User:Tamjwh/sandbox P-T-t path

I(This sandbox is the Wikipedia draft page) The Pressure-Temperature-time path (P-T-t path) is a record of the complete set of pressure-temperature (P-T) conditions that a rock experienced throughout its metamorphic history.

Metamorphism is a dynamic process which involves the mineralogical and textural changes of the pre-existing rocks (protoliths) under different pressures and temperatures conditions in solid state. The changes in pressures and temperatures with time experienced by the metamorphic rocks are often investigated by petrological P-T reconstruction methods, radiometric dating techniques and thermodynamic modeling. As the variations of pressures and temperatures in a rock are considered to be directly related to the tectonic processes, investigating the P-T-t paths would enhance the understanding of the tectonic evolutionary history at the time of the metamorphic events.

For instance, the P-T diagram on the right is an illustration of a typical clockwise P-T-t path, which is commonly found in subduction zones or continental collision settings. Upon changing pressure and temperature, different metamorphic minerals such as garnet and cordierite are formed, but they do not reach complete phase equilibrium when discovered on the surface. Therefore, investigating these minerals in the rock can obtain information about the metamorphic and tectonic history. From 1910 Ma to 1840 Ma, the rock experienced an increase in pressure and temperature, which is believed to be related to burial and heating due to crustal thickening. After that, the rock went through a great decrease in pressure around 1840 Ma, which is likely attributed to an uplift event such as thrusting of the buried rock. Finally, the continuous drop in pressure and temperature in 1800 Ma is resulted from further erosion and exhumation.

Metamorphism
Metamorphism is the alteration in mineral assemblages and geologic textures of the pre-existing rock (protolith) under solid state in temperatures and pressures that are different from the time when the protolith was formed. According to Le Chatelier's Principle, where there is a change in the condition in the environment (e.g. temperature, pressure, concentration of chemical compounds etc.), the original compounds would adjust itself until the effect of change is invalidated. The alteration of the compound under different P-T conditions is related to the Gibbs free energy. The Gibbs free energy represents the stability of the mineral under a specific environment, and minerals tend to lower its Gibbs free energy to obtain the greatest stability. For example, calcium carbonate (CaCO3) occurs naturally as calcite or aragonite. Under atmospheric environment, the Gibbs free energy of calcite is lower than aragonite, therefore CaCO3 tends to exist in the form of calcite. In high pressure conditions, the Gibbs free energy of aragonite is lower than calcite, therefore CaCO3 occurs as aragonite. If the Gibbs free energy of both minerals are equal at a specific environment, both are stable under the condition. In metamorphic regions, since the original minerals in the protolith are unstable under the changing P-T conditions, the minerals undergo phase alteration and eventually form new stable metamorphic minerals and textures at their phase equilibrium. Depending on the location, the chemistry of protolith and types of tectonic activities, the rock would result in different mineral assemblages and textures. In addition, geologists discovered that some mineral assemblages could form only under a certain range of P-T conditions, which has brought about the development of metamorphic classification systems regarding the pressure and temperature variations.

Metamorphic facies
Metamorphic facies is a classification system first introduced by Pentti Eskola in 1920 to classify a particular metamorphic mineral assemblages that are stable under a range of P-T conditions. Before the development of plate tectonics in the 1960s, geologists studied metamorphic rocks as phase equilibrium of heterogeneous systems. The objective at that time was to develop a system to classify different mineral assemblages into appropriate P-T ranges. The domain of the mineral assemblages is expressed in a temperature vs pressure graph. Each facies represents a mineral assemblage that is in equilibrium at a certain range of P-T condition. Before the mid-1970s, geologists utilized the metamorphic facies classification to investigate metamorphic rocks and determined their P-T characteristics. However, little was known about the evolutionary processes of these P-T conditions and how metamorphic rocks reach the surface at that time.

Metamorphic path
The relation between metamorphism and tectonic setting was not well investigated until 1974, which Oxburgh and Turcotte suggested that the origin of the metamorphic belt is a result of the thermal effects brought by continental collision. The idea was picked up by England and Richardson and further research was done in 1977, and the P-T-t path concept was fully developed by Richardson and Thompson in 1984.

In normal cases, the temperature experienced by a rock follows the geothermal gradient of 25 °C per km of depth in the shallow crust at steady state. However, the thickness of crust would vary upon subduction or continental collision, which as a result would disturb the thermodynamic equilibrium of the steady state geothermal gradient. The thermal modeling from Richardson and Thompson (1984) reveals that in every case of thermal relaxation after the tectonic event, there is a large portion of heat equilibrium before being significantly influenced by erosion, i.e. the rate of metamorphism is found to be much slower than duration of the thermal event. This infers that the rock is a poor heat conductor, which the maximum temperature experienced by the rock as well as its temperature change are insensitive to erosion rate. Therefore both the evidence of the maximum pressures and temperatures experienced by the buried layers can be imprinted in the underlying metamorphic rocks. This finding also implies that although most minerals reached phase equilibrium, some are not in equilibrium at the time of discovery. Hence, the buried depth as well as plausible tectonic settings can also be deduced. Altogether with various dating techniques, geologists can even determine the time scale of the tectonic events in respect to the metamorphic events. It should also be noted that if the metamorphic rock is in perfect phase equilibrium, no information about the P-T path can be determined.

Since, extensive investigations on the P-T-t paths of various major tectonic settings have been carried out over the world.

Metamorphic cycle
P-T-t paths often reflect various stages of the metamorphic cycle. A metamorphic cycle implies the series of processes that a rock experienced from burial to uplift and erosion. The P-T conditions experienced by a rock throughout these processes can be classified into three main stages according to temperature changes:
 * 1) Prograde (Pre-peak) metamorphism: the process when the rock is buried and heated in environments such as basins or subduction zones. Devolatilization reactions (release of gases e.g. CO2, H2O) are common.
 * 2) Peak metamorphism: the maximum temperature reached throughout the metamorphic history.
 * 3) Retrograde (Post-peak) metamorphism: the metamorphism occurred during uplift and cooling of the rock.

Petrological P-T reconsturction
Petrological reconstruction is a backward approach which utilizes mineral compositions of rocks samples to deduce the possible P-T conditions. Common techniques include optical microscopy, geothermobarometry and geochronology.

Optical microscopy
In qualitative reconsturction of P-T conditions, geologists examine thin sections under polarized light microscope to determine the sequence of formation of the minerals. This is due to incomplete replacement of the host mineral under changing P-T conditions, hence minerals formed at various P-T environments can be found in the same rock specimen. As different minerals have different optical characteristics and textures, it allows accurate determination of the mineral composition in metamorphic rocks.

Mineral inclusions (poikiloblastic texture) are often regarded to be formed at the pre-peak stage of metamorphism. For example, in thin section examination, biotite is included in a garnet grain. Since biotite forms at a lower P-T condition compared to garnet, therefore it is considered that the biotite crystal formed at an earlier time.

Minerals that formed at the peak stage have a porphyroblastic-matrix texture, which large euhedral crystals inside a fine groundmass are found. The matrix minerals of the porphyroblasts are also formed at this stage.

At the post-peak stage, minerals formed at lower P-T conditions in retrograde metamorphism commonly occur as a corona (reaction rim) surrounding the higher grade mineral. Finger-like symplectitic textures are also common. Some retrograde minerals also cross-cut the minerals formed at the peak stage.

It should be noted that not all rock samples exhibit all the P-T conditions they experienced throughout geological evolution. This is attributed to the complexity of the geological processes, which the samples may have undergone complicated thermodynamic histories, or of inappropriate mineral compositions to produce minerals that record their metamorphic events.

Geothermobarometry
Geothermobarometry is a quantitative measurement of the P-T conditions, which is widely used in analyzing the P-T conditions of metamorphic and intrusive igneous rocks. Geothermobarometry is a combination of geothermometry and geobarometry. Geothermometry is the measurement of temperature changes of the crust by using equilibrium of minerals that are insensitive to pressure variations; while geobarometry uses equilibrium of minerals that are of little dependence on temperature change to accurately determine the pressure changes.

A scanning electron microscope (SEM) or electron microprobe is usually used to measure the distribution of components in the minerals in geothermobarometry, which allows the precise determination of the chemical equilibrium within the rock. Its underlying principle is by utilizing the equilibrium constants of mineral assemblages in a rock to infer the metamorphic P-T conditions.

Geothermometers are usually represented by exchange reactions, which are sensitive to temperature but with little effect under changing pressure, such as exchange of Fe2+ and Mg2+ between garnet-biotite reaction :

$$Fe_3Al_2Si_3O_{12}+KMg_3AlSi_3O_{10}(OH)_2\rightleftharpoons Mg_3Al_2Si_3O_{12}+KFe_3AlSi_3O_{10}(OH)_2$$

Geobarometers are typically occurred as net-transfer reactions, which are sensitive to pressure but have little change with temperature, such as garnet-plagioclase-muscovite-biotite reaction that involves a significant volume reduction upon high pressure :

$$Fe_3Al_2Si_3O_{12}+Ca_3Al_2Si_3O_{12}+KAl_3Si_3O_{10}(OH)2\rightleftharpoons 3CaAl_2Si_2O_8+KFe_3AlSi_3O_{10}(OH)_2$$

Since mineral assemblages at equilibrium are dependent on pressures and temperatures, by measuring the composition of the coexisting minerals, together with using suitable activity models, the P-T conditions experienced by the rock can be determined. After one equilibrium constant is found, a line would be plotted on the P-T diagram. As different equilibrium constants of mineral assemblages would occur as lines with different slopes in the P-T diagram, therefore, by finding the intersection of at least two lines in the P-T diagram, the P-T condition of the specimen can be obtained.

Despite the usefulness of geothermobarometry, special attention should be paid to whether the mineral assemblages represent an equilibrium, any occurrence of retrograde equilibrium in the rock, and appropriateness of calibration of the results.

Garnet growth zoning
Garnet growth zoning is a special type of geothermobarometry that focuses on the composition variations in garnet. Zoning is a texture in solid-solution minerals which forms concentric rings from core to rim upon changing P-T conditions. In a changing environment, minerals would be unstable and alter itself to reduce its Gibbs free energy, however sometimes the mineral core has not reached equilibrium upon the environmental change and zoning occurs. Zoning is also found in other minerals such as plagioclase and fluorite. In practice, garnet is commonly used in study of metamorphic rocks due to its refractory nature. In past studies, garnet is found to be a mineral that is stable under a wide range of P-T conditions, meanwhile chemically displays responses (e.g. ions exchange) to the P-T variations throughout its metamorphic history without reaching complete equilibrium. The non-equilibriated garnet formed previously are often zoned by younger garnet. Therefore, many past P-T characteristics are preserved in the zoned areas. Electron microprobes are used to measure the composition of the zoned garnets.

However, melting within garnet sometimes occurs or diffusion rate is too rapid at high temperature, some garnet zones are merged and cannot provide sufficient information about the complete metamorphic history of the rocks.

Gibbs method
The Gibbs method formalism is an application of differential thermodynamic equations based on Duhem's Theorem to aid the P-T analysis of mineral zoning and textural changes from reactions. It attempts to simulate the garnet growth zoning numerically by solving a set of differential equations involving variables pressure (P), temperature (T), chemical potential (μ), mineral composition (X). Modal abundance of mineral phases (M) was later added as an extensive variable in the Gibbs method with mass balance added as a constraint. The aim of this analysis is to search for the absolute P-T condition during different zonal growth and matches the observed composition of zones in the sample. The computer program  GIBBS  is commonly used for calculation of the equations.

Geochronology
To figure out the age of the metamorphic events, geochronological techniques are used. It utilizes the idea of radioactive decay of long-lived unstable isotopes in minerals to search for the age of events.

In the study of metamorphic petrology, U-Th-Pb dating of monazite (monazite geochronology) is an effective method to determine the P-T history. Monazite is a phosphate mineral containing light rare-earth-elements (LREE). that occurs in a wide range of rock types. In metamorphic rocks, it usually occurs as inclusions in the porphyroblasts. Its high closure temperature (>1000°C), variable composition, zonal growth pattern upon changing P-T conditions and robustness under a large temperature range help in the record of geological history in metamorphic rocks. The dating method is usually done by using an electron microprobe to observe the compositional zones of monazite, then analyzing the U-Th-Pb age of each zone to reconstruct the time of the relevant P-T conditions.

Zircon is another suitable mineral for dating metamorphic rocks, however it is less reactive than monazite under metamorphic events, and performs better in dating igneous rocks.

Thermal modeling
Unlike using traditional petrological investigation methods (e.g. optical microscopy, geothermobarometry) to inversely infer the metamorphic events from rock samples, thermal modeling is a forward method that attempts to work on the geological evolution model of rocks. This approach applies numerical modeling techniques based on heat transfer equations, different plate tectonics models and metamorphic reactions to simulate the possible metamorphic events. An advantage of thermal modeling is that it provides a holistic estimation of the duration of different stages of metamorphism, which is somehow difficult to completely extract from geochronological methods.

The model simulation involves solving the continuous time-dependent differential heat transfer equation by its approximate discrete finite difference form using computer programs such as  FORTRAN  :

Differential form of heat transfer equation:

$$\operatorname{d}\!T/\operatorname{d}\!t = \kappa{\partial^2T\over\partial^2z} - v_z{\partial{T}\over\partial z}+{\operatorname{A}\!\over\operatorname{\rho}C\!}$$

Finite difference form of heat transfer equation:

$$\Delta\!T/\Delta\!t = \kappa{\Delta^2T\over\Delta^2z} - v_z{\Delta{T}\over\Delta z}+{\operatorname{A}\!\over\operatorname{\rho}C\!}$$

After the equations are set, a grid of nodes is generated for calculation of each point. Boundary conditions are input into the equations to calculate the temperature at boundaries. Results are compared with petrological experimental results for validation.

By combining petrological methods and thermal modeling techniques, the understanding of metamorphic processes due to tectonic events is facilitated. Petrological results provide realistic variables to be plugged into a model simulation, while numerical modeling techniques often place constraints on the possible tectonic environments. The two methods complement the limitations of each other, and formulate a comprehensive evolutionary history of the metamorphic and tectonic events.

Path trajectories and tectonic implications
After the realization of the relation between metamorphic P-T-t paths and tectonics, geolgists started to use metamorphic rocks to investigate various geological regions. From investigations of P-T-t paths since the 1980s, it is found that P-T-t paths for metamorphic provinces can generally be classified into two types: clockwise P-T-t paths and anticlockwise P-T-t paths. The two types of P-T-t paths are related to different tectonic settings.

Clockwise P-T-t paths
Metamorphic rocks with clockwise P-T-t paths, especially for near-isothermal decompressional P-T trajectories, are usually formed under subduction zones or collision-related tectonic events.

Clockwise P-T-t path normally consists of three parts: Ideally, the rock reaches its peak metamorphism at the peak temperature and pressure at similar time and near-isothermal decompression P-T-t path is observed at its stage 1 metamorphism. However, in reality, the path does not always perfectly exhibit near-isothermal decompression pattern and is sometimes found to be reaching the peak pressure prior to the peak temperature. This is due to the insensitivity of rocks to thermal events. Therefore, when the rock is experiencing the peak pressure, it has not reached the steady state of the geothermal gradient immediately after the crustal thickening event. While during uplifting and exhumation, due to the poor conductivity of rock upon external thermal changes, the rock was continuously heating up and gradually reached its highest temperature. In addition, recent studies based on mechanical analysis reveals that peak pressure recorded in clockwise P-T paths does not necessarily represent the maximum depth of burial, but can also represent a change in the tectonic pattern.
 * 1) Initial heating and compression until arriving a high pressure-low temperature (HPLT) peak, suggesting an early phase of progressing burial due to crustal thickening without having much heating when reaching peak metamorphism. (Prograde metamorphism until peak)
 * 2) Near-isothermal decompression after the peak, which involves uplift and exhumation of the compressed rock in the orogenic belt or forearc. (Stage 1 retrograde metamorphism)
 * 3) Further decompression and cooling at a slow rate, implying further erosion after the tectonic event. (Stage 2 retrograde metamorphism)

Examples of clockwise P-T-t paths of metamorphic rocks can be found at:
 * Trans-North China orogen, North China Craton
 * Bohemian Massif, Austria
 * Southern Brittany, France
 * Northern Gallatin Range, South-western Montana, USA
 * Southern Prince Charles Mountains, East Antarctica

Anticlockwise P-T-t paths
For metamorphic rocks displaying anticlockwise P-T-t paths patterns, especially for near-isobaric cooling P-T trajectories, are commonly associated with intrusions and magmatic underplating at magmatic arc regions, hotspots or rifts.

Anticlockwise P-T-t path also consists of two parts: Examples of anticlokwise P-T-t paths of metamorphic rocks can be found at:
 * 1) Initial heating and compression until reaching a low pressure-high temperature (LPHT) peak, implying an event of heating and slightly thickened. This reflects the action of magma intrusion and erupted as sills, resulting in a slight increase in pressure but a great increase in temperature. (Prograde metamorphism until peak)
 * 2) Near-isobaric cooling after the peak, which the rock stays at the same position, and the magma cools. (Retrograde metamorphism)
 * Arunta Block, Central Australia
 * Andes, USA
 * Yinshan Block, North China Craton
 * Coastal Cordillera, South-Central Chile

Paired metamorphic belts
Paired metamorphic belts displaying two contrasting mineral assemblages sets, a high pressure-low temperature (HPLT), and low pressure-high temperature (LPHT) belt, are often found along convergent plate boundaries. HPLT metamorphic belt is located along subduction zones, and commonly associated with a clockwise P-T-t path. The HPLT condition is resulted from crustal thickening due to convergence meanwhile without being heated by magma. While LPHT metamorphic belt is observed at volcanic arcs or back-arc basins, which is attributed to magma intrusion derived from partial melting of the subducting slab, and the melt rises to the crust. This area is associated with an anticlockwise P-T-t path. The above suggests that both clockwise and anticlockwise metamorphic P-T-t paths can be found at convergent plate boundaries.

The P-T-t paths provide in-depth investigations and implications of the mechanisms in the lithosphere, and further support the plate tectonic theory.

Plume tectonics
Apart from acting as a supporting evidence for the plate tectonic theory, P-T-t paths also play an important role in the development of plume tectonics.

Inspired by the hot spots in the Hawaiian Islands, the plume tectonic theory is hypothesized by John Tuzon Wilson in the 1960s, around the same period as plate tectonic theory, to account for the intraplate volcanism in the Hawaiian Islands which cannot be explained by plate tectonics. It is believed that mantle plumes are generated from the core and rise to the surface. The plume tectonic theory suggested that mantle doming is a geodynamic process forming a small part of the lithosphere, and plate tectonic theory is not the only process that forms the earth. Since, the plume tectonic theory has incorporated into the plate tectonic theory, and is considered as the main driving force of plates ,and they also account for a small part of the lithosphere.

However, with evidence from the study of the Archean cratonic blocks in the North China Craton in the 2000s, the plume tectonics are considered to be the dominant process forming the Archean crust. It is found that anticlockwise P-T paths with near-isobaric cooling after the peak are normally in the Archean rocks, suggesting an intrusion origin. The lack of a paired metamorphic belt as well as a paired clockwise P-T path in the Archean rocks eliminates the possibility of the volcanic arc formation. Evidenced together by a large doming structure, widespread of komatiites and bimodal volcanism, it is proposed that plume tectonics is the major crust-forming process in the Archean. This has led to further research on the beginning of plate tectonics and numerical modeling of the earth Earth condition.

Deformation
Deformation is the change in size or shape of the object under changes in forces and temperatures. Apart from inferring the tectonic environment, P-T-t paths can also be applied to deformation mechanics. Heat does not only transfer directly from mantle to crust by large scale burial and uplift, it also transfer in terms of small scale advective heat flow such as during thrusting and folding of metamorphic rocks. For example, during the formation of fault-bend-fold, the rocks in the lower segment (footwall) is heated due to contact with the hotter upper thrust sheet (hanging wall), while the upper thrust sheet is cooling because of losing heat in a downward direction. Thus, the lower segment and the upper thrust sheet are undergoing prograde metamorphism and retrograde metamorphism respectively.

P-T-t paths can be used to estimate possible structures in the field. Nevertheless, special attention should be taken to the effect of multiple thrusting such as duplexes, where the initial lower plate in an earlier thrust would become the upper plate in a latter thrusting event. Depending on the location of the rock, a variety of complex P-T trajectories can be found, which may make interpretation of a terrain challenging.

Future development
Metamorphic P-T-t paths have been widely recognized as a useful tool in determining the metamorphic history and tectonic evolution of an area. Potential future research directions for P-T-t paths will be likely developed in the following areas:
 * Refining dating methods and techniques
 * Refining geodynamic models
 * Spatial permeability of rocks upon metamorphism and deformation
 * Origin of metamorphic mineral inclusions
 * Unified theory of lithosphere evolution and formation
 * P-T-t changes of rocks under shock metamorphism
 * Thermal evolution of meteorites and their parent asteroids