Summary: Cell dimensions obtained from X-ray powder photographs of twenty-four natural olivines and one synthetic forsterite have been related to the cation contents by a new statistical procedure developed by M. H. Hey. Unlike conventional statistical analysis, which assumes error only in one parameter, this procedure simultaneously considers the estimated errors in all variables.
Linear terms in Ca, Mn, Mg (or Fe(≡ 1-Mg-Ca-Mn)) satisfactorily account for the cell dimensions, and there was no need to invoke a term in Mg2. Since there are three cell dimensions and three chemical unknowns, it is theoretically possible to estimate the major cations in olivine just from the cell dimensions. However, the coefficients for Mn and Fe are so similar and the ranges of Ca and Mn are so small that the technique would be impractical.
Data for ideal (Mg,Fe) olivines were estimated by adjusting the cell dimensions by linear extrapolation from the cell dimensions of tephroite and monticellite. A simple chemical term was sufficient to account for each cell dimension. The linear relation between cell volume and Mg is consistent with the complete disorder of Mg and Fe revealed by parallel single-crystal X-ray studies.
The cell dimensions of a synthetic fayalite deviate significantly from those of natural fayalites after correction for the effects of Ca and Mn substitution in the latter: some structural or chemical difference, probably involving ferric iron, is indicated.
No superstructure lines have been found, in contradiction to Eliséev's data.