It is well known that the Fourier analysis of X-ray diffraction peak profiles (as implemented by Warren and Averbach) can accurately determine the areaweighted average grain size of a fine-grained sample. Less well known is the fact that this method simultaneously yields a volume-weighted average grain size. Under certain circumstances, knowledge of these two weighted average grain sizes is sufficient to permit reliable estimation of the grain-size distribution, even when the distribution cannot be calculated directly from the Fourier coefficients, as is usually the case. We demonstrate this for a nanocrystalline Pd sample prepared by inert-gas condensation; average grain sizes and the grain-size distribution are estimated by X-ray diffraction profile analysis and compared with the same quantities measured directly by transmission electron microscopy (TEM). Very good agreement between the resulting average grain sizes is achieved only after compensating for the fact that diffraction profile analy...

Estimating grain-size distributions in nanocrystalline materials from X-ray diffraction profile analysis

The Warren-Averbach (WA) analysis and other simplified methods that are commonly used to determine the grain size of nanocrystalline materials are discussed in terms of accuracy and applicabilities. The nanocrystalline materials used in the present study are prepared by cryomilling of A1 powders and subsequent consolidation (hot isostatic pressing and extrusion). Transmission electron microscopy observations of the as-extruded nanocrystalline A1 reveal a bimodal distribution of grain sizes centered around 50 to 100 nm and 250 to 300 nm. It is shown that the grain size determined by the WA analysis agrees with the lower bound grain size (e.g., 50 to 100 nm) observed experimentally. In the case of the integral method, it is useful to use a parabolic (Cauchy-Gaussian (CG)) relationship to approximate instrumental broadening and separate the intrinsic broadening. Compared to the Cauchy-Cauchy (CC) and Gaussian-Gaussian (GG) approximations, this is shown to give the best results. In addition, the reliability of the Scherrer equation is also discussed.

On the analysis of grain size in bulk nanocrystalline materials via x-ray diffraction

An EXAFS (extended x-ray-absorption fine structure) study of nanocrystalline iron prepared by high-energy ball milling is presented Accurate data analysis has been performed using a recently developed ab initio multiple-scattering method (GNXAS) The crystalline iron EXAFS spectrum, taken as reference, has been analyzed taking proper account of the important multiple-scattering signal Results of the data analysis are shown to be in good agreement with known structural values The dramatic decrease of the first-neighbor coordination number found in nanocrystalline iron, as a function of the milling time, is shown to be related to the presence of a large defect density The corresponding decrease of the coordination numbers of the second and further neighbors, as well as the significant decrease of the multiplicities of the three-atom configurations, confirms this interpretation A simple model which takes into account the presence of atomic defects is shown to lead to marked reduction of coordination numbers and three-atom multiplicities in agreement with the experimental data Selected models without lattice defects are shown to be unable to give a quantitative explanation of the intensity reduction of the EXAFS signal found in milled nanocrystalline iron An in situ annealing of the sample (up to about 1100 \ifmmode^\circ\else\textdegree\fi{}C) milled for the longer time (32 h) is shown to reduce considerably the density of the defects, as expected, although no complete recovering of the crystalline order is found The transition from \ensuremath{\alpha} iron to \ensuremath{\gamma} iron has been directly observed for such nanocrystalline material

Microstructural defects in nanocrystalline iron probed by x-ray-absorption spectroscopy

Influence of attrition milling on nano-grain boundaries

The formation of a nanocrystalline tungsten‐rhenium solid solution by mechanical alloying in a SPEX mill using tungsten carbide vial and balls was investigated. The milling process was monitored by X-ray diffraction and electron microscopy techniques. It was shown that mechanical alloying of a W‐25 wt.% Re powder mixture resulted in the formation of a W‐Re solid solution with a very small volume fraction of the s phase. The grain size of the solid solution phase is in the nanometer range. Sintering of the mechanically alloyed powder resulted in a dense and high-purity product. © 1998 Elsevier Science S.A. All rights reserved.

Synthesis of a nanocrystalline W-25 wt.% Re alloy by mechanical alloying

Tungsten powder (99.9% purity, 12 μm particle size) was milled in a hardened steel vial with six 440C stainless steel balls for 1–50 h. Because of the hardness of W, contamination and later alloying with Fe from abrasion of the stainless steel balls occurred. X-ray chemical analysis and weight-gain measurements of the milled powder indicated Fe contents varying from 3 at.% after 1 h to approximately 40 at.% after 50h milling. The powder pattern peaks of the nanocrystalline W were subjected to a Fourier analysis to determine the effective particle size and the microstrains within these particles. After 20 h milling, a particle size of 35 A and microstrains of 0.5% were observed. The diffraction patterns from the W powder milled for 20 and 50 h were also analyzed in terms of the structure factor (interference function) and the atomic distribution function. The 20 h sample was predominantly nanocrystalline with a broad diffuse peak under the (110) and (211) reflections, while the 50 h sample was predominantly amorphous. After subtracting the remnant crystalline peaks, the position of the first peak in the reduced atomic distribution function, GI(r), was found to be 2.7 A.

The structure of amorphous and nanocrystalline WFe alloys prepared by high-energy ball milling

The structure of nanocrystalline Fe, W and NiAl powders prepared by high-energy ball-milling

The Structure of Nanocrystalline Iron and Tungsten Powders Prepared by High-Energy Ball Milling

Amorphous and nanocrystalline materials exhibit broad or diffuse peaks in their x-ray, neutron, or electron diffraction patterns. A detailed analysis of these patterns permits us to evaluate the atomic short-range order in amorphous materials, and the size of the coherently diffracting domains (particle size), the elastic strains within these domains, and the dynamic and static atomic displacements in nanocrystalline materials.

Diffraction Studies of the Structure of Amorphous and Nanocrystalline Fe-W Alloys

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The structure of amorphous and nanocrystalline WFe alloys prepared by high-energy ball milling

The structure of nanocrystalline Fe, W and NiAl powders prepared by high-energy ball-milling

The Structure of Nanocrystalline Iron and Tungsten Powders Prepared by High-Energy Ball Milling

Diffraction Studies of the Structure of Amorphous and Nanocrystalline Fe-W Alloys