ies

id

l J.

iences

metal oxide binary systems, is of interest as it implies

positive Gibbs free energies of mixing such that two

different liquid compositions have identical chemical

* Corresponding author.

Chemical Geology 213 (200E-mail addresses: hovisguy@lafayette.edu (G.L. Hovis)8mtoplis@crpg.cnrs-nancy.fr (M. Toplis)8 richet@ipgp.jussieu.frbCRPG-CNRS, BP20, F-54501, Vandoeuvre-les-Nancy, FrancecPhysique des Mineraux et des Magmas, UMR CNRS 7047, Institut de Physique du Globe, 4 place Jussieu, 75252 Paris Cedex 05, France

Received 20 December 2003; received in revised form 4 May 2004; accepted 31 August 2004

Abstract

Enthalpies of solution have been measured for synthetic glasses in the SiO2Na2O system from 0 to 50 mol% Na2O. The

positive enthalpies of mixing determined for the compositional range between 0 and 33.3 mol% Na2O, combined with entropies

for the same compositions based on ideal mixing involving Q4 and Q3 species, allowed us to calculate a liquidliquid solvus in

good agreement with the experimental data of Haller et al. [Haller, W., Blackburn, D.H., Simmons, J.H., 1974. Miscibility gaps

in alkalisilicate binariesdata and thermodynamic interpretation. J. Am. Ceram. Soc. 57, 120126]. This demonstrates a high

degree of compatibility among the data for entropy, enthalpy, and phase equilibrium and also confirms the requirement of

positive enthalpies of mixing for liquid immiscibility in the SiO2Na2O system.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Sodium silicate liquids; Solution calorimetry; Excess enthalpy; Configurational entropy; Thermodynamic mixing; Solvus

1. Introduction

In view of their simple chemistry and relatively low

glass transition temperatures, sodium silicates have

long been used as a starting point for investigating the

relationships among the structure, chemical composi-

tion and physical properties of silicate glasses and

melts (e.g. Mysen, 1988). Liquidus phase relationships

in the system SiO2Na2O were determined as early as

1930 (Kracek, 1930) but it was almost 40 years later

that the existence of a metastable miscibility gap in the

liquid phase at SiO2-rich compositions was discovered

(Porai-Koshits and Averjanov, 1968; Haller et al.,

1974). This latter feature, common to many silicaThermodynamic mixing propert

implications for liqu

Guy L. Hovisa,*, Michae

aDepartment of Geology and Environmental Geosc0009-2541/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.chemgeo.2004.08.041

(P. Richet).1Present address: DTP (UMR 5562), Observatoire Midi-

Pyrenees 14, Ave. Edouard Belin F-31400, Toulouse, France.of sodium silicate liquids and

liquid immiscibility

Toplisb,1, Pascal Richetc

, Lafayette College, Easton, PA 18042-1708, USA

4) 173186

www.elsevier.com/locate/chemgeoonents at the samepotentials of endmember comptemperature. Therefore, although the assumption of

ideal mixingwould appear to be sufficient to rationalize

the cup into water. The annealing temperatures were

measured with a newly prepared PtRh6PtRh30

al Gethe liquidus phase relations in this system (e.g. Halter

and Mysen, 2004), it is clear that a complete

thermodynamic model of sodium silicate liquids must

take into account the presence of the miscibility gap.

Ideally, the assessment of such thermodynamic models

requires the possibility of separating the enthalpic and

entropic contributions to the Gibbs free energy of

mixing.

In this respect it is of note that within the

framework of the theory of structural relaxation in

viscous liquids proposed by Adam and Gibbs (1965),

configurational entropies of liquids can be estimated

from viscosity and heat capacity data (Richet, 1984).

For the system SiO2Na2O, such an analysis infers

strongly positive configurational entropies of mixing

in the silicic part of the system (Toplis, 2001). Thus, if

both entropies (Sex) and Gibbs free energies of mixing

(Gex) are positive, then enthalpies of mixing (Hex)

also must be positive for immiscibility to exist, owing

to the standard thermodynamic relationship Gex=

HexTSex, where T is absolute temperature.Several studies have attempted to determine enthal-

pies of mixing from measurements of enthalpies of

solution of SiO2Na2O binary glasses either in hydro-

fluoric acid (HF) solutions near room temperature

(Hummel and Schweite, 1959; Tischer, 1969; Takaha-

shi and Yoshio, 1970) or in a molten salt near 970 K

(Rogez and Mathieu, 1985). None have concluded that

large positive heats of mixing exist for silicic compo-

sitions. However, none of the previous studies adjusted

data to calculate the isothermal variation of enthalpy as

a function of composition in the liquid state. This

essential step must be performed before attempting any

quantitative modeling of liquidliquid, or liquidsolid

phase equilibria because of the large difference in

fictive temperature of pure SiO2 versus Na-bearing

compositions.

A new calorimetric investigation of sodium silicates

is reported in this paper. Because of their ready

dissolution, glasses in this system have been dissolved

in HF solution at 50 8C, where the measurements canhave high precision (Hovis et al., 1998). From these

experiments enthalpies of solution between SiO2 and

Na2SiO3 have been determined, with average standard

errors of F0.51 (2r) kJ/mol. After correction for thefictive temperature we then assess to what extent the

G.L. Hovis et al. / Chemic174results are consistent with the known miscibility gap in

this system. Furthermore, owing to the considerablethermocouple placed in contact with the samples in

the electric muffle furnace.

Sodium silicate samples were synthesized from

reagent grade sodium carbonate and silica as describedstructural information available on sodium silicates,

our results may also be interpreted and discussed in

terms of the properties of the species that have been

identified in spectroscopic studies of melt structure.

2. Experimental procedures

2.1. Solution calorimetry

The hydrofluoric acid (HF) solution calorimetric

system utilized in this investigation has been described

by Hovis and Roux (1993) and Hovis et al. (1998). This

system has the potential to produce highly precise data

on small samples (Hovis et al., 1998), although in the

present study no dissolutions were performed on

samples smaller than 39 mg. Each calorimetric experi-

ment took place in 910.1 g (about 1liter) of 20.1 wt.%

HF at 50 8C under isoperibolic conditions (i.e. thetemperature of the medium surrounding the calorimeter

was held constant) using an internal sample container

(Waldbaum and Robie, 1970). Either one or two

experiments were performed in each liter of acid.

Multiple experiments in the same solution had no

detectable effect on the data, the result of the high

dilution of dissolved ions in the acid. Experiments were

conducted on materials ranging from lightly crushed to

more highly ground materials. The effects of grain size

are discussed below.

2.2. Sample synthesis

The SiO2 glass was the same high-purity sample as

that investigated by Richet et al. (1982) by drop

calorimetry. To investigate samples with different

fictive temperatures, 700 mg of coarse powders were

annealed in a light Pt cup at 1387, 1441 and 1526 K for

70, 7 and 0.3 h, respectively, after having being rinsed

for a few minutes in a fresh HF solution. The samples

then were quenched rapidly by dipping the bottom of

ology 213 (2004) 173186by Richet et al. (1984). The Na2SiO3 sample was

from the batch investigated in the latter study. Other

through 40 mol% Na2O, had developed NaOH on

the glass surfaces from exposure to air during

l Geoshipping. The NaOH in turn reacted with airborne

CO2 to form Na carbonate, a phenomenon that is

common in Na silicate glasses. Indeed, tests with

dilute HCl on these samples produced vigorous

bubbling. Simple drying at 125 8C would not haveeliminated contamination of the samples. The initial

calorimetric results on fine-grained sodic samples

therefore suffered from at least three factors: An

unwanted heat component from the dissolution of Na

carbonate, inaccurate sample weights for the glasses

themselves due to the added presence of Naglasses were those investigated by Jarry and Richet

(2001). For these new samples, chemical homoge-

neity was ensured by stirring of the fluid melts. After

synthesis, all except the two most sodic glasses were

ground (by request of GH), then sent by express mail

delivery to Lafayette College, where upon receipt

they were placed in desiccators. All samples were

dried at 125 8C for periods ranging from hours todays prior to the solution calorimetric dissolutions.

The glass compositions reported in this paper are the

nominal compositions.

3. Results

3.1. Calorimetric data

Calorimetric results for the original samples of this

study are recorded in Table 1 and shown as squares in

Fig. 1, where data are reported as the negatives of the

heats of solution (for which concave down curvature

indicates positive enthalpies of mixing). In general, the

initial solution calorimetric experiments, many of

which were made on finely ground glasses, produced

unsatisfactory data. Calorimetric reproducibility for

individual samples was as poor as 1%, in contrast to

numerous previous studies in which precision typically

has been 0.1% to 0.3%. Furthermore, it was difficult to

make sense of the variation of data with chemical

composition, particularly for Na-rich samples.

After these initial calorimetric experiments were

conducted, it was discovered that the most finely

ground samples, those with compositions from 25

G.L. Hovis et al. / Chemicacarbonate, and loss of heat during the calorimetric

experiments due to the escape of carbon dioxidefrom the calorimeter during HF dissolution of the Na

carbonate.

To resolve these problems, a new glass sample

(0202) at 40 mol% Na2O was synthesized at CRPG-

CNRS in Nancy, France. A portion of the resulting

glass was transported to the US as a single 7.15 g

specimen, stored in a desiccator, then crushed (not

ground) just prior to calorimetric dissolution. The

resulting calorimetric data differed substantially from

those of the original 40 mol% Na2O sample (0017).

Therefore, sample 0017 was remelted (1450 8C, 10min, air quench, producing sample 0301) and

dissolved anew. The resulting calorimetric data for

the remelted sample were indistinguishable from

those of 0202 (Fig. 2). The new calorimetric data

confirmed the aforementioned problems with the

original specimens. The results also indicated, how-

ever, that the Na-bearing glasses could be restored to

their original carbonate-free condition by simple

remelting for a short period of time.

Thus, all other glasses were remelted at 1450 8C.To minimize high-temperature loss of Na, most

specimens were heated for just 10 min, although

the higher viscosity glasses at 15 and 20 mol% Na2O

needed remelting periods of 3045 min. The glasses

were quenched in air, then immediately placed in

desiccators. The initial calorimetric dissolution on

each remelted glass was conducted within hours of

the remelting. Grain sizes for these dissolutions were

either fine chips or somewhat larger pieces (several

millimeters in diameter), but in no case powders.

Calorimetric experiments on remelted samples

(Table 1) reproduced original data for samples at 15

and 20 mol% Na2O (see Fig. 2). This can be

attributed to minimal carbonate formation in the

original samples due to their low Na content. In

fact, even after months of storage the powders of

the latter samples did not produce a visible reaction

with dilute HCl. The new experiments also repro-

duced original data on samples at 45 and 50 mol%

Na2O, most likely due to the coarse grain size and

small surface area of the original calorimetric

samples. Glasses with compositions between 25

and 40 mol% Na2O, however, for which early

results were based on finely ground samples, gave

very different data from initial results. Moreover,

logy 213 (2004) 173186 175the data for glasses with higher contents of Na2O

display greater differences from data on original

Table 1

Calorimetric data

Sample number

and Tg

Nominal

mole

fraction

Na2O

Gram

formula

weight

(g/mol)a

Calorimetric

experiment

no.

Sample

weight

(g)

Calorimeter Cp

before and after

dissolution (J/deg)

DT duringdissolution

(8C)

Heats of solution

based on Cp I

and II (kJ/mol)

DHa adjustmentto heats of solution

for Tr of 1000 K

(kJ/mol)

Pure-silica glasses

S 1387/1387 K 0.000 60.0848 895 0.07438 3870.28 3870.20 0.046607 145.425 145.421 3.57S 1387/1387 K 0.000 60.0848 898b 0.07821 3865.68 3866.27 0.044939 146.393 146.414 3.57S 1387/1387 K 0.000 60.0848 900b 0.07414 3865.81 3866.31 0.046669 145.917 145.938 3.57S 1387/1387 K 0.000 60.0848 901 0.07703 3870.79 3871.16 0.047982 144.581 144.598 3.57S 1441/1441 K 0.000 60.0848 904 0.09947 3870.12 3870.74 0.062652 146.172 146.197 4.01S 1441/1441 K 0.000 60.0848 905b 0.09778 3867.82 3868.07 0.061963 146.974 146.986 4.01S 1441/1441 K 0.000 60.0848 906 0.09927 3870.41 3870.41 0.062680 146.540 146.540 4.01S 1441/1441 K 0.000 60.0848 907b 0.09856 3866.10 3866.43 0.062452 146.899 146.911 4.01S 1526/1526 K 0.000 60.0848 896b 0.07667 3866.43 3866.52 0.048062 145.337 145.341 4.68S 1526/1526 K 0.000 60.0848 897 0.07377 3869.57 3869.49 0.046782 147.149 147.145 4.68S 1526/1526 K 0.000 60.0848 899 0.07590 3870.62 3869.57 0.048193 147.375 147.329 4.68S 1526/1526 K 0.000 60.0848 902b 0.07309 3866.77 3866.60 0.046253 146.732 146.723 4.68

Original Na-silicate glasses

0005/782 K 0.100 60.2742 930 0.11402 3871.12 3869.87 0.072571 148.210 148.160 2.570005/782 K 0.100 60.2742 940 0.10291 3871.46 3871.04 0.065298 147.767 147.751 2.570007/771 K 0.150 60.3689 929b 0.10038 3865.81 3865.76 0.064018 148.536 148.536 2.670007/771 K 0.150 60.3689 933b 0.09991 3867.44 3867.56 0.063542 148.189 148.193 2.670011/751 K 0.200 60.4636 925b 0.09896 3868.07 3867.44 0.064000 150.953 150.928 2.880011/751 K 0.200 60.4636 931b 0.10384 3867.86 3866.89 0.066946 150.469 150.435 2.880013/736 K 0.250 60.5584 927b 0.10326 3867.10 3868.19 0.066385 150.256 150.298 3.030013/736 K 0.250 60.5584 939b 0.10059 3867.69 3867.02 0.064476 149.830 149.805 3.030014/731 K 0.300 60.6531 926 0.09513 3870.37 3870.03 0.059909 147.542 147.529 3.030014/731 K 0.300 60.6531 935b 0.10241 3866.35 3867.10 0.064546 147.504 147.533 3.030015/716 K 0.350 60.7478 934 0.10481 3870.53 3870.95 0.064436 144.264 144.281 3.170015/716 K 0.350 60.7478 937b 0.10283 3867.61 3867.35 0.062598 142.740 142.731 3.170016/716 K 0.350 60.7478 928 0.10240 3872.00 3869.74 0.060849 139.491 139.408 3.170016/716 K 0.350 60.7478 932 0.09786 3871.25 3871.25 0.058057 139.241 139.241 3.170029/706 K 0.375 60.7951 951 0.25806 3871.37 3871.62 0.164544 149.772 149.780 3.280029/706 K 0.375 60.7951 952b 0.25020 3868.69 3870.16 0.157155 147.437 147.492 3.280017/695 K 0.400 60.8425 924 0.10161 3870.07 3869.41 0.064776 149.809 149.780 3.400017/695 K 0.400 60.8425 936 0.10373 3870.62 3871.41 0.058293 132.079 132.104 3.400017/695 K 0.400 60.8425 938 0.10700 3870.58 3870.03 0.059551 130.806 130.785 3.400017/695 K 0.400 60.8425 946 0.19537 3870.99 3871.20 0.108411 130.430 130.451 3.400021/692 K 0.425 60.8898 949 0.25030 3870.33 3870.99 0.155510 146.122 146.151 3.410021/692 K 0.425 60.8898 950b 0.24886 3868.02 3868.94 0.154319 145.759 145.792 3.410018/689 K 0.450 60.9372 942 0.21572 3872.71 3872.38 0.148649 162.294 162.278 3.410018/689 K 0.450 60.9372 943 0.47607 3870.87 3871.71 0.327042 161.714 161.751 3.410019/675K 0.500 61.0319 944b 0.21354 3869.61 3868.99 0.150542 166.161 166.136 3.540019/675K 0.500 61.0319 945 0.22096 3872.75 3872.12 0.154384 164.816 164.787 3.54

CRPG-CNRS Na-silicate glass

0202/695 K 0.400 60.8425 987 0.52739 3877.40 3880.49 0.356183 159.008 159.133 3.400202/695 K 0.400 60.8425 988 0.47664 3870.33 3868.86 0.322320 158.920 158.862 3.400202/695 K 0.400 60.8425 1002 0.13254 3869.28 3867.19 0.089005 157.776 157.689 3.40

Remelted Na-silicate glasses

0317/771 K 0.150 60.3689 1033b 0.04948 3864.97 3863.21 0.031740 149.371 149.300 2.670317/771 K 0.150 60.3689 1034 0.04604 3867.02 3865.01 0.029302 148.281 147.905 2.67

G.L. Hovis et al. / Chemical Geology 213 (2004) 173186176

samples (see Fig. 2), just as one might expect from 3.2. Comparison with previous studies

Table 1 (continued)

Sample number

and Tg

Nominal

mole

fraction

Na2O

Gram

formula

weight

(g/mol)a

Calorimetric

experiment

no.

Sample

weight

(g)

Calorimeter Cp

before and after

dissolution (J/deg)

DT duringdissolution

(8C)

Heats of solution

based on Cp I

and II (kJ/mol)

DHa adjustmentto heats of solution

for Tr of 1000 K

(kJ/mol)

Remelted Na-silicate glasses

0310/751 K 0.200 60.4636 1027 0.04550 3868.94 3864.80 0.029404 150.870 150.711 2.880310/751 K 0.200 60.4636 1030 0.05467 3869.78 3866.94 0.035197 150.335 150.227 2.880307/736 K 0.250 60.5584 1024 0.05586 3867.15 3866.73 0.036310 151.922 151.905 3.030307/736 K 0.250 60.5584 1035b 0.04993 3865.56 3863.25 0.032532 152.218 152.127 3.030304/731 K 0.300 60.6531 1023 0.07483 3867.90 3867.35 0.048614 152.106 152.081 3.030304/731 K 0.300 60.6531 1025 0.07115 3869.99 3867.61 0.046451 152.937 152.845 3.030302/716 K 0.350 60.7478 1022 0.09283 3873.25 3866.77 0.061332 155.146 154.887 3.170302/716 K 0.350 60.7478 1036 0.10028 3868.15 3864.55 0.065959 154.252 154.106 3.170301/695 K 0.400 60.8425 1021 0.10877 3864.64 3862.96 0.072838 157.142 157.075 3.400312/689 K 0.450 60.9372 1028b 0.06424 3865.18 3862.71 0.044652 163.384 163.284 3.410312/689 K 0.450 60.9372 1032 0.05024 3867.94 3865.10 0.034697 162.457 162.336 3.410309/675 K 0.500 61.0319 1026b 0.05612 3867.73 3866.14 0.038762 162.716 162.649 3.540315/675 K 0.500 61.0319 1031b 0.04973 3866.73 3863.97 0.034724 164.453 164.336 3.54

a A mole is defined as one mole of oxides.b Calorimetric dissolution performed in acid of preceding experiment.

G.L. Hovis et al. / Chemical Geology 213 (2004) 173186 177surface contamination that is a function of Na

content. Note that data on the remelted specimens

display much-improved systematic behavior with

composition.Fig. 1. Calorimetric data for the initial glass specimens, some of which w

various experiments for the specimen at 0.4 mol fraction Na2O. The tw

specimens at that composition. The scatter of data for pure silica results fThe results obtained in previous studies are

included in Fig. 3. Hummel and Schweite (1959)

performed solution calorimetric dissolutions in 39%ere contaminated by Na carbonate. Note the disagreement among

o clusters of data at 0.3 mol fraction Na2O are for two different

rom three specimens with three different fictive temperatures.

Fig. 2. Calorimetric data adjusted to a fictive temperature of 1000 K (values in Table 1). Final data selection is represented by larger symbols

with crosses: squares for original specimens, circles for sample 0202 synthesized at CRPG-CNRS (Nancy), and diamonds for remelted

specimens. Data at mol fractions of 0.15 and 0.20 Na2O for original and remelted samples are essentially superimposed. Note the agreement

between data for new sample 0202 and for remelted sample 0301 at the same composition, both of which are different from initial results.

Smaller open squares are discarded data for contaminated samples; note that differences between data for remelted samples and initial results

generally increase for samples with compositions from 0.25 to 0.40 mol fraction Na2O. Solid curve corresponds to the fourth-order fit to the

final selected data set (Eq. (2)); the dashed curve represents the fourth-order fit to heats of mixing (Eq. (3), Fig. 3) after addition to enthalpies of

solution along the line of ideal mixing.

Fig. 3. Comparison of present calorimetric data adjusted to a fictive temperature of 1000 K with data of previous workers, all of which are

unadjusted for fictive temperature. The data point of Takahashi and Yoshio (1970) for pure silica is hidden by data points from the present study.

Note the changes in slope of data from previous workers at Na2ON0.3.

G.L. Hovis et al. / Chemical Geology 213 (2004) 173186178

l GeoHF at 26.5 8C on glasses whose thermal history isunknown. Later, Tischer (1969) performed HF dis-

solutions with a Bunsen calorimeter in 39% HF at

26.91 8C on brapidly quenchedQ glasses using 1-gsamples enclosed in gelatin capsules introduced into

80 ml of acid. Note that the acid quantity and

concentration of these two studies are very different

from those of the present work. Enthalpies of solution

in both studies can be described by two linear

segments with a break in slope at approximately 33

mol% Na2O. However, in neither case were adjust-

ments made to account for the fact that glass transition

temperatures for each composition are different, an

essential consideration when calculating isothermal

enthalpies of mixing, as discussed below. Similar

measurements have also been made either in 5% HF

solutions and in pure water by Takahashi and Yoshio

(1970).

Other measurements have been reported only in a

graphical form at higher temperatures for composi-

tions from pure-silica to 50% Na2O by Rogez and

Mathieu (1985). Because dissolutions were made in

molten lead borate at 876 K, all samples but pure

SiO2 were supercooled liquids. When referenced to

pure silica and 50% Na2O end members, their data

show approximately ideal thermodynamic behavior

at silicic compositions, but strongly negative enthal-

pies of mixing between about 20 and 50 mol%

Na2O.

3.3. Adjustments for fictive temperature

Application of the data presented here to thermody-

namic calculations relative to the liquid state (e.g. the

solvus, as discussed below) is not immediate because

our solution calorimetry measurements have been

made on glasses. Although effects of thermal history

of glasses on enthalpies of mixing of liquids have long

been discussed (Richet and Bottinga, 1984), this

essential step in the treatment of data warrants some

discussion.

To convert measured heats of solution to those of

liquids under isothermal conditions, one must take

into account the fact that the temperature at which

the glass becomes a liquid (the glass transition

temperature, Tg) is different for each composition.

G.L. Hovis et al. / ChemicaAs previously discussed (Richet and Bottinga, 1984,

1986), relative enthalpies at a common referencetemperature in the liquid state may be calculated by

adjusting measured values of the enthalpy of glasses

with enthalpies of annealing given by:

DHa Z Tr

Tg

Cpl Cpg

dT 1

where DHa is the correction to be applied, Cpl andCpg are the heat capacities of the liquid and glass,

respectively, Tg is the glass transition temperature

and Tr is an arbitrary reference temperature.

Application of Eq. (1) is complicated by the fact

that even at fixed composition the glass transition

temperature is not uniquely defined, but rather a

function of the thermal history of the sample (with

the consequence that the enthalpy of a glass

depends on its thermal history, as illustrated by

the experiments of Tischer, 1969). In the simplest

case one may work on samples which have been

annealed at a known temperature for a sufficient

length of time that structural relaxation is complete,

then cooled sufficiently quickly that no further

structural changes occur. This is the approach which

has been employed for our SiO2 samples. Sodium

silicate samples have not been annealed, but for

these samples we make use of the fact that, even

for liquids continuously cooled across the glass

transition range, one may define a temperature

(called the fictive temperature) at which the actual

configuration of the glass would be the equilibrium

configuration of the supercooled liquid. For a given

cooling rate, the viscosity of liquids at the fictive

temperature is constant, thus this temperature may

be simply calculated if one knows the viscosity of

the liquid as a function of temperature and the

cooling rate (e.g. see equation and discussion in

Toplis et al., 2001). However, although the cooling

rates of our liquids are not known exactly, they are

similar for all sodium-bearing samples. Thus, we

have chosen to define the fictive temperature of all

Na-bearing glasses as the temperature at which the

viscosity is 1012 Pa s (values shown in Table 1),

using viscosities as determined by Jarry and Richet

(2001). We note too that as demonstrated by the

experiments of Sipp et al. (1997) Tg is affected only

1020 8C by typical laboratory cooling rates,

logy 213 (2004) 173186 179representing a second order effect relative to that

of changing composition, and one that would affect

al Geadjustment of the calorimetric data for Tg by a few

tenths of a kJ/mol at most.

Eq. (1) has been applied to our calorimetric

measurements assuming a reference temperature of

1000 K. Heat capacities of each composition were

calculated from values of partial molar heat capacity

of SiO2 and Na2O components given by Richet (1987)

and Richet et al. (1984) for glasses and liquids,

respectively. The resulting adjustments to DHa fromEq. (1) are slightly greater for the pure-SiO2 samples,

whose fictive temperatures are in the range 1387

1526 K, and of opposite sign to those of Na-bearing

glasses whose fictive temperatures are generally

between 700 and 800 K. The good agreement of

adjusted data for remelted samples at 15, 20, 45, and

50 mol%, and those for original samples at the same

compositions, confirms that any cooling rate depend-

ence of Tg for Na-bearing samples is not significant

relative to the precision of the data. The enthalpies

obtained from Eq. (1) have been included in Table 1

and subtracted from the measured enthalpies of

solution to yield isothermal enthalpy values (last

column, Table 1).

Fig. 2 shows the final selected data, all adjusted

for fictive temperature, but excluding inaccurate data

from contaminated samples. Included are data for

both original and remelted specimens at 15, 20, 45,

and 50 mol% Na2O, data for original specimens at

0% and 10% Na2O, and data for remelted specimens

(only) at compositions from 25 through 40 mol%

Na2O.

The negatives of the resulting enthalpies of

solution (Hsoln) are expressed well by a fourth-order

polynomial:

Hsoln kJ=mol 142:2 138:9XNa 757X 2Na 1984X 3Na 1632X 4Na

2

where XNa is mole fraction of Na2O in the glass.

One sees that the enthalpies of solution vary in an

essentially linear fashion for compositions between

50 and 30 mol% Na2O. However, distinct curvature

is found in the compositional region between 0 and

30 mol% Na2O, inferring the existence of excess

G.L. Hovis et al. / Chemic180enthalpies of mixing in this range, as discussed

below.4. Thermodynamic mixing properties for

SiO2Na2O liquids

4.1. The choice of mixing units

The enthalpy of mixing (Hex) is defined as the

difference between the measured enthalpy of a given

composition and that of an isochemical mechanical

mixture of relevant endmember compositions. For the

data presented here derivation of enthalpies of mixing

between pure SiO2 and Na2SiO3 would result in

complex variations of excess enthalpies across the

system. In light of the general form of heats of

solution shown in Fig. 2, and because there is

particular interest in accurate characterization of

relations at silica-rich compositions, three endmember

compositions at 0, 33.3 and 50 mol% Na2O are here

defined. These components effectively divide the

system into two binary subsystems. These compo-

nents correspond to Q4, Q3 and Q2 species defined

from NMR spectroscopic studies (silica tetrahedra

surrounded by 0, 1 and 2 non-bridging oxygens,

respectively). This fact therefore provides a physical

basis for this choice of components, as well as

justification for considering data in the range 0 to

33 mol% Na2O separately from that between 33 and

50 mol% Na2O.

Using these three endmembers, then, excess

enthalpies clearly exist in the range 033 mol%

Na2O. On the other hand, the heats of solution

between 33 and 50 mol% Na2O are nearly linear

with respect to composition, requiring little or no

excess heat related to mixing. Indeed, the change in

slope of the heats of solution near 33 mol% Na2O

could be ascribed to the fact that, in the range 033

mol% Na2O, addition of sodium predominantly

(although not exclusively) leads to creation of Q3-

species, while in the range 3350 mol% Na2O

additions of sodium predominantly lead to the

creation of Q2-species.

4.2. Enthalpies of mixing between 0 and 33 mol%

Na2O

Heats of mixing between 0 and 33 mol% Na2O

have been computed by subtracting heats of solution

ology 213 (2004) 173186along a line of bideal mixingQ from the observed en-thalpies of solution, after adjustment to a Tr of 1000 K.

This line was defined as: Hsoln,ideal (kJ/mol)=142.20+44.23XNa extending from the calorimetric

data for pure silica (142.2 kJ/mol, the average of12 measurements made on three SiO2 samples) to

the result for the 33.3 mol% Na2O composition

(taken to be 156.9 kJ/mol, a value that lies alonga line connecting calorimetric data for 30 and 35

mol% Na2O glasses). The resulting positive values

of Hex are compositionally asymmetric, displaying a

maximum value of about 4 kJ/mol (Fig. 3) at 10

mol% Na2O. A fourth-order polynomial fitted to

Hex values for samples with compositions from 0

through 35 mol% Na2O, and constrained to have

Hex equal zero for the 0 and 33.3 mol% Na2O

endmembers, is given by:

Hex kJ=mol 89:334XNa 770:4X 2Na 2454:7X 3Na 2842:5X 4Na 3

Alternative bstandardQ formalisms may be used todescribe excess enthalpies or free energies, the

interaction) adjustable parameter. In light of the

pronounced asymmetry of the calorimetric data

(Fig. 2), however, this formalism is clearly inappro-

priate in the present case. Still, the compositional

axis may be altered through choice of endmembers

selected to make the data symmetric with respect to

composition (a technique employed by Haller et al.,

1974); in such a case a regular solution model may

be applied. Fig. 4 shows such fits that pair a

Na2SiO3 endmember with silica endmembers having

stoichiometries of SiO2/0.5 and SiO2/0.45. The

effects of these choices will be discussed below in

connection with solvus calculations.

Whatever model is used for Hex, it should be noted

that the calculated enthalpies of mixing in this system

are independent of temperature, as there is no excess

heat capacity in the system for compositions between

0 and 50 mol% Na2O. This is evidenced by the fact

that the heat capacities (Cp) of sodium silicate liquids,

measured over temperature intervals that could reach

900 K, extrapolate linearly to the heat capacity value

of pure SiO2 liquid (Richet et al., 1984). This also

. 2 as

G.L. Hovis et al. / Chemical Geology 213 (2004) 173186 181simplest being a compositionally symmetric regular

solution model having only one Margules (or

Fig. 4. Enthalpies of mixing relative to the line of ideal mixing in Figvalues as described in the text and expressed by Eq. (3). The dotted curve

and the dashed curve represents Eq. (5) for the SiO2/(0.45) model.implies that the partial molar heat capacity of 81.37 J/

mol K measured for SiO2 liquid is valid over a

discussed in the text. The solid curve is a fourth-order fit to the Hex

represents Eq. (4) using the SiO2/(0.50) model discussed in the text,

occurs because bridging oxygens, which are necessa-

rily used to coordinate Na in the melt at low

al Geconcentrations of Na, provide insufficient electrostatic

shielding. Conversely, non-bridging oxygens would

provide much more efficient shielding, thus explain-

ing why melts richer in Na are more stable. The same

argument may be used to explain the asymmetry of

the observed heats of mixing.

5. Solvus calculations from thermodynamic data

5.1. Generalities

From a thermodynamic point of view equilibrium

liquidliquid immiscibility can occur only if the

compositional dependence of the Gibbs free energy

for the liquid is such that the free energy of a

mechanical mixture of two different liquids is lower

than that of a single liquid of identical bulk compo-

sition. Therefore, assessment of the existence of

immiscibility and calculation of the solvus requires a

mathematical expression for the excess Gibbs free

energy (Gex) that in turn is associated with expressions

for the excess enthalpies and entropies of mixing.

5.2. Choices for enthalpies and entropies of mixingtemperature range much wider than that actually

investigated in the liquid state by Richet et al. (1982).

4.3. The origin of heats of mixing between 0 and 33

mol% Na2O

The microscopic basis for immiscibility in binary

silicates has long been the subject of debate in the

literature (e.g. Levin, 1967). One of the most

convincing arguments is an electrostatic origin due

to coulombic repulsion of cations that are poorly

shielded from each other (McGahay and Tomozawa,

1989; Hess, 1995; Hudon and Baker, 2002a,b). As

discussed by McGahay and Tomozawa (1989) this

phenomenon lends itself to predictions of the critical

temperature of miscibility gaps in a number of binary

silicate systems containing cations of variable charge

and radius. Hess (1995) suggested that such repulsion

G.L. Hovis et al. / Chemic182Enthalpies of mixing will be considered relative to

0 and 33.3 mol% Na2O endmembers (Eq. (3)), usingthe fourth order polynomial presented above, as well

as the SiO2/(0.50) and SiO2/(0.45) models discussed

above. In the case of the latter two fits to the data,

variation of the enthalpy of mixing may be described

by the following fourth order polynomials:

Hex 0:5 kJ=mol 72:342XNa 526:13X 2Na 1408:8X 3Na 1446:0X 4Na

4and

Hex 0:45 kJ=mol 80:172XNa 627:54X 2Na 1807:9X 3Na 1942:9X 4Na

5both of which are shown in Fig. 3.

For the entropies of mixing, the simplest model is

to assume ideal mixing of the same endmember

components as defined for the enthalpy data such that

Smix R4 xlnx 1 x ln 1 x 6

where R is the gas constant and x=3*(1XSiO2). In thiscase the entropies of mixing are positive and symmetric

between SiO2 and Na0.66Si0.66O1.66, reaching a max-

imum value of 5.8 J/mol K. This choice of functional

form is somewhat arbitrary, but we may assess its

validity by comparing these theoretical values with

those estimated within the framework of the Adam and

Gibbs theory (Richet, 1984). Configurational entropies

of sodium silicate liquids at the glass transition have

been calculated in this way by Toplis (2001) using

viscosity measurements of Knoche et al. (1994). Here

those data have been complemented with values

determined from the viscosity data of Poole (1948),

which cover a wider temperature range than those of

Knoche et al. (1994) and, in particular, reach viscosities

greater than 1012 Pa s, thus maximizing the precision of

calculated values of entropy at the glass transition.

Comparison with the values derived from the viscos-

ities of Knoche et al. (1994) shows excellent general

agreement, with the exception of data at 40 mol%

Na2O. The origin of this discrepancy is unknown, but

we note that this has no bearing on consideration of

ology 213 (2004) 173186values in the range 033 mol% Na2O of interest here.

The only other discrepancy is at 20 mol% Na2O, where

one measurement of Knoche et al. (1994) is at odds

with the data of Poole (1948) and Sipp and Richet

(2002). This has the consequence that at this compo-

sition the calculated value of entropy at the glass

transition changes from 4.5 to 6.2 J/mol K.

All values of entropy at the glass transition

temperature were then adjusted to a common

temperature of 1000 K, shown in Fig. 5, using the

appropriate liquid heat capacities. Once adjusted to

1000 K the excess configurational entropies (Fig. 6)

were defined as the difference between the calcu-

lated values and a linear base-line connecting data at

0 and 33.3 mol% Na2O. Note that, as for excess

enthalpy discussed above, the choice of reference

temperature has no effect on calculated values of

excess entropy. When these values are compared

with the form of Eq. (6) (Fig. 6), there is general

agreement with positive entropies of mixing of the

correct order of magnitude. In detail, the agreement

with the theoretical form is not perfect, but the values

of excess entropy derived from viscosity data have

large uncertainties due not only to entropies of

compositions that have uncertainties of the same

order of magnitude. An additional point of note is

that viscosity and heat capacity measurements on

liquids at 15 mol% Na2O have been interpreted to

suggest that liquidliquid unmixing occurs on the

(relatively long) timescale of those measurements

(Jarry and Richet, 2001). If this is also the case during

the measurements of Poole (1948) and Knoche et al.

(1994), then the configurational entropy derived from

those determinations may be compromised. In the

absence of a theoretically more justifiable functional

form to describe the entropy of mixing, it is assumed

that Eq. (6) is a reasonable model for entropies in this

system. As an aside, we note that the rapidly

quenched samples at both 10 and 15 mol% Na2O

used for the calorimetric measurements presented here

were clear and transparent, and that there is no reason

to suspect that our enthalpy determinations are

affected by immiscibility.

5.3. Calculation of the solvus

G.L. Hovis et al. / Chemical Geology 213 (2004) 173186 183intermediate compositions that have uncertainties on

the order of 0.75 J/mol K, but to endmemberFig. 5. Calculated configurational entropies discussed in the text. Data are

(1984) (squares with Xs), and Knoche et al. (1994) (open circles).The SiO2Na2O liquidliquid solvus has been

calculated from the ideal entropies of mixingbased on the work of Poole (1948) (partially filled squares), Richet

ixin

G.L. Hovis et al. / Chemical Geology 213 (2004) 173186184between Q4 and Q3 species represented by Eq. (6)

used in conjunction with each of Eqs. (3)(5) for the

enthalpies of mixing. In detail, the critical temperature

Fig. 6. Configurational entropies of m(Tc) and critical composition (Xc) of the solvus can be

determined for each set of Gex by finding the lowest

Fig. 7. Calculated liquidliquid solvi for the SiO2Na2O system based on v

data of Haller et al. (1974).temperature for which the second derivative of Gexequals zero at a single composition. At temperatures

above T , the second derivative of G is positive (no

g calculated as described in the text.c ex

immiscibility), whereas at temperatures below Tc pairs

of coexisting compositions satisfy the condition that

arious models discussed in the text along with the directly measured

eats o

l Geo2 2

Fig. 8. Effect of variation in the h

G.L. Hovis et al. / ChemicaB Gex/B x=0 (a series of coordinates which define the

spinodal). The solvus has been located at each

temperature by finding the coexisting compositions

that have identical chemical potentials of SiO2,

defined as the extrapolation to pure SiO2 of the local

tangent to the Gex curve. Despite the similarity of the

three equations for excess enthalpy, the critical

compositions and temperatures of the solvus vary

from 10.2 mol% Na2O at 993 K [using Hex(0.5)] to

6.3 mol% Na2O at 1166 K [using Hex(4th order)].

The various calculated solvi are shown in Fig. 7. To

illustrate further the sensitivity of the solvus calcu-

lations, we have calculated the variation of the critical

temperature in response to multiplying values of Hexby F10% around their original values (Fig. 8). Thisshows that for each of the three equations for Hex a

1% change in Hex results in a change of calculated

critical temperature on the order of 10K. In view of

this sensitivity, one can appreciate that our calculated

solvi for the SiO2Na2O system are not far from the

experimentally determined solvus of Haller et al.

(1974), which has a critical temperature of 837 8C(1110 K) and a critical composition of 8 mol% Na2O

(Fig. 7). Indeed, one can generate a good match of

modeled and experimental data by using thef mixing on critical temperature.logy 213 (2004) 173186 185Hex(0.45) model discussed above, adjusted by just

4.2% (i.e. Hex multiplied by a constant value of

1.042; see Fig. 7).

6. Conclusions

Our calorimetric data on sodium silicate glasses

provide clear evidence for positive enthalpies of

mixing in the liquid state for the compositional range

between 0 and 33.3 mol% Na2O. When combined

with estimates of entropy based upon ideal mixing of

Q4 and Q3 species in the liquid we calculate the

presence of a miscibility gap in this system. Values

of the critical temperature and composition at the

crest of the solvus are shown to be very sensitive to

small variations in Hex, but despite this sensitivity,

the critical temperature and shape of the experimen-

tally determined solvus (Haller et al., 1974) are

perfectly consistent with our measurements. This

demonstrates a high degree of compatibility among

the data for entropy, enthalpy, and phase equilibrium

and also confirms the requirement of positive

enthalpies of mixing for liquid immiscibility in the

SiO2Na2O system.

Acknowledgements

binary oxide melts and glasses: I. Silicate systems. J. Non-Cryst.

Kracek, F.C., 1930. The system sodium oxide-silica. J. Phys. Chem.

34, 15831598.

Levin, E.M., 1967. Structural interpretation of miscibility in oxide

G.L. Hovis et al. / Chemical Geology 213 (2004) 173186186Solids 303, 299345.

Hudon, P., Baker, D.R., 2002b. The nature of phase separation in

binary oxide melts and glasses: II. Selective solution mecha-

nism. J. Non-Cryst. Solids 303, 346353.

Hummel, V.C., Schweite, H.E., 1959. Thermochemische Untersu-

chungen im System Na2OSiO2. Glastech. Ber. 32, 413420.

Jarry, P., Richet, P., 2001. Unmixing in sodium silicate melts:

influence on viscosity and heat capacity. J. Non-Cryst. Solids

293295, 232237.

Knoche, R., Dingwell, D.B., Seifert, F.A., Webb, S.L., 1994. Non-

linear properties of supercooled liquids in the system Na2O

SiO2. Chem. Geol. 116, 116.We thank Philippe Jarry for the synthesis of many

of the glasses utilized in this study. GLH thanks the

U.S. National Science Foundation for support of this

research via grant EAR-0000523. We extend our

thanks to Pavel Hrma (Pacific Northwest National

Laboratory) for information concerning the reaction of

Na silicate glasses with water and carbon dioxide, and

also to Emmanuelle Bourgue for related information

on K silicate glasses. Joyce Hovis kindly helped with

proof reading. [RR]

References

Adam, G., Gibbs, J.H., 1965. On the temperature dependence of

cooperative relaxation properties of glass-forming liquids.

J. Chem. Phys. 43, 139146.

Haller, W., Blackburn, D.H., Simmons, J.H., 1974. Miscibility gaps

in alkalisilicate binariesdata and thermodynamic interpreta-

tion. J. Am. Ceram. Soc. 57, 120126.

Halter, W.E., Mysen, B.O., 2004. Melt speciation in the system

Na2OSiO2. Chem. Geol. 213, 115123.

Hess, P.C., 1995. Thermodynamic mixing properties and the

structure of silicate melts. In: Stebbins, J.F., McMillan, P.F.,

Dingwell, D.B. (Eds.), Structure, Dynamics and Properties of

Silicate Melts, Mineralogical Society of America Reviews in

Mineralogy, vol. 32, pp. 145189.

Hovis, G.L., Roux, J., 1993. Thermodynamic mixing properties

of nephelinekalsilite crystalline solutions. Am. J. Sci. 293,

11081127.

Hovis, G.L., Roux, J., Richet, P., 1998. A new era in hydrofluoric

acid solution calorimetry: reduction of required sample size

below ten milligrams. Am. Miner. 83, 931934.

Hudon, P., Baker, D.R., 2002a. The nature of phase separation insystems: IV. Occurrence, extent and temperature of the

monotectic. J. Am. Ceram. Soc. 50, 2938.

McGahay, V., Tomozawa, M., 1989. The origin of phase separation

in silicate melts and glasses. J. Non-Cryst. Solids 109, 2734.

Mysen, B.O., 1988. The structure and properties of silicate melts.

Elsevier, Amsterdam.

Poole, J.P., 1948. Viscosite a` basse temperature des verres alcalino

silicates. Verres Refract. 2, 222228.

Porai-Koshits, E.A., Averjanov, V.I., 1968. Primary and secondary

phase separation of sodium silicate glasses. J. Non-Cryst. Solids

1, 2938.

Richet, P., 1987. Heat capacity of silicate glasses. Chem. Geol. 62,

111124.

Richet, P., 1984. Viscosity and configurational entropy of silicate

melts. Geochim. Cosmochim. Acta 48, 471483.

Richet, P., Bottinga, Y., 1984. Anorthite, andesine, wollastonite,

diopside, cordierite and pyrope: thermodynamics of melting,

glass transitions and thermodynamic properties of the amor-

phous phases. Earth Planet. Sci. Lett. 67, 415432.

Richet, P., Bottinga, Y., 1986. Thermochemical properties of silicate

glasses and liquids: a review. Rev. Geophys. 24, 125.

Richet, P., Bottinga, Y., Denielou, L., Petitet, J.P., Tequi, C., 1982.

Thermodynamic properties of quartz, cristobalite, and amor-

phous SiO2: drop calorimetry measurements between 1000 and

1800 K and a review from 0 to 2000 K. Geochim. Cosmochim.

Acta 46, 26392658.

Richet, P., Bottinga, Y., Tequi, C., 1984. Heat capacity of sodium

silicate liquids. J. Am. Ceram. Soc. 67, C6C8.

Rogez, J., Mathieu, J.-C., 1985. Enthalpies de formation dans le

syste`me Na2OK2OSiO2. Phys. Chem. Liq. 14, 259272.

Sipp, A., Richet, P., 2002. Equivalence of volume, enthalpy and

viscosity relaxation kinetics in glass-forming silicate liquids.

J. Non-Cryst. Solids 298, 202212.

Sipp, A., Neuville, D.R., Richet, P., 1997. Viscosity, configurational

entropy and relaxation kinetics of borosilicate melts. J. Non-

Cryst. Solids 211, 281293.

Takahashi, K., Yoshio, T., 1970. Energy relations in alkali silicates

by solution calorimetry. Yogyo Kyokaishi 78, 2938.

Tischer, R.E., 1969. Heat of annealing in simple alkali silicate

glasses. J. Am. Ceram. Soc. 52, 499503.

Toplis, M.J., 2001. Quantitative links between microscopic proper-

ties and viscosity of liquids in the system SiO2Na2O. Chem.

Geol. 174, 321331.

Toplis, M.J., Gottsmann, J., Knoche, R., Dingwell, D.B., 2001. Heat

capacities of haplogranitic glasses and liquids. Geochim.

Cosmochim. Acta 65, 19851994.

Waldbaum, D.R., Robie, R.A., 1970. An internal sample

container for hydrofluoric acid solution calorimetry. J. Geol.

78, 736741.

Thermodynamic mixing properties of sodium silicate liquids and implications for liquid-liquid immiscibilityIntroductionExperimental proceduresSolution calorimetrySample synthesis

ResultsCalorimetric dataComparison with previous studiesAdjustments for fictive temperature

Thermodynamic mixing properties for SiO2-Na2O liquidsThe choice of mixing unitsEnthalpies of mixing between 0 and 33 mol% Na2OThe origin of heats of mixing between 0 and 33 mol% Na2O

Solvus calculations from thermodynamic dataGeneralitiesChoices for enthalpies and entropies of mixingCalculation of the solvus

ConclusionsAcknowledgementsReferences