J. metamorphic Geol., 2007, 25, 37–50 doi:10.1111/j.1525-1314.2006.00677.x

Excess silica in omphacite and the formation of free silica in

H. W. DAY AND S. R. MULCAHY Department of Geology, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA ([email protected])

ABSTRACT Silica lamellae in eclogitic clinopyroxene are widely interpreted as evidence of exsolution during decompression of eclogite. However, mechanisms other than exsolution might produce free silica, and the possible mechanisms depend in part on the nature and definition of excess silica. ÔExcessÕ silica may occur in both stoichiometric and non-stoichiometric . Although the issue has been debated, we show that all common definitions of excess silica in non-stoichiometric clinopyroxene are internally consistent, interchangeable, and therefore equivalent. The excess silica content of pyroxene is easily illustrated in a three-component, condensed composition space and may be plotted directly from a structural formula unit or recalculated end-members. In order to evaluate possible mechanisms for the formation of free silica in eclogite, we examined the net-transfer reactions in model using a Thompson reaction space. We show that there are at least three broad classes of reactions that release free silica in eclogite: (i) vacancy consumption in non-stoichiometric pyroxene; (ii) dissolution of Ti-phases in pyroxene or ; (iii) reactions between accessory phases and either pyroxene or garnet. We suggest that reliable interpretation of the significance of silica lamellae in natural clinopyroxene will require the evaluation not only of silica solubility, but also of solubility, and the possible roles of accessory phases and inclusions on the balance of free silica. Key words: eclogite; excess silica; omphacite; pyroxene; ultrahigh-pressure.

eclogite. Eventually, experimental confirmation and INTRODUCTION calibration of some key reactions will also be re- The origin and interpretation of excess silica in quired. omphacitic pyroxene have been controversial since The goals of this study were to provide an internally Eskola (1921) first reported Ôpseudojadeite moleculeÕ consistent overview and reconciliation of several defi- [(Ca, Mg)(Al, Fe)2Si4O12] in analyses of natural nitions of excess silica and to examine the mechanisms pyroxene from Norwegian eclogites, and Kushiro by which free silica may form in eclogite. We show that (1969) inferred its presence in synthetic clinopyroxene. ÔexcessÕ silica occurs in both stoichiometric and non- Excess silica and alumina associated with vacancies in stoichiometric pyroxene and that all common defini- the structural formula have been recognized in pyrox- tions of excess silica in non-stoichiometric pyroxene ene from high- and ultrahigh-pressure rocks (Williams, are internally consistent, compatible, and therefore 1932; O’Hara & Yoder, 1967; Sobolev et al., 1968; equivalent. We will also show that free silica may form Smith & Cheeney, 1980; Smyth, 1980; Wang et al., in eclogite not only by consumption of vacancies in 1993). Based in part on those observations, oriented pyroxene, but also by dissolution of Ti-bearing min- inclusions of or in clinopyroxene have erals and reactions of garnet and clinopyroxene with been widely interpreted as the result of exsolution of accessory phases. that excess silica from the host during decompression Our considerations are limited to processes that from high or ultrahigh pressure (Liou et al., 1998; might form lamellae or other inclusions of silica Dobrzhinetskaya et al., 2002; Klemd, 2003; Zhang polymorphs in true eclogite, which lacks plagioclase. et al., 2005). However, mechanisms other than exsolu- Free silica formed by the breakdown of plagioclase in tion might also yield free silica as quartz, coesite, or precursor rocks may be present in eclogite, but those , and those mechanisms depend in part on the processes are not considered here. nature and definition of excess silica. Because there has been some recent debate about In order to evaluate the possible mechanisms by how best to express the compositions of pyroxene which free silica might form, a common under- (Katayama et al., 2000; Tsai & Liou, 2000; Klemd, standing is needed of how excess silica may be 2003; Zhang et al., 2003; Page et al., 2005), we begin defined and measured, and a clear view of the spec- by considering the nature of excess silica in natural and trum of reactions by which silica might be released in synthetic pyroxene.

2007 Blackwell Publishing Ltd 37 38 H. W. DAY & S. R. MULCAHY

PYROXENE COMPOSITION SPACE Table 1. Formula units of end-members and components.

The essential features of excess silica in omphacite can Name Abbrev. Formula be illustrated in the simplified system CaO-MgO- Al O -SiO (CMAS, Fig. 1). Although omphacite also Anorthite An CaAl2Si2O8 2 3 2 Ca Eskola pyroxene CaEs Ca0.5[]0.5AlSi2O6 contains other major elements such as and Ca Tschermak pyroxene CaTs CaAl2SiO6 , the substitutions of these elements can be Corundum Crn Al2O3 Di CaMgSi2O6 described with exchange operators that have no effect Enstatite En Mg Si O 2+ 3+ 2 2 6 on silica content (e.g. Fe Mg)1,Fe Al)1, NaAlCa)1 Fo Mg2SiO4 Geikielite Gk MgTiO3 Mg)1; Thompson, 1982). Consequently, it is conveni- Grossular Grs Ca3Al2Si3O12 ent to consider model pyroxene compositions that can Jd NaAlSi2O6 be described with only four independent components, Ky Al2SiO5 and, for the purpose of understanding the silica bal- Mg Eskola pyroxene MgEs Mg0.5[]0.5AlSi2O6 Mg Tschermak pyroxene MgTs MgAl2SiO6 ance, it is not necessary to treat directly important end- Na-pyroxene NaPx NaMg 0.5Si 0.5Si2O6 members such as jadeite. Prp Mg3Al2Si3O12 Quartz Qtz SiO2 Excess silica in pyroxene is closely linked to non- 3Qtz Si3O6 quadrilateral components such as . Rt TiO2 clinopyroxene accommodates aluminium by a coupled Spl MgAl2O4 Wollastonite Wo Ca2Si2O6 substitution, AlAlMg)1Si)1, yielding the calcium Exchange components Jadeite exchange jd NaAlCa) Mg) Tschermak component (CaAl2SiO6, CaTs; Table 1) 1 1 (Tschermak, 1871; Doelter, 1883) or by a vacancy Mg-Ca exchange mc MgCa)1 Tschermak exchange tk Al2Mg)1Si)1 substitution mechanism leading to calcium Eskola Ti-Si exchange ts TiSi)1 Vacancy-Si exchange vs [ ]SiCa)1Mg)1 component (Ca0.5AlSi2O6, CaEs; Table 1) (Eskola, 1921). Aluminous clinopyroxene was synthesized in early experiments (Zvetkov, 1945; Segnit, 1953; Clark In CMAS, stoichiometric pyroxene compositions et al., 1962), and Hays (1966, 1967) demonstrated that lie in the En-Wo-Crn plane and contain four cations pure CaAl SiO has a stability field above 1.2 GPa. 2 6 per six . Non-stoichiometric compositions with Up to 20–30 mol.% of CaEs can be accommodated in cation vacancies lie in the volume above that plane and Di-CaTs pyroxene (Wood & Henderson, 1978; Wood, necessarily contain more silica than stoichiometric 1979) but the pure compound apparently has no sta- pyroxene (Fig. 1). Consequently, four independent bility field. components are required in order to describe the observed range of pyroxene compositions. Excess silica in pyroxene compositions has commonly been ex- SiO , Qtz pressed by using either CaEs or Qtz (Fig. 1) as a fourth 2 component (e.g. Khanukhova et al., 1976a,b; Gayk et al., 1995; Tsai & Liou, 2000). In CMAS, the fourth component can conveniently be chosen to be Ky, Qtz, CaEs, MgEs, or even Fo or Spl (Fig. 1), but the sign of the fourth component and the calculated mole frac- CaEs Wo tions of the remaining three components depend on MgEs that choice. Di An Grs En Regardless of the choice of components, any trans- CaO formation of the coordinate system from the oxides to Prp a structural formula or end-members must contain Ky CaTs Fo exactly equivalent information and the same number MgTs of independent components. Consequently, there is a direct relationship between structural formulae and any set of end-member components. Figure 2a,b shows a new way to view the direct relationship between two commonly chosen end- MgO member coordinate systems and the structural formula of clinopyroxene, which is used to clarify ambiguity Spl about the definitions of excess silica. For purposes of illustration, it was assumed that clinopyroxene can be Al O , Crn 2 3 described in a degenerate three-component system, and all components, including silica, are written as six- Fig. 1. Compositions in the system CaO-MgO-Al2O3-SiO2 (CMAS). All formula units and abbreviations are listed in oxygen formula units. It is convenient to use 3Qtz as a Table 1. The joins Di-CaTs, Prp-Grs, and MgTs-CaTs lie in the component because, as discussed below, isopleths of Si plane En-Wo-Crn. per formula unit (pfu) are parallel and the mole

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contain two Si per six oxygen anions. Note that (a) pyroxene below this join contains only IVSi whereas those above must also have some VISi. Contours of total cation content (R ¼ total cations 3Qtz Si = 3.0 = 3 per six oxygen) are parallel to the Di-CaTs join in each Ca = 0 coordinate system. Compositions above the Di-CaTs Si = 2.5 join have fewer than four cations, corresponding to vacancies in the structure. Although vacancies cannot Si = 2.0 = 3.5 CaEs be assigned to a particular site without additional Ca = 0.5 assumptions, the contours of total cations are unique Si = 1.5 and a useful measure of deviation from stoichiometry. Si=Ocat An Compositions below the Di-CaTs join have more than Si=Mcat Si = 1 four cations per six-oxygen formula unit, indicating = 4 NaPx– jd Di CaTs Ca = 1 interstitial cations, anion vacancies or analytical error. Grt join Compositions above the Di-CaEs join contain more M M M M 1 g g g 2 g than can be accommodated in the tetrahedral – 0 ======0 1 l 1 l 1 l 0 l sites and must have M-site silicon. The intersection of .5 A A .5 A A the Si ¼ 2.5 contour with the Di-CaTs join at negative CaTs content (Fig. 2) corresponds to a composition with no vacancies and 0.5M-site Si (CaMg1.5Al)1- Si = 2.5 3Qtz Si2.5O6). Although this composition cannot be phys- ically attained in the CMAS system, it is directly (b) related to the sodium pyroxene (NaPx, NaMg0.5Si0.5- Si O ) described by Angel et al. (1988) by the jadeite = 2.0 2 6¢ Si exchange vector: Ca = 0.5 CaEs = 3.5 CaMg1:5Al1Si2:5O6 ¼ NaMg0:5Si0:5Si2O6

NaAlCa1Mg1: Si = 1.5 Consequently, stoichiometric sodium pyroxene with Si=Ocat An octahedral silica can be illustrated in the sodium-free plane by condensing their compositions along the Si=Mcat jadeite exchange vector (Thompson, 1982). = 1.0 Si The simplicity of the coordinate systems illustrated Ca = 1.0 NaPx– jd Di Grt join CaTs in Figs 1 and 2 shows that the composition of clino- = 4.0 pyroxene can be expressed with equal rigour by using

M M M M the structural formula or by choosing Qtz (Fig. 1), Al = –1 g Al = 0g Al = 1g Al = 2 g = 5 = = 5 = 3Qtz (Fig. 2a) or CaEs (Fig. 2b) as a component in 1 1 0 0 . . addition to Di and CaTs. The essential identity of these choices is illustrated in part by the fact that Fig. 2b is Fig. 2. Two coordinate systems for pyroxene compositions in entirely contained within Fig. 2a. Because pure CaEs CMAS. (a) Di-CaTs-3Qtz. (b) Di-CaTs-CaEs; abbreviations in contains 3.5 total cations (R ¼ 3.5), and the mole Table 1. Dashed lines are contours of constant cation content and ÔRÕ is total cations (per six-oxygen formula unit). The point fractions X3Qtz and XQtz, in CaEs, are 0.5 and 0.75, labelled ÔGrt joinÕ marks the piercing point of the Prp-Grs join respectively, it follows that in clinopyroxene: (Fig. 1). ÔOcatÕ is the sum of all cations excluding Si. ÔMcatÕ is the sum of M-site cations, excluding Si. The Si ¼ Ocat line intersects 2XQtz XCaEs ð4:0 RÞ¼X3Qtz ¼ ¼ : the CaTs-3Qtz and CaTs-CaEs joins at XCaTs ¼ 0.6 and 0.2 3 2 respectively. The Si ¼ Mcat line intersects these joins at XCaTs ¼ 0.66 and 0.33 respectively. See text for further discus- One of these coordinate systems may be more con- sion. venient or illuminating in a particular circumstance, but they are completely interchangeable, and therefore equivalent. We suggest that using the graphical fraction of 3Qtz is numerically equal to the calculated approach adopted in Fig. 2 simplifies considerations of cationic deficiency. The component 3Qtz (Si3O6)is Ôexcess silicaÕ and removes ambiguity about its defini- identical to the component ÔsupersilipyxÕ defined by tion. Smith (2006). In each of the coordinate systems, isopleths of constant Ca, Mg, Al and Si are parallel to lines of zero content of each cation. For example, Excess silica in pyroxene isopleths of Si (pfu) are parallel to the Di-CaEs join in There are at least five possible definitions of excess sil- both coordinate systems because both end-members ica in stoichiometric and non-stoichiometric pyroxene,

2007 Blackwell Publishing Ltd 40 H. W. DAY & S. R. MULCAHY which are conveniently summarized in the model com- because Si > Mcat (2.5Si > 1.5Mcat) or Si > Ocat position space (Fig. 2). Most studies of non-stoichio- (2.5Si > 1.5 Ocat). metric pyroxene have implicitly or explicitly defined Both stoichiometric and non-stoichiometric pyrox- excess silica as a deviation from the stoichiometric Di- ene may contain Ôexcess silicaÕ. The various measures of CaTs join, and have expressed the excess either as a excess silica in non-stoichiometric pyroxene are closely CaEs or Qtz component (e.g. Kushiro, 1969; Bell & related and internally consistent, but lead to different Mao, 1971; Wood & Henderson, 1978; Gayk et al., numerical scales of excess silica content. As shown 1995). below, both ÔstoichiometricÕ and Ônon-stoichiometricÕ Smith & Cheeney (1980) proposed that natural, non- excess silica can be anticipated in natural and synthetic stoichiometric pyroxene has excess silica if (Si + pyroxene. Ti ) 2Na) > (Ca + Mg + Fe + Ni + Mn) pfu, and there has been some confusion about the appro- priate application of this criterion (Zhang et al., 2002; Natural and synthetic pyroxene compositions Klemd, 2003). However, their criterion is directly Figure 3 shows natural and synthetic pyroxene com- related to the commonly used definitions of excess positions in a portion of Robinson’s (1980) Ôcondensed silica. The basis of their formulation lies in the alge- oxideÕ space that has the same geometry as Di-CaTs- braic transformation of coordinates from a cation 3Qtz (Fig. 2) and is also similar to a portion of the reference frame to calculated end-member formula SAND diagram used by Smith (2006). The choice of units (Greenwood, 1975; Spear et al., 1982; Appendix, end-members and derivation of the plotting coordi- Table A1). For example, in the four-component sys- nates (Fig. 3) are summarized in detail in the Appendix tem Di-Jd-CaTs-SiO2, with pyroxene end-members (Table A2). The recalculated analyses are summarized written as six-oxygen formula units, SiO2 is given by: in Tables A3 & A4.

SiO2 ¼ Si-Ca-Mg-2Na. Consequently, XSiO2 ranges Briefly, the end-member components chosen have from zero, on the Di-Jd-CaTs plane, to one, at pure 1 Si (ROR2O3SiO2), 2 Si (2RO2SiO2) or 3 Si pfu SiO2. If pyroxene contains ÔexcessÕ silica, then by defi- (Si3O6), such that each end-member component cor- nition SiO2 > 0, and Si-2Na > Ca + Mg, which is responds to a different independently variable cation. directly analogous to the Smith and Cheeney criterion. Two end-members with one Si pfu are condensed as Alternatively, if the formula unit for silica is Si3O6 the ÔTsÕ component in Fig. 3 [CaTs (for Al) and (Fig. 2a), Si3O6 ¼ 1/3(Si-Ca-Mg-2Na). Either formu- Ca(Mg0.5Ti0.5)SiAlO6 (for Ti)], whereas the ÔPxÕ com- lation measures the deviation of a composition from ponent is the sum of nine end-members with 2 Si pfu the Di-Jd-CaTs plane in terms of excess, pure silica and [diopside (Ca), hedenbergite (Fe2+), enstatite (Mg), is, therefore, equivalent to using Qtz as a component. johannsenite (Mn), Ni-pyroxene (Ni), kosmochlor An expanded derivation of the Smith and Cheeney (Cr), jadeite (Na), aegirine (Fe3+), and K-pyroxene criterion is given in the Appendix. (K)]. The only end-member containing three Si or Stoichiometric pyroxene also may be considered to vacancies is Ô3QtzÕ. As in Fig. 2, contours of total contain Ôexcess silicaÕ if Si > 2 and M-sites contain cations are parallel to the base of the diagram, repre- silicon. Octahedral coordination of silica is favoured at senting stoichiometric pyroxene, and contours of Si pressures on the order of 10.0 GPa (Gasparik, 1989). pfu are parallel to the Px-CaEs join. The orientations Angel et al. (1988) determined the of a of other isopleths of cation content are not preserved synthetic sodium pyroxene (NaPx) having the com- in the condensed oxide space. Although we have not position Na(Mg0.5Si0.5)Si2O6 and confirmed that the considered many elements that occur in pyroxene, excess silica is accommodated in the octahedral, M1 most common analyses can be plotted in this diagram site. Although sodium pyroxene is supersilicic, because directly from a structural formula or indirectly from it has Si > 2, it does not satisfy the most commonly recalculated end-member components. used definitions of Ôexcess silicaÕ because it is also sto- End-members were chosen for convenience, subject ichiometric and coplanar with Di-Jd-CaTs (Fig. 2). only to the constraints that: (i) all end-members were Khanukhova et al. (1976a) suggested a definition of calculated with six oxygen and contain at least one excess silica that can be applied equally well to non- silicon; (ii) the end-members be independent and suf- stoichiometric and stoichiometric pyroxene. They ficient to span the compositions considered; (iii) only considered that Ôexcess silicaÕ is present if the number one end-member contains vacancies (3Qtz). Under of silicon cations pfu is greater than the sum of M-site these conditions, a different choice of end-members, cations excluding Si (Si:Mcat > 1:1; Fig. 2). Unfor- especially for Ti and Fe3+, may change the Ts/Px tunately, the content of the M-sites remains ambiguous ratio, but the proportion of 3Qtz remains constant, because of the need to make assumptions about the and does not affect conclusions about excess silica. distribution of vacancies between M and T sites, as The reported compositions of natural omphacite and discussed above. A definition of Ôexcess silicaÕ that jadeite are summarized in the Appendix (Table A3) requires silicon to exceed the sum of all other cations and illustrated in Fig. 3a. Pyroxene compositions that (Si:Ocat > 1:1; Fig. 2) would be more robust. End- have been ÔreconstructedÕ by reintegration of silica member NaPx satisfies both definitions of excess silica lamellae are not illustrated. The data show excess silica

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3Qtz = 3.0

(a) Natural Pyroxene All Fe as Fe3+ Fe as reported

Si = 2.5

Fig. 3. Natural and synthetic pyroxene = 3.5 CaEs compositions in condensed oxide space. (a) Natural pyroxene. Filled circles: analyses Si = 2.0 with Fe as reported; open circles: all Fe calculated as Fe2O3. W&S indicates the sample reported by Wang & Sueno (1996). An D indicates two of the samples summarized D Si = 1.5 by Deer et al. (1978) (b) Pyroxene compo- D sitions synthesized in NCMAS. Open W&S squares: Gasparik (1984a,b, 1985a,b, 1989, = 4.0 1996). Closed squares: All others (Kushiro, NaPx Grt Ts 1969; Bell & Mao, 1971; Khanukhova Px et al., 1976a,b, 1977; Wood & Henderson, 3Qtz 3Qtz 1978; Wood, 1979). B&M: Bell & Mao, Si = 2.5 1971. K: Khanukhova et al., 1976b). Con- (b) Synthetic Pyroxene tours of Si and R as in Fig. 2. Contours of Gasparik Ca, Mg and Al are no longer possible be- all others = 3.5 CaEs cause of the projection. Uncertainties (±2r) for standard microprobe analyses Si = 2.0 are probably about one or two times the K size of the symbols. The plotting coordi- B&M nates in terms of cations per six oxygen An are: 3Qtz ¼ 0.33(Si + Ti-Fe2+-Mn-Ni-Mg- Ca) ) 0.67(Na + K); Ts ¼ Si = 1.5 Ti + 0.5(Al + Cr + Fe3+-Na-K); 3+ Px ¼ )Ti ) 0.25(Al + Cr + Fe ) + 0.5 = 4.0 (Fe2+ + Mn + Ni + Mg + Ca) +1.25(Na + K) (Table A2). NaPx Px Grt Ts up to about 11 mol.% 3Qtz (22% CaEs component) Bakun-Czubarow, 1992). Second, the calculation of and contain up to 27% of Ts components (or more if all some iron as Fe3+ is sufficient to remove most of the iron is calculated as Fe3+). Synthetic pyroxene com- negative Ts and 3Qtz components (Fig. 3a). This positions span the entire stoichiometric pyroxene join behaviour is required because calculation of Fe3+ has from NaPx to Ts (Fig. 3b). Similar to the natural data, the effect of reducing the number of total cations, thus the synthetic compositions occupy the region between increasing the amount of 3Qtz. In our calculation the Px-Ts and Px-CaEs joins and extend beyond them scheme, Fe3+ is calculated as aegirine and combined in both directions. In contrast to the natural data, with Na in the Px component, thus releasing Al from however, synthetic pyroxene contains up to 28% 3Qtz jadeite to form additional Ts component. (56% CaEs; Bell & Mao, 1971) indicating excess silica The effects of analytical uncertainty are difficult to in the octahedral site up to 2.1 Si pfu. evaluate carefully because few authors have presented The synthetic compositions are iron-free, and the discussions of uncertainty that are adequate for the small scatter below the stoichiometric join may give a task. Microprobe analyses of homogeneous, coarse- reasonable indication of uncertainties resulting from grained natural samples may lead to uncertainties in R analytical error. However, the natural compositions and Si that are quite modest (±0.007 and ±0.01, 2r, include many analyses in which iron was reported as respectively). This estimate is based on the propagated FeO, as well as some that reported both FeO and uncertainties in the analysis of a standard , as Fe2O3. The natural pyroxene ranges to )11% 3Qtz and described by Giaramita & Day (1990), (Table 2). to )13% Ts components. Although negative Ts might Wood (1979) reported the standard deviations of correspond to the NaPx component in the pyroxene, multiple analyses for synthetic pyroxene, analysed and negative 3Qtz corresponds to excess cations, two using an electron microscope microanalyser. The pro- lines of evidence suggest that the negative values are pagated uncertainties of R and Si in a typical analysis primarily the result of unanalysed ferric iron. First, are larger than conventional microprobe analyses most of the pyroxene for which ferric iron was repor- (±0.07 and ±0.09, 2r respectively; sample C164, ted contains only positive Ts or 3Qtz (Table A3, Table 3; Wood, 1979). Taken together, these results Eskola, 1921; Sobolev et al., 1968; Deer et al., 1978; suggest that the small scatter of synthetic compositions

2007 Blackwell Publishing Ltd 42 H. W. DAY & S. R. MULCAHY

Table 2. Mass balances in CMAS. All reactions were calculated skeptically. However, Wang & Sueno (1996) reported using program REACTION (Finger & Burt, 1972). an inclusion in diamond with a composition approxi-

REACTION Phase components mately NaPx16En84, which requires Si > 2 (W&S, Fig. 3a). On the basis of experimental results (Gas- Di Prp Qtz Ky mc tk vs parik, 1989), they predicted that this pyroxene com- R1 )10 3 000)1 position should have a garnet structure. Wang & R2 ¼ )R3)2R9 0 1 4 )4030Gasparik (2000) described unpublished data that show R3 2 )100210 R4 ¼ )R1+R9 0 0 )52)1 )21that the inclusion does indeed have the garnet structure R5 ¼ 4R1+5R3+6R9 0 )5 0 12 4 )7 )4 and must have been derived from pressures greater R6 ¼ )2R1)R3 0 1 )60)2 )12than 16.5 GPa. The recognition of such garnet inclu- R7 ¼ 3R1+2R3+R9 0 )27230)3 R8 ¼ )2R1)3R9 5 0 0 )6362sions suggests that appropriate compositions exist in R9 )10)22)1 )20the mantle to stabilize NaPx as a component in R10 ¼ 2R1+6R3+3R9 7 )60690)2 pyroxene at slightly lower pressures, below the R11 ¼ 4R1+3R3+6R9 )4 )3 0 12 0 )9 )4 R12 ¼ )2R3)R9 )32 2)2 )300pyroxene–garnet transition. Thus, it should be antici- All reactions in the R1–R3 plane conserve Ky pated that stoichiometric, supersilicic pyroxene might R6 ¼ )2R1)R3 0 1 )60)2 )12 All reactions in the R1–R9 plane conserve Prp be recovered from the mantle. R4 ¼ )R1+R9 0 0 )52)1 )21 The data demonstrate that two distinct kinds of R8 ¼ )2R1)3R9 5 0 0 )6362ÔexcessÕ silica may be anticipated in both nature and All reactions in the R3–R9 plane conserve vs R2 ¼ )R3)2R9 0 1 4 )4030experiments. Stoichiometric pyroxene may be consid- R12 ¼ )2R3)R9 )32 2)2 )300ered to contain ÔexcessÕ silica if Si > 2 whereas non- All reactions in the R3–R8 plane conserve Qtz stoichiometric pyroxene containing vacancies may R5 ¼ 5R3–2R8 0 )5 0 12 4 )7 )4 R10 ¼ 6R3–R8 7 )60690)2 have Si < 2, but requires compositions that lie on the R11 ¼ 3R3–2R8 )4 )3 0 12 0 )9 )4 silica-rich side of the stoichiometric pyroxene join All reactions in the R2–R4 plane conserve Di R5 ¼ )5R2)4R4 0 )5 0 12 4 )7 )4 (Figs 1–3). In the following section, we explore the R6 ¼ R2+2R4 0 1 )60)2 )12mechanisms by which free silica may be formed in R7 ¼ )2R2)3R4 0 )27230)3 eclogite and whether these two kinds of excess Si lead to different mechanisms. The approach begins by examining the set of all possible reactions in model Table 3. Qtz-forming reactions in CMAST. Labels in paren- eclogite compositions using a Thompson reaction theses indicate reactions in Tables 2 and A6. space (Thompson, 1982). It is shown that free silica can be formed not only by the consumption of vacancies in Reactions that conserve both vs and ts components 4Ky ¼ 4Qtz + Prp + 3tk (R2) non-stoichiometric pyroxene, but also by reaction with 2Ky ¼ 2Qtz + Di + mc +2tk ()R9) accessory phases and by dissolving or rutile in 3Di + 2Ky + 3mc ¼ 2Qtz + 2Prp (R12) pyroxene or garnet. Di + 2Rt + mc ¼ 2Qtz + 2Gk (GR4) Ky + Rt ¼ 2Qtz + Gk + tk ()GR6) Prp + Rt ¼ 4Qtz+ 4Gk + tk ()GR9) Prp + 3Rt ¼ 2Qtz + Ky + 3Gk ()GR10) A REACTION SPACE FOR ECLOGITE Reactions that conserve vs component and control ts content Rt ¼ Qtz + ts (Rt1) The analysis of all possible reactions is begun by Ky + ts ¼ Qtz + Gk + tk (G3) constructing a reaction space based on common phases Ky + 3Gk ¼ Qtz + Prp + 3ts (G4) Reactions that control vs content in the system CaO-MgO-Al2O3-SiO2 (CMAS). The Di + vs ¼ 3Qtz (R1) major phases in eclogite are clinopyroxene (Cpx) and 2Ky + vs ¼ 5Qtz + mc +2tk (R4) garnet (Grt). Common accessory phases in a model Prp + 2vs ¼ 6Qtz + 2mc + tk (R6) 2Prp + 3vs ¼ 7Qtz + 2Ky + 3mc (R7) eclogite might include a silica polymorph, summarized 2Gk + vs ¼ Qtz + 2Rt + mc (GR2) as quartz, and an aluminium silicate polymorph, Gk + vs ¼ 3Qtz + mc +2ts ()G5) assumed to be kyanite. For the purpose of balancing reactions, SiO2 is used, rather than Si3O6, as the for- mula unit for Qtz because reaction coefficients are below the Px-Ts join and above the Px-Es join reflects simpler. We then examine the effects of additional analytical uncertainties. However, some sodic and components and phases, and expand the reaction space calcic pyroxene compositions probably represent stoi- to include Ti-bearing accessory minerals. chiometric and non-stoichiometric phases with Si > 2 (Fig. 3b, Bell & Mao, 1971; Khanukhova et al., 1976b; Gasparik, 1989). Derivation in CMAS Natural pyroxene shows little evidence for excess A model eclogite in CMAS (Fig. 1) requires four silica in the octahedral site (Si > 2), outside the independent system components. If four or fewer uncertainty because of analytical error or unanalysed phases are present (e.g. clinopyroxene, garnet, kyanite, ferric iron. Only two jadeite analyses (D, Fig. 3a; Deer and quartz or coesite), and polymorphic transitions are et al., 1978, table 49, nos 6 & 9; Table A3) contain Si ignored, most reactions are continuous and have two significantly greater than two, and should be viewed or more degrees of freedom in the phase rule. In order

2007 Blackwell Publishing Ltd FREE SILICA IN ECLOGITE 43 to describe the continuous reactions, it is useful to Burt, 1972; see Andrew & Linde, 1980, for a cau- choose independently variable phase components suf- tionary note). Three useful mass balances, R1, R3, and ficient to describe the possible variations of the modes R9, were chosen as basis vectors of a reaction space and compositions of the phases (Thompson, 1982). (Fig. 4a): Typically, one chooses a single end-member as the additive component for each phase, which monitors Di þ vs ¼ 3Qtz ðR1Þ the abundance of the phase, and a number of exchange components, which describe variations of phase com- Prp ¼ 2Di þ 2mc þ tk ðR3Þ position but have no effect on phase abundances (Thompson, 1982). Table 1 lists the formula units of Di þ 2Qtz þ mc þ 2tk ¼ 2Ky: ðR9Þ end-members, additive components and exchange components that will be considered here. Because it is Simple inspection shows that the three mass balances important to distinguish between mineral phases and are independent because each contains a unique phase phase components, abbreviations are used for phase component. The exchange component vs appears only components and full names for mineral phases. in R1, and the additive components Prp and Ky The possible modal and compositional variations of appear only in R3 and R9, respectively. The three mass eclogite phases in CMAS can be described with seven balances also are sufficient to span the reaction space independently variable phase components (Di, Prp, because all other mass balances can be formed as linear Ky, Qtz, mc, tk, vs, Table 1). It was assumed that silica combinations of the three basis vectors, as shown in and aluminium silicate polymorphs have constant Table 2. compositions and need only additive components, Qtz The exchange components have not been assigned to and Ky, but both clinopyroxene and garnet display phases, and it is not necessary to do so in order to extensive solid solution (Fig. 1). The Di end-member evaluate all possible net-transfer reactions. Although was chosen as the additive component for clinopy- vs is best known in pyroxene, the tk and mc exchanges roxene, but any end-member pyroxene could have been are important in both pyroxene and garnet (e.g. used. All variations of stoichiometric clinopyroxene Thompson, 1982). Identification of the exchange towards end-member enstatite, wollastonite, or cal- capacities with particular phases greatly increases the cium Tschermak pyroxene can be described by linear number of possible reactions, but does not change the combinations of the additive component, Di, and two essential nature of the net transfers involved. For exchange components, tk and mc (Table 1). All non- example, if the generalized tk and mc components are stoichiometric clinopyroxene compositions above the identified with garnet and clinopyroxene (tkGrt, tkCpx, En-Wo-CaTs-MgTs join (Fig. 1) can be described mcGrt, mcCpx), the number of calculated net-transfer using the additional vacancy-silicon exchange compo- reactions expands from 12 (Table 2) to 35. The new net nent, vs (e.g. CaEs ¼ Di + 0.5tk + 0.5vs). The Prp transfers are all related to one or more companion end-member was chosen as the additive component for reactions by two exchange reactions (tkGrt ¼ tkCpx, garnet, and variations of composition towards gros- mcGrt ¼ mcCpx). The exchange reactions control the sular and garnet may be described using the phase in which the exchange capacity is located (i.e. the mc and tk exchanges. For this study, it was assumed composition of the phases), but have no effect on that vs component is nil in garnet (but see W&S; the abundance of phases participating in the net Fig. 3a and Smith, 2006). These seven additive and transfers. Consequently, no new information about the exchange components are sufficient to monitor pro- nature of the net-transfer reactions is gained by gress on all possible net-transfer and exchange reac- assigning exchange capacity to specific phases. tions in model eclogites in CMAS. Inspection of Fig. 1 shows that no more than four independent components are required in order to des- Properties of the CMAS reaction space cribe the four phases clinopyroxene, garnet, kyanite The three basis vectors define a three-dimensional and quartz. Singular value decomposition of the com- reaction space (Fig. 4a) and monitor different aspects position matrix (Fisher, 1989; Appendix, Table A5) of eclogite mineralogy. Positive progress on the basis confirms that four independent system components are vectors is defined as progress to the right as written necessary and sufficient to describe the seven phase above, and is illustrated by the arrows (Fig. 4a). components, and that three independent mass balances Reaction R1 is the only basis vector that contains the (or reactions) are necessary and sufficient to describe exchange component vs, so it is a useful monitor of the all mass balances among the phase components. vacancy content of clinopyroxene. Reaction R3 Although the results of singular value decomposi- involves only the major phases garnet and clinopy- tion provide one possible choice of three independent roxene. It is the only reaction that involves no acces- reactions (Table A5), it proved more convenient to sory phase, such as quartz or kyanite (Table 2). choose three reactions from the set of all possible Because mc and tk exchange capacity are found only in balanced reactions among phase components calcula- clinopyroxene and garnet, R3 monitors the pyroxene ted using the program REACTION (Table 2) (Finger & to garnet transition and the changing compositions of

2007 Blackwell Publishing Ltd 44 H. W. DAY & S. R. MULCAHY

R3 R3 (a) [Ky, Qtz, vs] (b) [Ky]

[vs]

tk

+ +

p

tk

mc

r

P

+ +

p

mc mc

r P [Ky, Prp] 2 + 2Di R1 vs + 5Di + 3 2 + 2Di Di [Qtz] tz mc + 6 3Q R8 tk + 2vs 6Ky Di + 2Qtz + mc+2tk [Prp] Di + 2Qtz + tk 2Ky R9 Qtz+ Qtz – y 2Ky mc Prp + 4Qtz4K + 3 +2 mc tk [Di, mc]

R2 [Prp,vs] 2Prp + 2Qtz R9 Di + 2Ky + 3 3 [tk] [Qtz] R12 (c) R3 (d) R3 R10 R5 [Qtz] [vs] [tk] [Di] [Ky] [Qtz] c

k c

t m m + tk + vs 9 s 4 +

v R11 + 4 + c mc y [mc]

p y +

p

m r r K s K k v

2 t 2

P P 4 6 7 1 + + 6Prp+2

+ + k

i t 9

i rp D

2Di + 2 + 2Di + D P 2 5 rp y 7 P 3 2K Fig. 4. Reaction space for eclogite in i + 1 4D CMAS. All reactions among phase compo- Di + vs 5Di + 3mc + 6tk + 2vs nents are positive as written in Table 2. Basis [mc, tk] [Prp] [Prp] vs 3Qtz R1 R8 6Ky vectors are shown as heavy arrows with + 2 tk rp + P mc arbitrary unit lengths and are positive in the + 2 tz 6Q direction shown by arrows. Reactants writ-

[Di] ten on same side of reaction as arrowhead. R6 Components written in square brackets are conserved in the labelled reaction. The [vs] component written in the top left of each figure is conserved in all reactions in that (e) R8 (f) R2 [Qtz] [2mc] plane. (a) Basis vectors in the three-dimen-

[Prp] [Di] k

t sional reaction space. Reaction R8 is a Qtz- 3

5

D + i

z

+ y conservative reaction that lies in the R1–R9 t

3 K

m Q

4 4

c plane. Reactions R8 and R3 define a Qtz- 6 + R6 + K 6 [Ky] p

y P r tk rp conservative plane that separates Qtz-pro- 6 + P + Qtz 2v 2 + s v 2m ducing and Qtz-consuming half-spaces. All s c + tk linear combinations of the basis vectors that Di +vs 2Ky +vs [mc, tk] [Ky] [Prp] pass behind this plane produce Qtz; those 3Qtz R1 R4 5Qtz + mc + 2tk that pass in front consume Qtz. All subse-

quent diagrams illustrate a plane in the k t 2

2 7 P

Q s k t rp reaction space. (b) R3–R9 plane. Contains v t + 5 z + 2 P + 3 + + c r 2 v

y c 1 p K s m y y K 2 + all [vs] reactions. (c) R3–R1 plane. Contains 2 m K + + K 7 3 + y mc 2 t z z k [tk] t t + Q 4 + all [Ky] reactions. (d) R3–R8 plane. Con- 5 Q m 4 R7 2 v c s

[Di] + tains all [Qtz] reactions. (e) R1–R9 plane.

R4 i D [vs] [Qtz] Contains all [Prp] reactions. (f) R2–R4 R9 R5 plane. Contains all [Di] reactions. the two phases during the transition. Reaction R9 in- tions that conserve the additive component (and volves the accessory phases quartz and kyanite and is phase) Ky. The R3–R8 plane (Fig. 4d) includes the the only basis vector involving Ky. reactions that conserve the additive component (and The three-dimensional reaction space (Fig. 4a) phase) Qtz. Any reaction vector not in this plane includes all possible net-transfer reactions in the model produces or consumes free silica. eclogites, which must be linear combinations of the The R1–R9 plane (Fig. 4e), which contains all three basis vectors. All reactions lie in one of five key reactions that conserve additive Prp, illustrates two planes in the reaction space (Fig. 4b,f), which are a independent ways in which free silica can be produced. convenient summary of the kinds of net-transfer The consumption of vacancies in non-stoichiometric reactions that are possible in CMAS. The reactions pyroxene yields free silica as does the decomposition of that conserve vs component lie in the R3–R9 plane kyanite to a stoichiometric pyroxene and a silica (Fig. 4b) and are useful for considering stoichiometric polymorph. Note that the latter reaction could also pyroxene. Any direction in reaction space that does not proceed with non-stoichiometric pyroxene as long as vs lie in the R3–R9 plane represents a reaction that con- is conserved. sumes or produces vacancies in pyroxene. The plane R2–R4 (Fig. 4f) contains all Di-conser- Two planes are particularly useful for examining vative reactions, including R7. This plane is not easily eclogites that lack kyanite or quartz as accessory visualized in Fig. 4a because it is defined by R2 (in the minerals. The R3–R1 plane (Fig. 4c) contains reac- R3–R9 plane, Fig. 4b) and R4 (in the R1–R9 plane;

2007 Blackwell Publishing Ltd FREE SILICA IN ECLOGITE 45

Fig. 4e). All diopside-conservative reactions involve vector for geikielite G1 involves no free silica and is not one or more of the two accessory phases, kyanite and shown in Table 3. It describes the precipitation of quartz (Table 2). geikielite from pyroxene by consumption of En (Di + mc) and ts components. In the absence of rutile, Gk participates in only three reactions involving Qtz Other components and phases (G3, G4 & G5; Table 3), each of which conserves Di. Although jadeite is a major constituent of omphacite, The basis vector Rt1 may be used to eliminate ts sodium was not included in the model reaction space component from previously derived Rt-conservative because it does not require the presence of a new reactions (G1, G2, G3 G5 & R12; Tables 2, 3 & A6) eclogite phase. Consequently, the number and nature leading to five new reactions among Gk, Rt and Qtz of the net-transfer reactions remain unchanged. Like- (GR reactions, Table 3). Such reactions illustrate how wise, the net-transfer reactions are not affected by the silica may be released in the presence of rutile and presence of a second pyroxene, such as enstatite. ilmenite (Gk) without changing the titanium (ts) con- Because diopside and enstatite compositions are sim- tent of any phase. ply related (Di + mc ¼ En), the additive component Di may be used to represent total pyroxene without serious inconvenience. Although phase rule variance DISCUSSION changes if a second pyroxene is present, the basic Ô Õ nature of the net transfer does not, so a second Excess silica and pyroxene compositions pyroxene phase was not included in the model. ÔExcess silicaÕ may be present in both stoichiometric It is useful to consider the effects of titanium on the and non-stoichiometric pyroxene. In non-stoichio- model reactions because ilmenite and rutile are com- metric pyroxene, ÔexcessÕ is commonly defined as the mon accessory phases in eclogite (e.g. Smith, 1988), amount of silica beyond that needed to form stoichi- and reactions of any non-silicate phase with silicate ometric pyroxene. Such pyroxene is not rare in eclogite minerals may release free silica. All variations of Ti and are easily identified by having a deficiency of cat- content in pyroxene and garnet can be expressed with a ions (R < 4) outside analytical uncertainty. Stoichio- single additional exchange component: ts ¼ TiSi)1.It metric pyroxene may also be considered to contain is important to note that the ts exchange does not ÔexcessÕ silica if Si < 2. Both sodium and calcium necessarily imply tetrahedral coordination of titanium pyroxene with Si > 2 have been synthesized, and the because VITi might be incorporated through the octahedral coordination of Si has been confirmed (Bell VI IV VI IV exchange Ti Al ( Al Si))1, which is equivalent to & Mao, 1971; Angel et al., 1988; Gasparik, 1989). ts (Mu¨ ntener & Hermann, 1994; Labotka, 1995). Although stoichiometric pyroxene with Si > 2 has yet Papike (1980) noted that Al and Ti contents of to be demonstrated in nature, a garnet inclusion in pyroxene are highly correlated and suggested that the diamond has the composition of a supersilicic pyrox- substitution takes place by a Ti-Tschermak type of ene with both kinds of excess silica, because it has exchange (TiAl2Mg)1Si)2), which is equivalent to Si > 2 and R < 4 (Fig. 3a; Wang & Sueno, 1996). ts + tk. Labotka (1995) concluded that Ti variability This garnet, therefore, contains excess silica (cf. Smith, in garnet is best described by using the component 2006) and suggests that similar pyroxene might be Ca3Mg0.5AlTi1.5Si2O12, which corresponds to Grs + recovered from the mantle. 1.5ts ) 0.5tk. Note, however, that the addition of ts For the purpose of precise scientific communica- component has no effect on the number or kind of net- tions, it is useful to have a common means of transfer reactions present, unless an additional phase is describing pyroxene composition and Ôexcess silicaÕ. stabilized. The mole fraction of 3Qtz (or ÔsupersilipyxÕ, Smith, The effects of ilmenite and rutile on the production 2006) is a convenient component to express Ôexcess or consumption of free quartz can be modelled in silicaÕ in non-stoichiometric pyroxene because it is pure CMAST if geikielite (MgTiO3) is used as a proxy for silica, it is numerically equivalent to the cation defici- ilmenite. All reactions involving rutile or geikielite in ency in a six-oxygen formula unit, and isopleths of the expanded model system can be described with constant Si content are parallel and evenly spaced in the addition of two new basis vectors (Appendix; simple composition diagrams (Figs 2 & 3). Never- Table A6): theless, Qtz or CaEs are acceptable and directly related ) Rt ¼ Qtz þ ts ðRt1Þ to the cation deficiency [(4.0 R) ¼ X3Qtz ¼ 2XQtz/ 3 ¼ XCaEs/2]. If excess silica is the primary focus of a and study, it is convenient that the values of these mole Di þ mc þ 2ts ¼ 2Gk: ðG1Þ fractions are not affected by the choice of other pyroxene components, as long as those components Table 3 summarizes all 16 reactions that involve are based on six oxygen formula units and only one quartz in the expanded model system. In the absence of component is chosen to contain vacancies. The cati- geikielite, the basis vector for rutile Rt1 is the only new onic criterion for excess silica (Smith & Cheeney, 1980) reaction in CMAST that releases free silica. The basis is equivalent to using SiO2 as a component. Because all

2007 Blackwell Publishing Ltd 46 H. W. DAY & S. R. MULCAHY such criteria are internally consistent and directly re- artifacts of unstated assumptions, approximations, or lated, they are considered to be equivalent and inter- errors by earlier authors. With an appropriate choice changeable. of components, all methods of calculating Ôexcess silicaÕ We have shown that the term ÔexcessÕ silica has been are equivalent. used in at least five ways, most commonly for a composition that contains more silica than a stoichio- metric pyroxene with no vacancies, but also for Formation of free silica pyroxene containing more than 2 Si pfu. The term ÔsupersilicicÕ is also commonly used in the literature and Stoichiometric pyroxene Smith (2006) has suggested that the term should be If pyroxene and garnet are stoichiometric and contain synonymous with Ôexcess silicaÕ and restricted to non- no vs components, all reactions must conserve vs stoichiometric compositions having the ability to component, and free silica can form only by reactions exsolve SiO2 and leave behind a stoichiometric pyrox- with accessory phases (Table 3). This is clearly dem- ene. His approach leaves no way to describe stoichio- onstrated in the CMAS system, in which all reactions metric pyroxene with Si > 2, which we would describe that conserve the vs component of pyroxene lie in the as ÔsupersilicicÕ. We have also been hesitant to accept R3–R9 plane (Fig. 4b). These are the only reactions this definition because the ability to exsolve SiO2 de- that can be used to describe processes involving stoi- pends upon the location of the silica saturation surface chiometric, vacancy-free pyroxene. In the absence of in composition space (e.g. Khanukhova et al., 1976a,b, accessory phases, R3 is the only possible reaction. This 1977), which may vary with P–T, or mineral assem- reaction monitors the pyroxene to garnet transition blage. Thus, a sample of given 3Qtz content would and associated changes of mineral composition. All contain Ôexcess silicaÕ at conditions of super-saturation other reactions involving stoichiometric pyroxene in but would not contain Ôexcess silicaÕ at conditions CMAS (R2, R9 & R12; Table 3) must involve both where the same composition is under-saturated. kyanite and quartz, and a change in the abundance of One way of resolving the terminology dilemma one accessory mineral requires a complementary might be to use Ôexcess silicaÕ, ÔsupersilicicÕ and ÔsilicicÕ change in the other. Note that all reactions in the R3– to describe compositions without reference to silica R9 plane can also proceed with non-stoichiometric saturation. ÔExcess silicaÕ could be a general term pyroxene, as long as the vs component is conserved. requiring definition in context. ÔSupersilicicÕ could be All net-transfer reactions that require titanium as an used to describe any pyroxene with Si > 2 and ÔsilicicÕ additional component necessarily involve an accessory might refer to all pyroxene compositions that have phase such as rutile or geikielite, our proxy for ilmenite Si < 2, but greater than the variable Si in stoichio- (Appendix Table A6). Seven reactions conserve the vs metric pyroxene. Alternatively, it may be simpler and component and can be used to describe silica precipi- less contentious to define the terms as necessary for tation involving stoichiometric pyroxene (Table 3). clarity. Four of the seven reactions (GR4, GR6, GR9 & We have depended heavily on standard algebraic GR10; Table 3) produce geikielite and quartz by methods (e.g. Greenwood, 1975; Spear et al., 1982) to reaction of rutile with other phases and do not require calculate pyroxene compositions and to derive plotting a change in the titanium content of any phase. In coordinates for simple composition diagrams (see particular, reaction GR4 suggests that rutile inclusions Appendix). Page et al. (2005) suggested that the Ômat- in pyroxene might react with En component rix methodÕ systematically overestimates Ôexcess silicaÕ (Di + mc) to produce geikielite (or ilmenite) and free in pyroxene and pointed to several discrepancies in the quartz. Three other reactions involve the ts component literature. Any mineral composition may be described (Rt1, G3 & G4; Table 3). The basis vector for rutile completely and rigorously using a wide variety of (Rt1, Table 3) implies that consuming (or dissolving) possible components: cations pfu, end-members, or rutile as ts component in either garnet or pyroxene additive and exchange operators. If the transformation releases free silica. from one coordinate system to another is done rigor- ously, by matrix inversion or otherwise, the coordinate systems are interchangeable and, to that extent, Non-stoichiometric pyroxene equivalent. One coordinate system might be more In the absence of accessory phases, all reactions cap- effective than another for calculation, pedagogy, or able of producing free silica proceed by the consump- illustration, but the method of calculating the com- tion of the vacancies in non-stoichiometric pyroxene ponents should not affect any conclusion derived from (Table 3). In CMAS, reactions that conserve accessory the data. Typically, we reproduced precisely the results Ky occur in the R3–R1 plane (R1, R6; Table 2; of well-known data sets in the literature by several Fig. 4c). Reaction R3 neither produces nor consumes methods of calculation. Discrepancies cited by Page Qtz. Reaction R1 produces Qtz at the expense of the et al. (2005) between estimates of excess silica based on Di and vs components of pyroxene, whereas R6 yields structural formulas and those based on algebraic cal- Qtz at the expense of Prp and vs components. In the culations of end-member components probably are absence of accessory Ky, therefore, all mechanisms of

2007 Blackwell Publishing Ltd FREE SILICA IN ECLOGITE 47 producing the free silica in CMAS eclogites require the silica. The precipitation of free silica will accompany destruction of vacancies in non-stoichiometric pyrox- the dissolution of rutile as ts component in either ene. pyroxene or garnet (Rt1, Table 3) or the dissolution of The destruction of vacancies does not necessarily ilmenite in pyroxene at the expense of the vs compo- require the precipitation of free silica, however. This is nent (G5, Table 3). Consequently, any change in demonstrated in Fig. 4d, which illustrates the reactions physical conditions that affects rutile or ilmenite that conserve Qtz in the R3–R8 plane. Most of these saturation in eclogite, will also affect the balance of reactions consume vacancies while producing Ky (R5, free silica. Reactions G3 and G4, also demonstrate R8, R10 & R11; Table 2), and may help control the that titanium saturation in the stability field of compositions of pyroxene and garnet in kyanite quartz + kyanite + geikielite (or ilmenite) may affect eclogite. Reaction R8 may provide a mechanism for the precipitation of free silica. the precipitation of aluminium silicate inclusions in Silica precipitation is also controlled by the vacancy pyroxene (Williams, 1932; O’Hara & Yoder, 1967). (vs) content of non-stoichiometric pyroxene through All other reactions involving accessory kyanite and six reactions. Reaction R1 (Table 3) corresponds to the vs component that also release free silica are contained direct precipitation of free silica from clinopyroxene, in the Di-conservative plane (Fig. 4f). Four of the five but all the other reactions require the interaction of reactions in Fig. 4f (R2, R4, R6 & R7; Table 2) release another phase with the vacancies in clinopyroxene. Qtz at the expense of Prp or Ky. Note that the pro- These reactions suggest that inclusions of garnet, duction of free silica by these reactions does not kyanite or ilmenite (Gk) could interact with vacancies require the consumption of additive pyroxene, in the host pyroxene to produce free silica. It is possible although the composition of the pyroxene may change that the balance of free silica might be affected as much because of the exchange components participating in by these interactions as by the direct precipitation of the reactions. silica via reaction R1 (Table 3). If titanium is added to the model system, only two It is important to note that vacancy content cannot additional net-transfer reactions describe interactions be an independent monitor of the potential to produce between accessory phases and non-stoichiometric free silica, because vacancies can be consumed without pyroxene. Reaction G5 (Table 3) provides a mechan- the precipitation of free silica (Fig. 4d). Moreover, ism by which geikielite (or ilmenite) inclusions could silica can be released by mechanisms that do not react with vacancies in host pyroxene to produce free involve vacancies. silica. Reaction GR2 (Table 3) consumes vacancies to Titanium and vacancy contents might be equally produce free silica and rutile, but does not require a important controls on the balance of free silica in change in the titanium content (ts) of any phase. eclogite. Pyroxene is known to contain as much as 0.3 Ti (Robinson, 1980, Table 1) and cation deficiency as high as 0.3 (R ¼ 3.7, Fig. 3; Bell & Mao, 1971), but Controls on silica precipitation in eclogite the effects of P–T and phase assemblage on Ti and The reactions in CMAST demonstrate three broad vacancy contents are poorly understood. controls on the precipitation of free silica in eclogite: (i) There seems little doubt that high pressures favour the presence or absence of accessory phases; (ii) the the stability of non-stoichiometric pyroxene (Khanu- titanium content of pyroxene or garnet; (iii) the khova et al., 1976a,b, 1977; Wood & Henderson, 1978; vacancy content of pyroxene. Wood, 1979; Gasparik & Lindsley, 1980; Gasparik, Table 3 demonstrates the critical role of accessory 1984a). Although it seems reasonable to infer that free phases in the formation of free silica. All but two of the silica might be released on decompression, consider- 16 reactions (R1 & R6) require the presence of an able caution is warranted because the effects of pres- accessory phase (kyanite, rutile or geikielite). Eclogite sure vary with mineral assemblage in both true eclogite with stoichiometric pyroxene may form free silica only and plagioclase-bearing assemblages and have not by the first 10 reactions, all of which require an been explored systematically. The vacancy content of accessory phase as a reactant and conserve vs compo- clinopyroxene coexisting with plagioclase or plagio- nent. In the absence of accessory phases, free quartz clase + quartz, in the CMAS and NCAS systems, cannot form by reaction in an eclogite with stoichio- increases with pressure up to about 3.0 GPa (Wood, metric pyroxene. This restriction also applies to 1979; Gasparik & Lindsley, 1980; Gasparik, 1985a). At supersilicic (Si > 2), stoichiometric pyroxene with higher pressures, however, vacancy content shows a elevated NaPx content, because their compositions are strong negative dependence on pressure in the assem- coplanar with the more familiar stoichiometric blage Cpx + Pl + Qtz, and little or no variation with (Figs 2 & 3). Obviously, this conclusion P–T in the ÔeclogiteÕ assemblage Cpx + Grs + does not mean that eclogite could not already be sa- Ky + Qtz (Gasparik, 1985a). Sekine et al. (1986) and turated with excess silica because of bulk chemical Irifune et al. (1986) also found that the CaEs content composition. of pyroxene is approximately constant in eclogite of The titanium content of pyroxene and garnet might MORB composition in the pressure region 5.0– also be an important control on the formation of free 9.5 GPa, above which the CaEs content decreases

2007 Blackwell Publishing Ltd 48 H. W. DAY & S. R. MULCAHY markedly, as stishovite is precipitated. Okamoto & Our examination of all possible net-transfer reac- Maruyama (2004) reported a similar decrease of CaEs tions in simple model eclogite shows that there are content at somewhat lower temperatures in the region three broad mechanisms by which free silica can be 10.0–18.0 GPa. released: (i) vacancy consumption in non-stoichio- The available evidence shows that high pressure metric pyroxene; (ii) dissolution of rutile or ilmenite in favours low titanium content of clinopyroxene. Yagi & pyroxene or garnet; (iii) reactions among accessory Onuma (1967) successfully synthesized aluminous phases, garnet and pyroxene. diopside containing up to about 0.2 Ti pfu at atmo- The vacancy content of pyroxene cannot be used as spheric pressure, whereas, at 1.0–2.5 GPa, the solu- an independent monitor of the potential for producing bility of Ti was nil. These results are reinforced by data free silica because vacancies can be consumed by Qtz- showing that Ti substitutions in pyroxene increase the conserving reactions and silica can be released by molar volume (Onuma et al., 1968; Redhammer reactions not involving vacancies. et al., 2003). Zhang et al. (2003) conducted experi- ments on a natural ilmenite-rich garnet clinopyroxenite at pressures from 4 to 10 GPa. They found that ACKNOWLEDGEMENTS diopside-rich clinopyroxene contained only about Our efforts to understand these issues began as an 0.01 Ti pfu, despite saturation with ilmenite or rutile, outgrowth of a graduate seminar on eclogites con- and that Ti content was only a weak function of ducted jointly with C. Lesher. We are grateful for pressure. On the other hand, coexisting garnet con- careful reviews by H. Green, S. Roeske and D. C. tained up to 0.25 Ti pfu and Ti content was strongly Smith. dependent on pressure. Both lines of evidence suggest that Ti saturation decreases in clinopyroxene with increasing pressure. REFERENCES As lower pressures appear to favour higher Ti and Andrew, A. S. & Linde, J., 1980. MRF: A FORTRAN IV lower vacancy contents in clinopyroxene, reactions R1 computer program for the generation of univariant phase and Rt1 should each proceed in the direction that equilibria. Computers & Geosciences, 6, 227–236. Angel, R. J., Gasparik, T., Ross, N. L., Finger, L. W., Prewitt, precipitates free silica during decompression from the C. T. & Hazen, R. M., 1988. A silica-rich sodium pyroxene coesite stability field (Table 3). Thus, both solution of phase with six-coordinated silicon. Nature, 335, 156–158. rutile and destruction of vacancies may contribute to Bakun-Czubarow, N., 1992. Quartz pseudomorphs after coesite growth of quartz or coesite lamellae in clinopyroxene. and quartz exsolutions in eclogitic omphacites of the Zlote Mountains in the Sudetes (SW Poland). Archiwum Mineralo- At pressures above 9.5 GPa, in the stishovite field, free giczne, 48, 3–25. silica may be released as pressure increases (Sekine Bell, P. M. & Mao, H. K., 1971. Composition of clinopyroxene et al., 1986). in the system NaAlSi2O6–CaAl2Si2O8. Carnegie Institution of We have not attempted an exhaustive exploration of Washington Yearbook, 70, 131. pyroxene composition space or of the implications of Clark, S. P., Schairer, J. F. & de Neufville, J., 1962. Phase relations in the system CaMgSi2O6–CaAl2SiO6-SiO2 at low other possible accessory phases for the origin of free and high pressure. Carnegie Institution of Washington Year- silica in eclogite (e.g. , phosphate, carbonate). book, 61, 59–68. Nevertheless, our observations suggest that, in the Deer, W. A., Howie, R. A. & Zussman, J., 1978. Rock-forming most common eclogite compositions, reliable inter- Minerals, Vol. 2A, Single-chain Silicates. 668 pp. Wiley, New York. pretation of the significance of silica lamellae and Dobrzhinetskaya, L. F., Schweinehage, R., Massonne, H. J. & inclusions in natural clinopyroxene will require the Green, H. W., 2002. Silica precipitates in omphacite from evaluation not only of silica solubility, but also Ti eclogite at Alpe Arami, Switzerland: evidence of deep sub- solubility, and the possible roles of accessory phases duction. Journal of Metamorphic Geology, 20, 481–492. and inclusions on the balance of free silica. Doelter, C., 1883. Uber einige Augite von bermerkenswerther Zusammensetzung. Mineralogische und Petrographische Mitt- heilungen, 5, 224–233. Eskola, P., 1921. On the eclogites of Norway. Videnskapsselsk- CONCLUSIONS apets i Kristiana Skrifter I. Matamatisk - Naturvidenskabelig ÔExcess silicaÕ may be found in either stoichiometric or Klasse, 8, 1–118. Finger, L. W. & Burt, D. M., 1972. Reaction, a FORTRAN IV non-stoichiometric pyroxene, but the meaning of Ôex- computer program to balance chemical reactions. Carnegie cessÕ is different in the two cases. In the first instance, Institution of Washington Yearbook, 71, 616–620. Si cations exceed the amount that can be accommo- Fisher, G. W., 1989. Matrix analysis of metamorphic mineral dated in the tetrahedral site of a pyroxene. In the assemblages and reactions. Contributions to Mineralogy and second, the composition of a pyroxene with vacancies Petrology, 102, 69–77. Gasparik, T., 1984a. Experimental study of subsolidus phase- in the M-sites can be described as a stoichiometric relations and mixing properties of pyroxene in the system pyroxene plus excess silica. Nevertheless, we find that CaO-Al2O3-SiO2. Geochimica et Cosmochimica Acta, 48, all commonly used reference frames or definitions 2537–2545. of excess silica in non-stoichiometric pyroxene are Gasparik, T., 1984b. 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Wang, W. & Sueno, S., 1996. Discovery of a NaPx-En inclusion from inclusions of coesite pseudomorphs in garnet and from in diamond: possible transition zone origin. Mineralogical quartz exsolution lamellae in omphacite in eclogites. American Journal, 18, 9–16. Mineralogist, 87, 853–860. Wang, Q. C., Ishiwatari, A., Zhao, Z. Y. et al., 1993. Coesite- Zhang, L., Ellis, D., Williams, S. & Jiang, W., 2003. Ultra- bearing granulite retrograded from eclogite in Weihai, eastern high-pressure metamorphism in eclogites from the western China. European Journal Of Mineralogy, 5, 141–151. Tianshan, China – reply. American Mineralogist, 88, 1157– Williams, A. F., 1932. The Genesis of the Diamond, 2 volumes. 1160. Ernest Benn Limited, London. Zhang, L. F., Song, S. G., Liou, J. G., Ai, Y. L. & Li, X. P., Wood, B. J., 1979. Activity-composition relationships in Ca(Mg, 2005. Relict coesite exsolution in omphacite from Western Fe)Si2O6-CaAl2SiO6 clinopyroxene solid-solutions. American Tianshan eclogites, China. American Mineralogist, 90, 181– Journal Of Science, 279, 854–875. 186. Wood, B. J. & Henderson, C. M. B., 1978. Compositions and Zvetkov, A. I., 1945. Synthesis of alumina pyroxenes and unit-cell parameters of synthetic non-stoichiometric tscher- dependence of their optics on composition (in Russian with makitic clinopyroxenes. American Mineralogist, 63, 66–72. English summary). Memoires de la Societe russe de mineralo- Yagi, K. & Onuma, K., 1967. The join CaMg2Si2O6–CaTiAl2O6 gie, 74, 215–222. and its bearing on the titanaugites. Journal of the Faculty of Science, Hokkaido University, series 4, 13, 463–483. Zhang, L. F., Ellis, D. J. & Jiang, W., 2002. Ultrahigh-pressure metamorphism in western Tianshan, China: Part I. Evidence Received 20 June 2006; revision accepted 11 October 2006.

SUPPLEMENTARY MATERIAL aegirine (Ag), hedenbergite (Hd), johannsenite (Jh), Ni-pyroxene (NiPx), enstatite (En), jadeite (Jd), and K-pyroxene (KPx). Coeffi- The authors have provided the following supplementary material, cients of the condensed oxides are the sums of the appropriate rows which is available alongside the article at http://www.blackwell- of transformation matrix [VCat])1, as described in the text and are synergy.com. recast as plotting coordinates in the last three rows of the table. Appendix S1 Criterion for excess silica (Smith & Cheeney, 1980) Table A3. Compositions of natural pyroxene in text Fig. 3a. All Table A1. Transformation from cation basis to end-member basis. analyses were recalculated on a six-oxygen basis. Matrix [VCat] contains the vectors of new end-members written in Table A4. Compositions of synthetic pyroxene in text Fig. 3b. terms of the old cation components. The transformation matrix re- Table A5. Singular value decomposition of the composition matrix quired to write mineral compositions in terms of the end-member for seven phase components in CMAS. All calculations performed components is [VCat])1. using MATLAB software (Mathworks, Inc., Natick, MA, USA). Table A2. Transformation from cations to end-members in con- Table A6. Mass balances in CMAST. densed oxide space. Abbreviations: quartz, (3Qtz), Ca-Ti pyroxene (CTPx), calcium Tschermak pyroxene (CaTs), kosmochlor (Ko),

2007 Blackwell Publishing Ltd