Discerning crystal growth from diffusion profiles in

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ScienceDirect Geochimica et Cosmochimica Acta 123 (2013) 302–321 www.elsevier.com/locate/gca

Discerning crystal growth from diffusion profiles in zoned olivine by in situ Mg–Fe isotopic analyses Corliss Kin I Sio a,⇑, Nicolas Dauphas a, Fang-Zhen Teng b,1, Marc Chaussidon c, Rosalind T. Helz d, Mathieu Roskosz e a

Origins Laboratory, Department of the Geophysical Sciences and Enrico Fermi Institute, The University of Chicago, 5734 South Ellis Avenue, Chicago, IL 60637, USA b Isotope Laboratory, Department of Geosciences and Arkansas Center for Space and Planetary Sciences, University of Arkansas, 113 Ozark Hall, Fayetteville, AR 72701, USA c CRPG-CNRS, 15 rue Notre-Dame des Pauvres, 54501 Vandoeuvre-le`s-Nancy Cedex, France d U.S. Geological Survey, Reston, VA 20192, USA e Unite´ Mate´riaux et Transformations, Universite´ de Lille 1, CNRS UMR 8207, 59655 Villeneuve d’Ascq, France Received 10 November 2012; accepted in revised form 3 June 2013; available online 18 June 2013

Abstract Mineral zoning is used in diffusion-based geospeedometry to determine magmatic timescales. Progress in this field has been hampered by the challenge to discern mineral zoning produced by diffusion from concentration gradients inherited from crystal growth. A zoned olivine phenocryst from Kilauea Iki lava lake (Hawaii) was selected for this study to evaluate the potential of Mg and Fe isotopes for distinguishing these two processes. Microdrilling of the phenocryst (300 lm drill holes) followed by MC-ICPMS analysis of the powders revealed negatively coupled Mg and Fe isotopic fractionations (d26Mg from +0.1& to 0.2& and d56Fe from 1.2& to 0.2& from core to rim), which can only be explained by Mg–Fe exchange between melt and olivine. The data can be explained with ratios of diffusivities of Mg and Fe isotopes in olivine scaling as D2/D1 = (m1/m2)b with bMg 0.16 and bFe 0.27. LA-MC-ICPMS and MC-SIMS Fe isotopic measurements are developed and are demonstrated to yield accurate d56Fe measurements within precisions of 0.2& (1 SD) at spatial resolutions of 50 lm. d56Fe and d26Mg stay constant with Fo# in the rim (late-stage overgrowth), whereas in the core (original phenocryst) d56Fe steeply trends toward lighter compositions and d26Mg trends toward heavier compositions with higher Fo#. A plot of d56Fe vs. Fo# immediately distinguishes growth-controlled from diffusion-controlled zoning in these two regions. The results are consistent with the idea that large isotopic fractionation accompanies chemical diffusion in crystals, whereas fractional crystallization induces little or no isotopic fractionation. The cooling timescale inferred from the chemical-isotope zoning profiles is consistent with the documented cooling history of the lava lake. In the absence of geologic context, in situ stable isotopic measurements may now be used to interpret the nature of mineral zoning. Stable isotope measurements by LA-MCICPMS and MC-SIMS can be used as standard petrologic tools to identify samples for diffusion-based geospeedometry. Ó 2013 Elsevier Ltd. All rights reserved.

1. INTRODUCTION

⇑ Corresponding author.

E-mail address: [email protected] (Corliss Kin I Sio). Present address: Isotope Laboratory, Department of Earth and Space Sciences, University of Washington, Seattle, 4000 15th Avenue NE, Seattle, WA 98195, USA. 1

0016-7037/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.gca.2013.06.008

Chemical diffusion profiles in zoned minerals may be used to infer the thermal history of geological systems. Zoned plagioclase, olivine, and pyroxene have been used for such diffusion-based geospeedometry in igneous rocks (e.g., Grove et al., 1984; Costa and Chakraborty, 2004; Saunders et al., 2012, see Costa et al., 2008 for a review).

C.K.I. Sio et al. / Geochimica et Cosmochimica Acta 123 (2013) 302–321

A major challenge with these methods is that diffusion-driven zoning cannot always be discerned from crystal growth zoning. That is, fractional crystallization in a solid solution series can produce identical chemical profiles as diffusive transport. Costa and Dungan (2005) suggested using multi-element models on a single crystal to recognize diffusion-controlled zoning. The idea is that diffusion rates are different for the multiple elements in olivine. If diffusion calculations for all profiles converge to the same magmatic timescale, it is likely that the zonings are diffusion-controlled. However, the mineral-melt partition coefficients and diffusion coefficients of minor elements are uncertain (Chakraborty, 2010; Spandler and O’Neill, 2010). Furthermore, model parameters (crystal growth, surface boundary conditions, crystal geometry, fO2–P–T path) are often unknown. These difficulties make such an approach non-diagnostic of diffusive processes in complex systems. An unambiguous way to identify diffusive transport is to look into evidence recorded by the diffusing species. Such evidence is present in the form of isotopic variations along diffusion profiles (Beck et al., 2006; Teng et al., 2006; Dauphas, 2007; Jeffcoate et al., 2007; Parkinson et al., 2007; Gallagher and Elliott, 2009; Dohmen et al., 2010; Chopra et al., 2012). Dauphas et al. (2010) and Teng et al. (2011) introduced a new isotopic method to unambiguously identify diffusiondriven zoning in minerals. Chemical diffusion can induce large isotopic fractionations because light isotopes always diffuse faster than their heavier counterparts (Richter et al., 2009b and references therein). Dauphas et al. (2010) calculated that Mg–Fe interdiffusion in olivine should result in a negative correlation of Mg and Fe isotopic compositions. Teng et al. (2011) reported this negative correlation of Mg and Fe isotopic compositions in olivine fragments from Kilauea Iki lava lake (Hawaii), which directly implicated Mg–Fe interdiffusion in controlling the stable isotopic compositions of these elements in olivine. The large Fe isotope variations measured in olivines from various basalts from Germany and the Canary Islands may also be due to diffusion but no isotopic profile or Mg–Fe isotope correlation was provided to ascertain the cause of these variations (Weyer and Seitz, 2012). Here we report spatially resolved, negatively coupled Mg and Fe isotopic profiles in a single olivine from Kilauea Iki lava lake. By comparing with results from microdrilling, we show that laser-ablation multi-collector inductively coupled plasma mass spectrometry (LA-MC-ICPMS) and multi-collector secondary ion mass spectrometry (MC-SIMS) can provide accurate Fe isotope measurements in zoned olivines at higher spatial resolutions than what is achievable by microdrilling, suggesting that these instruments can be powerful tools for understanding the nature of zoning in minerals. 2. SAMPLES The Kilauea Iki lava lake was formed in 1959 by flow of magma into a pre-existing crater. The crust stabilized within a few days after the eruption, allowing the lava lake to act as a self-roofed magma chamber. The lava lake was

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drilled repeatedly since 1960 to monitor magmatic differentiation through time (Helz, 1980, 1987a). The drill cores have been extensively studied (e.g., Murata and Richter, 1966; Helz et al., 1989; Helz, 2009). Data on the compositions and equilibration temperatures of the drill cores were used to constrain the thermal history of the lava lake (Helz, 1987b; Helz and Thornber, 1987; Helz et al., in press). Olivine has been identified as the only phenocryst in the lava lake (Helz, 1987b). It has been recognized that some of these olivines re-equilibrated with the evolving melt through Mg–Fe exchange during slow cooling (Helz, 1987b; Teng et al., 2011). A virtue of these samples is that diffusion models for olivine phenocrysts can be tested against observation – the cooling timescale is the time between the 1959 eruption and quenching of the samples by core drilling. The sample KI81-5-254.5 (drill year 1981, core #5, 254.5 ft or 77.6 m depth) was selected for this study as it shows extensive zoning in olivine crystals (Teng et al., 2011). The olivine rim compositions, Fo68 [Fo# = 100 atomic Mg/(Mg + Fe)], are much more Fe-rich than those found in all other drill cores (Fo80) at similar depths (Helz et al., in press). Another important observation with this core (KI81-5) is that it was drilled only 6.9 m away from another core (KI81-1) that penetrated to a similar depth 3 weeks before (Helz and Wright, 1983). Furthermore, thermal and seismic experiments took place continuously before KI81-5 (our sample) was retrieved (e.g., Hardee et al., 1981). These observations suggest that the distinctively high Fe rims in the olivines in KI81-5254.5 may be overgrowths resulting from the rapid cooling induced by nearby activities. As a result, we began this study under the hypothesis that the olivine phenocrysts in KI81-5-254.5 experienced two stages of thermal evolution. First, the phenocryst cooled slowly for 21.4 years in a magma of evolving composition (drilling date for KI81-1 minus eruption date), which was followed by a short stage of accelerated cooling (3 weeks) that led to the formation of the overgrowths. A section of KI81-5-254.5 was made to expose a 4.5 mm 2.7 mm olivine phenocryst. This sample was mounted in epoxy and polished. The olivine is anhedral, with overgrowth texture at the rim enclosing glass and smaller augite crystals, which grew in situ in the lava lake (Fig. 1a). The matrix consists of plagioclase laths, augite, ilmenite, glass, and groundmass olivines (2–3 vol.%). For the development of in situ Fe isotopic measurements, a suite of natural olivine crystals was collected to evaluate the influence of sample matrix on measurements obtained by LA-MC-ICPMS and MC-SIMS (see Table 1 for details). These olivines cover the whole solid solution from fayalite (Fo0) to forsterite (Fo95). All standards were mounted in epoxy and studied under the SEM. Fo0 (Rockport fayalite) contains inclusions of magnetite, biotite, and grunerite (Rose et al., 2009). Eight small fragments were dissolved, analyzed independently, and were found to have identical iron isotopic compositions. Fo6 and Fo16 are small and inclusion-free olivines (200 lm) embedded in rock fragments. These olivines were crushed and extreme care was utilized in handpicking clear olivine fragments for solu-

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Fig. 1. (a) BSE image of the Kilauea Iki olivine phenocryst. The top corner shows stereographic projections of the olivine’s crystallographic orientation. (b) False-color chemical map superimposed on microdrilling casts. (c) Shape of the olivine after re-polishing for the final LA-MCICPMS and MC-SIMS sessions. The arrows show where the isotopic and trace element analyses were done. The yellow arrows are the starting points for the horizontal and vertical profiles. The two orange boxes show the locations where FIB sections were made. The scale bar is the same for all images. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

tion MC-ICPMS measurements. Fo54 and Fo64 came as sorted grains of 100 lm in diameter. Those single grains are unzoned but small compositional differences can be detected from grain to grain. Fo76 to Fo95 are large and homogenous grains that can be easily handpicked under a microscope.

3. METHODS LA-MC-ICPMS and MC-SIMS provide high spatial resolution for in situ isotopic measurements. However, these techniques are susceptible to matrix effects – the influence of isotopic analyses of an element due to the presence

Fo0 Fo6 Fo16 Fo54 Fo64 Fo76 Fo79 Fo85 Fo88 Fo90* Fo91 Fo92 Fo95

Fo# (EMPA)

Condition

Locality

Source

Catalogue #

Fo# d56Fe (sol)

d57Fe

0.17 ± 0.06 6.14 ± 0.38 15.71 ± 1.62 54.09 ± 2.70 64.34 ± 0.98 75.75 ± 0.48 78.62 ± 0.44 85.39 ± 0.22 88.44 ± 0.14 90.49 ± 0.14 91.34 ± 0.14 91.89 ± 0.22 95.22 ± 0.22

Impure grain Rock Impure grains Sorted grains Sorted grains Rock Rock Single grain Single grain Single grain Single grain Grains Rock

Rockport, Massachusetts, USA Soutpansberg, Transvaal, South Africa Skaergaard, East Greenland Vampula, Susimaki, Finland – Haleakala Observatory Mooihoek, Transvaal, South Africa Mt. Vesuvius, Italy San Carlos, Arizona, USA San Carlos, Arizona, USA Navajo Nation, New Mexico, USA W North Carolina, USA Mt. Vesuvius, Italy

Chicago Field Museum Chicago Field Museum University of Chicago Smithsonian Institute University of Chicago University of Chicago Chicago Field Museum Chicago Field Museum Chicago Field Museum Chicago Field Museum Chicago Field Museum Chicago Field Museum Chicago Field Museum

M7652 M18152 YS5/EG4145 135839 TS 8 HM18 M18156 M16636 M7688 H1849 H1853 M17315 M16643

0.5 0.269 ± 0.035 0.394 ± 0.047 – 0.806 ± 0.048 1.157 ± 0.085 14.1 0.065 ± 0.037 0.106 ± 0.052 55.8 0.020 ± 0.036 0.031 ± 0.049 65.9 0.351 ± 0.037 0.527 ± 0.052 77.1 0.084 ± 0.037 0.136 ± 0.052 78.7 0.048 ± 0.041 0.062 ± 0.060 85.4 0.021 ± 0.038 0.045 ± 0.060 88.5 0.034 ± 0.038 0.080 ± 0.060 91.1 0.015 ± 0.038 0.026 ± 0.060 92.1 0.031 ± 0.050 0.051 ± 0.061 91.6 0.008 ± 0.050 0.019 ± 0.061 95.3 0.093 ± 0.036 0.154 ± 0.049

d25Mg

d26Mg

– – 0.140 ± 0.034 0.191 ± 0.057 0.090 ± 0.057 0.161 ± 0.040 0.180 ± 0.039 0.186 ± 0.032 0.178 ± 0.041 0.110 ± 0.039 0.191 ± 0.039 0.128 ± 0.033 1.067 ± 0.033

– – 0.280 ± 0.054 0.378 ± 0.060 0.180 ± 0.059 0.303 ± 0.042 0.336 ± 0.048 0.375 ± 0.040 0.318 ± 0.037 0.251 ± 0.048 0.384 ± 0.048 0.242 ± 0.042 2.044 ± 0.042

Fo# = 100 atomic Mg/(Mg + Fe), diFe = [(iFe/54Fesample)/(iFe/54FeIRMM014) 1] 1000. diMg = [(iMg/24Mgsample)/(iMg/24MgDSM3) 1] 1000. Fo# (EMPA) were measured at Universite´ de Lille 1. They are compared with Fo# (sol) measured by solution MC-ICPMS to show that only clean olivine fragments were dissolved for Fe and Mg isotopic analyses. Uncertainties are 95% confidence intervals for Fe and Mg isotopes (Dauphas et al., 2009). * This SC used as the bracketing standard for LA-MC-ICPMS measurements.


Table 1 Characterization of olivine matrix standards.

305

306


Fig. 2. (a) Fo# and minor elements profiles. Fig. 1c shows the location of the traverse where these analyses were made (from 0 at the center to 2.5 mm at the rim of the olivine phenocryst). The uncertainties are 1.6% relative for CaO, 8% for Cr2O3, and 6% for Al2O3. (b–e) Minor elements plotted against Fo#. Measurements for panels a–d were done with the electron-probe at the University of Chicago; measurements for panel e (NiO wt% vs. Fo#) were done with the electron-probe at the Universite´ de Lille 1.

of other elements (e.g., Norman et al., 2006; Knight et al., 2009; Janney et al., 2011). For this reason, the d56Fe values of microdrilled samples and olivine standards were measured by solution MC-ICPMS for calibration and accuracy assessment of in situ measurements by LA-MC-ICPMS and MC-SIMS.

3.1. Chemical characterizations Prior to isotopic measurements, more than 500 pointanalyses on the olivine phenocryst were done using a JEOL SEM at the University of Chicago to generate the


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Fig. 3. Schematic mounts used for LA-MC-ICPMS and MC-SIMS measurements. (a) The Kilauea Iki lava lake olivine phenocryst is spatially bracketed by San Carlos olivine (SC, marked R for right, L for left, T for top, and B for bottom). Each profile was measured 4 times along 4 directions in the sample chambers by rotating the mount 4 90°. The matrix standards (Fo76 to Fo95) in this mount were not used for LA-MCICPMS matrix correction because they are not spatially bracketed by SC. These matrix standards were only used for MC-SIMS measurements. (b) Schematic matrix standard mount for MC-SIMS analyses in which all crystals were mounted in a restricted central area of the mount. The numbers indicate the Fo# of the matrix standards. The MC-SIMS iron isotopic compositions for Fo# between 76 to 95 were measured in both mounts (a and b) and were found to have identical compositions. (c) Schematic matrix standards mount specifically made for the LA-MC-ICPMS measurements to minimize the sample chamber position effect. Each matrix standard is spatially bracketed in all directions by SC. The numbers indicate the Fo# of the matrix standards. (d) Example of data collection by LA-MC-ICPMS for a horizontal traverse across the Kilauea Iki olivine phenocryst. Each spot measurement is bracketed in space and time. For example, to correct for instrumental and sample position effects a traverse measured from left to right will be measured in a sequence LSC, sample, RSC, sample, LSC, and so on.

308


compositional map shown in Fig. 1b. All analyses done on cracks or that did not sum to olivine stoichiometry were discarded. After the LA-MC-ICPMS and MC-SIMS sessions, the olivine phenocryst was analyzed by electron-probe in order to determine the chemical composition at each measurement spot and to correct for matrix-induced instrumental mass fractionation (IMF) on the Fe isotopic measurements. Mg, Si, Fe, and Ni concentrations were measured by a Cameca SX100 microprobe at the Universite´ de Lille 1, France (15 kV, 15 nA). In this same session, the Fo# for all olivine standards were also measured. Each Fo# is the average of at least ten analyses over a large grain or many small grains. Al, Ca, Cr, and Fe profiles from the core to the rim of the olivine phenocryst were made using a Cameca SX-50 electron-probe at the University of Chicago (20 kV, 150 nA, Fig. 2). Backgrounds were collected between each point analysis, and X-rays intensities were acquired for 30 s at each position. Points were manually selected so as to avoid cracks in the sample. In this session, all concentrations were determined by comparing measured counts to inhouse standards using the technique of Bence and Albee (1968) with a-factors from Albee and Ray (1970). 3.2. Crystallographic orientation of olivine Because Mg–Fe interdiffusion in olivine is strongly anisotropic (Buening and Buseck, 1973; Misener, 1974; Chakraborty, 1997), it is important to calculate the appropriate DMg–Fe to use along the traverses where chemical-isotopic profiles were taken (Costa et al., 2008). Two focused ion beam (FIB) sections were cut parallel to the surface of the olivine phenocryst, close to the 3rd and the 11th microdrill holes along the horizontal profile (marked as orange boxes in Fig. 1c). They were prepared on a dual beam microscope Fei Strata DB 235, operated at 5 kV at the Universite´ de Lille 1, France. Electron diffraction patterns were generated using a Nanomegas “Spinning Star” precession system using a Philips CM30 TEM (300 kV) at the Universite´ de Lille 1, France. The diffraction patterns were indexed using inhouse software. 3.3. FTIR Mg–Fe interdiffusion rate doubles when the water content in olivine exceeds 10 ppm (Costa and Chakraborty, 2008). To determine the water content in the olivines in KI81-5-254.5, IR spectra were recorded using a Bruker Hyperion 3000 microscope system attached to a Bruker Vertex 70 FT-IR spectrometer equipped with a liquid-nitrogen cooled MCT detector at the Universite´ de Lille 1, France. Measurements were performed at the centers of three olivine phenocrysts using an unpolarized beam of 60 60 lm with a resolution of 4 cm1; 256 scans were accumulated per spectrum. 3.4. Microdrilling and solution MC-ICPMS A New Wave Research microdrill/micromill apparatus was used for precise position drilling with a 300 lm

diameter tungsten carbide drill bit purchased from Brasseler USA (catalogue# H52.11.003). The drill depth was approximately 300 lm. A drop of Milli-Q water was placed on the sample surface before drilling, in order to trap the powder. The powder produced by drilling each spot was then collected along with Milli-Q water using a pipette, and transferred into a 6-ml Teflon beaker. Sample surface was washed with Milli-Q water to recover the remaining powder. The drill bit and sample surface were then rinsed and dried with commercial compressed gas duster between drillings. The drilled samples were evaporated in Teflon beakers for digestion. The drilled samples and olivine matrix standards were digested in HF, HNO3, HCl, and HClO4 acids (Dauphas et al., 2009). For the drilled samples, approximately 8 lg of Fe and 43 lg of Mg were dissolved. The digested solution was split into 0.4:0.4:0.2 aliquots where the numbers indicate the fractions of material used for Fe isotope, Mg isotope, and Fo# measurements. Iron column chromatography and mass spectrometry were performed following the procedures described in Dauphas et al. (2009) at the University of Chicago. The Fe procedural blank is 20 ng. Iron isotopic compositions are reported in d notation: " # ði Fe=54 FeÞunknown i d Fe ¼ i 1 103 ; ð Fe=54 FeÞIRMM014 where i can be either 56 or 57. Each Fe sample was measured 7 to 9 times. Magnesium column chromatography and mass spectrometry procedures were performed at the University of Arkansas, following the procedure of Teng et al. (2010). The Mg procedural blank is 80; Sections 2 and 5.1). The model is also limited to the right side of the phenocryst, which contains the vertical profile and the more Mg-rich core (Sections 2 and 4.1). Spherical geometry for the olivine is assumed, and the partial differential equation used for composition dependent diffusion is: @X Mg 1 @ @X Mg r2 D ; ¼ 2 r @r @t @r where XMg is the mole fraction of Mg in olivine [Mg/ (Mg + Fe)], t is time, and r is the radial distance from the center of the sphere. The diffusion coefficient, D, is a


317

Table 5 Values and explanations for variables used in the diffusion model. Variable

Value used

Explanations

T0

1230 °C

Ti Tq XMg,0 XMg,q

1190 °C 1130 °C 0.865 0.8

a

1175, 670 lm NNO 44.7 1 bar 0.16 0.27

Peak temperature of the magma prior to eruption, initial equilibration temperature of olivine phenocrysts (Helz, 1987b) Initial temperature of the lava lake (Helz, 2009; Helz et al., in press) Quench temperature of the lava lake at 77 m of the 1981 drill cores (Helz, 2009; Helz et al., in press) Starting composition of olivine [atomic Mg/(Mg + Fe)] (Helz et al., in press) Composition of olivine at quench at 77 m for the 1981 drill cores and the Fo# below which d56Fe and d26Mg stay relatively constant for the olivine phenocryst of this study (Fig. 5c and 8c) Radius of the phenocryst outlined by the Fo80 contour to omit late-stage overgrowth; horizontal and vertical directions Oxygen fugacity determined by Fe–Ti oxide oxybarometry (Helz and Thornber, 1987) Time constant in cooling model (the results are insensitive to this value) Pressure in the lava lake b-exponent in D2/D1 = (m1/m2)b, obtained by fitting to the Mg isotopic profiles b-exponent in D2/D1 = (m1/m2)b, obtained by fitting to the Fe isotopic profiles Time Temperature Distance from core of phenocryst Atomic Mg/(Mg + Fe) of the olivine in equilibrium with the evolving melt Diffusion coefficient expression from Dohmen and Chakraborty (2007)

fO2 c P bMg bFe t T r XMg D

function of temperature, pressure, oxygen fugacity, and Fo content of the olivine, parameterized by Dohmen and Chakraborty (2007). The PDE is solved using Mathematica and the embedded finite difference method. The mathematical code is provided in Electronic Annex. Solution to the PDE requires two boundary conditions. One is given by the condition of the spherical geometry, with no flux at the center of the crystal: @X Mg ¼ 0; r ¼ 0: @r The other boundary condition describes the Fo content at the rim of the olivine as a function of temperature in the lava lake, XMg(T(t), r = a), where T is temperature, t is time, and a is the radius of the olivine (see Section 5.2.2). 5.2.1. Temperature and initial conditions Chemical diffusion occurred at the onset of the 1959 eruption that formed the Kilauea Iki lava lake. Prior to eruption, temperature in the magma chamber was close to 1230 °C, and olivine phenocrysts had a constant composition of Fo86.5 (Helz et al., in press). Therefore, the initial conditions are: T 0 ¼ 1230 C; X Mg ðT 0 ; rÞ ¼ X Mg; 0 ¼ 0:865: The erupted magma rapidly cooled to the initial temperature of the lava lake, 1190 °C (Helz, 2009; Helz et al., in press). The present study assumes that the temperature drop from 1230 to 1190 °C occurred during the eruption period of 36 days. Peck et al. (1977) and Helz et al. (in press) showed that the lava lakes of ‘Alae and Kilauea Iki cooled in the conductive cooling regime, which is described by an error function. The thermal evolution at the center of the lava lake is therefore (shown in Fig. 9):

( T ðtÞ ¼

T 0 T 0DtT i t pffiffiffiffiffiffi T i erf c=t;

0 days 6 t 6 36 days 36 days < t

where T0 is the pre-eruption temperature, Ti is the initial lava lake temperature, t is time, Dt is duration of the eruption (=36 days), and c is a time constant. 5.2.2. Boundary condition at olivine rim Helz and Thornber (1987) found empirically that the Mg content in the melt decreases linearly with temperature. The rim composition of olivine also evolves as a function of temperature (Helz, 1987b; Helz et al., in press): X Mg ðT ðtÞ; aÞ ¼

T 0 X Mg; q T q X Mg; 0 þ T ðtÞ T0 Tq X Mg 0 X Mg; q T0 Tq

where XMg,q is the rim composition of the olivine at the time of quenching by core drilling, and Tq is the temperature at quench. Note that XMg,q and Tq were not obtained directly from the phenocryst of the present study. As discussed in Sections 2 and 5.1, this olivine went through a late-stage of rapid growth unique to KI81-5 core samples, so the values of a more pristine drill core (KI81-1) were used (XMg,q = 0.80, Tq = 1130 °C; Helz et al., in press). 5.2.3. Olivine growth accompanying chemical diffusion The olivine phenocryst could have grown during its residence time in the lava lake. The size of this growth rim was assessed by studying a sample that did not experience latestage overgrowth. Particularly, the sizes of groundmass olivines and the sizes of phenocryst rims that enclose augite crystals were measured in a thin section of KI79-1-189.0 (Fig. S2). By both methods, it was found that the phenocrysts grew less than 100 lm in radius, which is small

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compared to the radius of the phenocryst. Therefore, crystal growth can be neglected in the diffusion calculation. 5.2.4. Modeling isotopic fractionations It is assumed that diffusivities scale as the masses of the isotopes involved. The empirical formula from Richter et al. (1999) is used: b Di; 1 mi; 2 i ¼ ; Di; 2 mi; 1 where 1 and 2 are isotopes of element i, which is Fe or Mg in this study. The b-exponents are estimated by fitting the isotopic profiles. It is worth noting that b-values depend strongly on the boundary conditions used in the modeling. Reasonable estimates may be obtained from natural samples only if their boundary conditions are well constrained. This highlights the virtue of laboratory experiments, from which determinations of b-values can help to constrain boundary conditions for natural systems. A list of variables and the values used in the diffusion model can be found in Table 5. 5.3. Modeling results For the observed cooling timescale of 21.4 years and at the crystallographic directions of the chemical-isotopic profiles, the parameterization of Dohmen and Chakraborty (2007) predicts a DMg–Fe that is too low by a factor of 4 relative to what is needed to explain the diffusion profiles. The measured water content by FTIR is only 0.3 ppm, much less than the 10 ppm required for water to affect the rate of Mg–Fe interdiffusion in olivine (Hier-Majumder et al., 2005; Costa and Chakraborty, 2008). Dohmen and Chakraborty (2007) quoted half an order of magnitude uncertainty on predicted DMg–Fe values, so the inconsistency may only be apparent. The bFe and bMg extracted from the diffusion model (Figs. 5 and 8) are insensitive to the DMg–Fe values (i.e., changing the radius of crystal and DMg–Fe simultaneously to reproduce the range of Fo# does not change b-values required to reproduce the range of isotopic fractionations). However, the b-values are sensitive to the surface boundary conditions, which is driven by the thermal evolution of the lava lake. The b-exponents required to reproduce the isotopic profiles are bMg 0.16, and bFe 0.27 (Figs. 5 and 8). Changing model parameters within acceptable ranges yields uncertainties of ±0.05 in bMg and ±0.04 in bFe. The slope of d56Fe vs. d26Mg measured in the olivine phenocryst constrains the bFe/bMg ratio to be 1.8±0.3 (Fig. 5d; Dauphas et al. 2010). The estimated bMg is higher than those found in basalt-rhyolite melt couples (bMg 0.05, Richter et al., 2009a), but similar to those found in anorthite-diopside melts (bMg 0.1, Watkins et al., 2011), MgO liquids (bMg 0.1, theoretical estimate, Tsuchiyama et al., 1994), and MgSiO3 liquids (bMg 0.14, theoretical estimate, Goel et al., 2012). The estimated bFe is also higher than those found in basalt-rhyolite melt couples (bFe 0.03, Richter et al., 2009a), but similar to those found in metallic alloys (bFe 0.3; Mullen, 1961; Roskosz et al., 2006; Dauphas,

2007 and references therein). The similarity in bFe values between olivine and metals may suggest that crystalline materials have higher b-values than liquids. Further experimental work is needed to test this hypothesis and to ascertain the b-values estimated in this study. 5.4. Future applications to natural olivines The Kilauea Iki olivine phenocryst is unique in the sense that core drilling and thorough petrologic studies provide many constraints for the diffusion model. In most other cases, modeling parameters would be more poorly constrained. Here we discuss how close one can approximate magmatic timescales using measurements constrained by a thin section and by knowing the original lava composition. In particular, we treat Kilauea Iki olivine as a case study by posing the question: what timescale would we have obtained if the olivine that we studied came from a random rock with little geologic context? We applied the MELTS algorithm (Ghiorso and Sack, 1995) to estimate how boundary conditions evolve with falling temperature given a starting composition. The most magnesian glass composition in the eruption pumice in Table 25.4 of Helz (1987b) was taken as the original lava composition. From the MELTS algorithm, the calculated liquidus temperature is 1231 °C at NNO, corresponding to an equilibrium olivine composition of Fo85.5, which would be the assumed starting olivine composition. At 1145 °C, the olivine reaches Fo80 (rim of olivine phenocryst) marking quenching of the sample. An error function is used to model conductive cooling, which is a good assumption for igneous bodies, and proven to work well for the 1963 ‘Alae and the 1959 Kilauea Iki lava lakes (Section 5.2.1). Following this study, a factor of 4 in DMg–Fe is applied to the oriented olivine in both vertical and horizontal traverses. The retrieved cooling timescales are 19.8 and 47.8 years for the vertical and horizontal traverses, respectively. The difference in the timescales results from the uncertainty in the geometry of the olivine. In some studies, linear cooling was assumed (e.g., Miyamoto et al., 1986); this cooling regime will generate timescales of 8.5 and 25.5 years for the vertical and horizontal profiles, respectively. Overall, the MELTS application is able to retrieve the cooling timescales of the lava lake, paying attention to the choice of fO2, starting composition, and crystallographic orientation of the olivine. 6. CONCLUSION It has been previously recognized that diffusive transport in olivine is accompanied by large Mg and Fe isotopic fractionations (Dauphas et al., 2010; Teng et al., 2011). For the first time, these isotopic fractionations are spatially resolved using in situ measurements. We calibrated LA-MC-ICPMS and MC-SIMS using microdrilling followed by solution MC-ICPMS to show that accurate Fe isotopic measurements can be obtained. The ability to resolve diffusion-driven isotopic fractionations for the major elements in zoned olivine has significant implications


for the field of diffusion-based geospeedometry: diffusioncontrolled zoning may now be unambiguously teased apart from growth-controlled zoning, as the former process is accompanied with large isotopic fractionations. Using the Fe and Mg isotopic measurements, we discerned a core olivine composition that was affected by diffusion and a rim overgrowth that also shows some zoning but was not affected by diffusion. Chemically, the overgrowth cannot be distinguished from the core, demonstrating the usefulness of isotopic measurements to recognize diffusion in zoned minerals. As in situ stable isotopic measurements can be done routinely using matrix-matched standards, we propose that these techniques be used as standard petrologic tools for the study of zoned minerals in igneous and metamorphic rocks. It remains to be investigated whether other commonly zoned minerals such as garnet, pyroxenes, plagioclase, and oxides display similar diffusion-driven, intracrystalline isotopic profiles. ACKNOWLEDGMENTS We thank Yan Xiao and Shuijiong Wang for assistance with Mg isotopic measurements, Thomas Ireland for assistance with development of the LA-MC-ICPMS technique, David Troadec for making the FIB sections, Ahmed Addad and Patrick Cordier for TEM crystallographic orientation measurements, Jannick Ingrin for assistance with FTIR analyses in olivine, Claire RollionBard for assistance with MC-SIMS, Ian Steele and Severine Bellayer for assistance with EMPA, Will Vaughan for writing a data reduction program for the SEM at the University of Chicago, and Haolan Tang for showing us internally normalized Fe isotope data for IRMM014. This manuscript benefited from discussions with Frank Richter, and constructive reviews by Summit Chakraborty, Jan Schuessler, and Bruce Watson, and editorial handling by Stefan Weyer. This work was supported by Chateaubriand fellowship to C.K.I.S., NSF Petrology and Geochemistry (EAR1144429) and NASA Cosmochemistry (NNX12AH60G) to N.D., NSF (EAR-0838227 and EAR-1056713) to F.-Z.T., and ANR program (2011JS56 004 01, FrIHIDDA) to M.R. The EPMA facility in Lille is supported by the European Regional Development Fund (ERDF). The TEM national facility in Lille is supported by the Conseil Regional du Nord-Pas de Calais, ERDF, and Institut National des Sciences de l’Univers (INSU, CNRS).

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