Predicting Olivine Composition using Raman Spectroscopy through Band Shifts and Multivariate Analyses

L. B. Breitenfeld1, M. D. Dyar1, C. Carey2, T. J. Tague, Jr.3, and P. Wang3, 1Department of Astronomy, Mount Holyoke College, South Hadley, MA 01075, breit22l@mtholyoke.edu, 2University of Massachusetts Amherst, Amherst MA 01003, 3Bruker Optics, Inc., Billerica, MA 01821.

Figure 4. Raman spectra of the olivine doublets (DB1 and DB2) in thisstudy from both Bruker spectrometers. Spectra were baseline-correctedusing Air-PLS and normalized.

Figure 5. Relationships among peak centroids and forsterite content.RRUFF data acquired from http://rruff.info/. Kuebler et al. (2006) fits herematch those published. Other literature (purple) refers to values from [1, 4-6,8-15].

Figure 6. Prediction errors for data sets (Senterra, BRAVO and RRUFF)when the trained models use spectra from the same or differentinstrument(s).

Why is This Important?• Olivine composition varies over a solid solution between forsterite

(Mg2SiO4) and fayalite (Fe2SiO4).

• Fe/Mg is diagnostic of crystallization temperature (Figure 1).

• Fe/Mg also affects phase relations. For example, forsterite does not

occur with quartz, and is stable to great depths, while fayalite occurs

only rarely in granites and high-Si rocks like rhyolites.

• Olivine minerals control many of the properties of Earth’s upper mantle,

affect rheology, and may store H in the mantle.

Acknowledgments: We are grateful for support from the Massachusetts Space Grant Consortium and the

NASA RIS4E SSERVI node.

References: [1] Chopelas A. (1991) Amer. Mineral., 76, 1101-1109. [2] Wang A. et al. (2004) J. Raman

Spectros., 35, 504-514. [3] Kuebler K. E. et al. (2006) Geochim. Cosmochim. Acta, 70, 6201-6222. [4]

Ishibashi H. et al. (2011) J. Raman Spectros., 43, 331-337. [5] McKeown, D.A. et al. (2010) Amer. Mineral.,

95, 980-986. [6] Iishi K. (1978) Amer. Mineral., 63, 1198-1208. [7] Price, G.D. et al. (1987) Mineral Mag., 51,

157-170. [8] Guyot F. et al. (1986) Phys. Chem. Mins., 13, 91-95. [9] Mohanan K. et al. (1993) Amer.

Mineral., 78, 42-48. [10] Kolesov B.A. et al. (1996) Mat. Res. Bull., 31, 1035-1044. [11] Foster N.J. et al.

(2007) Met. Soc. Mtng., 70, #5186. [12] Yasuzuka T. et al. (2009) J. Mineral. Petrol. Sci., 104, 395-400. [13]

Abdu Y.A et al. (2011) Met. Soc. Mtng., 74, #5112. [14] Ishibashi H. (2008) J. Raman Spectros., 39, 1653-

1659. [15] Weber I. et al. (2014) Planet. Space Sci., 104, 163-172. [16] Tucker J. et al. (2010) Chem. Geol.,

277, 137-148. [17] Dyar M. D. et al. (2016) Spectrochim. Acta B, 123, 93-104. [18] Carey C. et al. (2017)

LPS XLVIII, #1097. [19] Dyar M. D. et al. (2012) Amer. Mineral., 97, 1726-1740. [20] Dyar M. D. et al. (2016)

Amer. Mineral., 101, 1171-1189.

Strategy: • Use 93 well-characterized synthetic and naturally occurring olivines.

• Test existing univariate methods for prediction of Fe/Mg from Raman

data that build on effects of Raman shift with composition (Figure 2).

• Develop improved machine learning algorithms with quantitatively

determined accuracies for measuring Mg and Fe in olivine with

Raman.

Figure 1. Phasediagram showingthe relationshipbetween olivinecomposition andtemperature.

Figure 2. Normalized Raman spectra of laihunite (blue), forsterite (orange)and fayalite (green). The high intensity doublet (DB1 and DB2) is present inall samples between 815 and 857 cm-1.

Peak shift with composition

Diagnostic olivine modes:There are 36 Raman active modes including:

(11Ag + 11 B1g + 7B2g + 7B3g) [5]

The olivine doublet that is key to this study occurs at:

~815-825 cm-1 (DB1) and ~838-857 cm-1 (DB2) [3]

Five vibrational modes form this doublet:

(2Ag + 2B1g + B2g) [1,3,6,7]

Figure 3. Histogram of compositions of 93 samples used in this study.Typical natural olivines form with ≈90%Fo, resulting in an imbalanceddistribution on the Fo-Fa series.

Methods:• EMPA at Brown University to determine composition (Figure 3).

• Mössbauer spectroscopy at Mount Holyoke for %Fe3+.

• Raman spectra (Figure 4) acquired on two Bruker instruments:

1) BRAVO dual laser system (758/852 nm): Powdered samples

with 3 sample scans and 10s integration.

2) Senterra 532 nm laser: Single crystals using 10mW laser, 2

sample scans and 10s integration.

• Baseline correction using AirPLS (smoothness =100).

• Normalization to account for arbitrary intensity differences.

• Multivariate (MVA) models used partial least-squares (PLS), least

absolute shrinkage and selection operator (lasso), or least angle

regression (LARS). See nemo.umass.cs.edu:54321 for tools.

Univariate (2-peak) Results: • Fo-Fa ratio can be estimated [3] using central peak positions of the

olivine peaks (DB1 and DB2) as in the literature.

• Linear, 2nd, and 3rd-order polynomial fits relating peak position to

composition were performed (Figure 5).

• Equations for fits are given in Table 1 with the R2 of the fit and the

RMSE-CV in units of %Fo. The latter is the error bar obtained using

leave-one-out cross validation.

Table 1. Comparison of regression vs. multivariate methods for

%Fo predictions. Multivariate models use wavenumber range of

800-880cm-1. Only BRAVO spectrometer data.

DB1

~820 cm-1

Equation: %Fo = R2 RMSE-CV

9.25x-7525.74 0.83±0.00 9.46±8.92

-1.16x2+1912.64x-788200.00 0.88±0.00 7.69±8.60

0x3+2.35x2-969.95x-3.55 0.88±0.00 7.69±8.59

DB1

~850 cm-1

4.01x-3338.10 0.96±0.00 4.26±3.77

-0.02x2+31.78x-15083.90 0.97±0.00 4.35±4.08

0x3+10.62x2-8963.42x+2519900.00 0.97±0.00 4.84±4.11

Model Components/alpha R2 RMSE-CV

PLS 7 0.99 2.56

Lasso 0.01 0.99 2.33

Lars 2 0.93 7.32

Multivariate (800-880 cm-1) Results: • Machine learning methods using MVA significantly outperform peak

centroid-based regression models, as is also observed in LIBS[16,17] and XAS [19,20] spectroscopies.

• PLS or Lasso are preferred techniques for determining Fo contentswhen optimum prediction accuracy is desired.

Effects of Instrument: • To examine the generalizability of our results, we predicted each

data set independently and with aggregated data sets (Figure 6).

• Predictions from each data set (BRAVO, Senterra and RRUFF) predict their own Fo contents most accurately, despite differences in detection sensitivities, resolutions and number of spectra within the model. These factors must be detangled.

• Further work comparing data on the same set of samples on multiple instruments is in progress.

Conclusions and Ongoing Work: • Multivariate models produce far superior prediction accuracy

using data from wavenumbers covering from 800-880 cm-1.

• We are working to develop a penultimate general model forpredicting Fo (Mg vs. Fe) composition from Raman data.