# P-T-t Paths

## What is a P-T-t path?

Metamorphism is a dynamic process, involving changes in temperature ± pressure through time. The pressure (P) - temperature (T) - time (t) path of a metamorphic rock is the set of all P-T conditions experienced by a rock during its metamorphic history (Figure 1).

Figure 1. A common pressure-temperature path for regional metamorphism. The rate of prograde metamorphism (heating) and rate of retrograde metamorphism (cooling) may not be the same. The duration of the path from start (onset of metamorphism) to finish (exposure of the rock at the Earth's surface) will vary from rock to rock depending on the tectonic history

The trajectory and shape of the P-T path, the rates of metamorphic processes, and the duration of metamorphism are a function of the source of heat and the mechanisms of burial and unroofing (if pressure change is involved). Therefore, the shape of the path, combined with time information, provides information about the driving forces of metamorphism.

In many cases, P-T information may be known, but not t (time) information. The next few sections involve discussion of aspects of P-T path trajectories without specific reference to time variables (e.g. rate, duration).

## What are some common P-T paths?

P-T paths are commonly described as 'clockwise' or 'anticlockwise' (a.k.a. 'counterclockwise') (Figure 2a). It is important to note that these descriptions specifically refer to the shapes of paths drawn on a diagram with a horizontal temperature axis (temperature increasing from left to right) and a vertical pressure axis (pressure increasing from bottom to top).

Paths can be clockwise or anticlockwise, and can also vary in terms of (1) how different the prograde and retrograde segments of the path are – very similar or very different (Figure 2b), and (2) how different the maximum pressure and maximum temperature are from each other (Figure 2c).

Figure 2. Common P-T paths, including (a) Clockwise versus counterclockwise paths, (b) Paths with similar vs different prograde and retrograde segments, and (c) Paths with coincident maximum P and T conditions vs paths with very different maximum P and T conditions. Note that the T maximum is known as the 'peak' of metamorphism.

## How are P-T paths determined?

For some rocks, the only part of the P-T path recorded in the mineral assemblage and texture of the rock is the 'peak' of metamorphism – the conditions of the thermal maximum (i.e., the maximum temperature and the pressure at the maximum temperature). If the rock had a sedimentary or volcanic protolith, you can infer that the rock started at the surface, reached peak conditions at some temperature and depth in the Earth, and returned to the surface (where the rock was collected). At the peak of metamorphism, the mineral assemblage presumably equilibrated, and no (or little) further reaction took place as the rock cooled and decompressed en route to the Earth's surface.

Some rocks may record more of their P-T paths. If a rock contains a partial record of its P-T path, this is both good and bad. This is good because we want as much P-T path information as possible, so as to be able to interpret the thermal/tectonic processes and history as well as possible. This is bad because the mineralogical and textural evidence for P-T path segments other than the conditions of the peak of metamorphism represent disequilibrium. In most cases, however, the evidence for disequilibrium can be very useful because it can be used to reconstruct P-T path segments.

A few common methods for inferring P-T path segments are:

1. Mineral inclusions
2. Some minerals contain inclusions of other minerals. For example, garnets commonly contain inclusions of minerals that were present in the rock matrix as the garnet grew, but that were not completely eliminated by metamorphic reactions during progressive metamorphism. The growing garnets surrounded these relict minerals as the garnets grew, and the relict minerals are preserved as mineralogical evidence of an earlier stage in the metamorphic history of the rock.

Figure 3. Left: Photomicrograph (plane light) of kyanite inclusions in garnet; field of view = 2 mm. Right: Photomicrograph (crossed polars) of sillimanite in the matrix; field of view = 4 mm.

Some inclusions don't contain a lot of information about P-T conditions because the minerals are stable over such a wide range of conditions (for example: quartz). Other mineral inclusions are very useful for inferring P-T conditions and path segments, especially if these minerals no longer exist in the matrix of the rock (that is, outside the garnet). In Figure 3, kyanite inclusions occur in garnet in a rock that has only sillimanite in the matrix, indicating that the rock was previously in the kyanite stability field but that P-T conditions changed. When the matrix of the rock (including the garnet rim) equilibrated, the rock was in the silliminate stability field (Fig. 4).

Figure 4. P-T diagram showing stability fields of the Al2SiO5 polymorphs: andalusite, kyanite, and sillimanite (after Holdaway, 1971). Two possible P-T paths are shown to illustrate different ways that kyanite can be replaced by sillimanite: one path (a) involves a decrease in pressure (decompression); the other (b) involves an increase in temperature (prograde metamorphism).

Even though it may not be possible to determine the trajectory of the P-T path from inclusions alone, inclusions may be used with other chemical and textural information to better define the path. In addition, the composition of inclusions may be used in thermobarometry to determine P-T conditions along the path, provided the inclusions have not chemically reacted with their host mineral (e.g., Whitney, 1991).

3. Element zoning
4. Metamorphic (and igneous) minerals may change composition in response to changing chemical and physical conditions, such as changes in pressure-temperature conditions, deformation variables, or chemical factors (e.g., presence of fluids). The chemical response of a mineral to these changes may be recorded in minerals that have crystal chemical and structural characteristics that allow compositions acquired early in the mineral's growth history to be preserved during later stages of growth at different conditions. Crystals that have different regions with different compositions are zoned .

A very common zoning pattern involves a difference in composition of a mineral's center (core) compared to its rim, and concentric rings of different compositions arranged between the core and the rim (Fig. 5). Minerals that typically show this type of zoning in the major or trace elements are garnet, plagioclase, zircon, and tourmaline (Fig. 5). Of these, garnet and plagioclase are relevant to studies of metamorphic P-T paths, and zircon is relevant to determination of the timing of petrologic events.

Figure 5. Common zoned minerals. (a) False color X-ray map showing Mn distribution in a garnet from Iran (Sepahi et al., 2003). The garnet core contains more Mn than the garnet rim (or the matrix); this is typical growth zoning. The garnet is 1.3 mm in diameter; (b) Photomicrograph (crossed polarized light) showing zoning in plagioclase in a metamorphosed igneous rock; oscillatory zoning is common in igneous plagioclase, but metamorphic plagioclase may also be zoned in the anorthite (Ca) and albite (Na) components; field of view = 2 mm; (c) Photomicrograph (plane polarized light) of a zoned tourmaline crystal in a kyanite schist; field of view = 2 mm; (d) Cathodoluminescence image of isotopically zoned zircon from the Nigde Massif, Turkey, with the U-Pb age of the core and rim labeled in millions of years (Whitney et al., 2003).

Using zoning information to reconstruct the part of the P-T path experienced by the zoned mineral is not simple, but a few general aspects of the relationship of zoning to P-T path may easily be inferred:
(a) Garnets with Mn-rich cores and Mn-poorer rims record growth zoning that represents the change from the lower-T conditions at which the garnet core grew to the higher-T conditions at which the garnet rim grew (i.e., prograde metamorphism involving increasing temperature and pressure). Mn is preferentially partitioned into garnet relative to most other common minerals, so Mn is sequestered in early-formed garnet, depleting the local environment of the growing garnet in Mn.
(b) Minerals that show major element growth zoning probably did not experience very high metamorphic temperatures. At high temperature (> 700 C) and sufficient duration, zoning may be homogenized as intracrystalline diffusion becomes more effective at eliminating compositional variation. An unzoned mineral that is typically zoned at low-medium metamorphic grades has either experienced high temperature conditions or was never zoned (owing to a simple reaction history at limited P-T or to growth entirely at high-T).

5. Reaction textures
6. Some metamorphic rocks contain evidence for incomplete reactions or other textural evidence for part of the P-T path. A simple example is the partial replacement of andalusite by sillimanite (Fig. 6a) by the polymorphic transformation of andalusite to sillimanite. Textural evidence may also be useful in cases where the reactants have been completely consumed if the shape of one or more reactants are preserved; for example, pseudomorphs (Figs. 6b-d).
An example of a more complex reaction texture involves the formation of coronas , which consist of one or more shells (rims, moats) of a mineral or minerals around a central (reactant) phase (Fig. 6e). In many cases, coronas also involve the fine-scale intergrowth of minerals in a texture known as symplectite (Figs. 6e-f).

Figure 6. Images of reaction textures. (a) Photomicrograph (plane light) showing the partial replacement of andalusite by sillimanite in a schist from Iran. Note: The crystallization sequence (sillimanite after andalusite) can't be inferred only from this photo; (b) Photomicrograph (plane light) showing the complete replacement of kyanite by sillimanite in a sample of gneiss from the Thor-Odin dome, British Columbia. The former presence of kyanite is known because some pseudomorphs (not shown) contain relict kyanite. Without these relics, and based only on the tabular shape of the pseudomorph, it would be difficult to infer whether the original mineral was kyanite or andalusite; (c) Crossed polar view of (b) showing the randomly oriented sillimanite in the pseudomorph; (d) Photomicrograph (plane light) showing a partial pseudomorph of chlorite after garnet from a retrograded eclogite, Turkey. Garnet relics are present, but the former presence of garnet is clear also from the shape of the pseudomorph; (e) Photomicrograph (plane light) showing a corona texture from a Thor-Odin dome gneiss. The central Al2SiO5 phase (sillimanite after kyanite) is rimmed by an inner shell of spinel + cordierite symplectite and an outer shell of cordierit; (f) Backscattered electron image of spinel (brightest phase) + cordierite (darkest gray) + anorthite (medium gray) from a Thor-Odin symplectite.

## How are P-T-t paths interpreted?

An important part of using P-T paths or P-T-t paths to understand metamorphic and tectonic processes is to relate the P-T conditions, path shape, and (if age information is available) duration and rate of P-T path segments to the driving forces of metamorphism.

P-T path shape by itself does not provide a unique interpretation of tectonic process or metamorphic driving forces. For example, clockwise paths can form in continental collision belts of subduction zones. Similarly, some subduction zone rocks record clockwise paths and some record counterclockwise paths. However, the integration of P-T path characteristics, time/rate information, structural data, and other petrologic information can provide significant information about metamorphic and tectonic processes. Therefore, although subduction zone rocks can follow various paths during subduction and exhumation, determining the specific path that a particular exhumed subduction zone rock followed is important for understanding subduction dynamics.

## Integrating deformation into P-T-t histories: P-T-t-d paths

The idealized view of P-T paths is that mineral assemblages equilibrate at every stage of the path from the onset of metamorphism to the peak of metamorphism, at which the final assemblage is locked in. This view ignores kinetic factors related to the energetics of nucleation and growth of minerals, although these factors may be important for some metamorphic phases and reactions. For example, the presence of coexisting andalusite and sillimanite (Fig. 6a) in a rock that equilibrated at P-T conditions corresponding to the stability field of sillimanite illustrates that the sluggish kinetics of the andalusite-to-sillimanite transformation allowed andalusite to persist metastably outside its stability field.

It is important to recognize the influence of deformation on metamorphic reactions, and the extent to which deformation (strain energy) may assist reactions. It is possible that two rocks of the same bulk composition that follow the same P-T path but that have different deformation histories (e.g., one is pervasively deformed and the other is not, perhaps because strain is localized in weaker rocks nearby) will contain different mineral assemblages. The deformed rock may contain the predicted equilibrium assemblage for the P-T conditions attained by the rock, whereas the undeformed or less deformed rock may contain more metastable phases. P-T conditions and paths should therefore be considered in their structural context, and, if possible, a P-T-t-d path (Pressure-Temperature-time-deformation) constructed.

## Examples

• Metapelites Lab (Acrobat (PDF) 160kB Mar29 07) - This one week exercise, provided by Dave Pattison at the University of Calgary, includes problems sets involving petrogenetic grids, AFM diagrams, bulk compositions, mineral assemblages and isograds, as well as the use of program Gibbs.
• Phase Diagram Projections and Phase Diagram Sections Lab (Microsoft Word 40kB Mar29 07) - This two week exercise, provided by Dave Pattison at the University of Calgary, includes problems sets involving phase diagram sections using Gibbs (for demonstration of principles) and Perple_X.