Journal of Petrology Advance Access originally published online on August 27, 2004
Journal of Petrology 2004 45(10):2101-2132; doi:10.1093/petrology/egh049
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Journal of Petrology 45(10) © Oxford University Press 2004; all rights reserved
Crystal Size Distribution (CSD) and Textural Evolution of Accessory Apatite, Titanite and Allanite during Four Stages of Metamorphism: an Example from the Moine Supergroup, Scotland
MINERALOGISCHES INSTITUT DER UNIVERSTITÄT WÜRZBURG, AM HUBLAND, D-97074 WÜRZBURG, GERMANY
RECEIVED MARCH 20, 2003; ACCEPTED JUNE 10, 2004
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONSUMMARY AND CONCLUSIONSAPPENDIX A: RESULTS OF...REFERENCES |
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Crystal size distributions (CSD) and shapes of accessory apatite, titanite and allanite are investigated in three texturally distinct garnet zones (Z1–Z3) and in the matrix (Z4) of a garnet–epidote–biotite gneiss from the Moine Supergroup. Additionally, textural relationships and interactions between the accessory minerals and surrounding rock-forming minerals are considered, results of numerical CSD modelling are presented, and geochronological and geological consequences of the inferred CSD evolutions are discussed. Textures and CSDs indicate that the accessory minerals were in, or near, a stage of nucleation and initial growth immediately prior to garnet Z1 overgrowth, and formed within less than 20 000 years, either by a size-independent or size-dependent growth mechanism. Subsequently, the CSDs were modified by different growth mechanisms, as supported by several parameters including CSDs, grain numbers, grain sizes, specific volumes and others. The apatite CSD evolution from Z1 to Z4 is consistent with open-system LPE (Law of Proportionate Effects) growth accompanied and followed by supply controlled random ripening, whereas transformation of the original titanite CSD is more consistent with Ostwald ripening, temporarily accompanied by positive or negative McCabe growth. The allanite CSDs also point to Ostwald ripening between Z3 and Z4. The textural observations indicate that the growth evolution of the accessory phases was influenced by mineral reactions with surrounding rock-forming minerals, as well as by deformation and matrix coarsening, in a manner similar to that found in more simple ceramic systems. The observed textures require a successive temperature rise throughout the tectono-metamorphic evolution of the investigated rock, in agreement with existing P–T data. Fast nucleation and initial growth of the accessory minerals during Z1 was perhaps initiated by contact metamorphism, whereas subsequent growth and annealing (Z2–Z4) result from regional metamorphic events.
KEY WORDS: apatite; titanite; allanite; CSD; Moine Supergroup; textures; kinetics
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONSUMMARY AND CONCLUSIONSAPPENDIX A: RESULTS OF...REFERENCES |
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Relatively little attention has been paid by geologists to unravelling the contemporaneous textural evolution of accessory phases (ACP) and associated rock-forming minerals (RFM) in metamorphic rocks. However, such information is important for the correct interpretation of isotope data (Sm–Nd, U–Pb, etc.) used to constrain the timing of metamorphic and/or polymetamorphic events (Ayers et al., 1999
; Romer & Rötzler, 2001), of geochemical patterns in crustal melts (Watson et al., 1989; Ayers & Watson, 1991; Ayers et al., 1999), and for P–T estimates involving ACPs and related RFMs (e.g. Heinrich et al., 1997; Pyle & Spear, 1999). For all these applications, the following three questions are of great interest. (1) When was an ACP formed in respect to other ACPs or RFMs? (2) How was it formed? (3) What happens to it during the later tectono-metamorphic evolution(s)? Point (1) comprises two general problems: was the ACP formed within the metamorphic rock or was it inherited (e.g. from a metasedimentary protolith)? How is its nucleation and growth related to the evolution of the surrounding RFMs and to other ACPs? Point (2) comprises thermodynamic and kinetic parameters that control nucleation and growth (e.g. Walther & Wood, 1984; Carlson, 1989, 1999; Eberl et al., 1998; Kile et al., 2000; Kile & Eberl, 2003). Point (3) deals with the problems of chemical and mechanical modifications after nucleation and initial growth of the ACPs; for example, as a result of subsequent reactions, deformation, recrystallization, diffusion and annealing (e.g. Cashman & Ferry, 1988; Watson et al., 1989; Eberl et al., 1998, 2002; Ayers et al., 1999, 2003).
Commonly, ACPs in metamorphic rocks, together with their associated RFMs, represent end products, which result from a series of chemical and mechanical processes (e.g. Cashman & Ferry, 1988). Thus, the interpretation of their compositions and textures is difficult and commonly ambiguous. However, as shown in this study, some metamorphic rocks preserve several stages of the textural evolution of ACPs and, thus, can help to clarify our understanding of the complex chemical and textural interactions between ACPs and RFMs during the tectono-metamorphic history, and of the growth mechanisms that the ACPs underwent.
For this study, I selected a garnet–epidote–biotite gneiss sample from the Moine Supergroup, whose tectono-metamorphic evolution was previously well constrained (Zeh & Millar, 2001). This sample contains abundant accessory apatite, titanite and allanite in four distinct textural domains and subdomains. Crystal shapes and textures of all three accessory minerals in the respective domains are quantified by means of length and width measurements and by estimation of their crystal size distributions (CSD). These data are used to derive information about (1) original conditions during nucleation and initial growth of the ACPs, and (2) subsequent processes, such as chemical reactions, mechanical processes and annealing, which caused a modification of the initial CSDs. Finally, I will test whether or not the observed textures conform to a regional and/or a contact metamorphic overprint. In fact, such a discrimination has previously been suggested by Cashman & Ferry (1988), who investigated RFM, magnetite and titanite from contact and regional metamorphic rocks, employing a CSD theory, which was based on the assumption that the observed CSDs result from nucleation and size-independent growth (here CSDi theory) followed by Ostwald ripening according to the LSW theory (Lifshitz & Slyozov, 1961; Wagner, 1961). The CSDi theory was initially suggested to explain crystallization in chemical engineering (e.g. Randolph & Larson, 1971) and introduced into geology by Marsh (1988). However, it was recently challenged by Eberl et al. (1998, 2002), who suggested that most CSDs observed in nature result from size-dependent growth mechanisms (here CSDd theory), following the Law of Proportionate Effects (LPE), and result in different kinetic interpretations of CSDs with respect to the CSDi theory (Eberl et al., 2002). Here, both theories are employed and compared, to explain the CSD evolution of the investigated ACPs. So far, no systematic CSD studies of accessory apatite, titanite and allanite from complex metamorphic rocks have been published.
Sample description
The investigated garnet–epidote–biotite gneiss sample was collected from the Glen Doe area in the Glenfinnan formation of the Moine Supergroup. A detailed description of the gneiss sample, comprising all rock-forming minerals, their compositions, zonations and relations to tectonic processes, has been given by Zeh & Millar (2001). Here only key observations important for the interpretation of the accessory textures will be repeated (Fig. 1a–d).
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Rock-forming minerals
Garnet. The gneiss sample contains sparse large and abundant small garnets within a layered matrix comprising alternating bands of biotite–epidote–quartz and plagioclase–quartz, which locally contain centimetre-scale isoclinal rootless folds. Four garnet types (A–D) can be distinguished [see Fig. 1a and b, and Zeh & Millar (2001
, fig. 6)]. Garnet type A is c. 3 cm in diameter and contains four zones (Z1–Z4); type B is c. 0·7 cm in diameter and has three zones (Z2–Z4); type C is c. 0·5 cm in diameter and has two zones (Z3 and Z4); type D is up to 0·1 cm in diameter and has one zone (Z4). The transition between the garnet zones is well defined by marked changes in the chemical zonation (Fig. 1c), the orientation of mineral inclusions and, as shown in this study, the size and number of accessory minerals.
Garnet zone Z1 forms the euhedral core of garnet A (Fig. 1a), which is c. 2 cm in diameter and chemically nearly unzoned (Fig. 1c). It contains abundant inclusions of randomly oriented quartz grains and apatite needles (Figs 2a, 3a and e), which indicate garnet growth under static conditions. In contrast, garnet zone Z2 formed under pure shear deformation (D1), leading to the formation of three distinct garnet subdomains (Z2a, b, c). Domain Z2a is a low-strain domain, which occurs on two opposite sides (Ls1 in Fig. 1a). It contains abundant quartz inclusions, which are larger than those enclosed by zone Z1 (Fig. 2a). These inclusions are randomly oriented at the direct contact with zone Z1, but form trails oblique to the garnet Z1 surface and toward the rim of domain Z2a. In contrast to Z2a, inclusions in the high-strain domains Z2b and c are parallel to the surface of Z1 ([Fig. 3b and g; and Zeh & Millar (2001, fig. 3a)]. Domain Z2b forms the inner zone in direct contact with the euhedral garnet zone Z1 and contains abundant ilmenite grains, whereas Z2c grew later and is ilmenite-free (Fig. 1d). In contrast to Z2a, domains Z2b and c contain only a few quartz inclusions. A chemical profile from Z2b to Z2c rim is characterized by a continuous increase of Xalm, Xpy and Xgrs, and a decrease of Xspss, whereas the low-strain domain Z2a shows a compositional plateau (Fig. 1c). Zones Z3 and Z4 together form a narrow rim (between 0·0 and 1·0 mm in thickness) around garnets of type A, even around garnet grains that were sheared after zone Z2 growth (Zeh & Millar, 2001, fig. 6). This provides evidence for a second deformation (D2) under simple shear after Z2 formation but prior to Z3 overgrowth. During deformation, D2 sigma-shaped ‘pressure shadows’ were formed around garnets of type A, which have a c. 60° offset to the low-strain domain Ls1 (Ls2 in Fig. 1a). Under the microscope, it is not possible to distinguish zones Z3 and Z4 in garnet type A (Fig. 2a). However, this can be done for garnet type C (Figs 1b and 2b), where zone Z3 contains abundant quartz inclusions, which are generally larger than those in zone Z2a (Fig. 2b). These quartz inclusions trace a foliation (Fig. 2b), which can be related to D2. Complex embayments at the transition between garnet zone Z2 and Z3 are interpreted to result from garnet Z2 resorption prior to garnet zone Z3 overgrowth (Zeh & Millar, 2001, fig. 5). Chemically, the onset of garnet zone Z3 is well defined by an abrupt increase of Xgrs (Fig. 1c). Towards garnet zone Z4, Xgrs decreases either continuously (garnet type A) or abruptly (garnet type C) (Fig. 1c). In summary, garnet Z1 was formed under static conditions, Z2 during pure shear (D1), Z3 after a simple shear deformation (D2), and Z4 under static conditions again. Another point to note is that the garnet nucleation density increased successively from 10 to 40 and to 400 garnets/1000 cm3, during garnet zone Z1–Z3 formation (Zeh & Millar, 2001).
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Epidote. Epidote occurs in all garnet zones. Epidote in garnet zones Z1–Z3 always has allanite cores, which can also be observed in many matrix epidotes (Fig. 3i–m). Epidote enclosed by garnet zone Z1 and Z2 has pistazite components [(Xps = Fe3+/(Fe3+ + Al)] between 16 and 23 mol %. In garnet zone Z3, Xps increases more or less abruptly from 23 to 30 mol % (Zeh & Millar, 2001
). Matrix epidotes commonly show complete zonation profiles from Xps 16 to 30 mol %. Quartz textures. Quartz (c. 20 vol. %) is the third most abundant mineral in the investigated rock, after garnet (25 vol. %) and biotite (c. 25 vol. %). As shown in Fig. 2, the quartz grain size increases from zone Z1 to Z4 (matrix). Garnet zones Z1, Z2a and Z3 contain abundant aggregates of two or more quartz grains, which are separated by straight to slightly lobate boundaries and merge at 120° triple point junctions (Fig. 4a, c and d). These features in conjunction with the absence of quartz subgrains and undulatory extinction indicate that the quartz fabric preserved in all investigated garnet zones was in a state of static recrystallization prior to garnet overgrowth. In contact with garnet, quartz grains are often rounded (especially in garnet zones Z1 and Z2a; Fig. 4e), and occasionally garnet encroaches quartz–quartz grain boundaries (Fig. 4c and e). The first feature provides evidence for quartz consumption during garnet growth.
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In contrast to quartz inclusions in garnet, matrix quartz grains show sutured boundaries and have irregular shapes (Figs 2 and 3h). They are commonly subgrain-free and seldom show undulatory extinction. All these features provide evidence that the matrix quartz fabric results from secondary grain growth, a common mechanism under high-grade metamorphic conditions >700°C (Passchier & Trouw, 1996
). This temperature is slightly higher than that estimated by Zeh & Millar (2001) for garnet zone Z4 growth (c. 680°C).
Accessory minerals
Apatite. Apatite occurs in all four garnet zones and in the matrix. In garnet zone Z1, euhedral apatite needles are randomly oriented and are overgrown by garnet, quartz, titanite, and rarely by allanite + epidote inclusions (Figs 3a and e, and 4a and b). Commonly, apatite needles form individual grains. Coalescence of apatite crystals parallel to their c-axis can rarely be observed. Such grains invariably show complex terminations, which in most cases make it possible to distinguish between individual crystals. In the low-strain garnet domain Z2a, abundant apatite needles are overgrown by quartz and titanite inclusions (Figs 3f and 4c–f). These needles are randomly oriented in the centre of zone Z2a but becomes successively oriented toward the high-strain domain Z2b. Apatite needles overgrown by garnet Z2b + c are parallel to the rim of garnet Z1 (Fig. 3b). In garnet zone Z3 (garnet C), most apatite grains are either completely enclosed by garnet or occur on quartz–quartz or garnet–quartz grain boundaries (similar to Fig. 4e). Apatite inclusions completely surrounded by quartz are rare. Matrix apatite is abundant in biotite–epidote–garnet–quartz-rich domains, but is nearly absent in plagioclase–quartz-rich domains (e.g. Ls2, Fig. 1a). Matrix apatite grains are commonly intergrown with biotite, epidote, and garnet Z4, or occur on quartz–biotite boundaries (Fig. 3d). Additionally, there are abundant apatite grains, which are completely enclosed by large, irregular quartz grains. It should be noted that matrix quartz never contains tiny apatite needles, as commonly observed in garnet zone Z1, Z2 and occasionally in Z3 (Figs 2 and 3h; for explanations see below).
Titanite. Titanite occurs in all garnet zones, and shows a general increase in size from zone Z1 to Z4 + matrix. In garnet zone Z1, titanite forms lens-shaped crystals, which either occur as single grains or more commonly, form aggregates of two or three crystals (Figs 3e and 4b). Titanite is either completely enclosed by garnet or occurs along quartz–garnet or quartz–quartz boundaries (Fig. 4a–c). Only small grains are completely enclosed by quartz inclusions (Fig. 4c). In garnet zone Z1, two titanite-bearing domains can be distinguished. Domain Z1s contains numerous, very tiny titanite crystals (Fig. 3a), whereas domain Z1b contains many fewer, but larger titanite crystals (Fig. 3e). Both domains grade continuously into each other. Domain Z1b is predominant. Euhedral, lens-shaped titanite crystals were also observed in the low-strain garnet domain Z2a (Figs 3f and 4c), whereas titanite is nearly absent in the domain Z2b, which is dominated by ilmenite. Titanite in the high-strain garnet domains Z2c is commonly irregular, has anomalously large sizes, and forms complex aggregates. These titanite grains and aggregates often contain ilmenite inclusions, indicating that they formed at the expense of ilmenite (Fig. 3g). Furthermore, they invariably show subgrain patterns, indicating titanite deformation followed by recovery and recrystallization (Fig. 4f). Titanite in garnet zones Z3, Z4 and the matrix is again lens shaped. Titanites occur either enclosed by garnet or along quartz–quartz, quartz–garnet or biotite–quartz boundaries.
Allanite. Allanite occurs in all four garnet zones. In garnet zone Z1 and Z2 many allanite grains show tiny epidote rims (Fig. 3i and k), whereas allanite in zones Z3, Z4 and the matrix are, with very few exceptions (Fig. 3l), overgrown by large epidote crystals (Figs 3m and 5). The size of the surrounding epidote is independent of the allanite size (Fig. 5). Allanite not enclosed by epidote is rarely observed within the matrix (1%), as well as in garnet zones Z1–Z3 (e.g. Fig. 3l).
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P–T evolution and reaction history
Petrological investigations carried out by Zeh & Millar (2001)
provide evidence that garnet zone Z1 formed during a very slight temperature rise of at most 10°C from 550 to 560°C at 4–6 kbar. The first garnet-forming reaction was
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). Reactions that led to the formation of garnet zone Z3 and Z4 are less well constrained. Here we suggest
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, garnet zone Z3 formation took place at P–T conditions of about 640°C and 6–9 kbar, whereas Z4 was formed during heating from 640 to 680°C at 5 kbar.
Because of the absence of any geochronological data, it is unclear whether the different garnet zones were formed during a single metamorphic history or result from two or three distinct metamorphic evolutions with large time gaps between. It is speculated that garnet zone Z1 formation resulted from contact metamorphism, caused by emplacement of the nearby Ardgour granite gneiss protolith, which took place during a rifting event in the Moine Supergroup at about 870 Ma (Millar, 1999). By analogy with P–T–t investigations of Vance et al. (1998) it is presumed that garnet zone Z2 grew during crustal stacking at about 800 Ma, caused by collision during the Knoydartian orogeny. Finally, it is speculated that growth of garnet zones Z3 and Z4 took place during the Caledonian orogeny.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONSUMMARY AND CONCLUSIONSAPPENDIX A: RESULTS OF...REFERENCES |
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Grain size analysis
A prerequisite for a successful crystal size distribution (CSD) analysis is the exact knowledge of the size (Li) and number (Ni) of all grains of a mineral species in a specific rock volume (Vt,i). Commonly, it is difficult to obtain L and N of minerals in a certain rock volume, because in most cases only random sections through minerals can be measured from thin sections. Commonly, minerals are measured in 2D, e.g. in thin sections, and then the 2D information is translated into 3D by appropriate mathematical algorithms, which commonly include a large number of assumptions (for more details, see Higgins, 1994
, 2000; Peterson, 1996). Only in cases where minerals can be separated from their surrounding matrix, e.g. by dissolution of a calcite matrix (e.g. Galway & Jones, 1966; Kretz, 1966) or analysed by tomography (e.g. Denison & Carlson, 1997), can the CSD be estimated directly. Another direct method, which is among others used in this study, is to project mineral grains (ACPs) enclosed in a certain, transparent rock volume on a 2D plane (projection method). Apatite crystals in garnet zones Z1–Z3 of the investigated samples have diameters that are smaller than the thin-section thickness (0·025 mm). Thus, if the diameter is used as the size parameter (Lap; diameter of apatite needles), the CSD can be obtained directly from the thin section. Furthermore, as apatite is nearly round perpendicular to its c-axis, the shortest length will always be the diameter, irrespective of the apatite orientation. The rock volume is precisely defined by the thin-section thickness (0·025 mm) and the area from which the grains were measured (e.g. 1 mm2).
Apatite grains in zones Z1, Z2a and Z2b were analysed in garnet of type A, and those in zone Z3 in a garnet of type C (Fig. 1a and b). In zones Z1, Z2a and Z2b, the thin section was photographed with a digital camera (Leica DMRXP) with a magnification of 400x, using three focus steps for the same thin-section location. In zones Z1, Z2a and Z2b, three thin-section locations were investigated, and in zone Z3 20 locations with just two focus steps. For calibration of the digital imaging system, a micrometre scale was photographed as well. Subsequently, the digital photographs were enlarged to a size of c. 2000x, and the apatite grains were measured, using the imaging software ‘dhssolution V1.1’ produced by Dietermann & Heuser Solution GmbH. Care was taken to avoid double measurements of single grains, which pass through several focus levels. This was done by careful comparison of images photographed with different focus levels. If apatite grains showed coalescence, the diameter of the individual grains, which commonly can be observed at the termination of these grains, was measured. For CSD analyses all apatite grains, irrespective of whether they are included in garnet, quartz or titanite in the respective volumes, were measured. Apatite lengths were estimated only on single grains whose c-axes were parallel to the thin section surface.
As matrix apatite grains are much larger than the thickness of the thin section (0·025 mm), their size was estimated by a series of nine grinding steps obtained from a thick section with an original thickness of 0·5 mm and a size of 20 mm x 30 mm. After each grinding step of 0·05 mm, the surface was polished and photographed in transmitted and reflected light. The position of apatite, titanite and allanite (see below) in the series was additionally traced under the microscope, marked on the photographs, and then measured. For CSD analysis, the largest diameter of an individual apatite grain obtained by either reflected or transmitted light was used, and all apatite grains in the investigated rock volume were counted. Apatite lengths were estimated only on single grains whose c-axes were nearly parallel to the thin section surface.
For titanite, the largest diameter of individual grains was measured (Lttn; largest diameter of titanite lenses). Matrix titanite was analysed from the same thick section and with the same procedure as outlined above for apatite. Titanite grains in garnet zone Z3 were measured from two garnet grains of type C, which have diameters of about 5 mm (Figs 1b and 2). Measurement was started at a thin-section thickness of 0·25 mm (last four grinding steps). Titanites in zones Z1b and Z2a were measured in a garnet of type A (the same as used for apatite measurements). The original thickness was 0·1 mm, which was then ground in four steps to a thickness of 0·025 mm. For titanite agglomerates, care was taken to measure the length of individual grains separately. Titanite in the schlieric domain Z1s was analysed in a thin section of 0·025 mm thickness.
Allanite grains commonly show a columnar shape with three distinct axes. The a-axis is the shortest, b the intermediate, and c the longest axis. For CSD analyses, the b-axis was used (Lall = b), as it was most easy to obtain in thin and thick sections. Allanite numbers and b-axis length were measured in garnet zones Z1, Z2 and Z3 of a garnet of type A (the same as used for apatite and titanite), using a thick section with an initial thickness of 0·1 mm and four grinding steps. As mentioned above, allanite in these zones often shows epidote overgrowths. Here, only the size of the allanite inclusions was measured.
Matrix allanites of different sizes are, with very few exceptions, overgrown by euhedral epidote crystals. For size analysis, 514 euhedral epidote grains with allanite inclusions were randomly selected from a heavy mineral concentrate (Fig. 5). Because the epidote size is independent of the size of the allanite inclusions (Fig. 5, see above), the allanite grains enclosed by epidote should reflect the CSD prior to epidote overgrowth. The a-, b- and c-axis lengths were measured on all 514 allanite inclusions, to obtain information about changes of the shape during allanite growth. The number of matrix allanite grains per volume was estimated by counting all allanite grains in a thick section of 0·5 mm size (see above), the same as used for matrix apatite and titanite measurements, excluding the volumes occupied by garnet.
To obtain additional information about the grain size relationship between host quartz and texturally related ACPs, the size parameter, L, of apatite and titanite grains enclosed by quartz, and located along quartz–quartz boundaries, was measured. Furthermore, the diameter of host quartz was analysed (Fig. 4). If an ACP occurred on a grain boundary of two host quartz grains, the average diameter of both quartz grains was used.
Data processing
The CSD of apatite, titanite and allanite obtained from different rock domains is shown in number (N) vs crystal size (L) histograms in Fig. 6, which also shows the curves of the cumulative number of crystals N(L) vs L, and the lognormal fits of the measured CSDs. Related parameters such as the mean size (L'i), the natural log-based variance (ß2), the mean of the logarithms of the crystal dimension (
), and the significance levels (SL) obtained by 
2 test for each lognormal fit are presented in Tables 1 and 2. The lognormal fits and related parameters were calculated with the subprograms Lognor and ChiAnal [2 test, SL(2)], of the software package GALOPER of Eberl et al. (2000). Additionally, the CSDs are shown in population density diagrams [ln(n) vs L; Fig. 7], and in normalized frequency vs size diagrams (f/fmax vs L/L'; Fig. 8). According to Randolph & Larsen (1971) the population density n(L) is defined as
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, linear correlations in the ln(n) vs L diagrams have the function
 | (2) |
is the effective residence time. In CSDd theory, b only describes the instantaneous slope of a CSD, but cannot be used to quantify G and (see Eberl et al., 2002).
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Here, values for n° and b were obtained with the exponential function feature of EXCEL®, and are shown in Table 1. In most population density diagrams, ln(n) values of the smaller crystal size class(es) plot significantly below the linear CSD lines (Fig. 7), which is defined by the larger crystal size classes. In these cases, the smaller crystal size class(es) were excluded from the fitting procedure (Fig. 7). The resulting slopes are defined as b* and the intercepts at L = 0 as n°*. Reasons for the deviations of the smaller size classes are discussed below. As shown by Cashman & Ferry (1988)
and Marsh (1988), specific moments (mi) can be obtained from function (2), providing that the CSD in the ln(n) vs (L) diagram is log–linear. The zeroth moment (m0) gives the specific total number (i.e. Nt per unit volume) of crystals having sizes within the interval 0 to L. The first moment (m1) gives the specific total length of crystals (Lt per volume unit, interval 0 to L). The second moment (m2) gives the cumulative area (At per volume unit, interval 0 to L). Finally, the third moment (m3) gives the specific cumulative volume (Vt per volume unit, interval 0 to L). The moments m0 to m3 can be calculated from n° and b as following:
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 | (4) |
 | (5) |
 | (6) |
A and V, respectively, are needed, which convert the characteristic area (L2) or volume (L3) to the true, specific area (At,i = A,iLi 2 = A,im2) or volume (Vt,i = v,iLi3 = V,im3) of phase i. Further details have been given by Marsh (1988) and Higgins (2002a). Values for Nt and Lt are shown in Table 1. As outlined by Higgins (2002a), equation (6) can be used only for straight CSDs. For more curved CSDs, Higgins (2002a) suggested the following equation to calculate the specific total volume Vt,i of phase i:
 | (7) |
V,i is the shape factor of phase i, j is the number of the interval, ni(L'j) is the population density for size L'j, Wj is the width of the interval, and L'j is the mean size of the interval j. However, equation (7) works successfully only if the shape factor V,i is constant between zero and L = 
. If V,i itself is dependent on L, as shown below, Vt,i can be calculated as follows:
 | (8) |
V,j is the shape factor valid for the mean grain sizes of the interval j. Clearly, as a result of the mathematic manipulations during estimation of n(L) (see above), Vt,i obtained by equations (6)–(8) contains uncertainties. To obtain a more accurate estimate of Vt,i it is better to use the directly measured parameters N and L as follows:
 | (9) |
V,i with Li can be obtained, if the volumes of grains (
) with different sizes (Li) can be estimated. In this study, this is done for apatite and allanite (Fig. 9). Volumes of individual apatite, allanite and titanite grains were calculated from measured parameters as follows:
 | (10) |
 | (11) |
 | (12) |
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONSUMMARY AND CONCLUSIONSAPPENDIX A: RESULTS OF...REFERENCES |
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Apatite
In general, the mean size of apatite (L'ap) increases from zone Z1 to Z4 (matrix) from 2·0 to 81 µm, whereas the number of apatite grains (Nap) decreases significantly from 5·7 x 107 cm–3 to 1·2 x 104 cm–3 (Table 1). The distribution of Lap spreads continuously from Z1 to Z4 (Z1, 0–7·2 µm; Z2, 0–22 µm; Z3, 3–38 µm; Z4, 15–210 µm) (Figs 6 and 7). The variance (ß2) of the CSDs increases steadily from Z1 to Z3 (ß2 0·28–0·41) and remains constant from Z3 to Z4, whereas
(defined in the footnote to Table 2) increases continuously from Z1 to Z4 (: 7·44–11·1) (Fig. 6o, Table 2). The significance level obtained by 2 test is 10–20% for Z1 and Z3, and 2·5–5% for Z2b and Z4 (Table 2), indicating that the lognormal distribution of the CSDs was maintained from Z1 to Z4. One exception is represented by the CSD obtained from apatite grains occluded in garnet zone Z2a, which have a SL(2) <1%. The ß2 and values of this CSD plot significantly above the trend defined by the other CSDs (Fig. 6o). In the f/fmax vs L/L' diagram all apatite curves are left skewed and show no similarity to the steady-state profiles predicted by the LSW theory (Fig. 8a).
As shown in Fig. 9, the length/diameter ratio (l/d) of apatite decreases with increasing diameter. This causes the grain surface/volume ratio of apatite (
) to decrease significantly with increasing apatite size from c. 8 to 0·03. Furthermore, the shape factor V,ap changes with L. This change can be approximated by the formula
 | (13) |
(see above). By combining equations (9) and (13) the total specific apatite volume (Vt,ap) can be calculated. Vt,ap increases from zone Z1 to Z2a and to Z2b, from 6·5 x 109 to 2·0 x 1010 and to 2·6 x 1010 µm3/cm3, respectively, and decreases slightly to 1·5 x 1010 and 1·8 x 1010 µm3/cm3 in zone Z3 and Z4 (Fig. 10).
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As shown in the population density diagrams in Fig. 7a and b, the smallest crystal size class(es) invariably plot below the linear trend defined by the larger crystal size classes. This deviation is small in Z1 but becomes increasingly obvious from Z1 to Z4. The only exception is presented by the CSD obtained from apatite in the low-strain domain Z2a, where the smallest size class plots above the straight CSD (Fig. 7a). In general, the slope (b*) becomes shallower from Z1 to Z4 (Fig. 7a and b; Table 1), forming a CSD fan (for explanation see below).
Titanite
Similar to apatite, the average size of titanite (L'ttn) increases from 13·7 to 230 µm from zone Z1 to Z4 (matrix), whereas the number of titanite grains (Nttn) decreases significantly from 2·5 x 107 cm–3 to 4·8 x 103 cm–3 (Table 1). The distribution of Lttn spreads continuously from Z1 to Z4 (Z1, 2·5–76 µm; Z2a, 3·1–106 µm; Z3, 12·1–158 µm; Z4, 104–359 µm) (Figs 6 and 7), causing a successive flattening of the N(L) vs L curve (Fig. 6). In a further analogy to apatite, the titanite CSDs in the population density diagrams becomes successively curved, and the linear slopes (b*), derived from the larger sizes classes, become shallower from Z1 to Z4, forming a CSD fan (Fig. 7c and d; Table 1). The specific titanite volume (Vt,ttn) is nearly identical in domain Z1s (5·51 x 1010 µm3/cm3), Z1b (4·65 x 1010 µm3/cm3), and Z3 (5·10 x 1010 µm3/cm3), but is significantly lower in the domains Z2a (2·53 x 1010 µm3/cm3) and Z4 (1·11 x 1010 µm3/cm3) (Fig. 10).
In contrast to the apatite CSDs, the titanite CSDs show a decrease of ß2 from Z1 to Z4 (from 0·79 to 0·09), whereas increases from 9·1 to 12·3 (Fig. 6o). This trend is accompanied by a continuous decrease of SL(2) from >10 (Z1b, Z2) to 5–10 (Z3) and to 2·5–5 (Z4) (Table 2). The only exception is presented by the Z1s CSD, which is asymptotic and has an SL(2) <1%. It should be noted that SL(2) of the lognormal fit of the Z4 CSD is identical to that obtained from the normal distribution fit (Table 2, Fig. 6k). This indicates that the lognormal shape of the CSD is lost from Z1 to Z4 and is successively transformed into a more normal distribution (for explanation, see Discussion). This is also reflected in the f/fmax vs L/L' diagram (Fig. 8b), where the curves successively constrict, and finally approach a steady-state profile predicted for Ostwald ripening (more see below).
Allanite
Allanite CSDs were obtained from garnet zones Z1, Z2 (comprising Z2a, b and c) and from the matrix (Z4; inclusions in epidote). In zone Z3, only 28 grains could be measured. Allanite shows a slight increase of the mean size (L'all) from 18·1, to 20·0 and to 25·0 µm from zone Z1, to Z2 and to Z3, and similar size distribution spreads (Z1, 4·9–35 µm; Z2, 4·6–58 µm; Z3, 8·6–49 µm). In contrast, allanite grains enclosed by matrix epidote (Z4) have a significantly larger average size of L'all = 49 µm and a much wider size spread (5·2–129 µm). In the population density diagrams in Fig. 7e, the smallest size classes of allanite from all zones plot below the straight CSD line defined by the larger grain size classes. This effect is most pronounced for allanite grains enclosed by matrix epidote (Z4). The straight lines defined by the large size classes from zone Z1 and Z2 have nearly identical slopes and intercepts at n°*, whereas that of Z4 is shallower (Fig. 7e, Table 1).
As shown in Table 2 and Fig. 6o, ß2 increases from Z1 to Z2 (from 0·11 to 0·27) and then remains constant from Z2 to Z4, whereas is constant from Z1 to Z2 (9·7) and increases from Z2 to Z4 (from 9·7 to 10·3). The significance level [SL(2)] of the CSDs is >20% for zones Z1 and Z2, but <1% for zone Z4 (Table 2), indicating that the lognormal shape was lost between Z2 and Z4. This is also reflected in the f/fmax vs L/L' diagram in Fig. 8c, which shows that the Z1 and Z2 curves are left skewed, and the Z4 curve is right skewed (further discussed below).
The axis ratio b/a of all measured allanite grains is nearly constant (average 1·5) and independent of the grain size, whereas the axis ratio c/b decreases from c. 2·5 to 1·5 with increasing b = Lall (Fig. 9). As was the case with apatite, this means that the surface/volume ratio (
) of allanite decreases significantly with increasing allanite grain size from 0·33 to 0·05. Furthermore, the shape factor V,all changes with the grain size. The latter can be expressed by the formula
 | (14) |
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONSUMMARY AND CONCLUSIONSAPPENDIX A: RESULTS OF...REFERENCES |
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Generalities
The grain size data obtained from apatite, titanite and allanite show many similarities. In general, the grain sizes and grain size spreads of all three minerals increase successively from garnet zone Z1 to Z4, whereas the number of grains per volume unit decreases (Table 1). Furthermore, the smallest grain size classes plot, with a few exceptions, below the linear trend defined by the larger size classes in the respective population density diagrams (Fig. 7), and the slopes of the straight lines (b*) decrease successively from zone Z1 to Z4, which causes the formation of CSD fans (Fig. 7). Nevertheless, there are some important differences. The most obvious is reflected by the different evolution trends of apatite, titanite and allanite in the
–ß2 diagram (Fig. 6o). Furthermore, there are right and left skewed curves in the f/fmax vs L/L' diagrams (Fig. 8), and significant variations of the specific volumes of the ACPs from Z1 to Z4 (Fig. 10).
To explain all these features five general processes must be taken into account: (1) nucleation and initial growth, (2) open-system crystal growth, (3) ripening, as well as (4) chemical and (5) textural interactions of the respective ACPs with surrounding RFMs. To show consequences that result from processes (1), (2) and (3), numerical growth calculations were carried out with EXCEL®. A detailed description of the calculation procedures has been presented by Eberl et al. (1998, 2000), and additional information is given in Appendix A. Graphical results are presented in the Figs 11–13. For processes (1) and (2) results are shown in relative frequency (N) vs L diagrams, population density diagrams and –ß2 diagrams. For process (2) normalized f/fmax vs L/L' diagrams are additionally presented. First, the results of the theoretical calculations will be discussed, and these will then be used to interpret the observed CSDs, in combination with textural information.
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Results of theoretical calculations
Nucleation and initial growth
Nucleation and initial crystal growth generally lead to an increase of the grain number (Ni) and the specific volume (Vt,i) of an ACP with time (open-system process). However, the nucleation process can take place by different mechanisms, which can cause the formation of identical or distinct CSDs. Asymptotic CSDs in frequency vs L diagrams, e.g. titanite in domain Z1s, can result either from an exponential increase of the nucleation rate at a constant growth rate (see Randolph & Larson, 1971
; Cashman & Ferry, 1988; Marsh, 1998; mechanism A in Fig. 11a), or from a constant nucleation rate accompanied by a size-dependent growth mechanism (see Eberl et al., 2002; mechanism B in Fig. 11b). Mechanism A requires a crystal size-independent growth (CSDi theory), which can be described by McCabe's ‘
L law’ (McCabe, 1929) and simulated mathematically by
 | (15) |
 | (16) |
j is a random number between zero and one, which is newly defined for each new growth step [for more details see Eberl et al. (1998)].
In addition to asymptotic curves, lognormal CSDs can be established if the nucleation rate decays during LPE growth (mechanism C in Fig. 11e), and may be caused by a decrease of supersaturation at the end of the nucleation process. Similarly curved CSDs, however, can also be formed when an exponential nucleation rate is decaying during constant growth (see Marsh, 1998, fig. 4).
Although mechanisms A and B both lead to the formation of finally asymptotic curves, the evolution of the population density is different, as illustrated in Fig. 11b and d. Mechanism A causes a parallel shift of the straight CSD line in the ln(n) vs L diagram (b is constant, n° increases, Appendix A), whereas mechanism B lead to an anticlockwise rotation of the straight CSD line (b decreases, n° decreases slightly), resulting in the formation of a CSD fan (Fig. 11d, Appendix A). Similar slope rotation and CSD fan formation results from mechanism C (Fig. 11f). However, in contrast to mechanism B, the smaller size class(es) of the CSDs formed by mechanism C plot below the straight line defined by the larger size classes. Furthermore, the slope of the evolution curve in the –ß2 diagram for mechanism C is shallower than those for mechanism B (Fig. 11a, c and e).
Open-system crystal growth
Once nucleation and initial growth ceased, later material supply will cause the growth of the previously formed crystals. Material supply can result from mineral reactions either within the considered rock volume, causing the production of a respective ACP at the expense of other minerals, or outside the volume, perhaps as a result of material supply by fluid convection. Typical features of open-system crystal growth are that the crystal number (Ni) will be constant, whereas the total volume (Vt,i) of the considered ACP increases (Appendix A). In general, open-system crystal growth can be maintained by several distinct processes. It can occur either by size-independent McCabe growth [equation (15)], or by size-dependent LPE growth [equation (16)]; either surface or supply controlled. In case of surface controlled LPE growth, material supply is faster than needed for crystal growth, whereas during supply controlled LPE growth the amount of nutrients during growth is less than needed for free crystal growth [for mathematical formulations of these processes, see Eberl et al. (1998)].
Figure 12 shows consequences of the different growth mechanisms during a CSD evolution. It should be noted that all calculations were carried out assuming that the CSDs were lognormal prior to open-system growth, and may be due to nucleation and initial growth according to mechanism C. In the case of McCabe growth (mechanism D, Fig. 12a and b) the lognormality of the original CSD disappears during growth [SL(2) decreases from >20% to <1%; Appendix A], whereas the original CSD spread is maintained. Furthermore, ß2 decreases exponentially with increase (Fig. 12a), and the curves in the population density diagram shift nearly parallel (b* remains nearly constant, whereas n°* increases) (Fig. 12b, Appendix A).
In contrast to mechanism D, the lognormality of the original CSD is maintained during supply controlled LPE growth (mechanism E, Fig. 12c and d) [SL(2) >20%; Appendix A], the CSD spread increases, and ß2 remains nearly constant during a increase (Fig. 12c). Furthermore, n°* and b* decrease, causing the formation of a CSD fan (Appendix A). Similar features also result from surface controlled LPE growth (mechanism F; Fig. 12e and f) with the difference that ß2 increases linearly with (Fig. 12e).
Ripening
Once nucleation and/or open-system growth ceased, perhaps because of the exhaustion of a certain element in the reservoir (e.g. depletion of phosphate needed for apatite growth), no new crystals will be formed and the existing populations may continue to grow so as to minimize their surface free energy. This can occur either by coarsening of minerals in a monomineralic rock (e.g. quartz in a quartzite; Joesten, 1995) or by a ripening process of ACPs. General features, which indicate a ripening process, are that the specific volume of a mineral phase will remain constant, whereas the grain number decreases. In general two ripening processes can be distinguished: (1) Ostwald ripening (Ostwald, 1900), the consequences of which can be described by the LSW theory (Lifshitz & Slyozov, 1961; Wagner, 1961); (2) kinetic ripening (Söhel & Garside, 1992; Eberl et al., 1998).
During Ostwald ripening dispersed crystals below a critical radius (rc) will be consumed, whereas grains larger than rc continue to grow at the expense of the smaller ones. rc is not a constant but increases with time (see Baronnet, 1982, fig. 3). This is because the system will not be in a stable thermodynamic equilibrium until all material of a certain mineral is gathered in a single crystal, or at least until all grains in a certain rock domain have approximately the same size. The change of rc with time is related by the formula
 | (17) |
 | (18) |
 | (19) |
, Joesten (1995) and Eberl et al. (1998). According to the LSW theory, Ostwald ripening for n = 2 and n = 3 will lead to the formation of typical steady-state curves in the f/fmax vs L/L' diagram, as shown in Figs 8 and 13.
Figure 13a–c and Appendix A show modelling results for diffusion controlled Ostwald ripening (mechanism G), which starts for the assumption that the original CSD was lognormal. The results show that the CSD spreads, and that the lognormal CSD shape disappears during ripening [SL(2) decreases from >20% to <1%; Appendix A]. This is because the CSD curves become symmetrically and finally right skewed in the frequency vs L diagram (Fig. 13a). Furthermore, ß2 decreases with increase during Ostwald ripening, and in the population density diagram a CSD fan is established (n°* and b* decrease) with smaller size classes falling below the straight CSD line defined by the slope b* (Fig. 13b). In the f/fmax vs L/L' diagram the curves successively constrict and finally approach the theoretically predicted LSW steady-state profile for n = 3. At this point it is interesting to note that a transitional CSD shape is established during the CSD evolution, which is similar to the steady-state profile for n = 2 (Fig. 13c).
During kinetic ripening dissolution of grains is not a function of crystal size, but depends on other properties including crystal defect density, chemical composition, structural heterogeneity, strain, or environmental heterogeneity. A special form of kinetic ripening, supply controlled random ripening, is simulated here using the procedure as outlined by Eberl et al. (1998). The results of random ripening modelling are shown in Fig. 13d–f (mechanism H) and in Appendix A. As in the case of Ostwald ripening, random ripening causes an increase of the grain size spread, a successive decrease of n°* and b*, and the formation of a CSD fan (Fig. 13e). In contrast to Ostwald ripening, the lognormal shape is maintained [SL(2) >20%], and ß2 remains constant during increase (Appendix A). Furthermore, a left skewed steady-state profile is established in the f/fmax vs L/L' diagram (Fig. 13f). Another important point is that for a similar change of the CSD a much larger grain volume is recycled (dissolved and reprecipitated) during random ripening than during Ostwald ripening (compare Fig. 13b and e).
In summary, the modelling results indicate that different growth mechanisms can cause the formation of asymptotic, lognormal or non-lognormal CSDs, and can lead to the formation of similar or different CSD arrays in population density diagrams. They show that CSD fans including curved CSDs do not necessarily result from a ripening process as suggested by Higgins (1998, 2002b), but can also be formed during nucleation and size-dependent growth (mechanisms B and C) or open-system LPE growth (mechanisms E and F).
The results also show that the different growth mechanisms have typical fingerprints, which are reflected by the evolution trends of the parameters Li, Vt,i, Ni, , ß2, and supported by SL(2) (Appendix A). In principle, the modelling results are very useful in explaining most of the observed CSDs (Figs 6–8; see below). However, they can give no explanation for the observation that the smallest size class for apatite Z2a in the population density diagram plots above the straight line defined by the larger size classes (Fig. 7a). Furthermore, they do not take into account that the considered metamorphic rock underwent a complex chemical and mechanical evolution, which may have caused variations in Vt,i and Ni, independent of nucleation and growth mechanisms. Thus, before a final interpretation of the observed CSDs can be given, chemical and textural interactions between ACPs and RFMs must also be considered.
Chemical interactions between ACPs and RFMs
As shown in Fig. 10, the specific volumes of apatite (Vt,ap), titanite (Vt,ttn) and allanite (Vt,all) are not constant from zone Z1 to Z4 but show significant variations, which cannot be explained by errors in the grain analysis in the respective domains. To interpret these differences, we have to find answers to the following three questions: were the ACPs (1) homogeneously distributed in the investigated rock prior to garnet Z1 formation, (2) consumed or produced by reactions after nucleation and initial growth, and (3) conserved in the investigated rock volume during the metamorphic history (closed or open system)?
Homogeneous distribution of apatite, titanite and allanite prior to garnet Z1 growth is supported by the observation that all three minerals show identical sizes, orientation and amounts in all type A garnet grains within the investigated rock sample of about 1000 cm3. Apatite, titanite and allanite grains counted from zone Z1 of three garnet porphyroblasts gave nearly identical values (Nap = 5·3 x 107, 5·5 x 107 and 5·7 x 107 cm–3; Nttn = 2·3 x 107, 2·5 x 107 and 2·7 x 107 cm–3; Nall = 4·4 x 104, 3·8 x 104 and 5·1 x 104 cm–3).
A closed system with respect to apatite is very likely, as apatite is less soluble in supercritical fluids. According to Ayers & Watson (1991), the solubility of apatite in pure H2O is less than 0·4 wt %, independent of P, T, XH2O and MNaCl (the molality of NaCl), and dissolved silicate concentrations have little effect on apatite solubility. The solubility of apatite increases significantly only in fluids with low pH. However, if apatite has interacted with an acid solution, I would expect to find strongly rounded or even irregular apatite grains. Instead, apatite grains in all investigated domains invariably show columnar shapes and frequently show sharp edges (Fig. 3a–d). Thus, apatite transfer from or to the investigated rock volume seems to be less likely. Unfortunately, no experimental solubility data exist for titanite and allanite. Thus, an effect on the specific volumes of these minerals as a result of mass transfer from or to the investigated rock volume cannot completely be excluded.
Taking these points into account, the significant increase of Vt,ap from zone Z1 to Z2–Z4 from 6·5 x 109 to (1·5–2·6) x 1010 µm/cm3 can be interpreted to result either from compaction of the considered rock volume, initiated by the dehydration reaction (R1), and/or from material supply owing to reactions among the RFMs in the rock volume. Reaction (R1) caused abundant H2O previously enclosed by chlorite and epidote to be released, and subsequently expelled from the rock volume. As shown by Zeh & Millar (2001), c. 10 vol. % chlorite and c. 10 vol. % epidote were consumed during garnet Z1 and Z2 growth, releasing c. 6 vol. % H2O. Because of its low solubility in H2O, apatite remained in the original rock volume and, thus, was relatively enriched during garnet zone Z1 and Z2 growth. However, the c. 6 vol. % H2O release cannot account for the c. 100 vol. % apatite increase. Thus, it is very likely that new apatite was formed between Z1 and Z2 caused by mineral reactions. However, the source for the additionally needed phosporus is not clear so far. The much higher Vt,ap in the high-strain domain Z2b (2·6 x 1010 µm3/cm3) in contrast to the low-strain domain Z2a (2·0 x 1010 µm3/cm3) can be explained by differential compaction. The rock volume around the high-strain domain Z2b was more compacted during deformation D1 than that of the low-strain domain Z2a. This is also supported by the fact that Nap in domain Z2b is much higher than in domain Z2a (Table 1). Variation of Vt,ap within garnet zones Z2a, Z3 and Z4 probably reflects a heterogeneous apatite distribution, which perhaps became increasingly significant during the progressive tectono-metamorphic evolution, influenced by deformation and mineral segregation. For example, matrix apatite is concentrated in biotite–epidote–garnet-rich domains, but nearly absent in plagioclase–quartz domains (e.g. Ls2 in Fig. 1a). The relatively constant volume from Z2 to Z4 supports the conclusion that the CSD evolution was finally controlled by ripening.
In clear contrast to apatite, the specific volume of titanite (Vt,ttn) generally decreases from zone Z1 to Z4 (from 5·51 x 1010 to 1·11 x 1010 µm3/cm3), with the exception of zone Z3 (Fig. 10, Table 1). This decrease can be explained by chemical interactions with biotite, which incorporates successively higher titanium amounts with rising metamorphic temperatures (from 550°C for Z1, to 680°C for Z4). The amount of biotite in the investigated gneiss sample was c. 25–30 vol. % throughout the metamorphic evolution (Zeh & Millar, 2001). Matrix biotite now contains up to 3·6 wt % TiO2. In garnet zones Z2a and Z4 (matrix) the decrease of Vt,ttn was probably enhanced by the additional formation of ilmenite, which occurs in both domains together with titanite. In garnet zone Z2b, titanite was quantitatively consumed at the expense of ilmenite as constrained by the thin-section observations (see above). However, there is no conclusive evidence that this happens to all titanite grains in the surrounding matrix. If this was the case, titanite now observed in garnet zones Z3 and Z4 must have been newly nucleated, after garnet Z2b growth ceased. The positive ‘anomaly’ of the specific titanite volume in zone Z3 (Fig. 9) reflects the situation that no ilmenite was present during garnet Z3 formation. Thus, the volume data for titanite in combination with the thin-section observations indicate titanite production during Z1 and Z3, and consumption during Z2 and Z4.
The specific allanite volume (Vt,all) shows slight variations from Z1 to Z4. The barely higher allanite volume in zone Z2 (6·67 x 108 µm3/cm3) relative to Z1 (5·41 x 108 µm3/cm3) could be explained by compaction, as outlined above for apatite, whereas the lower specific volume of allanite enclosed in matrix epidote Z4 (2·50 x 108 µm3/cm3) points to allanite consumption after garnet Z2 growth.
Textural interactions between ACPs and host minerals
Generalities
The CSDs and textural features indicate that apatite, titanite and allanite enclosed in the different garnet domains reflect instantaneous moments of their growth evolutions. This implies that ACPs, once overgrown by garnet, were excluded from further material transfer, but that ACPs in the surrounding matrix must have been able to anneal or react prior to overgrowth by the next garnet generation, and underwent material exchange with other ACPs and RFMs. In this context it must be emphasized that allanite grains in all domains (Z1–Z4) are enclosed by epidote, and thus should not have taken part in further reactions or coarsening processes (Figs 3i–m and 5; see below for more information).
As shown by theory and experiments, effective material transfer between accessory phases in polycrystalline rocks can occur only if the accessory minerals are located on grain boundaries of host minerals (Watson et al., 1989; Ayers et al., 1999). This is because grain-boundary diffusion that allows material transfer is much faster than volume diffusion through a crystal structure. In the presence of aqueous fluids, which commonly occur in metapelitic rocks as a result of dehydration reactions [e.g. reaction (R1)], diffusion along grain boundaries will be greatly enhanced, especially if the fluid film between the grains becomes wider than 10 Å (Walther & Wood, 1984). However, whether an ACP will remain on the grain boundary of host minerals (e.g. quartz) or be occluded during grain boundary migration (GBM), depends on the relative size difference between an ACP and the surrounding host mineral [see theoretical considerations of Watson et al. (1989)]. As large accessory minerals have lower surface free energies than smaller ones, they are predestined to occur on host grain boundaries, whereas small grains are more susceptible to overgrowth. If we now consider that the host minerals also undergo coarsening with time, as is generally the case in ceramics and geological systems, the host interfacial energy will decrease. In these circumstances, an accessory phase can remain on the host grain boundary only if it immobilizes the grain boundary, e.g. by ‘pinning’, or if it recrystallizes fast enough to maintain its position on the moving grain boundary. If no reaction occurs, coarsening of an ACP can be achieved only if another crystal of the same phase is dissolved at the same time, and the dissolved material is transferred to the growing crystal (ripening). In general, dissolution and transport is facilitated by an aqueous fluid phase. Thus, the dissolution–reprecipitation progress depends on the mobility of the accessory mineral. An ACP has a high mobility if it is highly soluble in the fluid and its dissolved components have high aqueous diffusivities [for more details see Ayers et al. (1999)].
The theoretical outline mentioned above is well constrained by coarsening experiments on ceramics (e.g. Rahaman, 1995) and on geological materials (e.g. Watson et al., 1989; Ayers et al., 1999), carried out using simple systems, which commonly contained one host (e.g. quartz or Al2O3) and one accessory phase of more or less equidimensional shape (e.g. zircon, monazite or MgO). In contrast, the investigated metamorphic rock is much more complex. It contains at least 10 phases (Fig. 1c), was affected by several reactions, and underwent two distinct deformation events (see above), processes not considered in the coarsening experiments. Furthermore, the apatite shape in zones Z1–Z3 is not equidimensional but strongly columnar. Clearly, because of the complexity in the investigated rocks, not all interactions between all minerals can be taken into account.
Apatite– and titanite–host quartz interactions
As shown in Fig. 14, small apatite and titanite grains form inclusions in host quartz (Apin and Ttnin), whereas larger apatite and titanite grains either occur on or cross over host quartz boundaries (Apon and Ttnon) (Fig. 4). The lines that separate Apin/Apon and Ttnin/Ttnon, respectively, are positively correlated with the size of host quartz, in agreement with theoretical considerations and experiments (see above). The trend line is linear from zone Z1 to Z3 but shows a significant kink toward garnet zone Z4 (matrix), which is best seen for the apatite–host quartz relationships (Fig. 14a). This kink is assumed to result from the change of the quartz growth mechanism, from GBM in zones Z1–Z3, to secondary grain growth in the matrix. The latter mechanism had the result that even very large apatite grains were completely enclosed by quartz, an effect rarely seen for titanite. The ACPs–host quartz relationships clearly indicate that titanite and apatite coarsened together with their host minerals, and that large ACPs were able to remain on the host grain boundaries, whereas smaller grains were overgrown (e.g. Fig. 4c–e).
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Nevertheless, the ACP–host quartz relationships shown in Fig. 14 are very static, and give no explanation for another observation, showing that the minimum size of apatite and titanite inclusions in host quartz generally increases from zone Z1 to Z4, e.g. apatite from c. 0·1 to 20 µm, respectively. This observation indicates that matrix quartz must have been able to ‘release’ previously enclosed apatite grains between the garnet growth stages. This process can be related to deformation D1 and D2, which caused the destruction of previously formed host quartz fabrics and allowed fluids to dissolve apatite and titanite grains formerly enclosed by quartz GBM.
The only domain where quartz destruction did not obviously happen is the low-strain garnet domain Z2a, where quartz contains abundant apatite needles with sizes typical for garnet zone Z1 (Fig. 4c–e). This situation is well reflected by the apatite CSD obtained from domain Z2a, where the smallest apatite size class plots above the straight line defined by the larger size classes (Fig. 7a). This CSD kink is interpreted to result from ‘textural mixing’, caused by preservation of grains related to a previous evolution stage (apatite inclusions in quartz) together with grains that changed their shapes afterwards (apatite grains on quartz grain boundaries). Such an interpretation conforms with that of Marsh (1988, 1998) for mixing in open magmatic systems.
Allanite–epidote interactions
In contrast to apatite and titanite, which show relatively steady grain growth, more or less influenced by reactions, deformation and interactions with surrounding RFM (Figs 6 and 7), the grain size evolution of allanite is different in some details. The nearly identical Nall, Vall, size spreads and CSDs obtained from garnet zones Z1, Z2 and Z3 (Fig. 7, Table 1) indicate that allanite growth was obviously prevented during garnet zone Z1–Z3 formation. The most straightforward explanation would be that allanite in all three domains was overgrown by epidote (Fig. 3i–m), which prevented dissolution and material exchange. However, ‘matrix’ allanite grains (Z4) are also completely enclosed by epidote (Fig. 5). Thus, it could be expected that they should show a similar CSD to that obtained from the other three domains. This, however, is not the case (Fig. 7).
The increase of the average allanite size between garnet zones Z3 and Z4 (Table 1) could be interpreted to result from allanite growth after garnet zone Z3 formation. This, however, is in clear disagreement with the observation that allanite grains in garnet zone Z3 and in the matrix are, with very few exceptions, surrounded by thick epidote rims, which show identical chemical zonation patterns (see Zeh & Millar, 2001, fig. 8). These features indicate that abundant epidote must have grown over allanite prior to and/or during garnet zone Z3 and Z4 formation.
Another explanation would be that the CSD obtained from allanite inclusions in matrix epidote was established during garnet Z1 growth, prior to the first epidote overgrowth. This interpretation conforms with the observation that epidote in direct contact with allanite commonly shows a pistacite component of Xps = 16 (observed in garnet zone Z1–Z4), which is typical for epidote formed during garnet zone Z1 growth. In contrast, epidotes formed during garnet zone Z2 and Z4 growth have higher Xps, between 23 and 33 (see Zeh & Millar, 2001, fig. 8). Nevertheless, this interpretation conflicts with the CSDs obtained from allanite inclusions in garnet zones Z1, Z2 and Z4 (Fig. 7).
An alternative explanation is that the interactions between epidote and allanite were more dynamic than reflected by the CSDs. As shown by Zeh & Millar (2001), abundant epidote was consumed during the formation of garnet Z1 and Z2 [reaction (R1)]. Thus, at least some of the previously enclosed allanite grains could have been ‘liberated’ from their epidote armouring and were able to grow and to interact with other minerals, prior to overgrowth by the next epidote generation. This interpretation is supported by the observation that at least some allanite grains in garnet zones Z1 and Z2 show little or no overgrowth by epidote (Fig. 3l). Nevertheless, without any additional information, e.g. about the chemical zonation of allanite or isotopic data, an unambiguous interpretation about the timing of the observed matrix allanite CSD cannot be given.
Apatite–titanite interactions
The textural relationships indicate that abundant apatite grains are overgrown by titanite in garnet zones Z1 and Z2a, Z2c (Figs 3g and 4b and f), whereas few apatites are overgrown by titanite in garnet zone Z3. Matrix titanite grains are apatite-free (Fig. 3h). As with the ACP–host quartz interactions, there is good correlation between the size of apatite grains completely enclosed by titanite in Z1 and Z2, and those that cross the titanite grain boundaries (Fig. 14c). The observations lead to two conclusions: (1) titanite formed during garnet zone Z1 and Z2 growth must have ‘released’ apatite inclusions, prior to formation of garnet zones Z3 and Z4; (2) the interaction mechanism between the two minerals changed after garnet Z2 growth. Point (1) can be explained by titanite recrystallization after garnet Z2 growth, as a result of deformation D2, which is well supported by the observation that the irregularly shaped titanite aggregates enclosed in garnet zone Z2c (Figs 3g and 4f) are ‘replaced’ by lens-shaped, subgrain-free titanite crystals in garnet zone Z3 and the matrix. Point (2) can be explained by the different grain size evolutions of apatite and titanite from Z1 to Z4. As shown in Fig. 15, there is a large difference between the average surface/volume ratio of apatite (
) and titanite (
) during growth of garnet zones Z1 and Z2, which becomes significantly reduced and compensated during growth of garnet zones Z3 and Z4. This reduction is most likely to be the reason for apatite grains in contact with titanite being overgrown in garnet zones Z1 and Z2, but not during formation of garnet zones Z3 and Z4.
|
) of apatite, titanite and allanite from garnet zone Z1 to Z4. It should be noted that the differences become successively lower.Apatite– and titanite–allanite interactions
In contrast to titanite, only a very few apatite inclusions were observed enclosed by allanite in garnet zones Z1 and Z2, even though allanite is much larger than apatite and has a
ratio even lower than that of titanite (Fig. 15). It seems very likely that the commonly observed tiny epidote overgrowths prevented apatite from being overgrown by allanite. Titanite was never found enclosed by allanite.
Interpretation of the CSD evolution of apatite, titanite and apatite
Nucleation and growth
The CSDs of apatite, titanite and allanite in garnet zone Z1 reflect the earliest stage of their respective evolutions. The textures and CSDs provide evidence that all three ACPs are not inherited, but result from mineral reactions that caused nucleation and growth prior to garnet zone Z1 overgrowth. Nevertheless, unambiguous evidence for a nucleation and growth stage is presented only by the asymptotic CSD obtained from titanite in domain Z1s (Fig. 6f), which is in agreement with the models discussed above (Fig. 11a and c). However, whether or not this asymptotic CSD results from a size-dependent (mechanism A) or size-independent growth mechanism (mechanism B) cannot be decided from the obtained dataset, as we see only the final distribution and not the evolution (Fig. 11b and d).
In contrast to titanite–Z1s, the CSDs of apatite–Z1, allanite–Z1 and titanite–Z1b show a lognormal shape [SL(2) >10–20; Table 2], which, as shown above, can result from several distinct growth mechanisms (Figs 11–13). The most straightforward interpretations are that the lognormal CSDs result either from a decaying constant nucleation rate accompanied by LPE growth (mechanism C) or from a decaying exponential nucleation rate accompanied by constant growth (see Marsh, 1998, fig. 4). Alternatively, it is likely that the lognormal CSDs result from a two-stage process. They could have been formed by nucleation and initial growth according to mechanism A or B (asymptotic CSD), followed by a surface controlled LPE growth (mechanism F) or by the initiation of Ostwald ripening (mechanism G), or from nucleation and LPE growth according to mechanism C (lognormal CSD), followed by random ripening (mechanism H). Other growth mechanisms, e.g. growth rate dispersion after an instantaneous nucleation event or simultaneously changing nucleation and growth rates with time can be excluded. As shown by Marsh (1988) and (Kerrick et al., 1995), these processes led to the formation of concave-upward curves in the ln(n) vs L diagram that are not seen in this study (Fig. 7). Furthermore, Ostwald ripening during nucleation and initial growth, when the grains were on a nanometre scale, can also be excluded. Such a mechanism would not result in the formation of a lognormal CSD (see Kile et al., 2000).
The two distinct titanite CSDs (Z1s and Z1b) observed side by side in garnet zone Z1 (Fig. 3a and e) indicate that nucleation and initial growth of titanite could have been maintained by LPE growth (CSDd theory); with a constant nucleation rate and LPE growth in domain Z1s, and a decaying nucleation rate during LPE growth in domain Z1b. The different nucleation mechanisms in close vicinity could be explained by spatial variations of the physico-chemical–mechanical conditions during nucleation and initial growth. In fact, such variations are common in technical systems, and were found in grain growth experiments (see Kile et al. 2000; Kile & Eberl, 2003). Nevertheless, even if the two distinct titanite CSDs are formed by a different LPE growth mechanism, it does not necessarily mean that the same mechanism also led to the establishment of the observed apatite and allanite CSDs in garnet zone Z1.
In summary, the kinetic growth mechanisms, which finally led to the formation of the ACP-CSDs in garnet zone Z1, are ambiguous. They result from either a one-step process, explainable by CSDd and CSDi theory, or a two-step process. A CSDd growth mechanism was favoured for all natural systems by Eberl et al. (2002) and Kile et al. (2000), whereas the CSDi growth mechanism was considered to be the most likely for metamorphic and magmatic batch systems by Cashman & Ferry (1988) and Marsh (1988, 1998). Before I illuminate growth processes that caused the formation of the CSDs in garnet zones Z2–Z4 (open-system growth and ripening), crystal growth rates, nucleation rates and growth times will be estimated from the CSDs obtained from garnet zone Z1.
Crystal growth rates, nucleation rates and growth times
Providing that the ACP-CSDs in garnet zone Z1 were formed by a CSDi growth mechanism, original conditions of nucleation and growth can be estimated from the population density function [equation (2)], if either the CSD forms a log–linear line including all size classes in the population density diagram (e.g. titanite–Z1s), or the straight, negative slope defined by the larger size classes has not changed during subsequent growth processes (Cashman & Ferry, 1988). In such a case, the average linear nucleation rate (J') and growth rate (G') can be estimated from the slope b and the zeroth and second moments of the CSD function [equation (3)], if the average growth time (t') is known. The relationships are
 | (20) |
 | (21) |
. A detailed description of the procedure used here is given in Appendix B.
For apatite, titanite and allanite enclosed by garnet zone Z1 the CSD criteria required above are nearly fulfilled, even though some of the smaller size class(es), which are very close to L = 0, plot below the straight line defined by b*. Neglecting this effect, J', G' and t' are estimated for all three minerals enclosed by garnet zone Z1, using Walther & Wood's empirical growth law (see Appendix B), with the assumption that transport is not rate limiting, and that the investigated minerals have a similar growth behaviour to the silicates investigated by Wood & Walther (1983).
The parameters used in this study and the results are presented in Table 3 and Fig. 16. Figure 16 shows the relationships between the average growth time t', the reaction overstep (T), heating rates (h), and the minimal (1 cal/mol-deg) and maximal entropy (20 cal/mol-deg) change (S), related to polymorphic transitions and dehydration reactions, respectively. The stippled field comprises the time during which mineral growth and nucleation must have occurred. In general, the growth time is limited by two parameters. A maximum growth time is achieved if T is just controlled by a constant linear h, due to the relation
 | (22) |
). A minimum growth time is achieved if the reaction overstep is controlled by other kinetic factors, e.g. the sluggishness of nucleation. In Fig. 16, T = 10°C is used as an upper limit for reaction overstep, even though higher values are possible (Waters & Lovegrove, 2002; Zeh & Holness, 2003).
|
|
As shown in Table 3, minimum average growth times (t') for all three minerals range between 0·39 and 45 years. Maximum average growth times are dependent upon the heating rate, which is unknown. If we make the very conservative assumption of h = 1°C/Ma, which can occur during regional metamorphism, we obtain maximum average growth times between c. 880 years (apatite) and 9500 years (allanite). However, if the minerals were formed during contact metamorphism, e.g. as a result of the intrusion of the nearby Ardgour granite gneiss, as suggested by Zeh & Millar (2001)
, the heating rate would be much higher (e.g. h = 0·02°C/year; Norton & Knight, 1977), which gives maximum average growth times between 6·2 years (apatite) and 108 years (allanite) (Table 3). In summary, the results show that all three minerals must have been grown within a very short time interval, of between 0·4 and <9500 years. This time becomes longer if the largest grain diameters rather than the mean values are considered. In this case the maximum times for apatite, titanite and allanite growth are 10 480, 21 390 and 17 310 years, respectively (Table 3).
To compare the average nucleation and growth rates with the results of other workers, G' and J' were calculated for T = 1, and S = 1 and 20 cal/mol-deg, respectively (Table 3). In fact, the average growth rates are similar for apatite (4·33 x 10–13 cm/s) and allanite (5·29 x 10–13 cm/s), but faster for titanite (1·04 x 10–12 cm/s). The values obtained for apatite and allanite are higher than those estimated by Cashman & Ferry (1988) for magnetite, pyroxene and olivine from contact metamorphic rocks (6·5 x 10–12 cm/s), but similar to those obtained from regional metamorphic garnet and magnetite [(1·0–5·07) x 10–13 cm/s]. The average nucleation rates differ significantly among the three minerals. J' is highest for apatite (4·10 x 103 cm–3 s–1) and much less for titanite (1·36 x 102 cm–3 s–1) and allanite (1·37 cm–3 s–1) (Table 3).
From the time relationships and observed textures it can be concluded that nucleation and initial growth of all three minerals took place ‘immediately’ prior to garnet Z1 overgrowth, and that all three ACPs grew in a chemical and textural equilibrium. In this context it is interesting to note that the initial apatite, titanite and allanite nucleation and growth patterns were not modified during garnet overgrowth, i.e. the grains were not pushed away during garnet porphyroblast formation, a phenomenon occasionally seen in metamorphic rocks (e.g. Ferguson et al., 1980). The identical apatite textures from core to rim of garnet Z1 give a clue that growth of the c. 2 cm diameter garnet Z1 probably took place in less than 0·4–20 000 years. Very fast garnet overgrowth would be in agreement with the fact that garnet Z1 is nearly unzoned (Fig. 1c), which requires garnet formation under nearly constant P–T–X conditions. This, in turn, is in agreement with the P–T models of Zeh & Millar (2001), who showed that garnet Z1 grew during a slight temperature rise of c. 10°C at 4–6 kbar.
Finally, it should be noted that the average nucleation and growth rates obtained will be meaningless if the ACP-CSDs in garnet zone Z1 were formed by a size-dependent growth mechanism (B or C) (see Eberl et al., 2002). For that case, the nucleation rates could have been much higher than given above. Furthermore, the time for the formation of the largest grains would be shorter.
Open-system growth and ripening
Apatite. As shown above, the specific apatite volume (Vt,ap) increases significantly between garnet zones Z1 and Z2 (a and b), a phenomenon that cannot be explained by mechanical compaction alone. Furthermore, the mean apatite size and grain size spread increase (Table 1). These features point to an open-system growth of apatite after garnet Z1 growth but prior to garnet Z2 overgrowth. The –ß2 evolution trend from Z1 to Z2b (Fig. 6o) is consistent with a surface controlled LPE growth mechanism (Fig. 12e). This interpretation agrees with the observations that the lognormal CSD shape is maintained from Z1 to Z2b, and that the CSD slope (b*) rotates anticlockwise in the population density diagram (Fig. 12e and f). In contrast, the loss of the lognormal shape from Z1 to Z2a, and the exotic position of point Z2a in the –ß2 diagram (Fig. 6o) can be explained by textural mixing, as a result of interactions between apatite and quartz in domain Z2a (see above). The decrease of Nap from Z1 to Z2 (Table 1) indicates that apatite growth cannot be caused solely by open-system LPE growth, but must have been accompanied by a ripening process. As the lognormal shape is maintained from Z1 to Z2b, random ripening as an additional mechanism is likely.
From Z2 to Z4, Vap remains nearly constant, whereas Nap decreases significantly (Table 1), indicating that the CSD evolution from Z2 to Z4 was controlled by a ripening process. Maintenance of the lognormal CSD shape from Z2 to Z4, the increase of the Lap spread, the rotation of b*, and the horizontal evolution trend in the –ß2 diagram (Fig. 6o) are in agreement with a supply controlled random ripening mechanism. This is supported by the steady-state profiles shown in the f/fmax vs L/L' diagram, where all curves are left skewed (Fig. 8a).
Titanite. In contrast to apatite, the data points obtained from titanite Z1 to Z4 follow a negatively correlated trend in the –ß2 diagram (Fig. 6o). The distinct positions of the data points Z1s and Z1b probably result from different LPE growth mechanisms during final nucleation, as discussed above. The subsequent –ß2 trend from Z1b to Z4 can be interpreted to result either from Ostwald ripening (mechanism G), or from open-system McCabe growth (mechanism D), in agreement with the simple models presented (Figs 12a and 13a). Ostwald ripening is likely, as Nttn decreases from Z1 to Z4, and the Lttn spread increases (Table 1). Furthermore, we see a CSD fan in the population density diagram (Fig. 7d), and the CSDs become more symmetrical from Z1 to Z4 (Fig. 6k, Table 2). Additionally, the curves in the f/fmax vs L/L' diagram become successively constricted from Z1b to Z4 (Fig. 8b), and finally approach the steady-state profile for surface controlled Ostwald ripening (n = 2). This, however, does not necessarily mean that Ostwald ripening was really surface controlled. Alternatively, the Z4 curve in Fig. 8b also could reflect a transitional stage during diffusion controlled Ostwald ripening (n = 3), meaning that the final steady-state profile for n = 3 was not yet achieved (see above).
Although Ostwald ripening can account for many features of the titanite CSD evolution, the variations of Vttn from Z1 to Z4 provide evidence that the ripening process was accompanied by positive and negative material supply, which requires an additional growth mechanism. The decrease of Vttn between Z1b and Z2a (Fig. 10b), together with the slight anticlockwise rotation of b* in the population density diagram (Fig. 7a), could be explained by Ostwald ripening accompanied by negative McCabe growth. This interpretation agrees with the –ß2 evolution trend shown in Fig. 6o. In fact, negative McCabe growth causes an exponential ß2 increase with decrease, whereas Ostwald ripening follows the opposite trend. Thus, the titanite evolution from Z2 to Z4 is likely to result from a combination of diffusion-controlled Ostwald ripening, which was at least temporarily accompanied by positive (Z3) or negative (Z4) McCabe growth.
Allanite. The CSDs obtained from allanite in garnet zone Z1–Z2(Z3) are nearly identical, as indicated by the small variations of Nall, L'all and Lall spreads (Tables 1, and 2). Furthermore, the Z1–Z2 CSDs are lognormal (Table 2) and show a left-skewed curve in the f/fmax vs L/L' diagram (Fig. 8c). CSD transformation between Z1 and Z3 was obviously prevented by epidote overgrowths, as discussed above, and the CSDs reflect either the nucleation and initial growth stage or a more advanced stage including nucleation followed by open-system growth. In contrast to Z1–Z3, the allanite Z4-CSD is not lognormally distributed, and shows a larger L'all and a wider Lall spread (Tables 1 and 2). Furthermore, the Z4 curve is right skewed in the f/fmax vs L/L' diagram, and fits well the steady-state profile for surface controlled Ostwald ripening (n = 2) (Fig. 8c). These features and the decrease of Vall and Nall from garnet zone Z2(Z3) to Z4 (Table 1, Fig. 10c) support the interpretation that the CSD transformation from Z2(Z3) to Z4 was probably facilitated by surface controlled Ostwald ripening in combination with a negative grain growth mechanism.
Geochronological and geological implications
Textural observations and CSDs indicate that the ACPs enclosed by garnet zone Z1 were close to a stage of nucleation and growth immediately prior to garnet zone Z1 overgrowth, whereas accessory phases in garnet zone Z2, Z3 and in the matrix (Z4) were successively modified by open-system growth, ripening, mineral reactions and deformation. This provides evidence that all three ACPs enclosed by garnet zone Z1 are not inherited, but that their evolution is closely related to the evolution of the surrounding garnet Z1. Thus, dating of the accessory minerals enclosed in garnet Z1 should reflect the absolute time of garnet Z1 growth. By contrast, dating of minerals from zones Z2 to Z4 may be complicated by inherited components, as a result of overgrowth of older grains during open-system growth and ripening. However, the amount of inheritance depends on the grain growth mechanism, and whether or not the ACPs underwent additional recrystallization and/or diffusion prior to and after overgrowth by the respective garnet zones.
The dataset shown in Table 1 and the derived growth mechanisms provide evidence that between garnet zones Z1 and Z2 c. 70% of the apatite volume was newly formed by a supply controlled growth mechanism, and that about two-thirds of the grains were dissolved by random ripening. From these data, and the fact that during random ripening a large amount of the original grain volume is recycled (see above), it can be concluded that apatite in garnet zone Z2 contains only a very little inherited component. Inheritances in garnet zones Z3 and Z4(matrix) are even less likely, as random ripening here caused an enormous increase of the average apatite volume (
) between garnet zone Z2 and Z3 growth and after garnet Z4 formation (Table 1).
The titanite CSD evolution from Z1 to Z4 was probably controlled or at least influenced by Ostwald ripening, accompanied by either positive or negative McCabe growth. From the specific volumes and the titanite CSDs it is calculated that c. 50 vol. % of titanite was recycled by ripening between garnet zones Z1 and Z2, c. 70 vol. % between Z2 and Z3, and c. 99 vol. % between Z3 and Z4(matrix). This indicates that titanite in garnet zones Z2 and Z3 could have inherited cores. However, the influence of inherited cores seems to be meaningless for geochronology, as titanite was additionally affected by deformation (D1 and D2) during and after garnet Z2 growth, accompanied and followed by recrystallization (see above). These deformation events may also have affected apatite. Thus, it is very likely that the isotope systems of apatite and titanite were completely reset between the garnet overgrowth events. In contrast to apatite and titanite, the redistribution behaviour of allanite is more difficult to access, as it is commonly armoured by epidote. This armouring could have prevented recrystallization and isotope redistribution between formation of the various garnet zones and, thus, allanite in zone Z2–Z4 is likely to contain inherited isotopic components.
Another important point is that nucleation and growth of the ACPs enclosed by garnet zone Z1 occurred within much less than 20 000 years (Table 2), which requires that overgrowth of the c. 2 cm large garnet zone Z1 was even faster (Fig. 1a). This result is amazing, and implies that abundant garnet growth (c. 20 vol. %, Zeh & Millar, 2001) can occur within a very short time span, which in fact is much shorter than so far concluded from geochronological results (e.g. 2·9 ± 1·5 Ma given by Sm–Nd dating; Vance & O'Nions, 1992). Fast growth of the garnet core (Z1), which shows nearly no growth zonation, could be explained by an important reaction overstep (see Zeh & Holness, 2003), which may have been caused by the sluggishness of garnet nucleation during either a regional or a contact metamorphic event. Contact metamorphism could be explained by the intrusion of the nearby West Highland granite gneiss, which was emplaced at c. 870 Ma (Friend et al., 1997). In contrast, the subsequent CSD evolution from Z1 to Z4 is more likely to result from regional metamorphic events, during the Knoydartian and/or the Caledonian orogeny (see above).
The steady increase in the grain size of the ACPs and RFMs (e.g. quartz) from garnet zone Z1 to Z4 provides unambiguous evidence that the textural evolution of the investigated rock was accompanied by a successive temperature rise, which conforms with P–T estimates carried out by Zeh & Millar (2001). The investigated sample therefore does not conform to the traditional view of the Glenfinnan Group of the Moine Supergroup, in which the highest-grade metamorphic events occurred early in its polymetamorphic history (e.g. Roberts & Harris, 1983).
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SUMMARY AND CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONSUMMARY AND CONCLUSIONSAPPENDIX A: RESULTS OF...REFERENCES |
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(1) CSDs of accessory apatite, titanite and allanite are investigated in three texturally distinct garnet zones (Z1–Z3) and in the matrix (Z4) of a garnet–epidote–biotite gneiss, and the CSD evolution trends obtained are compared with those simulated by CSD modelling. The CSDs of all three ACPs enclosed by garnet Z1 indicate that they are not inherited, but were in or near a stage of nucleation and initial growth, prior to garnet zone (Z1) overgrowth. This is indicated by asymptotic and lognormal CSD shapes, whose formation can be explained by either CSDi or CSDd theory. The Z1 stage, including the formation of garnet grains up to 2 cm in size, was very short and lasted for less than 20 000 years, if Wood & Walther's (1983)
empirical growth law is employed.
(2) Subsequently, the Z1 CSDs of the ACPs were modified by different growth mechanisms, as supported by the evolution trends of the parameters L'i, Li spreads, Ni, Vt,i, , ß2, SL(2), b* and n°*, as well as by CSD fans in the population density diagrams and curves in f/fmax vs L/L' diagrams. All the data together support an interpretation that the apatite CSD evolution between Z1 and Z2 perhaps was controlled by an open-system LPE growth mechanism in combination with supply controlled random ripening, and between Z2 and Z4 by random ripening. In contrast, the CSD evolution of titanite from Z1 to Z4 is more consistent with Ostwald ripening temporarily accompanied by positive or negative McCabe growth. The allanite CSD remained nearly constant from Z1 to Z3. Their subsequent transformation from Z3 to Z4 could be explained by Ostwald ripening in combination with a negative growth mechanism. In summary, the data presented indicate that formation and transformation of different ACPs within the same volume of a metamorphic rock is achieved by different kinetic growth mechanisms.
(3) Textural observations provide evidence that ACP nucleation, growth and ripening interfered with dehydration reactions among RFMs (garnet-forming reactions), was influenced by contemporaneous matrix coarsening, and was affected by pure and simple shear deformation (D1 and D2). These processes in combination resulted in a reduction of the original rock volume, in particular during garnet Z1 and Z2 growth, and caused segregation, redistribution and recrystallization of RFMs and ACPs within the matrix. Furthermore, deformation-induced recrystallization of RFM led to a ‘release’ of titanite and apatite grains, formerly armoured by host quartz, and may have completely reset the isotope systems of titanite and apatite between the garnet overgrowth events. For allanite, the latter was probably prevented by epidote overgrowth.
(4) The increase of the ACP and RFM grain sizes from Z1 to Z4 provides unambiguous evidence that the textural evolution of the investigated rock results from a successive temperature rise. This contradicts some earlier models, which suggested that the highest metamorphic grades were achieved early in the polymetamorphic evolution of the Moine Supergroup.
(5) Results of numerical modelling indicate that CSD fans in population density diagrams can result from different growth mechanisms. They can be formed during nucleation and LPE growth, open-system LPE growth, and by different ripening mechanisms. Discrimination between the various mechanisms is possible if the evolution trends of Ni and Vt,i are known.
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APPENDIX A: RESULTS OF NUMERICAL CSD MODELLING |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONSUMMARY AND CONCLUSIONSAPPENDIX A: RESULTS OF...REFERENCES |
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1. Nucleation and growth (open system)
(the parameters are explained in the text and in Tables 1 and 2)
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2. Growth (open system)
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3. Ripening (closed system)
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APPENDIX B: GROWTH AND NUCLEATION RATE CALCULATIONS
Growth and nucleation rate calculations were carried out according to the formulae outlined by Walther & Wood (1984), but using non-specific shapes for the respective minerals. The parameters are explained at the end of the Appendix.
Apatite (columnar shape)
Calculations for reaction overstep control
 | (A1) |
(Walther & Wood, 1984) and –G = S(T – Teq).
 | (A2) |
 | (A2a) |
 | (A3) |
 | (A4) |
 | (A5) |
 | (A6) |
Calculations for heating rate control
 | (A7) |
].
Titanite (double cone)
Calculations for reaction overstep control
 | (A8) |
 | (A9) |
 | (A10) |
 | (A10a) |
 | (A11) |
 | (A12) |
Calculations for heating rate control
 | (A13) |
Allanite (orthorhombic shape)
Calculations for reaction overstep control
 | (A14) |
 | (A14a) |
 | (A15) |
 | (A16) |
 | (A16a) |
 | (A17) |
 | (A18) |
Calculations for heating rate control
 | (A19) |
Parameters used
- K, growth rate constant (oxygen g atom/cm2 s)
- Ni, oxygen g atom per cm3 of phase i (Napatite = 0·0822; Ntitanite = 0·0898; Nallanite = 0·0944)
- R, universal gas constant (1·987 cal/mol K)
- T, temperature (K)
- t, time (s)
- ri, length parameter of phase i (cm) [rapatite, average radius of apatite needles = 1/(b*2); rtitanite, average radius of titanite lenses = 1/(b*2); rallanite, average b-axis of allanite crystals =1/b]
- b, slope of function n [see equation (2)]
G, free energy (cal/mol); –G = S(T – Teq)
S, entropy of reaction (cal/mol K)
- n, oxygen g atom of a certain mineral volume (oxygen g atom x n cm3)
- s, mineral surface (cm2)
- h, heating rate (K/s)
- Ni, oxygen g atom per cm3 of phase i (Napatite = 0·0822; Ntitanite = 0·0898; Nallanite = 0·0944)
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ACKNOWLEDGEMENTS |
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A.Z. thanks Ian Millar for some critical comments and English corrections, and Marian Holness for some stimulating discussions. Furthermore, I thank Bruce Marsh, Michael Higgins, William Carlson, John Ayers and an anonymous reviewer for their helpful reviews, and Dennis Eberl for his critical but enlightening comments on an earlier version of the manuscript.
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FOOTNOTES |
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* Telephone: +49-931-888-5415. E-mail: armin.zeh{at}mail.uni-wuerzburg.de
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REFERENCES |
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Ayers, J. C., Miller, C., Gorisch, B. & Milleman, J. (1999). Textural development of monazite during high-grade metamorphism: hydrothermal growth kinetics, with implications for U, Th–Pb geochronology. American Mineralogist 84, 1766–1780.[Abstract]
Ayers, J. C., DeLaCruz, K., Miller, C. & Switzer, O. (2003). Experimental study of zircon coarsening in quartzite ± H2O at 1·0 GPa and 1000°C, with implications for geochronological studies of high-grade metamorphism. American Mineralogist 88, 365–376.
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