Practical 4. The interpretation of PT grids

In this practical we will look at the
interpretation of PT grids, focussing on the diagrams presented in the
Dymoke & Sandiford (1992) paper in* Contributions to Mineralogy and
Petrology. *These diagrams were constructed to help understand the
distribution of metamorphic assemblages in the eastern Mount Lofty Ranges,
but they are relevant to a number of other Australian metamorphic terrains
(Martin has used have them to understand metamorphic assemblages in the
northern Arunta Inlier). Because these grids are relatively simple they
provide a useful introduction to the interpretation of PT grids.

4.1. The PT grid

Basics of PT grids

The basic PT grid adapted from Dymoke & Sandiford (1992), as shown below, involves 9 reaction lines, separting 7 distinct fields and intersecting at 3 points.

The details of the reaction relationships in the circled area is shown below:

(Note that this diagram was calculated using the 1991
thermodynamic database of Holland & Powell, with calculations
performed using the program *Thermocalc*. Because our knowledge of
the thermodynamic data for natural minerals is constantly improving, more
recent studies have modified this basic diagram, and extended it to more
complex systems involving additional phases such as chloritoid ).

This grid is appropriate to the KFMASH (6 component) system involving 9 phases , 4 of which are treated as being in excess (that is, as saturating phases). The phases are

andalusite, staurolite, garnet, cordierite,
chlorite*, muscovite, biotite, quartz *and* vapour* (with
saturating phases in italics).

The system is therefore an n+3 system, where n stands for the number of phases. As we will see below, a 6-component, 9-phase system (which in petrological terms is quite simple) involves the possibility of a great many reactions and intersections. Depicting the full system on PT grid makes for very complicated diagrams and thus it is often more useful to deal with a reduced or pseudo-system in which some of the phases are considered as saturating phases. For each saturating phase we effectively reduce the dimensionality of the system by 1-degree in terms of both the effective number of component s and phases. Thus by using 4 saturating phases in the above PT-grid (bt, mu, q and v) , we have effectively reduced our system to 2-component system with five phases (note that the n+3 factor remains!). In the following exercises we will be mostly restricted to dealing with this pseudo (2-component, 5-phase) system, but will occasionally reference the full (6-component, 9-phase) system - so you will have to wary!

Note that the saturating phases are by definition involved in each reaction shown on the PT grid (but are not listed so as not to clutter the reaction labelling).

Several important aspects should be noted from this PT grid.

- Firstly, the
__basic operation__involved in making a PT grid involves a mapping from P-T-G space. This is because PT grids are designed to show the mineral assemblages that minimises Gibbs energy at any P-T co-ordinate. Since the Gibbs energy of individual phases (and therefore also of rock systems) is a function of T and P, we should expect different mineral assemblages to be stable at different PT conditions. PT grids explicitly depict the limits to the stability fields of individual mineral associations by marking the limiting reactions. Normally, the mineral associations in the fields beneath the reaction lines must be inferred by examining the way compatibility relations change across the reactions that bound a particular stability field. - Generally, a PT grid consists of univariant lines (that is fields which involve n+1 phases) which bound divariant (or trivariant) fields (that is, fields with n phases or less). The intersection of two or more univariant curves involving (n+2) phases (and no more) is termed an invariant point (note some apparent intersections appear to involve more than (n+2) phases and have no petrogenetic significance - see below).
- By convention, univariant reactions can be labelled by enclosing the phases not involved in the reaction in round brackets ( ). For example, the reaction involving cd + st + and (ie not involving chl and gt cn be designated by (chl, gt). Similarly, invariant points can be marked by the absent phase in square brackets [ ]. thus the garnet-absent invariant point, [gt], is an invariant point which involves the intersection of reactions which do not involve gt, ie (gt).

Q.4.1. Draw schematic AFM diagrams for each of the distinct AFM stability fields.

Q.4.2. Write out in full all reactions in the PT grid, explicitly including both biotite and muscovite. Label the reactions with the absent phases marked in round brackets ().

Stability and metastability

Just as we think about stable and metastable assemblages, we can think about stable and metastable reactions and invariant points. Only stable univariant reactions and invariant points are depicted on a PT grid.

In order to work out which invariant points are metastable we need to understand how many possible invariant assemblages there are in this n_3 system. This question is equivalent to asking how many different combinations of 8 (or n+2) phases can we make out of the total of 9 (or n+1) phases. The answer is obviously 9, and considering that four of these will not involve the saturating phases (ie, [bt], [mu], [q], and [v]), we are left with 5 possible invariant to consider. Since three stable invariant points are shown on the diagram (namely, [gt], [and] and [chl]), the remaining two ([cd] and [st]) must be metastable.

In a similar vein, to work out which univariant assemblages are metastable we need to understand how many possible univariant reactions there are. This question is equivalent to asking how many different combinations of 7 (or n+1) phases can we make out of the total of 9 (or n+1) phases. Considering all phases (including the saturating phases, we have 9 invariant assemblages . By leaving out one of the involved phases, we can write 8 univariant reactions for each invariant point. This may lead you to think that we could write 9x8 =72 distinct univariant reactions in total. However, the situation is slightly more complex because not all univariant reactions associated with a particular invariant point are unique to that univariant point. In order to understand this point, consider the [gt] absent invariant point. With reference to [gt], the (chl) absent univariant (involving, and, st, cd as well as bt, mu, q + v) extends to the [chl] invariant point. In general each univariant will be common to two of the possible (but not necessarily stable) invariant points. In total, then, the number of possible univariant curves is 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 = 36. Considering bt, mu, q and v to be saturating phases, the number of relevant reactions is 4 + 3 + 2 + 1 + 0 = 10 (hopefully this example also illustrates the benefits of describing reactions and invariant points by the absent phases).

Q.4.3 List all 10 possible univariant reactions relevant to this system (you can do this by marking the reactions by the absent phase ), Note which reactions are metastable.

Q.4.4 Of all possible conceivable mineral associations in the pseudo-system, are there any which are not allowed!

A more complicated grid

The PT grid shown in the previses section is obviously restricted because it only deals with a relatively few phases. A simple extension of this system involves adding the other two polymorphs, kyanite and sillimanite , as shown in the next figure. This extension increases the complexity by making an (n+5) system.

Q.4.5 How many reactions are possible in the expanded, n+5, pseudo-system.

Note that a number of new invariant points (labelled by the small circle) occur at the intersections of most of the FMASH and Al2SiO5-polymorph reactions ( note that these have not been labelled by the absent phase method). An important points to note about his extended grid that not all apparent intersections on a PT grid represent true invariant points. For example, the intersection of (cd,and) with the kyanite -> andalusite reaction is not an invariant point.

Q.4.6. why is this so?

4.1 T-X diagrams and PT-pseudosections

The next important step in really understanding PT grids is to see how the information contained on T-X (or P-X) diagrams might map onto such grids. PT grids which show such inofrmation ar called pseudo-sections. To begin with we need to recap about the relationship between compatibility diagrams and T-X (or P-X) diagrams.

We begin by considering the gt+chl field appropriate to low-T side of the PT grids described above we can see that there are a number of possible different assemblages depending on where we are with respect to bulk composition, Pressure and temperature. For example, at low temperuters , we may have an AFM diagram like the one on th eleft below, which shows the gt-chl-bt tie triangle shiifted to the left, As we move to higher tempertures (to the centre diagram the tie traingle moves to the right and consequntly stabilising garnet in increasingly more magnesian compositions.

Obvioulsy the rock with biulk composition B undegoes considerable reaction as it is heated, without criossing a single univariant reatcion. these types of ‘continuous reactions’ caused by the sliding of divariant compatibility fields across the bulk coimpositiona s T (and/or P are changed incremently are known as divariant reactions (or continuous reactions) and are best illustrated using T-X (or P-X) diagrams as shwon in the figure below.

This type of information can also be mapped from the T-X plane to the PT- plane as shown below, with the proviso that we can represent the disrtbution of divariant and trivariant fields for one bulk composition only.

The diagrams below show calculated pseudo-sections from Dymoke & Sandiford for two differnt bulk compositions.