Precision Lattice Constants from X-Ray Powder Photographs

Abstract

A very general method is given for the calculation of lattice constants from powder photographs in which there is taken into account the various systematic errors inevitable in such photographs, including radius errors, film shrinkage, absorption, eccentricity and finite slit height. While the solution of the data is made by least squares, it is not at all laborious and is much simpler than the various methods, both analytical and graphical, which have previously been proposed. Examples are given of cubic, hexagonal and orthorhombic structures solved in this way using data from Debye and focusing cameras, extension to other structures and cameras being made evident. In effect, powder cameras become absolute instruments, independent of calibrating substances, and dependent only on the value of the x-ray wavelength.