Titanium in biotite from metapelitic rocks: Temperature effects, crystal-chemical controls, and petrologic applications

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1 American Mineralogist, Volume 87, pages , 2002 Titanium in biotite from metapelitic rocks: Temperature effects, crystal-chemical controls, and petrologic applications DARRELL J. HENRY 1, * AND CHARLES V. GUIDOTTI 2 1 Department of Geology and Geophysics, Louisiana State University, Baton Rouge, Louisiana 70803, U.S.A. 2 Department of Geological Sciences, University of Maine, Orono, Maine 04469, U.S.A. ABSTRACT An extensive natural biotite data set from western Maine constrains the temperature and crystalchemical controls on the saturation Ti levels in biotites from metapelites. The geologically and petrologically well-characterized metamorphic terrain associated with the M3 metamorphism of the Acadian Orogeny of western Maine is ideal for this approach in that metamorphism occurred at roughly isobaric conditions of 3.3 kbar, and chemical equilibrium was closely approached. The data set from these metapelites exhibits systematic variations in Ti contents over a continuum of metamorphic grades (garnet through sillimanite-k-feldspar zones), mineral assemblages, and bulk compositional ranges. Samples were selected so that competing substitutions are restricted to those in metapelites with quartz, aluminous phases (chlorite, staurolite, or sillimanite), Ti phases (ilmenite or rutile), and graphite. Due to crystal-chemical factors, in any given metamorphic zone, an inverse linear relationship exists between Ti and Mg contents. Decreasing octahedral Ti and increasing tetrahedral Si in Mg-rich biotite helps alleviate size disparity between octahedral and tetrahedral sheets. For a biotite with a given Mg content, Ti most dramatically increases above staurolite zone conditions. Our constrained data set allows us to calculate a Ti saturation surface for natural biotite as a function of temperature and Mg content at 3.3 kbar. The Ti saturation surface can be used to establish several important metamorphic features in similar metamorphic settings. These include a general approach to equilibrium, local and/or subtle departures from equilibrium due to minor alteration to chlorite, and relative and absolute geothermometry based on Ti in biotite inclusions in refractory minerals and in matrix biotite. INTRODUCTION Biotite is an important mineral in metamorphic rocks over a wide range of bulk compositions and metamorphic grades. One of the more interesting biotite substituents is Ti. This quadrivalent cation is preferentially partitioned into biotite relative to other typical metapelitic silicate minerals, and substitutes for octahedrally coordinated divalent or trivalent cations (e.g., Guidotti 1984). The common petrographic observation that reddish-brown coloration in biotite is more intense in highgrade biotite relative to lower-grade biotite in similar lithologies is generally attributed to the greater amount of Ti solid solution at higher temperature (e.g., Faye 1968; Guidotti 1984). In fact, the degree to which Ti substitutes in biotite is more than a simple functional relationship with temperature, but involves relatively complex interactions among temperature, pressure, biotite crystal chemistry, and coexisting mineral assemblages (e.g., Guidotti et al. 1977, 1988; Dymek 1983; Labotka 1983; Guidotti 1984; Tracy and Robinson 1988). Experimental investigations have helped quantify several of the parameters that influence Ti concentrations in biotite. Earlier experimental work has demonstrated that Ti solubility in phlogopite increases with temperature and decreases with * glhenr@unix1.sncc.lsu.edu pressure (Forbes and Flower 1974; Robert 1976; Arima and Edgar 1981; Tronnes et al. 1985). For instance, Robert (1976) showed that Ti solubility is relatively low, 0.07 Ti atoms per formula unit (apfu; based on a 22 oxygen atom normalization) at 600 C and 1 kbar, and increases significantly to 0.2 Ti apfu at 800 C, 1 kbar, and to 0.7 Ti apfu at 1000 C, 1 kbar. In turn, with an increase in pressure to 7 kbar, the Ti concentration in phlogopite drops to 0.2 Ti apfu at 1000 C (Robert 1976). Furthermore, limited experimental data on Fe-Mg biotite indicate that Ti contents generally increase as Fe and/or f O 2 increase (Arima and Edgar 1981; Abrecht and Hewitt 1988). Patiño Douce and Johnston (1991) examined Ti concentrations in biotite from a series of partial-melting experiments on natural peraluminous metapelitic starting materials at C and 7 13 kbar. Based on these experiments, Patiño Douce (1993) noted that Ti increases with temperature in a non-linear fashion over these conditions, and he calculated that for Fe-Mg aluminous biotite (X Mg = 0.5) a pressure increase from 5 to 15 kbar results in a decrease of Ti by 0.24 apfu at 900 C and by 0.1 apfu at 800 C. Despite such advances, difficulty persists in extrapolating these experimentally derived relations to the thermal and baric conditions and bulk compositions found over the general range of natural metapelitic rocks. An additional complication is that the exact nature of Ti substitution mechanism(s) is uncertain. A number of crystallo X/02/ $

2 376 HENRY AND GUIDOTTI: TITANIUM IN BIOTITE graphic, experimental, and theoretical studies have delineated the most likely substitutions (e.g., Robert 1976; Forbes and Flower 1974; Dymek 1983; Tronnes et al. 1985; Abrecht and Hewitt 1988; Ahlin 1988; Burt 1988; Brigatti et al. 1991; and many others). Table 1 lists several of the Ti substitution mechanisms for biotite that seem to be the most plausible for metapelitic rocks. Octahedral vacancies ( ) and Al are common participants in these potential substitution mechanisms such that factors that influence the amount of these constituents will also likely influence the incorporation of Ti in biotite. In addition to Ti R 2, octahedral vacancies and Al can also be introduced via the dioctahedral muscovite exchange component ( Al 2 R 3 ). However, the bulk of the octahedral Al is probably introduced via the Tschermaks substitution (Al 2 R 1 Si 1 ) to form an eastonite component in biotite (e.g., Dymek 1983). Once muscovite is no longer present in the sillimanite-k-feldspar zone, there is no longer a phase that saturates the biotite with respect to the Al 2 R 3 exchange vector, and its influence on the Ti R 2 vector will likely change. Labotka (1983) and Guidotti and Dyar (1991) found evidence for this phenomenon in their biotite data sets. An effective way to determine the magnitude of the factors that control Ti concentrations in metamorphic biotite is to evaluate biotite compositions in metapelitic rocks in geologically and petrologically well-characterized metamorphic terrains. The metamorphic terrain associated with the Acadian Orogeny of western Maine serves as an ideal setting for this approach (Guidotti 1989). The extensive natural biotite data set from metapelitic schists of western Maine exhibits systematic variations in Ti contents over a continuum of metamorphic grade and mineral chemistry (Guidotti et al. 1988). This data set contains biotite compositions from metapelitic rocks ranging from garnet through sillimanite-k-feldspar zones at roughly isobaric conditions of 3.3 kbar (Guidotti 1989). Consequently, this paper explores the interrelationships primarily among Ti concentrations in biotite, biotite mineral chemistry, mineral assemblage, and temperature from the well-characterized and thoroughly equilibrated metapelitic rocks from western Maine. In essence, it examines the Ti saturation surface for natural biotite as a function of temperature and Mg content at 3.3 kbar. GEOLOGIC AND PETROLOGIC FRAMEWORK TABLE 1. Possible substitution schemes for incorporation of Ti into biotite Site substitution Exchange vector 2 VI R 2+ = VI Ti + VI * Ti R 2 2 VI Al = Ti + VI R 2+ TiRAl 2 VI R IV Si = VI Ti + 2 IV Al TiAl 2 R 1 Si 2 VI R OH 1 = VI Ti + 2O 2 TiO 2 R 1 OH 2 * VI R 2+ represents the sum of the divalent cations in the octahedral site and VI represents the octahedral site vacancies. Geologic setting The biotite-bearing metapelitic samples are mainly from metamorphosed Ordovician-Devonian strata of western Maine that were extensively metamorphosed in the Siluro-Devonian (Osberg et al. 1985; Guidotti 1989). The Siluro-Devonian Acadian metamorphism involves regionally developed recrystallization with grades ranging from sub-greenschist to upperamphibolite facies (Guidotti 1989). The polymetamorphic history of the metapelitic samples under consideration includes initial greenschist facies regional metamorphism (M1) and regional/contact metamorphic overprints (M2 and M3) that are largely postkinematic (Table 2). In terms of this biotite study, the most important feature is that the M3 metamorphism is the dominant overprint and that the minerals in the metapelites are thoroughly equilibrated under isobaric conditions of 3.3 kbar. The samples under consideration are primarily from the Rangeley, Oquossoc, Rumford, and Old Speck Mountain 15' quadrangles of western Maine. The isograd patterns of the metapelitic schists roughly follow the outlines of the intruding pluton borders (Fig. 1). This isograd pattern, in conjunction with both systematic compositional variation of solid-solution phases as a function of grade and the systematic element partitioning among the silicate and oxide minerals, suggests chemical equilibrium is likely attained during the M3 metamorphic overprint (e.g., Cheney 1975; Henry 1981; Guidotti et al. 1988, 1991). For example, the Mg- Fe partitioning between coexisting biotite and chlorite from 95 staurolite zone metapelites have a well-constrained partition coefficient of 1.15 ± 0.03 (Fig. 2). Based on the isograd systematics of the area, Guidotti et al. (1988) and Guidotti and Dyar (1991) defined 4 major zones related to discontinuous AFM reactions, i.e., garnet, staurolite, sillimanite and sillimanite-k-feldspar zones (Table 3). In turn, several of these major zones are further subdivided into lower, middle, and upper portions of the major zone based on progressive changes in the composition of solid-solution phases (muscovite, biotite, and/or chlorite) from specific limiting assemblages (e.g., Guidotti et al. 1988, 1991). This approach has yielded 9 zones that can be used to estimate temperatures of individual samples. An additional garnet-cordierite zone is also considered from complementary literature data of Tracy and Robinson (1988). The temperature of each sample is estimated by assuming that the mapped isograds are essentially isotherms. Temperatures are assigned to each of the isograds by assuming a pressure of 3.3 kbar and determining the intersecting temperature using the Spear and Cheney (1989) petrogenetic grid TABLE 2. Metamorphic history of western Maine Regional deformation and greenschist facies metamorphism* M1 Dehydration of Ordovician to Devonian basinal sediments under chlorite zone conditions (slightly >400 Ma) D1 Passive flow folding producing NE-trending tight folds and slaty cleavage Regional/contact metamorphism M2 Related to ~400 Ma granitoid plutons low pressure (~3 kbar) with andalusite-staurolite-biotite assemblages metamorphism outlasts the D2 deformation D2 Late slip cleavage M3 Related to intrusion of ~380 Ma sill-like granitoid plutons Higher P (~3.3 kbar) sillimanite-bearing assemblages Spatial relationship between isograds and plutons Post-kinematic metamorphic event Dominant reequilibration event * Metamorphic history after Guidotti (1970a, 1970b, 1974, 1985, 1989), Conatore (1974), Cheney (1975), Henry (1981), Holdaway et al. (1982, 1988), Guidotti et al. (1983), and deyoreo et al. (1989).

3 HENRY AND GUIDOTTI: TITANIUM IN BIOTITE 377 FIGURE 1. Distribution of metamorphic zones in the Rangeley-Oquossoc area, Maine. The Mooselookmeguntic granitoid pluton is shown in darkest gray. Solid hachured curves represent metamorphic isograds. Broken hachured curves represent contours of metamorphic grade based on continuous reactions (Guidotti et al. 1988). FIGURE 2. Mg-Fe partitioning between coexisting chlorite and biotite in 95 staurolite zone metapelite samples. The systematic array of data implies an approach to equilibrium. The range of Mg/Fe is influenced by sulfide-silicate reactions (Henry 1981). for metapelites (Table 3). In turn, a temperature for each sample is determined by its position relative to the mapped isograds and interpolating the temperature between isograd reaction temperatures. Biotite data set The basic western Maine biotite data set (>450 analyses) was chosen to maximize the internal consistency of the data set. The series of rocks were collected as an extension of field and mineral chemistry investigations of the metapelites from western Maine (Guidotti 1970a, 1970b, 1974, 1984; Bussa 1973; Conatore 1974; Cheney 1975; Guidotti et al. 1975, 1977, 1988, 1991; Cheney and Guidotti 1979; Lonker 1975; Henry 1981). Most of the biotite analyses were done at the University of Wisconsin-Madison using common techniques and standards. Additional biotite analyses at the University of Massachusetts and Louisiana State University were done only after extensive interlaboratory calibrations. The extensive natural biotite data set from metapelitic schists of western Maine, ranging from garnet through sillimanite-kfeldspar zones, were selected so that competing substitutions are limited through careful choice of mineral assemblages coexisting with biotite. They were restricted to pelitic schists that contain quartz, aluminous phases (such as chlorite, staurolite, or sillimanite), Ti phases (ilmenite or rutile), and graphite. In essence, this maximizes Si, Al, and Ti at saturation levels in biotite for a given temperature and limits bulk-compositional effects for these elements. The occurrence of graphite in the metapelitic schists restricts the metapelites to low and fairly constant f and biotites to low amounts of O 2 Fe3+ (~12% of Fe total ) (Guidotti and Dyar 1991). These relative Fe 3+ amounts are essentially constant throughout metamorphic grades. Muscovite is present in all samples below the sillimanite-k-feldspar zone

4 378 HENRY AND GUIDOTTI: TITANIUM IN BIOTITE TABLE 3. Temperature constraints for biotite-bearing samples from western Maine Zone no. Zone name Isograd reaction Temperature ( C)* 1 Lower garnet (500) 2 Middle garnet (520) 3 Upper garnet (540) Grt + Chl = St + Bt Lower staurolite (560) 5 Upper staurolite (580) 6 Transition (590) St + Chl = Bt + Sil Lower sillimanite (610) St = Grt + Bt + Sil Upper sillimanite (650) Ms = Kfs + Sil Sillimanite-K-feldspar (690) * Temperatures are based on locations of isograd reactions at 3.3 kbar calibrated against Spear and Cheney (1989) petrogenetic grid. The temperatures in parentheses represent the estimated temperature in the middle of each zone. Abbreviations: Bt = biotite, Chl = chlorite, Grt = garnet, Kfs = K-feldspar, Ms = muscovite, Sil = sillimanite and St = staurolite. so that the biotites should also exhibit maximal dioctahedral character. The biotites have a wide range of Mg/(Mg + Fe) due to sulfide-silicate interactions (Henry 1981; Guidotti et al. 1988). For simplicity, and because of the relatively constant and low amounts of Fe 3+, biotite was normalized on the basis of 22 oxygen atoms. To extend the compositional and temperature ranges of the biotite data, additional data sets from the literature were considered. Ferry (1981) examined graphitic sulfide-rich schists from south-central Maine that equilibrated under similar baric conditions to western Maine. Several of the Mg-rich biotites were reported for peraluminous mineral assemblages similar to those of the western Maine samples, but for biotite- and garnet-zone conditions ( C). Two additional biotite data sets were considered for higher-grade graphitic, peraluminous metapelitic rocks that also exhibited some sulfide-silicate reactions, thereby extending the range of temperature and Mg/ Fe ratios available for biotite (Tracy 1978; Tracy and Robinson 1988). These latter data equilibrated at somewhat higher pressure (6 kbar) and range from upper-sillimanite zone to sillimanite-k-feldspar zone to garnet-cordierite zone. Using the petrogenetic grid approach to estimate temperatures for these rocks, the higher pressure results in higher temperature intersections with the isograd reactions, i.e., C. Because experiments demonstrate that increase in pressure decreases the Ti concentrations in biotite, these latter 6 kbar data likely slightly underestimate the values of Ti for the 3.3 kbar Ti-saturation surface. RESULTS For purposes of comparison, the biotite data are broken into the major metamorphic zones (Figs. 3a e). Garnet zone data are relatively clustered, with the exception of the complementary Mg-rich biotite data of Ferry (1981) (Fig. 3a). The maximal Ti contents are slightly above 0.2 Ti apfu for X Mg values of Staurolite zone biotites are also clustered with a similar maximal Ti of 0.2 Ti apfu at X Mg = 0.4 (Fig 3b). However, there is a more notable dispersion of the data to lower Ti values as the biotite becomes more magnesian. The tight pattern of this large data set is an additional indication of the approach to chemical equilibrium. At higher grades, transition zone and above, Ti concentrations dramatically increase as a general function of grade for a given biotite X Mg (Figs. 3c, 3d, and 3e). This is particularly true for biotites from the upper-sillimanite zone and above (Figs. 3d and 3e). Even the high-grade Mg-rich biotites show an enhanced Ti concentration relative to lower-grade Mg-rich biotites. Within a given metamorphic zone there is a systematic inverse linear relationship between Ti and Mg contents of biotite (Figs. 3a 3e). A similar linear inverse relationship exists between IV Al and Mg contents in biotite (e.g., Guidotti et al. 1988). These relationships are likely controlled by crystal-chemical factors such that substitution of the relatively small Ti 4+ cations in the octahedral layer and Si 4+ cations in the tetrahedral layer compensates for any octahedral-tetrahedral layer misfit that results from substitution of larger Fe 2+ cations for smaller Mg 2+ cations in the octahedral layer (Guidotti et al. 1977). These data can be used to generate an isobaric Ti-saturation surface for natural peraluminous biotites at roughly 3.3 kbar. The data, expressed in terms of T C (x) vs. X Mg (y) vs. Ti (apfu) (z), was fit with over 500 candidate surface-fit equations of various types using the TableCurve3D software. All of the data points were given equal weighting. The candidate surface-fit equations were sorted by the F-statistic criterion (ratio of the mean-square regression to the mean-square error) because the top equations typically represent the best possible models for describing the data. This type of sort generally brings simpler equations nearer the top of the list. Using this criterion, the optimal surface-fit equation is considered to be ln z = a + bx 3 + cy 3. (1) The coefficients for this surface-fit equation and several statistical parameters for the fit are given in Table 4. In general, the fit to the data is relatively good with a correlation coefficient (r 2 ) of Because of the nonuniform distribution of the data, improvements are possible with an expansion of the range of data. Nonetheless, the functional morphology of the 3.3 kilobar Ti saturation surface is attained. Figure 4 gives two perspective three-dimensional views of the surface and illustrates the relationship among T C, X Mg, and Ti in the biotite. Figure 5 is a projection of the Ti isopleths on a T C vs. X Mg [=Mg/(Mg + Fe)] diagram for the biotite data set. The Ti isopleths will only be valid below Ti = 0.5 apfu. Clearly, higher Ti contents are found in the high temperature biotites, but increasing Mg content also strongly diminishes the Ti saturation limit. Under the appropriate assemblage, baric, and equilibrium con- TABLE 4. Summary of surface-fit equation coefficients and statistical parameters* for the full biotite data set using the equation ln z = a + bx 3 + cy 3 Coefficient Value Standard error 95% confidence limits a b e e e e 9 c * This surface-fit equation has a coefficient of determination (r 2 ) of for these data, where r 2 = 1 (SSE/SSM). SSE is the sum of the squares due to error and SSM is the sum of the squares about the mean.

5 HENRY AND GUIDOTTI: TITANIUM IN BIOTITE 379 FIGURE 3. Relationship between Ti and Mg/(Mg + Fe) ratios for the major metamorphic zones. (a) Garnet zone data with additional Mg-rich biotite data (shaded circles) from Ferry (1981), (b) Staurolite zone data. Note the inverse relationship between Ti concentrations and Mg/(Mg + Fe), (c) Transition and Lower sillimanite zone data, (d) Upper sillimanite zone data. Notice the increased scatter in Ti for a given Mg/(Mg + Fe), and (e) Sillimanite-K-feldspar and Garnet-cordierite data. The shaded circles are the highest-grade (6 kbar) data from Tracy (1978) and Tracy and Robinson (1988).

6 380 HENRY AND GUIDOTTI: TITANIUM IN BIOTITE FIGURE 5. Titanium isopleths calculated from the surface-fit equation on a T ( C) vs. Mg/(Mg + Fe) diagram. Because the western Maine data set does not have Ti values > 0.5 apfu, geothermometric inferences should not be made in this region. FIGURE 4. Titanium-saturation surface for natural peraluminous biotites at 3.3 kbar. (a) Perspective view of the surface highlights the influence of Mg content on Ti. Vertical lines connect individual data points above and below the fitted surface. (b) Perspective view of the surface highlights the influence of temperature on Ti. This biotite data set does not include values of Ti > 0.5 apfu and Mg/(Mg + Fe) < 0.3. ditions, the isopleths of Figure 5 could be used as an absolute or relative geothermometer based on measured Mg/(Mg + Fe) and Ti values in biotite. DISCUSSION The Ti-saturation surface developed with the western Maine data is, in the strictest sense, a 3.3 kbar isobaric saturation surface. However, the functional forms of other isobaric surfaces are likely to be very similar, but displaced to higher or lower Ti concentrations depending on the pressures of equilibration. Clearly, these saturation surfaces could be extended to additional P-T conditions with additional natural and experimental data that meet the assemblage and equilibrium criteria used in the western Maine data set. These surfaces have a number of potentially useful petrologic applications. Monitor of chemical equilibrium and re-equilibration If petrologic inferences about the temperature, pressure, and/ or fluid evolution are to be based upon considerations of experimental studies or theoretical phase equilibria involving biotite, it is absolutely crucial that an approach to chemical equilibrium be demonstrated for biotite and coexisting minerals. However, establishing that a given biotite or portion of a biotite grain has attained equilibrium compositions with a par- ticular set of minerals can be uncertain. Criteria for textural equilibrium are important but they do not necessarily imply chemical equilibrium has been attained or retained (e.g., Guidotti et al. 1991). Nonetheless, if they are combined with chemical equilibrium criteria it is much more probable that equilibrium biotite compositions can be assumed. Chemical criteria such as systematic element partitioning involving exchangeable cations (e.g., Mg and Fe2+) among coexisting phases have long been considered one of the strongest arguments (e.g., Deb and Saxena 1976; Stephenson 1979). However, this procedure requires that a substantial amount of chemical data exist among coexisting phases in a single sample as well as among a number of samples from a spatially restricted area, i.e., one having roughly constant temperature and pressure. A second ancillary criterion is that a given mineral is chemically homogeneous. This criterion may not be strictly met for refractory phases such as garnet or tourmaline whose rim compositions may be the only portion of the grains in chemical equilibrium with the matrix minerals. However, biotite generally is less refractory and responds much more readily to changing conditions (cf., Loomis 1976). The use of Ti in biotite to monitor equilibrium requires several considerations. Titanium is potentially very sensitive to small shifts in equilibrium because it preferentially partitions into biotite relative to other typical metapelitic silicate minerals. However, it also involves heterovalent-coupled substitutions that are typically more refractory than simple homovalent exchange reactions. As such, biotite compositions can change along different paths depending on their post-equilibrium history. The different ways include (1) cooling and retrograde cation exchange; (2) thermal overprint following cooling; or (3) alteration and replacement of a pre-existing biotite. As such, intracrystalline and intercrystalline homogeneity or shifts of Ti contents in biotite grains can provide a particularly discriminating guide to the attainment, retention, and the extent of

7 HENRY AND GUIDOTTI: TITANIUM IN BIOTITE 381 chemical equilibrium. There is an interplay of two effects: (1) the exchange of Mg and Fe on cooling without a significant corresponding change of Ti (because it involves a simple coupled substitution) and (2) the change of Ti contents due to reconstitution of biotite due to reaction/alteration to other phases (e.g., chlorite + rutile) or saturation with respect to Ti, i.e., rutile or titanite needles (e.g., Veblen and Ferry 1983; Shau et al. 1991). For example, in granulite-facies rocks, biotite in contact with garnet are commonly enriched in Mg due to Mg-Fe exchange on cooling (e.g., Edwards and Essene 1989; Frost and Chacko 1990). In some instances, this exchange may develop to the point at which rutile needles precipitate. In this case, the biotite may have reached TiO 2 -saturation levels due to the increase in Mg and/or decrease in temperature. Intercrystalline heterogeneity A relatively common observation in granulite facies rocks is the presence of biotites with two colors in the same thin section. Texturally, it is not always obvious which of these is the most likely equilibrium composition, e.g., green vs. brown biotite in a single granulite sample. For example, a granulitefacies quartzite (770 C, 5.15 kbar) from the Beartooth Mountains, Montana has metamorphic assemblage is quartz + plagioclase + garnet + biotite + orthopyroxene + ilmenite (Henry, unpublished data). There are two populations of biotites: brown and green. The ubiquitous brown biotite has 2.5 wt% TiO 2 and X Mg = 0.51, and yields thermometry consistent with peak conditions (770 C). Not surprisingly, the less-common green biotite has substantially lower TiO 2 (0.9 wt%) and higher X Mg (0.55), and yields anomalously low temperatures (600 C). Inclusion thermometry and relative temperature paths An important part of understanding pressure-temperaturetime paths in metamorphic rocks is the ability to estimate temperatures at different stages of development of the rocks. In some favorable cases, this is fairly straightforward for peak metamorphic assemblages through the standard application of a wide variety of geothermometers. However, determining the temperatures prior to and subsequent to the peak metamorphism can be quite difficult and uncertain. There are currently two types of approaches used for this task: (1) note the mineral or assemblage of minerals included in some refractory host mineral such as garnet or tourmaline and relate these minerals to their stability fields in a quantitative petrogenetic grid or (2) use the compositional zoning of a refractory mineral such as garnet and calculate the differential change in pressure and temperature relative to the peak metamorphic conditions (e.g., Spear and Selverstone 1983). However, both of these approaches are fraught with problems such as poor thermal resolution, inherent uncertainties in the assumptions of the calculation models, the possibility of volume diffusion affecting the zoning of the host at high temperatures, and significant cation exchange between included and host minerals (e.g., Frost and Chacko 1989). An alternative approach is to use an included mineral that is compositionally sensitive to temperature changes prior to entrapment but whose temperature dependent component will not undergo significant amounts of cation exchange with the host mineral. Titanium levels in biotite may serve this purpose. Included biotite can be used as a geothermometer using the functional relations defined for the metapelites of western Maine, provided that all of the appropriate criteria were met by the biotite at the time in which it was included. In other words, the included biotite must have coexisted with quartz, an aluminous phase, a Ti-phase, and graphite. Two additional factors to consider are the probable change in Mg/Fe ratios due to exchange with a refractory mafic mineral host, such as garnet, and the effects of pressure. (1) Biotite included in a mafic-mineral host will tend to become enriched in Mg on cooling. The magnitude of this change, in turn, is a function of cooling rate, mass of the biotite relative to the mafic-mineral host, and the presence/absence of a trapped fluid. Slow cooling or multiple heating events, small biotite mass relative to that of the host, and the presence of a fluid will all enhance Mg-Fe exchange involving biotite. However, biotite included in a non-mafic mineral such as kyanite or quartz will not undergo Mg-Fe exchange and may be used more effectively for inclusion thermometry. (2) The general effect of increasing pressure is to decrease the solubility of Ti in biotite. In the case of biotite that grew under roughly isobaric conditions, this latter factor would have no effect. However, in biotite trapped at significantly different baric conditions, the pressure effects on Ti incorporation will become a consideration. ACKNOWLEDGMENTS We acknowledge Michael J. Holdaway for his long interest and leadership in the roles of crystal chemistry of minerals in natural settings as they relate to petrology. We also acknowledge all of our colleagues who have contributed to the biotite data set over the years including Kathy Bussa, Jack Cheney, Paul Conatore, Angela LaGrange, Steve Lonker, and Marty Yates. Brian Marx provided invaluable insight in the vagaries of statistical analysis. Kurt Hollocher, John Schumacher, and Barb Dutrow made important suggestions that greatly improved the manuscript. REFERENCES CITED Abrecht, J. and Hewitt, D.A. (1988) Experimental evidence on the substitution of Ti in biotite. American Mineralogist, 73, Ahlin, S. (1988) Interpretation of biotite-garnet partitioning data from two Svecokarelian metamorphic rock units. Lithos, 22, Arima, M. and Edgar, A.D. (1981) Substitution mechanisms and solubility of titanium in phlogopites from rocks of probable mantle origin. 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