Chapter 2Charaterisation of exsolutionmirostrutures in Grt

(Part of this Chapter has been published in Terra Nova (2004), v. 16, pp. 325-330.)

2.1 Introdution 352.1 IntrodutionMirostrutural relations in and between minerals provide useful information on arok's history. Examples are relis of assemblages and phases, whih did not breakdown in response to hanged physio-hemial onditions, traes left behind fromperolating �uids and imprints of a deformation regime. In partiular, mirostru-tures in orogeni peridotite give valuable information on the history and evolutionof the sub-ontinental lithospheri mantle (SCLM). In this hapter exsolution mi-rostrutures in mantle minerals will be haraterized and quanti�ed to reonstrutthe hemistry of the early preursor phases.Exsolution produts (matrix and preipitates) from mineral solid solutions(solid-state dissolutions) form regular patterns with a rystallographi relationshipto eah other, whih is in agreement with theoretial onsiderations (Boudeulle,1994). The knowledge of the rystallography of a mirostruture and its spatialontinuation in 3D allows the relationship between exsolution produts and othermirostrutures (like reation textures or entrapped �uids) to be distinguished.If the pre-exsolved phase an be determined, then their experimental andthermodynamial dedued stability onditions give diret information on theenvironment of rok formation. Even though exsolved phases are often very smalland o

ur in minor amounts, an a

urate quanti�ation of the hemistry and thevolume of these phases is essential if preursor minerals are to be reonstruted.The reliability of a reonstrution is therefore often sensitive to the preision andthe a

uray of the used method.This hapter gives a brief overview of the di�erent types of Pyx mirostruturesreognised in Otrøy mantle lithologies, whih are interpreted to have formed by ex-solution from an unstable preursor phase. The preursors were stable at relativelyHT and HP. Examples of the mirostrutures are shown for four rok types: Grt-linopyroxenite (99NR6, DS0295), Grt-harzburgite (DS0289), Cpx-Grt-harzburgite(DS0278, DS0287) and garnetite (DS0297, DS0298). The fous is then direted tothe haraterisation of the intrarystalline majoriti mirostruture (f. Van Roer-mund and Drury (1998)). Crystallographi relationships will be desribed and themajoriti preursor phase will be determined using two di�erent methods. Resultsare applied using thermodynamial and experimental data sets to onstrain theorigin of the intrarystalline mirostruture. Together with geothermobarometriestimates, a shemati P�T path is derived at the end.2.2 Types of Pyx mirostrutures2.2.1 Pyroxene in garnetMirostrutureThe solid solution of Pyx in Grt is known to be strongly P sensitive due to theonversion of some tetrahedral oordinated SiIV into otahedral oordinated SiVI

36 2. EXSOLUTION MICROSTRUCTURES

(a) (b)3mmGrt2Opx2I *

() (d)Grt2Opx2 60 µmGrt2 Opx2

?

Cpx2?

Figure 2.1: Optial light and eletron mirographs of well preserved Pyx2 mirostrutures inGrt2 from a megarystalline garnetite (DS0297). (a) Grt2 rystals ≥5mm in size have ores(darker grey) ontaining Pyx2 needles and rims (lighter grey) free of Pyx2. Single Grt2 rystalsare deorated by mm-sale Pyx2 interstitials, whih are predominantly situated in triple juntions(sanned image). (b) Detail of a Grt2 ore ontaining Pyx2 needles in four visible diretions: threeare sub-horizontal forming a triangular shape, the fourth is vertial (PPL). () Close-up of a Grtrim showing two interstitial Opx2 grains with 120 ° grain boundary angles (tilted fore-satter SEMimage). (d) Close-up of a Grt2 ore showing single-phase and poly-phase Pyx2 needles in the fourvisible diretions (BSE image).(Akaogi and Akimoto, 1977; Canil, 1991; Fei and Bertka, 1999; Gasparik, 2003).The inverse reation, exsolution of Pyx from a supersilii Grt (Mj), is desribed as:M3(Al2−2nMnSin) [Si3O12]→ (1− n) M3Al2 [Si3O12] + 4n M2 [Si2O6] (2.1)with M = (Mg, Fe, Ca) and 0 ≤ n ≤ 1. Natural examples ontaining Pyx mi-rostrutures in the form of elongated lamellae in Grt were �rst desribed fromSouth Afrian kimberlite xenoliths (Haggerty and Sautter, 1990). The Pyx lamellaewere proposed to be exsolved from Mj and to follow the {111} planes in a periodi

ylindrial paking model for Grt (Andersson and O'Kee�e, 1977). Similar Pyxmirostrutures in Grt have been disovered in m�dm sale polyrystalline Grt2 inorogeni Grt-peridotite from Otrøy (Van Roermund and Drury, 1998). The term`garnetite' will further be used for dm-sale polyrystalline Grt2, the term `nodule'

2.2 Types of Pyx mirostrutures 37

(a) (b)?6

� Pyx2 Grt2 Grt2 Grt3 Cpx3

Figure 2.2: Optial light mirographs showing Pyx2 needles in porphyrolasti Grt2. (a)Bifringing Grt2 ore in peridotite (DS0289) with relits of Pyx2 needles (XPL). (b) Grt-pyroxenite (DS0295) ontaining Grt2 porphyrolasts with small Pyx2 needles in the Grt2 oresand preipitation-free Grt2 rims. Grt2 porphyrolasts are surrounded by rerystallized grains ofCpx3 and Grt3 laking Pyx preipitates (almost XPL).for polyrystalline Grt2 several m (≥3 m) in size and the term `porphyrolasti'Grt2 for all other non-rerystallized Grt in peridotite and pyroxenite.Pyx2 mirostrutures in Grt2 o

ur in all Grt-bearing lithologies of the Ugelvik,Raudhaugene and Midsundvatnet peridotite bodies on Otrøy. Two types have beendistinguished:Pyx2 needles are rystallographially oriented, prismati needles of Opx2 andCpx2, sometimes assoiated with minor Prg, whih o

ur in the ores of in-dividual Grt2 grains (Fig. 2.1). The Pyx2 needles are either single-phase orpoly-phase and have sizes of 500× 25µm and less (Fig. 2.1(b) and (d)). TheGrt2 ores are surrounded by Pyx2 needle free rims with a width ranging from1 to 2mm (Fig. 2.1(a)). This type of mirostruture o

urs partiularily ingarnetite, but an also be reognised in Grt2 nodules of peridotite and in Grt2of pyroxenite (Fig. 2.2).Pyx2 interstitials are grains of Opx2, Cpx2 and minor Ol2 situated in 120 ° triplejuntions of individual Grt2 grains (Fig. 2.1(a) and ()). Interstitial phaseshave grain sizes of ≤2mm. This type of mirostruture o

urs in garnetite,in Grt2 nodules and may be assoiated with single Grt2 grains in peridotite(Fig. 2.3).Both types of Pyx2 mirostruture are best preserved in garnetite and Grt2nodules, whih lak any form of strain-indued rerystallization. The width of pre-ipitation free Grt2 rims onstrains the single Grt2 grain size to about 5mm, abovewhih Pyx2 needles are preserved (Fig. 2.1(a)). The needles are still reognisablein the ores of some porphyrolasti Grt2 of pyroxenite and peridotite (Fig. 2.2(a)),but may be absent in ores of other porphyrolasti Grt2 and rerystallized Grt3.

38 2. EXSOLUTION MICROSTRUCTURES

(a) (b)1mmGrt2Cpx2 serp. Pyx2or Ol2� :� 2mm

Grt2Cpx2 Ol2� -M

Figure 2.3: Optial light mirographs showing Pyx2 and Ol2 grains assoiated with porphyro-lasti Grt2 in peridotite. (a) Cpx-Grt-harzburgite (DS0278) with Pyx2 and serpentinized Pyx2 orOl2 grains in embayments around a single Grt2 rystal (PPL). (b) Cpx-Grt-harzburgite (DS0287)ontaining m-sale porphyrolasti Grt2 with inlusions of Cpx2 grains and an Ol2 grain (PPL).In general, Pyx2 needles are smaller in size in Grt2 ores of pyroxenite, a few µmin width and a few tens of µm in length, than in garnetite (Fig. 2.1 and 2.2(b)).Cm-sale porphyrolasti Grt2 in peridotite may ontain Pyx2 grains as inlusionsand in embayments at the rystal margins (Fig. 2.3). These Pyx2 grains are sim-ilar in shape and size to interstitial Pyx2. Grains of Cpx2 assoiated with theseporphyrolasts are generally fresh, whereas Opx2 and minor Ol2 may be partly orompletely serpentinized.Mineral hemistryMajor element mineral ompositions were determined using a JEOL JXA8600 su-perprobe, equipped with �ve WDS spetrometer, at standard onditions (15 kV,20 nA, beam ∅ 1µm) at Universiteit Utreht (Appendix A.6). Compositional pro-�les aross several single Grt2 grains in garnetite and pyroxenite show �at oresand minor variations at the rims. Porphyrolasti Grt2 in peridotite may preservesteep ompositional zoning in the outermost rims (Chapter 4). Mineral omposi-tions of the M2 mirostruture in garnetite DS0297 (Grt2+Opx2±Ol2±Cpx2) andGrt-linopyroxenite 99NR-6 (Grt2+Cpx2±Opx2±Amp2) were investigated in moredetail; representative ompositions are given in Table 2.1 .The garnetite sample ontains interstitial Opx2 with homogeneous CaO on-entrations (0.12�0.17wt%) and Al2O3 onentrations that vary from the ores(≥0.45wt%) towards the rims (≤1.5wt%). The FeO ontent of interstitial Ol2may derease by minor amounts from the ore (5.15wt%) to the rim (4.95wt%).Pyx2 needles are homogeneous in omposition (in wt%; for Cpx2: CaO ∼22.0,Na2O ∼1.6, Al2O3 2.7�2.9; for Opx2: CaO 0.14�0.16, Al2O3 ∼1.0). Grt2 has rel-atively high TiO2 ontent (0.05�0.10wt%) and has ore ompositions, whih areelevated in Cr2O3 ontent (0.9wt%) ompared to the rims (0.7wt%). CaO is on-stant (∼4.2wt%), FeO is inreased at the rims (6.4wt%) ompared to the �at ores(5.1wt%) and MgO is vie versa (22.4 and 23.2wt%, respetively).

2.2 Types of Pyx mirostrutures 39Sample g a r n e t i t e D S 0 2 9 7 Grt-linopyroxenite 9 9 N R 6Mineral Grt2 Grt2 Opx2 Cpx2 Opx2 Opx2 Ol2 Grt2 Grt2 Opx2 Cpx2 Hbl2Type host host needle needle interst. interst. interst. host host needle needle needle(ore) (rim) (ore) (rim) (ore) (ore) (rim)wt%SiO2 42.91 43.25 58.69 55.17 58.86 58.57 41.47 42.82 42.65 56.42 53.83 42.49TiO2 0.05 0.09 0.05 0.16 0.03 0.02 0.00 0.02 0.03 0.04 0.08 0.91Al2O3 23.21 23.29 1.01 2.79 0.49 1.51 0.00 23.31 23.13 2.21 1.41 16.50FeO 5.25 6.40 2.54 0.70 2.67 3.17 5.13 10.14 10.41 5.87 2.06 2.5MnO 0.15 0.18 0.01 0.03 0.00 0.02 0.05 0.42 0.43 0.09 0.07 0.02MgO 23.28 22.44 37.16 16.28 38.38 37.16 53.12 19.60 19.47 34.74 17.45 18.04CaO 4.27 4.17 0.14 22.01 0.12 0.14 0.00 4.26 4.20 0.17 23.23 11.87Na2O 0.02 0.00 0.02 1.63 0.01 0.02 0.00 0.00 0.00 0.00 0.72 3.61K2O n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. 0.00 0.00Cr2O3 0.88 0.68 0.06 0.51 0.05 0.03 0.00 0.14 0.14 0.04 0.13 0.21NiO 0.01 0.02 0.19 0.09 0.15 0.10 0.97 0.03 0.01 0.03 n.a. n.a.Total 100.02 100.52 99.88 99.36 100.77 100.75 100.74 100.73 100.47 99.61 98.98 96.15O base 12 12 6 6 6 6 4 12 12 6 6 23*Cationes per formula unitSi 2.997 3.017 1.988 1.991 1.980 1.972 0.992 3.028 3.029 1.947 1.972 6.018Ti 0.003 0.005 0.001 0.004 0.001 0.001 0.000 0.001 0.001 0.001 0.002 0.097Al 1.911 1.914 0.040 0.119 0.020 0.060 0.000 1.943 1.936 0.090 0.061 2.754Fe2+ 0.307 0.373 0.072 0.021 0.075 0.089 0.103 0.600 0.618 0.169 0.063 0.296Mn 0.009 0.011 0.000 0.001 0.000 0.001 0.001 0.025 0.026 0.003 0.002 0.002Mg 2.424 2.333 1.876 0.876 1.924 1.865 1.894 2.066 2.061 1.788 0.953 3.809Ca 0.319 0.312 0.005 0.851 0.004 0.005 0.000 0.323 0.319 0.006 0.912 1.801Na 0.002 0.000 0.002 0.114 0.001 0.001 0.000 0.000 0.001 0.000 0.051 0.991K � � � � � � � � � � 0.000 0.000Cr 0.049 0.037 0.002 0.015 0.001 0.001 0.000 0.008 0.008 0.001 0.004 0.024Ni 0.000 0.000 0.005 0.002 0.004 0.003 0.019 0.000 0.000 0.001 � �Total 8.021 8.002 3.991 3.995 4.010 3.998 3.008 7.993 7.998 4.006 4.019 15.793Table 2.1: Representative mineral ompositions for the Pyx2 mirostrutures in garnetite DS0297and Grt-linopyroxenite 99NR6; n.a. not analysed; ∗normalized to 13 ations exlusive Ca, Na, K.Porphyrolasti Grt2 in Grt-linopyroxenite ontains Pyx2 needles with a narrowompositional range (in wt%; for Cpx2: CaO∼22.6�23.2, Na2O∼0.7, Al2O3 1.4�1.7;for Opx2: CaO 0.17�0.20, Al2O3 2.2�2.8). Minor Hbl2 is pargasiti in omposition.Grt2 is low in TiO2 ontent (∼0.03wt%) and Cr2O3 ontent (0.12�0.16wt%). CaO isonstant (∼4.2wt%), FeO shows a minor inrease at the rims (10.4wt%) omparedto the ores (10.1wt%) and MgO is vie versa (19.4 and 19.6wt%, respetively).P�T estimatesThe omposition of the minerals in the mirostrutures (Table 2.1) have been usedfor P�T estimates with the following experimentally determined alibrations:(1) the Al�in�Opx barometer of Brey and Köhler (1990) inluding the Ts om-ponent in Opx (Carswell, 1991) in ombination with the Fe�Mg exhangethermometer of Brey and Köhler (1990) (Grt�Opx),(2) the Al�in�Opx barometer of Carswell and Harley (1990) in ombination withthe Fe�Mg exhange thermometer of Carswell and Harley (1990) (Grt�Opx),

40 2. EXSOLUTION MICROSTRUCTURES(3) the Fe�Mg exhange thermometer of Powell (1985) (Grt�Cpx) in ombinationwith P estimates from (1) and (2),(4) the empirial thermobarometer of Ernst and Liu (1998) based on the Ti andAl systematis in Amp,(5) the Fe�Mg exhange thermometer of O'Neill and Wood (1979) (Grt�Ol) inombination with P estimates from (1) and (2).They yield P and T onditions for the equilibration of the intra- and interrystallinemirostrutures in the order of:Calibration 99NR6 (needle) DS0297 (needle) DS0297 (interst.)(1) 1.36GPa / 680 °C 2.45GPa / 700 °C 3.80GPa / 790 °C(2) 1.67GPa / 775 °C 2.81GPa / 800 °C 4.24GPa / 890 °C(3) 750�760 °C 675�685 °C �(4) 2.30GPa / 720 °C � �(5) � � 1140�1160 °CT estimates, whih involve the omposition of Pyx2 needles in both samples,overlap within the range of 680�800 °C. These results an be regarded as minimumT onditions for the origin of the Pyx2 needles, beause ation di�usion betweendi�erent mineral phases may have overprinted an early T reord as the needlesare very thin, ≤20µm. The same may be valid for the P estimates based on thedistribution of Al between Opx2 needles and the hosting Grt2. The signi�antin�uene of di�usion is obvious from the large variation of Al2O3 between oreand rim of Opx2 interstitials. Supported by the Al�Ti systematis in Amp2, aminimum P of 2.3�2.8GPa an be estimated for the hemial equilibration of theintrarystalline mirostruture.The hemistry of the minerals in the interstitial mirostruture suggests thatthe garnetites equilibrated at higher T and higher P onditions of 840±50 °C and4.0±0.2GPa. This regime also represents minimum onditions, if the T suggested bythe Grt�Ol thermometer is reliable. The hemial preservation of very HT reordsof more than 1100 °C is strongly ontrolled by element di�usion rates, rystal sizeand ooling rates.−→Figure 2.4: BSE mirographs of Cpx2 lamellae in Opx2 and vie versa. Top: blebby and thinlamellae of Cpx2 in interstitial Opx2 (garnetite DS0298). Bottom: thin lamellae of Opx2 in theore of a porphyrolasti Cpx2 (Grt-linopyroxenite 99NR6).−→Table 2.2: Composition of seleted mineral pairs in the Pyx2 mirostruture shown on the left.

2.2 Types of Pyx mirostrutures 412.2.2 Pyroxene in pyroxeneMirostrutureCpx and Opx form a disontinuous solid solution series in the system(Ca, Mg)2Si2O6 (Di) and Mg2Si2O6 (En). The misibility gap betweenlow-Ca Di and high-Ca En inreases with dereasing T and is only weakly Pdependent (Lindsley, 1983). In onsequene of ooling from HT, low-Ca Di exsolvesa Ca-poor Pyx (Opx) and high-Ca Opx exsolves a Ca-rih Pyx (Cpx) in form ofrystallographially oriented lamellae after the reation:

M2 [(Si, Al)2O6] HT →M2 [(Si, Al)2O6] LT + (Mg, Fe)2 [Si2O6] LT (2.2)with M = (Mg, Fe, Ca, Al). Pyx lamellae are oriented (sub-)parallel to (100) and(001) of the host Pyx and form at relatively HT broadly spaed broad or blebbySample DS0298 DS0298 99NR6 99NR6Mineral Opx2 Cpx2 Opx2 Cpx2Type host lamellae lamellae hostwt%SiO2 58.60 55.31 56.09 53.86TiO2 0.00 0.06 0.02 0.06Al2O3 0.42 2.86 1.26 2.80FeO 3.30 0.90 7.03 1.96MnO 0.04 0.03 0.08 0.05MgO 37.62 16.35 33.91 16.31CaO 0.16 21.91 0.56 22.03Na2O 0.03 1.63 0.01 1.32Cr2O3 0.08 0.51 0.16 0.50NiO 0.15 0.11 0.07 0.02Total 100.41 99.66 99.19 98.91O base 6 6 6 6Cations per formula unitSi 1.984 1.991 1.959 1.968Ti 0.000 0.002 0.001 0.002Al 0.017 0.121 0.052 0.121Fe2+ 0.094 0.027 0.205 0.060Mn 0.001 0.001 0.002 0.002Mg 1.899 0.877 1.766 0.888Ca 0.006 0.845 0.021 0.862Na 0.002 0.114 0.001 0.093Cr 0.002 0.015 0.004 0.014Ni 0.004 0.003 0.002 0.001Total 4.008 3.996 4.013 4.01020 µmCpx2Opx2

?

400 µm

Cpx2Opx2 Grt2

Cpx2�R

42 2. EXSOLUTION MICROSTRUCTURESshaped lamellae (several tens to several hundreds of µm in width) and at relativelyLT narrowly spaed thin lamellae (less than . 20µm in width), whih may super-impose HT lamellae (Poldervaart and Hess, 1951; Sandiford and Powell, 1986; Ollilaet al., 1988).Crystallographially oriented lamellae of Cpx2 in Opx2 and vie versa o

urin Otrøy garnetite and Grt-linopyroxenite (Fig. 2.4). Similar, better preservedlamellae of Cpx2 in Opx2 have been reported from Grt-orthopyroxenite exposed onOtrøy and Fjørtoft (Carswell, 1973; Bruekner et al., 2002; Van Roermund et al.,2002; Carswell and Van Roermund, 2005). Otrøy garnetite ontains interstitialOpx2 grains, some of them enlose Cpx2 as elongated blebs 50�100µm in width oras thin lamellae

2.3 Determination of rystallographi relationships 432.3 Determination of rystallographi relationships2.3.1 Priniple of EBSDCrystallographi orientations of mineral phases an be determined using a sanningeletron mirosope equipped with an EBSD amera. This tehnique is based onthe physial property that a beam of inident eletrons is sattered elastially whenentering a rystal. These `baksattered' eletrons will subsequently be di�rated,if lattie planes are suitably oriented a

ording to Bragg's Law:n λ = 2d sin θB (2.5)with λ being the wavelength of the inident eletron beam at an angle θB to lattieplanes of spaing d. If λ of the inident eletron beam is known and θB an bemeasured experimentally, then the interplanar spaings in the rystal struture anbe worked out.In a SEM instrumentation, a beam of high energy eletrons is direted at apoint of interest on a tilted rystalline sample (Fig. 2.5(a)). Randomly baksat-tered eletrons beome di�rated and form a set of paired large angle ones orre-sponding to eah di�rating lattie plane. The ars of intersetion of these large radiipaired di�ration ones on the �uoresent sreen are thin paired lines alled `Kikuhibands'. Eah Kikuhi band represents a set of di�rating rystal lattie planes andseveral interseting Kikuhi bands together form the EBSD pattern (Fig. 2.5(b)).Analysis of these EBSD patterns allows the 3D orientation and phase determinationof the rystal at the point of beam inidene.In this setion, the orientation and phase data will be used to derive rystallo-graphi relations between preipitated Pyx2 and the host Grt2.

(a) (b)

1 1 23345Figure 2.5: Kikuhi bands in EBSD patterns. (a) Priniple: The inident eletron beam (1)`baksatters' mainly elastially in the interation volume (2). Subsequent di�ration o

urs ofthose eletrons, whih are inident on lattie planes at angles whih satisfy the Bragg equation (3).These di�rated baksatter eletrons form paired large angle ones (4). Eah pair orresponds toa set of di�rating lattie planes. Kikuhi lines are the intersetions of the ones with the sreen(5). (b) Example: Several Kikuhi bands in an EBSD pattern of Grt2. Indexed intersetions(`stars') represent rystal diretions (zone axes).

44 2. EXSOLUTION MICROSTRUCTURES2.3.2 Samples and resultsThe intrarystalline Pyx2 mirostruture in garnetite DS0297 was hosen for EBSDanalyses (Fig. 2.1(b) and (d)). An XL30 SFEG SEM at Utreht University wasused to ollet EBSD patterns, whih were indexed using the Channel 5 softwarefrom HKL Tehnology, Denmark (http://www.hkltehnology.om). EBSD patternswere olleted on one Grt2 ore and in several enlosed Pyx2 needles. The obtainedrystallographi axes are plotted in Fig. 2.6 . The orientations of axes of di�erentphases are learly related to eah other.

(a) Grt2 (n=6)(b) Opx2 (n=22)

() Cpx2 (n=9)Figure 2.6: Poles of rystallographi planes of (a) host Grt2 and (b)�() Pyx2 needles in oneGrt2 ore of garnetite DS0297, plotted as lower hemisphere equal area projetion. The patternshows a lear rystallographi relationship between the host phase and the preipitates. Dottedlines indiate {111} planes of Grt2.

2.3 Determination of rystallographi relationships 45

Figure 2.7: Hexotahedral rystal form of Prp (light grey, a=11.459Å) showing 4 axes of 〈111〉Grtfrom the rystal entre towards the front, along whih Pyx needles (dark grey) are oriented with[001℄Opx and [1̄02℄Cpx ‖ 〈111〉Grt. The hexagon on the left skethes a six-fold geometry for theorientation of [100℄Pyx and [010℄Pyx around 〈111〉Grt.The pole positions of (001)Opx and {111}Grt are idential. This demonstrates thatthe [001℄Opx axis of eah Opx needle is parallel to one of the four 〈111〉Grt axes. Thepoles of eah of the other two orthogonal major planes in Opx, (100)Opx and (010)Opx,form an equal angular relationship of 60 ° within the {111}Grt planes, representativefor a six-fold symmetry. In addition, the poles of (010)Opx and {110}Grt are idential.This shows that the orientation of eah [010℄Opx axis follows a six-fold symmetrywithin the {110}Grt planes, suh that eah Opx needle an take one of six possibleorientations by stepwize rotation of 60 ° around the [001℄Opx axis within the Grthost rystal. For example, if [001℄Opx is parallel to [11̄1℄Grt, then [010℄Opx is orientedparallel to one of the following diretions in Grt: [110℄, [011℄, [1̄01℄, [1̄1̄0℄, [01̄1̄℄,[101̄℄. The orresponding [100℄Opx axis is then parallel to the Grt axis (in the sameorder): [1̄12℄, [2̄1̄1℄, [121℄, [11̄2̄℄, [211̄℄, [1̄2̄1̄℄.Pole positions of Cpx (100)Cpx and (010)Cpx show the same orientation relation-ship to the rystal struture of the host Grt as Opx. The third orthogonal planediretion within the monolini Cpx struture is (1̄02). This plane is again parallelto {111}Grt. Analogous to Opx, the Cpx needles are oriented parallel to one of thefour 〈111〉Grt axes and an have one of six possible rystallographi orientations bystepwize rotation of 60 ° around the [1̄02℄Cpx axis. It follows that [001℄Cpx also hassix possible orientations with respet to eah of the four 〈111〉Grt axes. The resultsare visualised in Fig. 2.7 and an be summarized as:Opxneedle Grthost Cpxneedle(010) ‖ {110} ‖ (010)(001) ‖ {111} ‖ (1̄02)

46 2. EXSOLUTION MICROSTRUCTURES2.3.3 DisussionCrystallographi orientations of Opx2 and Cpx2 needles both follow a six-fold ge-ometry by rotation around their [001℄Opx and [1̄02℄Cpx axes, whih are parallel toeah of the four 〈111〉Grt axes. This gives 6 × 4 = 24 rystallographi relation-ships between a Pyx2 needle and the host Grt2. If the inverse needle diretions([001̄]Opx and [102̄℄Cpx) are inluded, then the Pyx2 needles and the Grt2 form intotal 2 × 6 × 4 = 48 rystallographi relationships. These are in fat symmetrymultiples of 4 diretions in the Grt2 rystal and 3 diretions of Pyx2 (=12 virtuallydi�erent orientation relationships).The strong rystallographi relationship between the host Grt2 and the enlosedPyx2 needles is onsistent with the exsolution hypothesis, whih is based on em-pirial and experimental studies and theoretial onsiderations (Boudeulle, 1994).The studied Pyx2 needles an therefore be interpreted to be exsolved from a Mj1preursor.The rystallographi relationship between Pyx2 needles and a Grt2 host rystaldetermined in this study is slightly di�erent to the one reported from an earlierstudy on South Afrian kimberlite xenoliths from Sautter et al. (1991). Theseauthors stated that [001℄Cpx is parallel to 〈111〉Grt based on eletron mirosopyobservations in a previous study from Haggerty and Sautter (1990). The latter inturn reported that `. . . the shape and orientation [of Pyx lamellae℄ suggest thatthe pyroxene is due to exsolution along the {111} garnet planes.' In ontrast,the measurements of this study learly show a di�erent relationship with [1̄02℄Cpxparallel to 〈111〉Grt.The oriented intergrowth relationships between Cpx2 and Opx2 preipitated froma Mj1 rystal (this study) are onsistent with results from an earlier study on areverse transformation, in whih Grt and Opx preipitated from a Cpx rystal (anand Rieder, 1983). This forms an additional argument for the exsolution origin ofPyx2 needles in Otrøy Grt2.The orientations of the Pyx2 needles follow the ubi Grt2 symmetry and implyan equal distribution of Pyx2 needles in the Grt2 struture. This is supported byoptial mirosopy, whih suggests that Pyx2 needles are homogeneously distributedin M2 Grt of >5mm in size (Fig. 2.1(a) and (b)). It an therefore be assumedthat any sample surfae through the ore of suh a Grt2 rystal will ontain Pyx2needles in quantities, whih are not biased by a preferred orientation or distribution.Quantitative estimates will therefore be representative.2.4 Quantifying the intrarystalline mirostrutureA major aim in quantifying Pyx exsolution mirostrutures in Grt is to determinethe exess Si in the mineral hemistry of the Mj preursor. Two di�erent ways maylead to this objetive. The diret approah is an integrated hemial analysis of a

2.4 Quantifying the intrarystalline mirostruture 47representative Grt portion ontaining preipitates (wet hemial analysis). Alterna-tively, the indiret approah is a separate hemial analysis of the exsolved phasesand their ratios ombined with a hemial realulation (defoussed mirosopy, im-age analysis, tomography). A diret analysis has the advantage that possible spatialhemial variations within the preipitates and the host phase will be inluded inthe result. This may be important, if not all exess Si in Grt preipitated into thePyx mirostruture. The indiret method ignores non-deteted variations in thephase hemistries, but an easily be applied, is fast and omparably heap.Two methods have been applied to several Grt2 ore areas to quantify exess Si inthe Mj1 preursors: 2D-image analysis in ombination with EMP spot analysis as anindiret method and defoussed integrated mapping with the EMP as a semi-diretmethod.2.4.1 Method 1: Volume estimates using 2D image analysisPrinipleDigital 2D image analysis enables the quanti�ation of surfae elements on pituresde�ned by the element's parameters, like grey value, size, perimeter et. The pro-gram analySIS (Soft Imaging System; http://www.soft-imaging.net) was used toanalyse BSE images taken from ores of Grt2, whih ontain rystallographiallyoriented needles (Fig. 2.8). The needles in the Grt2 ores of the studied samplesonsist of Opx2, Cpx2 and a

essory Prg2. The ratio of the surfaes overed by theneedles and by the host has been analysed based on the ompositional grey saleontrast. Subsequently, a homogeneous pre-exsolved Mj1 omposition was alu-lated based on the phase densities and the assumption that the area perentage is

(a) (b)Figure 2.8: The priniple of 2D image analysis on Grt ore areas ontaining Pyx preipitates. (a)BSE image (180×180 µm) of a Grt2 ore (99NR6-4grt72) showing arbitrary ross-setions of Cpx2needles. (b) Binarised image, based on the grey sale ontrast in (a) and used for the quanti�ationwith the program analySIS (white=Grt2; blak=Cpx2).

48 2. EXSOLUTION MICROSTRUCTURES

Figure 2.9: Binarised BSE image of a Grt2 ore (blak) with Cpx2 preipitates (light grey), whihshows gradually enlarged analytial frames for 2D digital image analysis (sample 99NR6-6Bgrt3).equal to the proportion of volume perentage of the exsolved phases. This requiresa random or non-preferred preipitate distribution in 3D, whih is reasonable as theorientation of the neddles follows equiangular orientations of the ubi rystal stru-ture of Grt (see above). For simpli�ation, molar volumes for Di (66.2 m3/mol), En(62.66 m3/mol) and Prp (113.16 m3/mol) at standard onditions have been usedfor the hemial alulation (Berman, 1988).In a �rst step, Grt2 ore areas of 180×180µm were regarded as large enoughwith respet to the size, distane and distribution of the preipitates at randomlyut surfaes of Grt2. Subsequently, the analytial region of interest was doubledin size to reord the in�uene of the spatial preipitate distribution at the studiedsurfaes (Fig. 2.9).Samples and resultsTwo samples were studied. The Grt-linopyroxenite 99NR6 (Fig. 2.2(b)) is om-posed of porphyrolasti Grt2, minor relit porphyrolasti Cpx2 and rerystallizedmatrix phases, whih inlude Grt3, Cpx3 and a

essory sympletites of Ol4, Ilm4 and±Rt4 (Setion 6.3.2). Ol4 is partly replaed by Srp and Chl. The seond sampleis polyrystalline garnetite DS0297 (Fig. 2.1) omposed of Grt2, Opx2 and ±Ol2.Needle-bearing Grt2 ore areas of several Grt2 grains were hosen for the analysis.Results obtained for eah analytial frame size in eah analysed Grt2 ore area areshown in Fig. 2.10 . The mean Pyx2 onentration represents the average of Pyx2deteted in similar analytial frame sizes in eah rok sample.Fig. 2.10 shows that the onentration of Pyx2 varies onsiderably in eah Grt2grain and in between di�erent Grt2 grains per sample. Small analytial frames of∼0.03mm2 in the pyroxenite and ∼0.1mm2 in the garnetite result in Pyx2 on-entrations, whih vary up to ±50%. This variation dereases to about ±20%towards the largest frame size applied, 0.5mm2 and 2.1mm2 respetively. The vari-ation in the Pyx2 onentration demonstrates that the in�uene of size, spaing

2.4 Quantifying the intrarystalline mirostruture 49

0 0.2 0.4 0.6 0.8 1 1.20

0.5

1

1.5

2

2.5

Analysed area (mm2)

Pyr

oxen

e ex

solu

tion

(vol

.%)

1grt14grt726Bgrt36Bgrt324Bgrt065Bgrt26Bgrt66Bgrt6b2mean

(a) Grt-linopyroxenite 99NR6 0 0.5 1 1.5 200.51

1.5

2

2.5

Analysed area (mm2)

Pyr

oxen

e ex

solu

tion

(vol

.%)

97b−grt197b−grt397b−grt497b−grt597b−grt697b−grt7mean(b) Garnetite DS0297Figure 2.10: Pyx2 ontent at Grt2 ore surfaes quanti�ed by using 2D digital image analysis.(a) Results obtained from 8 di�erent ore areas in Grt2 from Grt-linopyroxenite. (b) Results from6 di�erent Grt2 ores in garnetite. The analytial area of interest at eah seleted Grt2 ore wasgradually expanded, exept for area 6Bgrt6b2. The variation in the deteted Pyx2 onentrationdereases by inreasing the analytial frame size.and distribution of the needles at mirosale is very sensitive to the results ob-tained from relatively small analytial areas and remain signi�ant, if the analytialarea has been inreased by more than a magnitude. The amount of exsolved Pyx2an be estimated from the mean, whih yields about 0.7±0.1 vol.% in Grt2 oresfrom the pyroxenite (99NR6) and about 1.5±0.2 vol.% in ores of Grt2 from thegarnetite (DS0297). The orresponding silion omponents in ations per formularunit (pfu) for the preursor majoriti Grt ores (Mj1) are 3.006±0.001 (99NR6)and 3.014±0.002 (DS0297).Analytial error estimatesThe BSE signal is derived from inident beam eletrons that su�ered large elastide�etions in the sample and re-emerged from the surfae. The fration of theseinidental baksattered eletrons is known as the baksattering oe�ient η andvaries with the atomi number or mean atomi number for ompounds. Therefore,BSE images ontain ompositional information expressed in grey values. They anbe taken with a spatial resolution down to about 0.1µm and are suitable for quali�edand quanti�ed phase analysis.Image resolution and ontrast are the main limiting parameter for deteting andanalysing the modal amount of di�erent mineral phases with 2D image analysis.The image quality an be enhaned using digital image analysing failities, but thefollowing aspets are di�ult to solve with image proessing:Tiny preipitates within the magnitude of the resolution (sub-miron in size).A pixel, whih overs more than one phase, will have intermediate (mixed)grey values. Image proessing (binarization) would add suh tiny preipitates

50 2. EXSOLUTION MICROSTRUCTURESto the host phase (Grt2) and would underestimate the total amount of Pyx2preipitation. This fator might be negligible in the studied samples as themajority of the Pyx2 preipitates is muh larger than the resolution of theimages used.Edge e�ets at phase boundaries. Phase boundaries at high magni�ations mayappear with a ertain width and a grey sale gradient rather than as a sharpline (Fig. 2.11). This makes it di�ult to estimate the true edge of smallpreipitates. As a onsequene, the analytial error will inrease with dereas-ing partile size. In order to quantify this analytial error, the rims of suhsmall partiles were regarded to be �xed in width, 1.1µm. This enables errorestimates to be made depending on size and shape of the partiles (Fig. 2.12).The rim surfae of onentrial partiles an be desribed by the equation:Aerror(conc) = (πr

21)− (π(r1 − r2)2)

= π(2r1r2 − r22)= 6.912r1 − 3.801

(2.6)with r1 = maximal partile radius andr2 = marginal rim of 1.1µmThe rim surfae of elongated partiles is:

Aerror(long) = Aerror(conc) + 2r2(xmax − 2r1)= π(2.2r1 − 1.21) + 2.2xmax − 4.4r1= 2.512r1 + 2.2xmax − 3.801

(2.7)with xmax = maximal partile length.Regarding the middle of the rim (r2/2) as the true grain boundary andr1 − r2/2 as the true partile radius, then estimates of the rim surfae (Aerror)

Grt

CpxOpx

Amp

dust

30 µmFigure 2.11: BSE image showing unsharp ontats between preipitates and the host phase athigh magni�ation.

2.4 Quantifying the intrarystalline mirostruture 51r (

max)

1r (rim)2

r -(r /2)

1

2(a) onentri partile x(max) r (max)

1r (rim)2

r -(r /2)

1

2(b) elongated partile0

50

100

150

200

250

300

350

0 2 4 6 8 10

r (max) (µm)1

A(µ

m)

2

A(max)

A(edge)

r (max) (µm)1

r-(

r/2

) (%

)1

2

0

100

200

300

400

0 2 4 6 8 10

rel . error%() onentri partile errors 010203040502 4 6 8 10010

20

30

40

50

60

70

80

90

100

x(max) (µm)r1(max) (µm)

Rel

ativ

e er

ror

(%)

20

30

40

50

60

70

80

90

100

(d) elongated partile errorsFigure 2.12: Error estimates of partiles with an unsharp edge of 1.1 µm. (a)-(b): Skethes ofidealized partile shapes (dark grey = unsharp rim surfae; light + dark grey = maximum partilesurfae). ()-(d): Error estimates based on equations (2.6) and (2.7).an be expressed relative to the assumed true partile surfae. For onentripartiles, the rim surfae undergoes 25 % (= ±12.5 %) of the assumedtrue partile surfae, if the maximum partile radius r1 exeeds . 9µm(Fig. 2.12()). The proportion between rim surfae and true partile surfaefor elongated partiles dereases with inreasing partile length. Therefore,the error dereases too with ineasing partile length and is for the sameradius (r1=9µm) 20 % (= ±10 %) at xmax=30µm and is 15 % (= ±7.5 %) atxmax=50µm (Fig. 2.12(d)).Although the ut-surfae of Pyx2 needles di�er in shape and size, the analysedpartiles are generally smaller in the pyroxenite than in the garnetite. Maximumerror estimates an be made on the smaller partiles, beause they are more sensitiveto error. The larger Pyx2 partiles in the pyroxenite range in length between 12�15µm (Fig. 2.8), but the majority is smaller in size and not very well elongated.Therefore, a rough analytial error estimate for the pyroxenite might be well±12.5%(relative), orresponding to ±0.088 vol.% (absolute) from the obtained mean valueof 0.7 vol.%. The analytial error is herewith not larger than the statistial variationbetween single analyses estimated from Fig. 2.10(a) to be ±0.1 vol.%. The same isvalid for Pyx2 needles in the garnetite, whih analytial error might be even lessthan 12.5% due to larger partile sizes.

52 2. EXSOLUTION MICROSTRUCTURES2.4.2 Method 2: Chemial integration using defoussed EMPmappingPrinipleAn integrative tehnique was applied to an EMP to analyse the hemistry of Grt2ore areas, whih ontain several exsolved Pyx2 needles. This approah was used toanalyse TiO2 ontents in Ol (Haker et al., 1997). The eletron beam was widened tointegrate a large spot surfae together with its thin underlaying interation volume.Widened beam sizes of 10µm (and 5µm) were onsidered to be adequate to integratea surfae with a beam size appropriate to the width of the exsolution lamellae.Several line sans were performed on a grid with a spaing of 12µm (and 6µm)between eah line and between eah single measurement on a line as illustrated inFig. 2.13 .Eah single measurement represents the omposition of either one phase (Grt2or Pyx2) or a omposite of both phases. The interation volume depth underthe target surfae was estimated using the program `Eletron Flight Simulator'(http://www.2spi.om/atalog/software/efs.html). For a beam at standard ondi-tions (15 kV, 20 nA), the interation depth yields 0.75µm for stainless steel (meanatomi number: 26) and 2.5µm for Gr (atomi number: 6). As Grt2 in the studiedsamples is Prp-rih and may have a mean atomi number of ∼10, an interationvolume depth of . 2µm was estimated.Fig. 2.14 shows an example of an analysed Grt2 ore area after the measurementswith a widened beam (Fig. 2.8 shows the same area before the analysis) and theorresponding onentrations in deteted SiO2 per spot. The distribution of SiO2onentration reprodues the distribution of the Pyx2 preipitates. If all singlemeasurements of a mapped area are integrated, then a Si onentration of morethan 3 pfu (12 O) should be ahieved for a Grt omposition, whih may representthe hemial average of the pre-exsolved preursor (Mj1).The a

uray of EMP measurements is determined primarily by the alibration,but also by other fators like the stability of the beam, air P and T during the time

Figure 2.13: Skethed interation volume in the sample surfae during gridded defoussed EMPanalysis.

2.4 Quantifying the intrarystalline mirostruture 53onsuming analysis. If the tehnial settings are not ideal or if they hange after thealibration, then the statistial satter of pure Grt2 measurements will show a minor,but signi�ant o�set from the expeted mean onentration for Si (Fig. 2.15). Suho�sets will signi�antly over- or underestimate the exess Si omponent for the Mj1omposition during hemial integration. Therefore, the following bias orretionwas applied �rst before the measurements were integrated:All analyses from a mapped region were subdivided into three groups:(A) measurements of pure Grt2(B) measurements of pure Pyx2 and omposite measurements of Grt2 and Pyx2(C) measurements of artefatsThe last group (C) was rejeted. Eah single measurement of group (A) and (B)was realulated to a Grt omposition to display the frequeny of Si in a histogram.Subsequently, eah single Si value from (A) was equalized to 3.000 pfu. Then data(A) and (B) was used to alulate an arithmeti mean, whih was regarded to berepresentative for the Mj1 preursor. A orretion for the data from group (B) wasdisregarded for the following resons: the Si onentrations in the omposite analyses are muh higher than3.000 pfu ompared to an average data shift of ±0.020 pfu (Fig. 2.15) the signi�ane of a minor ompositional shift in a omponent, whih has alear but minor e�et on an arithmeti mean, is muh more minor (the amountof group (B) measurements overs . 2% of the total measurements) no alibration exists for bi-phase targets

(a) 20.95 21 21.05 21.173.773.7573.873.8542

44

46

48

50

52

54

x (mm)y (mm)

SiO

2 (w

t%)

(b)Figure 2.14: Defoussed EMP mapping of Grt2. (a) BSE mirograph after the analysis showinga subset of a Grt2 ore (dark) with Cpx2 preipitates (bright) and the spot positions (irles in thearbon oated surfae). Spot size 10 µm, spaing 12 µm, size 180×180 µm, sample 99NR6-4grt72.(b) Deteted SiO2 onentrations per spot reprodue the distribution of Cpx2 in (a).

54 2. EXSOLUTION MICROSTRUCTURES0

10

20

30

40

502.9

80

2.9

84

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00

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00

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00

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00

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00

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00

( 0.002) Bins ( 0.05)Δ Δ

~ ~~ ~

Fre

qu

en

cy

4grt72n=225

Si=3.010 cpfu

0

10

20

30

40

50

60

Fre

qu

en

cy

pure Grt2measurements

Grt & Pyx2 2measurements

meanexpectedmean

~ ~

6bgrt6b2n=400

Si=3.026 cpfu

2.9

80

2.9

84

2.9

88

2.9

92

2.9

96

3.0

00

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00

3.2

00

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3.4

00

3.5

00

3.6

00

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00

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00

3.9

00

4.0

00

( 0.002) Bins ( 0.05)Δ Δ

0

20

40

60

80

100

120

~ ~~ ~

Fre

qu

en

cy

6Bgrt3n=900

Si=3.014 cpfu

2.9

80

2.9

84

2.9

88

2.9

92

2.9

96

3.0

00

3.0

04

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00

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00

3.5

00

3.6

00

3.7

00

3.8

00

3.9

00

4.0

00

( 0.002) Bins ( 0.05)Δ Δ

0 ~ ~~ ~

10

20

30

40

50

Fre

qu

en

cy

7grtn=240

Si=3.019 cpfu

2.9

80

2.9

84

2.9

88

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92

2.9

96

3.0

00

3.0

04

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00

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00

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00

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00

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00

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00

( 0.002) Bins ( 0.05)Δ ΔFigure 2.15: Frequeny of Si (pfu) determined by defoussed EMP mapping on four Grt2ore areas (eah 180×180 µm, Grt-linopyroxenite 99NR6) displays a bimodal distribution. TheGaussian distribution represents pure Grt2 measurements and shows o�sets to the expeted meanfor Grt of 3.000 pfu. Smaller peaks to the right are omposite analyses of two phases and at theright edge of Pyx2. Numbers refer to the Grt2 ore area, the total amount of measurements perdataset and the obtained arithmeti mean (after bias orretion).Samples and resultsGrid sizes of 180×180µm were on�gured at four Grt2 ore areas from Grt-linopyroxenite 99NR6 after 2D image analysis. Realulated Si ompositions(12 O) for eah measurement are shown in histograms of Fig. 2.15 .The majority of pure Grt2 measurements in eah of the four studied Grt2 oreareas form a Gaussian distribution with an o�set of not more than ±0.020 pfu Sifrom the ideal omposition for Grt. The integrated Si omponents representativefor the Mj1 preursor result from 225�900 single measurements and range betweenthe studied samples with 3.010�3.026 pfu (Table 2.3).Analytial error estimatesX-ray photons emitted randomly from the sample spot will be measured as X-ray intensities via ounting pulses generated in the X-ray detetor of the WDSspetrometer. The number of ounts from one spot reorded in a given time is n.

2.4 Quantifying the intrarystalline mirostruture 55A series N of disrete measurements ni at the same spot would form a Gaussiandistribution around the mean:n̄ =

1

N

N∑

i=1

ni (2.8)with a standard deviation of:σ =

√

√

√

√

1

N

N∑

i=1

(ni − n̄)2 (2.9)and a standard error of:∆E =

σ√N − 1

(2.10)A suitable preision for a single measurement x is±2σ, as 95.5% of all measurementsfrom the Gaussian distribution fall into that range. To obtain a standard error (∆E)of ±1% (relative) with a preision of 2σ (on�dene interval), 4 × 104 ounts needto be olleted.Under the hosen WDS ondition of 15 kV and 20 nA, ounting rates for Si inPrp (standard) are in the order of 350 ounts s−1 nA−1. Measuring for 20 s leadsto a total amount of about 140000 ounts, whih orresponds to a ∆E = ±0.53 %with a preision of 2σ for eah single measurement. Realulated to the Si ontentin Prp with 37wt% SiO2 and 3 pfu Si respetively, a standard error of ±0.20wt%SiO2 and ±0.016 pfu Si an be obtained for eah single measurement x.Further preision re�nement will be ahieved statistially by integrating all sin-gle measurements xi of an analysed grid to a mean omposition x̄ a

ording toequation (2.8). As every xi has a standard error ∆Exi, their arithmeti mean x̄has a propagated standard error ∆X, whih is formulated after the Gaussian errorpropagation as:∆X =

√

√

√

√

N∑

i=1

(δx̄

δxi∆Exi)

2 (2.11)Solving the partial derivation yields:∆X =

1

N

√

√

√

√

N∑

i=1

(∆Exi)2 (2.12)As the relative error of eah xi is equal to ±0.53 %, the mean relative standard errorof the integrated dataset depends only on N :

∆Xrel. =1

N

√

N(0.53 %)2 (2.13)Consequently, the relative standard error of the integrated data sets dereases withan inreasing number of measurements.

56 2. EXSOLUTION MICROSTRUCTURESGrt2 grain N NB x̄Si (pfu) ∆XSi (pfu) ∆XSi,rel. (%)4grt72 225 8 3.010 ±0.006 ±0.197grt 240 9 3.019 ±0.005 ±0.186Bgrt6b2 400 19 3.026 ±0.004 ±0.126Bgrt3 900 20 3.014 ±0.004 ±0.12Table 2.3: Results and error estimates (2σ) of defoussed EMP analysis on four Grt2 ore areasin Grt-linopyroxenite 99NR6.The distribution from the total amount N of all single measurements xi in ananalysed area di�ers from the Gaussian distribution, beause not all xi representpure garnet ompositions. A

ordingly, N and xi are subdividied by the two groups(A) and (B) of measurements:N = NA + NB (2.14)

xi = xi(A) + xi(B) (2.15)As the bigger portion NA of the measurements is adjusted manually to a �xedvalue for normal Grt, only the smaller portion of Si-rih measurements NB on-tributes e�etively to the determination of a supersilii omponent in Grt. There-fore, only NB is used to alulate for the supersilii omponent of eah dataset theabsolute standard error ∆XSi from ∆XSi,rel. and the mean omposition x̄Si.The possible in�uene of some parameters are di�ult to estimate: the in�uene of a defoussed beam on inhomogeneous target ativation the in�uene of phase geometry and phase orientation in a bi-phase target(interation volume) there are no standards and no orretion parameters for bi-phase targets2.4.3 DisussionFour small Grt2 ore areas in linopyroxenite were applied to both methods. Thus,the obtained results enable a diret omparison of the methods a

uray (Fig. 2.16).The determined Si onentrations overlap within error for eah of the four Grt ores.This shows that both methods reprodue statistially indistinguishable onentra-tions of exess Si in the Pyx2 mirostruture after Mj1, although Si estimates appearslightly underestimated by 2D image analysis ompared to defoussed EMP map-ping. The EMP tehnique generates larger error, whih an be redued in two ways:by an inrease of the ounting rates per spot (time, beam intensity) and by the se-letion of a smaller beam diameter (= higher grid density). The latter inreases thenumber of those spots, whih are in�uened by an exsolved phase (NB) and would

2.4 Quantifying the intrarystalline mirostruture 57

Figure 2.16: Comparison of Si determined with both methods at the same Grt2 ore surfaeareas of 180× 180 µm (*120× 120 µm) in sample 99NR6.derease the analytial error more rapidly, if not a denser grid requires more singlemeasurements. It follows that an inrease in preision with the EMP is possible,but time onsuming.The EMP o�set shown in the pure Grt2 measurements is with ≤0.020 pfu Siin the order of the determined supersilii omponent and therefore too signi�antto be disregarded. In addition, the o�set ould be larger than minor irregularitiesof Si onentration in Grt2, whih did not exsolve. This hemial information getslost with the applied orretion proedure, whih is neessary to determine themirostruturally based supersilii omponent.The digital 2D image analysis provides smaller error, whih depends essentiallyon the quality of the images and the shape of the preipitates. Small preipitatesof less than about 10µm in size are more sensitive to error estimates and inreasethe analytial error. Larger preipitates have the opposite e�et and derease errorestimates. The size range of the preipitates has therefore an in�uene on the errors.This e�et has not been worked out in detail, as it is thought to be minor in in�ueneon the �nal result ompared to a muh greater e�et desribed below.The variation in Si onentration determined on di�erent grains in the samesample (Fig. 2.10 and 2.16) shows that miro-sale spatial preipitate distributionand variation signi�antly in�uene the obtained results. The geometri in�uenedereases with an inrease in size of the analysed area as demonstrated by themean. Therefore, small analytial areas suh as 180×180µm are not representativeto quantify the intrarystalline Pyx2 mirostruture, independent of the methodused. A reliable quanti�ation of the mirostruture an be ahieved by a statistialanalysis of large areas. In addition, a statistial approah dereases the error.The amount of Pyx2 needles in garnetite, 1.5±0.2 vol% (this study), is in betweenprevious estimates for Pyx2 needles in nodular Grt2, 1 vol% (determined with image

58 2. EXSOLUTION MICROSTRUCTURESanalysis by Van Roermund and Drury (1998)) and 2.7 vol% (determined with 3Ddefoussed mirosopy on a small area by Van Roermund et al. (2001)). The lattervalue is signi�antly higher ompared to the others, but may be regarded as slightlyoverestimated if the sensitivity of the area size used for the quanti�ation is takeninto a

ount.2.4.4 AppliationThe two exess Si omponents for the preursor of Grt2 obtained from Fig. 2.10 wereregarded to be representative for the two studied samples. These exess Si ontentswere applied to experimental and thermodynamial data sets to estimate the phys-ial onditions, at whih the Mj1 preursors were stable (Fig. 2.17). Experimentaldata on natural ompositions indiate T -dependent on�ning P of ≥4�6GPa forthe garnetite sample. Lower exess Si in the Ca-rih Grt-linopyroxenite yields mi-nor lower P estimates. The thermodynamial data sets (MAS and CMAS) takeompositional variations of the rok types into a

ount and suggest the stability ofmajoriti Grt ores (Mj1) in both di�erent samples at . 1200 °C and . 3.5GPa.These onditions are signi�antly lower than those indiated by the experimentaldata sets. The di�erene between the MAS and the CMAS dataset impressivelydemonstrates the signi�ant in�uene of the omposition, espeially Ca, on the Psensitivity of exess Si dissolved in the Grt struture. As both studied samples on-tain Ca, the MAS dataset may suggest only minimum P estimates. The e�et of Feon the supersiliity of Grt is not overed by the available thermodynami data sets,but is expeted to inrease P estimates, beause Fe is a substantial omponent inthe natural omposition used for the experiments. The disrepany between CMASand the experimental data sets allows in the �rst order only to obtain a P range of∼3�6GPa orresponding to a depth window, through whih the peridotites mighthave passed and the majoriti Grt ores (Mj1) su

essively exsolved their supersilii

omponents.Geothermobarometri estimates on exsolved phases in porphyrolasti Grt2 andrelit porphyrolasti Pyx2 vary tremendously, but indiate minimum T onditionsof 750�800 °C after the formation of the intrarystalline Pyx2 mirostruture in Grt2ores and Pyx2 ores (Fig. 2.1, 2.2 and 2.4). This T regime overlaps with that of theSandian peak elogite-faies rerystallization (Terry et al., 2000b; Carswell et al.,2003a). However, the rerystallized M3 assemblage laks the intrarystalline Pyxmirostruture in both Grt3 and Pyx3 as evident in Grt-linopyroxenite, for example.This suggests that the Sandian rerystallization M3 postdates the porphyrolastiM2, whih in turn had unexsolved preursors M1 that formed at signi�antly higherT than 750�800 °C.A seond hint for a HT origin for the intrarystalline preipitates in Grt2 issuggested by the interrystalline mirostruture, whih bears a reord of a HT equi-libration above 1100 °C. As both mirostrutures predate the relative LT Sandianrerystallization M3, a HT origin for the intrarystalline mirostruture an mostlikely be assumed. As a onsequene, the slope in the experimental and in the

2.4 Quantifying the intrarystalline mirostruture 59

Figure 2.17: P�T diagram with experimentally (Exp.) and thermodynamially (MAS, CMAS)derived data sets, whih illustrate the stability for pre-exsolved Grt2 ores supersaturated in Si(Mj1) as obtained from Grt-linopyroxenite 99NR6 and garnetite DS0297 (shaded). The disrep-any between experimental and thermodynamial data indiates a P�T window, through whihthe peridotites passed (hathed). Two dashed arrows shematially portray two di�erent originsfor the exsolved M2 assemblage in the studied samples: (A) by pre-Sandian ooling at lithospheridepth and (B) by syn-Sandian deompression. Exhumation path of Sandian UHP metamorphiroks (arrow) is from Terry et al. (2000b) and Carswell et al. (2003a). Exp. � experiments afterAkaogi and Akimoto (1977), Canil (1991) and Fei and Bertka (1999), redrawn after Van Roermundet al. (2000a) and Drury et al. (2001); MAS/CMAS � thermodynami system without/with Ca(partly interpolated) after Gasparik (1994, 2000); dry peridotite solidus from Walter (2003). P todepth onversion is from Anderson (1989).CMAS data sets suggests that an alternative mehanism to deompression ouldhave aused the exsolution of intrarystalline Pyx2 in Grt2 ores at SCLM depth:ooling (path A in Fig. 2.17). This is supported by the HT origin of an Otrøy Grt-orthopyroxenite lens interpreted to have rystallized from a melt at 1500�1600 °Cunder formation of M1 (Carswell, 1973), probably assoiated with asthenospheridiapirism (Drury et al., 2001), and to have exsolved M2 at 950�975 °C in the SCLM(Carswell, 1973).If alternatively the origin of the intrarystalline Pyx2 mirostruture in the oresof porphyrolasti Grt2 and porphyrolasti Pyx2 in the studied samples are relatedto the Sandian peak metamorphism, then the Sandian exhumation o

urred fromon�ning P of . 6GPa (path B in Fig. 2.17). A Sandian exsolution origin wassuggested by Bruekner et al. (2002) on the basis of a Sm�Nd age of . 670Mafrom exsolved M2 phases in an Otrøy Grt-orthopyroxenite. However, this age issigni�antly older than the . 410Ma Sandian metamorphi peak.

60 2. EXSOLUTION MICROSTRUCTURES2.5 ConlusionThe Otrøy Grt-peridotite ontains di�erent types of Pyx2 mirostrutures, whihare indiative for HT and HP metamorphi onditions. These mirostrutures arepreserved to di�erent degrees. One of these Pyx2 mirostrutures - the intrarys-talline mirostruture in Grt2 - has a strong rystalligraphi relationship in that theorientations of the Pyx2 needles follow 4×3 symmetry multiples of the host Grt2struture. Pyx2 needles in Grt2 ores are interpreted to be originated by exsolutionfrom Mj1. This mirostruture o

urs in megarysti garnetite and porphyrolastiGrt2, but is absent in elogite-faies rerystallized assemblages.The intrarystalline mirostruture in Grt2 was quanti�ed with two di�erentmethods to determine a homogeneous supersilii Grt preursor omposition: 2Ddigital image analysis and defoussed EMP mapping. Both methods gave overlap-ping results, but the 2D image analysis has a higher reliability due to potentiallysmaller errors and the onsideration of the spatial preipitate distribution.The appliation of experimental and thermodynamial data sets and geother-mobarometrial alibrations dedue minimum T onditions of 750�800 °C and aP window of 3�6GPa for the exsolution of Pyx2 needles in pyropi Grt2. A pre-Caledonian HT exsolution origin for the Pyx2 mirostruture in Grt2 is suspeted,but annot be quanti�ed in terms of T with the used methods.