AbstractNanocrystalline powders of Fe and W were prepared by mechanical working in a highenergy Spex 8000 mixer/mill. The diffraction patterns were recorded with Co Kα radiation and the line profiles were subjected to a Fourier analysis. The size 〈D〉 of the coherently diffracting domains (x-ray particle size) and the root-mean square strains 〈ε2L〉1/2 were determined with the Warren-Averbach method. In addition, the integral breadths were evaluated and corrected for instrumental broadening assuming Cauchy line profiles. In order to separate particle size and strains, the corrected breadths β(s) = βcosθ/λ were plotted as a function of s = 2sinθ/λ, i.e., β(s) =(1/D) + 2ε s, where D = 〈D2/〈D〉 and ε is a strain averaged over the domain size D.X-ray fluorescence analysis indicated that the W powders contained an iron and chromium contamination due to the abrasion of the stainless steel balls reaching a value of 24 at% Fe+Cr after 20h of milling. Since W is elastically isotropic, all available (hkl) reflections can be used in the Warren-Averbach and line breaddi analyses. After 20 h of milling, the W powder exhibited a particle size 〈D〉 = 35 Å and a strain 〈ε2〉1/2 = 0.52% at L = 30 Å. The integral breadths yielded the particle size D1 = 70 Å and the strain ε = 0.38%. in the case of Fe powder, also milled for 20 h, the (110) - (220) pair of reflections was used to calculate the particle size and strains. The Fourier analysis yielded the values 〈D〉 = 105 Å and 〈ε2〉1/2 = 0.59% at L = 30 Å. The corresponding integral breadth values are D1 = 280 Å and ε1 = 0.7%. The sum of the particle size Fourier coefficients is equal to the integral breadth particle size D1 = 125 Å, which is very close to value 〈D〉 = 105 Å indicating that the particle or domain sizes have a very narrow size distribution.
Diffraction line profiles of spherical hollow nanocrystals
