FEINBERG ET AL.: EPITAXIAL RELATIONSHIPS OF CLINOPYROXENE-HOSTED MAGNETITE 463American Mineralogist, Volume 89, pages 462–466, 2004

0003-004X/04/0203–462$05.00 462

INTRODUCTION

The electron backscatter diffraction (EBSD) technique has emerged as a method for rapidly determining lattice orienta-tions of minerals exposed in polished thin sections (see review by Randle and Engler 2000). Most EBSD work on minerals published to date has been applied to petrofabric analysis in deformed rocks. We report here an application of EBSD to the determination of lattice orientations across coherent and semi-co-herent phase boundaries produced by exsolution. Relative lattice orientations are critical to the application of the theory of optimal phase boundaries (Bollman 1970; Robinson et al. 1977) and to the calculation of exsolution temperatures based thereupon (Fleet et al. 1980). Although lattice orientations are routinely obtained by TEM and single-crystal XRD methods, EBSD is significantly less cumbersome and not as labor intensive.

Pyroxene and plagioclase in mafic plutonic and metamorphic rocks commonly contain oriented, highly elongated Fe-Ti oxide lamellae. In the case of clinopyroxenes collected from gabbros of the Messum Complex, Namibia, these inclusions comprise Ti-poor magnetite important in paleomagnetic and rock magnetic studies for their unusually stable magnetizations (e.g., Renne et al. 2002 and references therein). Interpretation of paleomagnetic data acquired from such rocks requires a detailed understanding of: (1) the formation temperature of the magnetite inclusions, (2) the timing of magnetization, and (3) the effects of extreme magnetic anisotropy. Determination of the orientation of the magnetite lattice with respect to the clinopyroxene host is a step-

ping stone to addressing all three of these issues. The epitaxial relationships between clinopyroxene and magnetite were first determined using single-crystal XRD (Bown and Gay 1959). Fleet et al. (1980) were the first to describe the orientation of magnetite with respect to its clinopyroxene host as a proxy for the temperature of exsolution (see discussion below). This geothermometer was later adapted to TEM studies by Doukhan et al. (1990) and Besson and Poirier (1994) to infer exsolution temperatures in metamorphic diopside and clinopyroxene phe-nocrysts, respectively. Doukhan et al. (1990) also suggested a balanced reaction involving hydrogen as a reactant and magnetite and tremolitic amphibole (which they observed) as products:

(Ca,Mg,Fe2+)2–2xFe3+2x[Al2xSi2–2x]O6 + x/4H2 →

3x/4Fe3O4 + (1–3x/2)·{(Ca,Mg,Fe2+)2–y/4Aly/4[Aly/4Si2–y/4]O6} + x/4{Ca,Mg,Fe2+)7–yAly[AlySi8–y]O22(OH)2} (1)

where y = 8x/(2 – x)Equation 1 is the first relationship, of which we are aware, to

show from a phase compositional perspective that an exsolution origin for both the magnetite and amphibole is plausible. Earlier studies argued for an oxidation origin for the magnetite inclusions and proposed reactions similar to that of Morse (1975):

3FeSiO3 + 1/2O2 = Fe3O4 + 3SiO2 (2)

However, the abundant silica expected from Equation 2 is not observed as either nonstoichiometric Si or as a Si-rich phase within clinopyroxenes containing oriented magnetite inclusions, and thus, there is little support for an oxidation origin for the inclusions.

The samples for this study were collected from gabbros of

* Present Address: Department of Earth and Planetary Science, University of California, Berkeley, California 94720, U.S.A. E-mail: feinberg@eps.berkeley.edu

Epitaxial relationships of clinopyroxene-hosted magnetite determined using electron backscatter diffraction (EBSD) technique

JOSHUA M. FEINBERG,1,* HANS-RUDOLF WENK,1 PAUL R. RENNE,1,2 AND GARY R. SCOTT2

1Department of Earth and Planetary Science, University of California, Berkeley, California 94720, U.S.A.2Berkeley Geochronology Center, 2455 Ridge Road, Berkeley, California 94709, U.S.A

ABSTRACT

Crystallographic relationships between exsolved phases and their hosts are typically character-ized using transmission electron microscopy (TEM) or single crystal X-ray diffraction (XRD). In this investigation, electron backscatter diffraction (EBSD) was used to determine the epitaxial relation-ships of exsolved laths of magnetite in clinopyroxenes from three sampling sites in the Cretaceous Messum Complex of Namibia. Two orientations of magnetite inclusions are found with their long axes subparallel to [100] and [001] of the host clinopyroxene. Inclusions subparallel to [100]c have [1–10]m // [010]c, (1

–1–1)m // (1–01)c, and [112]m // [101]c. Inclusions subparallel to [001]c have [1–10]m // [010]c, (111)m // (100)c, and [1–1–2]m // [001]c. The EBSD-derived orientation relationships agree well with previous TEM and XRD studies on similar materials.

The crystallographic relationships obtained with EBSD are used in conjunction with optimal phase boundary theory to determine the exsolution temperature of the magnetite inclusions, which is of im-portance to paleomagnetic studies. For one sample, this temperature (840 ± 50 °C) can be compared with that (865 ± 25 °C) derived from a more widely used cation exchange geothermometer. Thus it appears clear that exsolution occurred well above the Curie temperature of pure magnetite (580 °C).

FEINBERG ET AL.: EPITAXIAL RELATIONSHIPS OF CLINOPYROXENE-HOSTED MAGNETITE 463

the Messum Intrusive Complex, Namibia (21°26'S, 14°16'E). Emplaced as shallow cone sheets at ~133 Ma, the gabbros con-sist of clinopyroxene ± orthopyroxene + plagioclase + biotite + amphibole ± olivine + Fe-Ti oxides (Renne et al. 1996, 2002). In thin section, amphibole occurs both as large discrete crystals and as thin rims around, and as lamellar, regularly spaced inter-growths within, clinopyroxene. Magnetite inclusions occur inside clinopyroxene crystals parallel to (010), elongated subparallel to both [100] and [001], and will be referred to as “X” and “Z” respectively. The inclusions have lath-shaped dimensions with two axes <2 μm and a longer third axis from 5 to 150 μm long. Microprobe studies of clinopyroxenes from two samples, ET94-5 and ET94-6, yielded average compositions of Wo46En44Fs10 to Wo45En43Fs12, respectively (Table 1).

EXPERIMENTAL PROCEDUREThe EBSD technique requires an undisturbed crystal lattice at the sample

surface in order to form clear diffraction patterns. Standard petrographic thin sec-tions were prepared from bulk-rock samples from three sampling sites: ET94-2, ET94-5, and ET94-6. Structurally damaged and semi-amorphous material left behind from the standard polishing was chemically and mechanically removed during an eight hour final polish in Buehler Mastermet, a suspension of fine (0.06 micrometer) amorphous SiO2 particles in a high pH (9.8) aqueous base. No coating was applied to the samples.

Backscatter diffraction patterns were collected at the Department of Earth and Planetary Science at the University of California, Berkeley using a LEO 430 SEM equipped with a 14 bit, fully digitized slow-scan CCD camera. The SEM was operated with 20.0 kV accelerating voltage, 1 nA probe current, 1 second integration time, and a working distance of 28 mm. Before collecting a diffrac-tion pattern, the composition of the area of interest was verified using a Princeton Gamma-Tech EDX spectrometer. EBSD patterns were collected while the sample was tilted 70° relative to the incident electron beam and patterns were indexed using Flamenco 4.2 from HKL Technology. New diffraction files were created for magnetite and clinopyroxene using crystallographic data determined at room temperature and pressure conditions from previous studies. Lattice parameters for magnetite are taken from Lide (1998), where a = 8.394 Å with space group Fd3m. Lattice parameters for clinopyroxene of composition Wo46En44Fs10 are taken from Turnock (1973), where a = 9.760 Å, b = 8.940 Å, c = 5.245 Å, β = 106°, with space group C2/c. The orientation of the crystal lattice relative to the orientation of the sample inside the SEM chamber were calculated by Flamenco from indexed backscatter patterns and reported as Euler angles (ϕ1, φ, ϕ2) according to the Bunge (1965) convention.

Quantitative chemical analyses for pyroxene, amphibole, and associated pla-gioclase were determined with a customized Cameca SX-51 electron microprobe at the Department of Earth and Planetary Science at the University of California, Berkeley. The magnetite inclusions were too small for direct analysis by elec-tron microprobe, but small concentrations of Ti were documented by EDX. The microprobe is outfitted with five wavelength-dispersive spectrometers, one high-resolution quantitative energy dispersive spectrometer and is calibrated using a set of long-established standards. Data are background and spectral interference corrected and reduced using a modified Armstrong φ(ρz) correction technique

with Henke et al. (1982) mass-absorption coefficients using Probe for Windows software. Standards selected for quantitative analyses were albite and orthoclase for Al; diopside for Ca, and Mg; magnetite and fayalite for Fe; orthoclase for K; forsterite and diopside for Mg; nepheline and albite for Na; quartz, orthoclase and albite for Si; synthetic TiO2 for Ti; and synthetic V2O3 for V. Data were collected at 15 kV accelerating voltage and 20 nA beam current.

RESULTS

Orientation information was collected from 51 magnetite in-clusions and their neighboring host clinopyroxenes (Fig. 1). The smallest inclusion successfully indexed was 0.5 μm in diameter. The crystallographic relationships between the magnetite and clinopyroxene were identical for samples ET94-2, ET94-5, and ET94-6. Measured orientations from sample ET94-2 C2 are sum-marized as pole figures in Figure 2 and in Table 2. Both the “X” and “Z” inclusion arrays are oriented such that planes of roughly close-packed oxygen atoms in both phases, {111} in magnetite and (1–01) and (100) in clinopyroxene, are aligned.

EBSD patterns were collected from large numbers of inclu-sions from single clinopyroxene crystals, creating a need to summarize their average orientation and the statistical variation from that average. However, determining average orientations from Euler angles is not a trivial calculation. Statistical analysis of EBSD-derived orientation data shows that simple arithmetic means of Euler angles do not generate accurate orientation aver-ages due to the distortion inherent in Euler space (Krieger-Las-sen and Jensen 1994). Average orientations are more naturally calculated using the quaternion coefficient algebra of Humbert et al. (1996) and Humphreys et al. (2001). The Euler angles and equivalent angle/axis pairs characterizing the mean orientation of the “X” and “Z” inclusions and the host clinopyroxene in sample ET94-2 C2 are listed in Table 2. There is a small but distinct difference in the lattice orientations of the “X” and “Z” magnetite inclusions (Figs. 1 and 2). Although the φ values are

TABLE 1. Microprobe measurements of pyroxene, amphibole, and plagioclase in ET94-6 Slide 1

wt% Pyroxene Amphibole Plagioclase

(n = 40) Discrete (n = 5) Rim (n = 13) Internal (n = 7) Rim (n = 65)

SiO2 51.69 44.26 43.06 42.33 55.08Al2O3 3.07 10.18 10.98 11.58 27.92MnO 0.24 0.18 0.14 0.16 0.02MgO 15.37 14.81 13.42 13.48 0.02CaO 19.41 11.49 11.43 11.52 10.6FeO 8.14 10.09 10.99 11.36 0.16V2O3 0.06 0.09 0.12 0.09 0.02TiO2 0.9 2.86 3.24 2.58 0.05Cr2O3 0.05 0.03 0.05 0.05 0.02Na2O 0.52 2.65 2.59 2.51 5.62K2O 0.02 0.52 0.67 0.67 0.13 Total 99.46 97.16 96.69 96.33 99.64

FIGURE 1. (Left) Back-scattered electron image of “X” and “Z” magnetite inclusions in clinopyroxene in sample ET94-2 C2. (Right) EBSD patterns collected from “X” and “Z” magnetite inclusions show a <7˚ rotational difference.

FEINBERG ET AL.: EPITAXIAL RELATIONSHIPS OF CLINOPYROXENE-HOSTED MAGNETITE 464 FEINBERG ET AL.: EPITAXIAL RELATIONSHIPS OF CLINOPYROXENE-HOSTED MAGNETITE 465

indistinguishable, there is an ~6.5° difference in the ϕ1 values and ~0.5° in the ϕ2 values for the two magnetite orientations. The lattices of the two sets of inclusions can be brought into coinci-dence by a ~6.5° rotation around [110]m. The EBSD technique was capable of measuring the orientations of the inclusions and the host clinopyroxene with mean deviations of ~0.5°, proving that the technique has angular resolution similar to more labor-intensive methods such as TEM and X-ray precession. With this level of resolution, EBSD is certainly capable of resolving an ~6.5° misorientation between crystal lattices (Humphreys et al. 1998; Prior et al. 1999; Prior 1999).

Comparison with earlier workThe crystallographic relationships between magnetite and

clinopyroxene determined with EBSD agree well with previous TEM- and XRD-based investigations (Table 3). Earlier studies also observed similar but slightly different orientations for the two sets of magnetite inclusions in clinopyroxene. Doukhan et al. (1990) calculated a 5° rotation around [110]m, between the two sets of inclusions in a metamorphic diopside from India. Woensdregt et al. (1983) discerned a 6° difference in the [111]m orientations between the two sets of magnetite inclusions in a similar metamorphic clinopyroxene. Fleet et al. (1980) observed a 5˚ difference between the [111]m and an ~2° difference between the [1–11–11]m in each of the inclusions in clinopyroxene from gab-bros of the Grenville province. Okamura et al. (1976) reported a 6˚ rotation around [110]m between the two inclusion directions in clinopyroxene from spinel lherozolite nodules from the San Quintin volcanic field, Baja California. Bown and Gay (1959) were able to distinguish a 7° rotational difference about [110]m between magnetite inclusions in clinopyroxene crystals. The re-sults reported here fall within the margins of error associated with each of the techniques used in these previous studies.

Temperature of exsolutionTwo independent techniques can be used to determine the

exsolution temperature of the magnetite inclusions. The first technique is based on optimal phase boundary theory as first introduced by Bollman (1970) and later clarified for pyroxenes by Robinson et al. (1977). Optimal phase boundary theory aims to find the geometric fit between two crystal lattices that minimizes interfacial energy. This best fit varies as the lattice parameters of the two materials change with increasing temperature. Fleet et al. (1980) were the first to use optimal phase boundary theory to predict the elongation orientation of magnetite inclusions in clinopyroxene. In addition, Fleet et al. (1980) took advantage of the large contrast in thermal expansion coefficients between magnetite and clinopyroxene to create a geothermometer whose sole input is the angle between the two sets of elongate inclusions. Because this report is concerned primarily with the ease and accuracy of EBSD-derived orientations, we refer the reader to Fleet et al. (1980) and Robinson et al. (1977) for an extended de-scription of optimal phase boundary theory. The crystallographic relationships determined by EBSD (Table 3) were used to define new, nearly identical monoclinic unit cells for both magnetite and clinopyroxene (Fig. 3). The new monoclinic magnetite lat-tice has the following parameters: a = 6 d224, c = 3 d224, and β = [111]m^[1–11–11]m. The new monoclinic clinopyroxene lattice has a equal to the d100 along [101]p, c = c, and β = [001]c^[101]c. These new unit-cell parameters were combined with existing thermal expansion data for magnetite [α = 1.51 10–5 / °C (Gray 1971)] and clinopyroxene [α[100] = 0.623 10–5 / °C, α[001] = 0.813 10–5 / °C, αβ = –0.229 10–5 / °C (Robinson et al. 1977)] to calculate the optimal phase boundaries between 100 and 1000 °C. At each temperature two orientations of best-fits were calculated, cor-responding to the “X” and “Z” inclusion orientations. Figure 4 shows the predicted obtuse angle between the magnetite inclu-

TABLE 2. Mean orientation parameters for ET94-2 C2 relative to arbitrary Cartesian thin section coordinates X’ Inclusions Z’ Inclusions Clinopyroxene

Euler Angles φ1, Φ, φ2 (˚) 114.4 44.6 86.1 121.1 44.7 85.4 166.4 93.0 357.9Mean spread (˚) 0.6 0.5 0.4Maximum deviation (˚) 1.1 0.8 0.9Angle ω (˚) / Axis defined by x, y, z, vector components 92.1 / –0.242, –0.061, –0.600, 93.2 / –0.307, –0.099, –0.763172.3 / 0.027, 0.271, 0.256.

B.

c

a

A.

c

a

C.

c

a

Figure 2.

FIGURE 2. Stereographic projection of poles to crystallographic planes showing EBSD-derived relationships between the mean “X” (circles) and “Z” (crosses) magnetite inclusions and the host clinopyroxene lattice. The clinopyroxene a and c crystallographic directions are marked on each pole figure for reference. (A) <110>m and [010]c (square). (B) <111>m and (100)c (closed circle) and (1–01)c (square). (C) <211>m and [001]c

FEINBERG ET AL.: EPITAXIAL RELATIONSHIPS OF CLINOPYROXENE-HOSTED MAGNETITE 464 FEINBERG ET AL.: EPITAXIAL RELATIONSHIPS OF CLINOPYROXENE-HOSTED MAGNETITE 465

sions as a function of temperature. Renne et al. (2002) used a standard petrographic microscope to measure this angle directly on thin sections with specially oriented crystals. Samples ET94-2, ET4-5, and ET94-6 gave values of 105.7 ± 1.4° (N = 12), 105.8 ± 1.6° (N = 12), and 106.2 ± 1.2° (N = 10), respectively. The uncertainties in these estimates are most likely due to mea-surement error rather than real variation in the angle between the inclusions. The corresponding exsolution temperatures for samples at each of the three cone sheets (Fig. 4) are 780, 790, and 840 °C. Fleet et al. (1980) ascribe a conservative error of ±50 °C to the temperature estimates, which we adopt here. One fundamental limitation to the accuracy of the optimal phase boundary geothermometer is the lack of information about the effects of trace concentrations of elements such as Al and Ti on the lattice parameters of clinopyroxene. Additional sources of error in the lattice parameters include limited knowledge about the combined effects of temperature and pressure.

Assuming that the amphibole and the magnetite exsolved

simultaneously from the host clinopyroxene, as suggested in the balanced reaction of Doukhan et al. (1990), then it is possible to compare the exsolution temperatures determined using optimal phase boundary theory with the amphibole-plagioclase geother-mometer of Holland and Blundy (1994). Electron microprobe traverses of samples from ET94-6 show that the amphibole rims commonly observed surrounding clinopyroxene are composition-

TABLE 3. Lattice correspondence for crystallographically oriented magnetite inclusions in clinopyroxeneReference “X” “Z” Technique

Bown and Gay 1959 (1–

1–

3)m // (001)c (111)m // (100)c Single-crystal X-ray diffraction [11

–0]m // [010]c [1

–10]m // [010]c

(1–

1–

3)m ^ (001)c = 7˚Okamura et al. 1976 [113]m // [001]c (111)m // (100)c Single-crystal X-ray diffraction, Optical microscopy [1

–10]m // [010]c [1

–10]m // [010]c

Fleet et al. 1980 (1–

1–

1)m // (1–

01)c (111)m // (100)c Single-crystal X-ray diffraction, Optical microscopy [112]m // [101]c [1

–10]m // [010]c

[1–

10]m // [010]c [1–

1–

2]m // [001]c

Woensdregt et al. 1983 (100)m // (101)c (111)m // (100)c Transmission electron microscopy [31

–1–

]m // [001]c [01–

1]m // [010]c [01

–1]m // [010]c

Doukhan et al. 1990 (011)m // (010)c (011)m // (010)c Transmission electron microscopy (100)m // (101)c (11

–1–

)m // (100)c

Markl et al. 2001 (111)m // (100)c Transmission electron microscopy [011]m // [010]c

This work (1–

1–

1)m // (1–

01)c (111)m // (100)c Electron backscatter diffraction [1

–10]m // [010]c [1

–10]m // [010]c

[112]m // [101]c [1–

1–

2]m // [001]c

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����

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����������

��������

�����

�����

a'

c'

Figure 3.

FIGURE 3. Superposition of the magnetite and clinopyroxene lattices based on orientation relationships determined with EBSD. The magnetite lattice is rendered in dashed lines (underlined indices), and the clinopyroxene lattice is in solid lines. Figure is drawn on (010) of clinopyroxene and (1–10) of magnetite.

X-ZAngle

ET94-6

ET94-5ET94-2

100 200 300 400 500 600 700 800 900 1000

108˚

106˚

104˚

102˚

100˚

Temperature (˚C)

850 860 870 880 890 900 910 920 9300

5

10

15

Temperature (˚C)

Messumgabbrosemplaced<4 kbars

Pressure(kilobars)

A

B

Figure 4.

FIGURE 4. Temperature estimates for inclusion formation. (A) Angle between the two sets of magnetite inclusions as a function of temperature as predicted by optimal phase boundary theory. (B) Formation temperature estimates for sample ET94-6 calculated using the Holland and Blundy (1994) amphibole-plagioclase geothermometer. Only the temperatures associated with pressures less than 4 kbars apply to the Messum samples.

FEINBERG ET AL.: EPITAXIAL RELATIONSHIPS OF CLINOPYROXENE-HOSTED MAGNETITE 466

ally identical to the amphibole lamellae within the clinopyroxene, and therefore presumably also are products of the exsolution reaction. The lamellar shape and regular parallel spacing of the amphibole intergrowths within the clinopyroxene also support an exsolution origin. Discrete large amphiboles in the sample have distinct compositions, most notably in their higher Mg concen-trations (Table 1). Using data from rims of plagioclase adjacent to these amphibole rims on clinopyroxene, we anticipate equi-librium between the two phases. Because the Messum gabbros samples were collected from shallowly emplaced cone sheets, only pressures less than four kilobars were considered applicable (Fig. 4). This factor limits the temperature of amphibole exsolu-tion, and hence magnetite exsolution, to 865 ± 25 °C, which is indistinguishable from the optimal phase boundary exsolution temperature of 840 ± 50 °C.

CONCLUDING REMARKS

The EBSD technique is capable of rapidly and precisely de-termining the lattice orientation relationships between elongate, >0.5 μm diameter magnetite inclusions and their host clinopy-roxene. These orientation relationships are easily incorporated into optimal phase boundary theory for use as a geothermometer. Magnetite inclusions exsolved in clinopyroxene are the domi-nant carriers of magnetic remanence in gabbro samples from the Messum Complex (Renne et al. 2002), and the formation temperature of the inclusions is essential for interpreting the origin of remanent magnetization in these samples. Based on exsolution temperatures from two independent geothermometers, the initial formation of these inclusions occurred well above the Curie temperature of pure magnetite (580 °C). Thus the magnetic remanence associated with the inclusions appears to be thermal in origin, provided that there has been no subsequent phase segregation within the oxide inclusions themselves, nor pinning of magnetic domain walls by cooling-induced strain, or other complicating factors. Because of its greater ease and comparable accuracy with other more labor-intensive techniques, EBSD represents a technique with considerable potential for geothermometry.

ACKNOWLEDGMENTSWe thank John Donovan for his assistance with the electron microprobe and

Tim Teague for help with sample preparation. Jonathan Levine helped J.M.F. tackle the mathematical underpinnings of optimal phase boundary theory. This work was partially funded by NSF grants EAR0236925 and EAR9909517 to P.R.R.

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