STRUCTURAL CHARACTERIZATION OF NANOCRYSTALLINE MATERIALS BY X-RAY DIFFRACTION
C. E. Krill
Universität des Saarlandes, FB 10 Physik,
Gebäude 43, Postfach 151150, D-66041 Saarbrücken, Germany;
Email: krill@rz.uni-sb.de
Keywords: nanocrystalline materials, grain size, grain-size distribution, profile analysis, grain growth, mean-square displacements
Nanocrystalline materials are polycrystalline materials in which the average crystallite size <D> is smaller than approximately 50 nm. Owing to the inverse relationship between <D> and the total grain-boundary area, the proportion of atoms located at or near a grain boundary is much higher in nanocrystalline materials than in conventional coarse-grained materialsóso much so that the overall properties of nanocrystalline materials can be influenced or even dominated by the presence and properties of the interfaces [1].
Characterization of the microstructure of such fine-grained materials is performed primarily by direct-imaging techniques, such as TEM, and by powder diffractometry. The latter method holds several important advantages over techniques involving microscopy: diffraction measurements are typically nondestructive, the necessary sample preparation is usually much less time consuming, and a far larger specimen volume is sampled during characterization. Unfortunately, the information provided by diffractometry regarding <D> is indirectóit must be extracted from diffraction peak profiles, an often difficult procedure for which a variety of methods of varying flexibility and accuracy have been developed [2].
It will be seen that several of these techniques yield not one but two distinct measures for the average grain (crystallite) size of a sample, neither of which is comparable to the average size gained by microscopy! Nevertheless, these idiffractionî grain sizes can be related to the imicroscopyî grain size through appropriate averaging over the grain shape and the grain-size-distribution function g(D). We shall see that, in many cases, g(D) itself can be estimated from the values of the idiffractionî grain sizes if the form of the distribution function is known independently [3].
The experimental advantages afforded by the determination of <D> by means of diffraction have been exploited in a recent study of grain growth in nanocrystalline Fe performed at the European Synchrotron Radiation Facility (ESRF) [4]. The combination of high beam intensity and very small instrumental broadening characteristic of the high-resolution powder diffraction beamline BM16 enabled the grain-growth evolution in nanocrystalline Fe samples to be followed in situ for average sizes <D> ranging from 20 nm up to 1 m with one-minute resolution! This technique promises much more detailed experimental information regarding the kinetics of grain growth in metals and ceramics than can be obtained by conventional analysis of coarse-grained materials via the time-consuming and destructive method of optical microscopy.
Of course, besides the grain
size, diffraction can be used to study many other structural
parameters, such as the lattice parameter (which is expected to
depend on <D> as a
result of interfacial tension), the inhomogeneous strain (which,
curiously, is generally found to scale with the overall
grain-boundary area) and the mean-square atomic displacement <u2>
(which in nanocrystalline materials
can have a significant static component in addition to the usual
dynamic one). A rather strong grain-size dependence has been
reported for the static (i.e., temperature-independent) part of <u2> in nanocrystalline Cr [5]. We shall
compare this finding with our own measurements of <u2> in nanocrystalline Pt as a function of
temperature and processing history of the sample. The
difficulties of data analysis and interpretation that arise in
this case are representative of many of the challenges that
remain in the structural characterization of nanocrystalline
materials by diffraction.