.. _example-predominance-phreeplot-04: Fe-H\ :sub:`2`\ O Predominance ============================== One chemistry, eight diagrams. The iron-water system is the textbook Eh-pH diagram, and it is used here not for the chemistry -- which is the same in every figure on this page -- but as a fixed subject against which to vary the method. Two questions get answered. **How** should the plane be computed: every node, or only where the answer changes? And **how** should the redox axis be imposed and reported: as oxygen fugacity, as pe, as Eh? The three are equivalent in principle and are not equivalent in practice, which is the useful part. :ref:`example-predominance-01` makes the first point on algebraic functions. Here each node is a PHREEQC run, so it costs something. The system ---------- .. raw:: html :file: study_04 - Fe-H2O System.html 10 mmol/l ferric iron in 0.1 mol/l NaCl, with ferrihydrite allowed to precipitate. pH runs 2 to 12 and log fO2 from -90 to 0, on a 45 by 45 lattice. ``Fix_H+`` imposes pH as in the other PhreePlot examples. Grid against tracking --------------------- .. figure:: FugacityDiagramGrid_op_ex1_cp_.svg :alt: Predominance diagram of iron computed on the full grid :align: center The full lattice: 2025 PHREEQC simulations, one per node, no interpolation. Six aqueous iron species and the ferrihydrite field, with the water stability limits marked. This is the reference the other seven figures are judged against. .. figure:: FugacityDiagramHT_op_ex3_cp_.svg :alt: The same diagram computed by a tracking study :align: center The same diagram from a tracking study: a coarse pass, then refinement along the boundaries, then interpolation between the computed points. 1283 simulations -- about a third fewer -- and the boundaries fall in the same places. .. figure:: DatacomputedinPredomTrackStudy.svg :alt: The cells the tracking study actually simulated, small near boundaries and large inside fields :align: center What the tracking study actually did. Each simulated point owns the region nearest to it, drawn here in Grid mode rather than smoothed, so the cells are visible: small and dense along every boundary, large in the interiors where nothing changes. Where the two meet, some cells are thin wedges. This is the honest picture of a tracked diagram. The smooth version above is the same data with the boundaries interpolated, and comparing the two is how you judge whether the refinement went far enough. .. figure:: PredominanceFugacityZoom_op_ex4_cp_.svg :alt: A zoom into the acid oxidising corner of the diagram :align: center A zoom into pH 2 to 4, log fO2 -30 to 0 -- recomputed on that range, not magnified. Fe+3, FeOH+2 and Fe2(OH)2+4 share a corner that is a few pixels wide in the full diagram, and the hydrolysis sequence only becomes legible at this scale. Predominance diagrams hide fine structure at their edges almost by construction; the answer is to re-run on the interesting range. Three ways to say "redox" ------------------------- The remaining four figures carry the same chemistry up a different vertical axis. .. figure:: Predominancepe_op_ex6_1_cp_.svg :alt: The diagram computed by fixing pe directly, with gaps where PHREEQC failed to converge :align: center Computed by fixing **pe** directly, with a second dummy phase: .. code-block:: text Fix_pe e- = e- log_k 0.0 on a grid of pe -13 to 18. It works, and not everywhere: some combinations fail to converge and leave gaps in the diagram. Forcing an electron activity is numerically harder than forcing a gas fugacity, because there is no physical reservoir behind it. .. figure:: Predominancepefromfugacity_op_ex6_2_cp_.svg :alt: The same pe axis, computed from the oxygen fugacity run :align: center The same pe axis, from the **fugacity** runs instead -- pe is reported by PHREEQC in its output, so it can simply be plotted. No gaps. The two figures together are the practical advice: impose the condition that converges and report the quantity you want. Fixing the axis you intend to plot is the obvious approach and the worse one. .. figure:: PredominanceEhfrompe_op_ex7_1_cp_.svg :alt: The diagram against Eh, from the fixed-pe runs :align: center Against **Eh** in volts, from the fixed-pe runs. Eh and pe are the same quantity in different units, related by a factor that depends on temperature, so this is a relabelled axis rather than a new calculation -- and it inherits the convergence gaps. .. figure:: PredominanceEhfromfugacity_op_ex7_2_cp_.svg :alt: The diagram against Eh, from the fugacity runs :align: center And Eh from the fugacity runs. This is the figure to use: the familiar Eh-pH diagram of the iron system, computed the way that converges. What the eight say together --------------------------- * Track rather than grid when each node is a simulation, and look at the cells before trusting the smoothing. * Re-run on a narrower range rather than magnifying. * Impose oxygen fugacity; report pe or Eh. All three axes describe the same redox state, but only one of them is well-behaved as a constraint. Source ------ * Kinniburgh, D. G. and Cooper, D. M. (2011). *PhreePlot: Creating graphical output with PHREEQC.* These figures follow examples 1, 3, 4, 6 and 7 of the PhreePlot manual, including the ``Fix_H+`` and ``Fix_pe`` constructions. See `the PhreePlot website `_. * The thermodynamic data is ``wateq4f.dat``, distributed with PHREEQC (Parkhurst and Appelo, 2013).