Chemistry of igneous rocks--[Part] 1, Differentiation index

TLDR

Fractional crystallization of complex magmas drives liquids toward the SiO₂–NaAlSiO₄–KAlSiO₄ system, as confirmed by recent experiments building on Bowen’s 1937 work. The differentiation index quantifies how far a magma has progressed toward this target system by summing the norm of its residua components, and frequency‑distribution diagrams from 3,000 analyses illustrate this metric. The differentiation index serves as a coordinate for variation diagrams, indicating rock basicity, and allows quick comparison of any analysis against the average to spot deviations.

Abstract

Recent experimental studies corroborate the evidence Bowen used in 1937 to demonstrate that fractional crystallization of complex magmas produces liquids which move toward and, for all practical purposes, eventually reach the system SiO ₂ -NaAlSiO ₄ -KAlSiO ₄ , petrogeny9s residua system. In a volcanic rock series the distance a given magma has travelled toward this goal can be quantitatively measured by calculating the norm and summing the constituents of petrogeny9s residua system; this value is called the differentiation index. It is a useful coordinate for variation diagrams and is a measure of the "basicity" of a rock. A series of frequency distribution diagrams have been prepared from 3,000 analyses in Washington9s Tables. Using these diagrams, any rock analysis can be compared at a glance with all the analyses and any deviations from the "average" can readily be seen.