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U. S. Geological Survey Open-File Report 01-041

A Laboratory Manual for X-Ray Powder Diffraction


Many researchers still generate X-ray powder diffraction data using strip chart recorders. Either templates or conversion tables are then used to convert these patterns from degrees two theta to d-spacings (i.e. interplanar spacings) thereby allowing the Joint Committee on Powder Diffraction Standards (JCPDS) diffraction files to be used to determine which phases are present. Although most X-ray diffraction systems now commercially available are computerized and can automatically perform these conversions, the continued functionality of the older units and cost of the newer systems prevents many researchers and students accessing them.

The templates and conversion tables below were generated for copper radiation. While X-ray tubes with other target materials are available, in practice only copper is commonly used for geological applications. Copper K alpha radiation is preferred because of its relatively high peak energy, intensity, low peak-to-background ratio, convenient wavelength, the high heat conductivity of the target material, and the symmetry of the K alpha 1 and K alpha 2 composite peaks (Commeau and others, 1985).



Bragg Law equationThe merits of templates over conversion tables are the time and labor they save. The templates supplied below were generated for Cu K alpha weighted-mean radiation and a 2 degrees 2 theta scale increasing from left to right with an interactive computer program (Poppe and Dodd, 1989). This program utilizes the Bragg equation and was written in C programming language to operate under Unix system 5 or MS-DOS version 2 or later. The weighted-mean wavelengths were calculated using the equation:

(2(K alpha 1) + (K alpha 2)/3

This equation gives the K alpha 1 lines more "weight" because of their greater intensity relative to those of the K alpha 2 lines.

The templates, which are stored in the graphics directory of this CD-ROM, are supplied in both PDF, JPG, and TIF formats and may be output directly to a plotter fitted with mylar or acetate media. For those without access to a suitable plotter, the shorter templates are designed to fit on standard 8.5 by 11 inch page. Their size allows these shorter templates to be output directly to a standard printer fitted with transparencies, such as those used for overheads. If any slight adjustment for size is necessary, the shorter templates may also be printed on paper and transferred to transparent media and resized with the aid of a reducing/enlarging photocopy machine. 

Click here to get Adobe Acrobat reader.To view and print the PDF version, you must obtain and install the Acrobat® Reader, available at no charge from Adobe Systems.


A table has been generated in Microsoft Excel 97 using the Bragg equation that converts degrees two theta to interplanar spacings for Cu K alpha weighted-mean, K alpha 1, and K alpha 2 radiation. For the purposes of Microsoft Excel, the Bragg equation was rewritten as:

d = lambda/(2.0 * sin(0.5 * twotheta * D2R))

The wavelengths used for copper radiation (lambda) were: K alpha weighted-mean, 1.541838 angstroms; K alpha 1, 1.540562; and K alpha 2, 1.544390. The formula used to calculate the K alpha weighted-mean wavelength is the same as used above for the templates. The conversion factor used to change degrees to radians (D2R) was 0.0174532925199433, and d is in angstroms. The conversion tables that follow show calculated interplanar spacings to 0.01 degrees, and are supplied in Microsoft Excel and ASCII formats.

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