Geochemical Modelling of Igneous Processes – Principles And Recipes in R Language

Part of the series Springer Geochemistry pp 159-166


Direct Models

  • Vojtěch JanoušekAffiliated withCzech Geological Survey Email author 
  • , Jean-François MoyenAffiliated withUniversité Jean-Monnet
  • , Hervé MartinAffiliated withUniversité Blaise-Pascal
  • , Vojtěch ErbanAffiliated withCzech Geological Survey
  • , Colin FarrowAffiliated with

* Final gross prices may vary according to local VAT.

Get Access


The best proofs for operation of open-system processes remain radiogenic isotope ratios, which are generally not fractionated during closed-system processes such as melting or crystallization. The magmas formed should preserve the isotopic characteristics of their source. In other words, the radiogenic isotope data are totally transparent to mechanisms of magmatic differentiation but are very sensitive to mixing or contamination. This chapter explains mathematical formulae governing binary mixing for a single isotopic ratio (in diagrams such as Sr vs. 87Sr/86Sr or 1/Sr vs. 87Sr/86Sr) and for their pairs (e.g., in 87Sr/86Sr vs. 143Nd/144Nd plots). The following text adds the theoretical treatment of the Assimilation and Fractional Crystallization (AFC) processes and their bearing on isotopic composition of the evolving magmas.