.. _example-phreeqc-manual-10:

10 - Solid Solution
===================

Aragonite and strontianite -- CaCO₃ and SrCO₃ -- are not two separate
minerals that happen to be present together. They form a **solid solution**:
one crystal structure in which calcium and strontium substitute for each
other in any proportion.

That changes the thermodynamics. A pure phase has a fixed solubility
product; a solid solution's depends on its composition, and its composition
depends on the water it grew from, which in turn depends on what it has taken
out. The example works through the consequences.


The calculation
---------------

.. raw:: html
   :file: study_10 - Solid Solution.html

SrCO₃ is added progressively to a system containing the aragonite-
strontianite solid solution, and four quantities are followed.


The results
-----------

.. figure:: PlotA.svg
   :alt: Mole fractions of CaCO3 and SrCO3 in the solid against SrCO3 added
   :align: center

   **A -- the composition of the solid.** Mole fractions of the two
   components as strontium is added. This is what distinguishes a solid
   solution from a mixture of phases: there is one solid and its composition
   moves continuously.

.. figure:: PlotB.svg
   :alt: Activities of Ca and Sr in solution against SrCO3 added
   :align: center

   **B -- the water in equilibrium with it.** Calcium and strontium in
   solution. The ratio here is not the ratio in the solid: the solid
   preferentially takes one of the two, and the fractionation between them is
   the distribution coefficient.

   This is the quantity that makes solid solutions worth modelling. It is why
   the strontium content of a carbonate records the water it formed from, and
   it is the basis of a good deal of palaeo-environmental reconstruction.

.. figure:: PlotC.svg
   :alt: Moles of CaCO3 and SrCO3 in the solid against SrCO3 added
   :align: center

   **C -- the amounts.** Moles of each component in the solid, rather than
   fractions.

.. figure:: PlotD.svg
   :alt: Moles of the two solids where the solid solution unmixes into two phases
   :align: center

   **D -- two solids.** Over part of the range the system does not stay as
   one solid: the solid solution **unmixes** into two solids of different
   composition, and both are present together.

   That is a miscibility gap, and it is the same phenomenon as oil and water
   refusing to mix. Where the two end members are sufficiently unlike -- and
   Ca²⁺ and Sr²⁺ differ enough in size -- there is a range of compositions
   that is unstable, and a solid in that range separates into two.

   A model treating these as two independent pure phases would never produce
   this, and would also get the composition in plot A wrong everywhere else.


What it shows
-------------

That solid solutions need their own thermodynamics, and that the behaviour
that follows -- fractionation between solid and water, and unmixing -- is not
reproducible by treating the components separately.


Source
------

* Parkhurst, D. L. and Appelo, C. A. J. (2013). *Description of input and
  examples for PHREEQC version 3.* U.S. Geological Survey Techniques and
  Methods, book 6, chapter A43. This is Example 10 of that manual.
* Glynn, P. D. and Reardon, E. J. (1990). *Solid-solution aqueous-solution
  equilibria: thermodynamic theory and representation.* American Journal of
  Science 290, 164-201.