Analysis of the Broadening of Powder Pattern Peaks Using Variance, Integral Breadth, and Fourier Coefficients of the Line Profile
The broadening of powder pattern peaks has been studied by three methods—Fourier analysis, integral breadth measurements, and variance of the line profiles. The results obtained from the variances are compared with those obtained from the integral breadths and Fourier coefficients.
Tungsten filings were prepared at room temperature and their powder pattern peaks were recorded with a Norelco diffractometer using filtered Cu K α radiation. The variances, integral breadths, and Fourier coefficients were calculated with the IBM 7094 computer. The results indicate that the variance is very sensitive to the range of integration s2 — s1 = (2θ 2 — 2θ 1) cos θ0/λ. An error of ± 10% in this range due to the difficulty in choosing the correct background changes the values of the variance significantly and the integral breadth to a lesser extent. However, the same error does not affect the values of the Fourier coefficients.
Comparing the particle sizes and strains obtained by the three methods, it was found that the strains agreed remarkably well. The particle size calculated from the variance was smaller (D e W = 150Å) than that evaluated from the initial slope of the Fourier coefficients (D e = 210Å) and from the integral breadths 2D e≃ D I= 430Å.
KeywordsLine Profile Fourier Coefficient Acta Cryst Peak Profile Tungsten Filing
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