PAPER: FC-Modeler: a Microsoft® Excel© spreadsheet program for modeling Rayleigh fractionation vectors in closed magmatic systems

Citation: Keskin, M. (2002). FC-Modeler: a Microsoft^® Excel^© spreadsheet program for modeling Rayleigh fractionation vectors in closed magmatic systems, Computers & Geosciences, V. 28/8, pp. 919-928 (OCT/2002).

Abstract: FC-Modeler is a user-friendly, interactive Microsoft^® Excel^© spreadsheet program that models Rayleigh fractionation vectors and produces high quality graphic output in the form of log-log bivariate diagrams. It runs on Microsoft^® Excel^© 97 or later under Windows 95 or later. The design of the program provides the user with an opportunity to undertake petrologic modeling. Due to its interactive nature, this program updates the output simultaneously, when any parameter is changed, allowing the user to simulate the fractional crystallization (FC) process. FC-Modeler also permits plotting geochemical data beside the FC vectors and hence it can be used as a powerful tool to constrain the nature and amount of the fractional crystallization in a closed magmatic system. It produces a high quality graphic output, which can readily be used for publication.

The most downloaded 18^th article between May 2002-May 2003.

Introduction

A range of geological processes control trace element distributions in magmatic suites, including partial melting, fractional crystallization, magma mixing, crustal contamination and assimilation combined with fractional crystallization. Among these, crystal fractionation is of special interest as it is considered to be one of the most influential processes that exist in almost every magmatic system, controlling a great proportion of the element variations in magma chambers. Over the last few decades, advances in magmatic petrology and geochemistry have exerted a profound effect on our understanding of these magmatic processes. Developments of mathematical methods together with advances in computer hardware and software have provided researchers with a powerful tool for modeling and even simulating these processes.

A number of studies in the literature have focused on computer programs designed for the petrologic modeling of magmatic processes (Conrad, 1987; Holm, 1988; Nielsen, 1988; Defant and Nielsen, 1990; Holm, 1990; Harnois, 1991; Benito and López-Ruiz, 1992; Cebriá and López-Ruiz, 1992; D’Orazio, 1993; Verma et al., 1998; Folch et al., 1999). Among them, only Holm (1988 and 1990), Nielsen (1988), Harnois (1991), Cebriá and López-Ruiz (1992) and Verma et al. (1998) have specifically dealt with the modeling of the fractional crystallization (FC) process. Except for Holm’s two (1988 and 1990) studies, suggesting the effective use of spreadsheet software (i.e. Lotus 1-2-3), the rest presented programs running under DOS.

As pointed out by Holm (1990), there are several advantages of using spreadsheet software for petrologic modeling, most important of which is the rapid recalculation of equations and more flexibility in working the models. Unlike most DOS programs, spreadsheets do not require problematic data format conversions before and after data processing. They are designed to be very stable, so unexpected program terminations, which are quite common for DOS programs, are very rare. Moreover, they do not require any knowledge of computer programming; basic computer literacy is sufficient to use these programs.

Since the publication of Holm’s (1988 and 1990) papers, there have been great advances in both spreadsheet software and PC hardware. Today’s spreadsheet programs are equipped with numerous functions (e.g. statistical, mathematic, database and logical), which are extremely flexible and customizable. They run on much faster hardware and considerably better operation systems. Moreover, they are perfectly compatible and integrated with other programs such as word processors, databases, presentation programs and even web design software. Above all, they are widely available and easy to learn and use, yet very powerful in storing, manipulating and processing geochemical data. Hence, it is not surprising that most petrologists prefer to use spreadsheet programs for storing and evaluating their geochemical data. There are some examples of spreadsheet programs in the literature, addressing the specific issues in geology such as those written for modeling of steady-state groundwater flow (Ousey, 1986), classifying microprobe-derived amphibole analyses (Tindle, and Webb, 1994), plotting mineral stability diagrams (Biddle et al., 1995), converting relative bearings to XYZ coordinates (Grossenbacher et al., 1996), performing thermodynamic calculations (Martín, 1996) and computing the dynamic properties of particles in Newtonian fluids (Le Roux, 1997).

This paper presents a new user-friendly interactive spreadsheet program called FC-Modeler designed for the modeling of the Rayleigh fractionation process. The program is a Microsoft^® Excel^© Workbook containing dynamic links, enquiries and functions that perform routine calculations for modeling of up to eight Rayleigh fractionation vectors (Fig. 1, 2 and 3). It runs on Excel 97 or newer versions running under Windows 95 or later. It permits the user data entry, storage, calculation of the FC vectors and graphical output, which is ready for printing or importing into another Windows program, all in a single file. With its user-friendly interface, the program simplifies the modeling of closed-system FC which is otherwise a complex and time-consuming task prone to a series of possible mistakes.

FC-Modeler is designed to facilitate error-free modeling. Warning messages appear in particular sections of the program whenever the user makes a mistake. When there is an error, the program does not perform the whole or some parts of the modeling. The users have full control of every parameter in the program and can also store mineral/melt partition coefficient (K_d) values and their own geochemical data. They interact with the program using a graphical interface involving a table and a bivariate scatter chart on which the results of every adjustment on any parameter are simultaneously updated. Geochemical data can also be plotted beside the FC vectors. This provides a good opportunity for the user to simulate the FC process, observe the theoretical trends (vectors), compare them with natural trends that their data display, and test their working hypotheses. The program file occupies around 1.9 Mb of disk space but this may slightly vary depending on the data stored.

1. Description of the Program

The FC-Modeler program is a Microsoft^® Excel^© Workbook containing dynamic links, enquiries and functions that perform routine calculations for modeling of up to eight Rayleigh fractionation vectors (Fig. 1). It runs on Excel 97 or newer versions running under Windows 95 or later. It permits the user data entry, storage, calculation and graphical output of the FC vectors, which is ready for printing or importing into any other program, all in a single file.

The program file occupies around 1.9 MB of disk space but this may vary slightly depending on the data stored. The user interacts with the program using a graphical interface involving a table and a log-log bivariate scatter chart on which the results of every adjustment on any parameter are simultaneously updated. All the parameters including magma composition, mineral percentages, K_d values for various magma compositions are user modifiable. Geochemical data can also be stored in the program and plotted beside the FC vectors. This provides a good opportunity for the users to simulate closed system FC process, observe the theoretical trends (vectors), compare them with natural trends that their data display, and test their working hypothesis. With its user-friendly interface, the FC-Modeler program simplifies the FC modeling which is otherwise a complex and time-consuming task prone to a series of possible mistakes.

Special care was paid to the design of the program so that the user can carry out an error-free modeling. The program is controlled by several error codes. When there is an error, the program stops the modeling and gives an error message.

It should be noted that the whole workbook and some parts of the sheets are write-protected in order to maintain the integrity of the program. Also note that the user can rename the program file and move it into any folder, which does not interfere with anything in the program.

2. Structure of the program

There are four modules in the program (Table 1).  Three of these (i.e. K_d Matrices, Data series and User interface) are used for data input and storage.

1. K_d matrices:  Mineral/melt K_d values for basic, intermediate and acid magmas are stored in three separate spreadsheets. K_ds of a total of 45 elements for 16 minerals can be stored in each matrix. 

2. Data series: A total of six spreadsheets are reserved for storing the user’s geochemical data. Each sheet corresponds to a data series that can be displayed on the modeling graph with a different symbol. They are named accordingly as Data S 1 to 6. A total of 200 samples each containing up to 45 elements can be stored on each sheet.

3. User interface for modeling: This module is used for inputting a number of parameters such as magma composition, mineral percentages, elements, starting compositions and some parameters related to vectors. This is placed on a separate sheet named “Modeling”.

4. Results: This module is designed for presenting the results in a table and graphical format. It consists of three sheets: (a) Numeric output, (b) Summary, and (c) Graph.

   1. Numeric Output: This sheet contains a table whose columns correspond to the fraction of magma remaining (F) and rows to the elements (or ratios or multiplications of elements) chosen by the user for the modeling of each vector.

   2. Summary: This sheet contains all the details of the FC modeling on a single page. It summarizes everything about the modeling: the parameters used, name of the data series plotted, bulk partition coefficients (Ds) calculated together with the modeling graph generated.

Graph: This sheet includes an Excel chart containing results of the FC modeling. On this graph, modeled FC vectors and data points representing the data series are presented together with a legend. This graph is not write-protected. Hence, the users can copy the graph and paste it onto a document or another spreadsheet. If needed, the users can change the format of the graph after pasting it onto another spreadsheet.

 Table: 1. Schematic presentation of the program.

Figure: 1. Screen shot of the first page of the FC-Modeler program named “Modeling”. Only two fields of a total of six (see Table 2) are visible in this figure: “Table of FC vectors” is located above and “Table of calculated Ds” below.

3. Using the program

3.1. Entering data

You can enter three different types of data into the program: (1) K_d values for three different magma compositions (Fig. 2), (2) geochemical data that you can plot beside modeled FC vectors (Fig. 3), and (3) a number of petrologic parameters (e.g. magma compositions, proportions of minerals, elements etc.) that you can manipulate for your modeling (Fig. 1, 5 and 7). There is not a certain order for data entry. The program has such a dynamic structure that you can modify any value at any time. When you do this, everything in relation to this modification is simultaneously updated. However, I recommend that you start entering K_d values and geochemical data before starting the modeling.

3.1.1. Entering K_d values

You will find values already entered on mineral/melt K_d matrices for most of the elements. These are the most common values but they may not meet your special needs. Therefore, before commencing to FC-modeling, you should construct your own K_d database by checking K_d values for basic, intermediate and acid magmas in three sheets (Fig. 2) and modify them if necessary.

Figure: 2. Screen shot of the sheet named “Kds for Basic magmas”. Minerals are placed in the columns and elements along rows. Note that the empty cells are marked by greenish background.

On these three sheets, the K_d matrices are organized in a simple way: minerals are placed along columns and elements are placed in rows. The elements are sorted in an ascending alphabetical order. The bulk partition coefficients (i.e. table of calculated Ds on the Modeling sheet) and hence the vectors modeled are simultaneously updated in the program when you change any K_d value for any mineral that you have selected for your modeling. Note that the empty cells in K_d matrices remain colored in order to catch your attention. The program does not consider these empty cells as zero values in the calculation of D values and hence does not plot such vectors, giving warning messages (see 3.2.4. Warning messages).

3.1.2. Entering the data series

Having finished with the K_d database, you can enter your data series into the sheets named Data S 1 to 6 (Fig. 3). Each sheet corresponds to a data series that will be displayed on the modeling graph with a different symbol. The user has full control over which data series will be plotted on the modeling graph. Note that there are only 6 data series available in the program so the number of data series cannot exceed 6. Also note that only 200 samples can be entered in a single sheet. If your source data is in a spreadsheet format, you can copy them from the original file and paste them onto these sheets. But you should be careful about the order of elements.

Figure: 3. Screen view of the “Data Series 1” sheet.

On these sheets, elements are placed in columns and arranged in ascending alphabetical order. Element names are write-protected so you cannot modify any of them. Any changes in the element’s order are not allowed either. You can enter the name of each series into the cell located at the top left of the each sheet (i.e. C1 in Fig. 3). Please avoid long names and abbreviate them if needed. When entered, names of the Data Series will be displayed on the “Modeling” and “Summary” sheets.

On the first three data sheets, you will find some trace element data for Ba, Rb and Y elements. These data are provided to give you a chance to practice the program before entering your own data. Please do not forget to delete these data before beginning your modeling.

Important note! Please do not use Clear – All command in order to delete the data on these sheets, since this command write-protects the cells for some reason. It is recommended that you first select the cells you want to clear and then press the delete key on the keyboard.

Having completed the data entry, now you are ready for the FC vector modeling.

3.2. Modeling

After inputting the data, you can start constructing the FC modeling. The sheet named “Modeling” contains all the parameters and options that you can manipulate for the modeling of Rayleigh fractionation vectors. It is divided into five sections as shown in Table 2.

On this sheet, you can control the program by using two of these fields: (1) Table of FC vectors (Fig. 5), and (2) Graphical interface (Modeling & Graph in Fig. 7) including fields for elements and their starting compositions (a1 and a2 in Fig. 7) and the section for selecting the data series that will be displayed alongside the modeled vectors (the field “c” in Fig. 7). The other three fields are not user-modifiable; they either give information about the modeling or warn you about possible mistakes (Table 2).  When you change any of these parameters, the program will instantly update the results of your modeling.

Table: 2. The sections on the “Modeling” page and their functions.

3.2.1. Table of FC vectors

This is the table in which you can select the magma compositions and enter volume percentages of minerals for each of eight vectors (Fig. 5). The columns correspond to the vectors whereas the rows stand for the minerals in this table. The third row from the top contains the cells used for adjusting the magma composition for each vector. The letters on the left of each cell stand for magma compositions:  B for basic, I for intermediate, and A for acid. You can adjust the magma composition by clicking on the “spinner” on the right of each cell (Fig. 4). Clicking on arrows on each spinner brings one of four available choices in order: n/a, B, I and A. If you do not want to plot a particular vector, click on the downward-pointing arrow key until you get an “n/a” (i.e. non applicable) message (Fig. 4-b).

   

(a)                              (b)

Figure: 4. a) Select a magma composition by clicking on appropriate arrows on the “Spinner”.  b) If you do not want to plot a particular vector, click on the downward pointing arrow key until you get an n/a message.

The second row of the Table of FC vectors contains cells displaying the colors and symbols donated for each vector on the modeling diagram (Fig. 5). This legend is designed to help you easily see which column on the table corresponds to which vector on the diagram.

Figure: 5. Screen view of the “Table of FC vectors” on the sheet named “Modeling”.

Note that there are two columns for each vector on this table. The cells in the left column of each vector are used for entering the percentages of minerals, while the ones on the right, named “status”, are designed to display warning messages related to the corresponding minerals.

There are 16 minerals available for the modeling. The first 10 minerals, highlighted with white background color, are the ones that are crystallized from magmas of any composition in nature. However, the ones indicated by a grey background color cannot be crystallized from either one or two magma compositions.

The use of the “Table of FC vectors” is quite simple. In order to get a vector calculated and then plotted onto the modeling diagram, you should set magma composition by using the appropriate spinner and enter mineral percentages (over 100%) for that particular vector. When you enter a percentage value into a cell, its background color turns into bright yellow. This is intended to draw your attention to the minerals you have chosen for modeling. The sum of the mineral percentages is displayed at the bottom of each vector and should be equal to 100% (Fig. 5). I suggest you carefully check the cells in the status column of each vector to see if there are any warning messages about any mineral.

q     If a mineral is unlikely to crystallize from the magma composition, “Not crys” message becomes visible in the status bar beside the mineral (Fig. 5).

q     If K_d values of one or more elements are absent in the K_d matrices (the ones corresponding to the magma composition you selected for that particular vector) for a mineral, “Miss Kd!” message appears in the status bar alongside that particular mineral (Vectors 3 and 5 in Fig. 12).

To find out which element’s K_d value is absent, you can check the “Missing K_d!” message in the “table of calculated Ds”. For example, there is a “Miss Kd!” message for biotite in vector 5 in Fig. 12. If you carefully examine the “table of calculated Ds”, you can easily find out that the missing value in fact belongs to Y element.

While using the Table of FC vectors, you should regularly check the error and warning messages appearing in various parts of the modeling sheet.

If you do not want to plot a particular vector, you can either set composition to n/a by using corresponding spinner (Fig. 4-b) or delete all % values in the mineral % column of that particular vector. When you do this, the program gives the message “n/a” in the “table of calculated Ds” for that vector (Fig. 12, Vector 4). The same message will appear, if all cells are left empty in the mineral % column for a vector.

3.2.2. Table of calculated Ds

This table displays bulk partition coefficient values calculated by the program for the elements selected for each vector (Fig. 6). If there are any mistakes in the Table of FC vectors, the program does not calculate the D value for that particular vector; instead it displays a warning message in the corresponding cell on the table (see error messages).

Figure: 6. Screen shot of the table of calculated Ds.   See Table 3 for color codes for D values.

In this table, background color of the cells changes depending on the D value (Table 3).

 Table: 3. Color codes used for D values in table of calculated Ds.

Magma compositions are also color-coded: pink background for acid, pale blue for intermediate and light green for basic magmas (Fig. 6).

3.2.3. Graphical interface (Modeling & Graph)

A scatter diagram in the middle of the “Modeling” sheet performs the function of the monitor of the modeling since it instantaneously responds to any adjustment on any parameter (Fig. 7). The modeled FC mineral vectors and the selected data series are plotted on this diagram together with a legend. It also serves as the control center of the program since it is surrounded by the fields for manipulating all the variables related to the modeling.  There are three different types of fields as follows:

a)   Elements and concentrations field: There are two fields located at the bottom left of the graph corresponding to X- and Y-axis respectively (the areas marked by “a1 and a2” in Fig. 7). Elements and their concentrations are adjusted by using these two fields. You can select elements and adjust their starting concentrations by using combo boxes and browsers located next to the X- and Y-axis of the graph (Fig. 7 and 8). You can also set ratio or multiplication of two elements for any or both of X- and Y-axis. The use of combo boxes and browsers is exactly the same as the ones used in all Windows programs (Fig. 8). Note that if you want to deselect an element, you should pick “none” from the pull-down menu (Fig. 8-b).

Figure: 7. Screen shot of the section named “graphical interface” (Modeling & Graph) on the sheet named “Modeling”. There are three fields that are used for adjusting parameters of the modeling: (a) elements and concentrations field, (b) the vectors field, and (c) the data series field.

(a)                                              (b)

(c)                                                  (d)

(e)

Figure: 8. Screen shot of the fields that are used for selection of elements and their starting compositions. (a) General view, (b) Selection of an element by using the pull-down menu (combo box), (c) Adjustment of element concentration (in ppm) using the browser, (d) setting up of a ratio of two elements (here the ratio of Rb/Nb) for the Y axis, (e) The interface for setting up elements and their concentration on the X axis.

b) Vectors field: This field is located on the upper-right of the graph (the Fig. 9). It allows you to adjust two parameters related to Rayleigh fractionation vectors being modeled: (i) the point at which crystallization ends and (ii) intervals of the tick marks corresponding to intervals of crystallization. A total of thirteen predefined pairs of parameters are placed in a combo box located to the right of the graph. Available options are listed in Fig. 9-b. So, you can select one of these 13 choices from this combo box for your vector modeling.

 (a)                               (b)

Figure: 9. Figure displaying content of the combo box for setting up two parameters related to modeled vectors.  

c)  Data series field: This field contains the interface which is used for selecting the data series that will be plotted aside the modeled vectors on the graph (the area marked with “c” in Fig. 7). It contains a series of cells displaying the name of the data series, the symbols representing them and the number of data points plotted in each series. On the left of these cells, there is a series of combo boxes with pull-down menus. There are two choices on each pull-down menu: (1) “display” and (2) “don’t display” (Fig. 10). To have a particular data series displayed on the graph, you should select the “display” option from the combo box corresponding to that data series (e.g. Series 1 in Fig. 10). If you select the “don’t display” option for a particular data series, the data points for this series disappear from the graph. In that case, the background color of surrounding cells turns into purple (e.g. Fig. 10, Series: 5 and 6). Note that the symbols for each data series are shown next to each cell.

Figure: 10. (on the left) Screen shot of the section “The data series displayed”. In order to get a data series displayed on the graph, you should select “Display” from the pull-down menu on the left.

Figure: 11. (on the right) General view of the Warning messages section.

As you will discover, the program simultaneously responds to any adjustment you may make on any parameter. You can try numerous trial and error models in a very short time and produce several graphs. However, you should be also aware of possible errors in your modeling. The program is designed in such a way that it does not permit any errors in the modeling. When there is an error, the program does not plot such data on the modeling diagram and warns you with some messages appearing in several parts of the “Modeling” sheet.

3.2.4. Warning messages

The area located to the right of the graph is reserved for warning messages (Fig. 11). Only when there is an error or missing data in the program, do some messages in this area appear. Tables of “FC vectors” and “calculated Ds” also display error messages, when there is an error. These messages are listed below:

Not crys ! message: If a mineral is not crystallized from a particular magma composition, a message “Not crys” appears in the cell alongside the mineral in the status column and the color of this cell turns into red (Fig. 12). If you enter a percentage value for such a mineral, a warning message “Not crys !” appears on the “table of calculated Ds” (Fig. 12, Vector 1) and the vector under consideration is not plotted onto the modeling diagram. Such vectors are also marked as V1, V2,…V8 on the table of “Warning messages” (Fig. 11) placed to the right of the graph on the modeling sheet so that you can easily find out the mistakes and correct them.

Figure: 12. Error messages appearing on tables of vectors and calculated Ds.

Not crys!: some minerals cannot be crystallized from the magma composition selected (e.g. Vector 1); Error in %: the sum of mineral percentages is not equal to 100% (e.g. Vector 2); Missing K_d! or Miss K_d!: some K_d values are not entered in K_d Matrices (e.g. Vector 3); n/a: either the composition magma or mineral percentages are not entered (e.g. Vector 5).

If you either set the composition of magma to n/a (Fig. 4-b) or do not enter any minerals percentage values for a vector, the program does not calculate the D values for this particular vector (e.g. Fig. 12, Vector: 4). A message reading “n/a” is displayed in the corresponding cells on the “table of calculated Ds”. Such vectors are not displayed on the modeling graph either.

Error in % message: You can see the sums of mineral percentages below each vector (Fig. 12). If the total mineral percentages differ from 100% for a vector, the program neither calculates D values for the elements nor plots the vector on the diagram; instead it gives a message as “Error in %” in the table of calculated Ds (Fig. 12, Vector: 2). An error message also appears on the “table of warning messages” pointing to the vectors whose sum of mineral percentages is different from 100% (Fig. 11). This message is displayed until you correct them to equal to 100%.

Miss K_d! message: If one or more mineral/melt K_d values are not entered in the K_d database for a particular element, and if you attempt to use such elements and minerals for your FC modeling, a warning message reading “Miss K_d!” appears in the status column next to the mineral percentage you have just entered (Fig. 12, Vectors: 3 and 5). To find out which elements’ K_d values are absent, you can check the “table of calculated Ds” for the message “Missing K_d”  (Fig. 12, Vectors: 3 and 5). For example, if vector 5 in Fig. 12 is considered, K_d value of Y for biotite should be absent in the K_d matrix for acid magmas. Such warnings related to missing K_ds are also displayed on the “table of warning messages” under the heading “Missing K_d(s) at vector(s)” (Fig. 11). If a vector contains one or more missing mineral/melt K_d values, the program does not calculate it and hence does not plot it onto the modeling graph. You can also check the “K_d Monitor table” (Fig. 14) at the bottom of the Modeling page to find out which mineral/melt K_d values are absent for the elements and for the magma compositions you have selected. Once the missing K_d values are entered, the program starts calculation and the vectors are immediately plotted onto the modeling diagram.

n/a message: This message is displayed only in the “table of calculated Ds”. It comes into view when either the magma composition of a vector is set to n/a (see Fig. 4-b) or all the cells in mineral % column of that particular vector are left empty (Fig. 12, Vector 4). The program does not plot such vectors on the graph either.

The same elements selected! message: This message appears in a cell below the Data Series field (Fig. 13-b), when two elements you entered for a particular axis are the same (Fig. 13-a).

One of the signs is not entered! message: This message appears when you select two elements but do not define their relationship by selecting  “/” or “x” signs from the combo box provided (Fig. 13-b).

Zero concentration! message: This message comes into view below the element and concentration field of X-axis, when the concentrations of one or more elements are set at zero (Fig. 13-a and c).

  (a)                                               (b)

  (c)

3.2.5. K_d Monitor

This is the table designed to help you see immediately which minerals’ K_d values have not been entered in three K_d matrices for the elements selected for modeling. It contains three tables for basic, intermediate and acid magmas (Fig. 14). When you change any of the elements in the modeling, the cells in the table will be simultaneously updated.

Figure: 14. K_d monitor section located at the bottom of the “Modeling” sheet. The table displays which minerals’ K_d values have not been entered in three K_d matrices for the elements selected for modeling. 

3.3. Output

The output section is divided into three sheets: (1) Numeric output, (2) Summary, and (3) Graph.

3.3.1. Numeric output

This sheet contains a table whose columns correspond to the fraction of magma remaining and rows to the elements or ratios of elements chosen by the user for the modeling of each vector (Fig. 15). It basically displays the change in concentration of each element (or ratios or multiplications of elements) on each vector with increasing FC, in other words, with decreasing F .

Figure: 15. Screen shot of the page named “Numeric output”. The table displays the change in element concentrations as a function of fraction of magma remaining as the crystallization proceeds.

3.3.2. Summary

This sheet contains all the details of the FC modeling. It displays the parameters used, name of the data series plotted, together with the calculated D values and modeling graph (Fig. 16). This page is designed for you to see and print all the details about your modeling on a single page.

Figure: 16. General view of the sheet named “Summary”.

3.3.3. Graph

This sheet includes an Excel chart containing modeled FC vectors and points of data series together with a legend (Fig. 17). This sheet is not write-protected to enable you to copy the graph and paste it onto another sheet or a document. This provides you with a high quality output, which is ready for printing or importing into another program. If you wish, you can add some text and drawings, and change symbols and colors of data series on this chart after pasting it onto another spreadsheet.

 Figure: 17. A view of the sheet named “Graph”.

References

Benito R., López-Ruiz, J., 1992. ANATEX.BAS: a program for calculating the mineralogy of the residual solid and trace element fractionation in partial melting. Computers & Geosciences 18 (5), 603-615.

Biddle, D.L., Percival, H.J., Chittleborough, D.J., 1995. An interactive spreadsheet for graphing mineral stability diagrams. Computers & Geosciences 21 (1), 175-185.

Cebriá, J.M., López-Ruiz, J., 1992. TRAZAS: a program for trace-element modeling of igneous processes. Computers & Geosciences 18 (6), 689-696.

Condie, K.C., 1993. Chemical composition and evolution of the upper continental crust: contrasting results from surface samples and shales. Chemical Geology 104, 1-37.