MINERALOGICAL APPLICATIONS OF THE LATTICE-CONSTANT VARIANCE-COVARIANCE MATRICES

Direct and reciprocal lattice constant variance-covariance matrices when involved in the Law of Propagation of Errors can be used to gain a full evaluation of the error terms in mineralogical quantities expressed in terms of lattice constants. Properties and relationships which mutually connect the two matrices are discussed, with emphasis placed on physical dimensions. A practical application is given by calculating the error terms in the structural indicators Δ (bc) and Δ(α*γ*) of alkali feldspars. The differences between values obtained by using both variances plus covariances and those obtained using variances alone, are very small. However, as the calculations are completely automated, the full formulation using variances plus covariances represents a suitable better approach. © 1979 Springer-Verlag.