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Journal of Petrology Volume 42 Number 11 Pages 2083-2107 2001
© Oxford University Press 2001

Monazite–Xenotime–Garnet Equilibrium in Metapelites and a New Monazite–Garnet Thermometer

JOSEPH M. PYLE1,*, FRANK S. SPEAR1, ROBERTA L. RUDNICK2,{dagger} and WILLIAM F. McDONOUGH2,{dagger}

1DEPARTMENT OF EARTH AND ENVIRONMENTAL SCIENCES, RENSSELAER POLYTECHNIC INSTITUTE, TROY, NY 12180, USA
2DEPARTMENT OF EARTH AND PLANETARY SCIENCES, HARVARD UNIVERSITY, CAMBRIDGE, MA 01238, USA

Received August 15, 2000; Revised typescript accepted May 8, 2001


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 SAMPLE AND ANALYTICAL PROCEDURES
 RESULTS
 CONCLUSIONS
 APPENDIX: MOLE FRACTION...
 REFERENCES
 
Prograde suites of pelitic rocks were examined with electron microprobe and laser ablation inductively coupled plasma mass spectrometry to determine the systematics of element partitioning between coexisting monazite, xenotime, and garnet. Monazite grains that grew in equilibrium with xenotime are enriched in Y and Dy compared with monazite that grew in xenotime-absent assemblages. Y and heavy rare earth element contents of monazite coexisting with xenotime increase with rising temperature. Monazite–xenotime Y–Gd and Y–Dy partitioning is systematic within a metamorphic grade, and increases slightly with increasing metamorphic grade, suggesting that monazite–xenotime pairs approached partitioning equilibrium. Garnet and monazite in both xenotime-bearing and xenotime-absent assemblages show a strong ( R2 = 0·94) systematic relationship between inverse temperature and ln(KEq) for the net-transfer equilibrium YAG + OH-Ap + (25/4)Qtz = (5/4)Grs + (5/4)An + 3YPO4-Mnz + 1/2H2O, suggesting that garnet and monazite crystallized in compositional equilibrium. The following temperature–KEq relationship for the equilibrium above has been derived:

with a precision of some ±30°C for temperature estimates. Our observations suggest that major and accessory phases interact in a coupled fashion during metamorphism, and also approach a state of compositional equilibrium as reactions proceed.

KEY WORDS: garnet; monazite; partitioning; thermometry; xenotime


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 SAMPLE AND ANALYTICAL PROCEDURES
 RESULTS
 CONCLUSIONS
 APPENDIX: MOLE FRACTION...
 REFERENCES
 
Monazite [(Ce,La,Th)PO4] plays an important role in studies of igneous and metamorphic petrogenesis. Foremost, monazite is used to date specific events in a petrogenetic sequence (e.g. Parrish, 1990Go; Harrison et al., 1997Go; Hawkins & Bowring, 1999Go; Foster et al., 2000Go). Monazite may contain a large percentage of the sample rare earth element (REE) budget and, thus, exert an important influence on the evolution of melt composition (Wark & Miller, 1993Go; Bea, 1996Go). The thermobarometric potential of monazite (coexisting with xenotime) has been recognized, leading to calibration of monazite geothermometers (Gratz & Heinrich, 1997Go, 1998;Go Heinrich et al., 1997Go; Andrehs & Heinrich, 1998Go). In addition, the recognition that nearly all lead in monazite is radiogenic (Parrish, 1990Go; Montel et al., 1994Go) has led to development and application of electron microprobe monazite dating techniques (Suzuki & Adachi, 1991Go; Montel et al., 1996Go; Williams et al., 1999Go).

Full realization of monazite as a thermochronometer requires detailed understanding of the specific reactions responsible for its formation. Previous studies of monazite petrogenesis have focused on monazite compositional zonation (Zhu & O’Nions, 1999aGo, 1999bGo), monazite growth kinetics (Ayers et al., 1999Go), behavior of monazite during hydrothermal alteration (Poitrasson et al., 1996Go; Crowley & Ghent, 1999Go) and melting events (Watt, 1995Go), or, to a limited extent, the influence of major-phase mineral assemblage in monazite reactivity (Zhu & O’Nions, 1999bGo). Textural relationships between monazite and other accessory phases (allanite, apatite, epidote, titanite) indicate that monazite is involved in reaction relationships with other REE-accessory minerals (Broska & Siman; 1998;Go Finger et al., 1998Go), but only a limited number of studies address specific reactions responsible for formation of metamorphic monazite (Bingen et al., 1996Go; Pan, 1997Go; Ferry, 2000Go).

This paper focuses on monazite, xenotime, garnet, and, to a lesser extent, apatite because (1) they are significant geochronometers, (2) a large portion of a typical pelite REE and Y budget is contained in these phases, and (3) zoning in garnet and monazite record significant details of the reaction history. We attempt to demonstrate that metamorphic monazite approaches compositional equilibrium with both coexisting major and accessory phases. Moreover, we present element partitioning data for coexisting monazite, xenotime, and garnet that support the interpretation of an approach to compositional equilibrium between and among these minerals—a critical step in the process of identifying specific reactions responsible for the formation and destruction of metamorphic monazite. Finally, we demonstrate the utility of Y partitioning between garnet and monazite as a potential thermometer.


    SAMPLE AND ANALYTICAL PROCEDURES
 TOP
 ABSTRACT
 INTRODUCTION
 SAMPLE AND ANALYTICAL PROCEDURES
 RESULTS
 CONCLUSIONS
 APPENDIX: MOLE FRACTION...
 REFERENCES
 
Twenty-eight pelites with well-characterized PT histories from three localities (Table 1) were chosen for study. The samples are the same as those studied by Pyle & Spear (1999)Go, and field area details have been given therein. Additional information on the samples examined in this study has been given by Spear et al. (1990Go, 1995)Go, Spear (1992)Go, Kohn et al. (1993Go, 1997)Go, Menard & Spear (1993Go, 1994)Go, Spear & Kohn (1996)Go, and Spear & Parrish (1996)Go.


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Table 1: Sample grade and accessory mineral assemblage

 

Details of image acquisition, element map generation, and quantitative electron microprobe (EMP) analysis of garnet have been given by Pyle & Spear (1999)Go. X-ray maps were obtained and analyses were performed on a JEOL 733 Superprobe at Rensselaer Polytechnic Institute. For monazite element maps we used a 15 kV accelerating voltage, beam current of ~150 nA, map step size of 1–2 µm/pixel, and dwell times of 30–50 ms/pixel. For quantitative spot analysis of monazite and xenotime, a combination of natural and synthetic phosphate, silicate, and oxide standards was used (Table 2), with an accelerating voltage of 15 kV, beam current of ~50 nA, and counting times of 30 s each on peak and background. The ZAF matrix correction used was that of Armstrong (1984)Go. Selected monazite and xenotime grains (Tables 4 and 5) were reanalyzed at longer counting times and higher current (120 s, 100 nA) to improve detection limits. Minimum detection limit (MDL) is calculated using the relationship from Ziebold (1967)Go, MDL >= 3·29Cstd/(P/B)1/2, where Cstd is the weight per cent of the element of interest in the standard, P equals the total number of peak-background counts, and B equals the total number of background counts. In Table 2, 12 000 nA s detection limits for REE, Y, U, Pb, and Th are listed. Analyses listed in Tables 4 and 5 are single-spot analyses.


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Table 2: Analysis setup and operating conditions for xenotime and monazite EMP analyses

 

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Table 4: Representative analyses of xenotime (values in wt % oxide)

 

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Table 5: Representative analyses of monazite (values in wt % oxide)

 


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Table 6: Representative trace-element analyses of major pelitic phases (concentrations in ppm)

 
Quantitative analysis of REE phosphate generally requires some correction because of interference of overlapping characteristic X-ray peaks (Scherrer et al., 2000Go). Off-line corrections for interferences were made to the following elements (Table 3): P, U, Pb, Nd, Gd, Er. For monazite compositions in this study (0·0–9·5 wt % ThO2), Th interference (M2-O4 + M{zeta}1 and M{zeta}2) on Pb (M{alpha}) is minor (<=120 ppm apparent PbO from ThO2 interference) and is ignored. Interfering X-ray lines and correction factors are given in Table 3. Empirical correction factors calculated in this way broadly agree with correction factors calculated using the program Virtual WDS (Reed & Buckley, 1996Go; see also Scherrer et al., 2000Go).


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Table 3: Correction factors for inter-element interference in EMP analyses (accelerating voltage 15 keV)

 

Quantitative EMP analysis of apatite is hindered by F excitation phenomena (Stormer et al., 1993Go). Prioritization of F analysis, 10 µm spot size, low current (~20 nA on the Faraday cup) and short counting times (15 s on peak) were used to minimize F excitation. Repeated analyses on the same spot of Durango apatite using the above analysis schedule demonstrated F volatilization, but no apparent increase in F concentration. Repeated analyses on different spots of the Durango apatite standard gave an average value of 3·42 ± 0·11 (1{sigma}) wt % F (n = 21).

Major silicate phases from 11 of the 28 samples were analyzed for REE, U, Pb, and Th using the laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) system at the Department of Earth and Planetary Sciences, Harvard University. Samples were ablated using an excimer laser (Lambda Physik), which produces a 193 nm laser light with a 15 ns pulse duration. Spot size varied between 35 µm (for small grains) and 90 µm (for large grains) in diameter; ablated grains were typically between 500 and 20 000 µm in diameter, resulting in ablation percentages (on an area basis) of 0·002–0·5%. The ablated material was analyzed in fast peak hopping mode with a PQ II+ quadrupole ICP-MS (VG-Elemental) system. Each analysis incorporated a background acquisition of ~60 s, with total acquisition times varying between 120 and 240 s. Factory-supplied software was utilized in the acquisition of individual time-resolved analyses. Details of acquisition and calculation of transient signals have been described by Longerich et al. (1996)Go. External calibration was performed relative to NIST 610 and 43Ca was used as an internal standard. Barth et al. (2001)Go reported values assumed for NIST 610 as well as analyses of the BIR-1G and BCR-2G glass standards. The time-resolved spectra were processed off-line using a modified version of the program LAMTRACE (coded by Simon Jackson). Further details of laser and ICP-MS setup and operating conditions have been given by Horn et al. (2000)Go. Analyses generally consist of two spots per grain; exceptions are noted in Table 6. Where appropriate, the standard deviation of multiple analyses is given in parentheses.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 SAMPLE AND ANALYTICAL PROCEDURES
 RESULTS
 CONCLUSIONS
 APPENDIX: MOLE FRACTION...
 REFERENCES
 
Monazite and xenotime compositions
Representative analyses of xenotime and monazite are given in Tables 4 and 5. All point analyses with 97 < {Sigma} wt % oxide < 103 and 1·975 < sum cations < 2·025 are included for analysis and discussion (nMnz = 526, nXno = 56).

Pelitic xenotime is remarkably uniform in yttrium and heavy REE (HREE) contents (Table 4). Mole fraction YPO4 ranges from 0·71 to 0·87, with an average value of 0·791 ± 0·025. Dy, Yb, Gd, and Er are the other major constituents of xenotime, along with minor Ho; mole fraction HREEPO4 ranges from 0·12 to 0·25, with an average value of 0·195 ± 0·021. Xenotime light REE (LREE) content is low; Nd is present in all analyzed xenotime grains (0·05–1·02 wt % Nd2O3, average 0·30 ± 0·16 wt %); La, Ce, Pr, and Sm range from below detection limit to a few tenths of 1 wt %. Xenotime Th content is low, with a maximum Ca(Th,U,Pb)(PO4)2 (brabantite) component of 3·0 mol % and generally negative calculated (Th,U,Pb)SiO4 (huttonite) component. Xenotime is slightly depleted in Pb with respect to coexisting monazite, with PbO content between <0·02 and 0·26 wt % (average 0·11 ± 0·05 wt %).

Monazite is, on average, 1–2 orders of magnitude more abundant than xenotime in the pelites studied. Representative monazite analyses from 25 samples are listed in Table 5. In contrast to xenotime, pelitic monazite is compositionally fairly variable. Monazite is largely a (La–Sm)PO4 solid solution [(La–Sm)PO4 = 0·75–0·97, average 0·860 ± 0·030], but displays considerable variation in mole fraction of (Y+HREE)PO4 (0·01–0·18) and brabantite mole fraction (0·00–0·17). Huttonite component is generally close to zero or negative. Measured monazite PbO content ranges from <0·02 to 0·45 wt % (average 0·12 ± 0·08 wt %). Formulae for calculation of REE phosphate components are given in the Appendix. The grouping of Pb with Th and U in both the huttonite and brabantite components, rather than with Ca in the brabantite component, is based on the interpretation that all lead in both monazite and xenotime is derived by radioactive decay of a portion of the Th and U present at the time of monazite crystallization (Parrish, 1990Go). Measured PbO content in both phases is in general agreement with PbO content calculated using associated Th and U values and assuming an average age of 350 Ma.

The extent of brabantite vs huttonite exchange operational in monazite and xenotime is depicted in a plot of Th + U + Si vs REE + Y + P (Fig. 1). The brabantite exchange vector is clearly dominant in monazite. Owing to low concentrations of Ca, Th, U, and Si in monazite, the relative contributions of brabantite and huttonite exchange in xenotime are obscured. However, it is noted that the huttonite exchange in monazite is equivalent to the zircon exchange (ZrSiREE-1P-1) in xenotime.



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Fig. 1. Monazite and xenotime cation plot, normalized to 16 oxygens. REEPO4 phosphate plots at (8,0) and brabantite [Ca(Th,U)REE-2] and huttonite [(Th,U)SiREE-1P-1] exchange vectors are plotted. Huttonite exchange in monazite is analogous to zircon (ZrSiREE-1P-1) exchange in xenotime.

 

The decay of Th and U (+4) to Pb creates a charge imbalance in monazite, as it is generally accepted that, under most conditions of T and fO2 corresponding to regional metamorphism, +2 is the stable oxidation state of lead (Watson et al., 1997Go, and references therein). However, this charge imbalance is slight, because of low monazite Pb content. Overall, examination of all monazite analyses suggests that monazites in these samples are very nearly charge balanced. The means and standard deviations of the cation sums (calculated on an 8 oxygen basis) are as follows: Si + P = 0·997 ± 0·020; REE + Y + Th + U + Pb + Ca = 1·007 ± 0·032; Ca – (Th + U + Pb) = -0·005 ± 0·006; Ca + Si – (Th + U + Pb) = 0·005 ± 0·018. Figure 2 shows frequency histograms for Si + P and Ca + Si – (Th + U + Pb) in monazite. Both frequency distributions are approximately normal; high outliers in the Ca + Si – (Th + U + Pb) plot are from high-Si, low-Th monazite analyses that probably result from subsurface micro-inclusions of quartz in monazite. The slightly positive value of Ca + Si – (Th + U + Pb) suggests that there may be a slight Si excess in the analyzed monazites. To help rule out the possibility of systematic analytical error, Si + P and Ca + Si – (Th + U + Pb) were calculated for 46 monazite analyses taken from Franz et al. (1996)Go, Finger et al. (1998)Go, Förster (1998)Go, and Zhu & O’Nions (1999a)Go. Values from those studies are nearly identical to our data (Fig. 2c and d), and the mean Si + Ca – (Th + U + Pb) parameter is slightly positive (0·005).



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Fig. 2. Monazite cation sum frequency distribution histograms for this dataset (a, b) and for monazite analyses from Franz et al. (1996)Go, Finger et al. (1998)Go, Förster (1998)Go, Zhu & O’Nions (1999a)Go (c, d). Cation sums plotted are Si + P (a, c) and Ca + Si – (Th + U + Pb) (b, d). The mean and standard deviation of each sum is listed on each plot, along with the number of sums in each distribution. The distribution of cation sums in these datasets approximates a gaussian (normal) distribution [gray curves in (a) and (b)], and there is an average excess of Ca + Si over Th + U + Pb in each dataset, suggesting substitution of some Si for P in (REE,Y)PO4, with resultant charge deficit.

 

Importantly, examination of Table 5 reveals that much of the compositional variation in monazite is intragranular. Variations of up to ±8·5 wt % ThO2 (sample PUT-92C2) and ±4·5 wt % Y2O3 (sample V6B) have been recorded within a single grain of monazite. The implications of monazite intragranular compositional variation are addressed below.

Apatite compositions
Analyses from this suite of samples indicate apatite {Sigma}LREE (La–Sm) contents of the order of ~500–1000 ppm, and XOH-apatite of the order of 0·01–0·40. These REE numbers are lower than those of apatites from disparate diagenetic and metamorphic environments. For example, apatite from a clay-rich aquitard (Yan et al., 2000Go) contains {Sigma}LREE ~3800 ppm, apatite from migmatite (Bea, 1996Go) contains {Sigma}LREE ~4750 ppm. Cruft (1966)Go found that apatites from marble and pyroxenite contain 2000–22 000 ppm Y + La + Ce. Finger et al. (1998)Go found {Sigma}LREE content of >=15 000 ppm in apatite coronas around monazite in amphibolite-facies gneiss. Apatite may therefore be a significant contributor to the overall REE budget of a metamorphic rock, but the low abundance of REE in apatite in this suite of samples would require apatite mass of approximately three orders of magnitude greater than that of monazite to equal the contribution of monazite to the REE budget.

Of particular interest is the wide variation in OH-Ap component in apatite (0·0–0·40). In general, apatite included in garnet cores contains a larger fraction of the hydroxy-component than matrix apatite grains. Apatite Cl-component is near zero except for apatite grains from migmatitic sample V7C (Spear & Parrish, 1996Go); analyzed apatites (six grains, 10 spots) contain 0·11–0·13 XCl-Ap.

Major phase trace-element compositions
LA-ICP-MS analyses of several major pelite phases (Table 6) show the following.

  1. Biotite, muscovite, staurolite, and sillimanite (along with quartz) constitute the majority of the mineral mode (>=80 vol. %) and all contain negligible concentrations of REE, Y, Th, U, and Pb. These numbers are similar to the concentrations of REE, Y, Th, U, and Pb in biotite and muscovite reported by Bea (1996)Go and Yang & Rivers (2000)Go, both of whom noted that high REE contents in earlier analyses of micas (Bea et al., 1994Go; Yang et al., 1999Go) were probably due to minute inclusions of monazite, apatite, or xenotime.
  2. Plagioclase contributes a small, but non-negligible, amount of LREE to the whole-rock budget; sillimanite-zone plagioclase contains 17 ppm (La + Ce + Nd) and the LREE content of plagioclase increases to 52 ppm (La + Ce + Nd) in plagioclase from migmatite zone samples. Plagioclase from high-grade samples studied by Bea (1996)Go and Kretz et al. (1999)Go contain similar (La + Ce + Nd).
  3. Garnet is a significant major-phase host for HREE (Table 6), with HREE (Gd–Lu) content >=2000 ppm in xenotime-bearing garnet-zone samples; XHREE in garnet decreases with increasing metamorphic grade, analogous to the observed decrease of YAG component in garnet with increasing metamorphic grade (Pyle & Spear, 2000aGo). (YAG: Y3Al2Al3O12). HREE content of garnet in xenotime-absent samples is lower than the HREE content of garnet in xenotime-bearing samples of the same metamorphic grade.

Assessment of equilibrium between monazite and xenotime
The complexity of monazite intragrain compositional variation hinted at by spot analyses (Table 5) is revealed in monazite element distribution maps (Fig. 3). Approximately 100 separate monazite grains were mapped for element distribution in the 28 samples studied; three examples from different metamorphic grades are shown in Fig. 3. Thorough study of monazite element distribution maps, spot analysis variation, and texture reveals the following:



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Fig. 3. Monazite back-scatter electron images, Y, and Th element distribution maps. Brighter areas indicate higher concentration of element. (a–c) Monazite, sample 93-19A (garnet zone). Y is roughly homogeneous, and Th decreases towards the monazite rim, corresponding to back-scatter zoning. (d–f) Monazite, sample 89-22 (sillimanite zone). Back-scatter brightness corresponds to Th enrichment, and Y zoning is antithetic to Th zoning. (g–i) Monazite, sample BF-78 (transitional sillimanite–migmatite zone). Th is nearly homogeneous, but Y is complexly zoned (corresponding to back-scatter variation), with at least four distinct compositional zones visible in the map.

 
  1. in a large number of grains, variation in back-scattered electron (BSE) intensity is due largely to changes in yttrium concentration (Fig. 3g–i), although, in other cases, Th concentration variation contributes significantly (Fig. 3d–f), or is responsible for all of the BSE contrast (Fig. 3a–c). The large role of Y variation in BSE intensity variation differs from that reported in other monazite-bearing suites (Watt & Harley, 1993Go; Watt, 1995Go).
  2. Discontinuous thorium zoning is more common in monazite from low-grade samples (Fig. 3a–c), although exceptions do occur (Fig. 3d–f).
  3. If monazite is strongly zoned in thorium, the form of zoning generally consists of a Th-rich core and Th-poor outer region (Fig. 3c and f), whereas yttrium zonation may be bimodal, oscillatory, ‘patchy’, or a combination of the above forms (Fig. 3e and h).
  4. In garnet zone samples containing matrix xenotime, monazite yttrium distribution is largely homogeneous (Fig. 3b).
  5. Yttrium and thorium zoning may both vary strongly in an antithetic fashion (Fig. 3e and f), or still vary antithetically, but with much greater absolute yttrium variation than thorium variation (Fig. 3g–i).
  6. Monazites that are texturally associated with xenotime always have among the highest yttrium content of all monazites in that sample.

The non-correspondence of Th and Y zoning in monazite is an indication that different reservoirs are reacting to control monazite Y and Th distribution. Garnet growth has a profound effect on bulk-rock yttrium content and xenotime stability (Pyle & Spear, 1999Go, 2000aGo), and it follows that reaction of garnet exerts similar influence over the (Y,HREE) content of monazite. Factors controlling monazite Th distribution are less clear, as no other significant Th sink has been identified in these samples. Zircon of typical Th content (Bea, 1996Go) will exert some control over monazite Th distribution if the zircon is present in sufficient abundance and is not kinetically inhibited from reacting.

Criteria for inferring monazite–xenotime equilibrium
With the above observations as a guide, a set of criteria (Table 7) were established to aid in the interpretation of stable coexistence of monazite and xenotime. The reference to inclusion of monazite and/or xenotime in garnet porphyroblasts is specific, as other porphyroblasts (specifically biotite and staurolite) do not contain (or display) noticeable yttrium zoning discontinuities. The existence of such Y discontinuities in garnet in this dataset is interpreted to mark the loss of xenotime from the mineral assemblage (Pyle & Spear, 1999Go), and, consequently, the discontinuation of monazite–xenotime equilibrium.


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Table 7: Ranked textural and compositional criteria for assumption of monazite–xenotime compositional equilibrium

 

Using the Table 7 criteria as a guide, all monazite spot analyses were classified as having grown in either a xenotime-bearing or xenotime-absent mineral assemblage. The extent of compositional equilibration in monazite + xenotime assemblages is assessed by first examining the variation of Y, Dy, and Gd in all monazites (Fig. 4), followed by examination of monazite–xenotime Y/Gd and Y/Dy partitioning.



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Fig. 4. Monazite composition plots. (a–e) YPO4(Mnz) vs GdPO4(Mnz) and (f–j) YPO4(Mnz) vs DyPO4(Mnz) for (a, f) biotite–chlorite zone samples, (b, g) garnet zone samples, (c, h) staurolite zone samples, (d, i) sillimanite zone samples, and (e, j) migmatite zone samples. Gray squares, monazite from xenotime-absent assemblages; black squares, monazite in equilibrium with xenotime. Interpretation of monazite–xenotime equilibrium based on criteria given in Table 7.

 

Compositional variation of monazite
The mole fraction of GdPO4 component in monazite is largely insensitive to metamorphic grade (Fig. 4a–e), or the presence of xenotime in the mineral assemblage, and the value of GdPO4(Mnz) clusters about 0·02. DyPO4(Mnz) is uniformly low in xenotime-absent assemblages (<=0·01), but in xenotime-bearing assemblages correlates positively with YPO4(Mnz), increasing to a maximum of ~0·015 in the migmatite zone (Fig. 4f–j). YPO4(Mnz) in xenotime-bearing assemblages increases systematically with rising T, with maximum YPO4(Mnz) ~0·03 for garnet zone monazite, ~0·05 for staurolite zone samples, ~0·06 for sillimanite zone samples, and ~0·08 for migmatite zone samples. The spread in YPO4(Mnz) for high-grade xenotime-bearing samples results from either: (1) continuous monazite growth from garnet zone through to the maximum metamorphic grade, with xenotime as part of the assemblage at various points in the monazite growth history; or (2) multiple, separate episodes of monazite growth between garnet zone and migmatite zone PT conditions, with xenotime present in the assemblage for each monazite growth episode. In either case, the large spread in YPO4(Mnz) implies that monazite growth (whether continuous or discontinuous) in these samples occurred over a large part of the prograde PT path.

Monazite grains in contact with, or in close textural proximity to, xenotime are shown with coexisting xenotime in ternary LREE–HREE–Y (Fig. 5a) and LREE–(HREE + Y)–Th plots (Fig. 5b). Figure 5a again shows the systematic increase in YPO4(Mnz) with increasing metamorphic grade, but in addition shows that the increase of total Y + HREE(Mnz) occurs at a nearly constant Y/HREE ratio (~1:1), regardless of xenotime composition; further evidence for temperature rather than bulk-composition control of monazite composition. The apparent tie-line crossovers evident in Fig. 5a are reduced by inclusion of total Th component as a plotting element (Fig. 5b). Total Th component of monazite coexisting with xenotime does not appear to be a strong function of temperature.



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Fig. 5. Plots of coexisting monazite and xenotime. (a) Expanded LREEPO4–HREEPO4–YPO4 ternary showing tie-lines between coexisting monazite and xenotime. (b) Expanded LREEPO4–[HREEPO4 + YPO4]–[Ca(Th,U,Pb)(PO4)2 + (Th,U,Pb)SiO4] ternary. LREE, (La,Ce,Pr,Nd,Sm)PO4; HREE, (Gd,Dy,Ho,Er,Yb)PO4; Y, YPO4; Hut, Ca(Th,U,Pb)(PO4)2; Brb, (Th,U,Pb)SiO4; x, biotite + chlorite zone; {square}, garnet zone; {triangleup}, staurolite zone; {circ}, sillimanite zone; {lozenge}, migmatite zone.

 
Monazite–xenotime element partitioning
Figure 6 is a plot of ln(YPO4/i)(Mnz) vs ln(YPO4/i)(Xno) for xenotime-bearing assemblages, as a function of metamorphic grade, where i is GdPO4 (Fig. 6a–e), and DyPO4 (Fig. 6f–j), and diagonal lines are isopleths of KD for the reactions




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Fig. 6. Monazite–xenotime partitioning plots. (a–e) ln(YPO4/GdPO4)(Mnz) vs ln(YPO4/GdPO4)(Xno), and (f–j) ln(YPO4/DyPO4)(Mnz) vs ln(YPO4/DyPO4)(Xno) for (a, f) biotite + chlorite zone samples, (b, g) garnet zone samples, (c, h) staurolite zone samples, (d, i) sillimanite zone samples, and (e, j) migmatite zone samples. Plots represent partition coefficients for the total range of monazite compositions in a single sample, interpreted to be in equilibrium with xenotime, combined with 1–4 representative xenotime analyses per sample. Numbers on plots refer to sample numbers (see sidebar). Error bars represent propagation of analytical uncertainties (Bevington, 1969Go) in (5%), (1%), (7·5%), (5%), (25%), and (5%). Diagonal lines are isopleths of KD.

 
with distribution coefficients


Although care has been taken to plot only monazite grains that grew in a xenotime-bearing assemblage, it is unlikely that all monazite compositions in a single sample are in equilibrium with a single xenotime composition, as the latter shows some compositional variation. Therefore, between one and four ln(YPO4/i)(Xno) values are plotted against the entire range of xenotime-equilibrated ln(YPO4/i)(Mnz) values in an attempt to encompass the total compositional variability of xenotime in a given sample. For some samples, the range of xenotime compositions lies within the calculated analytical uncertainty. For others, xenotime displays a greater range in ln(YPO4/GdPO4) and ln(YPO4/DyPO4) than may be explained by analytical precision. Such compositional variability may be due to: (1) fractionation of non-essential xenotime components (e.g. Gd, Dy, Ho, Er, Yb) by garnet during or between periods of xenotime growth; (2) disequilibrium; or (3) PT control over monazite–xenotime element partitioning. Heinrich et al. (1997)Go showed that, whereas xenotime LREE content appears to increase with rising temperature, Dy and Gd content of xenotime appears to be independent of metamorphic grade. Differences in effective bulk composition as a result of fractionation of HREE by growing garnet should be reflected in a systematic difference in ln(YPO4/GdPO4)(Mnz), and ln(YPO4/DyPO4)(Mnz) as well, but such a sympathetic variation is not observed. The variation in ln(YPO4/GdPO4) and ln(YPO4/DyPO4) above and beyond that predicted by propagation of analytical uncertainty may reflect the ‘geological’ uncertainty associated with selecting equilibrium monazite–xenotime pairs when both minerals are zoned.

KD1 values for all samples cluster around a value of 0·05 (Fig. 6f–j), and KD2 values cluster around 0·3 (Fig. 6f–j). Intragrade variation of both distribution coefficients is greater than the variation in KD between grades, with KD values from migmatite-zone pairs displaying the greatest variation. This variation may reflect the more complex monazite reaction history of the highest-grade samples. In general, KD1 values show less overall variation than values of KD2. This observation is borne out in a plot of average KD vs metamorphic grade (Fig. 7). KD1 is largely invariant with metamorphic grade (Fig. 7a), and KD2 may correlate positively with temperature (Fig. 7b), but this variation may be obscured by uncertainties associated with analysis of Dy in monazite.



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Fig. 7. Plots of (a) average KD1 and (b) KD2 vs metamorphic grade. KD1 = (Y/Gd)Mnz/(Y/Gd)Xno and KD2 = (Y/Dy)Mnz/(Y/Dy)Xno. Bt-Chl, biotite–chlorite zone; Grt, garnet zone; St, staurolite zone; Sil, sillimanite zone; Mig, migmatite zone. Error bars represent ±1 standard deviation on the average value of KD for each metamorphic zone. Number of monazite analyses averaged per zone is given under the zone designation in part (a).

 

Application to monazite–xenotime thermometry
Coexisting monazite and xenotime in our sample suite have been shown to approach compositional equilibrium, based on the systematic behavior of monazite composition (increasing , constant Y/HREE) and monazite–xenotime element partitioning (nearly constant Y/Gd and Y/Dy). These findings are in accord with studies of synthetic (Gratz & Heinrich, 1997Go, 1998;Go Andrehs & Heinrich, 1998Go) and naturally occurring (Heinrich et al., 1997Go) monazite–xenotime pairs. Furthermore, the monazite limb of the monazite–xenotime miscibility gap from this study (Fig. 8) is in excellent agreement with that of Heinrich et al. (1997)Go, further evidence that these phases crystallized in near equilibrium.



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Fig. 8. (a) Temperature vs for coexisting monazite ({square}) and xenotime ({circ}). Temperature estimates from garnet–biotite thermometry (Hodges & Spear, 1982) and YAG–xenotime thermometry (Pyle & Spear, 2000aGo). Vertical error bars indicate ±25°C (±50°C for the lowest grade sample) and horizontal error bars indicate ±5 mol %. (b) Enlargement of (a) showing detail of monazite compositions. Monazite limb (continuous line with {square}; P et al.) is a logarithmic fit to the data from this study. Monazite limb from Heinrich et al. (1997Go: H et al.) with associated logarithmic fit is plotted for comparison.

 

Single-grain monazite ages (Parrish, 1990Go) and compositional maps clearly indicate that monazite growth is episodic and that determination of xenotime–monazite coexistence in samples with multi-stage monazite is non-trivial. Propagated temperature uncertainty associated with the monazite limb of the miscibility gap from this study is approximately ±20°C, but application of a ‘monazite-limb’ thermometer to monazite that grew in a xenotime-absent assemblage can result in a temperature error of well over 100°C. For example, reaction history analysis of the monazite shown in Fig. 3 indicates that the outermost low-Y zone grew at sillimanite-zone temperature conditions (580–620°C) in a xenotime-absent mineral assemblage. Application of the Gratz & Heinrich (1997Go, 1998)Go thermometer to the outer low-Y portion of the monazite (XY + HREE = 0·0418) yields a temperature estimate of 392°C. In this situation, the source of most of the inaccuracy is ‘geological uncertainty’ (Kohn & Spear, 1991Go), rather than inaccuracy in thermometer calibration.

Assessment of equilibrium between monazite and garnet
The distribution of yttrium in garnet is a strong function of accessory phase assemblage, and, hence, effective (matrix) bulk composition. Garnet in xenotime-bearing samples undergoes a systematic decrease in YAG component with rising temperature (Pyle & Spear, 2000aGo), but loss of xenotime from the mineral assemblage results in rapid, Rayleigh-type fractionation of available Y into growing garnet (Pyle & Spear, 1999Go). HREEs in garnet behave identically to Y in both cases. LA-ICP-MS analyses (Fig. 9) demonstrate the systematic decrease of Yb and Er in garnet from xenotime-bearing samples with increasing metamorphic grade, parallel to the garnet yttrium trend.



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Fig. 9. Plot of Y and selected HREE (Yb, Er, Dy) concentration in garnet vs metamorphic grade for garnet coexisting with xenotime. {lozenge}, Y; x, Yb; gray squares, Er; {triangleup}, Dy. Grt, garnet zone; St, staurolite zone; Sil, sillimanite zone; c, core analyses; r, rim analyses. Analyses ordered by metamorphic grade and by position (core vs rim).

 

The Y content of monazite depends strongly on whether xenotime is present. In xenotime-bearing assemblages, (Mnz) is buffered by the presence of xenotime, and its value increases with rising temperature. In contrast, in xenotime-absent assemblages, garnet and monazite may continue to grow and the remaining Y and HREE will be depleted as they are incorporated into growing monazite and garnet. On a modal (volumetric) basis, the (Y, HREE) uptake capacity of garnet is two or three orders of magnitude greater than that of monazite, but, at higher metamorphic grades, this uptake capacity of garnet for (Y, HREE) fractionation is counteracted by the lower solubility of (Y, HREE) in garnet (Pyle & Spear, 2000aGo).

The inclusion of monazite in garnet is commonly taken as evidence that monazite was a stable phase during the period of garnet growth. Implicit in this assumption is that garnet and the included monazite are in compositional equilibrium. As element distribution maps clearly demonstrate, both garnet (Pyle & Spear, 1999Go) and monazite (Fig. 3) diffuse very slowly with respect to Y and HREE. Therefore, monazite included in garnet is not likely to re-equilibrate with trace components in garnet by diffusive exchange over geologically relevant time scales, except perhaps under extreme conditions of metamorphism. For practical purposes, monazite composition is ‘frozen’ once it is isolated from the matrix by surrounding garnet. Furthermore, the complex zoning observed in many monazite grains (e.g. Fig. 3) indicates that intragranular diffusion of Y and Th in monazite is slow.

The importance of understanding the reaction relationship between two refractory phases for assessing equilibrium coexistence based on textural criteria is illustrated in Fig. 10. Of the four possible reaction histories shown in the figure, the only combination that will yield coexisting equilibrium compositions is the first (both garnet and monazite grow). Most importantly, the presence of an included monazite in a garnet porphyroblast such as illustrated in Fig. 10b does not assure two-phase equilibrium. This point illustrates that assumptions concerning equilibrium between porphyroblasts and included phases when both phases have extremely low diffusivities for the components of interest are prone to error without independent knowledge of the reaction relationship between the two phases of interest.



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Fig. 10. Schematic representation of the possible combinations of garnet and monazite reaction relationships and the implications of these for finding equilibrated garnet–monazite pairs. Left: continuous outlines show grain boundary positions at time 1 (t1). Right: continuous lines show grain positions at time 2 (t2), and dashed lines show former (t1) grain boundary positions. Garnet and monazite are assumed to be in equilibrium at t1, and both are assumed to be refractory (zoned) phases. (a) Garnet and monazite both grow between t1 and t2. The grain boundary of included monazite is in equilibrium with some portion of the occluding garnet between the monazite–garnet grain boundary and the garnet–matrix grain boundary. Rim of matrix monazite is in equilibrium with rim of garnet. (b) Garnet grows and monazite is consumed between t1 and t2. (c) Garnet is consumed and monazite grows between t1 and t2. (d) Garnet and monazite both consumed between t1 and t2. In (b), (c), and (d), no existing portion of garnet is in equilibrium with monazite.

 

A new garnet–monazite thermometer
Some possible reactions describing mass transfer between YAG and xenotime were discussed by Pyle & Spear (2000aGo). For each of those reactions, an equivalent reaction can be written, replacing YPO4(Xno) with YPO4(Mnz). One possible reaction relating mass transfer between garnet and monazite involves consumption of YAG component of garnet, OH component of apatite, and quartz to produce grossular component of garnet, anorthite component of plagioclase, YPO4 component of monazite, and a small amount of fluid:

with associated equilibrium constant

Assuming quartz is pure and single-site ionic ideal solution models for other phases, the equilibrium constant can be written as a function of composition:

This equilibrium constant was calculated for 14 well-equilibrated garnet–monazite pairs (Table 9). The selection of equilibrium monazite–garnet pairs is critical to the application of equilibrium relations in this system, and is fraught with potential pitfalls. In this study, the selection was based on element distribution maps of both phases combined with textural analysis and quantitative probe data. Additionally, Gibbs method modeling (e.g. Spear et al., 1991Go) has been used to predict the growth and/or consumption of garnet and accessory phases. Although the criteria for selection of equilibrium pairs are sample-specific, some general rules of thumb are given in Table 8. An additional, significant source of uncertainty arises from selection of plagioclase composition. In this study, garnet rim analyses were paired with the most albitic plagioclase in a particular sample, and garnet core analyses were paired with the highest anorthite content plagioclase in the sample. This is done under the assumption that in closed-system rocks without other calcic phases in significant abundance (i.e. Ca-carbonate or epidote), plagioclase becomes more albitic as garnet grows (Spear et al., 1991Go); the extent to which consumption of apatite during garnet growth buffers XGrs has not been studied.


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Table 9: Values used in regression of YAG–monazite thermometer

 

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Table 8: Ranked textural and compositional criteria for assumption of monazite–garnet compositional equilibrium

 

Temperatures and pressures of equilibration were determined for each garnet–monazite pair (Pyle & Spear, 2000aGo). The fugacity of H2O was calculated at P and T using the modified compensated Redlich–Kwong equation of Holland & Powell (1991)Go, and the standard deviation of f(H2O) was calculated with a Monte Carlo simulation consisting of 1000 trials. Variations in f(H2O) (an explicit function of P and T) also have only a small effect on the calculated equilibrium constant; changing the input value of f(H2O) by ±1000 results in a {Delta}T of ±3°C. The volume of YPO4 monazite was calculated using the linear regression of Ni et al. (1995)Go. {Delta}Vrxn for (3a) varies from -1·28 J/bar (BF-78) to -1·61 J/bar (V7C) over the PT range of the samples (450–800°C, 3–8 kbar).

Values of ln(KEq) + P{Delta}V/RT for equilibrium garnet–monazite pairs (Table 9) were regressed against reciprocal temperature (Fig. 11). The goodness of fit (R2 = 0·94) shown in Fig. 11 suggests that there is a systematic relationship between YAG component of garnet and YPO4(Mnz) over the range of temperatures examined. Assuming {Delta}Cp = 0, the least-squares fit to the data yields values of {Delta}Hrxn = 447·8 (±32·1) kJ and {Delta}Srxn = 0·57 (±0·04) kJ/K. The Clausius–Clapeyron relation yields dP/dT estimates of ~345–425 bars/°C for reaction (3a) over the PT range studied.



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Fig. 11. Plot of ln(KEq) + P{Delta}V/RT vs reciprocal temperature for the reaction YAG + OH-apatite + (25/4)quartz = (5/4)grossular + (5/4)anorthite + 3YPO4(monazite) + 1/2H2O [reaction (3a)]. {blacksquare}, xenotime-bearing assemblages; {square}, xenotime-absent assemblages. Least-squares regression line is fitted to all data points. Horizontal error bars represent temperature uncertainty of ±30°C. Vertical error bars are ±1{sigma} [ln(KEq) + P{Delta}V/RT ], derived from propagation of uncertainties in P (±1000 bars), T (±30°C), {Delta}Vrxn (1%), compositional parameters (0·001 mole fraction YAG, 0·01 mole fraction all others), and f(H2O) (±7·5; 1000 trial Monte Carlo simulation). Labels on graph indicate sample numbers.

 

Importantly, the systematic relationship between YAG and YPO4(Mnz) appears to hold for xenotime-absent samples as well. Textural and compositional analysis of samples PUT-92C2 (garnet zone), BF-17 and BF-52 (staurolite zone), and V7C (migmatite zone) indicates that some garnet growth in each of these samples occurred in a xenotime-absent assemblage. Monazite grains texturally associated with these low-Y garnets are depleted in yttrium compared with monazite texturally associated with xenotime. Values of ln(KEq) + P{Delta}V/RT for these four samples (open squares, Fig. 11) fall on the trend defined by ln(KEq) for xenotime-bearing samples, suggesting that equilibrium between garnet and monazite is achieved by a significant decrease in both YAG and YPO4(Mnz).

A YAG–monazite geothermometer using derived values of {Delta}H and {Delta}S for reaction (3a) relates temperature and ln(KEq) via

where -1·45 is an average value of {Delta}Vrxn3a (J/bar), and R = 8·314 J/mol K. Propagation of uncertainties in P (±1000 bars), {Delta}V (1%), {Delta}H, {Delta}S, and ln(KEq) results in temperature uncertainties of roughly ±20–30°C for all samples. However, these temperature uncertainties were propagated using typical electron microprobe analytical uncertainties (±1 mol % for major components, ±0·1% for YAG), and application of more accurate and/or precise analytical tools (LA-ICP-MS, ion probe) would reduce the propagated temperature uncertainty considerably.

Another potential source of error lies in assumptions of fluid composition. The calibration presented here assumes a pure H2O fluid, but other components (CO2, F, Cl) are likely to be present to some extent. However, the amount of fluid involved in reaction (3a) is small, and errors in estimation of fluid composition affect the calculated temperature only to a small degree; assumption of a pure H2O fluid where the true fluid composition is results in a temperature error of only ±2°C, an order of magnitude less than the precision associated with compositional uncertainties. In addition, isopleths of KEq in PT space (Fig. 12) are virtually linear above low confining pressures, as a result of the small amount of fluid evolved in reaction (3a).



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Fig. 12. PT plot contoured with isopleths of ln(KEq) for reaction (3a). Reaction (3a) evolves very little fluid on a molar basis, and the resulting isopleths are virtually linear except at very low (P < 500 bars) pressures. dP/dT of ln(KEq) varies from ~345 to 425 bars/°C over the PT range studied.

 

Application of the YAG–monazite thermometer
The application of the YAG–monazite thermometer to a sample with multistage monazite growth history is presented for sample BF-58, a staurolite-zone schist from north of Bellows Falls, VT, USA. The sample contains garnet discontinuously zoned in yttrium (Fig. 13a), with core composition of XYAG = 0·0045 (~2450 ppm Y) and rim composition of XYAG = 0·00012 (68 ppm Y). Monazite is bimodally zoned in yttrium (Fig. 13b and c) with cores of and rims of . Matrix plagioclase composition averages An6–7, and apatite inclusions in garnet have XOH-Ap = 0·33, in contrast to matrix apatite (XOH-Ap = 0·11).



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Fig. 13. Yttrium distribution maps of garnet (a) and matrix monazite (b, c) in staurolite-zone sample BF-58. Garnet contains Y-enriched (~2450 ppm) core and Y-poor (~65 ppm) rim. Matrix monazites are also discontinuously zoned in Y (~1·5 wt % Y2O3 core, ~0·7 wt % Y2O3 rim). Monazite ‘1’ grew in the assemblage Grt + Bt + Chl + Xno, whereas monazite ‘2’ grew in the assemblage Grt + Bt + St ± Chl (xenotime-absent). YAG–monazite thermometry pairing garnet and monazite ‘1’ with apatite included in garnet (XOHAp = 0·33) yields a low-garnet-zone temperature estimate (463 ± 20°C); garnet + monazite ‘2’ paired with matrix apatite (garnet (XOHAp = 0·10) yields a high-garnet-zone or staurolite-zone temperature estimate (541 ± 20°C).

 
Mass balance considerations and Gibbs method modeling (Pyle & Spear, 2000bGo) reveal that during prograde metamorphism of pelites, xenotime-bearing assemblages experience monazite growth and xenotime consumption simultaneous with Chl + Qtz = Grt + Fl. Upon loss of xenotime from the mineral assemblage, monazite is consumed during further garnet growth. At the staurolite isograd (Grt + Chl = St + Bt), a second episode of monazite growth is initiated (along with xenotime if sufficient Y is present), and monazite continues to grow along with garnet during the divariant (in KFMASH) Grt–Bt–St reaction (St + Ms = Grt + Bt). Thus, garnet cores are interpreted to be in equilibrium with high-Y monazite in an early Y-rich (xenotime-bearing?) assemblage. The garnet rims are interpreted to be in equilibrium with low-Y monazite rims, representing the xenotime-absent, post-staurolite isograd reaction assemblage. Apatite inclusions in garnet are paired with the early (garnet core–monazite core) assemblage, and matrix apatite with the rims of garnet and monazite. Assuming a value of , and plagioclase composition of An7, application of the YAG–monazite thermometer yields a garnet core temperature estimate of 463 ± 20°C, and a garnet-rim (staurolite zone) temperature estimate of 541 ± 20°C (both at P = 4 kbar).

These temperature estimates agree well with other thermometry estimates from these rocks (Spear et al., 1990Go), but, more importantly, demonstrate that garnet and monazite maintain compositional equilibrium even as garnet fractionation drastically changes the effective Y bulk composition of the sample. The change in composition between included and matrix apatite indicates that pelitic apatite also evolves compositionally during prograde metamorphism; pairing of included apatite (XOH = 0·33) with rim garnet and monazite introduces variation in temperature estimation of the same order as the propagated T uncertainty (i.e. ± 16°C).


    CONCLUSIONS
 TOP
 ABSTRACT
 INTRODUCTION
 SAMPLE AND ANALYTICAL PROCEDURES
 RESULTS
 CONCLUSIONS
 APPENDIX: MOLE FRACTION...
 REFERENCES
 
Monazite compositional zoning records multiple reaction events in a rock. This study demonstrates that monazite is not an inert temporal marker, but rather participates in reactions involving both accessory and major phases. The textural and compositional evidence presented in this paper shows that monazite composition is, in part, controlled by the major-phase mineral assemblage, and, hence, the reactions that produce and consume major phases.

Throughout a prograde metamorphic sequence, monazite approaches compositional equilibrium with both accessory phases (e.g. xenotime) and trace components of major phases (e.g. YAG in garnet), as shown by (1) consistency of elemental partitioning, and (2) systematic behavior of the equilibrium constant in coupled major-accessory phase net-transfer reactions. This demonstration of a close approach to compositional equilibrium has applications for both accessory-phase only geothermometry, and major phase–accessory phase geothermometry.

The importance of the detailed textural analysis combined with element distribution maps in a study such as this cannot be overstated. Selection of ‘equilibrium’ pairs of minerals requires careful investigation, and element distribution maps are required to reveal the complexity of a sample’s reaction history. Methods outlined above can be used to identify mineral pairs that represent part of an equilibrium mineral assemblage. Correlation of monazite growth with major phase growth and PT path allows the dating of specific points along a PT path, and allows for calculation of heating and loading rates.


    APPENDIX: MOLE FRACTION CALCULATIONS
 TOP
 ABSTRACT
 INTRODUCTION
 SAMPLE AND ANALYTICAL PROCEDURES
 RESULTS
 CONCLUSIONS
 APPENDIX: MOLE FRACTION...
 REFERENCES
 
The mole fractions for components in monazite and xenotime were calculated with the following equations.

Mole fraction AiPO4, where Ai = La, Ce, Sm, Pr, Nd, Gd, Dy, Yb, Er, Ho, Y:

Mole fraction brabantite (brb) [where brabantite formula is Ca(Th,U,Pb)(PO4)2] (note that Pb is included with U and Th, because it is assumed that all Pb is radiogenic):

Mole fraction huttonite (hut) [where huttonite formula is (Th,U,Pb)SiO4] (note that Pb is included with U and Th, because it is assumed that all Pb is radiogenic):

where D = [La + Ce + Sm + Pr + Nd + Gd + Dy + Yb + Er + Ho + Y + (2Ca) + (Th + U + Pb – Ca)]



    ACKNOWLEDGEMENTS
 
We thank David A. Wark and Kiera Becker for analytical support and maintenance of the JEOL 733 Superprobe at Rensselaer Polytechnic Institute. Ingo Horn and Jarek Labziewicz are also thanked for their assistance with LA-ICP-MS analyses and data reduction at the Department of Earth and Planetary Sciences, Harvard University. This study was funded by NSF grants EAR-9706463 and EAR-9903036 to F.S.S., and EAR-9711088 and EAR-9726058 to R.L.R. and W.F.M. Constructive, in-depth reviews by Gavin Foster, Jean-Marc Montel and Randy Parrish significantly improved the final version. Simon Harley is also thanked for his editorial handling of the manuscript.


    FOOTNOTES
 
*Corresponding author. Telephone: (518) 276-4899. Fax: (518) 276-6680. E-mail: pylej{at}rpi.edu Back

{dagger}Present address: Department of Geology, University of Maryland, College Park, MD 20742, USA. Back


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 INTRODUCTION
 SAMPLE AND ANALYTICAL PROCEDURES
 RESULTS
 CONCLUSIONS
 APPENDIX: MOLE FRACTION...
 REFERENCES
 
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