JOURNAL OF PETROLOGY VOLUME 49 NUMBER 5 PAGES 1027^1041 2008 doi:10.1093/petrology/egn015 Crystal^Melt Separation and the Development of Isotopic Heterogeneities in Hybrid Magmas JAMES S. BEARD* VIRGINIA MUSEUM OF NATURAL HISTORY, 21 STARLING AVENUE, MARTINSVILLE, VA 24112, USA RECEIVED FEBRUARY 21, 2007; ACCEPTED FEBRUARY 22, 2008 ADVANCE ACCESS PUBLICATION APRIL 4, 2008 isotopic heterogeneity; zoning; hybrid magma; crystal separation; Sr isotopes; aplite; rhyolite If a magma is a hybrid of two (or more) isotopically distinct endmembers, at least one of which is partially crystalline, separation of melt and crystals after hybridization will lead to the development of isotopic heterogeneities in the magma as long as some of the preexisting crystalline material (antecrysts) retains any of its original isotopic composition.This holds true whether the hybridization event is magma mixing as traditionally construed, bulk assimilation, or melt assimilation. Once a magma-scale isotopic heterogeneity is formed by crystal^melt separation, it is essentially permanent, persisting regardless of subsequent crystallization, mixing, or equilibration events. The magnitude of the isotopic variability resulting from crystal^melt separation can be as large as that resulting from differential contamination, multiple isotopically distinct sources, or in situ isotopic evolution. In one model, a redistribution of onethird of the antecryst cargo yielded a crystal-enriched sample with 87 Sr/86Sr of 07058, whereas the complementary crystal-poor sample has 87Sr/86Sr of 07068. In other models, crystal-rich samples are enriched in radiogenic Sr. Isotopic heterogeneities can be either continuous (controlled by the modal distribution of crystals and melt) or discontinuous (when there is complete separation of crystals and liquid). The first case may be exemplified by some isotopically zoned large-volume rhyolites, formed by the eruptive inversion of a modally zoned magma chamber. In the latter case, the isotopic composition of any (for example) interstitial liquid will be distinct from the isotopic composition of the bulk crystal fraction.The separation of such an interstitial liquid may explain the presence of isotopically distinct late-stage aplites in plutons. Crystal^melt separation provides an additional option for the interpretation of isotopically zoned or heterogeneous magmas.This option is particularly attractive for systems whose chemical variation is otherwise explicable by fractionation-dominated processes. Non-isotopic chemical heterogeneities can also develop in this fashion. Most large-volume, continental magmas are complex hybrids of mantle-derived basaltic melts and crustal rocks (e.g. Lipman, 1984; DePaolo et al., 1992; Davidson et al., 2005). Zoning and other heterogeneities both chemical and isotopic, are common in, if not characteristic of, large bodies of hybrid magma, both volcanic and plutonic (Noble & Hedge, 1969; Moll, 1981; Halliday et al., 1984; Kistler et al., 1986; Johnson, 1989; Johnson et al., 1990; Hildreth et al., 1991; Verplanck et al., 1995; Reiners et al., 1996; Chesner, 1998; Hildreth & Fierstein, 2000; Barbey et al., 2001; Tsuboi & Suzukiba, 2003; Mikoshiba et al., 2004; Dreher et al., 2005; Wilson et al., 2006). The most common interpretations of isotopic variations in magma bodies are differential contamination or magma mixing, source variability, or isotopic evolution in long-lived magma chambers with high Rb/Sr (Noble & Hedge, 1969; Moll, 1981; Johnson, 1989; Davies & Halliday, 1998; Hildreth & Fierstein, 2000; Mikoshiba et al., 2004). However, there is another mechanism by which isotopic variability can develop in magmas. Given a hybrid magma in which the end-members are isotopically distinct and one or more of the end-members is partially crystalline, isotopic variability can result from the simple separation of solids from liquids. The end-members can be either multiple magmas (hybridization mechanism ¼ magma mixing) or a magma that entrains partially molten xenoliths (hybridization mechanism ¼ contamination/bulk assimilation). *Corresponding author. E-mail: Jim.Beard@vmnh.virginia.gov ß The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@ oxfordjournals.org KEY WORDS: I N T RO D U C T I O N JOURNAL OF PETROLOGY VOLUME 49 The isotopic variability can be large and may be a major component of overall isotopic heterogeneity in hybrid systems. It should be noted at the outset that this is not isotope ‘fractionation’. It is rather, the preservation, propagation, and re-expression of extant isotopic and chemical variability. The principal assumption for the models proposed here is that the solid components of the mixed system retain their isotopic and chemical identity. In other words, crystals present at the time of mixing, including both phenocrysts present in magmas prior to mixing and any xenocrystic crystalline material derived from an assimilant [referred to together as antecrysts, an expansion of the term defined by Bacon & Lowenstern (2005) to include both xenocrystic and cognate solids], do not equilibrate with a thoroughly mixed melt. At the outset it is acknowledged that this is unlikely to be strictly true. However, the salient features modeled below will persist to a greater or lesser degree as long as some crystals inherited from the pre-mixing end-members retain any of their isotopic identity once the end-members are mixed. This is clearly not an unreasonable assumption, as both disparities in the isotopic compositions of phenocrysts and melt and isotopic zoning within phenocrysts are well-documented in both volcanic and plutonic rocks (Johnson et al., 1990; Davidson & Tepley, 1997; Knesel et al., 1999; Wolff et al., 1999; Baker et al., 2000; Waight et al., 2000, 2001; Halama et al., 2002; Tepley & Davidson, 2003; Wolff & Ramos, 2003; Gagnevin et al., 2005; Ramos & Reid, 2005; Wilson et al., 2006). In fact, it has been argued that most arc magmas are mixtures of melts and an unrelated, pre-existing ‘crystal cargo’ (Davidson et al., 2005). A second assumption, important for several of the models, is that, during partial melting of xenoliths, the isotopic composition of residual minerals and melt may be decoupled. Specifically, preferential melting or retention of minerals of unlike isotopic composition during (dehydration) melting will result in partial melts having different isotopic composition from the coexisting restite (e.g. Watson & Harrison, 1984; Hogan, 1995). This decoupling has been verified by observation and experiment for Sr isotopes and observed in migmatites and inferred from granite compositions for Nd (Hammouda et al., 1996; Tommasini & Davies, 1997; Ayres & Harris, 1997; Knesel & Davidson, 1999; Zeng et al., 2005a, 2005b). A note of clarification is in order here. Obviously, hybridization is an open-system process. However, for the purposes of this paper, it will be generally assumed that once hybridization has occurred, the system is closed to further material input. It is in this context that ‘closed-system’ behavior is discussed from time to time. This paper focuses on Sr isotope behavior, with a few exemplars using Nd isotopes. However, the principles NUMBER 5 MAY 2008 outlined here are, within the limits discussed above, applicable to any isotopic or, for that matter, chemical system. M I X I N G O F I S O T O P I C A L LY D I S T I N C T, PA RT I A L LY C RY S TA L L I N E M AG M A S The system chosen for modeling here is bulk assimilation of a partially molten xenolith by a partially crystalline basaltic magma. This system was chosen because it permits construction of models applicable to hybridization by either magma mixing or bulk assimilation. Models 1 and 2 (Figs 1 and 2), in which both end-members are in chemical and isotopic equilibrium prior to hybridization, are equally applicable to bulk assimilation (‘contamination’) or to magma mixing as traditionally construed (e.g. Eichelberger, 1975). Model 3 (Fig. 3), in which one partially molten end-member is not isotopically or chemically equilibrated, will apply, for the most part, to hybridization by bulk assimilation. All percentages used in this paper are weight percentages unless otherwise noted. Mixing calculations Two-component mixing lines are calculated using standard formulations (e.g. Faure, 1986). For components A and B with isotopically distinct Sr, ð87 Sr=86 SrÞmix ¼ ðfSrA SrB ½ð87 Sr=86 SrB Þ ð87 Sr=86 SrA Þg=½Srmix ðSrA SrB ÞÞ þ ðf½SrA ð87 Sr=86 SrA Þ ½SrB ð87 Sr=86 SrB Þg=ðSrA SrB ÞÞ where Srmix ¼ SrA XA þ SrB XB ð1Þ ð1aÞ and X is the weight fraction of component A or B. An identical formulation is used for Nd isotopes. In these models, the bulk mixture of host magma and xenolith lies along the bulk mixing line in Figs 1^3. The bulk mixing line is the commonly used means for relating the isotopic composition of a mixture to its end-member components. However, in the models presented here (in Fig. 1b, for example), four chemically and/or isotopically distinct components are recognized: (1) the liquid in the host magma; (2) the phenocrysts in the host magma; (3) the liquid in the partially molten xenolith; (4) the residual crystals in the partially molten xenolith. Thus, in addition to the bulk mixing line, mixing lines can be calculated between the liquid and solid components of the xenolith (xenolith solid^liquid mix), and the liquid and solid components of the host (host solid^liquid mix), the liquid components of host and xenolith (mixed liquids), and the solid components of host and xenolith (mixed solids) (Figs 1^3). When the host and assimilant are thoroughly mixed, the liquid in the mixed system will lie along the ‘mixed liquid’ line, the solids along the ‘mixed solids’ line. 1028 BEARD CRYSTAL^MELT SEPARATION Model 1: Xenolith plagioclase equilibrated during melting (a) Model 2: xenolith plagioclase consumed during melting (a) xenolith solid xenolith solid-liquid mix xenolith solid-liquid mix 0.711 xenolith solid ho ds % oli ds 0.705 Bulk Kd for Sr in host magma = 1 0.703 80% host mixing line host solid and liquid 0 (b) 100 200 300 0.703 500 0 (b) xenolith solid-liquid mix 0.711 400 line mi xe 60 0.705 ixin g 0.707 st m Sr/86Sr Sr/86Sr 87 Bulk Kd for Sr in host magma = 1 87 80% host mixing line 100 200 Sr/86Sr 87 Sr/86Sr 87 mix ed liqu ids so s host solid 500 600 80% host mixing line lid 0.705 host solid-liquid mix 400 line d e ixing lin 300 60% host mixing line ixe m 200 ing ds oli 100 mix ds e 0 0.707 Bulk Kd for Sr in host magma = 2 bulk xe g lin line st m host liquid 0.703 0.709 mi mixin ids 60 80% ho 500 xenolith liquid xenolith solid bulk d liqu ing t mix os %h 0.705 400 xenolith solid-liquid mix 0.711 Bulk Kd for Sr in host magma = 2 mixe 0.707 host solid and liquid 300 xenolith solid xenolith liquid 0.709 liquids mixed solids ne iqu ids 0.709 ne g li 60% host mixing line dl g li ixin mixed km mi xe 0.707 ixin bul 0.709 xenolith liquid km xenolith liquid bul 0.711 host liquid 0.703 700 Sr, ppm Fig. 1. Sr mixing models for 50% crystalline basalt host magma and partially molten gneissic assimilant. (See Table 1 for compositional information and Table 2 for a description of the models in Figs 1^3.) For Figs 1^3 labeled lines are as follows. ‘Xenolith solid^liquid mix’ and ‘host solid^liquid mix’ connect the compositions of coexisting solids and liquids in the assimilant and host, respectively. There is no ‘host solid^liquid mix’ for Figs 1a, 2a, and 3a because the crystals and liquid in the host have identical compositions (i.e. bulk Kd for Sr ¼1). The ‘mixed solids’ and mixed liquids’ lines connect the compositions of solids and liquids, respectively, in the host and assimilant. The bulk mixing line gives the range of compositions for any mixture of host and solid with end-points determined by the crystallinity of the host (always 50%) and the assimilant (75% for models 1 and 3 and 25% for model 2). The ‘60% host’and 80% host’ mixing lines represent the range of possible compositions for a given mixture of host and assimilant (i.e. either 60 or 80% host) when crystals and liquids are allowed to separate. Marks on lines are at 10% intervals unless omitted for clarity. (See text for further discussion.) In Fig. 1, plagioclase is chemically and isotopically equilibrated during xenolith melting prior to assimilation. This model is akin to magma mixing with a plagioclase-rich magma. In (a), bulk Kd for Sr in host basalt ¼1; in (b), bulk Kd for Sr in host ¼ 2. Distribution of Sr between melt and solid calculated for 50% Rayleigh fractionation. This effectively assumes that the plagioclase is zoned in Sr. Another set of solid^liquid mixing lines can be calculated for any binary mixture of xenolith and host. This requires several sets of mixing calculations. First, for a given mixture one must determine the fraction of solids and liquids derived from the end-members. For components A and B the weight fraction of solids 0 100 200 host solid-liquid mix 300 400 Sr, ppm 500 host solid 600 700 Fig. 2. Models where plagioclase is consumed during xenolith melting; akin to mixing with a plagioclase-poor magma. It should be noted that Fig. 1 is one melting^mixing end member whereas Fig. 2 is another. (a) Bulk Kd for Sr in host basalt ¼1; (b) bulk Kd for Sr in host ¼ 2. Distribution of Sr between melt and solid calculated for 50% Rayleigh fractionation. This effectively assumes that the plagioclase is zoned in Sr. Lines and other information as for Fig. 1. derived from component A in a given mixture (SA,m) is given by SA ,m ¼ ½ðXs,A ÞðXm,A Þ=½ðXs,A ÞðXm,A Þ þ ðXs,B ÞðXm,B Þ ð2Þ where Xs,A,B is the weight fraction solid in component A or B and Xm,A,B is the weight fraction of component A or B in the mixture. The weight fraction of liquid derived from a given component (LA,m) may be derived by an identical formulation: LA,m ¼ ½ðXl,A ÞðXm,A Þ=½ðXl,A ÞðXm,A Þ þ ðXl,B ÞðXm,B Þ: ð3Þ For an 80^20 (80% host, 20% assimilant) mixture of a host magma that is 50% solid and an assimilant that is 75% solid, 73% of the total solids and 89% of the total melt will derive from the host magma. Thus, in Fig. 1b 1029 JOURNAL OF PETROLOGY VOLUME 49 Model 3: Xenolith (restite) plagioclase non-reactive, non-equilibrated (a) 0.715 Bulk Kd for Sr in host magma = 1 xenolith liquid bu lk liq d- m ixi uid 87 0.8 0.7 s uid liq li so th 0.710 d ixe m li no xe Sr/86Sr 0.9 x mi ng 0 200 400 e 60% host mixing line xenolith solid 200 300 m Sr/86Sr 0 g in ne e g li lin ixin host liquid xenolith solid 0.700 200 xenolith-host solid mixing line omitted for clarity ix tm 200 400 600 k e hos 0.75 l bu lin 87 ng ixi m 0.705 ix id m -liqu st ho ds mixed liqui 80% 400 Bulk Kd for Sr in host magma = 2 0.95 xenolith liquid 0.85 d soli lith % 0.710 60 0.715 o xen (b) 0.720 host solid and liquid mixed solids 300 host solid-liquid mix 400 500 MAY 2008 Alternatively, if no separation occurs, the mixture will lie on the bulk mixing line and have the isotopic and chemical composition of the bulk mixture. However, the general case will involve incomplete separation of liquids and crystals. The chemical and isotopic compositions of these partially separated mixtures lie along the 80% host mixing line. Models for mixing of two solid^liquid mixtures lin 80% host mixing line 0.705 NUMBER 5 host solid 600 Sr, ppm Fig. 3. Models where plagioclase is indifferent (no reaction, melting, equilibration, or crystallization) during xenolith melting. As a consequence of this, isotopic compositions in the melt and restite are decoupled. Insets show full range of variability in the system. The area in boxes in the insets is the area of the main figure. Dashed lines continue off the diagram. (a) Bulk Kd for Sr in host basalt ¼1; (b) bulk Kd for Sr in host ¼ 2. Distribution of Sr between melt and solid calculated for 50% Rayleigh fractionation. This effectively assumes that the plagioclase is zoned in Sr. The ‘mixed solids’ line in (b) is omitted for clarity. Other lines and information as for Fig. 1. (for example) the end-points of the 80% host mixing line are the 73% host point on the ‘mixed solids’ line and the 89% host point on the ‘mixed liquids’ line. It should be noted, of course, that the line passes through the 80^20 mixture on the bulk mixing line. The line itself is calculated using equation (1) with A and B from equation (1) defined as the end-points of the line calculated using equations (2) and (3). Looking again at the 80% host mixing line in Fig. 1b, one can now calculate the chemical and isotopic variation along this line related to the relative proportions of crystals and liquids. If the liquid is extracted entirely from the solids, it will have the chemistry and isotopic composition of the end-point on the ‘mixed liquids’ line whereas the solid remainder will have the chemical and isotopic composition of the end-point on the ‘mixed solids’ line. The two end-members chosen for the mixing models are a 600 Ma biotite gneiss (assimilant or xenolith) which is assimilated by a mantle-derived basalt (host). For all models, the basalt host is taken to be 50% crystalline with liquid and crystals in chemical and isotopic equilibrium. The isotopic and appropriate chemical and mineralogical compositions of the two end-members are given in Table 1. Sr is strongly partitioned into plagioclase in comparison with other solid phases considered in the models below. Because of this, the behavior of plagioclase during melting will control the distribution of Sr between the solid and liquid fractions. The six models for Sr isotopes in Figs 1^3 represent three different behaviors of plagioclase during xenolith melting (models 1^3) and two different bulk Kd values for Sr in the host magma (a and b). In models 1a, 2a, and 3a, the bulk Kd for Sr in the host basalt is assumed to equal unity, hence the solid and liquid in the host have identical Sr concentration. In models 1b, 2b, and 3b the bulk Kd for Sr (modeled for Rayleigh fractionation) in the host is taken to be two, hence the host solids are enriched in Sr relative to the host liquid. For model 1 (Fig. 1) plagioclase and melt in the xenolith are in chemical and isotopic equilibrium prior to mixing. The melting reaction, 25bio þ 15qtz þ 60plagioclase1 ¼ 25melt þ ð4Þ 12opx þ 3FeTiox þ 60plagioclase2 is modified after Patin‹o Douce & Beard (1995) for the melting of a biotite gneiss at 9508C and 5 kbar (Table 2). This is an end-member case in which it is assumed that all plagioclase in the system re-equilibrates during partial melting (bulk Kd for Sr ¼ 2) and takes on the Sr isotopic composition of the bulk xenolith (87Sr/86Sr ¼ 071136). Most Sr resides in plagioclase (and, thus, the solids) and the 87 Sr/86Sr is equal for solids and liquids in both the host and xenolith, Hence, as is clear from inspection of Fig. 1, the solid component of the both the 60^40 and 80^20 mixtures is enriched in both total Sr and radiogenic Sr relative to the liquids in those mixtures (Fig. 1a and b). This assimilation model is akin to a magma mixing model where plagioclase is an abundant phenocryst phase in a magma that is then mixed into the basalt host. 1030 BEARD CRYSTAL^MELT SEPARATION Table 1: Compositions of starting materials Mineral Age (Ma) Mode Rb (ppm) Sr (ppm) Rb/Sr 87/86init 87/86now Sm Nd (ppm) (ppm) Sm/Nd 144/143init 144/143now 10 64 016 0512 512371 Xenolith biotite 600 25 300 36 83 0704 0914512 plagioclase 600 50 4 510 00078 0704 0704194 25 quartz 600 all minerals except biotitey 600 75 86 32 027 0512 0512634 bulk 600 100 77 264 029 0704 071136 895 40 021 0512 0512499 bulk 0 100 50 400 025 0704 0704 2 10 02 05127 05127 melt, Sr bulk D ¼ 1 0 50 50 400 025 0704 0704 325 1625 02 05127 05127 solids, Sr bulk D ¼ 1 0 50 50 400 025 0704 0704 075 375 02 05127 05127 melt, Sr bulk D ¼ 2 0 50 50 200 025 0704 0704 325 1625 02 05127 05127 solids, Sr bulk D ¼ 2 0 50 50 600 025 0704 0704 075 375 02 05127 05127 Host magmaz Quartz is assumed to contain insignificant Sr, Rb, and REE (1 ppm). y Includes REE-rich trace phases (e.g. apatite, sphene, zircon). z Plagioclase is assumed to contain 51 ppm Nd. Host bulk D for Nd, Sm ¼ 03. For model 2 (Fig 2a and b) it is assumed that all of the plagioclase is consumed during melting of the xenolith via the reaction 25bio þ 25qtz þ 50plag ¼ 75melt þ 15opx þ 5cpx þ 5FeTiox: ð5Þ Because the melting reaction involves the entire rock, solid and liquid components of the xenolith are again in chemical and isotopic equilibrium at the time of mixing. However, because melting of plagioclase has released most of the Sr to the melt phase (bulk Kd for Sr in a plagioclase-free system is 5003), liquid-rich compositions are enriched in Sr and that Sr is highly radiogenic. It should be noted that melting of the xenolith in model 2 is much more extensive than for models 1 and 3. This assimilation model is akin to a magma mixing model where plagioclase is not present as a phenocryst phase in a magma that is then mixed into the basalt host. For model 3 (Fig. 3a and b), plagioclase is indifferent to melting in the xenolith, neither reacting with, contributing to, consuming, nor equilibrating with the melt. The melting reaction 25bio þ 15qtz ¼ 25melt þ 12opx þ 3FeTiox ð6Þ is modified after Patin‹o Douce & Beard (1995) for the melting of a biotite gneiss at 9508C and 5 kbar (Table 2). In this model, all of the Sr in the partial melt of the xenolith is derived from the biotite, whereas essentially all of the Sr in the xenolith residua resides in plagioclase. Thus the liquid and solid share, respectively, the isotopic Table 2: Models for Sr during xenolith melting Sr (ppm) 87/86now Model 1 Melting reaction (plagioclase equilibrated, bulk D ¼ 2) 25bio þ 15qtz þ 60plag1 ¼ 25melt þ 12opx þ 3FeTiox þ 60plag2 xenolith melt 66 071136 xenolith restite 330 071136 bulk xenolith 264 071136 Model 2 Melting reaction (plagioclase-out) 25bio þ 25 qtz þ 50plag ¼ 75melt þ 15opx þ 5cpx þ 5FeTiox xenolith melt xenolith restite bulk xenolith 349 071136 9 071136 264 071136 Model 3 Melting reaction (plagioclase indifferent) 25bio þ 15qtz ¼ 25melt þ 12opx þ 3FeTiox xenolith melt 36 0914512 xenolith restite 340 0704194 bulk xenolith 264 071136 characteristics of biotite and plagioclase. The striking feature of Fig. 3a and b is the extremely radiogenic character of the xenolith melt (87Sr/86Sr ¼ 09145), a consequence of high Rb/Sr in the biotite (Table 1; 1031 JOURNAL OF PETROLOGY VOLUME 49 MAY 2008 For the equilibrium models (1 and 2), the isotopic composition of the solids and liquids does not vary between endmember models; only the Sr content of the solids and liquids is affected. However, even partial disequilibrium during xenolith melting will result in deviation from isotopic and chemical equilibrium. In particular, even small amounts of disequilibrium (e.g. 10%) during melting can have large effects on liquid compositions in a crystal-rich system and solid compositions in a melt-rich system (Fig. 4a and b). For model 3, if plagioclase is actually formed as a consequence of the melting reaction (e.g. amph ¼ plag þ melt), the composition of the solids will vary along the line in Fig. 4c. The consequences of neoblastic plagioclase formation on mixing relations are seen in Fig. 4d. It should be noted, in particular, that the solids in this case will have Knesel & Davidson, 1999). Thus, even though this melt contains only 36 ppm Sr (as opposed to 400 ppm in the host magma) it has a strong influence on the isotopic composition of the system. The xenolith solid, in contrast, is nearly as non-radiogenic as the host magma. In fact, it was necessary to omit the ‘mixed solids’ line in Fig. 3b for clarity. It should be noted that if the initial 87Sr/86Sr of the xenolith is elevated, 87Sr/86Sr in the plagioclase will be as well. In such cases, 87Sr/86Sr of a mixed solid in a mixed system could conceivably be as high as or higher than the mixed liquid (analogous to the behavior seen in Fig. 1). The range of xenolith solid and liquid compositions that can be produced by combinations of the three models lies within the areas outlined by the mixing lines in Fig. 4a (for liquid compositions) and Fig. 4b (for solid compositions). (b) 0.714 (a) model 3 pla gm ilibrates 0.708 s elt 0.8 plag melts 0.710 plag equilibrates plag equ xenolith liquid compositions model 1 model 2 0.712 0.9 plag 0.706 87 Sr/86Sr NUMBER 5 mel ts 0.704 model 2 plag melts xenolith solid compositions model 1 0.7 0 0.702 100 200 300 400 0 100 200 Sr, ppm (d) 0.716 xenolith solid composition: variation as new plag forms during melting, plagioclase/melt Kd = 2 Sr/86Sr soli d-liq bu lk solid 25% product plag 340 342 344 0.704 dl 0.7 lin e 200 400 iqu ids s lid so solid, model 3 (0% product plagioclase) xe m ixi ng 0.8 mix d 0.705 mi uid 0.9 xenolith liquid ixe 0.708 0.704 400 m 87 olith 0.712 0.706 0.703 338 25% plagioclase formed during xenolith melting xen 0.708 0.707 300 Sr, ppm (c) 0.710 0.709 model 3 60% host 80% host host solid and liquid 346 348 350 Sr, ppm 200 300 400 Sr, ppm Fig. 4. Summary of the effects of plagioclase behavior on the compositions of melt and crystals in the ‘xenolith’end member. (a) Effects on melt compositions. Melting of plagioclase drives melt composition towards the model 2 (plagioclase-free) composition. Equilibration of plagioclase without melting drives the unequilibrated melt from model 3 towards the equilibrated melt of model 1. The area outlined by the mixing lines defines the range of melt compositions that may form during melting of the xenolith. For an equilibrated system, the range of melt compositions is restricted to the mixing line connecting model 1 (no plagioclase in the melt) and model 2 (all plagioclase in the melt). (b) Effects on solid compositions. The area outlined by the mixing lines defines the range of solid compositions formed during the melting of the xenolith. (c) Effect on the bulk solid of the formation of additional modal plagioclase as a product of the melting reaction. This is an extreme (and unrealistic) example, intended only to demonstrate the effect. (d) Model 3a, recalculated assuming 25% product plagioclase. 1032 BEARD CRYSTAL^MELT SEPARATION a higher Sr content and 87Sr/86Sr than the liquids. These diagrams are shown for demonstration purposes only. Large amounts of new plagioclase will not generally form during dehydration melting of biotite gneiss (e.g. Patin‹o Douce & Beard, 1995). The two models for Nd isotopes (Table 3; Fig. 5a and b) are essentially equivalent to models 1 and 3 for Sr isotopes (Table 2). For both models, a bulk Kd for Nd of 03 is assumed for the host magma. In the first model, based on melting reaction (4) (Fig. 5a), the liquid and solid phases in the partially melted xenolith are in chemical and isotopic equilibrium. For this model, 143Nd/144Nd is lower in mixed solids than in the coexisting mixed liquids. In the second model, based on melting reaction (6) (Fig. 5b), all Nd in the partial melt of the xenolith is derived from biotite, which is modeled as having Sm/Nd of 016 (Yang et al., 1999). REE in the restite (Sm/Nd ¼ 027) are largely contained in trace phases such as apatite and sphene (Condie et al., 1995; Ayres & Harris, 1997; Bea & Montero, 1999). For this model, 143Nd/144Nd is lower in the mixed liquids than in the coexisting mixed solids. Mixing of liquids with a partially crystalline host magma 10556 051253 xenolith restite 1815 051253 bulk xenolith 4000 051253 In general, assimilation of a liquid by a partially crystalline magma will increase isotopic inequalities in the system. In the simplest case, where the crystals and liquid in the host magma have the same chemical and isotopic composition, the mixture appears to devolve to a simple mixing line (Fig. 6a). However, there will be significant differences in the chemical and isotopic compositions of the bulk mixture on the one hand and the mixed liquid on the other (Fig. 6a). Mixing relations become more apparent in Fig. 6b and c. These models are equivalent, the only difference being in the composition of the assimilant liquid. A noteworthy feature is the large potential isotopic heterogeneities manifest in Fig. 6c and d, where the melt modeled in Fig. 3a [derived from reaction (6)] is mixed directly with the host magma. Development of isotopic heterogeneity in homogenized binary mixtures of assimilant and host Table 3: Models for Nd during xenolith melting Nd (ppm) 144/143now Model 1 Melting reaction (restite equilibrated, bulk D ¼ 03) 25bio þ 15qtz ¼ 25melt þ 12opx þ 3FeTiox xenolith melt Model 2 Melting reaction (restite indifferent) 25bio þ 15qtz ¼ 25melt þ 12opx þ 3FeTiox xenolith melt 64 0512371 xenolith restite 32 051264 bulk xenolith 40 051253 Of particular interest for all models are the 60^40 and 80^20 host^assimilant mixing lines (labeled ‘60% host mixing line’ and ‘80% host mixing line’ in Figs 1^4). (a) (b) host solid-liquid mix mixed solids 60% host mixing line 80% host mixing line 80% host mixing line mixe lids 0.5125 bulk mix xe no lith ids so lid 0.5125 d liqu d so 144 Nd/143Nd ix bulk m 0.5127 mixe 0.5126 host solid-liquid mix Bulk Kd for Nd = 0.3 0.5127 60% host mixing line mix ed -liq uid mi x liqu ids xenolith solid-liquid mix 0.5123 0 50 100 150 0 20 40 60 Nd, ppm Nd, ppm Fig. 5. Nd mixing models. (See Table 1 for compositions and Table 3 for descriptions of models.) Mixing lines as described in Fig. 1. Bulk Kd for Nd in host ¼ 03 for both models and for xenolith in (a). Mineral and melt compositions calculated for Rayleigh fractionation. (a) Solid and liquid in xenolith are chemically and isotopically equilibrated prior to assimilation. Melting reaction as in Fig. 1b. (b) Xenolith Nd derived from biotite (Sm/Nd ¼ 016), restite Nd controlled by trace phases (Sm/Nd ¼ 027). Melting reaction as for Fig. 3a. It should be noted that the ‘60% host’ mix line lies very close to the liquid mix line and the ‘80% host’ mix line lies close to the bulk mix line. This is coincidental. 1033 JOURNAL OF PETROLOGY (a) VOLUME 49 (b) assimilant = 100% melt of xenolith assimilant = 100% melt of xenolith bul k liquid 0.705 80% host { 0.707 all solids 80% 0.705 60% hos 300 400 host liquid 0.703 100 200 0.77 500 300 400 600 700 (d) host 0.5127 0.72 60% 80% host 0.71 Nd/143Nd 144 ids 700 80% host 0.5125 60% hos host solid assimilant = 25% melt of xenolith 0.70 100 200 300 t host host liquid 0 iqu 500 dl 300 host 50% solid Sr bulk Kd host = 2 ix 100 host 50% solid Nd bulk Kd host = 0.3 xe line 0.7 0.73 km 0.8 mi bul ing mix uids 0.74 liquid solid 0.9 bulk mixed liq 0.75 Sr/86Sr 500 Sr, ppm assimilant = 25% melt of xenolith 0.76 87 t host solids Sr, ppm (c) hos t bulk host magma 0.703 200 mixed li } 60% host bulk e e lin liquid 0.707 host 50% solid Sr bulk Kd host = 2 g lin ng 0.709 quids ix i m host 50% solid Sr bulk Kd host = 1 in mix lk bu 0.709 Sr/86Sr MAY 2008 0.711 0.711 87 NUMBER 5 400 500 600 0.5123 700 0 10 20 30 40 50 60 70 Nd, ppm Sr, ppm Fig. 6. Assimilation of a liquid by a partially crystalline host magma. (a) Assimilant is a 100% melt of the gneiss, bulk Kd for Sr in the host ¼1. Although this appears to be a simple mixing line, the bulk and liquid compositions for the mixtures differ such that removal of crystals will produce chemical and isotopic heterogeneities. (b) As for (a), except bulk Kd for Sr in host ¼ 2. (c) Assimilant liquid is a 25% melt of the xenolith (compare Fig. 3a). Bulk Kd for Sr in host is 2. Inset shows complete range of variation in model. Box in inset outlines area of main figure. Dashed lines continue off diagram. (d) Nd isotopes modeled with a 50% crystalline host magma (bulk Kd for Nd ¼ 03) mixed with a liquid derived from 25% melting of the xenolith (compare Fig. 3a). The potential for extreme isotopic heterogeneity in (c) and (d) should be noted. 0.712 xenolith, bulk bu lk 0.710 xenolith liquid, 36 ppm Sr, 87Sr/86Sr = 0.9145 liquid in 60–40 mix m ix A 60% host mixing line t-r ich 0.708 liq 87 Sr/86Sr el m C 0.706 uid m ix bulk composition, 60-40 mix x'l h c -ri These binary mixtures can be used to represent crystal^ liquid separation in physically homogenized mixed magmas in which the antecrysts retain their isotopic identity. As an example, Fig. 7 shows an annotated expansion of part of Fig. 3a. The 60% host mixing line connects a point on the host^assimilant liquid mixing line (A) to a point on the host^assimilant solid mixing line (B). These two points are the compositions of, respectively, the liquid and the solid fractions of a bulk mixture consisting of 60% host magma and 40% assimilated xenolith. The intersection (C) of the 60% host liquid^solid mixing line with the bulk mixing line gives the relative proportions of solid and liquid in the mixed system, in this case (coincidently) 60% solid and 40% liquid. Thus for this model, a homogenized bulk mixture of 60% host and 40% assimilant will be 60% crystalline and have 87Sr/86Sr ¼ 070625. If we now allow solids and liquids in this homogenized 0.704 B xenolith solid solid in 60–40 mix 0.702 250 300 350 Sr, ppm Fig. 7. Expansion of Fig. 3a. (See text for discussion.) 1034 host solid, liquid & bulk 400 BEARD CRYSTAL^MELT SEPARATION (a) (b) xenolith 0.711 0.711 liquids liquid, 60% host mix bu ng lin e 0.709 ix 0.707 C Bulk Kd = 2 mixture = 60% host, 40% xenolith solid, 60% host mix B 0.705 300 350 Y solid-liquid tie lines, equilibrium crystallization 0.703 100 400 Sr, ppm solids mixture = 60% host, 40% xenolith host 0.703 250 100% crystallized (=bulk) 0.707 solid com sitions po fractional crystallization equilibrium crystallization 0.705 0 % crystallized m st Sr/86Sr ixi liquids 50 ho 87 m % 0.709 A 60 lk 100 Z 0% crystallized 200 300 400 500 Sr, ppm Fig. 8. Crystallization of the 60% host mixed magma from Fig. 3. Bulk Kd for Sr during crystallization ¼ 2. (a) Chemical and isotopic evolution of solids and liquids during fractional (Rayleigh) and equilibrium (Berthelot^Nernst) crystallization. The isotopic composition of the liquid remains unchanged during crystallization. 87Sr/86Sr in the bulk solid increases as crystals are mantled with newly crystallized material in isotopic and chemical equilibrium with the liquid. A, initial liquid composition; B, initial solid composition; C, bulk composition. At 100% crystallization, the solid composition ¼ the bulk composition. (b) Solid^liquid tie-lines (tick marks at 10% intervals) during equilibrium crystallization. Yand Z mark the solid and liquid compositions, respectively, at 90% crystallization. (See text for discussion.) system to separate without further crystallization, separation of the magma into solid- and liquid-rich regions will yield crystal-rich regions with relatively low 87Sr/86Sr and complementary melt-rich regions with higher 87Sr/86Sr (Fig. 7). Such separation occurring on the scale of a magma chamber will produce an isotopically zoned body. As an example, let us start with the homogenized bulk mixture with 60% crystals 87Sr/86Sr ¼ 070625. If onethird of the crystals are removed from one region of the magma [leaving it with 50% crystals (60^20 ¼ 40 mass units crystal, 40 mass units melt)] and added to another region of magma [which would now have 67% crystals (60 þ 20 ¼ 80 mass units crystal, 40 mass units melt)] an isotopic heterogeneity will be created. The volume of magma containing 50% crystals will have 87 Sr/86Sr ¼ 07068, and the complementary volume containing 67% crystals will have 87Sr/86Sr ¼ 07058. If the modal variation in antecryst content is continuous, zoning will be continuous as well. Crystallization of the homogenized hybrid magma The mixing behaviors shown in Fig. 8 reflect the assumption that pre-existing crystals (antecrysts) in the end-members retain their isotopic characteristics after hybridization (see the Introduction). However, once the system is mixed, any new solids that crystallize from the hybrid magma are assumed to be in chemical equilibrium with the hybrid melt phase, either in their entirety (equilibrium crystallization) or instantaneously (fractional crystallization). In either case, isotopic equilibrium between new solids and extant melt is to be expected. This will lead to isotopic zoning in the crystals, with a relict, disequilibrium antecrystic core and an isotopically equilibrated, neoblastic rim. Both fractional (Rayleigh) and equilibrium (Bertholot^ Nernst) crystallization paths were calculated using Cm ¼ Ci f ðD 1Þ ðRayleighÞ ð7Þ and Cm ¼ Ci =½D þ f ð1 DÞ ðBertholot NernstÞ ð8Þ where Cm is the concentration of Sr in the evolved melt, Ci is the the initial concentration of Sr in the melt, f is the melt fraction and D is the bulk partition coefficient for Sr. These formulae were used to calculate the composition of the newly crystallized solids. The newly crystallized solids are assumed to be in chemical and isotopic equilibrium with the melt (Figs 7 and 8a, point A). However, because the system is 60% solid (i.e. point B, Figs 7 and 8a) at the outset, the solids plotted along the crystallization paths are mixtures of pre-existing (disequilibrium, antecryst) and newly crystallized (equilibrium, neoblastic) solids. The isotopic characteristics of these mixed solids are calculated using equation (1) and the isotopic and chemical compositions at points A and B (Figs 7 and 8a). Now, let us close the system to further material input. During closed-system crystallization of the homogenized hybrid magma, the isotopic composition of the bulk solid evolves on curved paths towards the bulk isotopic composition of the system (point C, Fig. 8a) as it incorporates radiogenic Sr from the liquid. The isotopic composition of the liquid will not change during crystallization unless there is diffusive exchange with the antecrysts. However, the very act of crystallization will further isolate the 1035 JOURNAL OF PETROLOGY VOLUME 49 antecrystic cores and help prevent isotopic exchange between the liquid and relict antecrysts sequestered in the cores of crystals. In Fig. 8, the enrichment in Sr in the solid seen during the early stages of crystallization reflects a high bulk Kd for Sr (2) used in the crystallization models. If the bulk Kd ¼1, the solid evolution line will follow the mixing line toward the bulk composition, whereas the liquid composition will remain constant. Figure 8b shows tie-lines [actually, they are calculated as solid^liquid mixing lines using equation (1)] connecting coexisting solid and liquid compositions at various points during equilibrium crystallization of the homogenized hybrid magma. This emphasizes the continuing isotopic inequality (a consequence of the presence of antecrystic cores in the growing crystals) between solid and liquid in the system even as it crystallizes. In short, even though the neoblastic crystal rims are in isotopic equilibrium with the liquid, the bulk solid and bulk liquid will not be in equilibrium. This is shown diagrammatically in Fig. 9. It should be noted that at any point along the crystallization path, separation of crystals from liquid will, perforce, yield an isotopic heterogeneity in the magma whose magnitude can be calculated (as for Fig. 7) by reference to the 10% tick marks in Fig. 8b. This holds for both equilibrium and fractional crystallization paths. Partial equilibration of antecrysts during postmixing crystallization will move the liquid composition toward the bulk composition along the tie-lines in Fig. 8b. In a completely equilibrated system, of course, the final solid and liquid will be isotopically identical. In many or most hybrid systems, however, it is likely that some sort of isotopic heterogeneity will be preserved, even if it is not as extreme as that posited by Fig. 8. DISCUSSION Once isotopic inequality between the solid and liquid components of a magma is established, it tends to persist regardless of subsequent fractionation, crystallization, or mixing events (Fig. 8). This is because isotopic homogenization between the liquid and crystal fractions of the mixed magma can occur only via diffusion or recrystallization and, especially, only if isotopic homogenization occurs before crystal-enriched volumes of magma form. Sr in feldspar, in particular, preserves records of isotopic heterogeneity during the lifetime of many magma chambers (e.g. Davidson & Tepley, 1997), and, indeed for millions and even billions of years beyond that time in felsic and mafic plutons (Waight et al., 2000; Halama et al., 2002; Tepley & Davidson, 2003). If antecrysts do not fully equilibrate, the mixing behavior of isotopically dissimilar, partially crystalline magmas combined with normal (gravitational separation, sidewall accumulation, filterpressing, etc.) crystal^liquid separation processes will result, perforce, in the development of a magma-scale NUMBER 5 MAY 2008 isotopic heterogeneity. Although diffusive or other equilibration early in the mixing history can mitigate the development of large-scale isotopic heterogeneity in hybrid magmas, other factors, especially separation of melt from xenolith (Fig. 6), will tend to exacerbate it. Once magmascale heterogeneities form, they will be unaffected by any subsequent crystallization, mixing, or equilibration event. The heterogeneity can be mitigated only by diffusion at the scale of the magma chamber and, hence, is essentially permanent. Aplites and pegmatites From a mechanistic point of view, a logical interpretation of late, differentiated intrusions (e.g. aplites and pegmatites) that cut across many plutons is that of interstitial melt expressed during the last stages of crystallization. However, the isotopic composition of many late aplitic or pegmatitic intrusions differs from the bulk isotopic composition of the host pluton (e.g. Kistler et al., 1986; Johnson et al., 1990; Barbey et al., 2001; Ernst et al., 2003), leading to their interpretation, in many cases, as local injections of unrelated magma. The behavior of isotopes in partially crystalline mixtures provides a means whereby, in some cases, the chemical and mechanical interpretations can be reconciled (Figs 8 and 9). Of particular importance here is the idea that once crystal^liquid isotopic heterogeneities are established in a mixed magma, they persist. Let us take, for example, a liquid separated from solids after 90% crystallization (point Z, Fig. 8b). This liquid will have an isotopic composition inherited and unchanged from the original mixture. The bulk solid composition will have evolved along the line labeled ‘solids’ to point Y (Fig. 8b). Separation of liquid from solid at that point will yield a chemically differentiated liquid in apparent isotopic disequilibrium with its host as shown diagrammatically in Fig. 9. However, it is clear that the isotopic heterogeneity is, in this case, inherited from the original mixing event. There is no need to call upon a separate and unrelated aplite magma. Isotopic zonation in high-silica rhyolites The behavior of isotopes in mixed systems may have implications for a much more significant (volumetrically, at least) geological problem; the origin of large-volume rhyolite tuffs. Recent studies and syntheses across a variety of disciplines are now concluding [and confirming; see, for example, Buddington (1959) or Lipman (1984)] that caldera-forming rhyolites are the surface manifestation of the same large-volume magmatic events that produce granitic batholiths. Rhyolites represent the evolved, melt-rich part of the system, and granitic plutons represent the complementary crystal-rich portion (Halliday et al., 1991; Bachmann & Bergantz, 2004; Lipman, 2008). Implicit in this interpretation is that crystal^melt separation is important in the petrogenesis of large-volume rhyolites. 1036 BEARD CRYSTAL^MELT SEPARATION pre-mix 87Sr/86Sr ≠ 87Sr/86Sr homogenization (a) (b) crystallization of homogenized magma end-stage expulsion of interstitial melt (d) APLITE DIKE (c) 0.710 0.706 0.704 0.710 end crystal (to scale for 60% mixture) 0.706 87Sr/86Sr ≠ 87Sr/86Sr Fig. 9. Formation of a discontinuous isotopic heterogeneity (e.g. aplite) by crystal melt separation. (a) Pre-mixing configuration. (b) Hybrid magma immediately after homogenization. Gray and black rectangles represent antecrysts from the two end-members. Gray background is the chemically and isotopically homogenized mixed melt phase. (c) Crystallization of the hybrid magma forms neoblasts (open rectangles) and crystal overgrowths (open rims) in chemical / isotopic equilibrium with the liquid. Note that isotopic heterogeneity is carried only by the antecrysts. (d) Late aplite dike expressed from the largely crystalline system. The aplite will retain the isotopic composition of the original mixed melt phase. Coexisting solids carry a mixed antecryst^neoblast isotopic signature. Given that these rocks are exemplars of hybrid magmas, they would seem to provide an important test of the relationship between crystal^melt separation and the development of isotopic zoning in hybrid magmas Many zoned ash or ignimbrite eruptions are characterized by the early eruption of chemically and isotopically evolved, crystal-poor magma, followed by magma that is increasingly crystal-rich and less evolved. The process typically envisioned for this is the ‘inversion’of a zoned magma chamber (Smith & Bailey, 1966; Hildreth, 1979; Smith, 1979; Duffield et al, 1995; Brown et al., 1998; Hildreth & Fierstein, 2000; Dreher et al., 2005; Bindeman et al., 2006). Figure 10 is a diagrammatic illustration of the development of such a magma chamber by crystal^melt separation in a hybrid magma and its subsequent eruption as a zoned tuff. In magmas where recognizable, isotopically distinct antecryst populations are present and/or isotopic contrast is correlative with apparent fractionation relationships amongst similar (e.g. dacitic to rhyolitic) magmas, crystal^melt separation must be considered as a strong candidate for the source of isotopic variation. On the other hand, if isotopic zonation is manifest in glass separates, at least some of the zoning must be related to differential contamination or mixing. 1037 JOURNAL OF PETROLOGY VOLUME 49 NUMBER 5 pre-mix (a) (d) 87Sr/86Sr ≠ 87Sr/86Sr (b) homogenization (c) MAY 2008 crystallization of homogenized magma (e) eruption/inversion crystal-melt separation 0.7058 (f) 0.7058 0.7068 87Sr/86Sr ≠ 87Sr/86Sr 0.7068 Vertical Section Horizontal Section Fig. 10. Formation of a nominally continuous isotopic heterogeneity (e.g. zoned magma chamber) by crystal^melt separation. Mixing, homogenization and crystallization as in Fig. 9. Separation of crystals and melt to any degree will result in isotopic inequalities in the magma chamber. If variation in antecryst content is continuous, isotopic variation will be continuous as well. Eruption (and consequent inversion) of the magma chamber can result in a tuff zoned in crystal content and isotopic composition. Crystallization of the magma chamber can yield an isotopically zoned pluton. (a)^(c) as in Fig. 9. Symbols as in Fig. 9. (d) Crystals accumulate along the walls, roof, and floor of the magma chamber. (e) Inversion of the magma chamber (e.g. large-volume rhyolite eruption). (f) Depictions of a zoned magma chamber. Pluton edge and core isotopic compositions are as modeled for Fig. 7 (see text). Bright areas have the highest 87Sr/86Sr. If modal variation in antecryst content is continuous, isotopic zoning will be as well. Isotopic zoning in plutons An isotopically zoned magma chamber could, of course, freeze in place without erupting, yielding an isotopically zoned pluton (e.g. Fig. 10e and f). A note of caution, however, is in order. Large-volume rhyolites, however complex their petrogenesis, represent short-lived eruptive events rooted in a single, contemporaneously active magma system, perhaps even a single magma chamber. Large plutons on the other hand, may represent longerlived composites that, furthermore, are easily remobilized and reworked by subsequent magmatic events (Bindeman & Valley, 2003; Glazner et al., 2004; Bacon & Lowenstern, 2005; Bindeman et al., 2006; Lipman, 2008). The character of the zoning might provide a clue to its origin. If the modal abundance of isotopically distinct antecrysts correlates with the zoning pattern, not only might this explain 1038 BEARD CRYSTAL^MELT SEPARATION the origin of the zoning, but it may be an indication that the pluton represents a single-stage magma chamber. Obviously, if the zoning correlates with other features, such as chilled intrusive contacts, a composite origin may be indicated. CONC LUSIONS The solid and liquid components produced by the mixing of isotopically distinct, partially crystalline end-members will themselves be isotopically distinct. Thus crystal separation in hybrid magmas can be responsible for a significant component of the overall isotopic heterogeneity of the magma. The magnitude of the isotopic variability resulting from crystal^melt separation subsequent to hybridization may be as large as that resulting from differential contamination or multiple isotopically distinct sources. 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