Towards a structural model for the viscosity of geological melts

Earth and Planetary Science Letters 501 (2018) 202–212

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Earth and Planetary Science Letters www.elsevier.com/locate/epsl

Towards a structural model for the viscosity of geological melts D. Giordano a,∗ , J.K. Russell b a b

Earth Sciences Department, University of Turin, Via Valperga Caluso, 35, 10125 Turin, Italy Earth, Ocean & Atmospheric Sciences, The University of British Columbia, Vancouver, British Columbia, V6T 1Z4, Canada

a r t i c l e

i n f o

Article history: Received 9 February 2018 Received in revised form 7 August 2018 Accepted 17 August 2018 Available online xxxx Editor: T.A. Mather Keywords: viscosity silicate-melt structure Raman model volcanology

a b s t r a c t The viscosity of silicate melts is the most important physical property governing magma transport and eruption dynamics. This macroscopic property is controlled by composition and temperature but ultimately reflects the structural organization of the melt operating at the microscale. At present, there is no explicit relationship connecting viscosity to silicate melt structure and vice versa. Here, we use a single Raman spectroscopic parameter, indicative of melt structure, to accurately forecast the viscosity of natural, multicomponent silicate melts from spectroscopic measurements on glasses preserved on Earth and other planets. The Raman parameter is taken as the ratio of low and high frequency vibrational bands from the silicate glass by employing a green source laser wavelength of 514.5 nm (R 514.5 ). Our model is based on an empirical linkage between R 514.5 and coefficients in the Vogel–Fulcher–Tammann function for the temperature dependence of melt viscosity. The calibration of the Raman-based model for melt viscosity is based on 413 high-temperature measurements of viscosity on 23 melt compositions for which published Raman spectra are available. The empirical model obviates the need for chemical measurement of glass compositions, thereby, providing new opportunities for tracking physical and thermochemical properties of melts during igneous processes (e.g., differentiation, mixing, assimilation). Furthermore, our model serves as a milepost for the future use of Raman spectral data for predicting transport (and calorimetric) properties of natural melts at geological conditions (e.g., volatiles and pressure) and production. © 2018 Elsevier B.V. All rights reserved.

1. Introduction The viscosity of silicate melts is one of the most important physical properties governing magma transport and eruption dynamics. The viscosity (η ) of natural silicate melts spans at least 16 orders of magnitude (10−2 to 1014 Pa s) reflecting the pronounced effects of temperature (T ) and chemical composition ( X ). The effect of temperature is, itself, dependent on melt composition, and silicate melts can show nearly Arrhenian (strong melts) or strongly non-Arrhenian (fragile) behaviour (Toplis, 1998; Toplis et al., 1997; Russell et al., 2003). The accurate prediction of silicate melt viscosity as a function of geological conditions (T and X ) is of paramount importance for modelling and understanding magmatic and volcanic processes. Laboratory measurements have explored and elucidated the viscosity of silicate melts over virtually the full range of compositions and temperatures found on Earth (Giordano et al., 2008). The data have supported development of new models of melt

*

Corresponding author. E-mail address: [email protected] (D. Giordano).

https://doi.org/10.1016/j.epsl.2018.08.031 0012-821X/© 2018 Elsevier B.V. All rights reserved.

viscosity (Table 1) that have different capacities for extrapolation and for prediction of other transport properties (e.g., Shaw, 1972; Bottinga and Weil, 1972; Russell and Giordano, 2005; Giordano and Russell, 2007; Hui and Zhang, 2007; Giordano et al., 2008; Whittington et al., 2009; Sehlke and Whittington, 2016). The majority of these models are purely empirical calibrations of viscosity measurements against the chemical composition of the melt and have no direct connection to melt structure. Ultimately, viscosity is a macroscopic manifestation of the molecular structure and organization of the melt and is controlled by the degree and nature of polymerization (Bockris and Lowe, 1954; Lacy, 1965; Mysen et al., 1982). Providing a structural basis for predicting melt viscosity remains a seminal challenge in Earth Sciences (Richet and Bottinga, 1986, 1995; Richet and Neuville, 1992; Giordano et al., 2008). In simple chemical systems, the physical–chemical and transport properties are shown to be tied directly to melt structural properties (Bockris and Lowe, 1954; Lacy, 1965; Mysen et al., 1982; McMillan and Wolf, 1984; Bykov et al., 2009). Recently for example, Le Losq and Neuville (2017) following the work of others (Mysen, 1995) developed a model for melt viscosity in the simple system SiO2 –Na2 O–K2 O. Their 13-parameters model connects the transport and thermodynamic

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Table 1 Summary of chemical models for geological melts. Model source

Description

Modela

Melts (N)

Data (N)

Parameters

Shaw (1972) Bottinga and Weill (1972) Persikov (1991) Baker (1996) Hess and Dingwell (1996) Giordano and Dingwell (2003) Russell and Giordano (2005) Giordano and Russell (2007) Hui and Zhang (2007) Giordano et al. (2008) Ardia et al. (2008) Whittington et al. (2009) Sehlke and Whittington (2016)

Multicomponent, hydrous Multicomponent Multicomponent, hydrous Granite melt, hydrous Rhyolites, hydrous Multicomponent anhydrous An–Di–Ab system, anhydrous CMAS system, anhydrous Multicomponent, hydrous Multicomponent, hydrous Rhyolite, hydrous Dacite, hydrous Planetary tholeiite basalt

A A A (+P) NA, AG NA NA, VFT NA, VFT NA, VFT NA NA, VFT NA, VFT (+P) NA, VFT NA, AG

– – – 1 (+H2 O) 1 (+H2 O) 19 40 105 99 178 1 (+H2 O) 1 (+H2 O) 20

120 2440 – 34 111 350 585 968 1451 1770 374 76 496

25 ∼34 – 6 6 10 13 11 37 17 6 6 13

a

Abbreviations include: Arrhenian (A), Non-Arrhenian (NA), Pressure (P), Adam–Gibbs (AG), Vogel–Fulcher–Tammann (VFT).

properties of these simple melts explicitly to the structural state of the melt expressed via the abundances of Qn -species recovered from Raman spectral analysis of the glasses. Future progress in modelling the viscosity of multicomponent melts depends on our capacity to integrate the structural properties of melts into predictive models. Here, we present a first-order predictive model for melt viscosity based on a single parameter calculated from Raman spectra measured on the corresponding glasses. The intensity of different Raman lines relates to the identity and abundance of structural species in the glasses and, thus, informs on melt structural properties. On this basis, our empirical model explicitly links the structural properties of the multicomponent glasses to the viscosity of their corresponding melts. Furthermore, this preliminary model suggests an alternative means of predicting or calculating melt viscosity that does not require chemical analysis of the melt’s composition. The ability to estimate melt viscosity from a single Raman spectroscopic measurement of quenched glasses provides new opportunities to track the physical properties of melts (e.g. viscosity) throughout volcanological and petrological processes. For example, the proposed Raman-based viscosity model is ideal for situations where chemical measurements of quenched glasses are not feasible nor possible, or where the research questions require very large numbers of measurements or a continuous record of melt/glass compositions. 2. Experimental database We have compiled data on anhydrous silicate melts for which: i) compositions are known, ii) multiple viscosity–T (K) pairs are measured, and for which iii) published Raman spectral ratios are available (Table A1, Supplementary material). The data include 413 viscosity measurements on 23 melt compositions spanning most of the compositional range of natural terrestrial melts including: subalkaline, calc-alkaline, alkaline, and peralkaline melts (Fig. 1; Inset). The measured viscosities range from ∼10−0.2 to 1012 Pa s over a temperature interval of ∼600 to 1650 ◦ C (Fig. 1). We have also compiled published ratios of the intensities of Raman spectra collected for glasses (Mercier et al., 2009, 2010) produced by quenching of the same 23 melts (Supplementary Table A1). Combined, this is the widest compositional range of melts for which the temperature dependence of viscosity is measured and the Raman spectra for the corresponding glass are measured. The database derives from >10 published papers (see Supplementary Table A1) and provides a basis for exploring the correlations between melt structures and physical properties. 3. Raman spectral analysis of glasses Raman spectroscopy is a versatile non-destructive technique for probing the short-range structure of glasses and melts. Ra-

Fig. 1. Summary of data used in predictive model for melt viscosity based on Raman spectroscopic data. The suite of 413 measured values of melt viscosity for 23 multicomponent melts plotted against a reciprocal temperature T (K) spanning super-liquidus to near glass transition temperatures. The data illustrate the extreme range in melt viscosity arising from variations in T and composition. Inset is alkalies vs. SiO2 diagram showing compositional range of the 23 melts.

man spectroscopy has a high-spatial resolution of 1–2 μm2 but can also analyze large km-size targets (cf. Angel et al., 2012). Comprehensive reviews of the use of Raman spectroscopy in the earth and planetary sciences are provided by Simon et al. (2003), Tarcea et al. (2008), Rossano and Mysen (2012), and Angel et al. (2012). These reviews illustrate the broad range of applications of Raman spectroscopy for studying any optically accessible sample. Raman spectroscopy is also being used for in-situ measurements of glasses at high temperature and pressure and has the potential for remote use on planetary surfaces (e.g., Simon et al., 2003; Sharma et al., 2010; Klein et al., 2004; Malfait, 2018). Raman analysis involves relatively straightforward sample preparation and portable, miniaturized Raman spectrometers are now becoming available (e.g. Popp et al., 2002). Raman is highly suitable for studying natural glassy products (e.g., volcanic ash, pumice, scoria or obsidian) and has been used to estimate volatile contents and extents of iron oxidation in volcanic glasses (e.g., Mercier et al., 2009, 2010), and to estimate the composition of multicomponent silicate glasses (e.g. Di Genova et al., 2016). Although, it has not yet been used on molten lava, Sharma et al.’s (2010) work on minerals at high temperature (∼1003 K) and at target distances of ∼9 m, supports that potential. Raman has similar applications in industrial processes involving glassy or molten materials (e.g. Richet et al., 1993; Koroleva, 2017).

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Previous studies of simple and multicomponent melts have shown clear relationships between their macroscopic physical properties and their structure as inferred from Raman spectra (e.g. Le Losq and Neuville, 2017; Malfait, 2018; McMillan, 1984; Mysen, 1999). For anhydrous glasses, such as reported in this work, the low frequency bands (20–1500 cm−1 ) are sensitive to variations in the vibrational density of state for the aluminosilicate framework. These variations depend on the relative contributions of network forming and network modifying cations, which ultimately determine the distribution of BO (bridging oxygen) and NBO (non-bridging oxygen) in the silicate network. Commonly aluminosilicate glasses exhibit two main broad and asymmetric bands in the low frequency region, the first between 150 and 650 cm−1 and the second between 850 and 1250 cm−1 (referred to here as LF and HF, respectively; see Mercier et al., 2009, 2010; Le Losq et al., 2014). Between the LF and HF bands, a third band containing a peak at ∼800 cm−1 is due to rocking of Si in its oxygen cage (T2b vibrational mode of SiO4 tetrahedra) (see McMillan, 1984) and is commonly observed for more polymerized, less fragile (i.e. stronger) melts (e.g., rhyolites). The features of the LF band (150–650 cm−1 ) are due to delocalized vibrations of the aluminosilicate network involving displacement of bridging oxygens in tetrahedral T–O–T linkage (McMillan, 1984). Specifically, the vibrations have been ascribed to either symmetric oxygen stretching of the bent T–O–T linkages, with motion perpendicular to the T–T line, or as symmetric O–T–O angular deformation of the coupled TO4 groups (Galeener and Geissberger, 1983; McMillan and Hess, 1990; Ruiz et al., 2002; Ardia et al., 2014). These vibrations occur in ring structures of polymerized (rhyolite, silica, etc.) glasses, however, upon depolymerization, T– O–T vibrations including depolymerized units (i.e. Q2 , Q3 ) also contribute to this signal in the range of 500–600 cm−1 . The band observed near 490 cm−1 , termed the D1 band, indicates the presence of some proportion of 4-membered rings, while the long tail at lower frequency arises from stretching of O atoms in the 5, 6 or higher membered rings (Galeener, 1982; Le Losq et al., 2014) which form the aluminosilicate framework (Sharma et al., 1981; Mercier et al., 2009, 2010). The LF position shifts towards higher frequency as the target glasses become increasingly depolymerized (more fragile). Irrespective of the detailed interpretations of spectral components within the LF band, there is general agreement that the intensity of the LF frequency band is directly correlated with the degree of polymerization (e.g., Zotov and Keppler, 1998). The HF band corresponds to a broad band system (∼850– 1250 cm−1 ) centred, for the multicomponent melts investigated here, at ∼960 cm−1 . The HF band is the result of symmetric and asymmetric stretching of the (Si, Al)–NBO and (Si, Al)–BO bonds (Mysen et al., 1982; McMillan, 1984). This region is used to explore the symmetric stretching vibration of the TO4 units with 4, 3, 2, 1 and 0 bridging oxygens (Qn species, where n is number of BO).

comprising baseline correction, band deconvolution and band assignment, are fully described in the original published articles from which we compiled the Raman ratio dataset (Di Muro et al., 2006, 2009; Mercier et al., 2009, 2010; see Supplementary Table A1). We also included a single melt (e.g., Lipari_RR) for which the Raman intensity ratio was determined with a 532 nm wavelength light source (i.e. R 532 ; Mercier et al., 2010). We calculated the equivalent R 514.5 values using a linear relationship we established between the ILF /IHF values measured with the two different wavelength light sources (R 514.5 vs. R 532 ; Supplementary Fig. A1). The ratio R 514.5 has been shown to be strongly related to structural chemical parameters such as NBO/T (Mercier et al., 2009, 2010) and SM (Giordano and Dingwell, 2003; Giordano et al., 2009). Both NBO/T and SM, are calculated from chemical composition and recognized as chemical proxies for polymerization and structural organization of silicate glasses and melts. Values of NBO/T and SM calculated for these 23 melt compositions are negatively and non-linearly correlated with the corresponding

4. Raman intensity ratio (R 514.5 ) Raman spectra of silicate glasses have shapes controlled by the structural properties of the glasses which are, themselves, dictated by composition. We follow the work of previous authors (Mercier et al., 2009, 2010; Ardia et al., 2014) and use the ratio of intensities (I) for the two main Raman bands related to glass network vibrations: the lower frequency (LF) band centred at ∼490 cm−1 and the high frequency (HF) band centred at ∼960 cm−1 . All intensities (I) and ratios (ILF /IHF ) were measured using the 514.5 nm wavelength of an argon ion laser (i.e. ratios referred to here as R 514.5 ; Mercier et al., 2009). Detailed descriptions of the analytical conditions, measurement procedures, and the spectral treatment,

Fig. 2. Ratios of green source Raman spectral bands at 514.5 nm wavelength (R 514.5 ) after Mercier et al. (2009, 2010) and chemical proxies for polymerization and structural organization of silicate glasses and melts. (A) Values of R 514.5 plotted against NBO/T and SM values calculated from chemical compositions of the melts. The Raman ratio is negatively and non-linearly correlated to both NBO/T and SM and shows that increasing polymerization in melts and glasses corresponds to lower NBO/T and SM values and high Raman ratios. (B) Raman ratios show positive correlation with SiO2 content reflecting the strong connection between melt structure and chemical proxies for degree of polymerization. Conversely, R 514.5 is negatively correlated to values of melt fragility (m) derived from fitting the viscosity data to the VFT equation.

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measured Raman ratios (Fig. 2). As shown by previous workers (Mercier et al., 2009, 2010; Ardia et al., 2014), increasing polymerization in melts and glasses corresponds to lower NBO/T and SM values and high Raman ratios. The same data are plotted against SiO2 content and melt fragility (m) derived from the measured melt viscosity (Fig. 2). SiO2 is the most important network former and supports polymerization; highly-polymerized melts are strong and have low fragility. As expected, the Raman ratios for these melt compositions are positively correlated with SiO2 content and negatively correlated to melt fragility (Fig. 2B). 5. A Raman-based model for melt viscosity We have developed an empirical model for predicting the temperature and compositional-dependence of silicate melt viscosity using intensity ratio values of R 514.5 . The Vogel–Fulcher–Tammann (VFT) function is used to capture the temperature dependence of viscosity (η ) (e.g., Richet and Neuville, 1992; Hess and Dingwell, 1996; Giordano et al., 2008):

log η = A +

B

Fig. 3. Predictive model for melt viscosity based on Raman spectral ratios. Direct comparison of measured values of log η (N = 413) for 23 multicomponent silicate melts to values predicted by the Raman-based model. Solid symbols are data from sample Ves-G. Dashed lines represent ±0.5 log unit uncertainty in measured values of viscosity (see text).

(1)

T −C

and we treat the coefficients B and C as dependent on the values of R 514.5 (i.e. B R and C R ) assuming: b

2 B R = b1 R 514 .5

The function describing the B R coefficient (Eq. (2)) is positively correlated with R 514.5 (Fig. 4A) whereas C R is negatively correlated (Fig. 4B). The form of the functions used to model B R and C R implies the following:



(2) B R = b1

and c

2 C R = c 1 R 514 .5 + c 3 .

(3)

The form of Eqs. (2) and (3) and the number of adjustable parameters (2, b 1–2 and 3, c 1–3 ) are suggested by the observed covariation between the R 514.5 measurements and the values of B VFT and C VFT derived from fitting Eq. (1) to the log η –T datasets for each melt composition (see below). The variable A (Eq. (1)) is a constant representing the high-T limit to melt viscosity (Russell et al., 2003; Russell and Giordano, 2005) and we adopt a value of −4.55 as estimated previously for multicomponent silicate melts (Giordano et al., 2008). Optimal values for the adjustable parameters (i.e. b1 , b2 , c 1 , c 2 , c 3 ) are obtained by simultaneously fitting the model (i.e. Eqs. (1)–(3)) to 413 measurements of log η –T (K) on 23 anhydrous melt compositions for which there are also published values of R 514.5 (Supplementary Table A1). We have used the optimal b and c values reported in Table 2 and the measured values of R 514.5 to recalculate the original viscosity dataset from: b

log η = A +

2 b1 R 514 .5

c

2 T − c 1 R 514 .5 − c 3

.

(4)

The Raman-based model reproduces the original experimental data very well (Fig. 3). Most viscosities are reproduced to within ±0.5 log units which represents a 3σ (99% confidence) estimate of uncertainty for data compiled from different laboratories and produced on different instruments. Low-temperature, high viscosity measurements are slightly less well reproduced (±0.5–1 log units). Overall, the majority of scatter derives from the high-T , low viscosity measurements for one melt composition (e.g., Ves-G phonolite; Fig. 3). The implication is that our single Raman parameter (R 514.5 ) does an effective job of predicting VFT-parameters (i.e. B R and C R ) accounting for the effects of temperature on melt viscosity (i.e. Eq. (1)).

C R − c3

b2 /c2 .

c1

(5)

The model curve relating B R and C R is calculated for R 514.5 values 0 to 4 and plotted in Fig. 4C (solid line; Eq. (5)). The model line illustrates the strong, negative, induced covariation that arises partly because both B R and C R depend only on the Raman spectral ratio (R 514.5 ). Unique values of B VFT and C VFT derived from fitting viscosity data for each melt composition to Eq. (1) (Table 2) are plotted as symbols in Fig. 4 to compare against the model curve (Eq. (5)). The independently calculated values of B VFT and C VFT produce the same negative covariation (Fig. 4C, symbols vs. solid line). There is also very close agreement between the two sets of values (Fig. 4) indicating that the Raman-based model is recovering similar phenomenological coefficients (i.e. B R and C R ) to those from conventional fitting of VFT functions to viscosity datasets (i.e. B VFT and C VFT ) and vice versa. The Raman-based model uses a single parameter (i.e. R 514.5 ) to predict melt viscosity. The model reproduces the values and the temperature dependence of the original viscosity data well (Figs. 3–4). The model also extrapolates well as indicated by the calculated isothermal viscosity curves (800–1600 ◦ C) plotted as a function of R 514.5 over the full range of melt compositions and for all temperatures greater than the melt’s glass transition temperature (T g) (Fig. 5; solid lines). Corresponding isothermal viscosity values (800–1600 ◦ C) for the 23 melt compositions were calculated using the values of B VFT and C VFT (Table 2). These isothermal viscosity values (Fig. 5; symbols) plot within error of the Ramanbased model isothermal viscosity curves. The grey shaded field (Fig. 5) delineates the model limits and an inaccessible T –R 514.5 space defined by the change in derivatives of the log η –R 514.5 curves. The field corresponds to low values of T and R 514.5 and results from the denominator term in Eq. (1) [T − C R ] approaching c2 zero where C R = c 1 R 514 .5 + c 3 . Given the imposed functional dependence of C R on R 514.5 , the critical limit of R 514.5 for T > C is:

 R Limit <

T − c3 c1

1/c2 .

(6)

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We have compared the model values of B R and C R to the corresponding proxies for melt polymerization calculated from the chemical compositions of the melts: SM and NBO/T (Fig. 6). Conceptually, values of B R are representative of the pseudo-activation energy of viscous flow whilst values of C R (the so-called VFTtemperature) relate to the configurational properties of the melt (Richet and Bottinga, 1986, 1995; Russell and Giordano, 2017). Our model values of B R decrease strongly with increasing SM and NBO/T, indicative of lower activation energies associated with viscous flow of increasingly depolymerized (more fragile) melts. Conversely, values of C R increase non-linearly with increasing SM and NBO/T; we expect an increase in configurational properties as melts become increasingly depolymerized. We have also explored the connections between the measured Raman ratios (R 514.5 ) for the 23 glasses, the corresponding chemical proxies for melt structure (i.e. SM and NBO/T), and the model values of B R and C R . Normalized values of B R and C R are plotted against SM (Fig. 6E) and NBO/T (Fig. 6F) showing the same correlations as illustrated in Fig. 6A–D. We have contoured these diagrams for increasing values of R 514.5 . Increasingly depolymerized melts have higher values of SM and NBO/T and correlate with lower values of R 514.5 , lower values of B R and higher C R values. Values of R 514.5 offer a very effective representation of overall structural organization of melts based on its strong covariation with NBO/T and SM. We observe that SM is a slightly more effective chemical proxy for melt structure because it offers greater differentiation between the strong melts (i.e. high values R 514.5 and low values of SM). For example, all strong, highly polymerized melts having values of R 514.5 > 2.5 have NBO/T values of ∼0 whilst SM values vary from 0 to 10 (cf. Fig. 2A and 6E–F).

Fig. 5. Isothermal viscosity (800–1600 ◦ C) predicted for the full range (0–4) of R 514.5 values (solid lines). Values predicted by VFT functions for the same 23 melt compositions are plotted as filled symbols. The shaded field marks an inaccessible space (low values of T (K) and R 514.5 ) where the denominator in Eq. (1) (T –C R ) approaches zero and viscosity goes to infinity. It is delineated by the calculated change in derivatives of the log η –R 514.5 curves.

6. Verification of Raman-based viscosity model Fig. 4. Model VFT parameters B R and C R (Eq. (1)) and measured Raman spectral ratios (R 514.5 ). (A) Model curve (solid line) for B R (Eq. (2)) plotted as a function of R 514.5 . Symbols denote values of B VFT derived independently by fitting viscosity data for each melt to the VFT function. (B) Model function for C R plotted against R 514.5 (Eq. (3)); symbols are independent values of C VFT from fitting individual melts to the VFT function. (C) Model values of B R vs. C R calculated as a function of R 514.5 over the range of values 0–4. Symbols are B VFT and C VFT values calculated as in (A) and (B). In all diagrams the horizontal error bars are 10% uncertainty on R 514.5 ; vertical error bars are the uncertainties propagated onto the model parameter. The dashed lines indicate 95% confidence limits on the model curves.

For comparative purposes, we have used the widely-applied GRD model for the viscosity of geological melts (Giordano et al., 2008) to independently predict the viscosity dataset used to calibrate our Raman-based model. The GRD model is a purely “chemical model” for predicting silicate melt viscosity as a function of composition and temperature. The GRD model comprises 17 adjustable parameters calibrated on ∼2000 data points and reproduces most measured values of melt viscosity (Table 1). The model is parameterized as a function of molar oxide compositions and uses the VFT function for T -dependence. It has been shown to be

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Table 2 Calculated properties of 23 melt compositions used to create the Raman-based model for melt viscosity. Properties include: indices of melt polymerization (i.e. SM, NBO/T); Raman spectral ratios based on green light with different laser wavelengths (the 514.5 nm from Mercier et al., 2009 and the 532 nm from Mercier et al., 2010); VFT coefficients B, C and values of T g and m from this model (see text); corresponding GRD values of B, C , T g and m. Sample name

Rattlesnake Tuff Lipari_RR MDV_snt Mercato1600 PVC MNV AMS_B1 Newberry NYT_lm*13* UNZ MST CI_OF 104 FR_a Pompei TR MRP Ves_W Ves_G Min_2b Pollena GM ETN Ves_Gt NYI EIF Min Max a b

SM

8.12 9.22 8.98 17.15 14.47 15.23 17.35 10.17 18.86 16.86 19.69 16.01 22.22 23.49 25.23 24.15 24.50 25.58 29.77 31.22 31.15 35.92 43.61

NBO/T

0.00 0.01 0.05 0.05 0.06 0.07 0.10 0.02 0.12 0.14 0.15 0.16 0.19 0.23 0.26 0.26 0.28 0.30 0.44 0.51 0.53 0.73 1.16

Raman spectral ratiosa

VFT values ( A = −4.48)

Green.532

Green.514.5

B

C

T g (K)

m

B

C

T g (K)

m

B

C

T g (K)

m

4.67 4.3

0.29

3.25 2.90 2.83 1.75 1.86 1.61 1.31 2.5 1.16 1.41 1.1 1.38 0.74 1.08 0.8 0.77 0.61 0.77 0.65 0.48 0.55 0.25 0.29

12095.9 11592.9 11421.4 9927.1 10393.0 10304.8 10308.9 12056.9 8244.6 8247.4 7695.1 9452.3 7151.1 7829.8 6579.2 8100.7 8319.8 6861.0 6167.3 5477.4 6201.8 4911.2 4476.3

355.2 337.2 370.1 322.8 316.5 303.3 305.8 245.7 474.2 479.3 484.9 421.8 537.0 446.1 554.2 434.1 436.7 510.7 568.8 629.0 570.2 643.5 671.8

1089 1041 1063 925 947 929 931 977 974 980 952 995 971 921 953 926 942 927 943 961 947 941 943

24.5 24.4 25.3 25.3 24.8 24.5 24.5 22.0 32.1 32.3 33.6 28.6 36.9 32.0 39.4 31.0 30.7 36.7 41.5 47.7 41.5 52.1 57.2

13051.4 12459.9 12336.6 10144.5 10399.3 9806.0 9016.5 11729.5 8581.1 9290.6 8397.6 9209.6 7146.3 8335.1 7376.7 7262.8 6605.9 7262.8 6778.9 5991.9 6333.3 4594.7 4880.8

222.0 247.7 253.2 354.6 342.3 371.2 410.8 280.4 433.4 396.9 443.0 401.0 511.8 446.4 498.7 505.1 543.2 505.1 533.0 580.3 559.4 672.2 652.4

1011 1001 999 968 971 964 956 989 952 958 950 957 944 950 944 944 942 944 943 942 942 950 947

21.2 22.0 22.2 26.1 25.6 26.9 29.0 23.1 30.4 28.3 31.0 28.5 36.2 31.2 35.1 35.6 39.1 35.6 38.1 43.1 40.7 56.6 53.2

11859.5 11478.8 11708.8 9723.1 10158.4 9978.6 9401.8 11066.8 8702.5 8988.0 7573.4 10020.1 7482.3 8142.0 6287.5 7838.2 7850.4 6800.3 6593.7 5557.4 6256.3 5506.6 4456.9

302.1 294.9 370.3 354.5 330.7 341.8 385.5 323.5 443.1 436.6 522.3 354.5 503.8 460.2 578.1 475.7 472.5 541.7 550.0 600.5 564.9 584.6 669.0

1019 988 1078 942 944 945 954 992 969 980 980 960 956 952 958 949 947 953 948 936 943 917 938

23.5 23.6 25.2 26.5 25.5 25.9 27.8 24.6 30.5 29.9 35.4 26.2 35.0 32.0 41.7 33.2 33.0 38.4 39.4 46.1 41.3 45.6 57.7

0.3 4.7

0.3 3.3

4476 12096

246 672

921 1089

22 57

4595 13051

222 672

942 1011

21 57

4457 11860

295 669

917 1078

23.5 57.7

2.49 2.49

1.48 1.83 1.33

1.28 0.92 0.94 0.58 0.80 0.59 0.56

Raman modelb ( A = −4.55)

GRD values ( A = −4.55)

Raman parameters are from Mercier et al. (2009, 2010). .407 and C = −813.5R 0.2178 + 1273.6. Functions for predicting B and C from Raman spectral ratios (R 514.5 ): B = 8078.1R 0514 .5 514.5

capable of extrapolation beyond the limits of the original data in, both, pressure, temperature and composition (e.g. Chevrel et al., 2014; Ardia et al., 2008). It also predicts other independently verified calorimetric properties including glass transition temperatures, melt fragility, and configurational entropy (Chevrel et al., 2014; Russell and Giordano, 2017). On this basis, it offers an additional test of the relative effectiveness of our Raman-based model. Most importantly, it offers a comparison between an accepted model that uses chemical composition to forecast a transport property vs. a model calibrated on a single parameter that is sensitive to the material’s structural configuration. We have recalculated the viscosity values in the database (N = 413) with our Raman-based model and compared them to values predicted by the GRD model (Fig. 7A). The GRD model reproduces the measured viscosities to an average of ±0.35 log units and the level of misfit for our Raman-based model is essentially the same (Fig. 3). Fig. 7A is designed to show the agreement between the two models in terms of predicting melt viscosity. For this purpose, a soft measure of how well the models agree is provided by comparing the dispersion of data along the 1:1 line to the 3σ uncertainty estimate for the original measurements (i.e. ±0.5 log units). The two models mainly agree to within that tolerance even though they have completely different and independent calibrations. In addition, we note that the calculated values of B GRD and C GRD parallel the Raman-model predicted values of B R and C R (cf. Figs. 4–7B, C). It is worth emphasizing the independence of the computed values of B GRD and C GRD from the GRD model relative to the Raman-based values (Table 2). The values of B GRD and C GRD are explicitly dependent on melt composition (i.e. mol.% oxides) and are calculated solely from the compositions of the melts (see Table 2 in Giordano et al., 2008). The Raman-based values of B R and C R are calculated from the single variable R 514.5 (Table 2; Fig. 4) which is sensitive to the melt’s structural organization rather than its chemical composition. The two models predict melt viscosity

equally well (Fig. 7A) and there is strong correlation between their calculated VFT-parameters (Fig. 7B, C). Additionally, the magnitude and range of B and C values is equal for the two models (Figs. 4, 7B, C). We take this as verification that, although the GRD parameters (B GRD and C GRD ) are modelled as a function of composition (i.e. oxide mol.%), structural and configurational properties are implicitly embedded in them both. 7. Discussion 7.1. Tg, fragility and configurational properties A strong indicator of a model’s integrity is its capacity to predict independent derivative properties such as melt fragility and glass transition temperature (Table 2). Melt fragility, as expressed by the steepness index (m; Plazek and Ngai, 1991; Boehmer et al., 1993), is calculated here as: b

m=

c

2 2 2 b1 R 514 .5 (12 − A ) + (c 1 R 514.5 + c 3 )(12 − A )

b

2 b1 R 514 .5

(7)

and is a property implicit to the T -dependence of melt viscosity. Calculated values of fragility decrease with increasing R 514.5 indicating that low values of R 514.5 associate with fragile melts and high values with strong melts (Fig. 8A, solid lines). Fragility values predicted by the GRD model (mGRD ) parallel our model curve (Fig. 8A, symbols). The agreement is significant because our Raman-based model uses a property that is strongly associated with structure whilst mGRD is predicted from melt composition. There is some discord between fragility values predicted by the two models for the most fragile (i.e. non-Arrhenian) melts at low values of R 514.5 (<0.3). The magnitude of discrepancy between the two models is shown explicitly in the inset to Fig. 8A against

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Fig. 6. Model predictions of VFT parameters B R and C R vs. chemical proxies for melt polymerization, SM and NBO/T. (A, B) B R decreases strongly with increasing SM and NBO/T. (C, D) C R increases non-linearly with increasing SM and NBO/T. (E, F) Normalized values of B R (grey symbols) and C R (black symbols) plotted against SM and NBO/T. Solid lines are trend lines fitted to the 23 individual melt compositions. Vertical solid and dashed lines denote R 514.5 values contoured for 0.5, 1, 1.5, 2, 2.5, 3, 3.5. Increasing values of R 514.5 correlate with decreasing values of SM and NBO/T implying increasing polymerization and structural organization of the melt (see Fig. 2). Strong, highly polymerized melts have NBO/T values ∼0 and R 514.5 values >2.5 (cf. Figs. 2A and 6F).

dashed lines representing model differences up to 10% and may reflect the uncertainties in the measurements made at low values of R 514.5 . Glass transition temperatures (T (K) where η ∼1012 Pa s) predicted by the Raman-based model suggest a 70 K decrease with increasing fragility; GRD calculated values show a parallel decrease (Fig. 8B). In summary, we find the overall agreement between the values of ancillary transport properties predicted by the two mod-

els to be exceptional given that the models have different bases (spectroscopic vs. chemical) and are calibrated on entirely different datasets. The VFT parameters (i.e. A , B , C ; Eq. (1)) can also inform on the thermodynamic configurational properties of the melt at T g (Toplis et al., 1997; Russell and Giordano, 2017). The ratio of configurational heat capacity (Cp c ) and entropy at T g (i.e. S c _ T g ) are

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Fig. 7. Comparison of Raman-based viscosity model to the GRD chemical model. (A) Values predicted by the Raman model (N = 413) are based on measured values of R 514.5 and the measurement temperature. The GRD model computes values of log η from the measured temperature and melt composition. Dashed lines indicate ±0.5 log unit measurement uncertainty (see text). (B, C) Comparison of melt specific VFT parameters B R and C R from the Raman-based model vs. the GRD-model values (B GRD and C GRD ).

computed as (Toplis, 1998; Toplis et al., 1997; Russell and Giordano, 2017):

Cp c S c_T g

=

m 12 − A

− 1.

(8)

The maximum values of Cp c / S c _ T g calculated with the Ramanbased model for viscosity correspond to the most fragile melts and are associated with low values of R 514.5 (Fig. 8C). Strong melts are characterized by lower Cp c / S c _ T g values and feature higher R 514.5 values. On this basis, the Raman-based model connects melt viscosity to its thermodynamic configurational properties which reflect melt structures close to T g (Toplis, 1998; Toplis et al., 1997; Richet and Bottinga, 1986; Richet and Neuville, 1992; Russell and Giordano, 2017). Values of Cp c / S c _ T g predicted from the GRD model, plotted against their corresponding values of R 514.5 , are also consistent with our model trend. The inset to Fig. 8C shows the theoretical linear relationship between Cp c / S c _ T g and m (Eq. (8)); all melts plot on a single line having slope 1/(12 − A ) (Toplis, 1998; Russell and Giordano, 2017). The values predicted by the two models lie on the same theoretical line because of the common value of A; the separation in values (black vs. grey symbols) results from slight differences in the calculated fragility values. 7.2. The connection to melt structural organization This is the first effort to use Raman data for glasses to calculate directly the viscosity of multicomponent silicate melts. One important assumption, which is supported by our results, is that any structural changes occurring as the melts are quenched to super-

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cooled glasses are slight and do not affect the overall partitioning of Qn -species as recorded by the LF and HF bands. The model makes an empirical connection between VFT model parameters and the structural organization of multicomponent silicate melts and also predicts ancillary transport (i.e. m) and thermodynamic (i.e. Cp c / S c _ T g ) properties. Understanding the connection between the structural properties of glasses and viscosity of multicomponent silicate liquids also allows for a connection between their thermodynamic (equilibrium) and transport (kinetic) properties (Richet and Neuville, 1992; Russell and Giordano, 2017; Giordano and Russell, 2017; Le Losq and Neuville, 2017). The implications of this model for understanding how melt structure controls viscosity are significant and our parameterization makes an explicit linkage between multicomponent melt viscosity and structural organization (i.e. polymerization). The question arises: How is it that a single variable (R 514.5 ) and five adjustable parameters is so effective in predicting the temperature dependent viscosity of multicomponent melts? Previous chemical models for multicomponent silicate melt viscosity typically comprise 8 or more chemical components and many (8) adjustable parameters (Table 1; e.g., Shaw, 1972; Bottinga and Weill, 1972; Persikov, 1991; Baker, 1996; Hess and Dingwell, 1996; Giordano and Dingwell, 2003; Russell and Giordano, 2005; Giordano and Russell, 2007; Hui and Zhang, 2007; Giordano et al., 2008; Ardia et al., 2008; Whittington et al., 2009; Sehlke and Whittington, 2016). We suggest that the effectiveness of this simple Raman-based viscosity model emphasizes the importance of structural information, relative to composition, for controlling and predicting melt viscosity. Viscosity, as for most physical properties, is strongly controlled by the melt’s structural organization and, for these melts, our empirical parameter R 514.5 captures the most essential (not necessarily all) structural information. Melt structure does relate to composition, but, the relationship between composition and melt structure is complex. Chemical proxies for melt structure, such as NBO/T (Mysen et al., 1982, 1980) and SM (Giordano and Dingwell, 2003), depend on the concentrations of all major and some minor elements. In order to convey the same level of structural information as captured by R 514.5 , chemical models typically need many more adjustable parameters related to the concentrations of each component. Our approach may not extend to simpler (i.e. 2–3 components) chemical systems (Lacy, 1965; Mysen et al., 1982; Le Losq and Neuville, 2017). In these systems, small chemical changes induce strong structural rearrangements requiring more adjustable parameters to capture these effects (see Le Losq and Neuville, 2017). In multicomponent melts, such as the natural silicate melts that populate our planet, these effects are weak because their structures are less sensitive to small chemical changes. The component H2 O is an exception; small additions of H2 O to strong (i.e. nearArrhenian) multicomponent melts can cause substantial decreases in viscosity, T g, and m, implying significant changes in melt structure (Giordano et al., 2008; Hess and Dingwell, 1996; Di Genova et al., 2014). A logical extension to our Raman-based viscosity model, therefore, is to incorporate data on hydrous multicomponent silicate melts to account for the effects of H2 O. 7.3. Applications: present and future Silicate glasses are found in all geological environments on Earth, the moon and other planets. Raman spectroscopy is a wellestablished technique for characterization of properties of geological melts and molten slags. The methods for measurement of R 514.5 are relatively straightforward and can be performed on all glasses, melts and multiphase materials (e.g. from lava to industrial processes). The relative ease with which Raman spectra can be collected in the lab, in the field, or remotely suggests many

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diverse applications in the earth, planetary, and the industrial sciences (cf. Angel et al., 2012). Our predictive model is robust and works across a wide range of terrestrial melt compositions (Fig. 1) and all temperatures above T g (Fig. 2). The model obviates the need for measurements of melt composition and, thus, can expedite estimations of melt viscosity. Quenched glasses in nature are records of the liquid lines of descent of magmas undergoing differentiation, assimilation, melting, or mixing. In many instances the measurement of the preserved glass compositions is complicated, time consuming, or not possible (e.g., fine scale mingling of melts, melt inclusions) inhibiting our ability to estimate and track the physical properties of the melts. Our Raman-based model offers an alternative means of tracking the physical and thermochemical properties of these melts where individual melt compositions are not easily sampled or measured (e.g., mixed magmas) or where research questions demand very large datasets of melt composition and physical properties. The model may also find application in the monitoring of volcanic eruptions; it could support continuous field-based Raman measurements on quenched volcanic ash or glassy lava to record transient melt properties. Similarly, it may find use in industrial processes where continuous monitoring of melt and glass properties during production is important. In the foreseeable future, it is also reasonable to assume that Raman spectra collected with rover-mounted systems on other planets and moons will encounter preserved glasses (Sharma et al., 2003; Klein et al., 2004). In the absence of large geochemical samples or reliable chemical measurements, our model will allow the Raman spectra to be interrogated for the temperature-dependent viscosity, calorimetric, and thermochemical properties of the original melt. 8. Summary The viscosity of silicate melts is the most important property governing the physical behaviour of most volcanic and magmatic systems. Accurate prediction of melt viscosity across the range of temperatures, compositions, and pressures remains a seminal challenge, notwithstanding the highly-cited model of Giordano et al. (2008). To make the next advances requires parameterization based on structural aspects of the melt (in lieu of chemical composition alone). We have presented a preliminary model for the viscosity of anhydrous silicate liquids that spans the entire range of viscosity and temperature space accessible to experimentalists. Our model is unique. Rather than using chemical composition as the model basis, we use a single measurement derived from Raman spectroscopy data (R 514.5 ) obtained on glasses that serves as a proxy for the structural organization of the silicate melt. The model uses 5 adjustable parameters to convert measurements of R 514.5 to a temperature dependent melt viscosity. The attributes of this unique approach to modelling silicate melt viscosity are:

Fig. 8. Implications of Raman-based viscosity model for transport and structural properties of melts. (A) Values of melt fragility (m) predicted by the Raman-based model (solid line) and by the GRD model for the 23 melt compositions (symbols). Inset directly compares fragility values from the two models; dashed lines are for reference only and indicate model differences of ±10%. (B) Values of T g and fragility predicted as a function of R 514.5 over the range of 0 to 4 (solid line). Symbols denote T g and m values calculated independently with the GRD model for the 23 melt compositions. (C) The ratio Cp c / S c taken at T g predicted by the Ramanbased model (solid line). Symbols are corresponding values predicted by the GRD model for the 23 melt compositions. Inset shows the theoretical linear relationship between Cp c / S c and fragility and values predicted by the Raman-based (grey symbols) and GRD (black symbols) models.

i) its simplicity and predictive power should find extensive future use by the Earth Science (geochemists, volcanologists, planetary scientists and geophysicists), Material Science, and Archeological communities, amongst others; ii) the advent of portable devices makes it feasible to collect Raman spectra from glasses having low crystal contents in the field or remotely on Earth and other planets; iii) the Raman-based model may have potential use in real-time monitoring of physical and thermochemical properties of melts (e.g., monitoring volcanic eruptions, monitoring industrial production); and most importantly; iv) it serves as a milepost for using Raman spectral data, as the basis for modelling the transport (and calorimetric) properties

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of geological melts at geological conditions (e.g., volatiles and pressure). Ultimately, our approach can be extended to incorporate the so far uncalibrated effects of volatile contents, redox conditions, and pressure which would extend the utility of the predictive model significantly. Acknowledgements DG acknowledges research funding from the University of Turin. JKR acknowledges funding from the NSERC Discovery Grants and Discovery Accelerator Supplements programs (P.I. 15841). The clarity of our manuscript and its implications benefited greatly from thorough and critical reviews from two anonymous referees. We also thank the editor Tamsin Mather whose critical comments have helped improve the overall accessibility of our research. Appendix A. Supplementary material Supplementary material related to this article can be found online at https://doi.org/10.1016/j.epsl.2018.08.031. It contains (1) text providing an explanation for our choice of Raman spectra ratios for modelling melt viscosity and illustrating the linear calibration of the Raman spectral ratios R 532 and R 514.5 ; and (2) a spreadsheet containing a compiled database of paired measurements of T (K)–log η , chemical compositions of glasses, and Raman spectral values and calculated ratios. These data were used exclusively to constrain the Raman-based melt viscosity model presented here. References Angel, S.M., Gomer, N.R., Sharma, S.K., McKay, C., 2012. Remote Raman spectroscopy for planetary exploration: a review. Appl. Spectrosc. 66. Ardia, P., Di Muro, A., Giordano, D., Massare, D., Sanchez-Valle, C., Schmidt, M.W., 2014. Densification mechanisms of haplogranite glasses as a function of water content and pressure based on density and Raman data. Geochim. Cosmochim. Acta 138, 158–180. Ardia, P., Giordano, D., Schmidt, M.W., 2008. A model for the viscosity of rhyolite as a function of H2 O-content and pressure. Geochim. Cosmochim. Acta 72, 6103–6123. Baker, D., 1996. Granitic melt viscosities; empirical and configurational entropy models for their calculation. Am. Mineral. 81, 126–134. Bockris, J.O., Lowe, D.C., 1954. Viscosity and structure of molten silicate. Proc. R. Soc. 54, 423–435. Boehmer, R., Ngai, K.L., Angell, C.A., Plazek, D.J., 1993. Non-exponential relaxations in strong and fragile glass formers. J. Chem. Phys. 99, 4201–4209. Bottinga, Y., Weill, D., 1972. The viscosity of magmatic silicate liquids: a model for calculation. Am. J. Sci. 272, 438–475. Bykov, V.N., Koroleva, O.N., Osipov, A.A., 2009. Structure of silicate melts: Raman spectroscopic data and thermodynamic simulation results. Geochem. Int. 47, 1067–1074. Chevrel, M.O., Baratoux, D., Hess, K.U., Dingwell, D.B., 2014. Viscous flow behavior of tholeiitic and alkaline Fe-rich Martian basalts. Geochim. Cosmochim. Acta 124, 348–365. Di Genova, D., Hess, K.U., Chevrel, M.O., Dingwell, D.B., 2016. Models for the estimation of Fe3+ /Fetot ratio in terrestrial and extraterrestrial alkali- and iron-rich silicate glasses using Raman spectroscopy. Am. Mineral. 101, 943–952. Di Genova, D., Romano, C., Giordano, D., Alletti, M., 2014. Heat capacity, configurational heat capacity and fragility of hydrous magmas. Geochim. Cosmochim. Acta 142, 314–333. Di Muro, A., Giordano, D., Villemant, B., Montagnac, G., Romano, C., 2006. Influence of composition and thermal history of volcanic glasses on water content determination by micro-Raman spectrometry. Appl. Geochem. 21, 802–812. Di Muro, A., Métrich, N., Mercier, M., Giordano, D., Massare, D., Montagnac, G., 2009. Micro-Raman determination of iron redox state in dry natural glasses: application to peralkaline rhyolites and basalts. Chem. Geol. 259, 78–88. Galeener, F.L., 1982. Planar rings in vitreous silica. J. Non-Cryst. Solids 49, 53–62. Galeener, F., Geissberger, A., 1983. Vibrational dynamics in 30 Si-substituted vitreous SiO2 . Phys. Rev. B 27 (10), 6199–6204. Giordano, D., Ardia, P., Romano, C., Dingwell, D.B., Di Muro, A., Schmidt, M.W., Mangiacapra, A., Hess, K.-U., 2009. The rheological evolution of alkaline Vesuvius

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