5.2 The substitution of the rare earth elements in clinopyroxene
5.2.2 A summary of experimental method
The method is described in depth in the methods chapter (page 19).
Figure 84: CMS-diagram with experimental diopside starting compositions (Levin et al., 1964), please note the change in scale. Melt compositions were measured by EPMA after completion of the experiment.
The original starting compositions had an unintentionally high concentration of trace elements (20 wt. % total trace). These concentrations were diluted by mixing small portions with new major element mixes, however this resulted in some variation in major element compositions (Figure 84).
5.2.3 Results
Clinopyroxene is notoriously difficult to synthesis in large, homogenous crystals. These crystals are homogenous with <2% variation in each of the major element components. The major element compositions of the diopside crystals (Table 19) are close to stoichiometric.
The Ca/Mg ratio in the crystals are not 1:1, with all crystals displaying more magnesium than calcium. This suggests a small component of Mg2Si2O6 (enstatite) is included in these diopside. Although not end member diopside (CaMgSi2O6), the compositions are still classified in the diopside classification (45%-50% wollastonite component) (Deer et al., 1992). Although the major elements of the clinopyroxene are quite homogenous, the trace elements are zoned. The standard deviations from all the partition coefficients are included in all the models to ensure accuracy.
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Table 19: Stoichiometry of Experimental Diopside (Aluminium Free)
Run 20140728 20140811 20140811 20140924 20140924 Sample LS007 LS905 LS906 LS906 LS907 T2 1329 1349 1349 1370 1370 Category CMS-CaO CMS-SiO2 CMS-MgO CMS-MgO CMS-CaO MgO 19.08 19.91 19.48 19.96 19.35 Al2O3 0.00 0.00 0.00 0.02 0.00 SiO2 56.73 55.74 56.43 55.53 55.84 CaO 25.09 23.31 24.60 23.70 24.92 Total 100.90 98.96 100.51 99.21 100.11 Cations 6 6 6 6 6 Mg 1.01 1.07 1.04 1.07 1.04 Si 2.02 2.01 2.01 2.00 2.00 Ca 0.96 0.90 0.94 0.92 0.96 Total 3.98 3.99 3.99 4.00 4.00 Run 20140925 20140925 20150223 20150318 20150318 Sample LS905 LS906 LS026 LS025 LS026 T2 1373 1373 1379 1366 1366 Category CMS-SiO2 CMS-MgO CMS-MgO CMS-SiO2 CMS-MgO MgO 19.80 19.96 21.12 20.97 20.84 Al2O3 0.00 0.02 0.01 0.02 0.01 SiO2 55.28 55.46 55.88 56.02 56.12 CaO 23.72 23.75 22.99 22.98 22.93 Total 98.80 99.18 100.00 99.98 99.89 Cations 6 6 6 6 6 Mg 1.07 1.07 1.13 1.12 1.11 Si 2.00 2.00 2.00 2.00 2.01 Ca 0.92 0.92 0.88 0.88 0.88 Total 4.00 4.00 4.00 4.00 3.99
Henry’s Law predicts that the partition coefficients do not change when the concentration of the element in the melt increases. The experiments with extremely high concentrations of trace elements had a depressed liquidus for diopside and these experiments crystallised at much cooler temperatures. Experiments with the same melt composition with a 200ppm difference in trace element concentration show identical partition coefficients, and therefore Henry’s Law is obeyed. Adherence to Henry’s Law has been observed previously up to 2 wt.% individual element doping concentration (Gallahan and Nielsen, 1992).
Rare earth element partitioning in diopside
The rare earth elements are mostly trivalent, with the exception of Eu and Ce. Their large cation size (Lu3+; 0.977 Å, La3+; 1.16 Å in VIII-fold coordination) and very similar chemical behaviour leads to the assumption that all the rare earth elements will partition onto the same site; the calcium containing M2 site (Blundy et al., 1996; Gaetani and Grove, 1995; Gallahan and Nielsen, 1992; Sun and Liang, 2012; Wood and Blundy, 2014). Without aluminium, the rare earth elements will partition into the M2 site of diopside by the exchange outlined in Equation 73 (Wood and Blundy, 2014).
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This equation suggests that as the activity of CaO in the melt increases, the partitioning of rare earth elements into clinopyroxene will decrease. As the composition of the synthetic diopside crystals varies only slightly, the major variables in this series of experiments are temperature and melt composition.
If the partitioning of the rare earth elements is isolated to the M2 site, their partition coefficients against their ionic radius should define a simple parabola where the peak is the ideal radius for a trivalent cation in the M2 site of diopside.
Figure 85: diopside melt partitioning in CMS system at 1 atm and 1370°C against ionic radius in VIII fold coordination. A) Diopside partitioning in three varying melt compositions at 1370°C with an atmosphere at QFM. Experiments are categorised by their most abundant component (i.e. CaO - purple, MgO-green or SiO2-blue) Large errors are due to zoning in the crystal. B) Zoned clinopyroxene
individual laser analysis against average melt. Each colour represents an individual laser spot in a single experiment, against the averaged equilibrium melt composition (CMS-MgO).
The patterns of rare earth element partitioning do not define simple parabolas (Figure 85), which suggests that this is more complex than simple partitioning onto the M2 site of the pyroxene. Even in the highly zoned crystals, the inflection of the heavy rare earth elements is consistent between each individual laser analysis and is not an effect of averaging zoned crystals.
It is possible that this inflection is caused by the addition of the heavy rare earth elements onto the M1 site, in addition to the M2 site. This phenomenon has been noted in nature (Olin and Wolff, 2010) however is attributed to high Fe contents which cannot be the solution in the simple CMS system.
The M1 site of diopside is much smaller and more “rigid” than the M2 site and is thought to reject the addition of the large rare earth elements. Sc is a very small (0.745 Å in VI-
141 fold coordination) trivalent cation and thought to partition exclusively onto the M1 site (Gallahan and Nielsen, 1992). For comparison, the smallest rare earth element; Lu is 13% larger at 0.861 Å in VI-fold coordination.
The measured partition coefficients are fit to 3 different models. 1) The lattice strain model with the assumption that all rare earth elements partition onto the M2 site 2) the double lattice strain model where the HREE that do not fit on the M2 parabola are fit onto the M1 site (Figure 86) 3) orthogonal polynomials in an attempt to describe the entire partitioning pattern as a single equation.
For the M2 + M1 lattice strain model, Sc and In were also fit to the M1 parabola, however, they were not included in the calculation of the error of the fit.
Table 20: Error associated with various fits to the partitioning of rare earth elements in clinopyroxene.
Based off Equation χ2 χ2ν
Double lattice strain M1+M2 0.75 0.0157 Orthogonal poly. (5 parameters) 3.42 0.0591 Single lattice strain M2 only 13.81 0.1919 Orthogonal poly. (3 parameters) 16.24 1.8042
The double lattice strain, with both M1 and M2 components is by far the most accurate fit to the data. The orthogonal polynomial method is also very accurate but has difficulty in modelling the very sharp inflection in the heaviest rare earth elements. The orthogonal polynomial become less accurate as parameters are removed. The 3 parameter orthogonal polynomial is less accurate than the lattice strain model assuming all rare earth element partitioning on the M2 site.
Lattice Strain Model
The rare earth elements partition onto both the M1 and M2 sites in CMS diopside. Both these crystal sites will have an ideal radius (ro), a rigidity coefficient (E) and a partition coefficient for an ideal cation (Do). To determine what affects these components, each experiment was fit using a least squared regression to the lattice strain model.
One weakness of the lattice strain model is that it becomes difficult to precisely determine the lattice strain coefficients when only one limb of the parabola is defined. This is the case for the M1 site for trivalent cations. The parabola is defined only by Sc, and the remainder of the rare earth elements that do not fit the M2 site parabola (Figure 86). Other trivalent cations that are small enough to possibly fit onto the M1 site include; In, Ga, Al and B. Aluminium is thought to prefer the tetrahedral site, and in cases such as the
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calcium Tschermak’s molecule (CaAlAlSiO6), aluminium can exist in both the tetrahedral and M1 site (Hill et al., 2000; Okamura and Ghose, 1974). Ga behaves very similarly to aluminium and may also partition onto both the tetrahedral site and M1 sites. This means that only one limb of the parabola is defined using Sc and the HREE (and occasionally In when measured).
Figure 86: partitioning of trivalent cations into the M1 and M2 site of diopside. A) Rare earth elements into the VII-fold, M2 site of diopside, Open symbols were not included in the calculation of the lattice strain fit for the M2 site. b) Sc and HREE partitioning into the VI-fold, M1 site. Diamonds represent calculated partition coefficients from the difference between measured and calculated partitioning in the M2 site.
The data for r0 and E for trivalent cation partitioning in both M1 and M2 are similar to those calculated by Olin and Wolff (2010). The D0 values are much lower in this study as the partitioning for Sc is two orders of magnitude higher in Olin and Wolff (2010). In both the M1 and M2 site partitioning, E and r0 are highly positively correlated. This is very commonly observed (Sun and Liang, 2012) and is due to the relationship between E and ro in the lattice strain model.
To determine what component has the strongest effect on D0M2
,Gd will be used as a proxy, as it is one of the most compatible rare earth, and therefore will be similar to DM2
03+. Similarly, Sc is the most compatible trivalent cation that is assumed to partition exclusively in the M1 site and will be used to determine what effects D0M1.
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Table 21: Summary of lattice strain model parameters.
M1 (IV-fold) M2 (VIII-fold) D0M1 EM1 (GPa) R0M1 (Å) D0M2 EM2 (GPa) R0M2 (Å) n CMS-CaO average 0.79 1380 0.76 0.05 340 1.06 2 σ 0.16 79 0.001 0.014 3 0.002 CMS-MgO average 0.65 1588 0.76 0.07 322 1.05 3 σ 0.06 77 0.001 0.012 14 0.001 CMS-SiO2 average 1.03 1499 0.76 0.10 292 1.04 3 σ 0.50 262 0.009 0.044 38 0.003
Figure 87: Partitioning of trivalent cations in clinopyroxene in the CMS system a) effect of the mole fraction of calcium in the melt on the partitioning of Gd into the M2 site of clinopyroxene. b) Effect of the mole fraction of magnesium on the partitioning of Sc on the M2 site of clinopyroxene. C) Correlation between Ca on the M2 site (APFU) and the partitioning of Gd. D) correlation between the Mg on the M1 site of clinopyroxene and the partitioning of Sc.
Partitioning of the REE into the M2 is governed by Equation 73. As the calcium activity of the melt increases, there will be a decrease in the partitioning of the rare earth elements on the M2 site and like-wise, an increase in the MgO activity of the melt will decrease the partitioning of rare earth elements (and scandium) on the M1 site (Equation 74).
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A similar correlation should be made with the crystal chemistry of the pyroxene. An increase in the calcium content in the M2 site of the pyroxene would mean a decrease in the partitioning of the rare earth element on this site.
Unfortunately, the high error of the scandium partition coefficients makes conclusions difficult. There is a strong positive correlation between the XMgM1 and r0M1 however, all the r0M1 are within standard deviation of each other (Figure 87).
There is a strong correlation between the partitioning of Gd and partitioning of the divalent cations on the M2 site. The Ca content of the M2 site is negatively correlated with the partitioning of Gd which suggests it is partitioning onto this site (Equation 73). roM2 is strongly positively correlated with XCaM2.
5.2.4 Conclusions
The rare earth elements in diopside partition onto both the M1 and M2 site of diopside. The partitioning of the rare earth elements on the M2 site is highly dependent on calcium, both in the melt and in the M2 site of the crystal.
This study is not conclusive in determining if melt composition can play a role in the partitioning of rare earth elements but rather that melt and diopside chemistry are intrinsically linked and it is difficult to change the major element components of the melt without changing the composition of the diopside. This is due to pyroxene family having a huge range of solid solutions within the general pyroxene formula.
Combining this study with the more complex systems in the next section will allow for a more in-depth analysis of what controls the partitioning of the all the trace elements in clinopyroxene.
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