Figures and Tables

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Introduction

Emeralds are a variety of beryl (Be₃Al₂Si₆O₁₈) that are valued for their vibrant green colour, derived from the chromophore elements V, Cr and Fe. Emeralds are thought to form by the interaction of Be-enriched magmatic or aqueous fluids or hydrous evolved melts with V- and Cr-rich ultramafic or sedimentary country rocks (e.g., Giuliani et al., 2019

Giuliani, G., Groat, L.A., Marshall, D., Fallick, A.E., Branquet, Y. (2019) Emerald Deposits: A Review and Enhanced Classification. Minerals, 105, 1–63. https://doi.org/10.3390/min9020105

). Emeralds are important gemstones for examining crustal processes because, compared to other gems, they contain high abundances of trace elements that can reveal their provenance (e.g., Aurisicchio et al., 2018

Aurisicchio, C., Conte, A.M., Medeghini, L., Ottolini, L., De Vito, C. (2018) Major and trace element geochemistry of emerald from several deposits: Implications for genetic models and classification schemes. Ore Geology Reviews 94, 351–366. https://doi.org/10.1016/j.oregeorev.2018.02.001

; Giuliani et al., 2019

Giuliani, G., Groat, L.A., Marshall, D., Fallick, A.E., Branquet, Y. (2019) Emerald Deposits: A Review and Enhanced Classification. Minerals, 105, 1–63. https://doi.org/10.3390/min9020105

) and petrogenesis (Alonso-Perez and Day, 2021

Alonso-Perez, R., Day, J.M.D. (2021) Rare earth element and incompatible trace element abundances in emeralds reveal their formation environments. Minerals 11, 513, 1–21. https://doi.org/10.3390/min11050513

). Among trace elements, Rb and Sr can occur at concentrations >10 μg/g in bulk emeralds. Despite high concentrations of Rb and Sr, only a single study has utilised the commonly employed ⁸⁷Rb-⁸⁷Sr (t_1/2 = 4.72 × 10¹⁰ yr⁻¹) isotope system to study emeralds (Vidal et al., 1992

Vidal, Ph., Lasnier, B., Poirot, J.-P. (1992) Determination of the age and origin of emeralds using rubidium-strontium analysis. Journal of Gemmology 23, 198–200. https://doi.org/10.15506/JoG.1992.23.4.198

), showing that old emeralds (∼600 Ma) can host extremely radiogenic ⁸⁷Sr/⁸⁶Sr ratios (>65) due to the high ⁸⁷Rb/⁸⁶Sr ratios in some samples (up to ∼11,000).

Reported ages for emerald deposits have dominantly been obtained from the ⁴⁰K-⁴⁰Ar or ⁴⁰Ar-³⁹Ar ages of coexisting micas (Cheilletz et al., 1993

Cheilletz, A., Feraud, G., Giuliani, G., Ruffet, G. (1993) Emerald dating through ⁴⁰Ar/³⁹Ar step-heating and laser spot analysis of syngenetic phlogopite. Earth and Planetary Science Letters 120, 473–485. https://doi.org/10.1016/0012-821X(93)90258-B

; Svadlenak, 2015

Svadlenak, E. (2015) ⁴⁰Ar/³⁹Ar Ages and Trace Element Variations in Colombian Emeralds. [Honors Baccalaureate Thesis], Corvallis, Oregon State University.

) (Fig. 1a), not of the emeralds themselves. Given the often polymetamorphic nature of emerald deposits, such ages may only represent the minimum age for emerald mineralisation. For the presumed oldest emerald deposit in the world, Gravelotte-Leydsdorp (henceforth Gravelotte), South Africa, the assumed age of ∼2.97 Ga comes from indirect U-Pb zircon dating of associated rocks (Poujol, 2001

Poujol, M. (2001) U-Pb isotopic evidence for episodic granitoid emplacement in the Murchison greenstone belt, South Africa. Journal of African Earth Sciences 33, 155–163. https://doi.org/10.1016/S0899-5362(01)90096-X

; Lum et al., 2016

Lum, J.E., Viljoen, K.S., Cairncross, B. (2016) Mineralogical and geochemical characteristics of emeralds from the Leydsdorp area, South Africa. South African Journal of Geology 119, 2, 359–378. https://doi.org/10.2113/gssajg.119.2.359

). Gravelotte emeralds have been shown to have geochemical signatures consistent with an S-type granite protolith (Alonso-Perez and Day, 2021

Alonso-Perez, R., Day, J.M.D. (2021) Rare earth element and incompatible trace element abundances in emeralds reveal their formation environments. Minerals 11, 513, 1–21. https://doi.org/10.3390/min11050513

). Their association with the Pan-African metamorphic belt and other emeralds with similar compositions in Zambia and Madagascar may indicate that they date to only ∼900 to 600 Ma (Rino et al., 2008

Rino, S., Kon, Y., Sato, W., Maruyama, S., Santosh, M., Zhao, D. (2008) The Grenvillian and Pan-African orogens: World’s largest orogenies through geologic time, and their implications on the origin of superplume. Gondwana Research 14, 51–72. https://doi.org/10.1016/j.gr.2008.01.001

). To determine if Gravelotte emeralds are indeed Archean in age, we report Rb-Sr isotope systematics and trace element abundances for them, as well as for the younger Muzo deposit in Colombia. An Archean age for Gravelotte emeralds would indicate that collisional tectonics and hydrothermal alteration of the continental crust was taking place at ∼3 Ga.

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Samples and Methods

Eight cut Gravelotte emeralds (GE-1 to GE-8) were analysed and all showed dark inclusions (Fig. 1c, Supplementary Information), likely biotite that is abundant in Gravelotte emeralds (Lum et al., 2016

Lum, J.E., Viljoen, K.S., Cairncross, B. (2016) Mineralogical and geochemical characteristics of emeralds from the Leydsdorp area, South Africa. South African Journal of Geology 119, 2, 359–378. https://doi.org/10.2113/gssajg.119.2.359

). In addition, two samples from the same lot of uncut emeralds from the Muzo deposit, Colombia, were analysed (MGMH#97472-1 and MGMH#97472-2; Fig. 1b). Samples were digested using protocols outlined previously in Alonso Perez and Day (2021)

Alonso-Perez, R., Day, J.M.D. (2021) Rare earth element and incompatible trace element abundances in emeralds reveal their formation environments. Minerals 11, 513, 1–21. https://doi.org/10.3390/min11050513

at the Scripps Isotope Geochemistry Laboratory (SIGL, Scripps Institution of Oceanography). Digestions necessarily integrated the trace element and Rb-Sr isotopic signatures of the inclusions and their emerald lattices. A sample solution aliquot was analysed for major and trace element concentrations. Strontium separation chemistry was then performed using a two-step column chromatography procedure, after which purified Sr cuts were run on a ThermoScientific Triton thermal ionisation mass spectrometer at the SIGL. Details of the analytical methods and samples are provided in the Supplementary Information.

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Results

Major and trace element abundances and ⁸⁷Rb-⁸⁷Sr data are reported in Tables 1 and S-1 and the abundance data are consistent with those previously reported for their respective deposits (Alonso-Perez and Day, 2021

Alonso-Perez, R., Day, J.M.D. (2021) Rare earth element and incompatible trace element abundances in emeralds reveal their formation environments. Minerals 11, 513, 1–21. https://doi.org/10.3390/min11050513

) (Fig. 2). Gravelotte samples GE-1 through GE-5 have broadly similar REE patterns (normalised to continental crust, CC) with variable negative Ce anomalies, high La/Yb_CC (1.9 ± 1.1) and low Ho/Yb_CC (0.57 ± 0.19), consistent with their classification as Type IA emeralds (Alonso-Perez and Day, 2021

Alonso-Perez, R., Day, J.M.D. (2021) Rare earth element and incompatible trace element abundances in emeralds reveal their formation environments. Minerals 11, 513, 1–21. https://doi.org/10.3390/min11050513

). Emeralds GE-6 and GE-8 have flatter REE patterns with similar Ho/Yb_CC (0.46 ± 0.14) but lower La/Yb_CC (0.56 ± 0.12), and GE-7 is distinct in having elevated LREE/HREE (La/Yb_CC = 22; Ho/Yb_CC = 1). Samples GE-7 and GE-8 are heavily included, with dark fracture-filling material (Supplementary Information).

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Sample	Rb (μg/g)	Sr (μg/g)	87Rb/86Sr	2 s.d.	87Sr/86Sr	2 s.e.	(87Sr/86Sr)700 Ma	(87Sr/86Sr)2960 Ma
GE-1	8.62	1.10	24.5	1.7	1.867963	0.000029	1.63	0.85
GE-2	1.99	0.26	25.0	1.8	2.272476	0.000066	2.03	1.23
GE-3a	8.19	0.87	29.0	2.0	1.685235	0.000016	1.41	0.48
GE-3b	11.8	3.87	9.07	0.6	1.249522	0.000020	1.16	0.87
GE-3c	14.1	2.73	15.6	1.1	1.473472	0.000048	1.32	0.82
GE-3d	12.0	2.32	15.6	1.1	1.373425	0.000014	1.22	0.73
GE-3e	12.8	3.56	10.7	0.8	1.281804	0.000010	1.18	0.84
GE-4	10.4	0.37	102	7.2	3.68916	0.00057	2.71	−0.54
GE-5	10.7	0.73	49.5	3.5	2.67065	0.00012	2.19	0.61
GE-6	0.52	0.08	30.1	2.1	8.1644	0.0071	7.87	6.91
GE-7	0.83	0.09	38.7	2.7	6.0647	0.0024	5.69	4.46
GE-8	4.69	0.39	49.7	3.5	5.27496	0.00056	4.80	3.21
97472-1	0.28	0.14	5.85	0.4	0.72131	0.00032
97472-2	1.98	0.16	34.4	2.4	0.737875	0.000010
BHVO-2	9.11	396	0.065	0.005	0.703456	0.000005
BHVO-2	9.11	396	0.065	0.005	0.703453	0.000004

Gravelotte emeralds have ⁸⁷Rb/⁸⁶Sr and measured ⁸⁷Sr/⁸⁶Sr from 9.1 to 102 and from 1.25 to 8.16, respectively, more extreme than those for Muzo (⁸⁷Rb/⁸⁶Sr = 5.9–34.4, ⁸⁷Sr/⁸⁶Sr = 0.7213–0.7379). Notably, the Sr concentrations of the samples (0.08–3.87 μg/g) range to higher values than in situ data for global emeralds (0.02–0.11 μg/g; Aurisicchio et al., 2018

Aurisicchio, C., Conte, A.M., Medeghini, L., Ottolini, L., De Vito, C. (2018) Major and trace element geochemistry of emerald from several deposits: Implications for genetic models and classification schemes. Ore Geology Reviews 94, 351–366. https://doi.org/10.1016/j.oregeorev.2018.02.001

), indicating that a significant portion of the measured Sr was likely hosted in inclusions. Published in situ data for Colombian emeralds specifically (0.04–0.10 μg/g Sr; Aurisicchio et al., 2018

Aurisicchio, C., Conte, A.M., Medeghini, L., Ottolini, L., De Vito, C. (2018) Major and trace element geochemistry of emerald from several deposits: Implications for genetic models and classification schemes. Ore Geology Reviews 94, 351–366. https://doi.org/10.1016/j.oregeorev.2018.02.001

) are similarly lower than the new bulk Muzo data (0.14–0.16 μg/g Sr). Inclusion digestion likely also led to the lower Rb/Sr of the studied samples (2–28) compared to in situ Rb/Sr (13–6020; Aurisicchio et al., 2018

Aurisicchio, C., Conte, A.M., Medeghini, L., Ottolini, L., De Vito, C. (2018) Major and trace element geochemistry of emerald from several deposits: Implications for genetic models and classification schemes. Ore Geology Reviews 94, 351–366. https://doi.org/10.1016/j.oregeorev.2018.02.001

). The method employed here integrates the inclusions and emerald lattices and assumes that any inclusions are cogenetic with the emeralds.

Assuming similar origins for the Muzo and proximal Peñas Blancas deposits (Vidal et al., 1992

Vidal, Ph., Lasnier, B., Poirot, J.-P. (1992) Determination of the age and origin of emeralds using rubidium-strontium analysis. Journal of Gemmology 23, 198–200. https://doi.org/10.15506/JoG.1992.23.4.198

), these samples plot on an isochron (MSWD = 1.6) with an age of 48.7 ± 3.2 Ma and ⁸⁷Sr/⁸⁶Sr_i = 0.71724 ± 0.00057 (Fig. 3c). The Gravelotte data do not plot on a single isochron. Samples GE-1, GE-2, GE-3a–e, GE-4 and GE-5 show a positive correlation between ⁸⁷Rb/⁸⁶Sr and ⁸⁷Sr/⁸⁶Sr, whereas GE-6, GE-7 and GE-8 show extremely radiogenic ⁸⁷Sr/⁸⁶Sr ratios (5.27–8.16) and only moderate ⁸⁷Rb/⁸⁶Sr (30–50), plotting away from the other samples. The spatial relationships between these three emeralds and the other samples within the deposit are unknown. Excluding the anomalous emeralds (GE-6–8) on the basis of their distinct low-Al contents and REE patterns yields an errochron (MSWD = 11) with an age of 2883 ± 131 Ma and (⁸⁷Sr/⁸⁶Sr)_i = 0.841 ± 0.031 (Fig. 3b).

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Discussion

Dating emeralds using Rb-Sr isotope systematics. Emeralds extend to high ⁸⁷Sr/⁸⁶Sr (>65; Vidal et al., 1992

Vidal, Ph., Lasnier, B., Poirot, J.-P. (1992) Determination of the age and origin of emeralds using rubidium-strontium analysis. Journal of Gemmology 23, 198–200. https://doi.org/10.15506/JoG.1992.23.4.198

) due to the greater affinity of Rb over Sr for beryl and the Precambrian ages of some samples, making the ⁸⁷Rb-⁸⁷Sr system useful for dating their mineralisation. The newly reported data facilitate the first direct dating of the Gravelotte emerald deposit and offers age constraints on the economically important Colombian Western Emerald Zone.

Gravelotte samples GE-6, GE-7 and GE-8 have radiogenic Sr contents that are unsupported by their ⁸⁷Rb/⁸⁶Sr values. On the 1/Sr versus ⁸⁷Sr/⁸⁶Sr plot (Fig. 3a), these samples have the lowest Sr contents and highest Sr isotopic compositions of the data set. These three samples also have low, non-stochiometric Al₂O₃ contents (4.7–7.4 wt. %), indicating that they likely contain significant fractions of low-Al fluid and mineral inclusions, and so may have been susceptible to resetting. For the three samples to have been displaced from the isochron, they must have lost 83 % (GE-6), 70 % (GE-7), and 54 % (GE-8) of their Rb or gained radiogenic Sr. Rubidium is likely hosted either in saline fluid inclusions or within the channels formed by the beryl structure (Groat et al., 2008

Groat, L.A., Giuliani, G., Marshall, D.D., Turner, D. (2008) Emerald deposits and occurrences: A review. Ore Geology Reviews 34, 87–112. https://doi.org/10.1016/j.oregeorev.2007.09.003

). Consequently, emerald Sr isotopic compositions may be susceptible to metamorphic disturbance. The non-coherence of GE-6, GE-7 and GE-8 indicates that analyses of closely associated crystals within a deposit will be beneficial in future studies. Such Rb-Sr isotopic disturbances may also be useful for examining metamorphic heating events affecting emeralds. In the case of Gravelotte, GE-6, GE-7 and GE-8 do not yield meaningful ages, but, assuming Rb loss rather than ⁸⁷Sr gain, their high measured ⁸⁷Sr/⁸⁶Sr values might suggest relatively recent, rather than ancient, disturbances. These samples are excluded from further discussion of ages.

Archean Gravelotte emeralds. The remaining undisturbed Gravelotte samples yield a nine-point errorchron (MSWD = 11) with an age of 2883 ± 131 Ma and a radiogenic initial ⁸⁷Sr/⁸⁶Sr of 0.841 ± 0.031 (Fig. 3b). Although the high MSWD indicates additional uncertainty on the age, the measured initial ⁸⁷Sr/⁸⁶Sr of the samples lies within the permissible range of Archean continental crust (Table 1). The scatter of the data is likely due to ⁸⁷Sr/⁸⁶Sr heterogeneity at the time of deposit formation and possible minor isotopic disequilibrium between Sr-rich inclusions and the emerald lattice during mineralisation. The errorchron age is within the uncertainties of the 2.969 Ga age of coexisting pegmatites (Poujol, 2001

Poujol, M. (2001) U-Pb isotopic evidence for episodic granitoid emplacement in the Murchison greenstone belt, South Africa. Journal of African Earth Sciences 33, 155–163. https://doi.org/10.1016/S0899-5362(01)90096-X

). This Archean ⁸⁷Rb-⁸⁷Sr age confirms that the Gravelotte deposit was formed in the Archean, and not by regional metamorphism during the Pan-African Orogeny ∼900–600 Ma because the initial ⁸⁷Sr/⁸⁶Sr ratios are too radiogenic at 700 Ma (1.16–2.71) to be sourced from reasonable crustal protoliths. This age confirms that emerald formation, and corresponding extensive fractionation and alteration of the CC, was occurring in the Archean.

Rubidium-strontium isotopes in Colombian emeralds. Only two Muzo samples were measured, but Vidal et al. (1992)

Vidal, Ph., Lasnier, B., Poirot, J.-P. (1992) Determination of the age and origin of emeralds using rubidium-strontium analysis. Journal of Gemmology 23, 198–200. https://doi.org/10.15506/JoG.1992.23.4.198

measured Rb-Sr isotopes in samples from the Peñas Blancas deposit, also in the Colombian Western Emerald Zone. The combined isochron (MSWD = 1.6) for both deposits yields an age of 48.7 ± 3.2 Ma with ⁸⁷Sr/⁸⁶Sr_i = 0.71724 ± 0.00057 (Fig. 3c). This age is intermediate between the two groups of Muzo muscovite Ar-Ar ages at ∼62 Ma and ∼30 Ma (Svadlenak, 2015

Svadlenak, E. (2015) ⁴⁰Ar/³⁹Ar Ages and Trace Element Variations in Colombian Emeralds. [Honors Baccalaureate Thesis], Corvallis, Oregon State University.

), and younger than the ⁸⁷Rb-⁸⁷Sr age of the Peñas Blancas deposit alone (∼61 ± 5 Ma; Vidal et al., 1992

Vidal, Ph., Lasnier, B., Poirot, J.-P. (1992) Determination of the age and origin of emeralds using rubidium-strontium analysis. Journal of Gemmology 23, 198–200. https://doi.org/10.15506/JoG.1992.23.4.198

), suggesting the recent disturbance of the Muzo deposit but not the Peñas Blancas deposit. This is consistent with Muzo sample 97472-2 plotting to the right of the isochron (within the error envelope), indicating the possible late gain of Rb at ∼30 Ma (Fig. 3c). There is a need for further Rb-Sr isotope dating of individual Colombian crystals and associated minerals, especially as it is currently unknown if Peñas Blancas and Muzo emeralds formed contemporaneously from isotopically similar fluids. Furthermore, the Eastern Emerald Zone deposits of Colombia have more coherent muscovite Ar-Ar ages (65–60 Ma; Svadlenak, 2015

Svadlenak, E. (2015) ⁴⁰Ar/³⁹Ar Ages and Trace Element Variations in Colombian Emeralds. [Honors Baccalaureate Thesis], Corvallis, Oregon State University.

) and are therefore important targets for ⁸⁷Rb-⁸⁷Sr dating.

Using ⁸⁷Sr/⁸⁶Sr in emeralds to understand geological processes. Initial Sr isotopic compositions can reveal information on the sources of studied materials. In the case of the Gravelotte and Colombian Western Emerald Zone deposits, the age differences are matched by differences in ⁸⁷Sr/⁸⁶Sr_i. For the Colombian emeralds, the initial ⁸⁷Sr/⁸⁶Sr of 0.71724 is more radiogenic than typical Andean Northern Volcanic Zone lavas (∼0.7045; e.g., Errazuriz-Henao et al., 2019

Errazuriz-Henao, C., Gomez-Tuena, A., Duque-Trujillo, J., Weber, M. (2019) The role of subducted sediments in the formation of intermediate mantle-derived magmas from the Northern Colombian Andes. Lithos, 336–337, 151–168. https://doi.org/10.1016/j.lithos.2019.04.007

), but falls within the range of Colombian plutonic rocks (0.7165–0.778; McCourt et al., 1984

McCourt, W.J., Aspden, J.A., Brook, M. (1984) New geological and geochronological data from the Colombian Andes: continental growth by multiple accretion. Journal of the Geological Society 141, 831–845. https://doi.org/10.1144/gsjgs.141.5.0831

). The fluids that formed the Western Emerald Zone deposit were therefore likely sourced from the local CC, consistent with previous conclusions (Ottaway et al., 1994

Ottaway, T.L., Wicks, F.J., Bryndzia, L.T., Kyser, T.K., Spooner E.T.C. (1994) Formation of the Muzo hydrothermal emerald deposit in Colombia. Nature 369, 552–554. https://doi.org/10.1038/369552a0

). The Muzo CC-like REE patterns and initial Sr isotope compositions therefore support the ultimate derivation of those sediments from uplifted and eroded basement rocks.

In contrast with Colombian emeralds, the South African Gravelotte emeralds are characterised by high ⁸⁷Sr/⁸⁶Sr_i of ∼0.841 ± 0.031, more radiogenic than the average values of 3 Ga CC, which only range up to ∼0.73 (Goldstein, 1988

Goldstein, S.L. (1988) Decoupled evolution of Nd and Sr isotopes in the continental crust and the mantle. Nature 336, 733–738. https://doi.org/10.1038/336733a0

). The ⁸⁷Sr/⁸⁶Sr_i values of gneisses and plutons from the Barberton Greenstone belt, also in the Kaapvaal Craton but unrelated to Gravelotte, range from 0.7011 (3.35 Ga Barberton granodiorites) to 0.88 in younger (2.24 ± 0.36 Ga) Kaapvaal Craton Nhlangano gneisses (Barton et al., 1983

Barton Jr., J.M., Hunter, D.R., Jackson, M.P.A., Wilson, A.C. (1983) Geochronologic and Sr-isotopic studies of certain units in the Barberton granite-greenstone terrane, Swaziland. South African Journal of Geology 86, 71–80.

). Critically, some of the older plutons have high Rb/Sr (>10). These comparisons indicate that Gravelotte ⁸⁷Sr/⁸⁶Sr_i values are not unreasonable. Such conclusions await data on cogenetic rocks from Gravelotte. Both the likely presence of highly differentiated lithologies at Gravelotte at 3 Ga and the inferred presence of pre-existing ancient high-Rb/Sr material supports the formation of mature CC-like rocks by the Mesoarchean at the latest.

It has previously been shown that Gravelotte emeralds show an upturned HREE pattern diagnostic of emeralds from Type IA deposits, e.g., those associated with sediment melting during continent-continent collision (Alonso-Perez and Day, 2021

Alonso-Perez, R., Day, J.M.D. (2021) Rare earth element and incompatible trace element abundances in emeralds reveal their formation environments. Minerals 11, 513, 1–21. https://doi.org/10.3390/min11050513

). Our results for the Gravelotte emeralds confirm an Archean heritage, supporting the melting of S-type protoliths in the Mesoarchean and the concept that emerald geochemistry is useful for understanding collisional tectonics and plate tectonic processes (Alonso-Perez and Day, 2021

Alonso-Perez, R., Day, J.M.D. (2021) Rare earth element and incompatible trace element abundances in emeralds reveal their formation environments. Minerals 11, 513, 1–21. https://doi.org/10.3390/min11050513

).

In conclusion, new Rb-Sr isotope data show that Gravelotte is the oldest known emerald deposit and indicates that pegmatite formation was occurring at ∼3 Ga. Fluid inclusion-rich, high-Rb/Sr emeralds lost significant Rb in a later thermal metamorphic event after the in-growth of significant quantities of ⁸⁷Sr. This conclusion awaits further work on the diffusion of Sr and Rb in the beryl structure. Future Sr isotope studies, either in situ or of bulk emeralds isolated from their inclusions, are a necessary step in proliferating the use of the Rb-Sr isotope system in understanding beryl genesis. Given the ability of the Rb-Sr isotope system to directly date emerald mineralisation, more global deposits should be targeted. The Archean age and radiogenic ⁸⁷Sr/⁸⁶Sr_i value of the Gravelotte deposit suggests that emerald deposits in Precambrian terranes may be underexplored.

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Acknowledgements

Financial support for this work came from the Scripps Institution of Oceanography and the Mineralogical and Geological Museum, Harvard University (MGMH). We are grateful to S. and A. Pouroulis for their generous provision of samples and excellent knowledge of the Gravelotte deposit. This work was improved by comments from reviewers Elis Hoffmann and Rainer Thomas, editor Horst Marschall and the earlier comments of David Chew.

Editor: Horst R. Marschall

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References

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Supplementary Information

The Supplementary Information includes:

Supplementary Text

Table S-1

Figures S-1 to S-6

Supplementary Information References

Download the Supplementary Information (PDF).