A new method for the determination of precise values for the lattice parameters from powder patterns of trigonal and tetragonal crystals. Systematic errors and their partial elimination

A simple method for the precise determination of the lattice parameters of trigonal and tetragonal crystals using a value of the square of the axial ratio -/b c//sup 2///b a//sup 2/ is described. Also described is the influence of systematic errors on /b c //sup 2///b a//sup 2/ as well as on /b c/ and /b a/, and a simple method is described for elimination these effects in order to determine the corresponding error-free value /b c//sub 0 //sup 2///b a//sub 0//sup 2/, from which it is possible to calculate a value of /b c/ and /b a/ from each diffracted line and eventually to obtain /b c//sub 0/ and /b a //sub 0/ by extrapolation. These steps have been illustrated by a specimen of high-purity, natural alpha -quartz whose unit cell dimensions are: /b c//sub 0/=5.40510+/-0.00005 A , /b a//sub 0/=4.91360+/-0.00005 A and /b c//sub 0 ///b a//sub 0/=1.10003 at 25+/-0.5 degrees C. The volume of the hexagonal unit cell is 113.014+/-0.001 A /sup 3/ and the X-ray density /b D//sub x/=2.6484+/-0.0001 g/cm/sup 3/ at 25+/-0.5 degrees C.Anglai