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Cell["\<\
******************************************************************************\
**********************************************
File for modeling Fe-Mg diffusion in olivine using finite differences \
implicit method (e.g. Crank, 197?)
This program is associated with the manuscript Costa, F., Dohmen, R., \
Chakraborty, S. (2008) MSA
short course and the uses the finite differences metod and equations \
explained in Appendix I.

Below the variables are 'cleared' to avoid memory effects from previous \
calculations.
    **************************************************************************\
****************************************************\
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******************************************************************************\
************************
Temperature (T) in celsius,  Pressure (PRES) in bars, oxygen fugacity (fO2) \
in bars, forsterite content (Fo) in mol %.
 The value of Fo found below is the lowest found in the profile is used for \
stability check.

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the electron microprobe traverse and the (a,b,c) axes 
of the crystal. fO2 shown with respect to the Log NNO oxygen buffer of \
Huebner and Sato (197?) 
******************************************************************************\
***********************\
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 "****************************************************************************\
******************\n    Diffusion coefficient data for Fe-Mg (DFo) from \
Dohmen and Chakraborty (2007a), with corrections of Dohmen and Chakraborty \
(2007b).\n    Using diffusion parameters for fO2> ",
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axis in ",
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thus we have created a new set of diffusion \n    coefficients without the \
dependence and this will be directly incorporated in the diffusion loop.\n    \
DFox= diffusion coefficient parallel to the electron microprobe traverse.\n   \
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******************************************************************************\
****************"
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 "****************************************************************************\
******************\nHere we need to choose a time step (in seconds) = \
\[Delta]t , and a distance step in \[Mu]m = \[Delta]x. The total lenght of \
the profile\nwill then be \[Delta]x * ttgrid (= total number of grispoints), \
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******************************************************************************\
******************"
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******************************************************************************\
***********************************************
Importing and plotting data electron microprobe data (Fomin= minimum Fo; \
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datafo = natural data. Below the data has been already imported (you can use \
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******************************************************************************\
************************************************\
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******************************************************************************\
***********************************************
Choosing the total number of gridpoints (ttgrid) which will be the total \
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Cell["\<\
******************************************************************************\
*********************************************
Choosing the initial distribution (in this case homogeneous and equal to \
Foini) of Fo (= cFo) and seeting the
diffusion coefficients for the initial distribution (= DIFFo)
******************************************************************************\
**********************************************\
\>", "Text",
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Cell["\<\
******************************************************************************\
***********************************************
Diffusion algorithm

The first Do loop is for the time and executes the number of iterations \
(ttiter) that we have chosen.
It is typically better to set 'ttiter' to a moderate number and then hit \
shift + return a few times rather
than having a very large 'ttiter' value and only doing shift + return once. \
One needs to keep track
of how many times one hits shift + return, since total number of iterations \
will be this number
times 'ttiter'.
 
The first equality sets the variable bFo which stores the concentration of Fo \
after every time step. 
The two equalities that follow are the boundary conditions; For this case the \
left boundary is  closed
as it would be for the case of a profile that has reached the core, and the \
right represents the rim
of the crystal and is constant and would be a rim in equilibrium with an \
infinite liquid.


The second Do loop calculates the diffusion coefficient. This needs to be \
done at every time step
since DFo depends on the Fo concentration which is changing with time.

The third Do loop calculates the profile and contains the finite element \
formulation for the
diffusion coefficient which depends on concentration (see Short course \
Appendix I notes).

Plot shows a comparison of natural data and diffusion model.
******************************************************************************\
***********************************************\
\>", "Text",
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******************************************************************************\
*********************************************
The total time in seconds associated with each time one hits shift + return \
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