Chemical Geology 320–321 (2012) 140–146

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Chemical Geology

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Research paper

Mixed electrical conduction in a hydrous pantellerite glass

Brent T. Poe a,b,⁎, Claudia Romano c, Danilo Di Genova c, Harald Behrens d, Piergiorgio Scarlato b

a Dipartimento di Ingegneria e Geologia, Università degli Studi “G. d'Annunzio”-Chieti, Italyb Istituto Nazionale di Geofisica e Vulcanologia-Roma, Italyc Dipartimento di Scienze Geologiche, Università degli Studi Roma Tre-Roma, Italyd Institut für Mineralogie, Leibniz Universität, Hannover-Germany

⁎ Corresponding author at: DiGAT, Università degli StuE-mail addresses: poe@ingv.it (B.T. Poe), romano@u

ddigenova@uniroma3.it (D. Di Genova), h.behrens@min(H. Behrens), scarlato@ingv.it (P. Scarlato).

0009-2541/$ – see front matter © 2012 Elsevier B.V. Alldoi:10.1016/j.chemgeo.2012.05.023

a b s t r a c t

a r t i c l e i n f o

Article history:Received 11 January 2012Received in revised form 23 April 2012Accepted 26 May 2012Available online 1 June 2012

Editor: D.B. Dingwell

Keywords:Electrical conductivitySilicate meltsPantellerites

Electrical conductivitymeasurements were carried out on pantelleritic trachyte glasses containing up to 3.5 wt.%dissolved H2O. At temperatures below about 700 K, we find evidence for small polaron conduction due to thepresence of both ferrous and ferric iron in the glass. At the higher temperatures of the investigation (up to973 K), amarked change in the conductivity–temperature relation is observed, which suggests that an ionic con-duction mechanism becomes the dominant means of charge transport. In the ionic conduction regime, conduc-tivity increases with increasing H2O concentration. Activation energies are similar for both the anhydrous andhydrous glasses, indicating that the conductivity is controlled by sodium diffusion even for the highest H2O con-centration examined. A slight variation in activation energy is observed depending on the H2O concentration,which is most likely associated with the depolymerising effect of dissolved water on the silicate network struc-ture. At low temperatures, we find a dramatic effect of fO2 on the conductivity that supports an electronic con-duction mechanism based on small polaron hopping between Fe3+ and Fe2+ sites. This electronic pathwaycontrols the overall electrical conductivity in these alkali-rich glasses at temperatures exceeding 500 °C if condi-tions remain anhydrous at an oxygen fugacity of 0.2 atm.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Ultrasonic velocities in silicate melts vary by approximately 1% per100 K (Rivers and Carmichael, 1987), whereas electrical conductivitymay change by asmuch as a factor of 10 ormore over the same temper-ature range (Tickle, 1967; Presnall et al., 1972; Rai and Manghnani,1977). Because of this high sensitivity, monitoring techniques basedon magnetotellurics and electric self-potential can provide very impor-tant contributions to both the structural modeling and hazard evalua-tion of volcanic systems (Di Mai et al., 1997; Zlotnicki et al., 2003;Aizawa et al., 2005). To be able to interpret the geophysical data gath-ered with these methods, however, our understanding of charge trans-port processes in complex magmatic liquids must improve. Similar tomany observations made for silicate minerals, in which both electronicand ionic conduction may operate (Schock et al., 1989; Romano et al.,2006), electrical conductivity in silicate liquids is strongly dependenton chemical composition. Recent models that attempt to characterizethe conductivity of a silicate liquid (Poe et al., 2008; Pommier and LeTrong, 2011) do not account for the possible changes in the conductionmechanism with changes in temperature. Further, the addition ofdissolved H2O to a silicate liquid may or may not result in protonic

di “G. d'Annunzio”-Chieti, Italy.niroma3.it (C. Romano),eralogie.uni-hannover.de

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conduction to become the dominant charge transport mechanism(Behrens et al., 2002; Gaillard, 2004; Fanara and Behrens, 2011).

In the present study, we have examined silica-rich pantelleriticmelts containing iron, alkali cations, and dissolved water, which giverise to mixed electronic and ionic conduction pathways. Our choice ofa chemically complex natural starting material allows us to determinewhich chemical components are responsible for driving charge trans-port and over which temperature intervals, even in the presence ofminor components, which often can play an important role in the con-ductivity of more ordered systems such as silicate minerals. Moreover,an understanding of geologically relevant silicatemelts and glasses pro-vides the opportunity for interpretation of geophysical observationsand allows constraints to be placed on the dimensions, depth or meltfraction of a body of magma (Scarlato et al., 2004). The results of ourstudy allow us to identify the type of conduction mechanism that con-trols charge transport over a wide temperature range, given the bulkchemical composition, even for complex multi-component natural sili-cate melts.

Electrical conduction in silicate melts and glasses is governed by theabundance and mobility of their charge carriers, whether electronic(electrons, electron holes) or ionic (typically low-valence cations). Insimple binary alkali silicate liquids, conductivity increases sharply withincreasing total alkali content up to about 20 mol% alkali oxide, and con-tinues to increase even up to much higher alkali concentrations (Tickle,1967). Conductivity depends on the concentration and diffusivity ofthe network-modifying cation that moves throughout the polymerized

Table 1Chemical compositions of the two starting materials determined by EPMA. Units inwt.% (std error ±1%).

Sample PSGI PSGA PSRI

SiO2 69.31 68.25 68.24TiO2 0.49 0.50 0.46Al2O3 8.89 9.05 10.00Fe2O3

a 2.77 4.44 4.27FeOb 5.33 3.66 3.53MnO 0.36 0.31 0.28MgO 0.07 0.08 0.07CaO 0.58 0.59 0.54Na2O 6.63 6.43 5.92K2O 4.31 4.29 4.47P2O5 0.03 0.04 0.03H2O 0.00 0.00 0.00Tot. 98.77 98.58 97.80

a Fe2O3 determined by difference Fetot−FeO.b FeO concentrations were determined by K2Cr2O7 titration (std error ±5% relative).

141B.T. Poe et al. / Chemical Geology 320–321 (2012) 140–146

anionic framework formed by the silicate component of the liquid. Atlower temperatures, if crystallization is inhibited, the liquid passes intothe supercooled and glassy states, but rarely does one observe a changein the temperature dependence of conductivity, as the diffusive motionof monovalent networkmodifying cations is largely uncoupled from theconfigurational relaxation processes that define the glass transition(Angell, 1991).

Alkaline earth cations, while having twice the valence state to thatof alkalies, are not expected to play an important role in glass andmeltconduction due to their lower mobilities, yet Natrup et al. (2005)demonstrated that the substitution of Na2O for CaO in a silicate glassresulted in a conduction mechanism with the same activation energy(ca. 1.45 eV). Even in their “sodium-free” glass, they concluded thatNa impurities were the likely charge carriers. Barczynski andMurawski (2002) arrived at a similar conclusion in their investigationof Na2O–CaO–P2O5 glasses, which can be considered analogous tosilicate glasses in terms of a polymerized anionic network with lowvalence state cations occupying interstitial voids.

Due to the relatively large energy barrier that must be overcomein the thermally activated process of ionic diffusion, however, atlow temperatures, more efficient charge transport processes that donot require atomic displacement, such as electron and electron–hole(polaron) hopping become important (Schock et al., 1989). The pres-ence of multi-valence state species such as iron, for example, allowsfor charge transfer via small polaron hopping between Fe2+ and Fe3+

species. This mechanism has often been recognized as the dominantconduction mechanism in many iron–magnesium silicate mineralsover wide ranges of pressure and temperature encompassing a vastarray of conditions pertinent to Earth's mantle (cf. Xu et al., 2000;Romano et al., 2006). Activation energies are strongly dependent onboth the total Fe concentration and oxygen fugacity, but generally,they are lower than those for ionic conduction, and thus, even alkali-free silicates, such as olivine (Mg,Fe)2SiO4, exhibit ionic conduction athigh temperatures. These charge transport mechanisms operate viathe diffusion of lattice defect sites like oxygen or magnesium vacancies,and are typically characterized by very high (>3 eV) activation energies.

2. Experimental methods

The natural material chosen for our study was sampled from PuntaSpadillo that originates from a pantelleritic lava, a product fromthe most recent sequence of eruptions on the island of Pantelleria(10–4 ka, Civetta et al., 1984). The lava is approximately 40% porphy-ritic, containing anorthoclase (30%), clinopyroxene (5%), cossyrite (3%),fayalite (1.5%) and magnetite (0.5%). The groundmass material is com-posed of approximately 40% glass and 60% microlites, predominantlyanorthoclase, with occasional clinopyroxene and cossyrite.

We gauge the effect of different base chemical composition examin-ing two anhydrous samples: total rock (PSR) and glass matrix (PSG).Sample PSG was obtained by hand picking fragments of the glassygroundmass material from a crushed rock sample under a binocularmicroscope. Both samples were melted in air at 1400 °C and thenquenched, resulting in crystal-free glassy materials, confirmed by opti-cal microscopy. Chemical compositions of both samples, determined byEPMA, are shown in Table 1. In addition, the effect of oxygen activitywas also examined by melting sample PSG both in air (PSGA) and inan internally-heated pressure vessel (PSGI) in an Ar-gas pressuremedium (see additional details below). Fe oxidation state was deter-mined for selected samples by a redox titration method using K2Cr2O7

(Andrade et al., 2002) and results are also shown in Table 1.The effects of dissolved H2O were examined by hydrating the glassy

matrix sample PSG, using an internally heated pressure vessel at theInstitute for Mineralogy, University of Hannover. Samples were loadedin welded Pt capsules, 6 mm dia. and 30 mm length, with aliquots ofH2O providing nominal concentrations of 0.5, 1.0, 2.2 and 3.5 wt.%H2O. The syntheses were performed at 4 kbar using an Ar gas pressure

medium and 1200 °C over night and rapidly quenched in order toavoid crystallization by instantaneously dropping from the hotspot ofthe internal furnace to the cooler surroundings inside the autoclave(Berndt et al., 2002). Bulk H2O contents of the hydrated samples weredetermined by Karl–Fischer titration (KFT) also at the Institute forMineralogy, University of Hannover (Behrens et al., 1996).

Samples were cut and machined into disc-shaped wafers 4 mm indiameter and approximately 1 mm thick for complex impedance mea-surements. All electrical measurements were kept at temperatureslow enough (maximum 700 °C) to avoid crystallization. An 840 t uniax-ial press containing a Walker-type multianvil apparatus with cubic32 mm tungsten carbide anvils (17 mm edge length truncations) wasused to generate sample pressures up to 1 GPa. The multianvil appara-tus is typically used for generating much higher pressures (up to25 GPa), but in this case it was chosen because of the greater access tothe sample for the electrical measurements with respect to the pistoncylinder apparatus. Several studies (Xu et al., 1998; Katsura et al.,1998; Poe and Xu, 1999; Xu et al., 2000) have demonstrated that it ispossible to perform complex impedance spectroscopy in the multianvilat pressures and temperatures corresponding to mantle depths as lowas 700 km. The low pressure of this study, however, allowedmuch larg-er samples, contained in 25 mm edge length MgO octahedral, and sur-rounded by the necessary shielding, electrical insulation and chemicalbuffering required for proper characterization of the samples electricalproperties. Cylindrical, stepped graphite furnaces were used to heatthe sample up to 700 °C, measured by a WRe3–WRe25 thermocouple.Because the sample length (ca. 1 mm) is 1/4th that of a normal experi-ment in this type of multianvil cell, the temperature gradient is also sig-nificantly lower, on the order of 2 °C at 700 °C. The sample assemblyused in this study is identical to that used by Scarlato et al. (2004).

For the in-situ complex impedance measurements, the conduc-tivity cell contains a molybdenum foil shield, which is electricallygrounded at one end of the furnace. The shield improves the qualityof the electrical measurement by reducing interference between theAC furnace and the much weaker AC signals applied to and measuredat the sample. It also prevents current leakage due to surface conduc-tion, much like “guard ring” or “3-electrode” methods developed forother high pressure apparatus (e.g., Will et al., 1982; Will and Nover,1986). Complex impedance spectroscopy was carried out using aSolartron 1260 Impedance/Gain-phase analyser operating at an am-plitude of 1.0 V at frequencies ranging between 0.1 and 105 Hz. Com-plex impedance data were fitted to an expression for a simple RCparallel equivalent circuit, allowing for deviation of the circle centerfrom the real axis. Experimental error in conductivity is estimated tobe no greater than 5%, arisingmainly from uncertainties in the dimen-sions of the sample and any non-ideality of the form of the data withrespect to an RC parallel equivalent circuit.

Fig. 2. Conductivities for the three anhydrous samples illustrating the effects of bulkchemical composition (PSRI vs PSGI) and the effect of different oxygen fugacity (PSGI vsPSGA). Noneof the threedata sets is linear over the entire range of temperature, indicatingthat mixed electronic (low T) and ionic (high T) conduction pathways operate. Solid graylines indicate polaronic conduction according to Eq. (3) under reduced (Fe2+/Fetot=0.97)and oxidized (Fe2+/Fetot=0.5) conditions with activation energy W=0.3 eV and latticephonon frequency ν=1.5×1011 Hz. Dashed line corresponds to Fe2+/Fetot=0.5,W=1.0 eV and ν=1.5×1015 Hz. Average Fe2+–Fe3+ distance R=8×10−8 cm in all cases.

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3. Results and discussion

3.1. Complex impedance spectroscopy

A sample data set of complex impedances is shown in Fig. 1 in theform of an Argand diagram in which the real and imaginary parts ofthe complex impedance are plotted against one another, here at fre-quencies ranging from 100 kHz to 0.1 Hz. At the highest frequencies,data points are concentrated near the origin. As frequency decreases,the data form a semi-circular pattern, passing through a minimum inthe imaginary component as the real component continues to increase.The resistance component of the equivalent circuit is given by the over-all width of the least squares fitted semicircle. Like other silicates, bothcrystalline and amorphous, all samples display semiconducting behav-ior as we observe decreasing resistance with increasing temperature.

3.2. Conductivity-temperature relation in anhydrous pantelleritic glasses

In Fig. 2 we demonstrate the relatively strong effect that minorchanges in bulk chemical composition have on the conductivities ofthe two anhydrous glass specimens, PSGI (M52) and PSRI (M57).Most importantly, we observe that log conductivity does not vary line-arly with reciprocal temperature over the entire range of temperaturesinvestigated. The observed non-linear behavior is not the result of an ir-reversible change in the sample such as loss of Fe to the electrodes or re-crystallization during heating or cooling, as the data are found to be veryreproducible upon cycling the temperature back and forth between thetwo temperature regimes. In the low temperature range, conductivityshows a weak temperature dependence but is strongly sample depen-dent, owing to differences in chemical composition. In the higher tem-perature range, however, conductivities appear to merge for the threedata sets shown, with a stronger temperature dependence but very lit-tle differences from one sample to another.

We are able to fit all three data sets using a simple equation de-scribed by the sum of two Arrhenian expressions:

σ ¼ σ0i exp−HikT

� �þ σ0e exp

−HekT

� �ð1Þ

where σ0 and H are the pre-exponential term and activation enthal-py, respectively, of two independent conduction mechanisms, oneelectronic (e) and the other ionic (i). The most important differencesin composition between the two samples likely to be the cause aretotal alkali content and total Fe content. Tickle (1967) observed a

Fig. 1. Representative complex impedance spectra of a hydrous pantellerite glass at thetemperatures indicated. The data are presented in the form of an Argand diagram thatplots the real and imaginary parts of the complex impedance at frequency measured(100 kHz–0.1 Hz).

strong correlation between conductivity and total alkali concentra-tion in silicate melts at very high temperatures (>700 K). Waff andWeill (1975) arrived at a similar conclusion in their conductivitymeasurements of natural silicate melts. At low temperatures, howev-er, ionic mobilities become much slower: sodium diffusivity at 500 Kis more than a factor of 1000 slower than at 1000 K (Dingwell andWebb, 1990). Thus, electronic conduction mechanisms, which donot involve atomic transport, become increasingly more importantat lower temperatures. Even in silicate glasses with much greater con-centrations of Na2O compared to Fe2O3, at room temperature the dom-inant conduction mechanism has been shown to be electronic ratherthan ionic (Salman and Mekki, 2011). However, due to the large differ-ence in the temperature dependences of the two mechanisms, we ob-served mixed conductivity over a relatively small temperature range.This behavior has been observed in other amorphous materials con-taining both alkalies and iron. Al-Shahrani et al. (2005) observedmixed electronic and ionic conduction in Li–Na–Fe–phosphate glassesover the temperature range 50–220 °C.

3.3. Low T conduction — electronic via small polaron hopping

Sample PSGI has both a higher total alkali concentration and total Fecontent compared to the whole rock sample PSRI (see Table 1) and weobserve that it has a higher overall conductivity at both low and hightemperatures. The difference in total Fe content is rather small (PSGI8.1 wt.%, PSRI 7.8 wt.%) but its effect on electronic conduction is signif-icant as we see as much as a one order of magnitude difference at thelowest temperature of themeasurements. Their activation energies dif-fer by only 0.01 eV (Table 2) as theywere synthesized under the similarfO2 conditions of the internally heatedpressure vessel. Nonetheless, thisdifference can be important to electronic conduction mechanisms such

Table 2Results of fitting Eq. (1) to experimental data.

Expt N. Sample description σ0i (S/m) Hi (eV) σ0e (S/m) He (eV)

M52 PSGI 68,900 1.06 9.91×10−2 0.257M57 PSRI 26,120 1.02 7.03×10−3 0.247M51 PSGA 65,530 1.04 2.85×10−1 0.201M48 PSG+0.72% H2O (IHPV) 613,700 1.23 1.71×10−2 0.241M50 PSG+1.16% H2O (IHPV) 447,400 1.17 6.22×10−3 0.223M49 PSG+2.11% H2O (IHPV) 126,300 1.03 1.54×10−4 0.0169M47 PSG+3.57% H2O (IHPV) 58,720 0.938 1.47×10−3 0.119

Fig. 3. Conductivities (log) of the four hydrous samples (PSGbase composition) in thehighT region only where the 1/T dependence remains mostly linear (Arrhenian) allowing thedata to be fit by Eq. (4). The results of the fit are shown by the equation embedded in theplot and the solid lines demonstrate the goodness of fit to each of the four experimentaldata sets.

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as small polaron hopping. The more iron-rich sample has the loweractivation enthalpy, a trend that has also been commonly observed iniron-bearing silicate minerals (Seifert et al., 1982; Romano et al., 2006).At any given fO2, a higher total Fe concentration should result in a shorteraverage Fe2+–Fe3+ interatomic distance, which would lower the ener-getic barrier a small polaron would need to overcome to travel fromone site to the other.

In contrast, samples PSGI and PSGA have the same bulk chemicalcomposition, but were synthesized under different oxygen fugacities.PSGA was synthesized at ambient pressure in air whereas PSGI wassynthesized in an internally heated pressure vessel under an argonpressure medium, resulting in a significantly lower fO2. Although theoxygen fugacity was not measured in the pressure vessel, it is likely tohave been several orders of magnitude lower than its counterpart syn-thesis performed at 1 atm in air based on similar experiments carriedout in the same apparatus (Schuessler et al., 2008). The differences be-tween these latter two data sets are again more apparent at low tem-peratures at which the conductivity is dominated by small polaronhopping between Fe2+ and Fe3+ ions.

Mott (1968) described polaronic conduction in disordered mate-rials according to the following equation for a non-adiabatic hoppingmechanism,

σ ¼ vc 1−cð Þ e2

RKT

!exp −2αRð Þ exp −W

KT

� �ð2Þ

where ν represents the lattice phonon frequency, c is, in our case, theFe2+/Fetot ratio, R is the average Fe–Fe interatomic distance, α is thedecay parameter of the wave function of the electron in the Fe2+

state and W is the activation energy. If we assume an adiabatic pro-cess in which the hopping process is mainly governed by thermal ac-tivation then the exp(−2αR) term approaches unity, giving

σ ¼ vc 1−cð Þ e2

RKT

!exp

−WKT

� �: ð3Þ

The most sensitive parameters in this relation are c and W, as theminor differences in bulk chemical composition are unlikely to affectν and the small difference in total Fe concentration has a very smalleffect on R (we estimate R to be on the order of 8×10−8 cm for ourglasses based on composition and glass density, which was not mea-sured, but estimated to be on the order of 2.5–3.0 g/cm3). In Fig. 2 weshow the correlation between the experimental data and a few con-tours according to the form of Eq. (3). Good fits to the low T data(solid lines, W=0.3 eV) requires a lattice phonon frequency on theorder of 5.0×1011 Hz (ca. 20 cm−1), which is well within reason foran iron-bearing silicate glass (Murawski, 1982). In order to fit Eq. (3)to the high T data (dashed line, W=1 eV), however, an unreasonablyhigh lattice phonon frequency (ca 1015 Hz) would be required. Basedon this approximation of the data, we can conclude that themechanismfor charge transport in the lower T range is based on small polaronhopping between Fe2+ and Fe3+.

3.4. High T conduction mechanism — alkali diffusion

All three samples shown in Fig. 2 have very similar activation ener-gies for the high T ionic conduction mechanism, ranging from 1.02 eV(PSRI) to 1.04 eV (PSGI) to 1.06 eV (PSGA). These activation energiescompare favorably with the value of 0.96 eV for a phonolitic melt con-taining 2% Na2O and 6% K2O (Pommier et al., 2008), but are high com-pared to those of other alkali-rich melts (Gaillard, 2004; Poe et al.,2008). Pommier and Le Trong (2011) constructed theweb-based portalSIGMELTS for the estimation ofmelt, mineral andmixed-phase conduc-tivities. In their model, they consider only the concentrations of H2O,Na2O and SiO2 for the determination of melt phase conductivities. Poe

et al. (2008) found that the most important chemical parameters foran accurate estimation of the electrical conductivity of H2O-free silicatemelts were K2O, Na2O, MgO, CaO and Al2O3. We also note that at thesame fO2 conditions, sample PSGI (tot. alkali conc 10.9 wt.%) has ahigher absolute electrical conductivity compared to sample PSRI (tot.alkali conc. 10.4 wt.%).

3.5. Cross-over temperature from electronic to ionic conduction

The use of Eq. (1) to approximate the experimental data also allowsus to determine the temperature at which ionic conduction becomesthe dominant mechanism controlling the absolute conductivity ofeach sample. The relative proportions of alkali cations and iron appearto be themore influential factors that determine the cross-over temper-ature that vary nearly 200° from 320 °C for the Fe-poor, low fO2 samplePSRI to 514 °C for the Fe-rich, high fO2 sample PSGA.However, given thesmall variations in Na2O, K2O and total Fe concentrations among thesamples studied here, it is unwarranted to attempt any parameteriza-tion of this cross-over in terms of melt composition. It is also evidentthat the cross-over temperature from electronic to ionic conduction atany given chemical composition should be minimized at very low oxy-gen fugacities, at which the Fe3+ concentration is small in comparisonto ferrous iron.

3.6. Effect of H2O

Conductivities of the hydrous samples are plotted in Fig. 3. Tomore clearly illustrate the effect of dissolved H2O on the ionic conduc-tivity in the high temperature range, we first analyze only the hightemperature data where we find good correlation to the Arrheniusequation. If we constrain the temperature dependence to be thesame for each of the four data sets, we find that the following expres-sion, which includes an H2O concentration term (CW in wt.% H2O)best approximates the experimental data:

σ ¼ 1260⋅C1:25W ⋅ exp −0:812

kT

� �: ð4Þ

For restricted ranges of both composition and temperature, Ni etal. (2011) found a simple expression describing the conductivity be-havior of basaltic liquids containing up to 6% dissolved H2O, wherelog σ varied non-linearly as a function of reciprocal temperatureand as a function of the square root of the water concentration, a sig-nificantly weaker dependence than that observed here. In the case ofcrystalline phases, the exponent in the concentration term from

Fig. 5. Activation energies for the ionic conduction regime at high T for the hydroussamples plotted as a function of H2O concentration (open squares). Also shown is the var-iation in activation energy determined by Gaillard (2004) (solid line) and data taken fromPommier et al. (2008) (open circles).

144 B.T. Poe et al. / Chemical Geology 320–321 (2012) 140–146

Eq. (2) can be used to help identify the point-defect equilibrium re-sponsible for charge transport (Huang et al., 2005). In the case ofmelt and glassy phases, however, this term simply expresses the sen-sitivity of conductivity to changes in a compositional parameter suchas H2O concentration. We might expect, however, that its magnitudeis correlated to the other important chemical characteristics of thematerial. For example, the basaltic melts investigated by Ni et al.(2011) contained significantly less SiO2 (ca. 50 wt.%) compared toour pantelleritic materials (>65 wt.%).

We also chose not to constrain the temperature dependence of allH2O-bearing samples to a fixed value of Hi and He but rather fitEq. (1) to each individual data set (Fig. 4, Table 2). Given the lack ofsufficient data at low T for the hydrous samples, we make no attemptsto discuss the effects of H2O on the small polaronmechanism. Gaillard(2004) showed for a highly polymerized sodium-bearing silicate liq-uid, that increasing H2O content resulted in higher conductivity with-out significant change in activation enthalpy. He concluded that evenin the water-rich liquid (3 wt.% H2O), the conduction mechanismremained that of Na-diffusion, despite its lower atomic abundancecompared to hydrogen. However, it is clear that with increasing tem-perature, the effect of H2O on the conductivity in the ionic conductionregime becomes less important. Fig. 5 illustrates how the activationenthalpy for ionic conduction decreases with increasing H2O concen-tration. Activation enthalpy as a function of water concentration fromGaillard (2004) is also shown in Fig. 5 for comparison. While thevalues from Gaillard (2004) are low in comparison, a similar trendwas observed. Ni et al. (2011) also observed a strongly decreasing ac-tivation enthalpy with H2O concentration, which was also tempera-ture dependent (i.e. non-Arrhenian), this perhaps due to the veryhigh temperatures of those measurements (up to 1650 °C). At thelowest temperatures of their study, they found that activation enthal-py decreases from nearly 1.5 eV for their anhydrous basalt down toabout 1.2 eV at 4 wt.% H2O. Fanara and Behrens (2011) also observedsteadily decreasing activation enthalpies similar in magnitude to oursfor hydrous glasses of anorthite–diopside composition containingfrom 1.5 to 2.8 wt.% dissolved H2O. However, due to the lack of alkalications in their base glass, the mechanism for charge transport wasinterpreted to be proton conduction.

Over the H2O concentration range explored in this study, ourunconstrained fits show that the activation energy decreases from1.23 eV at 0.72 wt.% H2O to 0.94 eV at 3.56 wt.% H2O. These activationenthalpies are in very good agreement to the activation enthalpy of

Fig. 4. All conductivity data for the four hydrous samples, including at low temperaturesoverlapping the electronic (small polaron) conduction regime. These data sets were fittedindividually according to Eq. (1) in order to illustrate the continuous decrease in 1/Tdependence in the ionic conduction regime at higher temperatures with increasing H2Oconcentration (see Table 2).

the dry PSGI sample, having the same base chemical compositionand synthesized at the same fO2 conditions in the internally heatedpressure vessel. We can thus conclude that the mechanism for con-duction in this temperature range remains that of alkali diffusion,even at H2O concentrations above 3 wt.%.

A continuous decrease in activation energy with increasing H2Ocontent is more likely to be due to a continuous change in the meltstructure, rather than a change in the conduction mechanism. If thetype of charge carrier was different from that of the anhydrous meltphase, we would expect to observe an abrupt change in temperaturedependence from the dry to the lowest H2O-bearing melt. This mayindeed be the case for H2O-bearing phonolitic melts (Pommier etal., 2008) where the activation enthalpy decreased abruptly from0.96 eV for their nominally dry melt to 0.68 eV for the melt containing1.1 wt.% H2O and then to 0.63 eV for the melt containing 5.6 wt.% H2O(see Fig. 5). The mixed anorthite–diopside glasses from Fanara andBehrens (2011) also exhibited a sharp drop in activation enthalpyfrom 2.27 eV (anhydrous) to 1.28 eV (1.5 wt.% H2O), consistent withtheir interpretation that the charge carrying species in the hydrousglasses were proton-bearing.

A smooth change in activation enthalpy (see Table 2) is likely dueto the progressive depolymerization of the melt structure with in-creasing dissolved H2O content. Using the formulation for estimatingthe average number of non-bridging oxygens per tetrahedral cation(NBO/T) adopted by Mysen (1988), the anhydrous sample PSGI hasa NBO/T=0.14, which is quite low, and thus very polymerized, dueto its very high SiO2 content, whereas more depolymerised liquidssuch as basalts have NBO/T values on the order of 1 or more. Smallchanges in NBO/T, particularly for strongly polymerized melts, oftenlead to significant changes in their physical properties, such as viscos-ity and glass transition temperature (Dingwell, 1995). Even thoughshear relaxation times are associated with the breaking and reforma-tion of the strong Si\O bonds of the silicate network and dictate theviscous flow process (Farnan and Stebbins, 1990; McMillan et al.,1994), electrical conductivitymethods that are sensitive to themobilitiesof network-modifying cations have also shown good correlations to theglass transition temperature (Tg) and variations in viscosity withtemperature above Tg (Bagdassarov et al., 2004; Zhang et al., 2011).

3.7. Conductivity and cation diffusion

Both the overall increase in conductivity and decrease in activationenthalpy with added H2O are reflected in the results of cation diffusivitystudies of hydrous silicate melts. In the ionic conduction regime insilicate melts at high temperatures, conductivity and diffusivity of the

Fig. 6. Predicted electrical conductivity for anhydrous PSGA glass/melt using modelof Poe et al. (2008) (solid curve) and SIGMELTS (dashed curve).

145B.T. Poe et al. / Chemical Geology 320–321 (2012) 140–146

dominant ionic conductor are directly proportional to one anotheraccording to the Nernst–Einstein relation. Sodium–potassium inter-diffusivities increase by a factor of 4 from dry to 5.5 wt.% H2O-bearingalbite-orthoclase melts, while its activation energy decreases from ap-proximately 1.5 eV down to about 1.2 eV (Freda and Baker, 1998).Watson (1981), on the other hand, finds aminimal effect of water on so-dium diffusion in comparison to calcium mobilities. At low tempera-tures, approaching and descending below the glass transition, alkalidiffusivities should maintain the same temperature dependence andthus are decoupled from shear relaxation timescales associated withthe configurational changes of the silicate network that occur above Tgbut become frozen in below Tg. Any perceptible change in activationenergy at Tg can be explained by the inability of the glass to explore ad-ditional, energetically favorable, configurational states as the volumecontinues to decrease below Tg. If, however, more favorable electronicconduction pathways are not available at low T, then alkali diffusivityand conductivity should still be correlated (Kaps et al., 1986).

Similar to our observations of the anhydrous samples that showedmixed conduction over the investigated temperature range, the hy-drous samples also show a very wide range of cross-over temperaturesfrom electronic to ionic conduction depending on temperature. For thelowest H2O concentration (0.72 wt.% H2O), small polaron conductionswitches to ionic conduction at 384 °C whereas for the water rich sam-ple (3.57 wt.% H2O), ionic conduction begins to take over at 270 °C.Again, the small number of data indicative of electronic conduction inthe hydrous samples does not permit us to view this trend beyond aqualitative perspective. However, the presence of water appears to bemore influential on the ionic conduction mechanism compared to thesmall polaron mechanism, and therefore, cross-over temperaturesshould decrease with increasing H2O concentration. Additionally, ourresults do not appear to indicate that protonic conduction is importantat low T as the cross-over temperatures are lower compared to thenominally dry sample. The presence ofwater is not likely to inhibit elec-tronic conduction, but rather should augment it indirectly through itsautodissociation

H2O ¼ H2 þ 1=2O2 ð5Þwhich, in turn, elevates the oxygen fugacity and favors a higher con-centration of ferric iron. Thus traces of H2O in the nominally anhydroussamples synthesized in the IHPV could be responsible for the greaterthan expected Fe3+ contents (Table 1). Naturally, if the ferric concen-tration is initially very high (Pommier et al., 2010), then a decrease infO2 could also result in increasing conductivity in order to balance theFe3+/Fe2+ ratio as described above, where a 1:1 ratio would maximizeconductivity due to small polaron hopping as indicated by Eq. (2).

In the absence of alkali, or in the very low concentration limit of al-kali cations, we can expect a greater likelihood for protonic conduction.For example, Behrens et al. (2002) hydrated a barium disilicate glasswith up to 3.5 wt.% H2O to demonstrate protonic conduction. The anhy-drous glass was found to be insulating at temperatures up to 500 Kwhereas the hydrous glass was strongly conducting (σ0=106). Inter-estingly, the activation energy determined by Behrens et al. (2002)was 0.90 eV, which makes it nearly indistinguishable from alkali con-duction mechanisms displaying temperature dependences of similarmagnitude. Moreover, the variation of the protonic conduction activa-tion energy with increasing H2O concentration is also likely to behavesimilarly to that for alkali ionic conduction, even if their mechanismsare not similar (Abe et al., 1993).

4. Implications and conclusions

Inherent to the chemical complexities of natural silicate liquids, itremains a challenge to characterize their electrical properties in orderto apply them in our interpretation of geophysical data. Working toour advantage, however, is the very sensitive response of the electrical

conductivity to even small changes in either chemical composition ortemperature. Given an approximate chemical composition and temper-ature of a magmatic body, its dimensions and depth can be estimatedthrough forward calculations of the apparent resistivity (Scarlato etal., 2004).

The danger, however, becomes ostensive if extrapolations of exis-ting conductivity–temperature–composition relationships are madeunder the assumption that the conduction pathway is unaltered.

The recent empirical model developed by Poe et al. (2008) includesa non-Arrhenian temperature dependence and thus manages to repro-duce the observed change in conduction mechanism for the anhydroussample PSG (Fig. 6). This provides a telling statement that a significantportion of the published experimental data used to construct themodel is also characterized by mixed electrical conduction pathways.The results of our study serve as an important example that mixedelectronic and ionic conduction can be observed at crustal temperaturesin alkali+iron bearing magmatic systems. We find in alkali-richpantelleritic trachyte glasses (Na2O+K2O>10 wt.%) that electronic con-duction due to small polaron hopping can be observed at temperaturesexceeding 500 °C before crossing over to an ionic conductionmechanism.The temperature dependence of the ionic conduction mechanism is ap-proximately four times greater than that of the small polaronmechanism.The cross-over temperature is strongly fO2 dependent, and likely to bemaximized at any given bulk composition when equal amounts of ferricand ferrous iron are present. The effect of dissolved H2O, on the otherhand, has a greater effect on the ionic conduction mechanism observedat higher temperatures. The presence of dissolved H2O enhances alkalidiffusivities, and we observe an increase in conductivity by more than afactor of 10 over a small range of H2O concentration (0.72 to 3.57 wt.%H2O). The temperature dependence varies only slightly with H2O con-centration, such that the effect of water on conductivity diminisheswith increasing temperature. We conclude that the conductivity mecha-nism is characterized by the diffusivemotion of Na+, even at highest H2Oconcentration, due to its similar activation energy to that of the anhy-drous glass/melt, in agreement with Gaillard (2004). However, in theionic conduction regime, activation energies appear to be very sensitiveto bulk chemical composition. Althoughwe do not observe protonic con-duction in this study, we do not rule out the possibility of this conductionpathway in alkali-poor glass/melt systems.

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