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Geochimica et Cosmochimica Acta 123 (2013) 302–321

Discerning crystal growth from diffusion profiles in zonedolivine 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, USAb Isotope Laboratory, Department of Geosciences and Arkansas Center for Space and Planetary Sciences, University of Arkansas,

113 Ozark Hall, Fayetteville, AR 72701, USAc CRPG-CNRS, 15 rue Notre-Dame des Pauvres, 54501 Vandoeuvre-les-Nancy Cedex, France

d U.S. Geological Survey, Reston, VA 20192, USAe Unite Materiaux 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 beenhampered by the challenge to discern mineral zoning produced by diffusion from concentration gradients inherited from crys-tal growth. A zoned olivine phenocryst from Kilauea Iki lava lake (Hawaii) was selected for this study to evaluate the poten-tial 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 exchangebetween melt and olivine. The data can be explained with ratios of diffusivities of Mg and Fe isotopes in olivine scaling asD2/D1 = (m1/m2)b with bMg �0.16 and bFe �0.27. LA-MC-ICPMS and MC-SIMS Fe isotopic measurements are developedand 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 ofd56Fe vs. Fo# immediately distinguishes growth-controlled from diffusion-controlled zoning in these two regions. The resultsare consistent with the idea that large isotopic fractionation accompanies chemical diffusion in crystals, whereas fractionalcrystallization induces little or no isotopic fractionation. The cooling timescale inferred from the chemical-isotope zoningprofiles is consistent with the documented cooling history of the lava lake. In the absence of geologic context, in situ stableisotopic measurements may now be used to interpret the nature of mineral zoning. Stable isotope measurements by LA-MC-ICPMS and MC-SIMS can be used as standard petrologic tools to identify samples for diffusion-based geospeedometry.� 2013 Elsevier Ltd. All rights reserved.

0016-7037/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.gca.2013.06.008

⇑ Corresponding author.E-mail address: [email protected] (Corliss Kin I Sio).

1 Present address: Isotope Laboratory, Department of Earth andSpace Sciences, University of Washington, Seattle, 4000 15thAvenue NE, Seattle, WA 98195, USA.

1. INTRODUCTION

Chemical diffusion profiles in zoned minerals may beused to infer the thermal history of geological systems.Zoned plagioclase, olivine, and pyroxene have been usedfor 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).


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C.K.I. Sio et al. / Geochimica et Cosmochimica Acta 123 (2013) 302–321 303

A major challenge with these methods is that diffusion-dri-ven zoning cannot always be discerned from crystal growthzoning. That is, fractional crystallization in a solid solutionseries can produce identical chemical profiles as diffusivetransport. Costa and Dungan (2005) suggested using mul-ti-element models on a single crystal to recognize diffu-sion-controlled zoning. The idea is that diffusion rates aredifferent for the multiple elements in olivine. If diffusion cal-culations for all profiles converge to the same magmatictimescale, it is likely that the zonings are diffusion-con-trolled. However, the mineral-melt partition coefficientsand diffusion coefficients of minor elements are uncertain(Chakraborty, 2010; Spandler and O’Neill, 2010). Further-more, model parameters (crystal growth, surface boundaryconditions, crystal geometry, fO2–P–T path) are often un-known. These difficulties make such an approach non-diag-nostic of diffusive processes in complex systems. Anunambiguous way to identify diffusive transport is to lookinto evidence recorded by the diffusing species. Such evi-dence is present in the form of isotopic variations along dif-fusion 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) introduceda new isotopic method to unambiguously identify diffusion-driven zoning in minerals. Chemical diffusion can inducelarge isotopic fractionations because light isotopes alwaysdiffuse faster than their heavier counterparts (Richteret al., 2009b and references therein). Dauphas et al.(2010) calculated that Mg–Fe interdiffusion in olivineshould result in a negative correlation of Mg and Fe isoto-pic compositions. Teng et al. (2011) reported this negativecorrelation of Mg and Fe isotopic compositions in olivinefragments from Kilauea Iki lava lake (Hawaii), which di-rectly implicated Mg–Fe interdiffusion in controlling thestable isotopic compositions of these elements in olivine.The large Fe isotope variations measured in olivines fromvarious basalts from Germany and the Canary Islandsmay also be due to diffusion but no isotopic profile orMg–Fe isotope correlation was provided to ascertain thecause of these variations (Weyer and Seitz, 2012).

Here we report spatially resolved, negatively coupledMg and Fe isotopic profiles in a single olivine from KilaueaIki lava lake. By comparing with results from microdrilling,we show that laser-ablation multi-collector inductively cou-pled plasma mass spectrometry (LA-MC-ICPMS) and mul-ti-collector secondary ion mass spectrometry (MC-SIMS)can provide accurate Fe isotope measurements in zoned oli-vines at higher spatial resolutions than what is achievableby microdrilling, suggesting that these instruments can bepowerful tools for understanding the nature of zoning inminerals.

2. SAMPLES

The Kilauea Iki lava lake was formed in 1959 by flow ofmagma into a pre-existing crater. The crust stabilizedwithin a few days after the eruption, allowing the lava laketo act as a self-roofed magma chamber. The lava lake was

drilled repeatedly since 1960 to monitor magmatic differen-tiation through time (Helz, 1980, 1987a). The drill coreshave been extensively studied (e.g., Murata and Richter,1966; Helz et al., 1989; Helz, 2009). Data on the composi-tions and equilibration temperatures of the drill cores wereused 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 thelava lake (Helz, 1987b). It has been recognized that some ofthese olivines re-equilibrated with the evolving meltthrough Mg–Fe exchange during slow cooling (Helz,1987b; Teng et al., 2011). A virtue of these samples is thatdiffusion models for olivine phenocrysts can be testedagainst observation – the cooling timescale is the time be-tween the 1959 eruption and quenching of the samples bycore 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 itshows extensive zoning in olivine crystals (Teng et al.,2011). The olivine rim compositions, �Fo68

[Fo# = 100 � atomic Mg/(Mg + Fe)], are much more Fe-richthan those found in all other drill cores (Fo80) at similardepths (Helz et al., in press). Another important observa-tion with this core (KI81-5) is that it was drilled only6.9 m away from another core (KI81-1) that penetrated toa similar depth 3 weeks before (Helz and Wright, 1983).Furthermore, thermal and seismic experiments took placecontinuously before KI81-5 (our sample) was retrieved(e.g., Hardee et al., 1981). These observations suggest thatthe distinctively high Fe rims in the olivines in KI81-5-254.5 may be overgrowths resulting from the rapid coolinginduced by nearby activities. As a result, we began thisstudy under the hypothesis that the olivine phenocrysts inKI81-5-254.5 experienced two stages of thermal evolution.First, the phenocryst cooled slowly for 21.4 years in a mag-ma of evolving composition (drilling date for KI81-1 minuseruption date), which was followed by a short stage ofaccelerated cooling (3 weeks) that led to the formation ofthe overgrowths.

A section of KI81-5-254.5 was made to expose a4.5 mm � 2.7 mm olivine phenocryst. This sample wasmounted in epoxy and polished. The olivine is anhedral,with overgrowth texture at the rim enclosing glass andsmaller 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 measure-ments, a suite of natural olivine crystals was collected toevaluate the influence of sample matrix on measurementsobtained by LA-MC-ICPMS and MC-SIMS (see Table 1for details). These olivines cover the whole solid solutionfrom fayalite (Fo0) to forsterite (Fo95). All standards weremounted in epoxy and studied under the SEM. Fo0 (Rock-port fayalite) contains inclusions of magnetite, biotite, andgrunerite (Rose et al., 2009). Eight small fragments weredissolved, analyzed independently, and were found to haveidentical iron isotopic compositions. Fo6 and Fo16 are smalland inclusion-free olivines (�200 lm) embedded in rockfragments. These olivines were crushed and extreme carewas utilized in handpicking clear olivine fragments for solu-

Fig. 1. (a) BSE image of the Kilauea Iki olivine phenocryst. The top corner shows stereographic projections of the olivine’s crystallographicorientation. (b) False-color chemical map superimposed on microdrilling casts. (c) Shape of the olivine after re-polishing for the final LA-MC-ICPMS and MC-SIMS sessions. The arrows show where the isotopic and trace element analyses were done. The yellow arrows are the startingpoints for the horizontal and vertical profiles. The two orange boxes show the locations where FIB sections were made. The scale bar is thesame 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.)

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

tion MC-ICPMS measurements. Fo54 and Fo64 came assorted grains of �100 lm in diameter. Those single grainsare unzoned but small compositional differences can be de-tected from grain to grain. Fo76 to Fo95 are large andhomogenous grains that can be easily handpicked under amicroscope.

3. METHODS

LA-MC-ICPMS and MC-SIMS provide high spatialresolution for in situ isotopic measurements. However,these techniques are susceptible to matrix effects – the influ-ence of isotopic analyses of an element due to the presence

Table 1Characterization of olivine matrix standards.

Fo#(EMPA)

Condition Locality Source Catalogue#

Fo#(sol)

d56Fe d57Fe d25Mg d26Mg

Fo0 0.17 ± 0.06 Impure grain Rockport, Massachusetts, USA Chicago Field Museum M7652 0.5 0.269 ± 0.035 0.394 ± 0.047 – –Fo6 6.14 ± 0.38 Rock Soutpansberg, Transvaal, South Africa Chicago Field Museum M18152 – 0.806 ± 0.048 1.157 ± 0.085 – –Fo16 15.71 ± 1.62 Impure grains Skaergaard, East Greenland University of Chicago YS5/EG4145 14.1 0.065 ± 0.037 0.106 ± 0.052 0.140 ± 0.034 0.280 ± 0.054Fo54 54.09 ± 2.70 Sorted grains Vampula, Susimaki, Finland Smithsonian Institute 135839 55.8 0.020 ± 0.036 0.031 ± 0.049 �0.191 ± 0.057 �0.378 ± 0.060Fo64 64.34 ± 0.98 Sorted grains – University of Chicago TS 8 65.9 0.351 ± 0.037 0.527 ± 0.052 �0.090 ± 0.057 �0.180 ± 0.059Fo76 75.75 ± 0.48 Rock Haleakala Observatory University of Chicago HM18 77.1 0.084 ± 0.037 0.136 ± 0.052 �0.161 ± 0.040 �0.303 ± 0.042Fo79 78.62 ± 0.44 Rock Mooihoek, Transvaal, South Africa Chicago Field Museum M18156 78.7 �0.048 ± 0.041 �0.062 ± 0.060 �0.180 ± 0.039 �0.336 ± 0.048Fo85 85.39 ± 0.22 Single grain Mt. Vesuvius, Italy Chicago Field Museum M16636 85.4 0.021 ± 0.038 0.045 ± 0.060 �0.186 ± 0.032 �0.375 ± 0.040Fo88 88.44 ± 0.14 Single grain San Carlos, Arizona, USA Chicago Field Museum M7688 88.5 0.034 ± 0.038 0.080 ± 0.060 �0.178 ± 0.041 �0.318 ± 0.037Fo90

* 90.49 ± 0.14 Single grain San Carlos, Arizona, USA Chicago Field Museum H1849 91.1 0.015 ± 0.038 0.026 ± 0.060 �0.110 ± 0.039 �0.251 ± 0.048Fo91 91.34 ± 0.14 Single grain Navajo Nation, New Mexico, USA Chicago Field Museum H1853 92.1 0.031 ± 0.050 0.051 ± 0.061 �0.191 ± 0.039 �0.384 ± 0.048Fo92 91.89 ± 0.22 Grains W North Carolina, USA Chicago Field Museum M17315 91.6 �0.008 ± 0.050 0.019 ± 0.061 �0.128 ± 0.033 �0.242 ± 0.042Fo95 95.22 ± 0.22 Rock Mt. Vesuvius, Italy Chicago Field Museum M16643 95.3 �0.093 ± 0.036 �0.154 ± 0.049 �1.067 ± 0.033 �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 Mgisotopic 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.

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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 to2.5 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) Minorelements plotted against Fo#. Measurements for panels a–d were done with the electron-probe at the University of Chicago; measurementsfor 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 micro-drilled samples and olivine standards were measured by solu-tion MC-ICPMS for calibration and accuracy assessment ofin situ measurements by LA-MC-ICPMS and MC-SIMS.

3.1. Chemical characterizations

Prior to isotopic measurements, more than 500 point-analyses on the olivine phenocryst were done using a JEOLSEM at the University of Chicago to generate the

Fig. 3. Schematic mounts used for LA-MC-ICPMS and MC-SIMS measurements. (a) The Kilauea Iki lava lake olivine phenocryst is spatiallybracketed 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 4directions in the sample chambers by rotating the mount 4 � 90�. The matrix standards (Fo76 to Fo95) in this mount were not used for LA-MC-ICPMS 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. Thenumbers indicate the Fo# of the matrix standards. The MC-SIMS iron isotopic compositions for Fo# between 76 to 95 were measured in bothmounts (a and b) and were found to have identical compositions. (c) Schematic matrix standards mount specifically made for the LA-MC-ICPMSmeasurements to minimize the sample chamber position effect. Each matrix standard is spatially bracketed in all directions by SC. The numbersindicate the Fo# of the matrix standards. (d) Example of data collection by LA-MC-ICPMS for a horizontal traverse across the Kilauea Ikiolivine phenocryst. Each spot measurement is bracketed in space and time. For example, to correct for instrumental and sample position effects atraverse measured from left to right will be measured in a sequence LSC, sample, RSC, sample, LSC, and so on.



compositional map shown in Fig. 1b. All analyses done oncracks or that did not sum to olivine stoichiometry werediscarded.

After the LA-MC-ICPMS and MC-SIMS sessions, theolivine phenocryst was analyzed by electron-probe in orderto determine the chemical composition at each measurementspot and to correct for matrix-induced instrumental massfractionation (IMF) on the Fe isotopic measurements. Mg,Si, Fe, and Ni concentrations were measured by a CamecaSX100 microprobe at the Universite de Lille 1, France(15 kV, 15 nA). In this same session, the Fo# for all olivinestandards were also measured. Each Fo# is the average ofat least ten analyses over a large grain or many small grains.

Al, Ca, Cr, and Fe profiles from the core to the rim ofthe olivine phenocryst were made using a Cameca SX-50electron-probe at the University of Chicago (20 kV,150 nA, Fig. 2). Backgrounds were collected between eachpoint analysis, and X-rays intensities were acquired for30 s at each position. Points were manually selected so asto avoid cracks in the sample. In this session, all concentra-tions were determined by comparing measured counts to in-house 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 stronglyanisotropic (Buening and Buseck, 1973; Misener, 1974;Chakraborty, 1997), it is important to calculate the appro-priate DMg–Fe to use along the traverses where chemical-iso-topic profiles were taken (Costa et al., 2008). Two focusedion beam (FIB) sections were cut parallel to the surfaceof the olivine phenocryst, close to the 3rd and the 11thmicrodrill holes along the horizontal profile (marked as or-ange boxes in Fig. 1c). They were prepared on a dual beammicroscope Fei Strata DB 235, operated at 5 kV at the Uni-versite de Lille 1, France.

Electron diffraction patterns were generated using aNanomegas “Spinning Star” precession system using a Phi-lips CM30 TEM (300 kV) at the Universite de Lille 1,France. The diffraction patterns were indexed using in-house software.

3.3. FTIR

Mg–Fe interdiffusion rate doubles when the water con-tent in olivine exceeds 10 ppm (Costa and Chakraborty,2008). To determine the water content in the olivines inKI81-5-254.5, IR spectra were recorded using a BrukerHyperion 3000 microscope system attached to a BrukerVertex 70 FT-IR spectrometer equipped with a liquid-nitro-gen cooled MCT detector at the Universite de Lille 1,France. Measurements were performed at the centers ofthree olivine phenocrysts using an unpolarized beam of60 � 60 lm with a resolution of 4 cm�1; 256 scans wereaccumulated per spectrum.

3.4. Microdrilling and solution MC-ICPMS

A New Wave Research microdrill/micromill apparatuswas used for precise position drilling with a 300 lm

diameter tungsten carbide drill bit purchased from Brassel-er USA (catalogue# H52.11.003). The drill depth wasapproximately 300 lm. A drop of Milli-Q water was placedon the sample surface before drilling, in order to trap thepowder. The powder produced by drilling each spot wasthen collected along with Milli-Q water using a pipette,and transferred into a 6-ml Teflon beaker. Sample surfacewas washed with Milli-Q water to recover the remainingpowder. The drill bit and sample surface were then rinsedand dried with commercial compressed gas duster betweendrillings. The drilled samples were evaporated in Teflonbeakers for digestion.

The drilled samples and olivine matrix standards were di-gested in HF, HNO3, HCl, and HClO4 acids (Dauphas et al.,2009). For the drilled samples, approximately 8 lg of Fe and43 lg of Mg were dissolved. The digested solution was splitinto 0.4:0.4:0.2 aliquots where the numbers indicate the frac-tions of material used for Fe isotope, Mg isotope, and Fo#measurements. Iron column chromatography and mass spec-trometry were performed following the procedures describedin Dauphas et al. (2009) at the University of Chicago. The Feprocedural blank is �20 ng. Iron isotopic compositions arereported in d notation:

diFe ¼ ðiFe=54FeÞunknown

ðiFe=54FeÞIRMM014

� 1

" #� 103;

where i can be either 56 or 57. Each Fe sample was mea-sured 7 to 9 times.

Magnesium column chromatography and mass spec-trometry procedures were performed at the University ofArkansas, following the procedure of Teng et al. (2010).The Mg procedural blank is <10 ng. Mg isotopic composi-tions are also reported in d notation:

diMg ¼ ðiMg=24MgÞunknown

ðiMg=24MgÞDSM3

� 1

" #� 103;

where i can be either 25 or 26. Each Mg sample was mea-sured 2 to 4 times. IRMM014 and DSM3 are internationalisotopic standards for Fe and Mg isotopic analyses. Thedata follow mass-dependent fractionation, so only d26Mgand d56Fe are plotted in graphs.

3.5. LA-MC-ICPMS

LA-MC-ICPMS Fe isotope analyses were acquired usinga New Wave Research UP193HE laser-ablation system witha TUI Excistar M-100 excimer laser and a standard laser-ablation cell, connected to a Neptune MC-ICPMS at theUniversity of Chicago. High purity He and Ar were used ascarrier gas and make-up gas with flow rates of �0.8 and�0.7 L/min, respectively. The measurements were pro-grammed to fire the laser for 80 s at each spot, at a fluenceof �1 J/cm2 and a repetition rate of 4 Hz. The depth of theablated spots measured by focusing an optical microscopeto the bottom of the crater was �17 lm. A washout time of20 s was used in between every analysis, although 8 s weregenerally enough for the Fe signal to fall back to backgroundlevel. Data were integrated in cycles of 4.196 s. As illustratedin Fig. 3d, to match the 56Fe intensity of the sample to that of

Fig. 4. Instrumental mass fractionation (IMF) curves for (a) LA-MC-ICPMS and (b) MC-SIMS. These regressions were used to correct forIMF affected by sample matrix in the Kilauea Iki olivine phenocryst. The 68% confidence intervals were used as the uncertainties for IMFcorrections.


the San Carlos olivine standard (SC = Fo90, spot size 70 lm),different spot diameters were used for the rim (40 lm) and therest of the olivine phenocryst (55 lm). Data reduction wasdone using an in-house Fortran code to remove transientpoints at sample introduction and termination. A total of15 cycles were used for each spot analysis.

To correct for isobaric interference on 54Fe, 54Cr wascalculated from 53Cr intensity, assuming that they had thesame instrumental bias as iron (57Fe/56Fe ratio). For de-tailed technique discussions, the reader is referred to theSupplementary materials.

Initial tests to measure iron isotopic compositions byLA-MC-ICPMS revealed that a position-dependent artifactwas present, which could only be corrected by surroundingthe sample with standards. As a result, the sample was re-mounted and re-polished, resulting in the erosion or disap-pearance of microdrill holes.

Each spot analyzed was bracketed in space and in time(see Fig. 3a and d). Analyses were done in straight lineswith sample alternatively bracketed by SC on either sideof the profiles. Tests done to evaluate this position effectsuggested that linear interpolation of the 56Fe/54Fe ratiosof SC at each position was the best way to correct for theposition effect. A further strategy was adopted to removeany bias introduced by the location of the spot analysis inthe sample chamber. Each profile was analyzed four times,each time rotating the mount about its center by 90� fromits previous position in the sample chamber. For example,

the first position measured widely spaced points acrossthe horizontal and vertical profiles. Then, the mount wastaken out, rotated by 90�, and reinserted into the samplechamber. New spots were chosen adjacent to the previousspots. The process was repeated 2 more times to arrive at4 repeat analyses across the same traverse. This procedureyielded values relative to SC ðd56Fesmp

SC hLAiÞ that still haveto be corrected for matrix effect.

A special epoxy mount was made for the olivine matrixstandards: each sample with a given Fo# was surroundedon four sides by SC (Fig. 3c). Measurements were madeon the matrix standards by alternatively bracketing themfive times in the left and right directions, followed by fivetimes in the up and down directions. This method is effec-tive in minimizing sample chamber position effects, becauseSC spatially bracketed by itself shows no resolvable frac-tionation (0.01 ± 0.8&, 1 SD). This procedure yields ma-trix-induced shifts in d56Fe, which can be used to correctfor the instrumental mass fractionation (IMF),

DiFeðstd Fo#ÞhIMF; LAi ¼ diFestd Fo#SC hLAi

� ½diFestd Fo#IRMM hsoli

� diFeSCIRMMhsoli�:

The IMF curve shows a positive relationship with Fo#.SigmaPlot was used to generate a linear regression for thedata points (Fig. 4a). The 68% confidence interval was usedas the uncertainty for the IMF correction.


The IMF-corrected sample value relative to IRMM014is therefore,

diFesmpIRMMhLAi ¼ diFesmp

SC hLAi �DiFeðsmp Fo#ÞhIMF; LAiþ diFeSC

IRMMhsoli;

where the value of DiFe depends on the sample Fo#, calcu-lated from the average of four EMPA analyses done aroundeach crater after the LA-MC-ICPMS measurements. Theerrors on the Fo# are estimated to be 0.5 (2 SD).

For each of the four profiles made on the same traversein four directions by sample rotation, Fe isotopic composi-tions are linearly interpolated between data points. Each fi-nal data point is reported as an average of one actual LA-MC-ICPMS analysis, and up to three interpolated points.The error bars are calculated by quadratically combiningerrors (“E,” all 1 SD): point-to-point reproducibility aftercorrecting for the sample chamber position effect (=Esmp

�0.16& on d56Fe and �0.23& on d57Fe, based on testsran on a large SC grain), uncertainty in the IMF regression(=EIMF �0.04& on d56Fe and �0.06& on d57Fe), anduncertainty in the solution MC-ICPMS measurement ofSC olivine (=ESC �0.02& ond56Fe and �0.03& ond57Fe). The overall uncertainty is:

EhLAi ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðEsmphLAiÞ2 þ ðEIMFhLAiÞ2 þ ðESChLAiÞ2

q:

3.6. MC-SIMS

Analyses were carried out using a multi-collector IMS1280-HR ion probe at CRPG-CNRS, Nancy, France. Thesample was sputtered with O� beam at a current of�60 nA and 13 kV acceleration voltage. This beam pro-duced craters of �30 by 80 lm and several microns deep.Secondary ions were accelerated at 10 kV and analyzed ata mass resolving power (M/DM) of �4800. Typical signalon 56Fe for the olivine phenocryst was 1–2 � 108 cps. Iso-topes 54Fe, 56Fe, and 57Fe were collected in Faraday cupswhile 52Cr was collected on an electron multiplier. Theinterference of 54Cr on 54Fe was corrected by assuming thatthe instrumental fractionation for Cr was the same as thatmeasured for Fe isotopes. After Cr-correction all data ploton a mass fractionation line for 57Fe/54Fe vs. 56Fe/54Fe. Foreach analysis, a pre-sputtering time of 120 s was used. Asingle analysis consisted of 50 cycles with 5 s integrationtime.

In an effort to evaluate whether the measurements wereaffected by the sample location in the sample chamber, thesame isotopic traverse was measured in 4 different direc-tions as was done for the LA-MC-ICPMS measurements.This involved breaking the vacuum, physically rotating themount about its center by 90�, and putting it back in vac-uum for measurement in at different locations in thechamber.

All MC-SIMS iron isotopic compositions are calculatedas follows:

diFe ¼ ðiFe=54FeÞunknown

ðiFe=54FeÞIRMM014

� 1

" #� 103;

where in this case, iFe/54FeIRMM014 is the certifiedIRMM014 ratio of 57Fe/54Fe (0.36257) and internally nor-malized ratio of 56Fe/54Fe (15.7044) based on MC-ICPMSmeasurements (Schoenberg and von Blanckenburg, 2005;this study; see Supplementary material). Measurements onthe matrix standards from Fo76 to Fo95 were done on twoseparate mounts, with or without the Kilauea Iki olivinephenocryst (Fig. 3a and b, respectively). Matrix standardsfrom Fo76 to Fo95 were measured 10 to 28 times each, withanalyses spread across the two mounts. Iron isotopic mea-surements for each Fo# in the two mounts gave identicalresults within 1 SD uncertainty. The more Fe-rich matrixstandards were measured 2 to 8 times for each standardwith a given Fo#. These measurements were used to evalu-ate the effect of sample matrix on instrumental massfractionation:

DiFeðstd Fo#ÞhIMF; SIMSi ¼ diFestd Fo#IRMM hSIMSi

� diFestd Fo#IRMM hsoli:

As with LA-MC-ICPMS, the IMF curve for MC-SIMSalso defines a positive correlation. SigmaPlot was used torun a second order polynomial regression through the datapoints (Fig. 4b). A 68% confidence interval was calculatedfor the regression as an assessment of the uncertainty ofIMF correction.

The IMF-corrected values for the olivine phenocryst arereported relative to IRMM014:

diFesmpIRMMhSIMSi ¼ diFesmpðrawÞ

IRMM hSIMSi � DiFeðsmp Fo#ÞhIMF; SIMSi:

In a manner similar to that used for LA-MC-ICPMSanalyses, the value of DiFe depends on the Fo# of eachsputtered spot, calculated from the average of four EMPAanalyses done around each ion beam spot.

The reported values are calculated in a similar manneras was done for LA-MC-ICPMS: one actual measurementand up to 3 interpolated points were averaged. The overalluncertainty is also calculated the same way, where thepoint-to-point reproducibility (=Esmp �0.25& on d56Feand 0.32& on d57Fe) is added quadratically to the uncer-tainty in IMF correction (=EIMF �0.11& on d56Fe and�0.23& on d57Fe):

EhSIMSi ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðEsmphSIMSiÞ2 þ ðEIMFhSIMSiÞ2

q:

4. RESULTS

4.1. SEM and EMPA

SEM analyses done prior to in situ isotopic measure-ments revealed that the most Mg-rich composition lies onthe right side of the phenocryst (refer to the color imageof Fig. 1b). The rim of the olivine has a range of composi-tions from Fo66 to Fo72.

The chemical analysis obtained after in situ isotopicmeasurements revealed the presence of two Mg-rich coreswith normal zonings (Fo81 on the left side and Fo83.6 onthe right side). The joint zoning could result from apeanut-shaped crystal or from synneusis (attachment ofcrystals). Approximately 95% by mass of Kilauea Iki oli-

Fig. 5. Microdrill solution MC-ICPMS data for (a) the horizontal and (b) the vertical profiles. The curves represent diffusion models usingbFe = 0.27 and bMg = 0.16. (c) d56Fe and d26Mg are plotted against the Fo# of the solutions. (d) d56Fe plotted against d26Mg; the slope is��3.69 ± 0.39, similar to that reported by Teng et al. (2011) for bulk olivine fragments from the same sample KI81-5-254.5 (plotted in opensymbols). The Mg isotopes (orange squares) were measured at the University of Arkansas. The Fe isotopes (blue circles) and Fo# weremeasured at the University of Chicago. Some error bars are smaller than the sizes of the symbols.

Table 2Fe and Mg isotopic compositions of powders microdrilled from the Kilauea Iki olivine phenocryst (KI81-5-254.5), obtained by solution MC-ICPMS.

Spot # Dist. (mm) Fo# d56Fe d57Fe d25Mg d26Mg

Horizontal profile

1 0.15 75.6 �0.300 ± 0.047 �0.424 ± 0.059 �0.040 ± 0.037 �0.132 ± 0.0482 0.39 79.5 �0.316 ± 0.045 �0.466 ± 0.057 �0.135 ± 0.059 �0.183 ± 0.0803 0.60 81.2 �0.269 ± 0.045 �0.383 ± 0.057 �0.139 ± 0.044 �0.205 ± 0.0634 0.91 81.3 �0.323 ± 0.047 �0.479 ± 0.072 �0.103 ± 0.059 �0.206 ± 0.0805 1.19 81.1 �0.321 ± 0.047 �0.466 ± 0.072 �0.124 ± 0.044 �0.226 ± 0.0636 1.43 80.8 �0.339 ± 0.054 �0.435 ± 0.083 � �7 1.74 80.3 �0.486 ± 0.047 �0.698 ± 0.072 �0.090 ± 0.037 �0.166 ± 0.0488 2.13 82.9 �0.773 ± 0.048 �1.166 ± 0.085 �0.042 ± 0.037 �0.074 ± 0.0489 2.47 82.7 �1.096 ± 0.054 �1.637 ± 0.083 0.024 ± 0.035 0.048 ± 0.048

10 3.00 85.0 �1.164 ± 0.054 �1.791 ± 0.083 0.056 ± 0.040 0.094 ± 0.06311 3.33 82.9 �1.117 ± 0.050 �1.654 ± 0.077 � �12 3.71 81.0 �0.782 ± 0.045 �1.167 ± 0.060 0.021 ± 0.048 0.052 ± 0.10113 4.03 79.8 �0.422 ± 0.049 �0.629 ± 0.066 �0.098 ± 0.031 �0.153 ± 0.04614 4.27 76.2 �0.184 ± 0.049 �0.269 ± 0.066 �0.117 ± 0.065 �0.151 ± 0.100

Vertical profile

1 0.15 78.3 �0.241 ± 0.050 �0.361 ± 0.056 �0.102 ± 0.057 �0.224 ± 0.0872 0.45 80.8 �0.290 ± 0.050 �0.445 ± 0.056 �0.099 ± 0.057 �0.211 ± 0.0873 0.77 82.6 �0.619 ± 0.050 �0.942 ± 0.056 �0.051 ± 0.057 �0.123 ± 0.0874 1.07 82.9 �1.088 ± 0.050 �1.573 ± 0.056 �0.010 ± 0.057 �0.009 ± 0.0875 1.32 83.2 �1.108 ± 0.057 �1.678 ± 0.119 0.020 ± 0.043 0.043 ± 0.0666 1.56 80.6 �0.948 ± 0.050 �1.422 ± 0.056 0.000 ± 0.037 �0.027 ± 0.0497 1.93 77.1 �0.378 ± 0.050 �0.568 ± 0.056 �0.040 ± 0.043 �0.127 ± 0.0668 2.20 70.7 �0.160 ± 0.050 �0.237 ± 0.056 �0.058 ± 0.057 �0.134 ± 0.066

Distances are given relative to the left or top edges of the olivine (marked “H0” and “V0”, Fig. 1c).Fo# and delta notations are explained in Table 1.Fo# were measured by solution MC-ICPMS. The same solutions were used for Fe and Mg isotopic analyses. Uncertainties are 95%confidence intervals for Fe and Mg isotopes.


Fig. 6. LA-MC-ICPMS profiles across the horizontal (left panels) and vertical (right panels) traverses. The top row shows the Fo# of thetraverses; the middle row show the four repeat profiles across the same traverses. The numbers in the legend indicate the degrees of rotationfrom the first position in the sample chamber. The bottom row shows the final Fe isotopic profiles – data are the averages of one actualmeasurement and up to three linearly interpolated points. Linear interpolation is not done across the entire vertical profile marked by greendiamonds because the interpolation would miss the most fractionated part of the crystal. All iron isotopic compositions are referenced toIRMM014.


vines from the 1959 eruption scoria studied by Schwinding-er and Anderson (1989) are affected by synneusis and mostattached crystals have similar crystallographic orientations.Synneusis was also observed in the lava lake samples (thisstudy; see Supplementary material). Only the side that con-tains the vertical profile (right side) was used in the diffusionmodel.

Minor elements analyses reveal that CaO, Al2O3, Cr2O3,and NiO concentrations are zoned. Following the sugges-tion of Costa et al. (2008), we plotted the minor elementconcentrations against Fo# to test whether the minor ele-ments would show changes in behavior reflecting differentzoning regimes (diffusion-controlled vs. growth-controlledzoning). Fig. 2 shows that Cr2O3 and NiO wt% display sim-ple positive correlations with Fo# across the entire range ofFo#, while Al2O3 wt% is flat from the core to Fo80 and thendecreases with Fo#. By contrast, CaO wt% is negatively

correlated with Fo# from the core to Fo80, and the correla-tion becomes positive from Fo80 to the olivine rim. Thischange reflects the onset of augite and plagioclase crystalli-zation, but does not provide any clue on the nature of theprocess that established the profile. The rim more Fe-richthan Fo80 could have grown when augite and plagioclasewere crystallizing. The presence of augite crystals embeddedin the olivine rim indicates that this is a plausible hypothe-sis. Alternatively, the phenocryst was initially homogeneousin CaO wt%, but augite and plagioclase crystallizationchanged the boundary Ca concentration, which propagatedinto the crystal by diffusion.

4.2. Crystallographic orientation of olivine

The two FIB sections, taken close to the Mg-rich coresof the phenocryst, were found to have identical crystallo-

Table 3Fe isotopic data for the Kilauea Iki olivine phenocryst (KI81-5-254.5), obtained by LA-MC-ICPMS.

Spot # Dist. (mm) Fo# d56Fe d57Fe Spot # Dist. (mm) Fo# d56Fe d57Fe

Horizontal profile Vertical profile

1 0.600 74.5 �0.18 ± 0.16 �0.27 ± 0.26 1 0.200 73.4 �0.15 ± 0.16 �0.31 ± 0.262 0.731 77.6 �0.10 ± 0.16 �0.32 ± 0.26 2 0.294 74.1 0.05 ± 0.16 �0.08 ± 0.263 0.822 78.9 �0.01 ± 0.16 �0.18 ± 0.26 3 0.457 77.9 0.08 ± 0.16 �0.13 ± 0.264 0.937 79.9 �0.09 ± 0.16 �0.34 ± 0.26 4 0.551 79.5 �0.03 ± 0.16 �0.19 ± 0.265 1.162 81.1 �0.17 ± 0.16 �0.52 ± 0.26 5 0.676 80.2 �0.21 ± 0.16 �0.34 ± 0.266 1.272 81.3 �0.21 ± 0.16 �0.59 ± 0.26 6 0.779 80.9 �0.35 ± 0.16 �0.50 ± 0.267 1.391 81.5 �0.27 ± 0.16 �0.70 ± 0.26 7 0.872 81.5 �0.40 ± 0.16 �0.60 ± 0.268 1.541 81.6 �0.46 ± 0.16 �0.86 ± 0.26 8 0.969 82.0 �0.54 ± 0.16 �0.81 ± 0.269 1.649 81.5 �0.55 ± 0.16 �0.98 ± 0.26 9 1.078 82.5 �0.66 ± 0.16 �1.01 ± 0.26

10 1.738 81.7 �0.63 ± 0.16 �1.08 ± 0.26 10 1.176 82.8 �0.85 ± 0.16 �1.15 ± 0.2611 1.833 81.8 �0.71 ± 0.16 �1.18 ± 0.26 11 1.450 83.3 �0.92 ± 0.16 �1.24 ± 0.2612 1.909 82.4 �0.77 ± 0.16 �1.26 ± 0.26 12 1.555 83.2 �0.92 ± 0.16 �1.22 ± 0.2613 2.221 82.4 �0.91 ± 0.16 �1.44 ± 0.26 13 1.635 82.7 �0.87 ± 0.16 �1.16 ± 0.2614 2.611 83.1 �1.03 ± 0.16 �1.62 ± 0.26 14 1.753 82.1 �0.66 ± 0.16 �1.01 ± 0.2615 2.888 83.4 �1.09 ± 0.16 �1.71 ± 0.26 15 1.860 81.4 �0.59 ± 0.16 �0.88 ± 0.2616 3.039 83.3 �1.10 ± 0.16 �1.74 ± 0.26 16 1.968 80.4 �0.44 ± 0.16 �0.65 ± 0.2617 3.150 83.3 �1.10 ± 0.16 �1.74 ± 0.26 17 2.068 79.0 �0.38 ± 0.16 �0.51 ± 0.2618 3.268 83.1 �1.08 ± 0.16 �1.71 ± 0.26 18 2.173 77.6 �0.26 ± 0.16 �0.35 ± 0.2619 3.361 82.9 �1.06 ± 0.16 �1.68 ± 0.26 19 2.387 72.6 0.13 ± 0.16 0.29 ± 0.2620 3.469 82.6 �1.03 ± 0.16 �1.62 ± 0.2621 3.580 82.3 �0.95 ± 0.16 �1.51 ± 0.2622 3.694 82.1 �0.84 ± 0.16 �1.35 ± 0.2623 3.820 81.8 �0.67 ± 0.16 �1.11 ± 0.2624 3.919 81.5 �0.57 ± 0.16 �0.97 ± 0.2625 4.008 80.9 �0.48 ± 0.16 �0.84 ± 0.2626 4.121 80.3 �0.45 ± 0.16 �0.77 ± 0.2627 4.271 79.0 �0.40 ± 0.16 �0.67 ± 0.2628 4.429 74.5 �0.09 ± 0.16 �0.28 ± 0.26

Distances are given relative to the left or top edges of the olivine (marked “H0” and “V0”, Fig. 1c).Fo# were measured by taking the average of four EMPA analyses done around each measurement spot. diFe values are referenced toIRMM014. See text for details.


graphic orientation, which was confirmed using a petro-graphic microscope. The stereographic projections areshown in Fig. 1a.

4.3. FTIR

Characteristic FTIR spectra of three olivine singlegrains from KI81-5-254.5 were compared to a referenceolivine (“Kaapvaal” in Fig. S1), which has a comparablecrystallographic orientation and is known to contain19 ppm H2O (Fig. S1; Ingrin and Gregoire, 2010). Theabsorbances were normalized to the sample thicknesses.Typical bands of hydroxyl in olivine are barely resolvedin the Kilauea Iki olivine phenocrysts, indicating that thewater content is less than 1 ppm. The total water contentis estimated to be close to 0.3 ppm using the conventionalcalibration of Bell et al. (2003).

4.4. Microdrilling and solution MC-ICPMS

The d26Mg and d56Fe values of the microdrilled spotsare negatively correlated; d26Mg ranges from +0.09& to�0.23&, and d56Fe ranges from �1.16& to �0.16& fromcore to rim (Fig. 5; Table 2). The ranges of isotopic compo-sitions are consistent with previously reported values for

Kilauea Iki olivine fragments (see Fig. 5d; Teng et al.,2008, 2011). Teng et al. (2011) reported a negative correla-tion for d26Mg and d56Fe but for the first time, this relation-ship is spatially resolved through traverses across a singleolivine crystal.

The Fo# measured for the drilled samples and the oliv-ine matrix standards were close to the expected values. Toevaluate the precision and accuracy of the Fo# determina-tion by solution, four geostandards, UBN, BIR1a, W2a,and AGV were measured in the same session. The expectedFo# are 89.26, 62.85, 53.66, 34.52, and the measured num-bers are 89.37, 63.21, 53.49, 34.38, respectively. These geo-standard measurements give an overall uncertainty of �0.5(2 SD) for the Fo# of the microdrilled samples and olivinestandards, which were also measured to check purity ofhandpicked grains.

4.5. LA-MC-ICPMS

The difference in D56Fe(Fo#)<IMF, LA> between rimand core of the Kilauea Iki olivine phenocryst is only�0.18&.

Iron isotopic compositions range from +0.13& at therim to �1.10& at the core (Fig. 6c and f; Table 3). The er-ror bars of �0.16& on d56Fe (1 SD) are realistic given the

Fig. 7. MC-SIMS profiles across the horizontal (left panels) and vertical (right panels) traverses. See Fig. 6 caption for explanation.


sample chamber position effect. To assess the error barswithout this effect, a single SC grain was analyzed morethan 60 times, and the 1 SD value was 0.05& on d56Fe,and 0.07& on d57Fe. These errors are similar to those re-ported by Graham et al. (2004), Kosler et al. (2005), Hornet al. (2006), and Steinhoefel et al. (2009), but smaller thanthat reported by Hirata and Ohno (2001) and Nishizawaet al. (2010).

4.6. MC-SIMS

The difference in D56Fe(Fo#)<IMF, SIMS> betweenrim and core of the olivine is �1.3&, which is about therange of iron isotopic fractionation measured in the olivinephenocryst.

The final Fe isotopic compositions range from �1.28&

to +0.32& from core to rim (Fig. 7c and f; Table 4). Thepoint-to-point reproducibility of �0.25& on d56Fe (1 SD)is similar to that reported by Whitehouse and Fedo(2007) but larger than that reported by Marin-Carbonneet al. (2011). Precision on d57Fe (�0.32&, 1 SD) has notbeen reported previously. The internal precision given by

counting statistics was �0.02& on d56Fe and �0.04& ond57Fe (1 SD/

ffiffiffinp

with n = 50) for the olivine phenocryst.

4.7. Isotopic profiles

The profiles measured by microdrilling, MC-SIMS, andLA-MC-ICPMS are all very similar. For the horizontal tra-verse (Fig. 8a), relatively flat profiles are seen on the left fol-lowed by U-shape profiles. For the vertical profile (Fig. 8b),only the U-shape can be seen. Although the three datasetsindependently show the same features, direct comparisonis not straightforward because the profiles are not immedi-ately adjacent to one another. Because Fo# is a function ofdistance, Fe isotopic compositions can be plotted againstFo#. Such a plot shows excellent agreement between thethree techniques (Fig. 8c). The isotopic compositions inthe Fe-rich region for LA-MC-ICPMS and MC-SIMS dataare the least constrained because only one or two measure-ments could be made.

Different trends of d56Fe and d26Mg vs. Fo# can be seen.At compositions more Mg-rich than Fo80, d56Fe values aresteeply sloping toward lighter compositions, and d26Mg

Table 4Fe isotopic data for the Kilauea Iki olivine phenocryst (KI81-5-254.5), obtained by MC-SIMS.

Spot # Dist. (mm) Fo# d56Fe d57Fe Spot # Dist. (mm) Fo# d56Fe d57Fe

Horizontal profile Vertical profile

1 0.150 73.2 �0.44 ± 0.28 �1.06 ± 0.42 1 0.450 75.3 0.32 ± 0.28 1.05 ± 0.412 0.282 76.8 �0.28 ± 0.28 �0.53 ± 0.40 2 0.745 79.8 �0.54 ± 0.27 �0.81 ± 0.393 0.353 78.0 �0.34 ± 0.27 �0.48 ± 0.40 3 0.892 81.7 �0.79 ± 0.27 �1.24 ± 0.394 0.419 78.5 �0.32 ± 0.27 �0.48 ± 0.40 4 1.096 83.1 �1.07 ± 0.27 �1.77 ± 0.395 0.541 79.8 �0.41 ± 0.27 �0.54 ± 0.39 5 1.196 83.2 �1.25 ± 0.27 �2.27 ± 0.396 0.654 80.2 �0.45 ± 0.27 �0.62 ± 0.39 6 1.337 83.4 �1.22 ± 0.27 �2.19 ± 0.397 0.739 80.6 �0.47 ± 0.27 �0.64 ± 0.39 7 1.644 82.7 �1.03 ± 0.27 �1.82 ± 0.398 0.970 80.9 �0.53 ± 0.27 �0.68 ± 0.39 8 1.722 82.1 �0.92 ± 0.27 �1.65 ± 0.399 1.074 80.9 �0.52 ± 0.27 �0.68 ± 0.39 9 1.911 81.2 �0.66 ± 0.27 �1.30 ± 0.39

10 1.168 80.9 �0.53 ± 0.27 �0.70 ± 0.39 10 2.067 80.2 �0.47 ± 0.27 �1.02 ± 0.3911 1.253 80.8 �0.53 ± 0.27 �0.72 ± 0.39 11 2.152 79.9 �0.35 ± 0.27 �0.81 ± 0.3912 1.502 80.3 �0.46 ± 0.27 �0.69 ± 0.39 12 2.257 79.0 �0.22 ± 0.27 �0.73 ± 0.3913 1.611 80.0 �0.44 ± 0.27 �0.70 ± 0.39 13 2.356 77.1 �0.02 ± 0.27 �0.88 ± 0.4014 1.761 78.8 �0.45 ± 0.27 �0.72 ± 0.3915 1.856 78.4 �0.50 ± 0.27 �0.77 ± 0.3916 2.393 82.4 �0.91 ± 0.27 �1.23 ± 0.3917 2.661 82.8 �1.05 ± 0.27 �1.39 ± 0.3918 2.906 83.0 �1.20 ± 0.27 �1.65 ± 0.3919 3.194 83.2 �1.28 ± 0.27 �1.85 ± 0.3920 3.264 83.1 �1.28 ± 0.27 �1.88 ± 0.3921 3.340 82.9 �1.27 ± 0.27 �1.92 ± 0.3922 3.491 82.8 �1.14 ± 0.27 �1.78 ± 0.3923 3.571 82.5 �1.06 ± 0.27 �1.81 ± 0.3924 3.679 82.5 �0.94 ± 0.27 �1.70 ± 0.3925 3.792 82.2 �0.80 ± 0.27 �1.53 ± 0.3926 3.962 81.6 �0.60 ± 0.27 �1.29 ± 0.3927 4.098 80.3 �0.34 ± 0.27 �0.93 ± 0.3928 4.174 79.7 �0.60 ± 0.27 �1.02 ± 0.3929 4.400 74.2 �0.13 ± 0.28 �0.65 ± 0.42

Distances are given relative to the left or top edges of the olivine (marked “H0” and “V0”, Fig. 1c). See Table 3 caption and text for details.


values are sloping toward heavier compositions (Figs. 5 and8). At compositions more Fe-rich than Fo80, d56Fe andd26Mg stay constant (Figs. 5 and 8). The significance ofthese trends will be discussed below.

5. DISCUSSION

5.1. Origin of isotope zoning profiles

Possible mechanisms to explain the Mg and Fe isotopicprofiles are (1) Rayleigh distillation attending fractionalcrystallization with equilibrium isotopic fractionation atthe interface between melt and crystal, (2) diffusion-limitedgrowth for the olivine crystal, (3) Mg–Fe exchange of theolivine with surrounding melt. Each of these mechanismsis explored below.

The first possibility can be ruled out on the basis that thelargest isotopic shift (+0.35& for d26Mg and �1.27& ford56Fe relative to the bulk values of d26Mg = �0.26& andd56Fe = +0.11&, Teng et al., 2011) is measured in the coreof the olivine phenocryst, which is opposite to the expecta-tion for a Rayleigh distillation driven by fractional crystal-lization from a finite melt volume (Teng et al., 2008). Therim should display the largest isotopic shift from the bulk,as it is where the last increment of crystal growth should

have occurred from the most evolved melt. In the olivineanalyzed, the rim has d26Mg and d56Fe values close to thebulk and is therefore little fractionated isotopically.

During rapid growth, transport of elements from and tothe growing crystal surface can be limited by diffusion in theliquid medium, which can impart kinetic isotope fraction-ation (Dauphas and Rouxel, 2006; Watson and Muller,2009; DePaolo, 2011). The degree of isotopic fractionationis directly proportional to the elemental partitioning ratio,K, between olivine and melts (Watson and Muller, 2009).The KFeO

olivine-melt is �1.7, and the KMgOolivine-melt is �5.6

at 1130 �C (Roeder and Emslie, 1970). Given similar Mgand Fe diffusivities in a basaltic melt at 1130 �C (DMg

�5 � 10�12 m2/s, Chen and Zhang, 2008; DFe �10�12 m2/s,Lowry et al., 1982) and bMg � 0.05, bFe � 0.03 in silicatemelts (Richter et al., 2009a), Mg and Fe isotopes shouldbe fractionated in the same direction and fractionation ind26Mg should be an order of magnitude higher than thatof d56Fe. The Kilauea Iki olivine phenocryst, however,shows negatively correlated Mg and Fe isotopic composi-tions and variation in d26Mg is only about 1/3 of that ind56Fe. As a result, the isotopic fractionation observed can-not be attributed to diffusion-limited growth.

Evidence points toward Mg–Fe interdiffusion as theexplanation for the negatively coupled Mg and Fe isotopicfractionations (Dauphas et al., 2010; Teng et al., 2011).

Fig. 8. Comparison of the three techniques – microdrilling,LA-MC-ICPMS, and MC-SIMS. d56Fe plotted as a function ofdistance for (a) horizontal and for (b) vertical profiles. Theisotopically flat region in (a) could represent grain attachment; onlythe U-shape profile is modeled. (c) d56Fe plotted against Fo#. Theanalytical techniques show excellent agreement. For compositionsmore Mg-rich than Fo80, the trend is controlled by chemicaldiffusion. The red curve show the modeled trend (bFe = 0.27) ifzoning is diffusion-controlled. For compositions more Fe-rich thanFo80, the flat trend is indicative of zoning by rapid growthattending fractional crystallization.

Fig. 9. Cooling function used for the diffusion model. Temperaturedropped from pre-eruption temperature (T0 = 1230 �C) to initiallake temperature (Ti = 1190 �C) during the eruption period. It thenevolved as an error function (conductive cooling regime), whichpasses through the quench temperatures of two drill cores at 77.6 m(255 ft, red symbols), one drilled in 1981 (our sample) and the otherin 1988.


Petrographic observation suggests that melt compositionshad evolved to be less Mg-rich following the 1959 eruption(Helz and Thornber, 1987). In order to re-equilibrate, Mghas to diffuse out of and Fe has to diffuse into the olivinephenocryst. Because light isotopes diffuse faster than theirheavy counterparts (e.g., Richter et al., 2009b), light Mgisotopes are enriched in the rim of the olivine. Conversely,light Fe isotopes are enriched in the center of the olivine.Thus, d26Mg and d56Fe are negatively coupled because theydiffuse in opposite directions. Magnesium isotopes have alarger relative mass difference, so that isotopic fractiona-

tions are expected to be larger. However, this large fraction-ation is diluted by a larger background of isotopicallyunfractionated Mg.

A plot of d56Fe and d26Mg vs. Fo# reveals that for spotsmore Fe-rich than Fo80, the Fe and Mg isotopic composi-tions are constant, dramatically different from the trendsobserved for the higher Fo# (Figs. 5 and 8). The flatnessin d56Fe and in d26Mg suggests that the anomalously Fe-rich region (more Fe-rich than Fo80) was unaffected by dif-fusion. This is consistent with our hypothesis discussed inSection 2 that olivine with Fo# < 80 is late-stage over-growth. From Fo80 to the core, the zoning is controlledby chemical diffusion.

The two-stage thermal history of KI81-5-254.5 exempli-fies the virtue of using Mg and Fe isotopes to identify dif-fusive zoning in minerals. If zoning is due to fractionalcrystallization without re-equilibration through diffusion,no or little Mg and Fe isotopic fractionation should be de-tected. If zoning is diffusion-controlled, large and negativelycorrelated variations in Mg and Fe isotopes should beproduced.

5.2. Diffusion model

Here, we model the chemical-isotopic profiles of the re-gion affected by diffusion (Fo# > 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-richcore (Sections 2 and 4.1).

Spherical geometry for the olivine is assumed, and thepartial differential equation used for composition depen-dent diffusion is:

@X Mg

@t¼ 1

r2

@

@rr2D

@X Mg

@r

� �;

where XMg is the mole fraction of Mg in olivine [Mg/(Mg + Fe)], t is time, and r is the radial distance from thecenter of the sphere. The diffusion coefficient, D, is a

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

Variable Value used Explanations

T0 1230 �C Peak temperature of the magma prior to eruption, initial equilibration temperature of olivine phenocrysts (Helz,1987b)

Ti 1190 �C Initial temperature of the lava lake (Helz, 2009; Helz et al., in press)Tq 1130 �C Quench temperature of the lava lake at �77 m of the 1981 drill cores (Helz, 2009; Helz et al., in press)XMg,0 0.865 Starting composition of olivine [atomic Mg/(Mg + Fe)] (Helz et al., in press)XMg,q 0.8 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)a 1175,

670 lmRadius of the phenocryst outlined by the Fo80 contour to omit late-stage overgrowth; horizontal and verticaldirections

fO2 NNO Oxygen fugacity determined by Fe–Ti oxide oxybarometry (Helz and Thornber, 1987)c 44.7 Time constant in cooling model (the results are insensitive to this value)P 1 bar Pressure in the lava lakebMg 0.16 b-exponent in D2/D1 = (m1/m2)b, obtained by fitting to the Mg isotopic profilesbFe 0.27 b-exponent in D2/D1 = (m1/m2)b, obtained by fitting to the Fe isotopic profilest TimeT Temperaturer Distance from core of phenocrystXMg Atomic Mg/(Mg + Fe) of the olivine in equilibrium with the evolving meltD Diffusion coefficient expression from Dohmen and Chakraborty (2007)


function of temperature, pressure, oxygen fugacity, and Focontent of the olivine, parameterized by Dohmen andChakraborty (2007). The PDE is solved using Mathematicaand the embedded finite difference method. The mathematicalcode 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

@r¼ 0; r ¼ 0:

The other boundary condition describes the Fo contentat the rim of the olivine as a function of temperature inthe lava lake, XMg(T(t), r = a), where T is temperature, t

is time, and a is the radius of the olivine (seeSection 5.2.2).

5.2.1. Temperature and initial conditions

Chemical diffusion occurred at the onset of the 1959eruption that formed the Kilauea Iki lava lake. Prior toeruption, temperature in the magma chamber was close to1230 �C, and olivine phenocrysts had a constant composi-tion of Fo86.5 (Helz et al., in press). Therefore, the initialconditions are:

T 0 ¼ 1230 �C;

X MgðT 0; rÞ ¼ X Mg; 0 ¼ 0:865:

The erupted magma rapidly cooled to the initial tem-perature of the lava lake, 1190 �C (Helz, 2009; Helzet al., in press). The present study assumes that the tem-perature drop from 1230 to 1190 �C occurred during theeruption period of 36 days. Peck et al. (1977) and Helzet al. (in press) showed that the lava lakes of ‘Alae andKilauea Iki cooled in the conductive cooling regime,which is described by an error function. The thermal evo-lution at the center of the lava lake is therefore (shown inFig. 9):

T ðtÞ ¼T 0 � T 0�T i

Dt � t 0 days 6 t 6 36 days

T i � erfffiffiffiffiffiffic=t

p; 36 days < t

(

where T0 is the pre-eruption temperature, Ti is the initiallava lake temperature, t is time, Dt is duration of the erup-tion (=36 days), and c is a time constant.

5.2.2. Boundary condition at olivine rim

Helz and Thornber (1987) found empirically that the Mgcontent in the melt decreases linearly with temperature. Therim composition of olivine also evolves as a function oftemperature (Helz, 1987b; Helz et al., in press):

X MgðT ðtÞ; aÞ ¼ T 0 � X Mg; q � T q � X Mg; 0

T 0 � T qþ T ðtÞ

� X Mg 0 � X Mg; q

T 0 � T q

where XMg,q is the rim composition of the olivine at thetime of quenching by core drilling, and Tq is the tempera-ture at quench.

Note that XMg,q and Tq were not obtained directly fromthe phenocryst of the present study. As discussed in Sec-tions 2 and 5.1, this olivine went through a late-stage of ra-pid growth unique to KI81-5 core samples, so the values ofa 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 res-idence time in the lava lake. The size of this growth rim wasassessed by studying a sample that did not experience late-stage overgrowth. Particularly, the sizes of groundmass oli-vines and the sizes of phenocryst rims that enclose augitecrystals were measured in a thin section of KI79-1-189.0(Fig. S2). By both methods, it was found that the pheno-crysts grew less than 100 lm in radius, which is small


compared to the radius of the phenocryst. Therefore, crys-tal growth can be neglected in the diffusion calculation.

5.2.4. Modeling isotopic fractionations

It is assumed that diffusivities scale as the masses of theisotopes involved. The empirical formula from Richteret al. (1999) is used:

Di; 1

Di; 2¼ mi; 2

mi; 1

� �bi

;

where 1 and 2 are isotopes of element i, which is Fe or Mgin this study. The b-exponents are estimated by fitting theisotopic profiles. It is worth noting that b-values dependstrongly on the boundary conditions used in the modeling.Reasonable estimates may be obtained from natural sam-ples only if their boundary conditions are well constrained.This highlights the virtue of laboratory experiments, fromwhich determinations of b-values can help to constrainboundary conditions for natural systems.

A list of variables and the values used in the diffusionmodel can be found in Table 5.

5.3. Modeling results

For the observed cooling timescale of 21.4 years and atthe crystallographic directions of the chemical-isotopic pro-files, the parameterization of Dohmen and Chakraborty(2007) predicts a DMg–Fe that is too low by a factor of �4relative 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 therate of Mg–Fe interdiffusion in olivine (Hier-Majumderet al., 2005; Costa and Chakraborty, 2008). Dohmen andChakraborty (2007) quoted half an order of magnitudeuncertainty on predicted DMg–Fe values, so the inconsis-tency 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 simultaneouslyto reproduce the range of Fo# does not change b-values re-quired to reproduce the range of isotopic fractionations).However, the b-values are sensitive to the surface boundaryconditions, which is driven by the thermal evolution of thelava lake.

The b-exponents required to reproduce the isotopic pro-files are bMg �0.16, and bFe �0.27 (Figs. 5 and 8). Changingmodel parameters within acceptable ranges yields uncer-tainties of ±0.05 in bMg and ±0.04 in bFe. The slope ofd56Fe vs. d26Mg measured in the olivine phenocryst con-strains the bFe/bMg ratio to be 1.8±0.3 (Fig. 5d; Dauphaset al. 2010). The estimated bMg is higher than those foundin basalt-rhyolite melt couples (bMg � 0.05, Richter et al.,2009a), but similar to those found in anorthite-diopsidemelts (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, Goelet al., 2012). The estimated bFe is also higher than thosefound in basalt-rhyolite melt couples (bFe � 0.03, Richteret 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 valuesbetween olivine and metals may suggest that crystallinematerials have higher b-values than liquids. Further exper-imental work is needed to test this hypothesis and to ascer-tain the b-values estimated in this study.

5.4. Future applications to natural olivines

The Kilauea Iki olivine phenocryst is unique in the sensethat core drilling and thorough petrologic studies providemany constraints for the diffusion model. In most othercases, modeling parameters would be more poorly con-strained. Here we discuss how close one can approximatemagmatic timescales using measurements constrained by athin section and by knowing the original lava composition.In particular, we treat Kilauea Iki olivine as a case study byposing the question: what timescale would we have ob-tained if the olivine that we studied came from a randomrock with little geologic context?

We applied the MELTS algorithm (Ghiorso and Sack,1995) to estimate how boundary conditions evolve with fall-ing temperature given a starting composition. The mostmagnesian glass composition in the eruption pumice in Ta-ble 25.4 of Helz (1987b) was taken as the original lava com-position. From the MELTS algorithm, the calculatedliquidus temperature is 1231 �C at NNO, correspondingto an equilibrium olivine composition of Fo85.5, whichwould be the assumed starting olivine composition. At1145 �C, the olivine reaches Fo80 (rim of olivine pheno-cryst) marking quenching of the sample. An error functionis used to model conductive cooling, which is a goodassumption for igneous bodies, and proven to work wellfor the 1963 ‘Alae and the 1959 Kilauea Iki lava lakes (Sec-tion 5.2.1). Following this study, a factor of 4 in DMg–Fe isapplied to the oriented olivine in both vertical and horizon-tal traverses.

The retrieved cooling timescales are 19.8 and 47.8 yearsfor the vertical and horizontal traverses, respectively. Thedifference in the timescales results from the uncertainty inthe geometry of the olivine. In some studies, linear coolingwas assumed (e.g., Miyamoto et al., 1986); this cooling re-gime will generate timescales of 8.5 and 25.5 years for thevertical and horizontal profiles, respectively. Overall, theMELTS application is able to retrieve the cooling time-scales of the lava lake, paying attention to the choice offO2, starting composition, and crystallographic orientationof the olivine.

6. CONCLUSION

It has been previously recognized that diffusive transportin olivine is accompanied by large Mg and Fe isotopicfractionations (Dauphas et al., 2010; Teng et al., 2011).For the first time, these isotopic fractionations are spatiallyresolved using in situ measurements. We calibratedLA-MC-ICPMS and MC-SIMS using microdrillingfollowed by solution MC-ICPMS to show that accurateFe isotopic measurements can be obtained. The ability toresolve diffusion-driven isotopic fractionations for the ma-jor elements in zoned olivine has significant implications


for the field of diffusion-based geospeedometry: diffusion-controlled zoning may now be unambiguously teased apartfrom growth-controlled zoning, as the former process isaccompanied with large isotopic fractionations. Using theFe and Mg isotopic measurements, we discerned a coreolivine composition that was affected by diffusion and arim overgrowth that also shows some zoning but was notaffected by diffusion. Chemically, the overgrowth cannotbe distinguished from the core, demonstrating the useful-ness of isotopic measurements to recognize diffusion inzoned minerals.

As in situ stable isotopic measurements can be done rou-tinely using matrix-matched standards, we propose thatthese techniques be used as standard petrologic tools forthe study of zoned minerals in igneous and metamorphicrocks. It remains to be investigated whether other com-monly zoned minerals such as garnet, pyroxenes, plagio-clase, and oxides display similar diffusion-driven, intra-crystalline isotopic profiles.

ACKNOWLEDGMENTS

We thank Yan Xiao and Shuijiong Wang for assistance withMg isotopic measurements, Thomas Ireland for assistance withdevelopment of the LA-MC-ICPMS technique, David Troadecfor making the FIB sections, Ahmed Addad and Patrick Cordierfor TEM crystallographic orientation measurements, Jannick In-grin for assistance with FTIR analyses in olivine, Claire Rollion-Bard for assistance with MC-SIMS, Ian Steele and Severine Bellayerfor assistance with EMPA, Will Vaughan for writing a datareduction program for the SEM at the University of Chicago,and Haolan Tang for showing us internally normalized Fe isotopedata for IRMM014. This manuscript benefited from discussionswith Frank Richter, and constructive reviews by Summit Chakr-aborty, Jan Schuessler, and Bruce Watson, and editorial handlingby Stefan Weyer. This work was supported by Chateaubriand fel-lowship to C.K.I.S., NSF Petrology and Geochemistry(EAR1144429) and NASA Cosmochemistry (NNX12AH60G) toN.D., NSF (EAR-0838227 and EAR-1056713) to F.-Z.T., andANR program (2011JS56 004 01, FrIHIDDA) to M.R. The EPMAfacility in Lille is supported by the European Regional Develop-ment Fund (ERDF). The TEM national facility in Lille is sup-ported by the Conseil Regional du Nord-Pas de Calais, ERDF,and Institut National des Sciences de l’Univers (INSU, CNRS).

APPENDIX A. SUPPLEMENTARY DATA

Supplementary data associated with this article can befound, in the online version, at http://dx.doi.org/10.1016/j.gca.2013.06.008.

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