Compositional matrix effect

Breecker and Sharp (2007) measured a series of standards of varied composition by laser fluorination (LF). In their work they admit that LF of monazite is challenging and the partial fluorination (low yield) of phosphates produces inaccurate results. This issue was further discussed in Rubatto et al. (2014). By comparing laser fluorination values to ion microprobe measured values for every standard Breecker and Sharp (2007) determine a matrix-bias correction factor for SIMS analyses of oxygen in monazite according to Th content of monazite. Unfortunately, Breecker and Sharp (2007) do not describe the detail of their calculation. Didier et al. (2017) follow the same approach with a more precise dataset, comparing SIMS sample averages with LF values. Their conclusion is that the best indicator for bias in the measurement of oxygen isotopes by SIMS (Cameca 1280 HR) is the YREE endmember component in monazite.

Rubatto et al. (2014) took a slightly different approach in measuring an array of monazites from the same syenite magma that showed varying Th contents (sample MA 108). The assumption was made that different grains in the same sample had the same oxygen isotope composition because oxygen isotope fractionation during fractional crystallization is very small. Additionally, oxygen isotopes have been shown to diffuse quickly through monazite at magmatic temperature (e.g. Cherniak et al., 2004) so the magmatic monazites are expected to have equilibrated to the same value. In the MA108 sample investigated in Rubatto et al. (2014). Th in monazite is solely incorporated through the huttonite substitution (ThSiO4). A linear regression through the dataset

is used to calculate a correction factor for measured oxygen composition based on the Th content of the measured monazite domain. In this case, no assumption is made on the absolute oxygen isotope composition of the individual monazites, but their relative variation provides the basis for the correction.

The Dora Maira dataset provides an opportunity to use the same approach as for MA108 in Rubatto et al. 2014. This approach assumes that the variation in the measured δ18_{O is solely}

analytical and that no geological variation is present outside of the reported analytical uncertainty. This is a working hypothesis that is clearly imperfect as the variation in natural grains is typically larger than the analytical uncertainty (Ferry, 2010), the reasons for this choice are explained below. It is unlikely that the oxygen isotope composition might co-vary with Th incorporated with Ca or Si along the P-T path. In sample DM1C all intermediate and external zones in monazite crystallise with garnet at peak P-T, and garnet in DM1C shows a maximum 1 ‰ difference between core and rim (between 7.4 and 6.4 ‰, see Chapter 2), which is attributed to matrix-related effects and not actual zoning in δ18_{O. The direction of oxygen isotope variation in garnet is opposite to the}

lower δ18_{O recorded by the inner Th-rich monazite zones, supporting that this is not a bulk,}

correlated variation recorded by the two minerals. In DM51, DM52 and DM53, monazite also grew together with garnet, no δ18_{O zoning can be observed in garnet. Moreover, in the monazite}

in these samples there is only a weak correlation between Y and REE (decreasing with increasing mode of garnet on the prograde path) and the Ca, Si and Th content of the monazites (Figure 1 - 11); this makes a geological variation in δ18_{O unlikely. Differential fractionation could occur}

between cheralite, huttonite and monazite compared to quartz in natural systems. This can be estimated using the increment method: according to the calculations in Rubatto et al. (2014), a pure cheralite monazite in a quartz-dominated system is expected to yield a value that is 0.25 ‰ lower than a pure monazite at 700°C. As the chemical variation observed in DM1C is between 20 and 60% cheralite, the effect would scale down to about 0.1 ‰. This effect is well within the uncertainty quoted for the analytical method and thus cannot be responsible for the relatively large variations in measured oxygen isotope compositing on the DM monazite. Therefore it can be

concluded that the up to 5‰ δ18_{O variation measured in Dora Maira monazites cannot be ascribed}

to geological co-variations with Si, Ca and Th contents, and are likely the result of a matrix effect.

The variation in the measured oxygen isotope composition (expressed in δ18_{O) of DM samples}

standardized to S440-monazite is explored using different vectors of chemical composition (Figure 1 - 13). As proposed by Breecker and Sharp (2007), the matrix effect can be related to Th and U content (Figure 1 - 13a, here calculated with LA-ICPMS data available in Chapter 2,

Appendix table A2 – ESM3). Th and U are added in wt% as their atomic mass is not significantly different within the error of measurement. The obtained regression is:

𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝛿 𝑂18 = 𝟕. 𝟔𝟐 – 𝟎. 𝟏𝟗𝟐 ∗ (𝑻𝒉 + 𝑼 wt%) (1a)

The same regression using EMPA data (in Chapter 2) for Th and U yields a slightly better fit, with an R2 _{of 0.88:}

𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝛿 𝑂18 = 𝟕. 𝟓𝟗 – 𝟎. 𝟐𝟎𝟕 ∗ (𝑻𝒉 + 𝑼 wt%) (1b)

The same δ18_{O – Th+U correaltion was investigated by Didier et al. (2017) who obtained similar}

slopes of -0.210 (±0.050), -0.161 (±0.047) and -0.216 (±0.042) ‰/wt%. It has to be noted that Didier et al. (2017) plotted unstandardised δ18_{O values. A slope of 0.085 was instead calculated}

by Rubatto et al. (2014) for the MA108 sample. However, Th and U do not describe the variation in DM1C composition very well, and if this correction is applied the average corrected value of DM1C is still lower than the zircon value in the same sample.

An alternative correlation is calculated for the YREE monazite component (Figure 1 - 13b, again with LA-ICPMS data, formula calculated using method from Pyle et al., 2001):

𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝛿 𝑂18 = −𝟏. 𝟗𝟖 + 𝟗. 𝟏𝟒 ∗ 𝑿𝑹𝑬𝑬𝒀 (2)

This relation is comparable to the variation observed by Didier et al. (2017), although the slopes cannot be numerically compared since expressed in different units.

Figure 1 - 13. a. δ18_{O variation according to Th+ U content (wt%). b. δ}18_{O variation according to X} YREE as proposed by Didier et al. (2017). c. δ18_{O variation according to chemical vectors} corresponding to the two substitutions: Ca and Si. In all three diagrams, the apparent δ18_{O is not the} IMF as we have no LF data for the individual monazite zones, but the individual analyses standardized to S440, showing relative variations. The ‘true’ value for the samples is found at the intersection of the calibration line or plane, and the coordinates corresponding to the composition of S440.

Since DM51, DM52 and DM53 yield primarily a huttonite substitution and DM1C a cheralite substitution, it is possible and more suitable to define a correlation between measured δ18_{O and}

composition in terms of Ca and Si (EMPA measurements, available in Chapter 2, Appendix table

A2 – ESM9), indicators of the two substitions that incorporate Th (Figure 1 - 13c):

𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝛿 𝑂18 = 𝟕. 𝟏𝟐 (‰, 𝑠𝑒 0.12, [6.88; 7.37]) − 𝟎. 𝟖𝟖 ∗ 𝑺𝒊 (𝑤𝑡%, 𝑠𝑒 0.12, [−1.12; −0.63])

with a R2 _{of 0.93 and a residual standard deviation is 0.33 ‰. This can be translated into:}

𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝛿 𝑂18 = 𝟕. 𝟏𝟐 (‰, 𝑠𝑒 0.12)

− 𝟎. 𝟏𝟎𝟔 ∗ 𝑻𝒉 (𝐻𝑢𝑡𝑡, 𝑤𝑡%, 𝑠𝑒 0.20) − 𝟏. 𝟗𝟎 𝑻𝒉 (𝐶ℎ𝑒𝑟, 𝑤𝑡%, 𝑠𝑒 0.08) (3b)

This linear regression diverges slightly from the slopes of -0.192/-0.206 obtained by regression in the Th +U system, the latter appearing dominated by the cheralite-related matrix effect. The slopes for Si is identical to that found by Didier et al. (2017), using the R script developed above, in more monazite-rich samples -0.87*Si (wt%). However, the slope in Didier et al. (2017) was much larger for Ca at -3.02*Ca (wt%), although they don’t report its uncertainty which is likely large as it is calculated over a small variation of 0.7 wt% Ca vs. 4.5 wt% Ca in our study. The fact that the slope for Th included by cheralite substitution is statistically different from the slope of Th included by huttonite substitution at the 95% confidence level indicates that it is better to perform a two-step correction compared to a Th-based correction when correcting our dataset. The residual of 0.33 ‰ on the 3D correlation is of the same order as the repeatability in the standard measurements, which is a good indication that the two-step correction successfully eliminates matrix-related variations.

The approach by Didier et al. (2017) looking at XYREE (in a way the left-over from cheralite and

huttonite substitution in monazite) introduces an artificial constraint which is that the matrix bias induced by 1 mol of huttonite is the same as by 1 mol of cheralite. While this assumption seems plausible within error of our dataset, the two-step approach allows for a truly independent regression (as far as possible when dealing with compositional data).

In summary, in contrast to other studies, the DM dataset covers a large range in composition, especially along the monazite-cheralite solid solution. This allows calculating matrix correction coefficients despite the noise in the single-measurement data. This is done with trace element zoned monazites, with the assumption that the grains and zones are in isotopic equilibrium as indicated by zircon and garnet in the same samples. Here, to calculate the matrix correction coefficients, the data is not anchored in absolute δ18_{O but examined on a relative basis. While}

this cannot replace studies such as Didier et al. (2017) in developing high precision standards using LF, this approach allows mapping a much larger chemical space, and can thus enlighten non-linearity in the behaviour of the matrix bias according to composition (not seen here). In addition, the two-component matrix correction approach uses only two chemical measurements (Si and Ca) that can easily be done by EMPA.