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A Computer Program for Calculating Mineral Size Distributions from X-ray Diffraction Data

We have developed a computer code that calculates crystallite size distributions and strain for minerals from X-ray diffraction data. This technique was developed (as part of the research program of the Water Resources Division of the USGS) in order to measure the particle size distributions of minerals in rocks and soils. Mineral particle size distributions may yield geological information about a mineral's provenance, degree of metamorphism, degree of weathering, etc. We currently are using this program for research applications in the earth sciences. However, this program also would be useful to many types of manufacturers who use or synthesize clay-size (i.e. very fine grained) crystalline materials, because a material's particle size and structural strain may strongly influence its physical and chemical properties (e.g. its rheology, surface area, cation exchange capacity, solubility, reflectivity, etc.).

Clay-size crystals generally are too fine to be measured by light microscopy (~2 to 100 nm in thickness). Laser scattering methods give only average particle sizes, and particle size cannot be measured in a particular crystallographic direction. Also, the particles measured by laser techniques may be composed of several different phases, and some particles may be agglomerations of individual crystals. Individual particle dimensions may be measured by electron and scanning force microscopy, but it often takes several days of intensive effort to measure a few hundred particles per sample, which may yield an accurate mean size for a sample, but is often too few measurements to determine an accurate size distribution. Furthermore, such instrumentation is usually not available outside a research setting.

Measurement of size distributions by X-ray diffraction (XRD) solves these shortcomings. An X-ray scan of a sample is automated, taking a few minutes to a few hours. The resulting XRD peaks average diffraction effects from billions of individual clay-size particles. The size that is measured by XRD may (see below) be related to the "fundamental" particle size of a mineral, i.e. to the size of the individual crystalline domains, rather than to the size of particles formed by the agglomeration of crys tals. Furthermore, one can determine the size of an individual phase within a mixture, and the dimension of particles in a particular crystallographic direction. Crystallite shape can be determined by measuring crystallite size in several different crystallographic directions.

The XRD method is based on the regular broadening of XRD peaks as a function of decreasing crystallite size. This broadening is a fundamental property of XRD, described by well-established theory. Our method for determining particle size distributions uses the shapes of XRD peaks to calculate crystallite size distributions and structural strain for crystalline samples. The term crystallite size is synonymous with X-ray scattering domain size and may or may not correspond to physical particle dimensions, which is one limitation of the XRD technique. However, our experience with measuring the thickness of clay minerals indicates that crystallite size and particle thickness are usually synonymous. The program accurately calculates sizes in the range from ~2 nm to ~100 nm. The upper limit for size determination depends significantly on the accuracy of instrumental standards. The code (4 Mb in size) is written in Microsoft Excel using a spreadsheet interface for input/output, with macro routines for calculation. Excel is a widely used spreadsheet package available for the IBM and Macintosh operating systems.

Additional information about this opportunity for partnership with USGS can be obtained by contacting:

Dennis D. Eberl
U.S. Geological Survey
Water Resources Division
3215 Marine Street
Boulder, Colorado 80303-1066
Phone: 303-541-3028
Fax: 303-447-2505

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