Estimating unit cell volumes from powder diffraction data: the triclinic case

In the computer indexing of powder diffraction patterns, an advance estimate of the volume of the unit cell is extremely valuable. This paper describes a method for estimating it directly from powder-pattern data for the case of triclinic materials. The method involves an easily prepared graphical plot, the slope of which is proportional to the unit-cell volume. First, the diffraction lines are numbered consecutively, starting with the largest d value (N = 1). A plot is then made of 1/N versus d³. Theoretically, the resulting line has a slope of 3/(2πV) = 0.4775/V for triclinic compounds, where V is the unit-cell volume. Examination of the graphs plotted for a number of triclinic materials where the experimental data are of high quality shows that the slope consistently falls around 0.60/V. Hence, the volume of the unit cell and/or the calculated density can be estimated. In addition, this analysis gives a numerical measure of the fraction of possible diffraction lines actually observed.