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Size-strain analysis using the fundamental parameter (FP) method

Summer 2012, Volume 28, No. 2
Akihiro Himeda

Crystallite size and strain affect the physical (mechanical, electric, magnetic and optical) properties of materials. It is quite important to quantify size and strain, and to clarify the relationship between them in the field of material science.

The effects of finite crystallite size and lattice strain can be observed as deformations in the shape of diffraction curves. Thus, information can be obtained by investigating their shapes. However, the deformation occurs due to not only size-strain effects but also instrumental effects.

In conventional estimation, only the width of the peaks is used, not the whole peak shape. To eliminate the instrumental effect, width correction is carried out by measuring standard samples and subtracting the breadths of peaks of the width standard sample from those of a sample being investigated. With the 2-theta dependence of the corrected peak width, we can extract the crystallite size and lattice strain quantities.

However, the method of subtraction depends on whether the peak shape is assumed to be Gaussian or Lorentzian. In addition to this, the peak shape will not necessarily express a Gaussian or Lorentzian function.  Moreover, so-called “super Lorentzian” peak shapes are reported for samples with broader distribution of crystallite size. Based on this, applied width corrections may have limited validity.

In contrast to the above, the fundamental parameter method (FP method) has recently been used to analyze the effect of profile shape originated from instrumental conditions. In the FP method, the peak shape is calculated by convoluting the instrumental profile shapes assuming a theoretical model of instrument and profiles originated from crystallite size and lattice strain.  In this way, we can obtain size-strain information and eliminate the instrumental effects without measuring standard samples.

Size distribution can also be quantified by analyzing the precise peak shape. Size distribution affects the sharpness close to the peak top and slow fading off of its tails.

In PDXL 2, crystallite size, size distribution and strain can be analyzed with the FP method more easily than the ordinary Rietveld method. In this report, theoretical background to analyze them and some applications of actual samples using PDXL are described.


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