Contrib Mineral Petrol (2011) 161:153–173 DOI 10.1007/s00410-010-0518-y ORIGINAL PAPER Crystal growth during dike injection of MOR basaltic melts: evidence from preservation of local Sr disequilibria in plagioclase Georg F. Zellmer • Kenneth H. Rubin • Peter Dulski • Yoshiyuki Iizuka • Steven L. Goldstein • Michael R. Perfit Received: 3 December 2009 / Accepted: 25 March 2010 / Published online: 10 April 2010 Ó Springer-Verlag 2010 Abstract Profiles of a total of 23 plagioclase crystals erupted within the 1982–1991 and 1993 flows of the Coaxial segment of the Juan de Fuca ridge, the 1996 flow of the North Gorda ridge, and from the Western Volcanic Zone of the ultra-slow spreading Gakkel Ridge, have been studied for variations in major and trace element concentrations. We derive equilibration times for the relatively rapidly diffusing Sr in mid-ocean ridge basalt (MORB) plagioclase crystals of the order of months to a few years in each case. All crystals preserve diffusive disequilibria of Communicated by J. Hoefs. Electronic supplementary material The online version of this article (doi:10.1007/s00410-010-0518-y) contains supplementary material, which is available to authorized users. G. F. Zellmer (&) Y. Iizuka Institute of Earth Sciences, Academia Sinica, 128 Academia Road, Section 2, Nankang, Taipei 11529, Taiwan, ROC e-mail: [email protected] G. F. Zellmer S. L. Goldstein Lamont-Doherty Earth Observatory of Columbia University, 61 Route 9W, Palisades, NY 10964, USA K. H. Rubin Department of Geology and Geophysics, SOEST, University of Hawaii at Manoa, 1680 East West Road, Honolulu, HI 96822, USA P. Dulski Section 3.3, GFZ German Research Centre for Geosciences, Helmholtz Centre Potsdam, Telegrafenberg, 14473 Potsdam, Germany M. R. Perfit Department of Geological Sciences, University of Florida, Gainsville, FL 32611, USA strontium and barium. Crystal residence times at MORB magmatic temperatures are thus significantly shorter, of the order of days to a few months at most, precluding prolonged crystal storage in axial magma chambers and instead pointing to rapid crystal growth (up to *10-8 cm s-1) and cooling (up to *1°C h-1) shortly prior to eruption of these samples. Growth of these crystals is therefore inferred to occur almost entirely within oceanic layer 2 during dike injection. Crystals that grew at lower crustal levels or earlier in the differentiation sequence appear to have been excluded from the erupted magmas, as might occur if most of the gabbroic rocks in oceanic layer 3 formed an interlocking crystal framework, with viscosities that are too high to carry earlier formed crystals with the melt. The vertical extent of eruptible, crystal-poor melt lenses within the gabbroic zone is constrained to *1 m or less by considering the width of local equilibrium growth zones, equilibration times, and crystal settling velocities. This lengthscale is consistent with field evidence from ophiolites. Finally, crystal aggregates within the Gakkel ridge sample studied here are the result of synneusis within the propagating dike during melt ascent. Keywords Partitioning Diffusion Axial magma chamber Dike injection Synneusis Introduction Mid-ocean ridge (MOR) volcanism produces most of Earth’s surface igneous crust. There is an extensive literature on how aspects of ocean crust creation (melting, magma accumulation, differentiation, heat loss, and eruption) vary within and between ridge segments. Much remains to be learned about the details of such processes, 123 154 particularly the range of magmatic conditions associated with individual MOR eruptions, where spatial geochemical patterns within individual lava flows may record axial magma reservoir conditions (e.g. variable melt delivery and along-axis mixing) as a function of crustal temperature and magma supply (e.g. Sinton and Detrick 1992; Perfit and Chadwick 1998; Rubin et al. 2001; Bergmanis et al. 2007; Soule et al. 2007). Erupted MORB compositions reflect a variable overprint of differentiation and mixing on mantle-derived primary liquids (e.g. Elthon 1979; Stolper 1980; Rubin et al. 2009). Global variations in lava chemistry as a function of geography, spreading rate, and crustal structure constrain how MOR volcanism samples the mantle, such as melting extent and melt supply to the crust (e.g. Klein and Langmuir 1987; Niu and Batiza 1991; Langmuir et al. 1992; Rubin and Sinton 2007; Niu and O’Hara 2008). All of these processes modulate chemical signals of mantle heterogeneity and obscure information about the length scales and magnitudes of compositional variance in MORB (e.g. Sinton et al. 1983; Thompson et al. 1985; Langmuir et al. 1986, 1992; Klein and Langmuir 1987; Niu and Batiza 1991; Sinton et al. 1991; Grove et al. 1992; Reynolds et al. 1992; Perfit et al. 1994; Smith et al. 1994; Kelemen et al. 1997a; Michael and Cornell 1998; Herzberg 2004). However, these overprints are also a useful indicator of the conditions of magma transport and accumulation at ridges, a series of steps that have collectively been termed the ‘‘Ridge Filter’’ (Rubin et al. 2009). There are numerous first-order physical features of spreading centres (e.g. axial morphology, relief, structure, magmatic, and hydrothermal systems) that relate primarily to the balance of heat supplied by new magma intrusion and heat lost by conductive and convective (hydrothermal) cooling of the seafloor (e.g. Chen and Morgan 1990; Phipps Morgan and Chen 1993). Because magma supply varies directly with spreading rate at constant crustal thickness, i.e. away from hot spots or offsets, many physical attributes of ridges vary with spreading rate. MOR magma chambers are commonly considered as composite magma bodies floored by thick, gabbroic crystal mushes that are only locally topped by smaller, mostly liquid melt segregations or melt lenses (Sinton and Detrick 1992). Such melt segregations have been seismically detected beneath ridges with moderate to high spreading rates. Two important features of such magma chambers are that a considerable proportion of magma evolution occurs at conditions of relatively high crystallinity in the crust, where the mineralogy of the solid phases is significantly more mafic than erupted lavas (e.g. Langmuir 1989; Sinton and Detrick 1992; Ridley et al. 2006; Rubin and Sinton 2007), and that liquid-dominated melt lenses, wherein more extensive fractionation occurs, exist only fleetingly, or are long-lived only in regions that are replenished 123 Contrib Mineral Petrol (2011) 161:153–173 frequently enough to counteract the effects of cooling in the shallow crust. Further, Rubin and Sinton (2007) have suggested that there may be multiple melt segregations in the crust, whose number and proportion increase with melt supply, which results in progressively lower mean magma temperatures, greater amounts of differentiation, more variable extents of differentiation, shallower crustal depths, and greater homogenization of mantle compositional attributes as melt supply increases. Relatively little is known about the temporal aspects of MOR volcanism. Only recently have the timescales of magma genesis and melt transfer been investigated through the use of U-series isotopes. Early studies of 230Th-238U disequilibria in MORB suggested timescales of not more than *105 years (Condomines et al. 1981). Improvements in analytical capabilities later allowed the measurement of shorter-lived isotopes and reduced this timescale to *103 years based on 226Ra-230Th disequilibria (Rubin and Macdougall 1988; Sims et al. 2002), and more recently to as little as a few decades based on 210Pb-226Ra disequilibria (Rubin et al. 2005). An understanding of the time scales of crystallization in young magmatic systems is critical in gaining insights into the dynamics of the magma ascent, storage, and differentiation, as is evident from studies at volcanic arc and hot spot settings (e.g. Zellmer and Annen 2008, and references therein). There are a number of techniques available to constrain crystallization times in recently erupted volcanic rocks, including crystal size distribution studies (e.g. Cashman and Marsh 1988; Marsh 1988; Higgins 1996, 2000; Turner et al. 2003; Morgan et al. 2007), and mineral isochron dating using 238U-230Th isotopes (e.g. Allègre and Condomines 1976; Pyle et al. 1988; Condomines 1997; Heath et al. 1998; Turner et al. 2003; Zellmer et al. 2000, 2008) and 226Ra-230Th isotopes (e.g. Volpe and Hammond 1991; Schaefer et al. 1993; Cooper et al. 2003; Turner et al. 2003; Zellmer et al. 2008; Rubin and Zellmer 2009). Alternatively, if the temperature of a magma is known, the residence times of individual crystals may be determined by modelling the diffusive equilibration of elements within and between crystals (e.g. Gerlach and Grove 1982; Nabelek and Langmuir 1986; Humler and Whitechurch 1988; Kohn et al. 1989; Nakamura 1995; Pan and Batiza 2002; Morgan et al. 2004; Costa and Dungan 2005; Morgan and Blake 2006; Zellmer and Clavero 2006). Strontium diffusion and magnesium diffusion within plagioclase crystals have recently led to the determination of residence times of this major mineral phase (Costa et al. 2003, 2010; Zellmer et al. 1999, 2003). So far there have been two systematic studies of crystal ages within MORB: Pan and Batiza (2002) used Fe–Mg interdiffusion to calculate olivine crystal residence times of hours to years at the East Pacific Rise, with the majority of Contrib Mineral Petrol (2011) 161:153–173 crystals yielding ages of less than 2 months. They modelled crystal zoning patterns using a continuously fed axial magma chamber with mean magma residence times of 1–3 months. Conversely, Costa et al. (2010) interpreted Mg profiles in plagioclase crystals from slow to intermediate spreading ridges and calculated minimum plagioclase residence times of about 1–10 years. They suggested that plagioclase crystals resided in a crystal mush zone for years to decades and were remobilized by disintegration and entrainment into the magma shortly prior to eruption. In this contribution, we investigate samples from a handful of well-characterized MOR eruptions from ridges of intermediate to ultra-slow spreading rates and apply strontium diffusion systematics, using previously published techniques (Zellmer et al. 1999, 2003). In contrast to Costa et al. (2010), we find ubiquitous short plagioclase residence times of the order of days to a few months at most, pointing to rapid crystal growth. These short residence times are most consistent with crystallization during dike injection within oceanic layer 2 just prior to eruption. Geological background and sample description We have studied plagioclase crystals from two MORB from the Juan de Fuca Coaxial segment and from one sample each of the North Gorda Segment and the ultraslow spreading Gakkel Ridge. In this section, the geological background of each of these ridges is reviewed, and the samples are briefly described. Background geochemical constraints are provided in Table 1. Juan de Fuca Ridge, Coaxial segment, and recent eruptions The intermediate spreading Coaxial segment of the Juan de Fuca (JdF) Ridge (*5.8 cm year-1; DeMets et al. 1994) has a magmatically robust morphology that changes character moving northward away from the Axial seamount (Embley et al. 1995). In the south, the neovolcanic zone is dominated by a constructional axial volcanic ridge bisecting a 9-km-wide axial valley, which transitions to a diffuse series of isolated hills, ridges, and depressions in the north (Embley et al. 1995). A shallow crustal magma lens was imaged in the southern part of the segment (Menke et al. 2002). A later seismic experiment imaged an axial magma chamber (AMC) along several portions of the segment, getting deeper in its northern part (Carbotte et al. 2006). The Coaxial segment has had three geochemically distinct (and hence genetically unrelated) eruptions during an unusually active period between 1981 and 1993 (Chadwick et al. 1995; Perfit and Chadwick 1998; Smith 1999). Here, we have studied a sample (2794-2R) from the historical 155 1993 eruption in the northern part of the segment, at a location called the FLOW site. The eruption lasted several weeks (Fox et al. 1995) and produced approximately 8.7 9 106 m3 of pillow lava (Perfit and Chadwick 1998). Two earlier eruptions, one at the FLOW site and one further south at a site know as ‘‘FLOC’’, are presumed to have occurred sometime between 1981 and 1991 (Embley et al. 2000). We have also studied a sample (2792-4R) from the earlier FLOW site eruption. Full geochemical details of the two Coaxial samples investigated here can be found in Smith (1999). The 1993 flow is more evolved than most older Coaxial lavas and exhibits moderate internal chemical heterogeneity compared to other mapped MORB lava flows (Rubin et al. 2001). Sample 2794-2R, with *7.9 vol% plagioclase and *4.6 vol% olivine, is fairly representative of the flow on average. The earlier FLOW site eruption is slightly less differentiated. Sample 2792-4R, with *7.8 vol% plagioclase and *5.1 vol% olivine, is again fairly representative of its flow on average. Samples of both flows also are some of the most incompatible element depleted of the entire JdF, and in addition have relatively non-radiogenic Sr isotopic compositions (Smith 1999; Embley et al. 2000), indicating that the Coaxial segment has a magmatic system that is distinct and separate from the other segments of the JdF ridge (Perfit and Chadwick 1998). North Gorda Ridge The intermediate spreading rate of 5.5 cm year-1 of the North Gorda Ridge is similar to that of the southern Juande-Fuca ridge (DeMets et al. 1994), but North Gorda has a deep axial valley more typical of ridges at slow spreading rates (Chadwick et al. 1998). Early petrological and geochemical studies (Davis and Clague 1987; Davis and Clague 1990) indicated that the North Gorda segment is characterized by a depleted source and a great diversity of lava compositions, which was attributed to variations in the degree of melting and to crystallization and mixing processes within small, isolated magma chambers. More recently, it has been suggested that the morphology and increased compositional diversity of North Gorda Ridge MORB in general reflect a temporal shift in melt production and aggregation under waning melt supply (Davis et al. 2008). However, lavas from the only documented historical eruption of this ridge, the 1996 fissure eruption in the Narrowgate region, are generally more magnesian (i.e. less differentiated) than most older samples from the region (Rubin et al. 1998, cf. Table 1). A similar compositional pattern is observed at the East Pacific Rise at 18.5°S, where the most recent, higher MgO lavas have been interpreted to reflect a magmatic rejuvenation on a local portion of the ridge following a period of lower volcanic productivity and 123 156 Contrib Mineral Petrol (2011) 161:153–173 Table 1 Background geochemical data on studied MORB samples Sample Flow 2792-4R JdF 1982–1991 FLOW site 2794-2R JdF 1993 FLOW site W9604-C3 North Gorda 1996 D27-16 Gakkel WVZ Sample glassa Flow av. (n = 10)a WRb Sample glassa Flow av. (n = 24)c WRb Sample glassd Flow av. (n = 12)c WRb Sample glasse Dredge av. (n = 5) WRb SiO2 (wt%) 49.6 49.4 49.4 50.6 50.5 50.3 51.0 51.0 50.7 48.3 49.2 48.2 TiO2 (wt%) Al2O3 (wt%) 2.02 14.4 2.00 14.5 1.77 14.9 1.65 13.5 1.68 13.6 1.46 14.1 1.23 15.7 1.26 15.8 1.10 16.0 0.88 18.0 1.07 17.1 0.52 24.4 FeO (wt%) 12.3 12.4 11.4 12.7 12.8 11.7 8.20 8.57 7.86 7.85 8.61 4.80 MnO (wt%) 0.20 0.23 0.18 0.23 0.24 0.20 0.14 0.13 0.13 0.12 0.16 0.07 MgO (wt%) 6.95 7.00 8.93 6.67 6.73 8.42 8.26 8.37 9.94 8.84 9.10 5.85 CaO (wt%) 10.8 10.9 10.5 11.3 11.32 11.0 11.8 12.3 11.5 11.8 12.0 13.8 Na2O (wt%) 2.74 2.80 2.64 2.65 2.67 2.59 2.69 2.85 2.56 2.60 2.66 2.33 K2O (wt%) 0.16 0.16 0.14 0.12 0.12 0.11 0.11 0.10 0.10 0.04 0.06 0.03 P2O (wt%) 0.21 0.20 0.18 0.14 0.15 0.12 0.12 0.11 0.11 0.07 0.09 0.04 f Sr (ppm) 103 ND ND 91 ND ND 160 ND ND ND ND ND Ba (ppm) 36 ND ND 25 ND ND 7.1f ND ND ND ND ND ND not determined Smith (1999) a b Calculated by mixing glasses with phenocryst phases (olivine Fo90 and plagioclase of average composition at each eruption site) in the appropriate vol. proportions, which are: ol : plag (vol%) = 5.1 : 7.8 (2792-4R), 4.6 : 7.9 (2794-2R), 4.6 : 6.7 (W9604-C3), 1.15 : 45.1 (D27-16); and assuming a basalt density of 3 g cm-3 and appropriate phase densities c Rubin et al. (2001) d Rubin et al. (1998), unless indicated otherwise e EPMA average of 1,156 groundmass analyses, this study f Unpublished metadata from Rubin et al. (1998) rifting (Sinton et al. 2002). Recent magmatic activity at the North Gorda eruption site, which is near the mid-segment high, may thus reflect a local magmatic rejuvenation that is superimposed on the waning regional magmatic trend indentified by Davis et al. (2008). The 1996 fissure eruption produced approximately 18 9 106 m3 of lava (Chadwick et al. 1998) over a period of several weeks (Fox and Dziak 1998; Rubin et al. 1998). The sample investigated here (W9604-C3) is a dated N-MORB from that eruption and geochemically fairly representative of the entire flow. It is a fresh, glassy pillow fragment containing *6.7 vol% plagioclase phenocrysts and *4.6 vol% olivine microphenocrysts. An earlier attempt to constrain plagioclase crystallization timescales in this sample used 226Ra-230Th disequilibrium (Cooper et al. 2003). That study did not yield an age, but concluded that crystal growth was rapid over a short time span relative to the 1.6 kyear half-life of 226Ra. continental margin of the Laptev Sea in the East (DeMets et al. 1994). The ridge can be divided into a remarkably linear western volcanic zone (WVZ), a central sparsely magmatic zone, and an eastern volcanic zone of widely spaced volcanoes (Michael et al. 2003). The WVZ segment has five axial volcanic ridges that are magmatically robust. The sample studied here (Gakkel D27-16) is part of a very fresh lava tube with megacrysts (up to *1 cm in size) of plagioclase feldspar, recovered in dredge 27 by the USCGC Healy crew on 20 August 2001 during the Arctic Mid-Ocean Ridge Expedition (AMORE) from the deep between the two largest volcanic ridges in the centre of the WVZ (cf. Michael et al. 2003). Due to the porphyritic nature ([45% crystals) of this sample (D27-16A) and the small amount of material available, we have used the electron microprobe to analyse the groundmass composition. The average of 1,156 analyses compares fairly well with an average of five other MORB samples from this same dredge (cf. Table 1). Gakkel Ridge, Western Volcanic zone Methodology review The ultra-slow spreading Arctic Gakkel Ridge (Dick et al. 2003) lies in the northern extension of the Mid-Atlantic Ridge (MAR). Its spreading rate ranges from 1.5 cm year-1 near the Lena Trough in the West to 0.6 cm year-1 at the 123 The geospeedometric method applied here is based on the previous work of Zellmer et al. (1999) and Zellmer et al. (2003), which is briefly reviewed below. In general, Contrib Mineral Petrol (2011) 161:153–173 157 calculating crystal residence times at magmatic temperatures involves (1) determination of the chemical equilibrium concentration of a trace element within the plagioclase crystal under consideration, (2) choosing an appropriate initial trace element concentration profile, and (3) applying known trace element diffusion rates within the crystal to derive a residence time. Here, as previously, we use Sr as the trace element of choice. Determination of Sr chemical equilibrium In chemical equilibrium, the relative Sr concentration of any two parts i and j of a plagioclase crystal will be determined by a solid–solid partition coefficient Di/j, which is a function of the difference in their anorthite contents, XAn, and of temperature, T: ! i j 26; 700 XAn XAn i=j DSr ¼ exp ; ð1Þ RT where R is the universal gas constant (8.31451 J mol-1 K-1). In practice, absolute bulk crystal equilibrium profiles are calculated by adopting a boundary condition such as preservation of total Sr content within the crystal (e.g. Zellmer et al. 1999, 2003; this study), or chemical equilibrium of the crystal with an infinite melt reservoir of the composition of the glass (e.g. Costa et al. 2003, 2010). However, regardless of which boundary condition is used, the assessment of Sr chemical equilibrium or deviation thereof involves comparing Sr concentration ratios of different parts of a plagioclase crystal (rather than their absolute Sr concentrations) to the expected chemical equilibrium ratios derived for these parts. Chemical equilibrium between two parts i and j of a crystal is attained when i Cobs j Cobs ¼ i Cequil j Cequil ¼ Di=j ; ð2Þ where C denotes trace element (in this case, Sr) concentration, implying that in equilibrium, j i Cobs Cobs ¼ : i j Cequil Cequil ð3Þ If parts i and j are adjacent points within a traverse, local equilibration may be assessed as follows: We define q as the ratio between observed and equilibrium concentration at each point within the traverse, based on any chosen boundary condition: q¼ Cobs : Cequil ð4Þ Local equilibration is attained where the q-profile has no slope, i.e. when dq/dx = 0, x being distance along the traverse. It should be noted that distinct crystal growth zone boundaries are not required to assess local chemical equilibrium between adjacent parts of a crystal. This is a major advantage over conventional geospeedometric approaches, which use diffusion across sharp compositional contrasts to estimate crystal residence times. In practice, the assessment of local disequilibria requires knowledge of the uncertainties in both anorthite contents and trace element concentrations under consideration. It can be demonstrated (Zellmer et al. 2003) that concentrations Ci and Cj can be considered in equilibrium at the 95% confidence limit if i qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C Di=j 2 rðCi =C j Þ 2 þðrDi=j Þ2 ; ð5Þ C j where r denotes standard deviation, and rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2ffi w i=j i rDi=j ¼ D rXAn þ rX j ; An RT ð6Þ where the constant w is dependent on the element in question. It was shown by Blundy and Wood (1991) that wSr = -26,700 ± 1,900 J mol-1 and wBa = -38,200 ± 3,200 J mol-1. Choosing an appropriate initial Sr concentration profile The choice of an initial Sr concentration profile is the least constrained task in determining plagioclase crystal residence times. In conventional geospeedometry, sharp compositional contrasts, e.g. in major element chemistry, are assumed to have initially also been displayed by the diffusing species, providing a strong boundary condition (e.g. Costa et al. 2003). In the absence of sharp compositional contrasts, however, other constraints need to be applied. For example, extreme initial concentration contrasts across adjacent crystal growth zones can be employed to derive residence time maxima (e.g. Zellmer et al. 1999). Alternatively, initial concentration profiles may be modelled if reasonable assumptions can be made about the petrogenetic processes operating during crystal growth. For example, Zellmer et al. (2003) demonstrated that in plagioclase from the Soufriere Hills andesites, Montserrat, initial Sr concentrations were relatively invariant across phenocrysts due to the counterbalancing effect of Sr depletion in the melt during crystallization with Dplagjmelt [ 1 and increasSr ing partitioning of Sr into progressively less calcic plagioclase that formed during progressive crystallization from the evolving melt. Constraints on melt trace element evolution during crystallization were also employed by Costa et al. (2010), who used Mg diffusion in plagioclase to calculate MORB plagioclase residence times and argued that the evolving melt would be progressively depleted in Mg due to concurrent crystallization of olivine. However, 123 158 Contrib Mineral Petrol (2011) 161:153–173 as crystallization in their samples was apparently dominated by plagioclase with Dplagjmelt \1, the melt Mg conMg tent may in fact have increased with progressive evolution. As a result, their observed Mg concentration profiles may have been close to chemical equilibrium initially, rather than as a result of diffusive equilibration. (A similar case has previously been made for Ba, cf. Zellmer et al. 2003.) This example shows that the assumptions made in choosing an initial concentration profile are critical and need to be carefully evaluated. In this contribution, we apply a model of extreme initial compositional contrasts between adjacent parts of a crystal to obtain residence time maxima (see the section on ‘‘Diffusive equilibration of Sr disequilibria’’, below, for details), and refrain from any assumptions that require an a priori knowledge of the petrogenetic processes operating. preserved (e.g. Zellmer et al. 1999, 2003; Costa et al. 2010), indicating that crystal residence times at magmatic temperatures are generally much shorter than required for bulk crystal equilibration. However, one of the strengths of the methodology applied here is that it allows the assessment of local chemical disequilibria between closely spaced parts of a plagioclase crystal, irrespective of distinct growth zone boundaries. Thus, while the entire crystal may not have attained complete chemical equilibration through Sr diffusion, some parts of the crystal may already have equilibrated locally. Yet, if significant chemical disequilibria are retained at a local level in many parts of the crystal, very short crystal residence times are implied (cf. Zellmer et al. 2003). Therefore, fine scale analysis potentially allows crystal residence time constraints to be extended to very short timescales. Deriving crystal residence times through known Sr diffusion rates Analytical techniques Anorthite profiles are preserved over the time scales considered here, because coupled diffusion of Na, Ca, Al, and Si is very slow (Morse 1984) compared to diffusion of Sr (Cherniak and Watson 1994; Giletti and Casserly 1994). The diffusion coefficient of Sr in plagioclase, ÐSr (where the use of Ð is to avoid confusion with the partition coefficient, D), is a function of temperature and anorthite content: ( ) ÐSr = 10 − (4 .1 X An + 4 .08 ) exp − 3.32 × 10 4 T , (7) where the analytical uncertainty of ÐSr is approximately a factor of 2 at the ±2r level (Giletti and Casserly 1994). Zellmer et al. (1999) defined the undiffused fraction d of initial Sr chemical disequilibrium as d¼ CSr CSr;equil ; CSr;0 CSr;equil ð8Þ where CSr, CSr,0, and CSr,equil are the measured, initial, and equilibrium Sr concentrations of a crystal growth zone, respectively. They also showed that for plagioclase, d = 10% after a time t & b2/Ð, where b is the half-width of the growth zone. We will show in this contribution (see section on ‘‘Equilibration of extreme initial disequilibria in MORB plagioclase crystals’’, below) that even for unrealistically extreme initial Sr variations, b2/Ð is sufficient time to achieve equilibration at the 95% confidence limit, as governed by Eqs. 5 and 6. Crystals that show Sr concentration profiles in chemical disequilibrium have cooled to temperatures below which Sr diffusion is insignificant, before being able to fully equilibrate. In nature, bulk crystal Sr disequilibria are frequently 123 Major and trace element profiles of all samples were measured by laser ablation inductively coupled plasma mass spectrometry (LA-ICPMS) at the GeoForschungsZentrum Potsdam, Germany. Details on the instrument, analytical conditions, experimental procedure, and data reduction are given in the ‘‘Appendix’’. Quantitative electron probe microanalysis (EPMA) of crystals and groundmass and elemental distribution mapping of selected crystals were conducted using a field emission probe at the Institute of Earth Sciences, Academia Sinica, in Taipei, Taiwan. All details are provided in the ‘‘Appendix’’. We have compared EPMA-derived and LA-ICPMSderived anorthite contents (cf. supplementary Fig. S1) and conclude that the use of LA-ICPMS-derived XAn values is preferable, because they are based on exactly the same volume of ablated material, such that artefacts introduced by compositional heterogeneities within that volume affect both major and trace elements to a similar degree. We therefore use the LA-ICPMS-derived XAn values here. For details, see the ‘‘Appendix’’. Results Plagioclase petrography Major element zonation in the plagioclase crystals studied here is generally minor, with an average anorthite range for individual crystals of 0.06 ± 0.04 (1 stdev, n = 23) mole fraction units. As a result, enhanced elemental maps are required to illustrate zoning patterns, which are generally not imaged well enough by backscattered electrons (cf. Contrib Mineral Petrol (2011) 161:153–173 Fig. 1 Sodium elemental maps and backscattered electron images of selected plagioclase crystals. Within each image, warmer colours indicate higher Na concentration, but note that there is no cross-calibration between the different images. Juan-de-Fuca Ridge: a 27942R-1, b 2794-2R-2, c 2794-2R3, d 2792-4R-2, e 2792-4R-5 and 2792-4R-6; Gorda Ridge: f W9604-C3-4, g W9604-C3-6 amongst other crystals, h W9604-C3-7 amongst other crystals; Gakkel Ridge: i Euhedral plagioclase megacryst (*1.3 mm across) from sample D27-16, displaying complex but concentric zoning. j A larger ([3 mm across), subhedral, blocky plagioclase megacryst from sample D27-16, pointing to aggregation of several large crystals into one compound megacryst. The lower part of this megacryst contains microinclusions of resorbed amphiboles 159 Juan de Fuca Ridge (b) (a) (c) (e) (d) Gorda Ridge (g) (f) (h) Gakkel Ridge (i) Fig. 1). While some crystals are virtually unzoned (Fig. 1a–c), minor zonation patterns include normal zoning (Fig. 1d) and complex concentric zoning (Fig. 1e–i). Even in the case of complex zoning, internal growth surfaces are generally euhedral. Resorption surfaces are rare and if observed are generally subhedral and not especially prominent. Several of the images show crystals that touch each other and begin to grow together. The effect of crystals growing together is most apparent in the large subhedral Gakkel megacrysts (e.g. Fig. 1j), which represent blocky (j) crystal aggregates, composed of several large crystals of plagioclase with variable contents of microinclusions. The result is complex non-concentric zoning. These crystal aggregates are dominantly monomineralic and texturally very different from polymineralic xenocrysts that commonly display sieve textures caused by internal remelting (cf. Ridley et al. 2006). Crystal aggregates were avoided during the microanalytical work undertaken in this study, which instead targeted simpler, but large, individual crystals of up to 2 mm size, which either displayed concentric zoning (cf. Fig. 1j) or were not visibly zoned. 123 160 Plagioclase crystal chemistry The full mineral chemistry of all plagioclase analyses of the crystals studied here is given in supplementary Table S1. In summary, the crystals display a relatively restricted range in anorthite content, with An62-79, An65-72, An70-84, and An79-84 for the 1982–1991 JdF, 1993 JdF, 1996 Gorda, and the Gakkel sample, respectively. Plagioclase strontium and barium concentrations ranges vary, but overlap between individual crystals of each eruption. Strontium concentrations of 150–187, 133–159, 139–255, and 161– 264 ppm, and barium concentrations of 0.6–8.0, 2.0–5.6, 0.6–3.4, and 0.4–3.3 ppm were measured in crystals from the 1982–1991 JdF, 1993 JdF, 1996 Gorda, and the Gakkel sample, respectively. The lower relative concentration range in Sr compared to Ba is expected due to the counterbalancing effect of increasing Sr partitioning with decreasing anorthite content and concomitantly decreasing melt Sr content, as discussed in detail previously (Zellmer et al. 2003). Rim-to-rim geochemical profiles Given the size of the laser ablation pits, the so called ‘‘rim’’ spot analyses in this study are not representative of the actual crystal rims, but instead of the composition of the crystal just inbound of the rim. Therefore, our data do not provide any information about potential disequilibria between crystal rims and adjacent glass. Typical XAn, Sr, and Ba rim-to-rim geochemical profiles of one each of the crystals from the 1982–1991 JdF, 1993 JdF, 1996 Gorda, and the Gakkel sample are shown in Figs. 2, 3, 4, and 5, respectively. The XAn and Sr profiles of the remaining 19 crystals studied here are provided in supplementary Figs. S2 to S5. Each diagram displays (i) the measured variation in LA-ICPMS-derived anorthite content constrained by plagioclase stoichiometry, (ii) the measured variation in Sr (and Ba) across a crystal, (iii) the expected variation in Sr (and Ba) at chemical equilibrium as calculated from the variation in anorthite content (cf. Eq. 1) at the temperatures given in Table 2, and (iv) the variation of local disequilibria between adjacent parts of the crystal (dq/dx), see the ‘‘Methodology review’’ for details. Zoning patterns are variable, but large compositional jumps in XAn that would point to prominent resorption zones are very rare. There do not appear to be typical zoning patterns for crystals from individual MORB samples, or consistent differences in zoning patters between crystals from different eruption sites. As the rim spot analyses of an individual crystal are not always equidistant from the actual crystal rim, they are not expected to be within analytical error of each other. Compositional variations within each crystal are large 123 Contrib Mineral Petrol (2011) 161:153–173 enough to account for discrepancies that are occasionally observed. In any case, it is evident that although local chemical equilibrium is attained between some adjacent growth zones, all of the crystals studied do preserve significant local disequilibria, and none of the crystals have attained complete chemical equilibrium through diffusion of Sr or Ba. Furthermore, local disequilibria do not systematically decrease towards the crystal cores. Therefore, it is possible to put constraints on crystal growth rates and residence times at magmatic temperatures if equilibration times can be estimated. Finally, the broad rim-to-rim symmetry of trace element distributions within the two largest analysed Gakkel crystals suggests that these are indeed individual phenocrysts rather than crystal aggregates and are therefore suitable for the geospeedometric work presented in this contribution. Diffusive equilibration of Sr disequilibria An upper limit of crystal residence times at magmatic temperatures can be derived on basis of preservation of intracrystalline chemical disequilibria of Sr compared to the time required to reach a totally equilibrated profile. In this section, we first constrain the applicable diffusion coefficients for Sr in MORB plagioclase. We then consider the general requirements for equilibration of unrealistically extreme initial concentration profiles in MORB plagioclase crystals. Finally, equilibration time maxima are derived for each of the crystals studied here. Applicable Sr diffusion coefficients Diffusion of trace elements in plagioclase depends on temperature and anorthite content, with more rapid diffusion at higher temperature and lower XAn. For Sr, this relationship has been measured and parameterized by Giletti and Casserly (1994, cf. section ‘‘Deriving crystal residence times through known Sr diffusion rates’’ above), and their parameterization is shown graphically in Fig. 6 for a typical MORB magmatic temperature range. Superimposed are arrows indicating the plagioclase compositional evolution by fractional crystallization within dry and wet (0.5 wt% H2O) MORB during cooling, as calculated using the MELTS algorithm (Ghiorso and Sack 1995; Smith and Asimow 2005) on basis of the bulk compositions of the four samples studied here (cf. Table 1). Note that liquidus temperatures and plagioclase compositional evolution are largely independent of pressure and oxygen fugacity, but do change with water content of the melt (for details, see caption of Fig. 6). It is evident that plagioclase compositional trends are subparallel to lines of constant diffusivities. From the maximum and minimum anorthite Contrib Mineral Petrol (2011) 161:153–173 (a) JdF-2792-4R- 1 0.74 XAn 161 0.70 0.66 200 0.020 (b) 0.015 160 120 0.005 0.000 80 dρSr/dx (μm-1) Sr (ppm) 0.010 -0.005 40 -0.010 -0.015 0 (c) 0.030 Ba (ppm) 0.010 0.000 4 -0.010 dρBa/dx (μm-1) 0.020 6 -0.020 2 -0.030 -0.040 0 0 50 100 150 200 250 300 x (μm) Fig. 2 a Variation in LA-ICPMS-derived anorthite content of plagioclase crystal JdF 2792-4R-1. Intracrystalline disequilibria of this crystal are assessed in terms of b strontium and c barium. Observed Sr and Ba concentrations are given as solid squares. From the measured anorthite content, a bulk traverse equilibrium profile has been calculated (solid line with error bars) and can be compared with the observed concentrations. The ratio q of observed and bulk traverse equilibrium concentrations provides insights into local disequilibrium between individual zones: qSr = Srobs/Srequil; qBa = Baobs/Baequil. Adjacent zones are in local equilibrium when their q values are identical, i.e. where dq/dx = 0 (solid straight line). From a series of linear regressions through adjacent q values, the dq/dx profile is calculated as a measure of local disequilibria (solid stepped line), together with their 95% confidence limits (dashed envelope). Linear regressions were chosen such that the errors were minimized. Local equilibrium is reached where dq/dx = 0 within the uncertainties provided. Equilibration time and growth rate estimate in Table 2 are based on the shaded zone of local disequilibrium. Additional Sr profiles from the 1982–1991 FLOW eruption of the northern Coaxial segment are given in Fig. S2 contents measured within each of the four samples studied, the range in Sr diffusivity applicable for the plagioclase crystals can be deduced, as indicated by the grey fields in Fig. 6. Although there are small variations between the samples, a typical diffusion coefficient of 1 9 10-17 m2 s-1 is evidently a good order of magnitude estimate for all samples. Equilibration of extreme initial disequilibria in MORB plagioclase crystals In the following, we show that for MORB plagioclase, t & b2/Ð is sufficient time to achieve equilibration at the 2r (*95%) confidence limit, even for unrealistically extreme initial Sr variations. In MORB, using the 123 162 0.74 XAn (a) JdF-2794-2R-6 0.72 0.70 0.68 0.66 0.010 160 (b) 0.008 0.004 0.002 80 0.000 dρSr/dx (μm-1) 0.006 120 Sr (ppm) Fig. 3 a Variation in LAICPMS-derived anorthite content of plagioclase crystal JdF 2794-2R-6. Intracrystalline disequilibria of this crystal are assessed in terms of b strontium and c barium. Symbols and notation as in Fig. 2. Additional Sr profiles from the 1993 FLOW eruption of the northern Coaxial segment are given in Fig. S3 Contrib Mineral Petrol (2011) 161:153–173 -0.002 40 -0.004 -0.006 0 (c) 0.025 4 0.020 0.010 0.005 2 0.000 dρBa/dx (μm-1) Ba (ppm) 0.015 3 -0.005 1 -0.010 -0.015 0 0 50 100 150 200 250 x (μm) parameterization of Blundy and Wood (1991) and appropriate formation temperatures, DSr ranges from *2.7 for XAn = 0.6 to *1.4 for XAn = 0.85. An unrealistically extreme initial disequilibrium profile may thus be envisaged for a hypothetical crystal with alternating overgrowth zones generated by crystallization from cool E-MORB and hot N-MORB, with initial Sr concentrations alternating between 419 ppm within XAn = 0.6 (domain i) and 126 ppm within XAn = 0.85 (domain j), using the above partition coefficients and typical E-MORB and N-MORB Sr concentrations (Sun and McDonough 1989). In this case, taking conservative analytical uncertainties of 1.5% for XAn and 1.2% for CSr, we obtain for substitution into Eq. 5: rðCi =C j Þ ¼ 0:056; rDi=j ¼ 0:069 (cf. Eq. 6); and thus Sr Sr Sr C i Srj Di=j 0:18 (cf. Eq. 5) for domains i and j to be in Sr C Sr 123 equilibrium at the 95% confidence limit at the low temi=j perature end of crystal growth (*1,050°C, i.e. DSr ¼ 1:83 as calculated using the above anorthite contents of the two domains and the parameterization of Blundy and Wood 1991, cf. Eq. 1). At this low temperature end of crystal growth, equilibrium Sr concentrations are 352 within domain i and 193 ppm within domain j of this hypothetical crystal. Thus, after a time t & b2/Ð, when initial disequilibria have decreased by 90% (cf. section ‘‘Deriving crystal residence times through known Sr diffusion rates’’), Sr concentrations of 359 and 186 ppm would be observed within low and high anorthite domains of the crystal. We obtain C i i CSr i=j Sr ¼ 1:93, and hence C j DSr ¼ 0:10\0:18, finding CSrj Sr that the condition for equilibrium is in fact met well before Contrib Mineral Petrol (2011) 161:153–173 0.85 (a) Gorda W9604-C3-4 0.81 XAn Fig. 4 a Variation in LAICPMS-derived anorthite content of plagioclase crystal Gorda W9604-C3-4. Intracrystalline disequilibria of this crystal are assessed in terms of b strontium and c barium. Symbols and notation as in Fig. 2. Additional Sr profiles from the 1996 North Gorda eruption are given in Fig. S4 163 0.77 0.73 0.69 0.012 300 (b) 0.010 0.006 Sr (ppm) 200 0.004 0.002 dρSr/dx (μm-1) 0.008 0.000 100 -0.002 -0.004 -0.006 0 (c) 0.040 3 Ba (ppm) 0.020 2 0.010 0.000 1 dρBa/dx (μm-1) 0.030 -0.010 -0.020 0 0 50 100 150 200 250 -0.030 300 x (μm) time t & b2/Ð. To be conservative, we refer to b2/Ð as the equilibration time. Equilibration times and residence times of the crystals investigated Typical timescales to reach a totally equilibrated profile can be calculated for the crystals studied by appropriate choice of growth zone width (2b). Growth zone spacing is not immediately apparent from the profiles. Here, we use the minimum spacing over which local disequilibria are preserved within the central part of the rim-to-rim profiles obtained in this study, marked in grey in Figs. 2, 3, 4, and 5, and S2 to S5. Local disequilibria are calculated following Zellmer et al. (2003), as reviewed in the section on ‘‘Determination of Sr chemical equilibrium’’, above: the ratio between observed and equilibrium concentration is defined as q, and local disequilibria are identified in zones of the crystal where dq/dx = 0. Note that in order to derive growth zone spacings from Figs. 2, 3, 4, and 5, and S2 to S5, we plot dq/dx itself, rather than its absolute value |dq/dx|, which was employed by Zellmer et al. (2003) as a means of identifying the magnitude of local disequilibria. Crystal residence times to achieve complete equilibration are of the order of months to a few years (*0.6– 14 years for JdF2792-4R, *0.5–6.1 years for JdF2794-2R, *0.5–2.5 years for Gorda W9604-C3, and *2.2–34 years for Gakkel D27-16, cf. Table 2). These equilibration times are extreme overestimates because they are based on an unrealistically extreme initial disequilibrium profile as outlined in the previous section. Hence, more realistic timescales for crystals to fully equilibrate are likely shorter. 123 164 0.88 (a) Gakkel D27-16-E XAn 0.84 0.80 0.004 300 (b) 0.003 0.002 Sr (ppm) 200 0.001 dρSr/dx (μm-1) Fig. 5 a Variation in LAICPMS-derived anorthite content of plagioclase crystal Gakkel D27-16-E. Intracrystalline disequilibria of this crystal are assessed in terms of b strontium and c barium. Symbols and notation as in Fig. 2. Additional Sr profiles from this sample of the Gakkel Ridge are given in Fig. S5 Contrib Mineral Petrol (2011) 161:153–173 0.000 100 -0.001 -0.002 0 (c) 0.050 2 Ba (ppm) 0.030 0.020 1 0.010 dρBa/dx (μm-1) 0.040 0.000 -0.010 0 0 600 1200 -0.020 1800 x (μm) However, the fact that local chemical disequilibria are preserved in all of the crystals studied here suggests that more realistic, shorter equilibration times still significantly overestimate actual crystal residence times. We would therefore argue that actual crystal residence times are likely at least one order of magnitude shorter than the calculated equilibration times, i.e. generally ranging from days to a few months at most. Longer equilibration and residence times are only possible if crystals resided at much lower temperatures than those calculated from the least calcic growth zones. Strikingly, the observed ranges in crystal residence times are very similar in all the ridges studied and do not appear to be strongly dependent on differences in spreading rates or melt supply. 123 Discussion Crystallization during dike injection The preservation of significant local disequilibria as evident from Figs. 2, 3, 4, and 5, and S2 to S5 indicates that the crystals studied here had an order of magnitude shorter residence times at magmatic temperatures than the calculated equilibration times. Further, the fact that local disequilibria do not systematically decrease towards the crystal cores suggests that crystal growth was too rapid to be resolved by Sr diffusive equilibration, even locally. As shown above, it is hence evident that crystals grew rapidly and on the order of days to at most a few months prior to Contrib Mineral Petrol (2011) 161:153–173 165 Table 2 Determining minimum growth rates for all studied crystals Crystal XAn range Min. T (°C)a ÐSr (cf. Fig. 6) (10-17 m2 s-1) JdF 2792-4R-1 0.64–0.72 1,080 *1 JdF 2792-4R-2 0.67–0.79 1,080 JdF 2792-4R-4 0.62–0.72 1,080 JdF 2792-4R-5 0.67–0.79 JdF 2792-4R-6 JdF 2792-4R-7 Zone width 2b (mm)b Equil. time b2/ÐSr (years)c Distance to rim (mm) 31 0.8 149 6.2 *1 94 7.0 88 0.4 *1 132 14 96 0.2 1,080 *1 27 0.6 94 5.2 0.68–0.77 1,080 *1 29 0.7 180 8.6 0.69–0.74 1,080 *1 28 0.6 94 4.8 JdF 2794-2R-1 JdF 2794-2R-2 0.65–0.71 0.66–0.68 1,100 1,100 *1 *1 35 30 1.0 0.7 154 156 5.0 6.9 JdF 2794-2R-3 0.67–0.72 1,100 *1 33 0.9 139 5.1 JdF 2794-2R-4 0.67–0.69 1,100 *1 88 6.1 107 0.6 JdF 2794-2R-5 0.67–0.72 1,100 *1 26 0.5 79 4.7 JdF 2794-2R-6 0.67–0.70 1,100 *1 25 0.5 135 8.6 JdF 2794-2R-7 0.67–0.71 1,100 *1 30 0.7 268 11.9 Gorda W9604-C3-1 0.79–0.82 1,130 *1 46 1.7 80 1.5 Gorda W9604-C3-2 0.75–0.80 1,130 *1 56 2.5 132 1.7 Gorda W9604-C3-3 0.73–0.76 1,130 *1 25 0.5 100 6.4 Gorda W9604-C3-4 0.70–0.83 1,130 *1 25 0.5 147 9.4 Gorda W9604-C3-5 0.70–0.72 1,130 *1 26 0.5 69 4.1 Gorda W9604-C3-6 0.71–0.81 1,130 *1 34 0.9 115 4.0 Gorda W9604-C3-7 0.76–0.84 1,130 *1 33 0.9 189 6.9 Gakkel D27-16-E 0.81–0.84 1,145 *1 53 2.2 805 11.5 Gakkel D27-16-H Gakkel D27-16-O 0.79–0.84 0.81–0.84 1,145 1,145 *1 *1 60 206 2.9 34 973 460 10.8 0.4 a Min. growth rate (10-10 cm s-1)d Based on the lowest anorthite content of all crystals in each rock sample, and assuming 0.5 wt% H2O in the primitive magma b This is the width of the disequilibrium zone marked in grey in Figs. 2, 3, 4, and 5, and S2 to S5 c Actual crystal residence times are likely at least one order of magnitude lower, see text for discussion d These are effective growth rates that do not account for limited intermittent dissolution. Actual growth rates are likely at least one order of magnitude greater, see text for discussion eruption on the ocean floor. These short crystal residence times compare to estimates of days to a few years for olivines in MORB from the Mid-Atlantic Ridge and the East-Pacific Rise, based on Ni diffusion and Fe–Mg interdiffusion (Nabelek and Langmuir 1986; Pan and Batiza 2002) and are compatible with short magma differentiation and transport times required for the preservation of 210Pb-226Ra disequilibria that are generated during mantle melting (Rubin et al. 2005). They are, however, significantly shorter than recently reported minimum MORB plagioclase residence times of about 1–10 years (Costa et al. 2010). Based on the calculated equilibration times and the distance of central zones of local disequilibria from their crystal rims, we obtain minimum plagioclase crystal growth rates of the order of 10-9–10-11 cm s-1 (cf. Table 2). An order of magnitude shorter crystal residence times indicate growth rates of up to 10-8 cm s-1, implying cooling rates of up to 1°C h-1 (cf. Cashman 1993). Cooling rates upon eruption within submarine lava flows, where rapid quenching prevents significant crystal overgrowth and produces glassy or microcrystalline groundmasses such as those in which the crystals studied here are found, are typically at least two orders of magnitude faster (e.g. Grove 1990). Conversely, cooling rates within the gabbroic lower crust (oceanic layer 3) are four to six orders of magnitude slower (VanTongeren et al. 2008). Cooling rates of up to *1°C h-1, yielded by the crystals studied here, are most consistent with crystal growth occurring during dike injection (cf. Cashman 1993). One caveat to this scenario might be the inclusion of older crystals stored for long periods of time at significantly lower temperatures. Each 100°C decrease in temperature would result in a decrease in strontium diffusivity of about one order of magnitude. Thus, if the crystals studied here were more than a few years old, they would have had to be stored at C 200 degrees lower temperatures for most of that time. Even in the hydrous case, crystallinity would in this case 123 166 Contrib Mineral Petrol (2011) 161:153–173 XAn 0 0.2 0.4 XAn 0.6 0.8 0 0.2 0.4 0.6 0.8 1 1300 1300 (a) JdF2792-4R (b) JdF2794-2R 1200 T (°C) H2O wt% 0.5 m2 s -1 1100 m2 s -1 10 -1 8 m2 s -1 7 10 -1 10 -1 6 m2 s -1 m2 s -1 10 -1 5 0.5 10 -1 8 m2 s -1 7 10 -1 10 -1 6 m2 s -1 10 -15 1100 wt% m2 s -1 H2O T (°C) dr y dr y 1200 1000 1000 (d) Gakkel D27-16 0.5 w t% H 2 O dry (c) Gorda W9604-C3 1200 T (°C) 1100 m2 s -1 8 m2 s -1 10 -1 7 10 -1 10 -1 m2 s -1 10 -1 6 m2 s -1 8 m2 s -1 7 10 -1 10 -1 6 m2 s -1 10 -1 10 -1 5 5 1100 m2 s -1 m2 s -1 0.5 wt% T (°C) H2O dr y 1200 1000 1000 0 0.2 0.4 0.6 0.8 XAn 0 0.2 0.4 0.6 0.8 1 XAn Fig. 6 Evolution of anorthite content calculated by MELTS fractional crystallization modelling of MORB whole rock compositions (Ghiorso and Sack 1995; Smith and Asimow 2005), superimposed on diffusion coefficients as parameterized by Giletti and Casserly (1994). MELTS modelling used the FMQ-1 oxygen buffer, as appropriate for MORB evolution (cf. Christie et al. 1986; Bezos and Humler 2005), and employed dry MORB versus 0.5 wt% H2O in the parental melt to cover the range of H2O contents observed within MORB with up to 0.2 wt% K2O (cf. Almeev et al. 2008). Solid circles indicate the highest and lowest anorthite content observed within each sample, and symbol sizes represent ±2r uncertainties. Small discrepancies between the observed and predicted highest anorthite content, particularly in (a) and (c), may be related to flow heterogeneities (Rubin et al. 2001), with the samples studied not representative of the least evolved parts of each flow have exceeded 70% at the magmatic compositions of the studied basalts (Kelemen and Aharonov 1998), thereby effectively forming an uneruptable viscous crystal mush (e.g. Lejeune and Richet 1995) containing plagioclase crystals of much lower anorthite content (AnB50) than those observed in the samples studied here. Although more sodic crystal rims may have been resorbed prior to eruption due to immersion of such crystals into hotter, more mafic magma, it is difficult to envisage a scenario that would remobilize crystals from such a mush zone without at least preserving some crystal clots with more sodic plagioclase, or evidence for internal melting such as sieve textured crystals or prominent resorption zones. We therefore consider this scenario as highly unlikely. Our findings appear to be in contrast with the significantly longer minimum plagioclase residence times of years to decades in samples from the Mid-Atlantic Ridge and the Costa Rica Rift proposed on basis of Mg profiles, which were interpreted to reflect crystal residence in and remobilization from a lower crustal mush zone (Costa et al. 2010). However, as indicated above, the assumption that Mg disequilibria were introduced during crystal growth, on 123 Contrib Mineral Petrol (2011) 161:153–173 which those residence times are based, needs to be carefully considered. If crystals grew closer to Mg chemical equilibrium than assumed, the residence times calculated for these crystals on basis of intra-crystalline diffusion may be overestimates. A detailed re-evaluation of those published data is beyond the scope of this study, and remobilization of selected crystals from a mush zone remains possible at some sites. However, significant local Sr disequilibria are also observed within the plagioclase crystals studied by Costa et al. (2010), which would indicate that the residence times of at least some crystals erupted from those ridges may be shorter than previously thought. Effects on erupted phenocryst size The size of phenocrysts, once nucleated, will be controlled by the time available for crystal growth, which depends on magma rise rate and ascent distance. Although magma flow is controlled by dike width and melt viscosity (Rubin 1995), the widths of dikes at oceanic spreading centres typically range from 0.5 to 1.5 m and do not vary consistently with spreading rate (Qin and Buck 2008). Similarly, no systematic variations in MOR melt viscosities are expected. Thus, variations in the length of the melt ascent path are anticipated to perceptibly affect the size of large, early nucleated phenocrysts. Globally, Rubin and Sinton (2007) have shown that with decreasing overall melt supply to midocean ridges (based on spreading rates), the depth of axial magma lenses increases, implying that the dike section concomitantly thickens. This is consistent with geophysical observations of variations in axial magma chamber depth along individual ridge segments of the Juan de Fuca Ridge (Canales et al. 2005). Thus, if phenocrysts indeed grow mainly during diking, then the size of the large crystals studied here would be expected to broadly anti-correlate with melt supply, due to the greater magma ascent path. It is noteworthy that samples from the fast spreading East Pacific Rise were not studied here because of their general lack of sufficiently large plagioclase crystals and their commonly aphyric nature. In the areas where our basalts were recovered, the North Gorda eruption took place near the mid-segment high of this intermediate spreading ridge, implying relatively high melt supply, and crystals are generally small. The northern end of the JdF Coaxial segment, where the two FLOW eruptions were extruded, has an isolated hill-ridge-depression morphology, implying relatively lower melt supply, and crystals reach a slightly larger size. The largest crystals are present in the sample taken from the deep between two volcanic ridges of the ultra-slow spreading Gakkel ridge (cf. Table 2). These observations are thus consistent with crystal growth occurring dominantly during dike injection, rather than within axial magma chambers of the gabbroic oceanic layer 3. 167 Constraints on conditions within the upper gabbroic layer In the previous sections, we have argued that crystal growth occurred during dike injection, implying that melts extracted from the gabbroic layer are essentially aphyric. However, we cannot preclude the existence of microlites carried by these melts at the onset of diking. The width of zones within local Sr equilibrium occasionally observed in the crystals studied here is typically around 50 lm and rarely exceeds 100 lm. While most of these zones likely grew in equilibrium, rather than having equilibrated by diffusion, a small proportion might represent microlites that were suspended within magma lenses of the gabbroic zone for sufficiently long to have attained equilibrium, and that were then used as nuclei for more rapid overgrowth prior to eruption. We can use the 100-lm-length scale to put constraints on the vertical extent of such magma lenses through Stokes’ Law of particle settling: cs ¼ 2 gDq 2 a ; 9 qm m ð9Þ where cs is the terminal settling velocity of a spherical crystal, g is the acceleration due to gravity, Dq is the density contrast between the crystal and the magma, a is the diameter of the crystal, and qm and m are the density and kinematic viscosity of the melt, respectively. For anorthitic plagioclase in tholeiitic melts, Dq & 50 kg m-3, qm & 2,700 kg m-3 (Huppert and Sparks 1980), and m may be as low as 10-2 m2 s-1 (Martin and Nokes 1989), yielding plagioclase settling velocities in basalts of B4 9 10-8 m s-1 for small crystals of B100 lm diameter (cf. Martin and Nokes 1989). Even in anorthitic plagioclase crystals, chemical equilibrium between two adjacent 50 lm growth zones (to total a 100 lm nucleus) will have been well attained within less than 3 years (cf. Gakkel samples E and H in Table 2). After this time, the small crystals considered above will have settled less than 4 m. Larger crystals settle faster and would have settled out of the magma lens into the viscous mush zone. The absence of equilibrium crystal growth zones of [100 lm width in the crystals studied here indicates that once removed into the mush, individual crystals are not commonly remobilized into the melt and may only be erupted as part of cumulate xenoliths. However, the likely vertical dimension of melt lenses within the gabbroic oceanic layer 3 will be significantly smaller than the estimated 4 m because (i) maximum equilibration times in Table 2 overestimate actual equilibration times as outlined above, and (ii) convection within the inner part of a melt lens, if present, would decrease the rate with which crystals may be removed from the melt through a stagnant boundary layer (Martin and Nokes 1989). Hence, the vertical extent of the melt lenses 123 168 (c) Contrib Mineral Petrol (2011) 161:153–173 Our data do not rule out that magmas from such small melt lenses were subsequently aggregated into a larger body just prior to eruption. However, if this was the case, aggregation must have been very rapid and residence in the axial chamber very short. Origin of complex zoning and crystal aggregates (b) Given the limited lateral extent of individual sills within the layered gabbros (Ernewein et al. 1988; Boudier et al. 1996) and MORB lava flow volumes of several million cubic metres, melts from more than one sill must be combined in order to provide enough magma to sustain eruptions (Fig. 7a). The flow regime within the propagating dike will depend on the Reynolds number, Re. Spence et al. (1987) have shown that during buoyancy-driven magma ascent, the flow will be laminar if Re ¼ (a) Fig. 7 Petrogenetic model of melt extraction and magma ascent. a Initially aphyric melt from several melt lenses within the layered gabbros combine as diking is initiated. b Crystals begin to grow during laminar magma flow within the dike. Transfer of crystals across boundaries of melts with slightly different petrogenetic histories leads to complex zoning. c Grain dispersive pressures lead to crystal aggregation by synneusis in the centre of the dike if crystal content is high enough from which magmas were drained during the eruptions of the samples studied here probably did not exceed *1 m. This latter result is consistent with the dimension of sills within the layered cumulates of the Oman ophiolite, which have sill thicknesses ranging from centimetres to decimetres. Metre-sized layers are very scarce (cf. Ernewein et al. 1988; Boudier et al. 1996). The data from our study sites hence support models of lower oceanic crust formation by multiple sill intrusion (Kelemen et al. 1997b; Kelemen and Aharonov 1998; Kawamura et al. 2005) and are consistent with the notion that there exists a number of poorly connected melt lenses in the gabbroic crust beneath MORs (Rubin and Sinton 2007), rather than a single axial magma chamber as originally envisaged (Sinton and Detrick 1992). 123 ch \103 ; m ð10Þ where c is the dike propagation speed and h is the dike width. For reasonable values (c = 1 m s-1, h = 1 m, m C 10-2 m2 s-1), the flow regime will thus be laminar. Laminar flow is not as conductive to magma mixing as turbulent flow, and this may be the reason for some of the observed chemical heterogeneities of sampled MORB lava flows. Inefficient mixing may also result in the complex zoning observed in some of the phenocrysts studied here, if crystals are transferred between melt batches with different origins and storage histories during magma ascent (Fig. 7b). As crystallization progresses, grain dispersive pressures will lead to preferential migration of phenocrysts towards the centre of the dike, where velocity gradients are lowest (Komar 1972). When phenocryst concentration reaches a value of *8%, crystals in the centre of the dike begin to interact mechanically, and this may lead to phenocryst aggregation within the ascending melt by capillarity (Fig. 7c). This process is known as synneusis (Vance 1969) and is characterized by like minerals combining preferentially (Vance and Gilreath 1967). While some degree of phenocryst aggregation is observed in all of the samples studied here (cf. Fig. 1), synneusis appears to be most pronounced in the porphyritic Gakkel ridge sample with its largely monomineralic plagioclase aggregates. These are texturally very different from polymineralic xenoliths, which commonly display sieve textures caused by internal remelting (cf. Ridley et al. 2006). In addition, the change in crystal habit from prismatic to blocky with increasing crystal size of Gakkel ridge plagioclase is consistent with this process. Although Dowty (1980) has questioned if synneusis represents the principal mechanism in the formation of crystal aggregates in general, there is more Contrib Mineral Petrol (2011) 161:153–173 recent evidence for it to occur in experimentally cooled basaltic melts (Duchene et al. 2008; Pupier et al. 2008). Crystal aggregation is not as pronounced in the less porphyritic samples studied here, such that significantly lower phenocryst contents (\13% vs. [45% at Gakkel) likely resulted in less frequent mechanical interactions of phenocrysts during dike injection. 169 Science Foundation provided generous support for the Alvin and Jason dives. The research was funded by grants of the National Science Council of Taiwan (NSC 95-2116-M-001-006, 96-2116-M001-006, and 97-2628-M-001-027-MY2) and the Institute of Earth Sciences, Academia Sinica, to GFZ. Furthermore, partial support was provided by NSF grants to KHR (OCE-0732761 and OCE-9905463) and MRP (OCE-0221541 and OCE-9530299). Appendix Conclusions Laser ablation inductively coupled mass spectrometry (i) Plagioclase crystals erupted in MORB from intermediate to ultra-slow spreading ridges preserve significant intracrystalline chemical disequilibria for strontium and barium, implying crystal residence times of the order of days to at most a few months at magmatic temperatures, irrespective of spreading rate. (ii) Rapid crystal growth rates of up to 10-8 cm s-1 imply rapid cooling rates of up to 1°C h-1 and suggest that crystallization occurs during magma ascent in dikes, rather than within thermally buffered axial magma chambers. (iii) At lower melt supply, melt lenses are situated deeper, resulting in longer magma ascent times and the growth of larger crystals within erupted basalts (e.g. Gakkel). Higher melt supply, shallower melt lenses, and shorter magma ascent times limit crystal growth (e.g. EPR). (iv) Crystals larger than 100 lm may grow within the gabbroic layer but are not usually erupted, implying that they are retained in a rigid crystal mush. Rapid crystal settling velocities in basalts suggest that the vertical extent of axial melt lenses is unlikely to exceed *1 m in order to preclude incorporation of microphenocrysts into ascending magmas drained from such melt lenses. This result is consistent with field evidence of thin gabbroic sills exposed in the lower crustal section of the Oman ophiolite. (v) Complex zoning pattern in some crystals are due to phenocryst transfer during dike injection between mingling melts with different storage histories. Crystal aggregates in the porphyritic Gakkel ridge sample likely result from synneusis within the centre of the propagating dike during magma ascent. Acknowledgments GFZ acknowledges insightful communications with Daniel Morgan, Matthew Smith, and Steve Sparks, and is grateful to Jörg Erzinger for his hospitality and support at the GeoForschungZentrum. Earlier versions of this paper have been significantly improved by the constructive comments of Fidel Costa and two anonymous reviewers. We thank Michael Wiedenbeck for access to the AMNH feldspar standard during the analytical work in Potsdam. The NOAA Undersea Research Program and the National Major and trace element plagioclase rim-to-rim profiles of all samples were measured at the GeoForschungsZentrum Potsdam using a GEOLAS M Pro (Coherent, Germany) laser ablation device coupled to an ELAN DRC-e (PerkinElmer SCIEX, Canada) ICP-MS in dual detector mode. The LA device consisted of an excimer laser (COMPexPRO 102, Argon Fluoride 193 nm, Lambda Physik, Germany) with a maximum output energy of 200 mJ per pulse for repetition rates between 1 and 10 Hz, an optical beam path homogenizer to provide a homogeneous laser beam, an aperture mask with 10 circular holes with diameters of 0.125–4 mm (for ablation pit diameters of 5–160 lm), a petrographic microscope (Olympus BX 51), a 20 cm3 sample cell and a computer controlled x,y,z-stage. Samples were observed through the petrographic microscope with two lenses of different magnification (5 and 20 fold). During ablation, the sample image was continuously observed on a separate high-resolution monitor through a Schwarzschild objective (25-fold magnification) and a high-resolution CCD camera. Helium was used as carrier gas (1.0 L min-1), and argon as plasma (15 L min-1), auxiliary (1.2 L min-1), and nebulizer gas (0.7 L min-1). Elements of interest were measured using an output energy of 100 mJ, with 10 ms dwell time and 3 ms quadrupole settling time. Background intensities from the gas blank were measured for 30 s (laser firing, shutter closed) followed by acquiring transient signals of the analytes for 60 s (laser firing, shutter open) or until the laser beam had drilled through the sample and reached the sample holder (in case of thin sections). Each analytical batch consisted of up to 20 analyses. Samples were measured using a repetition rate of 5 Hz, an energy density of 6 J cm-2 and spot sizes of 16 or 24 lm. Rim-to-rim geochemical profiles were obtained for each crystal studied by spot analyses spaced between *20 and *100 lm apart, depending on crystal size. A reference glass standard (NIST 610) was measured twice at the beginning and twice at the end of an analytical batch for external calibration, using a repetition rate of 10 Hz, an energy density of 10 J cm-2, and a spot size of 32 lm. For data reduction, the LOTUS 123 macro-based spreadsheet programme LAMTRACE was employed. A 123 170 short, general description of its capabilities is given by van Achterbergh et al. (2001), and its algorithms are described in Longerich et al. (1996). The programme performs background correction, correction for instrumental drift, internal calibration, choice of integration intervals, and calculation of element concentrations using external calibration. The Ca signal was used for the calibration of trace element concentrations. Repeat analyses of gem labradorite AMNH 95557 revealed that LA-ICPMS-derived Na/Ca ratios were consistently about 11% higher than those derived by electron probe microanalysis (EPMA). This discrepancy was corrected for in the calculation of LAICPMS-derived anorthite contents, which was based on plagioclase stoichiometry (cf. Zellmer et al. 2003). The same repeat analyses also provide the basis for assessment of relative uncertainties for individual elements, and these are 1.5% for XAn, 1.2% for Sr, and 2.6% for Ba (1r, n = 16, cf. supplementary Table S1 for other elements). Electron probe microanalysis Following the LA-ICPMS analysis, the specimens were repolished using a vibration polisher with 0.3 lm particle alumina compounds to remove the debris of LA, and then carbon coated for microprobe analysis. Quantitative chemical analyses and, in some cases, elemental distribution (mapping) analyses were made by a field emission electron probe micro analyser (FE-EPMA: JEOL JXA-8500F) equipped with five wave-length dispersive spectrometers (WDS) at the Institute of Earth Sciences, Academia Sinica, in Taipei. Secondary- and back-scattered electron images were used to guide the analysis on target positions of minerals. A 2-lm defocused beam was operated for quantitative mineral analysis at an acceleration voltage of 12 kV with a beam current of 5 nA. Groundmass analyses were undertaken on the same instrument with a 5 lm beam diameter, 15 kV accelerating voltage, and 10 nA beam current. The measured X-ray intensities were ZAF-corrected using the standard calibration of synthetic chemical-known standard minerals with various diffracting crystals, as follows: wollastonite for Si with TAP crystal and Ca with PET crystal, rutile for Ti (PET), corundum for Al (TAP), chromium oxide for Cr (PET), fayalite for Fe with LiF crystal, tephroite for Mn (PET), pyrope for Mg (TAP), albite for Na (TAP), and adularia for K (PET). Counting times for peak and both upper and lower baselines were 20 s and 10 s, respectively, for each element. Relative standard deviations (RSD) for Si, Na, and K were less than 1%, and others were less than 0.6%. Detection limits were less than 500 ppm for all elements. To aid cross-correlation of EPMA and ICPMS analyses and to evaluate the general characteristics of crystal 123 Contrib Mineral Petrol (2011) 161:153–173 zoning, elemental distribution mapping of selected plagioclase crystals was performed with 15 kV, 20–50 nA, and 1–3 lm for the acceleration voltage, beam current and beam size, respectively. X-ray intensities of Ca-Ka, Na– Ka, and K-Ka were counted for 0.02–0.03 s in each spot, at 1- to 3-lm intervals. Comparison of EPMA-derived and LA-ICPMS-derived anorthite contents EPMA- and LA-ICPMS-derived anorthite contents are compared for a number of plagioclase crystals in Fig. S1. Due to the small EPMA beam size and closely spaced sampling interval, a range in XAn is obtained over the distance of 16–24 lm covered by the laser ablation spot analysis (cf. Fig. S1c). In Fig. S1a, the average and the respective range in EPMA-derived XAn is provided for each LA-ICPMS data point. Data between the two dashed lines are within the combined analytical uncertainties of each technique. The results are largely consistent between the two analytical methods, with exception of a few outliers, for which LA-ICPMS appears to slightly underestimate XAn. These outliers are more closely inspected in Fig. S1b and S1c. During the laser ablation analysis of one location from crystal W9604-C3-5, situated at the edge of a calcic growth zone, there is a clear increase in the Na signal with ablation time, suggesting that ablation progressed into an underlying, more sodic growth zone (Fig. S1b). Another example is crystal 2792-4R-2, where rim LA-ICPMS analyses again appear to underestimate XAn. Here, the outermost sodic rim contributes to the material sampled during ablation but is not sampled during the spatially restricted microprobe analysis (Fig. S1c). 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J Petrol 44:1413–1431 Zellmer GF, Rubin KH, Grönvold K, Jurado-Chichay Z (2008) On the recent bimodal magmatic processes and their rates in the Torfajökull-Veidivötn area, Iceland. Earth Planet Sci Lett 269:387–397 123 Contrib Mineral Petrol (2011) 161:175–176 DOI 10.1007/s00410-010-0595-y ERRATUM Erratum to: Crystal growth during dike injection of MOR basaltic melts: evidence from preservation of local Sr disequilibria in plagioclase Georg F. Zellmer • Kenneth H. Rubin • Peter Dulski • Yoshiyuki Iizuka • Steven L. Goldstein • Michael R. Perfit Published online: 27 November 2010 Ó Springer-Verlag 2010 Erratum to: Contrib Mineral Petrol DOI 10.1007/s00410-010-0518-y In the original paper, repeat analyses of gem labradorite AMNH 95557 provided the basis for assessment of relative uncertainties for individual elements and these were cited as 1.5% for XAn, 1.2% for Sr and 2.6% for Ba (1r, n = 16). Unfortunately, the beam conditions used during the ablation of this standard were not identical to The online version of the original article can be found under doi:10.1007/s00410-010-0518-y. G. F. Zellmer (&) Y. Iizuka Institute of Earth Sciences, Academia Sinica, 128 Academia Road, Section 2, Nankang, Taipei 11529, Taiwan, ROC e-mail: [email protected] G. F. Zellmer S. L. Goldstein Lamont-Doherty Earth Observatory of Columbia University, 61 Route 9W, Palisades, NY 10964, USA K. H. Rubin Department of Geology and Geophysics, SOEST, University of Hawaii at Manoa, 1680 East West Road, Honolulu, HI 96822, USA P. Dulski Section 3.3, GFZ German Research Centre for Geosciences, Helmholtz Centre Potsdam, Telegrafenberg, 14473 Potsdam, Germany M. R. Perfit Department of Geological Sciences, University of Florida, Gainsville, FL 32611, USA those used during sample analysis. We have recently reassessed the analytical uncertainties, employing the same analytical conditions as for our sample runs and using a homogeneous growth zone of one of the crystal samples as a working standard. We found that the relative uncertainties were in fact 0.5% for XAn, 1.9% for Sr and 15% for Ba (1r, n = 30). Thus, analytical uncertainties stated in the original paper were overestimated for XAn, underestimated for Sr and significantly underestimated for Ba. As a result, the precision on Ba is in fact often too low to resolve potential local Ba disequilibria. Many crystals are within error of complete chemical equilibrium for Ba. The conclusions of our study, however, were based on the observed local Sr disequilibria. Using the revised uncertainties in our calculations, we find that two of the 23 crystals studied (JdF-2794-2R-4 and Gakkel D27-16-O) are in fact within error of complete chemical equilibrium for Sr. Further, three other crystals (JdF-2794-2R-1, JdF-27942R-7 and Gorda W9604-C3-3) have growth zones of slightly more than 200 lm in width that are within error of local Sr equilibrium, but do preserve local Sr disequilibria. In the other crystals, the width of zones within local Sr equilibrium rarely exceeds 100 lm, as stated in our original contribution. Below, we provide the corrected version of Table 2, which summarizes our results. The great majority of crystals preserves local Sr disequilibria and displays only narrow zones in local Sr equilibrium. Equilibration times remain of the order of months to a few years, and minimum crystal growth rates remain of the order of 10-9–10-11 cm s-1. The original conclusions of our paper with regard to crystal residence times, growth rates and processes, and the typical size of melt lenses within the gabbroic rocks in oceanic layer 3, thus remain valid. 123 176 Contrib Mineral Petrol (2011) 161:175–176 Table 2 Determining minimum growth rates for all studied crystals Crystal XAn range Min. T (°C)a ÐSr (cf. Fig. 6) (10-17 m2 s-1) JdF 2792-4R-1 0.64–0.72 1,080 *1 JdF 2792-4R-2 0.67–0.79 1,080 *1 94 JdF 2792-4R-4 0.62–0.72 1,080 *1 132 JdF 2792-4R-5 0.67–0.79 1,080 *1 27 JdF 2792-4R-6 0.68–0.77 1,080 *1 JdF 2792-4R-7 0.69–0.74 1,080 JdF 2794-2R-1 JdF 2794-2R-2 0.65–0.71 0.66–0.68 JdF 2794-2R-3 JdF 2794-2R-4 Zone width 2b (lm) Equil. time b2/ÐSr (years)b Distance to rim (lm) Minimum growth rate (10-10 cm s-1)c 0.2 117 16.2 7.0 79 0.4 91 0.2 0.6 85 4.7 26 0.5 94 5.6 *1 28 0.6 68 3.5 1,100 1,100 *1 *1 44 29 1.5 0.7 106 78 2.2 3.7 0.67–0.72 1,100 *1 25 0.5 102 6.5 0.67–0.69 1,100 *1 JdF 2794-2R-5 0.67–0.72 1,100 *1 30 0.7 JdF 2794-2R-6 0.67–0.70 1,100 *1 55 2.4 87 1.2 JdF 2794-2R-7 0.67–0.71 1,100 *1 47 1.7 110 2.0 Gorda W9604-C3-1 0.79–0.82 1,130 *1 69 3.8 61 0.5 Gorda W9604-C3-2 0.75–0.80 1,130 *1 56 2.5 90 1.1 Gorda W9604-C3-3 0.73–0.76 1,130 *1 24 0.5 12 0.8 Gorda W9604-C3-4 0.70–0.83 1,130 *1 49 1.9 126 2.1 Gorda W9604-C3-5 0.70–0.72 1,130 *1 26 0.5 61 3.6 Gorda W9604-C3-6 0.71–0.81 1,130 *1 34 0.9 107 3.7 Gorda W9604-C3-7 0.76–0.84 1,130 *1 32 0.8 147 5.7 Gakkel D27-16-E 0.81–0.84 1,145 *1 105 8.7 683 2.5 Gakkel D27-16-H Gakkel D27-16-O 0.79–0.84 0.81–0.84 1,145 1,145 *1 *1 87 6.0 832 4.4 Within error of equilibrium, no information retained 17 14 Within error of equilibrium, no information retained 43 1.9 a Based on lowest anorthite content of all crystals in each rock sample and assuming 0.5 wt% H2O in the primitive magma b Actual crystal residence times are likely at least one order of magnitude lower, see text for discussion c These are effective minimum growth rates that do not account for limited intermittent dissolution. Actual growth rates are likely at least one order of magnitude greater, see text for discussion 123
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