed some preliminary work to choose the appropriate method for extraction of size-strain data from the observed XRD patterns which are far from the ideal (preferred orientation, absence of some reflections). Since the grain size distribution in nanocrystalline materials produced by the inert-gas condensation are known to be approximately log-normal, and the Fourier transform of a log-normal function is a Lorentzian function, the particle size broadening from the nanocrystalline samples will produce a Lorentzian-shaped diffraction profile. Due to the existing doubt whether strain broadening is described by Gaussian or Lorentzian profile function we performed calculations with both assumptions. We used seven analytical methods for the diffraction peak line profile analysis: (a) Rietveld profile fitting method, using profile function Thomson-Cox-Hastings pseudo-Voigt with Lorentzian part for size and Gaussian part for strain ; (b) Simultaneous determination of size and microstrain according to Scherrer and Wilson equation based on profile fitting to Lorentzian in Rietveld method ; (c) Warren & Averbach method ; (d) Least-square method of simultaneous determination of size and microstrain averaged in all reflections ; (e) Cutoff-single line approximation based on Rietveld profile fitting method using profile function pseudo-Voigt with Lorentzian size and Gaussian for strain ; (f) Cutoff-single line approximation based on Marquardt cutoff method and Rietveld profile fitting method using profile function Thomson-Cox-Hastings pseudo-Voigt with Lorentzian part for size and Gaussian part for strain ; (g) The Scherrer equation which usually gives reasonable results for grain sizes. According to the obtained results we concluded that in our case the most appropriate method for extraction of size-strain data from observed XRD patterns is method (f), because using the Marquardt cutoff method the problem with truncation of profile function presented in other methods based on Rietveld procedure is avoided. The problem with high background, which is the cause of "hook" effect in Warren & Averbach method, is also solved with (f) method. Finally, the absence of some reflections due to the textural structure of tungsten thin films, which causes the instabilities in Rietveld profile fitting, with cutoff procedure is also made less important for the analysis.

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