FC–AFC–FCA and mixing modeler: A Microsoft® Excel© spreadsheet program for modeling geochemical differentiation of magma by crystal fractionation, crustal assimilation and mixing☆

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Abstract

Several petrological processes, such as (1) fractional crystallization (FC), (2) combined and decoupled fractional crystallization and assimilation (AFC and FCA), and (3) mixing processes, which modify the geochemical composition of the magma, are graphically programmed using Microsoft® Excel© spreadsheet on the basis of differentiation equations. The FC–AFC–FCA and mixing modeler is an interactive program that models the consequent theoretical vectors of FC, AFC, FCA, and mixing processes, which are frequently used in modern petrology. The program enables the user to export outputs of linear- or logarithmic-scaled bivariate diagrams and also rare earth elements (REE)- and multi-element spider diagrams of the modeling results. It also plots some classification diagrams as well as bivariate Harker variation diagrams. Because the program is interactive in nature, changes in any parameters are simultaneously updated onto all diagrams.

Introduction

Magmatic rocks are differentiated by a range of petrological processes such as (a) different degrees of melting of the source rocks, (b) crystal fractionation in magma chambers (fractional crystallization, FC), (c) contamination of the magma via assimilation of the wall-rocks (assimilation), and (d) mixing of magmas of different compositions. Among these processes, FC and assimilation are generally combined and they may occur simultaneously (AFC; Taylor, 1980; DePaolo, 1981). Cribb and Barton (1996) have also suggested that FC and assimilation are not always related and that these two processes may be decoupled (FCA). The mixing of magmas having different compositions also resulted in changes to the original magma compositions.

A number of computer programs have been designed to theoretically graph the vectors of FC and AFC equations (see Keskin, 2002 for detail). As pointed out by Keskin (2002), the main advantage of spreadsheet programs is that they are easier and faster to use during data converting, storing, and evaluating. The FC–AFC–FCA and mixing program, presented in this study, has many advantages in data input, execution, and output. The data can easily be transferred to the FC–AFC–FCA and mixing program. The results of modeling in addition to several classification diagrams can be converted to a Graphics Interchange Format (GIF) file. Additionally, numerical results of the modeling can be derived as tables. Another main advantage of the program is that the modeling results of each magmatic process can be traced on the same diagram.

Section snippets

Modeling the magmatic processes

In this section we present a brief summary of calculations of magmatic processes and some parameters used in FC–AFC–FCA and the mixing program.

Program structure and operation

The FC–AFC–FCA and mixing modeler has been designed on several sheets that include data input and output sections. The data input section contains two sheets: (1) parameters and (2) samples. The output section is based on graphical and numerical sheets that consist of (1) modeling, (2) classification, (3) Harker1, (4) Harker2, (5) isotopes, and (6) numerical output sheets (Table 1).

The “parameters” sheet contains some tables that allow selection of (a) the elements (and isotopes) that will be

Application example

We present graphical outputs of FC, AFC, and FCA models for Rb, K, Sr, and Th. The results are plotted on K/Rb–Rb and Sr–Th (Fig. 4a and b). These elements have been selected for easy comparison with the graphical results of Cribb and Barton (1996) (Fig. 4c and d). The only differences between the calculations for Fig. 4a and c, and between Fig. 4b and d, arises from the partition coefficients used in modeling. We have used the bulk partition coefficients as KdK=0.980, KdRb=0.061, KdSr=1.220,

Conclusions

The FC–AFC–FCA and mixing modeler program presented here is a Microsoft® Excel© spreadsheet program designed on the basis of existing magmatic differentiation equations for crystal fractionation, assimilation, and mixing processes in magmatic systems. Geochemical analyses of magmatic rocks can easily be transferred to the program. The program also has the advantage that the user can output the graphical and/or numerical results of fractional crystallization (FC), combined assimilation and

Acknowledgements

The authors would like to thank S. Nasir Sultan and an anonymous reviewer for their constructive reviews. Ercan Aldanmaz and Mehmet Keskin are also thanked for their helpful comments. Martin Palmer helped with the English of the final text.

References (22)

  • M.J. Le Bas et al.

    A chemical classification of volcanic rocks based on the total alkali–silica diagram

    Journal of Petrology

    (1986)

    • Cited by (0)

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