Zircon and rutile are common accessory minerals whose essential structural constituents, Zr, Ti, and Si can replace one another to a limited extent. Here we present the combined results of high pressure–temperature experiments and analyses of natural zircons and rutile crystals that reveal systematic changes with temperature in the uptake of Ti in zircon and Zr in rutile. Detailed calibrations of the temperature dependencies are presented as two geothermometers—Ti content of zircon and Zr content of rutile—that may find wide application in crustal petrology. Synthetic zircons were crystallized in the presence of rutile at 1–2 GPa and 1,025–1,450°C from both silicate melts and hydrothermal solutions, and the resulting crystals were analyzed for Ti by electron microprobe (EMP). To augment and extend the experimental results, zircons hosted by five natural rocks of well-constrained but diverse origin (0.7–3 GPa; 580–1,070°C) were analyzed for Ti, in most cases by ion microprobe (IMP). The combined experimental and natural results define a log-linear dependence of equilibrium Ti content (expressed in ppm by weight) upon reciprocal temperature:

 $$\log ({\text{Ti}}_{{{\text{zircon}}}}) = (6.01 \pm 0.03) - \frac{{5080 \pm 30}}{{T\;(\hbox{K})}}.$$
 In a strategy similar to that used for zircon, rutile crystals were grown in the presence of zircon and quartz (or hydrous silicic melt) at 1–1.4 GPa and 675–1,450°C and analyzed for Zr by EMP. The experimental results were complemented by EMP analyses of rutile grains from six natural rocks of diverse origin spanning 0.35–3 GPa and 470–1,070°C. The concentration of Zr (ppm by weight) in the synthetic and natural rutiles also varies in log-linear fashion with T
 −1:

 $$\log ({\text{Zr}}_{{{\text{rutile}}}}) = (7.36 \pm 0.10) - \frac{{4470 \pm 120}}{{T\;(\hbox{K})}}.$$
 The zircon and rutile calibrations are consistent with one another across both the synthetic and natural samples, and are relatively insensitive to changes in pressure, particularly in the case of Ti in zircon. Applied to natural zircons and rutiles of unknown provenance and/or growth conditions, the thermometers have the potential to return temperatures with an estimated uncertainty of ±10 ° or better in the case of zircon and ±20° or better in the case of rutile over most of the temperature range of interest (∼400–1,000°C). Estimates of relative temperature or changes in temperature (e.g., from zoning profiles in a single mineral grain) made with these thermometers are subject to analytical uncertainty only, which can be better than ±5° depending on Ti or Zr concentration (i.e., temperature), and also upon the analytical instrument (e.g., IMP or EMP) and operating conditions.

Crystallization thermometers for zircon and rutile

The Ti content of biotite can serve as a geothermometer for graphitic, peraluminous metapelites that contain ilmenite or rutile and have equilibrated at roughly 4–6 kbar. The relationship between Ti-content, temperature, and Mg/(Mg + Fe) value was calibrated empirically using an extensive natural biotite data set (529 samples) from western Maine and south-central Massachusetts in combination with the petrogenetic grid of Spear et al. (1999). The calculated Ti-saturation surface is curved such that for a given Mg/(Mg + Fe) value, Ti concentration increases as a function of temperature in a nonlinear fashion, and for a given temperature Ti concentrations decrease with an increase in Mg/(Mg + Fe). The fit to the Ti-saturation surface can be reformulated as the geothermometric expression: T = {[ln(Ti) − a − c ( X Mg)3]/ b }0.333, in which T is temperature in degrees Celsius, Ti is the number of atoms per formula unit (apfu) normalized on the basis of 22 O atoms, X Mg is Mg/(Mg + Fe), a = −2.3594, b = 4.6482 × 10−9 and c = −1.7283. The calibration range for this expression is X Mg = 0.275–1.000, Ti = 0.04–0.60 apfu, and T = 480–800 °C. Precision of the Ti-in-biotite geothermometer is estimated to be ±24 °C at the lower temperature range and improves to ±12 °C at higher temperatures. Application of the Ti-in-biotite geothermometer to ilmenite- or rutile-bearing, graphitic, peraluminous metapelites equilibrated at 3–6 kbar is generally consistent with independent temperature determinations, but with some deviations that represent local reequilibration. Consequently, the Ti systematics in biotite can also serve as the basis of a very sensitive indicator of chemical equilibrium, or lack thereof. Application of the geothermometer to metapelites not containing the requisite mineral assemblages can lead to minor-to-significant errors in estimated temperatures.

Biotite Ti-substitution mechanisms are controlled by several factors. Based on the biotite calibration data set, magnesian biotites ( X Mg > 0.65) incorporate Ti in accordance with the exchange vector TiAl2R−1Si−2, where R is the sum of the divalent cations Mg + Fe + Mn. This substitution mechanism is primarily a response to misfit of the octahedral and tetrahedral layers in magnesian biotites. Intermediate biotites ( X Mg <0.65), particularly at higher temperatures, exhibit enhanced Ti concentrations, most consistent with the Ti-deprotonation TiO2R−1(OH) −2 exchange vector. Dominance of Ti-deprotonation substitution is largely a function of reduction of H2O activity at higher metamorphic grades. Supplementary biotite data from metaluminous amphibolites and mafic granulites, metamorphosed isothermally with variable H2O activities, reveal that low-Al biotite incorporates significantly higher concentrations of Ti relative to peraluminous biotite as a result of a combination of the exchange vectors TiO2R−1(OH) −2 and RSiAl−2 substituting in roughly an 8:1 ratio.

/pdf/the-ti-saturation-surface-for-low-to-medium-pressure-1zo0yqbab3.pdf

The Ti-saturation surface for low-to-medium pressure metapelitic biotites: Implications for geothermometry and Ti-substitution mechanisms

Multiple regression analysis on an extended dataset has been performed to refine the relationship between temperature, pressure, composition and the Fe-Mg distribution between garnet and clinopyroxene. In addition to a significant dependence between the distribution coeYcient K D and XGrt and XGrt , as shown by the experimental data, the eVect of XGrt has also been incorporated using data from natural Mn-rich garnet-clinopyroxene pairs. Multiple regression of data (n=360) covering a large span in pressure, tem- perature and composition from 27 experimental datasets, combined with 49 natural high-Mn granulites from Ruby Range, Montana, USA, and Karnataka, India, yields the P-T -compositional relationship (r2=0.98):

/pdf/the-garnet-clinopyroxene-fe2-mg-geothermometer-an-updated-fpkyzcgdml.pdf

The garnet–clinopyroxene Fe2+–Mg geothermometer: an updated calibration

This textbook provides a basic understanding of the formative processes of igneous and metamorphic rock through quantitative applications of simple physical and chemical principles. The book encourages a deeper comprehension of the subject by explaining the petrologic principles rather than simply presenting the student with petrologic facts and terminology. Assuming knowledge of only introductory college-level courses in physics, chemistry, and calculus, it lucidly outlines mathematical derivations fully and at an elementary level, and is ideal for intermediate and advanced courses in igneous and metamorphic petrology. The end-of-chapter quantitative problem sets facilitate student learning by working through simple applications. They also introduce several widely-used thermodynamic software programs for calculating igneous and metamorphic phase equilibria and image analysis software. With over 350 illustrations, this revised edition contains valuable new material on the structure of the Earth's mantle and core, the properties and behaviour of magmas, recent results from satellite imaging, and more.

Principles of igneous and metamorphic petrology

Titanium is one of many trace elements to substitute for silicon in the mineral quartz. Here, we describe the temperature dependence of that substitution, in the form of a new geothermometer. To calibrate the “TitaniQ” thermometer, we synthesized quartz in the presence of rutile and either aqueous fluid or hydrous silicate melt, at temperatures ranging from 600 to 1,000°C, at 1.0 GPa. The Ti contents of quartz (in ppm by weight) from 13 experiments increase exponentially with reciprocal T as described by: 

$$ {\text{Log}}{\left( {X^{{{\text{qtz}}}}_{{{\text{Ti}}}} } \right)} = (5.69 \pm 0.02) - \frac{{(3765 \pm 24)}} {{T(K)}}. $$

Application of this thermometer is straightforward, typically requiring analysis of only one phase (quartz). This can be accomplished either by EPMA for crystallization temperatures above 600°C, or by SIMS for temperatures down to at least 400°. Resulting temperature estimates are very precise (usually better than ±5°C), potentially allowing detailed characterization of thermal histories within individual quartz grains. Although calibrated for quartz crystallized in the presence of rutile, the thermometer can also be applied to rutile-absent systems if TiO2 activity is constrained.

TitaniQ: a titanium-in-quartz geothermometer

Thermobarometry in granulites: pitfalls and new approaches

Numerical models of the progressive evolution of pelitic schists in the NCMnKFMASH system with the assemblage garnet + biotite + chlorite ± staurolite + plagioclase + muscovite + quartz + H2O are presented with the goal of predicting compositional changes in garnet and plagioclase along different P-T paths. The numerical models support several conclusions that should prove useful for interpreting the P-T paths of natural parageneses: (i) Garnet may grow along P-T vectors ranging from heating with decompression to cooling with compression. P-T paths deduced from garnet zoning that are inconsistent with these growth vectors are self-contradictory. (ii) There is a systematic relation between garnet and plagioclase composition and growth such that for most P-T paths, garnet growth requires plagioclase consumption. Furthermore, mass balance in a closed system requires that as plagioclase is consumed the remaining plagioclase becomes increasingly albitic. Inclusions of plagioclase in the core of garnet should be more anorthitic than those near the rim and zoned matrix plagioclase should have rims that are more albitic than the cores. Complex plagioclase textures may arise from the local variability of growth and precipitation kinetics. (iii) A decrease of Fe/(Fe + Mg) in a garnet zoning profile is a reliable indicator of increasing temperature for the assemblage modelled. However, there is no single reliable ΔP monitor and inferences about ΔP can only be made by considering plagioclase and garnet together. (iv) Consumption of garnet during the production of staurolite removes material from the outer shell of a garnet and may make recovery of peak metamorphic compositions and P-T conditions impossible. Low ‘peak’temperatures typically recorded by staurolite-bearing assemblages may reflect this phenomenon. (v) Diffusional homogenization of garnet affects the computed P-T path and results in a clockwise rotation of the computed P-T vector relative to the true P-T path.

A model for garnet and plagioclase growth in pelitic schists: implications for thermobarometry and P‐T path determinations

The effect of intragranular diffusion on chemical zoning in garnet and on P-T paths calculated from that zoning was evaluated using a numerical model of multicomponent diffusion in combination with simulations of garnet growth. Syn-and post-growth diffusion of Mg−Fe−Mn−Ca species in garnet was calculated for a model pelitic assemblage over a range of temperatures from 485 to 635°C. Compositions from zoned garnet, as modified by diffusion, hypothetical inclusions of plagioclase within garnet and matrix phases were used to reconstruct pressure-temperature (P-T) paths from isobaric and polybaric model histories. P-T path calculations, based on numerical simulations conducted over an input isobaric heating path that reached peak temperatures between 585 and 635°C, show that relaxation of garnet compositional gradients by diffusion can induce modest to appreciable curvature in the inferred paths. Retrieved paths also indicated somewhat smaller overall temperature changes relative to the actual temperature difference of the input path. The magnitude of these distortions is shown to depend upon the heating and cooling rate and garnet crystal size as well as the actual peak temperature condition. The effect of diffusion on path trajectories in simulations with thermal histories that also included cooling were comparable to heating-only models that reached peak temperatures approximately 15–30°C higher. Compositions of garnets with radii less than 1 mm, that reached actual peak temperatures of 605°C along temperature-time histories characteristic of regional metamorphism, experienced sufficient diffusional relaxation to introduce errors of hundreds of bars to in excess of one kilobar in path trajectories. Path distortions were significant at heating/cooling rates less than 10°C/Ma, but rapidly diminished for rates faster than this. In polybaric simulations diffusion effects were least noticeable when the actual pressure-temperature conditions changed in a clockwise sense (i.e., convex to higher P and higher T), but apprecciable modification was seen in path models that underwent counterclockwise changes in P and T. Reequilibration of garnet rim compositions occurred during cooling on all paths, and temperature maxima obtained from garnet-biotite geothermometry underestimated actual peak conditions by 40 to 70°C. Calculations suggest that P-T path trajectories calculated from garnets of at least 1 mm size, and that experienced actual thermal maxima below 585°C, are not likely to be distorted by diffusional effects during regional metamorphism. However, P-T path reconstructions based on garnet zonation with smaller grains or higher temperatures may lead to misinterpretation of crystallization history. The partitioning record of peak metamorphic temperatures may be destroyed by diffusional reequilibration of garnet rim compositions during cooling, seriously complicating the task of quantitatively estimating diffusion effects on path calculations.

Effects of diffusional modification of garnet growth zoning on P-T path calculations

Computer programs for petrologic P-T-t path calculations

Mountain, Skitchewaug and Big Staurolite nappes. Reactivation of A new, detailed tectonic model is presented for the Acadian orogenic this fabric during thrusting is recorded in some rocks of the Big belt of central New England (Vermont and New Hampshire) that Staurolite nappe by rotated garnets that grew during near-isothermal accounts for a wide range of petrological and structural observations. loading. Only the sillimanite isograd crosses the Fall Mountain– Three belts are considered: the Eastern Vermont, Merrimack, and Skitchewaug nappe boundary. Metamorphic breaks across the Skitintervening Bronson Hill belts. Specific observations in eastern chewaug–Big Staurolite nappe boundary, at the base of the Big Vermont that are accounted for in the model include the following. Staurolite nappe, and at the margin of the Keene and Alstead domes P–T paths are clockwise with maximum pressures near the Athens, require post-metamorphic thrusting when P–T conditions were in Chester, and Strafford domes of 8–11 kbar, but with maximum the greenschist facies. These observations can be explained by a pressures decreasing to 3–5 kbar at the boundary with the Bronson relatively simple model involving in-sequence thrusting from east to Hill belt. Differential exhumation of the Vermont domes relative to west commencing in central New Hampshire at 400–410 Ma. the rocks in easternmost Vermont is required by the recorded differences Preservation of the low-grade belt along the Vermont–New Hampin maximum pressure (5–6 kbar; 15–20 km) and the present-day shire border requires that crustal thickening in Vermont was not geographical separation (7–10 km). Specific observations in New caused by emplacement of New Hampshire nappes onto eastern Hampshire that are explained include the following. P–T paths in Vermont and that the nappes of western New Hampshire had time the Merrimack belt are counter-clockwise with maximum pressures to cool before final juxtaposition against the low-grade belt. Cooling of 4–5 kbar and are related to high regional heat flow and heat ages constrain this final juxtaposition to have occurred in the transfer by early Acadian plutons. P–T paths in the Bronson Hill Carboniferous, suggesting that the Acadian was a prolonged event belt are intimately associated with structural position. An early spanning as much as 100 Myr. contact metamorphism is evidenced in the Skitchewaug and Fall Mountain nappes near contacts with the early Acadian Bethlehem gneiss (>400–410 Ma). Peak metamorphic temperature rises upwards in the nappe sequence (an inverted metamorphic sequence)

http://ees2.geo.rpi.edu/MetaPetaRen/Publications/PDFpapers/CNETectonics_2002.pdf

Frank P. Florence

Papers

Thermobarometry in granulites: pitfalls and new approaches

A model for garnet and plagioclase growth in pelitic schists: implications for thermobarometry and P‐T path determinations

Effects of diffusional modification of garnet growth zoning on P-T path calculations

Computer programs for petrologic P-T-t path calculations

Metamorphic, Thermal, and Tectonic Evolution of Central New England