Ludo K. Frevel

Chemical Analysis by X-Ray Diffraction: Classification and Use of X-Ray Diffraction Patterns

Editors Note: As part of our plan to reprint previously published papers of great historical interest, the editorial board is pleased to reproduce the following paper by Hanawalt, Frevel and Rinn. This paper was originally published in Volume 10 (1938) of the Analytical Ediction of “Industrial and Engineering Chemistry” and is considered by most diffractionists to be the classic work in qualitative identification of multiphase polycrystalline material. The original publication carried a foreword written by the editor of Industrial and Engineering Chemistry. This foreword ended with this prophetic statement : “There is reason to believe that this publication, which is made possible in this form by the generous financial assistance of the Dow Chemical Company, will serve to bring this method of analysis into general use in industrial and consulting analytical laboratories.”

JCPDS — International Centre for Diffraction Data Sample Preparation Methods in X-Ray Powder Diffraction

The aim of any diffraction experiment is to obtain reproducible data of high accuracy and precision so that the data can be correctly interpreted and analyzed. Various methods of sample preparation have been devised so that reproducibility, precision and accuracy can be obtained. The success of a diffraction experiment will often depend on the correct choice of preparation method for the sample being analyzed and for the instrument being used in the analysis. A diffraction pattern contains three types of useful information: the positions of the diffraction maxima, the peak intensities, and the intensity distribution as a function of diffraction angle. This information can be used to identify and quantify the contents of the sample, as well as to calculate the materials crystallite size and distribution, crystallinity, and stress and strain. The ideal preparation for a given experiment depends largely on information desired.

Single Wave‐Length X‐Rays for Powder Diffraction

WLα radiation filtered through a Cu–Zn foil is essentially monochromatic and has the advantage over filtered CuKα or MoKα radiation in that the WLα1 line is approximately ten times as intense as the WLα2 line. Moreover the comparatively wide Δλ‐spread (WLα2−WLα1) results in very sharp powder lines at those Bragg angles where the CuKα doublet or MoKα doublet is unresolved.

Indexing Powder Diffraction Patterns of Isomorphous Substances

Two methods of indexing powder diffraction patterns of isomorphous substances are presented: the first method depends on matching the log d values of two or more isomorphs (d being the interplanar spacing of a given reflection); the second method relates the spacing shifts Δd/d of two isomorphs to the symmetry of the particular crystal system. These methods are made practical by the publication of tabulated powder diffraction data.

A New Focusing Method for X‐Ray Powder Spectroscopy

A convergent Soller type slit, adaptable to a camera of arbitrary radius, serves to select those pencils of x‐rays which emanate from a broad focal spot and impinge upon any selected point on the equator of the cylindrical camera. The diffracting powder is mounted on the camera wall in the form of a thin sheet which intercepts the wedge of x‐radiation. In this manner all x‐rays diffracted at the same Bragg angle are brought to a focus at the equator of the camera.

Note on the Indexing of Powder Photographs

By taking two successive Debye‐Scherrer‐Hull pictures of a powder specimen at two different temperatures, one obtains on a single film a direct temperature shift of the diffraction pattern of the substance. An interval of 150°C or greater will generally suffice to produce easily measurable temperature shifts that can be related to the anisotropy of a crystalline substance. A systematic treatment of the various crystal systems has shown that the first four systems (cubic, tetragonal, hexagonal, and orthorhombic) can be indexed in a straightforward manner. Two cases of the monoclinic system: (1) ∂β/∂T=0 and (2) αb/2=(1/b)(∂b/∂T)>αa>αc>cot β∂β/∂T can be solved without time‐consuming mathematical calculations.