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Mineralogical Magazine, August 2000, Vol. 64(4), pp. 651–661

Trace element partitioning between wollastonite and silicate-carbonate melt K. M. LAW, J. D. BLUNDY*, B. J. WOOD

AND

K. V. RAGNARSDOTTIR

CETSEI, Department of Earth Sciences, University of Bristol, Wills Memorial Building, Queens Road, Bristol BS8 1RJ, UK

ABSTR ACT

We have performed an experimental study of the influence of varying size and charge on cation partitioning between wollastonite and silicate-carbonate melt in the system CaCO3-SiO2. The experimental conditions (3 GPa, 14208C) lie close to the wollastonite II tc/I tc phase boundary. Results for 1+, 2+, 3+ and 4+ partitioning show parabolic dependence of partition coefficients on ionic radius, which can be fitted to the elastic strain model of Blundy and Wood (1994), wherein partitioning is described using three parameters: site radius (r0), site elasticity (apparent Young’s Modulus) and the ‘strain-free’ partition coefficient (D0) for an element with radius r0. The apparent Young’s Modulus of the Ca site in wollastonite, obtained from modelling the 2+ partitioning data, is 99+3 GPa, similar to the bulk-crystal value for the polymorph wollastonite I tc. r0 decreases with increasing charge on the substituent cation, while D0 also shows an approximately parabolic dependence on charge, with a maximum for 2+ cations. Partition coefficients for divalent cations Zn, Co, Fe, Cd, Mn and Pb are lower than would be predicted from their ionic radii alone, indicating a preference for the melt. This may be a consequence either of cation-carbonate complexation in the melt, or of the more distorted nature of cation co-ordination environments in melts.

K EY WORDS : trace element partitioning, wollastonite, metasomatism, carbonate melt.

Introduction EXPERIMENTAL partition coefficients can be applied to natural magmatic rocks both to model their chemical evolution and to reconstruct melt compositions from crystal compositions. In recent years much emphasis has been placed on understanding the systematics of trace element partitioning (e.g. Beattie, 1994; Blundy and Wood, 1994) and on development of predictive models which describe such behaviour (e.g. Wood and Blundy, 1997). The chain silicate wollastonite (CaSiO3) is present in carbonatites (e.g. Gold, 1966) and associated silicate rocks (e.g. Dawson, 1998) and metamorphosed siliceous limestones and provides us with an end-member for partitioning into a Ca site in a silicate phase. In contrast to other Ca-bearing rock forming minerals

* E-mail: [email protected]

# 2000 The Mineralogical Society

(e.g. diopside, grossular) wollastonite is unusual in two ways. Firstly, it shows very little deviation from stoichiometric CaSiO3 in nature and hence it can be grown from very simple melts without concerns that the results will not be applicable to natural systems. Secondly, wollastonite has only one large cation site, into which substitution of cations with a wide range in radius can occur. For example, studies of trace element incorporation onto the Ca(Mg,Fe)Si2O6 clinopyroxene M2-site are hampered by the fact that small cations tend to preferentially enter the smaller M1 site, normally occupied by Mg, such that systematic investigations of cations over a wide range in ionic radius is not possible (e.g. Purton et al., 1996). Thus wollastonite may provide an idealized analogue for the large M2-site in clinopyroxene. The aim of this study is to determine for the first time the effects of charge and ionic radius on partitioning between wollastonite and carbonate-silicate melt at high pressure and temperature (3 GPa, 14208C).

K. M. LAW ETAL.

polymorphs I tc and II tc may lie in their ability to accommodate heterovalent charge-balancing cations, such as Al3+, in the tetrahedral site. This possibility requires further experimental investigations of Al partitioning across the phase boundary.

Our results have implications for trace element fractionation in carbonatite systems crystallising wollastonite, and possibly in subduction zone environments where wollastonite may be a residual phase during melting of subducted carbonates (Huang et al., 1980). Wollastonite polymorphs Four polymorphs of wollastonite, differing in space group and molar volume, are known to occur under different conditions of pressure and temperature (Chatterjee et al., 1984): pseudowollastonite (pseudohexagonal), wollastonite I tc, wollastonite II tc (both triclinic), and wollastonite II m (monoclinic). The experimental pressure used in this study (3 GPa, see below) lies within the wollastonite II tc phase field, although it is only 0.07 GPa above the phase boundary with wollastonite I tc as determined by Huang and Wyllie (1975), 0.37 GPa above that determined by Essene (1974), and 0.27 GPa above that presented by Chatterjee et al. (1984). Given the uncertainty in the position of the phase boundary as determined in different laboratories with different experimental design, accuracy and precision, it is not possible to determine from the phase diagram alone which polymorph was produced in our study. Moreover, as emphasized by Essene (1974) the I tc/II tc phase boundary is very sensitive to small differences in the levels of impurities in the two polymorphs. He estimates that for every extra mole percent impurity in I tc relative to II tc the phase boundary moves 0.032 GPa higher in pressure: the wollastonite in our experiment contains some 0.8 mol.% impurities. Unfortunately there was insufficient material in our experimental run product to confirm this proposal by X-ray diffraction. From consideration of the partitioning systematics we propose that wollastonite I tc was produced in our experiment. However, we emphasise that the precise designation of the wollastonite phase produced in our experiments has little bearing on our interpretation. This is because, in terms of the factors which control partitioning, both I tc and II tc are characterized by large Ca-sites, that will be highly disordered at near liquidus temperatures, and similar elastic properties (Swamy and Dubrovinsky, 1997). In both cases large cations are thought to partition into Ca-sites. In wollastonite I tc, these sites are 6-fold coordinated, with the M
O distances shown in Table 1. The only plausible difference between

Methods Experimental The starting composition was a mixture of 75% natural wollastonite and 25% analytical grade CaCO3 which was chosen to produce a mixture of ~20% crystals and ~80% melt at the run conditions according to the phase relations of Huang et al. (1980) in the system CaCO3-CaSiO3. Natural wollastonite from the Harz Mountains in Germany was hand-picked to ensure only the clearest crystals were used, and then ground under ethanol. This wollastonite was analysed using ion microprobe (IMP) and electron microprobe (EMP) and the trace element content is shown in Table 2. Additional trace elements (Ti, Cr, Lu, Yb, Sm, Nd, Pr, Ce, La, Al, Zn, Co, Fe, Mg, Mn, Cd, Sr, Pb, Ba, Rb, Cs, K, Na, Li, Zr, U, Th) were added to the wollastonite-carbonate mixture as Analar or Primar grade oxides at concentrations of 10
10000 ppm. The trace elements added and their concentrations were chosen so as to minimize interferences in IMP and EMP analysis. After doping, the starting material was ground under ethanol in an agate mortar, heated at 2758C for 24 h to remove adsorbed water, and stored at 1208C.

TABLE 1. Wollastonite I tc Ca site parameters from the CDS database (Fletcher et al., 1996); r0 is ˚ estimated assuming an oxygen radius of 1.38 A (Shannon, 1976). Site

Ca1

Ca2

Ca3

˚) Ca-O bond lengths (A

2.52 2.31 2.34 2.52 2.34 2.32

2.31 2.40 2.41 2.41 2.40 2.31

2.31 2.41 2.41 2.31 2.40 2.41

Mean distance Standard deviation Estimated r0 Co-ordination number

2.39 0.10 1.01 6

2.37 0.05 0.99 6

2.38 0.05 1.00 6

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TRACE ELEMENT PARTITIONING IN WOLLASTONITE

TABLE 2. Concentration of trace elements in the natural wollastonite starting material used in this study from IMP; %Ca and %Si from EMP. Element Concentration (ppm) Li Mg Al %Si K %Ca Ti Cr Fe Mn Co Zn

0.004 189 23.3 23.9 12.6 34.5 19.3 0.27 1150 263 29.5 780

Element Concentration (ppm) Na Sr Y Ba La Ce Pr Nd Sm Sr Cd

13.9 74 21.8 0.26 0.084 0.097 0.17 1.27 0.41 76.9 32.4

All experiments were performed in 3 mm diameter platinum capsules with graphite liners to prevent metals such as Fe alloying with the platinum (Van Westrenen et al., 1999). Immediately prior to welding, the capsule was held at 2758C for 1 h to drive off any remaining adsorbed water. The welded capsule was tightly packed into a crushable alumina cylinder and covered with an alumina disk to prevent intrusion of the W-3%Re/W-25%Re thermocouple into the capsule. Additional assembly parts included a cylindrical graphite furnace and BaCO3 outer sleeve. The vertical temperature variation across the capsule is ~108C (Frost and Wood, 1997), while the radial thermal gradient is ~58C mm
1 (Withers, 1997). The pressure correction for this assemblage at our run temperatures is
11% (Van Westrenen, pers. comm.). Experiments were brought to 14608C and 3 GPa using the hot piston-in technique and held for 10 min to fully melt the charge. In order to grow crystals large enough for IMP analysis, the temperature was then lowered rapidly to the run conditions of 14208C at the same pressure and held for 24 h with minor adjustments for loss of pressure. No correction was made for the dependence of thermocouple emf on pressure. Analytical Major element (Ca, Si) and some minor element (Co, Lu, Yb, Mn, Cr, Fe, Cd, Mg) contents of the experimental products were determined with the 653

JEOL 8600 EMP at Bristol University, using an accelerating voltage of 15 kV and a beam current of 10 nA. A defocused beam of 15 mm diameter was used for wollastonite and melt analysis. Count times were 30 s on the peak and 15 s on the background for major elements, and 60 s peak, 30 s background for minor elements. Standards were Cr, Zn and Co metals, CdS, Fe2O3 and MnO, natural olivine (Mg), wollastonite (Ca, Si) and synthetic REE glass (Yb, Lu). The results are given in Table 3a. Minor and trace elements were measured on Au-coated mounts with the Cameca IMS-4f IMP at Edinburgh University. The primary beam was 10 keV O
ions with 4
5 nA beam current, focused to a ~20 mm spot. To reduce transmission of molecular ion species an offset of 77+20 eV was applied to the 4.5 kV secondary ion accelerating voltage. The isotopes 7Li, 23Na, 26 Mg, 27Al, 30Si, 39K, 42Ca, 47Ti, 49Ti, 52Cr, 53 Cr, 54Fe, 55Mn, 59Co, 60Ni, 64Zn, 85Rb, 88Sr, 90 Zr, 113Cd, 114Cd, 113Cs, 138Ba, 139La, 140Ce, 141 Pr, 143Nd, 149Sm, 171Yb, 175Lu, 208Pb, 232Th and 238U were measured and ratioed to Ca, as determined by EMP. The background was monitored at mass 130.5 (typically zero counts s
1). Calibration was performed on NIST standard glass SRM610. Counting times were adjusted to obtain at least 1000 total counts per isotope per analysis. Three melt and three crystal analyses were made. Peak-stripping corrections were made for MgSi and CaO interferences on 54 Fe and 55Mn. No correction was made for MgMg interference on 52Cr, and the values for this element in Table 3b should be seen as maxima. No other significant molecular ion interferences were encountered: note for example the near-identical results obtained from duplicate masses of Ti, Cr and Cd (Table 3b). The ion yields of silicate-carbonate melts are unknown, therefore we used the following silicate and carbonate secondary standards to check the validity of using SRM 610 glass as our primary standard: in-house carbonatite calcite standards Oka-1 and AL42, and mantle clinopyroxene KH1 (Irving and Frey, 1984). For most elements, concentrations in KH1 are within 10% of the accepted value, consistent with previous IMP results for clinopyroxene (e.g. Blundy and Wood, 1994; Blundy et al., 1998; Blundy and Dalton, 2000) and garnet (Van Westrenen et al., 1999). In contrast, IMP analyses of calcite standards are +10
50% of the accepted value, clearly indicating that carbonate mineral ion yields are

K. M. LAW ETAL.

TABLE 3. Analyses of experimental run products (a) Electron microprobe data (16 analyses of each phase). Units are in wt.%. Uncertainties are 1 s.d. Elements not reported were below detection. Element Mg Si Ca Cr Fe Mn Zn Cd

X-ray line K K K K K K K L

Melt

Wollastonite

0.458 +0.017 17.4 +0.4 33.8 +0.5 0.20 +0.01 0.46 +0.03 0.025 +0.017 0.15 +0.03 0.34 +0.02

0.172 +0.009 23.9 +0.3 34.0 +0.1 0.010 +0.006 0.095 +0.020 0.022 +0.009 0.027 +0.011 0.26 +0.03

D 0.38 +0.02 1.37 +0.04 1.01 +0.02 0.05 +0.03 0.21 +0.05 0.88 +0.70 0.18 +0.08 0.76 +0.10

(b) IMP data (3 analyses). Normalized to Ca data in (a). Units are ppm by weight. Uncertainties are 1 s.d. Element Li Na Mg Al K Ti Ti Cr Cr Fe Mn Co Zn Rb Sr Zr Cd Cd Cs Ba La Ce Pr Nd Sm Yb Lu Pb Th U

Mass 7 23 26 27 39 47 49 52 53 54 55 59 66 85 88 90 113 114 133 138 139 140 141 143 149 171 175 208 232 238

Melt

Wollastonite

92 +2 197 +5 4460 +60 521 +2 43 +0.8 900 +6 874 +9 1950 +12 1590 +320 4970 +25 217 +4 130 +20 2310 +80 25 +1 1820 +15 935 +10 2070 +100 1940 +45 32 +1 128 +2 11 +0.1 2.3 +0.1 0.65 +0.02 87 + 2 108 +2 173 +2 82 +1 3410 +90 1710 +20 697 +10

654

1.9 +0.1 22 +1 1920 + 40 9.3 +0.5 4.96 +0.4 27 +1 26 +1 188 +11 185 +11 1000 +45 131 +10 33 +2 213 +15 0.28 +0.04 284 +6 0.36 +0.06 1550 +112 1400 +85 0.05 +0.01 0.7 +0.1 0.28 +0.02 0.12 +0.01 0.039 +0.002 6 +1 11.4 +2 57 +12 34 +3 107 +9 0.25 +0.1 0.14 +0.04

D 0.020 +0.001 0.112 +0.004 0.43 +0.01 0.018 +0.001 0.114 +0.009 0.030 +0.001 0.030 +0.001 0.097 +0.006 0.12 +0.02 0.201 +0.009 0.60 +0.05 0.26 +0.04 0.092 +0.007 0.0111 +0.0015 0.157 +0.004 0.0004 +6610
5 0.75 +0.06 0.72 +0.05 0.0017 +0.0003 0.0055 +0.0005 0.024 +0.002 0.051 +0.006 0.060 +0.004 0.070 +0.016 0.11 +0.02 0.33 +0.07 0.41 +0.04 0.031 +0.003 1610
4 +6610
5 2610
4 +6610
5

TRACE ELEMENT PARTITIONING IN WOLLASTONITE

not the same as silicate ion yields for some elements. This could be important in a system containing a silicate mineral and carbonatesilicate melt as different ion yields in the two phases would contribute to the overall value of the partition coefficient. However, Blundy and Dalton (2000) have shown that for analysis of a synthetic homogeneous carbonate silicate glass, ion yields are similar to SRM610 for most elements. We conclude that similar ion yields apply to both wollastonite carbonate-silicate glasses, and therefore that any ion yield contribution to partition coefficients is likely to be minor. This conclusion is borne out by the close similarity between EMP and IMP concentrations and partition coefficients for those elements analysed by both techniques, especially Fe and Cd (Table 3). Results and discussion The experiment produced a single large wollastonite crystal ~1 mm in length with coexisting melt which quenched to a glass. The crystal and melt were both found to be homogeneous in EMP and IMP analysis as shown by the small standard errors in the analysis (Table 3). This observation, coupled with the high temperature and long run duration suggest that equilibrium was attained. The systematic behaviour of trace element behaviour (see below) further supports this claim. For each trace element, i, averaged analyses of crystal and melt were converted into Nernst partition coefficients (Di): Di ¼

½Xicrystal  ½Ximelt 

ð1Þ

where Xi denotes weight fraction. The Di values for a range of valences plotted against ionic radius (Fig. 1) show the same near-parabolic dependence seen in previous trace element studies (e.g. Blundy and Wood, 1994; Beattie, 1994; Wood and Blundy, 1997; Blundy et al., 1998; Van Westrenen et al., 1999). As previously noted by

these workers the position and form of the parabola depends on the charge of the trace substituent (Fig. 1). The partition coefficients for ions of charge 1+, 2+, 3+ and 4+ were each least squares fitted to the equation of Blundy and Wood (1994), using a Levenberg-Marquardt-type non-linear least squares fitting routine (Press et al., 1992), (equation 2 below). This model has previously been applied to model trace element D’s for clinopyroxene-melt partitioning (Blundy and Wood, 1994; Purton et al., 1996; Wood and Blundy, 1997) and therefore should be applicable to the wollastonite-melt system. In the case of wollastonite, our treatment of the data assumes that at these high experimental temperatures all three of the Ca sites are similar and can be treated as equivalent (i.e. there is negligible Ca-site order). We have assumed sixfold co-ordination. The 2+ partitioning parabola (Fig. 1) is constrained by the alkaline-earth elements Mg, Ca, Sr and Ba and the model fit parameters are shown in Table 4. The fitted value for the Young’s Modulus of the Ca-site (E 2+ ) is 99+3 GPa. There are no independent data on the bulk-crystal Young’s Modulus of wollastonite I tc at high pressure and temperature with which to compare this value. However, Swamy and Dubrovinsky (1997) estimate a zero-pressure bulk modulus (K) of 75.5 GPa for wollastonite I tc. The Poisson’s ratio of wollastonite I tc is also not known, but if we assume a value of 0.25 then the value for K equates to a bulk-crystal Young’s Modulus of 113 GPa, in reasonable agreement with our estimate for the Ca-site. Blundy and Wood (1994) and Wood and Blundy (1997) have previously noted the similarity between Young’s Moduli for homovalent substitution into the large cation sites of clinopyroxene and plagioclase and the bulk-crystal Young’s Modulus for the same phase. In passing we note that K for the high pressure polymorph wollastonite II tc is some 25% larger than that of I tc (Swamy and

h i9 8 r0nþ 2 3 1 > > þ NA nþ Þ þ ðri
r0nþ Þ
4pE ðr
r n i 0 > > 2 3 > > > > Di ðP; T ; X Þ ¼ D0nþ ðP; T ; X Þ  exp> > > > : ; RT

ð2Þ

where En+ is the apparent Young’s Modulus of the site for a given valence (n+), r0n+ is the optimum n+ cation radius of the lattice site on which substitution occurs, ri is the radius of the substituent n+ cation, NA is Avogadro’s number and D0n+ describes strain-free substitution of an n+ cation with radius r0n+. 655

K. M. LAW ETAL.

FIG. 1. Plots of experimentally determined wollastonite partition coefficients vs. cation radius for selected elements. Ionic radii (Shannon, 1976) in this and subsequent plots are for 6-fold co-ordination for all ions except Ti4+ and Si4+ which are plotted for four-fold co-ordination. Standard deviations based on repeat analysis are shown where they exceed the size of the plot symbol. Curves drawn through a series of homovalent cations are obtained by using a least squares weighted fit to equation 2. Table 4 gives the output fit parameters. Only those cations used to constrain the fit are plotted for the divalent elements. For the monovalent fit all the elements are included; the trivalent includes the REE and Cr; the quadravalent includes Zr, U and Th. Ti appears to partition into the tetrahedral Si site. In the case of 2+ cations, data for Zn, Fe, Mn, Cd and Co are not shown, in the interests of clarity (see Fig. 2).

Dubrovinsky, 1997). The r02+ value ˚ (Table 4) is within 2 s.d. error 0.926+0.002 A of the crystal structure refinement estimate of r0 ˚ for wollastonite I tc Ca-sites of 1.000+0.065 A (Table 1). Heterovalent substitution of 1+ and 3+ cations is also well described by the model (Fig. 1). 1+ cations yield a smaller value for E1+ (51+2 GPa), ˚ ) than 2+ cations. but larger r01+ (1.170+0.004 A For the rare earth elements (REE3+) and Cr3+ we ˚ , somewhat obtain a best-fit r03+ of 0.805+0.002 A ˚ smaller than the value of 1.041 A derived by Wood and Blundy (1997) for M2 site in diopside, but consistent with the shorter M
O bond-lengths and lower coordination number (6 as opposed to 8) of wollastonite. The E3+ value of 220+10 GPa is lower than the equivalent clinopyroxene M2 value of ~278 GPa at the same pressure and temperature (Wood and Blundy, 1997), consistent with the greater compressibility of wollastonite compared to diopside. Although Al was not used

to constrain the parabola for trivalent ions, it nevertheless lies close to the parabola defined by the REE and Cr (Fig. 1). This suggests that, unlike in clinopyroxene, Al enters the Ca site in wollastonite rather than replacing Si in the smaller

TABLE 4. Fits of experimental partitioning data to lattice strain, equation 2. 1 s.d. uncertainties are given in terms of the last significant digit(s). Charge 1+ 2+ 3+ 4+

D0 0.158(6) 1.068(34) 0.454(36) 0.00050(7)

E (GPa) 51(2) 99(3) 220(10) 300*

˚) r0 (A 1.170(4) 0.926(2) 0.805(2) 0.786(13)

*A fit for the 4+ data was achieved by fixing E4+ at 300 GPa (see text).

656

TRACE ELEMENT PARTITIONING IN WOLLASTONITE

closer in radius to U4+ (6-coordinate radius ˚ ) than Th4+ (0.94 A ˚ ). (The high Ti4+ 0.89 A partition coefficient (Fig. 1) is most readily explained by substitution for Si in the T site.) By analogy with 3+ substitution, we propose that the likely charge balancing mechanism is:

T site. The apparent absence of Al in the T site means that the preferred charge balancing mechanism for substitution of 3+ cations is likely to be a combined Na+REE3+ = 2Ca2+ exchange, e.g. Na+ + La3+ + Ca3Si3O9 = NaCaLaSi3O9 + 2Ca2+

(3)

2Na++ Th4+ + Ca3Si3O9 = Na2ThSi3O9 + 3Ca2+ (4)

However, we note that the total number of moles of 1+ ion per formula unit of wollastonite exceeds that of 3+ cations. This may in part be a consequence of the high value for Cr in Table 3b (see above), although a value of 450 ppm is required to obviate this problem. Alternatively, some balancing of 3+ cations may involve Ca-site vacancies. In order to fit a parabola to the 4+ partitioning data, for which only three partition coefficients were measured (U, Th and Zr), it was necessary to fix E4+ at some appropriate value. We did this by assuming, following Blundy and Wood (1994), that E4+ is approximately 43E3+ = 300 GPa. Fit parameters are 0.00050+0.00007 for D04+ and ˚ for r04+ (Table 4). Note that DU > 0.786+0.013 A DTh for wollastonite (Table 3). This is in contrast to diopside where DTh is generally greater than DU, because the large M2-site is closest in size to ˚ in 8-fold co-ordination) (Wood et al., Th (1.05 A 1999). In the case of wollastonite this relationship is reversed because for 4+ cations the Ca-site is

The elements Cd, Fe, Zn, Co, Zn and Pb have D values below the 2+ parabola (Fig. 2), indicating a greater preference for the melt than would be expected based on their ionic radii alone. Both IMP and EMP results are included in Fig. 3 to emphasise that this feature is not an analytical artefact. Similar behaviour of these elements is found in high pressure-temperature partitioning between calcite and witherite (BaCO3) and carbonated silicate melt (Law, 1999). In the case of Zn this behaviour is analogous to that observed in forsterite-melt partitioning (Purton et al., 2000), where it was ascribed to the preference of Zn2+ for distorted co-ordination environments in the melt, relative to more regular crystal lattice sites. The same explanation may account for the anomalous behaviour of the other 2+ elements listed above. An alternative possibility is that these cations complex with carbonate groups in the melt, which enhances their stability in that phase. Circumstantial evidence for this comes from the observation that Cd partitioning between

FIG. 2. Plots of experimentally determined wollastonite partition coefficients vs. cation radius for all divalent elements determined in this study. Both IMP (Table 3b) and EMP (Table 3a) results are given for comparison. Standard deviations based on repeat analysis are shown where they exceed the size of the plot symbol. The lattice strain parabola (fitted to Mg, Ca, Sr and Ba only) is taken from Fig. 1.

657

K. M. LAW ETAL.

r0 (A˚)

FIG. 3. Variation in D0 (squares) and r0 (circles) with increasing charge on the substituent cation (Table 4). Uncertainties are smaller than the plot symbols.

forsterite and silicate melt (Purton et al., 2000), and Fe, Co, Mn partitioning between clinopyroxene and silicate melt (Purton et al., 1996), do not deviate from the lattice strain model. If carbonate complexation is the case then the partitioning behaviour of some cations may differ considerably in carbonate melt vs. silicate melt systems, thereby providing a means of distinguishing rival metasomatic agents. Blundy and Dalton (2000) arrive at a similar conclusion regarding the contrasting crystal-melt partitioning behaviour of some trace elements in clinopyroxene-silicate vs. clinopyroxene-carbonate systems. Figure 3 shows a significant decrease of r0 with increasing charge, a phenomenon also observed in garnet-melt partitioning experiments (Van Westrenen et al., 1999). This variation is clear evidence that factors in addition to crystal lattice strain influence partitioning. One possible explanation is that the decrease in r0 with charge is due to increasing polarization of the oxygen atoms around the substituent as the charge on the substituent increases. Increased polarization causes the oxygen atoms to repel one another more strongly and, in order to minimize strain, the structure responds by preferring a smaller substituent cation. We did not recognize this effect in our clinopyroxene-melt or plagioclasemelt partitioning studies (Blundy and Wood, 1994; Wood and Blundy, 1997), perhaps because an insufficient number of elements was investigated, or due to lower oxygen polarizability in these structures. Alternatively, the variation in 658

r0 with charge may reflect variations in the energy required to dissolve cations of different ionic radius in the melt. Although partitioning is dominated by lattice strain resulting from exchanging a trace cation for the host cation in the crystal, the corresponding cation exchange in the melt cannot be ignored. The energetics of the total partitioning reaction are the sum of these two processes (Purton et al., 1996). If the melt cation exchange energy varies systematically with ionic radius for a series of isovalent cations, then the effect will be to displace r0 from its expected value. Support for this possibility comes from the computer simulation study of trace cation incorporation into garnet of Van Westrenen et al. (2000) who showed that changing the coordination environment of cations in their ‘melt’ phase can have a profound influence on r0 for heterovalent substitution. Another interesting feature in this study is the near-parabolic dependence of D0 on the charge of the substituent ion (Fig. 3): D0 is maximum for 2+ cations, is 2
6 times lower for both 1+ and 3+ cations, but is reduced by over three orders of magnitude for 4+ cations (Fig. 3). This variation is more extreme than that observed in clinopyroxene, where D02+/D04+ is typically 100
200 (Wood et al., 1999), and may reflect the unfavourable energetics of the proposed 4+ cation charge-balancing mechanism in wollastonite (equation 4). The increase in Ca-site Young’s Modulus with charge is consistent with the relationship between the bulk modulus (K) and the quotient zc/d3

TRACE ELEMENT PARTITIONING IN WOLLASTONITE

observed by Hazen and Finger (1979) for oxides (where zc is the cation charge and d is the M
O ˚ ). To bond length, estimated here as r0+1.38 A enable comparison between E and K, we have adopted a Poisson’s ratio of 0.25, such that E = 1.5K (Blundy and Wood, 1994). A similar correspondence between values of E, determined from silicate partitioning experiments, and the Hazen and Finger (1979) relationship has been previously observed for clinopyroxene, plagioclase and garnet (Blundy and Wood 1994; Van Westrenen et al., 1999). In detail, the wollastonite data fall slightly below the Hazen and Finger trend (Fig. 4), which may be due to the large variation in r0 with charge (Fig. 3). Conclusions and implications The lattice strain model of Blundy and Wood (1994) can be used to describe partitioning of trace elements with charges of 1+ to 4+ between wollastonite and carbonate-silicate melt. The polymorph of the wollastonite synthesized is not known, but is probably I tc. A decrease in the ideal site radius (r0) occurs with increasing charge, either due to changes in the oxygen polarization, or

variation in cation exchange energies in the melt with ionic radius. The strain-free partition coefficient (D0) also shows a strong dependence on charge, with a maximum of 1.068 for 2+ cations and minimum of 5610
4 for 4+ cations. These trends are similar to those observed in other silicate mineral systems. The divalent cations Zn, Co, Fe, Cd, Mn and Pb all have D values lower than predicted from the their ionic radius alone, indicating a preference for the melt. This may be a consequence of complexation with carbonate in the melt, and could provide a method of chemically distinguishing the magmatic or metasomatic effects produced by carbonate melts. Although our experiment was performed at a single pressure and temperature in a simple system, some of the observations should be applicable to natural systems. For example, the observed systematics of wollastonite-melt partitioning could be used to model semi-quantitatively the evolution of CO 2 -rich magmas containing wollastonite phenocrysts (e.g. Dawson, 1998), or to model the partial melting of subducted carbonate material with residual wollastonite (e.g. Huang et al., 1980). In applying our partitioning data to natural systems, it is

FIG. 4. Variation in bulk moduli (K) estimated from partitioning experiments for 1+, 2+ and 3+ cations with the ˚ . K was quotient quotient zc/d3, where zc is the cation charge and d is the M
O bond length, estimated as r0+1.38 A converted from E (Table 4) using a conversion factor of 1.5. The line denotes the relationship for oxides observed by Hazen and Finger (1979).

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important to take account of the effects of temperature and pressure, which affect both the tightness of the parabola (see Wood and Blundy, 1997) and the value of D0. The former effect arises in two ways. First, temperature (and pressure) can affect E, although in most silicate minerals the magnitude is likely to be relatively minor (e.g. Wood and Blundy, 1997). Temperature also appears in the denominator of equation 2, as lattice strain energies increase in inverse proportion to temperature (Blundy and Wood, 1994). The effect of temperature on parabola tightness can therefore be incorporated to a large degree simply by using the appropriate value in equation 2. The dependence of D0 on temperature and pressure is less tractable, as it is closely related to the free energy of fusion of the end-member mineral component of interest (Blundy and Wood, 1994), e.g. in the case of 2+ cations this is CaSiO3, while for 1+ and 3+ cations this is the fictive NaCaLaSi3O9. Such data are lacking, and in the case of fictive components can only be estimated from the partitioning data themselves (Wood and Blundy, 1997). In general, however, the lower the temperature relative to the fusion temperature of the endmember component at the pressure of interest, the higher D0. Thus wollastonite phenocrysts precipitated from carbonated nephelinite melt at ~7008C (Dawson et al., 1996) will be characterized by much higher D0 values for all valences than in our experiment at 14208C. This is borne out by the data of Dawson et al. (1996) and Dawson (1998) which show that DCa (=D02+) between wollastonite and nephelinite is in the range 18
140, whereas in our experiment it is 1.0 (Table 3a). Clearly, wollastonite-melt partition coefficients in low-temperature carbonated silicate melts are likely to be appreciably larger than those in Table 3, although, the overall variation in partition coefficients with ionic radius, after accounting for the effect of temperature in equation 2, is likely to be similar. This proposal can be tested through trace element analyses of wollastonite phenocrysts and host matrices in volcanic rocks. Acknowledgements Thanks to Richard Hinton, John Craven and Stuart Kearns for their help and patience during SIMS and EMP analysis, and to Fred Wheeler, Mike Dury and Phil Boyd for technical assistance. Thanks also to Liz Loeffler at Bristol University

for providing the wollastonite starting material. KML acknowledg es NERC studentship GT49629E, and JDB acknowledges support through a University Research Fellowship from the Royal Society. The authors also wish to acknowledge the use of the EPSRC’s Chemical Database Service at Daresbury. References Beattie, P. (1994) Systematics and energetics of traceelement partitioning between olivine and silicate melts: Implications for the nature of mineral/melt partitioning. Chem. Geol., 117, 57
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[Manuscript received 22 December 1999]

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