Estimating the unit-cell volume from one line in a powder diffraction pattern: the triclinic case

In the computer indexing of powder diffraction patterns, an advance estimate of the volume of the unit cell is quite helpful. This paper describes an extremely rapid and easy to use method for estimating the cell volume directly from the powder diffraction data for the case of triclinic materials. Examination of a number of high-quality experimental patterns shows that the cell volume can often be estimated from only one line in the data. The relation is V = 13.39d³₂₀, where V is the cell volume and d³₂₀ is the d value of the 20th observed line. Other diffraction lines in the powder pattern can also be used for estimating unit-cell volumes. The analogous relations for the 25th and 30th lines are V = 17.24d³₂₅ and V = 21.32d³₃₀. This method is an outgrowth of one previously described by the author [Smith (1976), J. Appl. Cryst. 9, 424-4281 which involved the slope of a data plot. Within the set of some 40 high-quality triclinic patterns, the present one-line method predicts the unit-cell volume to an average discrepancy of 10.6%, 12.6% and 12.7% for the 20th, 25th and 30th lines respectively: the slope method, to 9.3%.