The partial molar volume and thermal expansivity of TiO2 in alkali silicate melts: Systematic variation with Ti coordination

Geochimica et Cosmochimica Acta, Vol. 65, No. 14, pp. 2379 –2393, 2001 Copyright © 2001 Elsevier Science Ltd Printed in the USA. All rights reserved 0016-7037/01 $20.00 ⫹ .00

Pergamon

PII S0016-7037(01)00565-8

The partial molar volume and thermal expansivity of TiO2 in alkali silicate melts: Systematic variation with Ti coordination QIONG LIU and REBECCA A. LANGE* Department of Geological Sciences, 2534 C.C. Little Building, University of Michigan, Ann Arbor, MI 48109-1063, USA (Received June 16, 2000; accepted in revised form January 2, 2001)

Abstract—The densities of seven K2O-TiO2-SiO2 (KTS) liquids and seven Na2O-TiO2-SiO2 (NTS) liquids have been measured between 1236 and 1771 K using the double-bob Archimedean method. In addition, the low-temperature density of these liquids at their limiting fictive temperature (T⬘f; near the glass transition) were also measured. Compositions range from 15 to 39 mol % K2O and Na2O, 10 to 35 mol % TiO2, and 33 to 61 mol % SiO2. Plots of molar volume vs. temperature are linear for all samples in the stable liquid region, but there is an increase in the slope (⭸V/⭸T) with decreasing temperature in the supercooled liquid region, analogous to that observed for the heat capacity of similar alkali titanosilicate liquids. Derived values of V¯TiO2 (at 1373 K) decrease systematically from 32.5 to 26.5 cm3/mol between 39 and 15 mol% K2O and from 29.6 to 25.7 cm3/mol between 39 and 25 mol% Na2O (and are nearly constant at ⬃25 ⫾ 0.5 cm3/mol between 25 and 15 mol% Na2O). Values of V¯TiO2 do not appear to be a function of the TiO2 concentration, but instead depend strongly on the nature of the alkali present (larger by ⬃3 cm3/mol in KTS vs. NTS liquids) and the degree of polymerization (increase with NBO/T). By comparing our values of V¯TiO2 at 1373 K to published Ti coordination numbers on samples of similar composition, we calculate that the average Ti coordination number varies from ⬃4.0 to 5.1 in the KTS liquids and from ⬃4.6 to 5.5 in the NTS liquids. The value of ⭸V¯TiO 2 in the stable liquid region correlates strongly with V¯TiO2 at 1373 K (and therefore with Ti coordination). ⭸T It is near zero when the average coordination is close to four, but reaches a maximum of ⬃6 to 8 ⫻ 10⫺3 cm3/mol-K when the average Ti coordination number is close to five. In all corresponding glasses, the value ⭸V¯TiO 2 ⭸V¯TiO 2 is zero. Together, these features require that in the liquid is associated with the presence of of ⭸T ⭸T [5] Ti and involves structural changes not available to solids. Copyright © 2001 Elsevier Science Ltd observed in several studies of silicate melt density (Lange and Carmichael, 1987; Johnson and Carmichael, 1987; Dingwell, 1992), where the partial molar volume of TiO2 (V¯TiO2) has been shown to be strongly dependent on composition, with the highest values found in potassic silicate melts (V¯TiO2 ⱕ 32 cm3/mole at 1373 K) and the lowest values in calcic silicate melts (V¯TiO2 ⱖ 23 cm3/mole at 1673 K). These results suggest a compaction of V¯TiO2 by ⬃28% as Ti4⫹ shifts from lower to higher coordination. The results of XANES spectra indicate average Ti coordination numbers that vary from 4.2 to 5.0 in potassic silicate glasses and from 5.2 to 5.6 in calcic silicate glasses (Dingwell et al., 1994; Farges et al., 1996b). These variations within the potassic and calcic systems, respectively, arise from the sensitivity of the average Ti coordination number to the NBO/T ratio and TiO2 content of the sample. This strong densification of the TiO2 component, associated with a shift in Ti4⫹ coordination, has important implications for the density of high-pressure mantle melts at conditions where Si4⫹ occurs in multiple coordination. Precise and detailed measurements of silicate melt density under the in situ conditions where Si4⫹ undergoes pressure-induced coordination change (⬎6 GPa) are extremely difficult compared to the ease with which the density of titanosilicate melts can be measured at one bar. By analogy to Si4⫹ and V¯SiO2, therefore, it is of interest to determine how V¯TiO2 varies as a function of the average Ti4⫹ coordination number. Is the relationship linear? How does the thermal expansivity of the TiO2 component

1. INTRODUCTION

Ti4⫹ is an important minor component in magmatic liquids, with concentrations typically ⱕ3 wt%. Even at these low concentrations, it has a significant influence on the physical and chemical properties of silicate melts owing to the multiple coordination environments that Ti can occupy. Although it has long been known that Ti4⫹ occurs in four-, five- and six-fold coordination in crystalline compounds, only recently have all three Ti4⫹ coordination sites been unequivocally confirmed in high-temperature silicate liquids utilizing Ti K-edge XANES (X-ray absorption near-edge structure) spectra (Farges, 1996c). The average coordination of Ti4⫹ in silicates is a complex function of composition, including the concentration of TiO2 present (Farges, 1997), the ratio of non-bridging oxygens to tetrahedral units, NBO/T, (Dingwell et al., 1994; Farges et al., 1996b), the nature and concentration of the alkali or alkalineearth cation that is present (Dingwell et al., 1994; Farges et al., 1996b; Farges, 1997), and the alumina concentration (Romano et al., 2000). Because the density of a silicate melt is largely determined by the geometrical packing and coordination of its networkforming ions, the capacity of Ti4⫹ to shift coordination strongly affects the density of titanosilicate liquids. This trend has been

*Author to whom correspondence should be addressed (becky@ umich.edu). 2379

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Q. Liu and R. A. Lange

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⭸V¯TiO 2 vary with Ti coordination? Unfortunately, most den⭸T sity measurements on titanosilicate melts have been measured over a narrow temperature interval (ⱕ200°) and the thermal expansivity of these liquids is currently poorly constrained. The purpose of this study is to address these questions by performing a series of density measurements on a variety of liquids in the Na2O-TiO2-SiO2 and K2O-TiO2-SiO2 systems. The reason for choosing these two ternary systems is manifold. First, they both are characterized by a low liquidus surface, which allows density measurements to be made over a large temperature range in the stable liquid region (⬃1150 –1750 K). Second, liquids within these two systems exhibit anomalous configurational contributions to their heat capacity immediately above Tg (Richet and Bottinga, 1985; Lange and Navrotsky, 1993; Tangeman and Lange, 1998; Bouhifd et al., 1999). It is unknown if similar, anomalous configurational changes contribute to the thermal expansivities of these liquids. Third, by systematically exploring variations in V¯TiO2 as a function of the alkali/silica ratio, the TiO2 concentration, and the substitution of K for Na, we may further constrain those compositional controls that influence Ti coordination. And last, there is a growing body of XANES spectra on alkali silicate glasses, indicating Ti coordination numbers that vary between at least 4.2 and 5.6 (Dingwell et al., 1994; Farges, 1996b; Farges, 1997). By examining our values of V¯TiO2 in liquid compositions for which the average Ti coordination is known in the corresponding glass, we can explore whether values of V¯TiO2 and ⭸V¯TiO 2 vary systematically with Ti4⫹ coordination number. ⭸T 2. EXPERIMENTAL METHODS

Table 1a. Compositions of samples (wt%). Sample

Na2O

K2O

TiO2

SiO2

Total

g.f.w.

NBO/T

NTS-2 (nominal) NTS-4 (nominal) NTS-6 (nominal) NTS-7 (nominal) NTS-8 (nominal) NTS-9 (nominal) NTS-10 (nominal) KTS-2 (nominal) KTS-3a KTS-6 (nominal) KTS-7a KTS-8a KTS-9 (nominal) KTS-10 *nominal)

22.89 23.65 33.64 33.02 14.30 14.23 28.06 28.34 36.50 37.68 19.06 18.95 18.45 18.39 – – – – – – – – – – –

– – – – – – – – – – – – – – 32.05 32.01 33.36 20.41 20.14 37.54 47.88 26.79 26.22 26.12 25.52

30.48 30.49 30.52 30.40 30.69 30.58 30.16 30.44 30.41 31.35 29.56 30.53 40.89 41.49 26.89 27.15 11.32 27.63 28.47 26.54 25.39 27.00 27.79 37.06 37.87

46.07 45.86 36.09 36.58 54.85 55.19 41.36 41.22 32.10 31.96 50.84 50.52 40.06 40.12 40.88 40.84 55.32 51.08 51.39 35.92 26.73 45.54 45.99 36.28 36.62

99.44 100.00 100.25 100.00 99.84 100.00 99.58 100.00 99.01 100.00 99.46 100.00 99.40 100.00 99.82 100.00 100.00 99.12 100.00 100.00 100.00 99.33 100.00 99.46 100.00

65.528

0.64

65.721

1.04

65.353

0.35

65.585

0.85

65.836

1.29

65.267

0.51

67.893

0.51

73.545

0.67

70.592 70.163

0.67 0.36

75.266 78.678 71.951

0.86 1.33 0.52

73.947

0.52

a

Nominal composition.

The conditions of the sample synthesis (and the high-temperature density measurements) were too oxidizing (performed in air) for the formation of detectable amounts Ti3⫹ in any of our samples. This is confirmed by the lack of the intense blue color that is characteristic of glasses with trace amounts of Ti3⫹. Henceforth, all references to Ti will imply Ti4⫹.

2.1. Sample Synthesis and Compositional Analysis

2.2. Low-Temperature Measurements of Liquid Volume at Tfⴕ

One of the fourteen samples investigated in this study was previously synthesized and analyzed by Tangeman and Lange (1998). This sample (NTS-2) was re-melted at 1373 K to eliminate any absorbed water. The quenched glass was then examined by optical methods to ensure that it was free of bubbles. The remaining samples (NTS-4, 6, 7, 8, 9, 10, KTS-2, 3, 6, 7, 8, 9, 10) were synthesized by mixing appropriate proportions of reagent grade Na2CO3, K2CO3, TiO2 and SiO2. The mixed powders were slowly dried and de-carbonated, and then fused at 1273 to 1673 K. The samples were quenched to glasses, ground to a powder and refused. To ensure sample homogeneity, this procedure was repeated twice. All samples before and after the density measurements were analyzed with a Cameca Cambex electron microprobe at the University of Michigan. Standard operating conditions consisted of a focused electron beam in raster mode, an accelerating voltage of 15 kV, and beam current of 5.4 nA. Standards included one K2O-TiO2-SiO2 glass (KTS-2) and one Na2O-TiO2-SiO2 glass (NTS-2) that were wet chemically analyzed by I.S.E. Carmichael at U.C. Berkeley. Three potassic samples (KTS-3, 7, 8) were so hygroscopic (a tendency for the glass surface to absorb water from the air) that they could not be analyzed by electron microprobe. Therefore, their nominal compositions were used; a comparison of analyzed vs. nominal compositions for all other samples indicates that this is not an unreasonable alternative (Table 1). All analyses are reported in Table 1, along with five melt compositions (LC-20, NTS-1, 5, KTS-5, 11) for which high-temperature density measurements were reported by Lange and Carmichael (1987) and Johnson and Carmichael (1987). For each composition, the gram formula weight (g.f.w. ⫽ ⌺XiMi) is tabulated, where Xi is the mole fraction of each oxide component, and Mi is the molecular weight of each oxide component. The uncertainties in g.f.w. range between 0.32 and 0.54%, owing to the analytical errors.

The technique to obtain liquid volume measurements at the limiting fictive temperature (T⬘f) is described in detail in Lange (1996, 1997) and Tangeman and Lange (2001). The T⬘f of any glass quenched from a liquid is uniquely defined on a volume vs. temperature curve as the extrapolated intersection of the glass and liquid properties within the glass transition interval (Moynihan et al., 1976; Scherer, 1992; Debenedetti, 1996). Because the volume of the glass is equal to that of the liquid at T⬘f, the following equation describes both: glass V liq共T⬘f兲 ⫽ V glass共T⬘f兲 ⫽ V glass 共T⬘f ⫺ 298兲兲, 298 exp共 ␣

(1)

where ␣ refers to an average or temperature-independent coefficient of thermal expansion for the glass between 298 K and T⬘f. The volume of a liquid at T⬘f can thus be obtained from three measurements: (1) the glass volume (density) at 298 K; (2) the glass thermal expansion coefficient between 298 K and the beginning of the glass transition interval (usually ⬃100 –150° below T⬘f); and (3) the value of T⬘f. glass

Table 1b. Compositions of samples from the literature (wt%). Sample

Na2O

K2O

TiO2

SiO2

Total

g.f.w.

NBO/T

NTS-1 NTS-5 KTS-5 KTS-11 LC-20

28.51 31.89 — — 25.50

– – 40.31 44.60 –

12.49 39.86 33.42 22.07 19.34

58.64 28.18 25.20 32.56 54.73

99.64 99.93 98.93 99.23 99.57

65.576 67.405 78.161 76.823 63.645

0.81 1.06 1.02 1.16 0.71

First four samples are from Johnson and Carmichael (1987); LC-20 is from Lange and Carmichael (1987).

The partial molar volume of TiO2 in silicate melts Table 2. Density of molten NaCl (g/cm3). Temp (K)

Data

1190 1190 1190 1190 1190 1190 1190 1289 1289 1289 1289 1289 1289 1289

1.493 1.504 1.494 1.505 1.500 1.502

2.3. High Temperature Measurements of Liquid Volume Mean

1.500 ⫾ .005

1.435 1.447 1.437 1.449 1.446 1.448

2381

1.444 ⫾ .006

The room temperature (298 K) density of each glass sample was measured using the Archimedean method with a microbalance. Each glass was weighed in air 10 to 12 times, then weighed below the balance 24 to 30 times while immersed in liquid toluene. Sample weights in air ranged from 242 to 1442 mg. The standard deviations in density, based on these replicates, range from 0.01 to 0.20% (Table 2). 1 ⭸L The linear thermal expansion coefficient of each glass samL ⭸T ple was measured with a Perkin-Elmer TMA-7 vertical dilatometer using a scan rate of 10 K/min from 298 K up to and a few degrees beyond the glass transition temperature for each sample. Experimental procedures are identical to those described in Lange (1997). Glass samples of 3 to 10 mm height were used, and considerable care was taken to ensure that the bottom and top surfaces of the glass samples were as flat and parallel as possible. Replicate measurements on several samples indicate a reproducibility in ␣glass that is better than 4% (Table 3), whereas comparison of our measurements on NIST standard-731 indicate an accuracy of 8%. An approximation of T⬘f for each glass sample was obtained by choosing the temperature corresponding to the onset of the rapid rise in ⭸L/L vs. T in the dilatometery curve at the glass transition. Tangeman and Lange (2001) showed that estimates of T⬘f obtained in this manner closely match quantitative determinations of T⬘f calculated from Cp heating curves. For the sixteen samples studied by Tangeman and Lange (2001), the deviation is 8° on average, with a maximum discrepancy of 17°. On this basis, we assume an uncertainty of ⬍20° in the derived values of T⬘f.

冉 冊

High-temperature, liquid density measurements were made on the fourteen samples using the Pt double-bob Archimedean method, described in detail by Lange and Carmichael (1987) and references therein. We only give a brief description here. Each sample glass was loaded piece-meal into a Pt crucible (7.5 cm long ⫻ 3.5 cm O.D.) and fused in a box furnace until the liquid depth was ⬃3 cm. The Pt crucible was then put into a vertical tube Deltech furnace, where it rested on an alumina platform in a fixed position so that the hot spot of the furnace coincided with the top 1.5 cm of the liquid depth (to eliminate thermal convection). An electronic balance mounted on an aluminum platform above the furnace was used to measure the buoyancy (weight in air corrected to vacuum less the weight in silicate liquid) of at least two bobs of different mass (⬃26.6 g and ⬃11.6 g). By using two bobs of different mass but identical stem diameters, the effect of surface tension was eliminated. Two to five bobs were used for each sample at each temperature of measurement. Two bobs (one large, one small) allow a single density determination, whereas five bobs (e.g., three large, two small) allow six density measurements to be made at each temperature. Standard deviations in the high temperature liquid densities range from 0.04 to 0.32%. Measurements were made at three to four different temperatures for each sample, spanning an interval that ranged from 181 to 293°. The lower temperature limit of the density experiments was constrained by liquidus temperatures and melt viscosity (the double-bob Archimedean method is optimal when melt viscosities are ⱕ102.0 Pa-s), whereas the upper temperature limit was constrained to temperatures where alkali loss was insignificant. An electronic temperature controller enabled the temperature in the furnace to be reproduced to within ⫾1.5 K at a given set-point, which allowed the buoyancy of two to five different Pt bobs to be measured at the same specific temperature. The temperature profile within the the top 1.5 cm of the liquid contained in the Pt crucible was determined from a calibration curve. This was achieved by filling the density Pt crucible with alumina powder (proxy for a silicate melt) to 3 cm depth, placing it in the density furnace with the alumina baffle system in place (see Stein et al., 1986, for a description of the baffle), and then inserting an S-type thermocouple down the center of the baffle tube into the alumina powder. The temperature in the top 1.5 cm was then recorded as function of the set-point controller temperature, providing a calibration curve. The calibration was checked several times during the course of the density experiments. The uncertainty in the temperature obtained in this manner is estimated to be ⬍5 K. This is confirmed by our density measurements for liquid NaCl at 1190 and 1289 K (Table 2; Fig. 1), obtained as a check on the accuracy of our high-temperature double-bob data. Our measurements are within 0.11 and ⫺0.15% of the fit to the NaCl density measurements of Stein et al. (1986) and Lange

Table 3. Density and volume of glasses at 298 K and T⬘f. Sample

␳ (298 K) (g/cm3)

Vol (298 K) (cm3/g.f.w.)

␣glass (10⫺5/K)

Vol (T⬘f) (cm3/g.f.w.)

T⬘f (K)

NTS-1 NTS-2 NTS-4 NTS-5 NTS-6 NTS-7 NTS-8 NTS-9 NTS-10 LC-20 KTS-2 KTS-3 KTS-6 KTS-7 KTS-9 KT-10

2.597 ⫾ .005 2.794 ⫾ .004 2.799 ⫾ .003 2.892 ⫾ .001 2.726 ⫾ .004 2.797 ⫾ .002 2.791 ⫾ .008 2.774 ⫾ .002 2.915 ⫾ .002 2.673 ⫾ .003 2.647 ⫾ .001 2.524 ⫾ .001 2.650 ⫾ .001 2.649 ⫾ .001 2.651 ⫾ .001 2.752 ⫾ .001

24.10 23.45 23.45 23.31 24.02 23.45 23.59 23.53 23.29 23.81 27.78 27.97 26.48 28.41 27.14 26.87

3.472 3.507 4.393 4.332 2.307 3.990 4.957 2.972 3.083 3.455 3.897 3.872 2.536 4.616 3.252 3.175

24.53 23.91 23.95 23.81 24.35 23.95 24.06 23.94 23.71 24.26 28.36 28.56 26.88 29.06 27.65 27.35

808 850 770 790 880 822 739 877 880 840 828 843 891 776 869 860

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Q. Liu and R. A. Lange

Fig. 1. Plot of measured density vs. temperature for molten NaCl. The equation from Janz, 1980 is shown as a solid line (␳ ⫽ 2.139 – 5.43 ⫻ 10⫺4 T(K)). The data from this study are shown as solid dots, the data from Lange and Carmichael (1987) are shown as open boxes, and the data of Stein et al. (1986) are shown as crosses. The measurements of this study, Lange and Carmichael (1987) and Stein et al. (1986) from different laboratories and different operators over a 14 y interval are all broadly consistent (dashed line: ␳ ⫽ 2.174 –5.68 ⫻ 10⫺4 T(K)).

and Carmichael (1987), and within ⫺0.45 and ⫺0.04% of the values recommended by NIST (Janz, 1980). 3. RESULTS

3.1. Density and Volume of the Glasses at 298 K For 16 samples (13 from this study plus NTS-1, NTS-5 and LC-20 from Johnson and Carmichael, 1987 and Lange and Carmichael, 1987 respectively), glass density was measured three times at 298 K, before and after each of two dilatometry experiments (during which the glass is heated into the glass transition interval) to evaluate the effect of any structural relaxation that may have occurred. Sample KTS-8 from this study, as well as samples KTS-5 and KTS-11 from Johnson and Carmichael (1987) were too hygroscopic for glass density measurements. A tabulation of the glass density data indicates that the difference between the first and second measurements ranges from 1.03% for LC-20 to 0.07% for KTS-3, with an average deviation for all samples of 0.34%. In contrast, the deviation between the second and third density measurements ranges from 0.19% for NTS-5 to 0.00% for KTS-2, with an average deviation for all samples of 0.07%. In general, the NTS glasses appear to undergo greater structural relaxation during heating than the KTS glasses. The difference between the first and second density measurements for the TiO2-bearing glasses (0.34% on average) is significantly larger than that observed under similar conditions for 24 different K2O-Na2O-CaOMgO-Al2O3-SiO2 glasses (0.11% on average; Lange, 1997), and likely reflects slower structural relaxation times in the TiO2-bearing vs. TiO2-free supercooled liquids. This effect has been observed more directly in a series of low-temperature viscosity measurements on alkali titanosilicate liquids by Bouhfid et al. (1999). The difference between the second and third density measurements (0.07% on average) is close to the experimental uncertainty. Therefore, in all further calculations the average of the last two density determinations was used. The volume of each glass at 298 K (Vglass 298 ) was calculated

Fig. 2. (a) A plot of ␣glass vs. XK2O for the KTS glasses in Table 3 and (b) a plot of ␣glass vs. XNa2O for the NTS glasses in Table 3. The glass thermal expansion coefficients are linear functions of their alkali concentration, within experimental resolution.

from the density at 298 K (␳ glass 298 ) and the gram formula weight (g.f.w.) using the following equation: glass V glass 298 ⫽ g.f.w./ ␳ 298

(2) glass 298

Owing to the errors in the g.f.w. (ⱕ0.5%), the errors in V are higher than those in ␳glass 298 and range from 0.3 to 0.6%. 3.2. Thermal Expansion and Tⴕf of the Glasses

Two replicate thermal expansion experiments were run for each glass sample. Examples of dilatometry runs are given in Lange (1996, 1997) and Tangeman and Lange (2001). The linear coefficient of thermal expansion for each glass was derived from the slope of ⭸L/L vs. T (where L is the length of the glass cylinder). The volume coefficient of thermal expan1 ⭸V sion, ␣glass ⫽ , was obtained by multiplying the linear V ⭸T coefficient by three. No temperature dependence to ␣glass could be resolved in this study. The difference in the values for ␣glass between the replicate TMA runs range from 4.1% (KTS-6) to 0.8% (KTS-9), with an average deviation of 2.6% for all samples. Values of ␣glass are a linear function of K2O and Na2O concentration as seen in Figure 2. The T⬘f values differ by less than 8° (2° on average) between the replicate runs for all glass 16 samples. The combined data for Vglass and T⬘f allow a 298 , ␣

The partial molar volume of TiO2 in silicate melts

2383

Table 4a. High-temperature density and volume of NTS liquids. Sample

Temperature (K)

Density (g/cm3)

N

Volume (cm3/g.f.w.)

NTS-2 NTS-2 NTS-2 NTS-2 NTS-4 NTS-4 NTS-4 NTS-4 NTS-6 NTS-6 NTS-6 NTS-6 NTS-7 NTS-7 NTS-7 NTS-8 NTS-8 NTS-8 NTS-8 NTS-9 NTS-9 NTS-9 NTS-9 NTS-10 NTS-10 NTS-10 NTS-10

1292 1392 1487 1578 1236 1337 1434 1526 1526 1616 1707 1752 1240 1342 1440 1240 1342 1440 1533 1434 1526 1616 1707 1487 1578 1671 1771

2.498 ⫾ .003 2.462 ⫾ .003 2.428 ⫾ .002 2.404 ⫾ .003 2.489 2.450 2.418 2.392 2.432 ⫾ .001 2.406 ⫾ .001 2.387 ⫾ .001 2.374 ⫾ .004 2.494 ⫾ .008 2.463 ⫾ .005 2.428 ⫾ .006 2.447 ⫾ .003 2.411 ⫾ .003 2.379 ⫾ .001 2.351 ⫾ .004 2.454 ⫾ .001 2.431 ⫾ .001 2.412 ⫾ .005 2.393 ⫾ .010 2.527 ⫾ .001 2.494 ⫾ .001 2.465 ⫾ .001 2.437 ⫾ .001

4 4 4 4 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

26.18 26.63 26.94 27.24 26.37 26.79 27.15 27.44 26.93 27.23 27.43 27.59 26.30 26.64 27.02 26.91 27.31 27.68 28.01 26.60 26.85 27.06 27.28 26.65 27.00 27.32 27.63

N ⫽ number of density measurements.

value for the volume of the silicate liquid to be calculated at T⬘f using Eqn. 1, which are presented in Table 3. 3.3. High Temperature Density, Volume, and Thermal Expansion of the Liquids High temperature density measurements on seven liquids in the Na2O-TiO2-SiO2 (NTS) system and seven liquids in the K2O-TiO2-SiO2 (KTS) system are presented in Table 4. These density data are converted to molar volumes, using Eqn. 2 (Table 4); uncertainties in molar volume are ⱕ0.6%. Plots of molar volume vs. temperature are shown in Figure 3a-s for these 14 liquids plus four liquids (NTS-1, 5, KTS-5, 11) from Johnson and Carmichael and one liquid (LC-20) from Lange and Carmichael (1987). For all liquids, including those spanning ⬎400° in temperature (NTS-5, LC-20, KTS-5, KTS-11), the slope of molar volume with temperature is linear. In contrast, when the low-temperature data at T⬘f are included in a plot of molar volume vs. temperature (Fig. 3), there is a clear increase in the slope (⭸V/⭸T) with decreasing temperature into the supercooled liquid region. In general, the curvature is most pronounced in liquids with the highest concentration of TiO2 (e.g., NTS-5, NTS-10 and KTS-10) and weakest in those with only ⬃10 mol% TiO2 (e.g., NTS-1 and KTS-3). These results indicate a negative temperature dependence to ⭸V/⭸T in the supercooled liquid region of these alkali titanosilicate melts that is analogous to that observed for their heat capacity (Richet and Bottinga, 1985; Navrotsky and Lange, 1993; Tangeman and Lange, 1998; Bouhifd et al., 1999). This pattern is completely different from that observed for 24 K2O-Na2O-CaO-

MgO-Al2O3-SiO2 liquids, where plots of molar volume vs. temperature (spanning 800 –1100°) are linear (Lange, 1996, 1997). An example is shown in Figure 3t for a TiO2-free, alkali silicate liquid (LC-19 from Lange, 1997). A linear fit to the high temperature volume data for this liquid recovers the lowtemperature volume measurement at T⬘f within 0.1% and clearly shows that the thermal expansivity of this TiO2-free liquid is a constant over 1100°. In contrast, a temperature dependence to the thermal expansivity of all the TiO2-bearing liquids is well resolved, with KTS-3 the only exception. Because of the absence of volume data at temperatures intermediate between T⬘f and the stable liquid region, details of how the thermal expansivity of the alkali titanosilicate liquids varies over this temperature interval are not known; the dashed lines in Figure 3 are just interpolations between the high and low temperature volume data. As a consequence, only the high-temperature double-bob density data are used to derive ⭸V¯TiO 2 values of V¯TiO2 and as a function of composition. ⭸T 3.4. The Partial Molar Volume and Thermal Expansivity of the TiO2 Component The stable-liquid volume data for the Na2O-TiO2-SiO2 and K2O-TiO2-SiO2 liquids in Table 3 were combined with density data from the literature on K2O-Na2O-CaO-MgO-Al2O3-SiO2 liquids (Bockris et al., 1956; Stein et al., 1986; Lange and Carmichael, 1987; Lange, 1996, 1997) to calibrate the following linear volume equation:

2384

Q. Liu and R. A. Lange Table 4b. High-temperature density and volume of KTS liquids. Sample

Temperature (K)

Density (g/cm3)

N

Volume (cm3/g.f.w.)

KTS-2 KTS-2 KTS-2 KTS-3 KTS-3 KTS-3 KTS-6 KTS-6 KTS-6 KTS-7 KTS-7 KTS-7 KTS-7 KTS-8 KTS-8 KTS-8 KTS-8 KTS-9 KTS-9 KTS-9 KTS-10 KTS-10 KTS-10

1289 1387 1480 1571 1662 1752 1480 1571 1662 1289 1387 1480 1571 1289 1387 1480 1571 1387 1480 1571 1434 1526 1616

2.378 ⫾ .001 2.349 2.317 2.238 ⫾ .003 2.213 ⫾ .003 2.192 ⫾ .002 2.378 ⫾ .002 2.351 ⫾ .001 2.331 ⫾ .004 2.350 2.323 2.293 2.267 2.305 ⫾ .001 2.279 ⫾ .002 2.253 ⫾ .002 2.225 ⫾ .001 2.379 ⫾ .001 2.351 ⫾ .004 2.328 ⫾ .003 2.411 ⫾ .001 2.382 ⫾ .001 2.357 ⫾ .003

2 1 1 6 6 6 2 2 2 1 1 1 1 2 2 2 2 2 2 2 4 4 4

30.93 31.31 31.74 31.54 31.90 32.20 29.51 29.84 30.10 32.03 32.40 32.82 33.20 34.13 34.52 34.92 35.36 30.25 30.61 30.91 30.67 31.04 31.37

N ⫽ number of density measurements.

V¯ liq共X,T兲 ⫽

冘 再

X i V¯ i,Tref ⫹

⭸V¯ i 共T ⫺ T ref兲 ⭸T

冎

(3)

where Xi is the mole fraction of each oxide component, V¯i,Tref is the partial molar volume of each oxide component at a refer⭸V¯i ence temperature (Tref ⫽ 1373 K) and is the partial molar ⭸T expansivity of each oxide component. The results of this regression lead to a poor fit to the data, in contrast to a regression of the same data set minus the TiO2-bearing liquids (Lange, 1997). This likely reflects the strong variation in V¯TiO2 with composition in silicate melts that has been previously documented by Lange and Carmichael (1987), Johnson and Carmichael (1987) and Dingwell (1992). Therefore, to examine ⭸V¯TiO 2 how V¯TiO2 and vary between the individual liquids ex⭸T amined in this study, the volume results of each experimental liquid from this study, as well as five from the literature (Table 1) were added singly to the TiO2-free data set in a series of regressions of Eqn. 3. The results are presented in Table 5 and Figures 4 and 5. Figure 4 is a plot of derived values of V¯TiO2 at 1373 K as a function of XK2O or XNa2O; the data for most of the K2O-TiO2SiO2 and Na2O-TiO2-SiO2 liquids fall along two, remarkably straight and parallel lines in which values of V¯TiO2 decrease systematically with decreasing alkali content. This linear relationship holds despite the fact that TiO2 concentrations vary in these melts from ⬃10 to 35 mol%. The values of V¯TiO2 at 1373 K for the KTS liquids are ⬃3 cm3/mol larger than those for NTS liquids at a given alkali concentration. For the KTS liquids, V¯TiO2 decreases linearly from 32.6 to 26.5 cm3/mole between 37 and 15 mol % K2O. For the NTS liquids, V¯TiO2 decreases linearly from 29.6 to 25.7 cm3/mole between 39 and

25 mol % Na2O, but then appears to vary little with composition (⬃25 ⫾ ⬃0.5 cm3/mol) between 25 and 15 mol% Na2O. Derived values of V¯TiO2 at 1373 K from the density measurements of Dingwell (1992) on KTS-5 and NTS-5 compare well with our results as shown in Figure 4. ⭸V¯TiO 2 as a function of XK2O or A plot of fitted values for ⭸T XNa2O also reveals a systematic pattern. For the KTS liquids, ⭸V¯TiO 2 values of increase linearly (within error) with decreasing ⭸T K2O concentration, and range between 0.9 and 5.7 ⫻ 10⫺3 ⭸V¯TiO 2 cm3/mol-K (Fig. 5a). For the NTS liquids, values of also ⭸T appear to increase linearly with decreasing Na2O concentration (from 3.0 – 8.0 ⫻ 10⫺3 cm3/mol-K), but only between 39 and 25 mol% Na2O. Thereafter, between 25 and 15 mol%, the ⭸V¯TiO 2 first decrease and then increase (Fig. 5b). values of ⭸T Perhaps the most intriguing result is that for 17 of 19 KTS and ⭸V¯TiO 2 NTS liquids (exceptions are NTS-9 and NTS-10), varies ⭸T ¯ ⭸VTiO 2 reach a systematically with V¯TiO2 (Fig. 6). Values of ⭸T ⫺3 3 maximum of ⬃6 to 8 ⫻ 10 cm /mol-K when V¯TiO2 is ⬃26 cm3/mole and then decrease linearly to values close to zero when V¯TiO2 is ⬃32 cm3/mole. 4. DISCUSSION

¯ TiO and Ti Coordination 4.1. V 2 Previous studies of titanosilicate melt density (Lange and Carmichael, 1987; Johnson and Carmichael, 1987; Dingwell,

The partial molar volume of TiO2 in silicate melts

Fig. 3. Continued

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Q. Liu and R. A. Lange

Fig. 3. Continued

The partial molar volume of TiO2 in silicate melts

2387

Fig. 3(a– d). Plots of liquid volume vs. temperature for samples NTS-1, NTS-2, NTS-4, and NTS-5, respectively. The high-temperature volume data (from the Pt double-bob method) are shown as solid boxes, whereas the low-temperature volume measurements at T⬘f are shown as an open boxes. The solid line is a linear fit to the high temperature data only, which is then extrapolated down to Tf’. The dashed line is an interpolation between all the data. All liquids show a strong temperature-dependent variation in ⭸V/⭸T. (e– h). Plots of liquid volume vs. temperature for samples NTS-6, NTS-7, NTS-8, and NTS-9, respectively. The high-temperature volume data (from the Pt double-bob method) are shown as solid boxes, whereas the low-temperature volume measurements at T⬘f are shown as an open boxes. The solid line is a linear fit to the high temperature data only, which is then extrapolated down to T⬘f. The dashed line is an interpolation between all the data. All liquids show a strong temperature-dependent variation in ⭸V/⭸T. (i–l). Plots of liquid volume vs. temperature for samples NTS-10, LC-20, KTS-2, and KTS-3, respectively. The high-temperature volume data (from the Pt double-bob method) are shown as solid boxes, whereas the low-temperature volume measurements at T⬘f are shown as an open boxes. The solid line is a linear fit to the high temperature data only, which is then extrapolated down to T⬘f. The dashed line is an interpolation between all the data. All liquids show a strong temperature-dependent variation in ⭸V/⭸T, except KTS-3 (which contains the lowest abundance of [5]Ti). (m–p). Plots of liquid volume vs. temperature for samples KTS-5, KTS-6, KTS-7, and KTS-8, respectively. The high-temperature volume data (from the Pt double-bob method) are shown as solid boxes, whereas the low-temperature volume measurements at T⬘f are shown as an open boxes. Low-temperature volumes are not shown for KTS-5 and KTS-8 because they were too hygroscopic for glass density measurements. The solid line is a linear fit to the high temperature data only, which is then extrapolated down to T⬘f. The dashed line is an interpolation between all the data. Both KTS-6 and KTS-7 show a strong temperature-dependent variation in ⭸V/⭸T. (q–t). Plots of liquid volume vs. temperature for samples KTS-9, KTS-10, KTS-11, and LC-19, respectively. The high-temperature volume data (from the Pt double-bob method) are shown as solid boxes, whereas the low-temperature volume measurements at T⬘f are shown as an open boxes. A low-temperature volume is not shown for KTS-11 because it was too hygroscopic for a glass density measurement. The solid line is a linear fit to the high temperature data only, which is then extrapolated down to T⬘f. The dashed line is an interpolation between all the data. Both KTS-9 and 10 show a strong temperature-dependent variation in ⭸V/⭸T. The volume data for a sodium potassium silicate (LC-19; Lange and Carmichael, 1987; Lange, 1997) is shown for comparison to illustrate a Ti-free liquid with a temperature-independent ⭸V/⭸T over a 1100 degree interval.

1992) have all suggested that observed variations in V¯TiO2 with melt composition are caused by a shift in the average coordination of Ti. Various proportions of [4]Ti, [5]Ti, and [6]Ti have been inferred in alkali titanosilicate glasses from a variety of Raman scattering, X-ray absorption, X-ray scattering, X-ray photoemission, and neutron scattering studies (e.g., Henderson and Fleet, 1995; Cormier et al., 1995; Mysen and Neuville, 1995; Yarker et al., 1986). However, the most direct structural probe of Ti coordination in silicate glasses is derived from

high-resolution XANES spectroscopy of the Ti K edge (i.e., an intense, preedge feature) on the basis of an extensive data set for model compounds with Ti in four, five and six-fold coordination sites (Farges et al., 1996a,b). A plot of two parameters from the pre-edge data (absolute pre-edge energy position and normalized pre-edge height) for the various Ti-bearing model compounds (Farges et al., 1996a) delineate three well-separated domains for [4]Ti, [5]Ti, and [6]Ti. Farges et al. (1996b), Farges and Brown (1997), Farges (1997) and Romano et al. (2000)

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¯ TiO and ⭸V¯ TiO and ⭸V¯ TiO /⭸T at 1373 Table 5. Fitted values for V 2 2 2 K from Eqn. 3. Sample

V¯ TiO 2 ⫾ 1␴ (cm3/mol)

⭸V¯ TiO 2/⭸T ⫾ 1␴ 10⫺3 cm3/mol-K

NTS-1 NTS-2 NTS-4 NTS-5 NTS-6 NTS-7 NTS-8 NTS-9 NTS-10 LC-20 KTS-2 KTS-3 KTS-5 KTS-6 KTS-7 KTS-8 KTS-9 KTS-10 KTS-11

26.04 ⫾ .56 25.73 ⫾ .14 27.71 ⫾ .12 28.29 ⫾ .13 25.24 ⫾ .39 26.87 ⫾ .15 29.58 ⫾ .12 25.44 ⫾ .26 24.63 ⫾ .22 26.46 ⫾ .27 28.93 ⫾ .17 27.56 ⫾ 1.62 31.28 ⫾ .17 26.51 ⫾ .47 30.22 ⫾ .17 32.47 ⫾ .19 27.43 ⫾ .29 27.93 ⫾ .26 32.58 ⫾ .27

7.92 ⫾ 4.27 7.18 ⫾ 1.08 4.30 ⫾ 1.04 4.10 ⫾ 0.54 6.87 ⫾ 1.32 5.27 ⫾ 1.64 3.01 ⫾ 1.04 3.83 ⫾ 1.16 5.33 ⫾ 0.78 7.95 ⫾ 1.20 4.91 ⫾ 2.08 6.20 ⫾ 5.43 0.91 ⫾ 0.68 5.74 ⫾ 2.20 2.21 ⫾ 1.33 ⫺2.08 ⫾ 1.35 4.38 ⫾ 2.17 3.91 ⫾ 1.55 1.64 ⫾ 1.06

have used this calibration of the two pre-edge features to determine the proportion of Ti in four, five and sixfold coordination in various “unknowns” (e.g., alkali titanosilicate glasses) with an estimated uncertainty of ⬃10% for each site. Farges (1997) argues that the use of both pre-edge parameters is necessary for deriving reliable coordination information for Ti. Currently, only two of the liquid compositions examined in this study (NTS-2 and KTS-2) match the compositions (within analytical error) of two glasses for which the average Ti coordination number (CN) has been determined (5.25 and 4.85, respectively) from XANES spectra utilizing the two pre-edge features (Farges, 1997). Two additional glass samples from Farges (1997) compositionally bracket two liquids in this study (NTS-9 and 10). The two samples from Farges (1997) have SiO2-TiO2-Na2O mol% concentrations of 60 to 20 to 20 and 40 to 40 to 20, whereas NTS-9 and 10 have SiO2-TiO2-Na2O mol% values of approximately 56 to 24 to 20 and 45 to 35 to 20, respectively. The average Ti coordination number for the two Farges (1997) samples are 5.35 and 5.25, whereas interpolated [4]Ti, [5]Ti, and [6]Ti concentrations for the NTS-9 and NTS-10 liquids lead to average Ti coordination numbers of 5.34 and 5.32, respectively. When fitted values of V¯TiO2 at 1373 K for these four samples (NTS-2, 9, 10 and KTS-2) are plotted as a function of their average Ti coordination number, a linear trend is observed (Fig. 7). Although more XANES data on the samples of this study are clearly needed, the relationship in Figure 7 strongly supports the hypothesis that the variation in V¯TiO2 with composition reflects a change in the average coordination of Ti. An additional constraint on the relationship between V¯TiO2 (at 1373 K) and the coordination of Ti is found from the plot of ⭸V¯TiO 2 ⭸V¯SiO 2 vs. V¯TiO2 in Figure 6. It is well established that and ⭸T ⭸T ¯ ⭸VAl 2O 3 are both zero in multi-component aluminosilicate liq⭸T uids where Si4⫹ and Al3⫹ are both predominantly in tetrahedral ⭸V¯TiO 2 is coordination (Lange, 1996, 1997). If we assume that ⭸T

Fig. 4. (a) A plot of fitted values for V¯TiO2 (⫾1␴) at 1373 K vs. XNa2O for the KTS liquids (Table 5), and (b) a plot of fitted values for V¯TiO2 (⫾1␴) at 1373 K vs. XNa2O for the NTS liquids (Table 5). The derived values of V¯TiO2 vary systematically with alkali concentration (except for those corresponding to NTS liquids with ⱕ20 mol% Na2O; these are shown as open circles and refer to samples that deviate from the linear trend in Fig. 5.) Derived values of V¯TiO2 at 1373 K for four samples from Dingwell (1992) (KTS-5, NTS-3, NTS-4 and NTS-5; only samples with analytical totals ⬎ 97% are given) are shown as open boxes and indicate good interlaboratory comparison.

also zero for [4]Ti4⫹, then the linear relationship in Figure 6 provides an estimate of the value of V¯TiO2 for the case when Ti ⭸V¯TiO 2 is entirely four-fold coordinated. The fitted line for ⭸T crosses zero when V¯TiO2 is 32.24 cm3/mol. When this estimate is combined with the XANES data for NTS-2 and KTS-2 in Figure 7, an excellent linear fit is obtained (R2 ⫽ 0.981). The average Ti coordination number for NTS-9 (not used in the fit) falls directly on the fitted line, whereas that for NTS-10 (not used in the fit) plots somewhat off the line. It is not known whether the discrepancy with NTS-10 is real or perhaps reflects errors in either our volume measurements or the XANES determination of Ti coordination number. As stated above, XANES spectra on all of the samples from this study are clearly needed. An intriguing application of the linear fit to the data in Figure 7 is to calculate the end-member value for V¯TiO2 at 1373 K for the case where Ti is entirely six-fold coordinated. Although the density of pure TiO2 liquid has been measured at high-temperature (Dingwell, 1991), this liquid may contain both [5]Ti and

The partial molar volume of TiO2 in silicate melts

2389

Fig. 6. A plot of fitted values for ⭸V¯TiO2/⭸T (⫾1␴) plotted as a function of V¯TiO2 at 1373 K. The solid line is a linear fit to all data (except those with ⱕ20 mol% Na2O; shown as open circles to be consistent with Figs. 4 and 5), where ⭸V¯TiO2/⭸T crosses zero at V¯TiO2 ⫽ 32.2 cm3/mol.

Fig. 5. (a) A plot of fitted values for ⭸V¯TiO2/⭸T (⫾1␴) vs. XK2O for the KTS liquids (Table 5), and (b) a plot of fitted values for ⭸V¯TiO2/⭸T (⫾1␴) at 1373 K vs. XNa2O for the NTS liquids (Table 5). The derived values of ⭸V¯TiO2 vary systematically with alkali concentration (except for those corresponding to NTS liquids with ⱕ20 mol% Na2O; shown as open circles).

[6] Ti. Therefore, we used the linear fit in Figure 7 to derive a value for V¯TiO2 of 22.5 cm3/mole for [6]Ti. This estimate is within 5% of the molar volume of anatase (the lowest density polymorph of crystalline TiO2), which is 21.4 cm3/mol at 1373 K (Robie and Hemingway, 1995; Taylor, 1984) and is a minimum volume for the liquid TiO2 component (assuming a positive volume of fusion) when Ti is entirely six-fold coordinated. From this analysis, the estimated difference in V¯TiO2 when Ti is entirely four-fold vs. six-fold coordinated is ⬃9.8 cm3/mole and represents a compaction of ⬃30.3%. For comparison, the densification between coesite and stishovite (Si4⫹ in four-fold and six-fold coordination, respectively) at 298 K is similar at ⬃31.7% (Robie and Hemingway, 1995) Another application of the linear fit in Figure 7 is to calculate the average Ti coordination number for the liquids in this study from their fitted values of V¯TiO2. The results are plotted for the KTS liquids in Figure 8a and suggest that the average Ti coordination varies systematically from ⬃4.0 to 5.1 as K2O concentration decreases from 37 to 15 mol%. The XANES data for KTS-2 (with 25 mol% K2O) indicate a mixture of ⬃85% [5] Ti and ⬃15% [4]Ti, with no [6]Ti (Farges, 1997). Therefore, for most of the KTS liquids in this study, Ti is primarily in four-

and five-fold coordination, with the average Ti coordination number controlled by the relative proportions of each. It thus appears that the primary effect of decreasing K2O concentration is convert [4]Ti to [5]Ti (and possibly minor amounts of [6] Ti). A similar plot of average Ti coordination number vs. Na2O concentration is shown for the NTS liquids in Figure 8b. This plot largely mirrors the trend seen for KTS liquids (increasing Ti coordination with decreasing Na2O concentration), although there appears to be a leveling off of coordination numbers at values of ⬃5.4 when Na2O is ⱕ20 mol%. One possible explanation for the breakdown in the trend, and the apparent “saturation” of the coordination number at ⬃5.4, is that it may mark the point where the concentration of [4]Ti goes to zero.

Fig. 7. A plot of average Ti coordination number (CN) vs. derived values for V¯TiO2. The solid dots correspond to samples NTS-2 and KTS-2 (volume data from this study; CN data from Farges, 1997) and the estimated value for V¯TiO2 (32.2 cm3/mol) when Ti is entirely four-fold coordinated (taken from Fig. 6), when ⭸V¯TiO2 /⭸T is zero). The open dots correspond to samples NTS-9 and NTS-10 (volume data from this study; interpolated CN data from Farges, 1997) and to the molar volume for crystalline anatase at 1373 K (Robie and Hemingway, 1995). The solid line corresponds to a linear fit to the solid dots (equation shown), with the dashed line showing its extrapolation to a Ti coordination number of six. The inverse linear fit is: V¯TiO2 ⫽ 52.5 ⫺ 5.0*(average Ti CN).

2390

Q. Liu and R. A. Lange

(where [4]Ti and [5]Ti are predominant). This trend can be explained in terms of the relative abundances of Q3 and Q4 species, and their role in transforming [4]Ti to [5]Ti (and possibly [6]Ti). Xue et al. (1991) have shown that abundances of [5]Si in alkali silicate glasses quenched from high pressure are maximized at tetrasilicate compositions, where Q3 and Q4 species (Qn refers to a tetrahedral unit with n bridging oxygens and 4-n nonbridging oxygens) are equally abundant. Similarly, Ueno et al. (1983) have shown that the average coordination number of Ge in glasses across the Na2Ge2O5-GeO2 join peaks near the Na2Ge4O9 composition. Xue et al. (1991) propose a mechanism where five-coordinated Si is formed by consumption of nonbridging oxgyen atoms in partially polymerized melts, via the following reaction: Q3 ⫹ Q4 ⫽ Q4* ⫹ [5]Si

(4)

where Q3 and Q4 are the dominant structural units and Q4* is a SiO4 species with three [4]Si and one [5]Si. A similar mechanism may be invoked to explain the formation of [5]Ti in the alkali titanosilicate liquids: Q(Ti)3 ⫹ Q(Ti)4 ⫽ Q(Ti)4* ⫹ [5]Ti

(5) [4]

Fig. 8. (a) A plot of calculated values for the average Ti coordination number (⫾0.2) vs. XK2O for the KTS liquids, and (b) vs. XNa2O for the NTS liquids. Ti coordination numbers vary from ⬃4.0 to 5.1 in the KTS liquids and from ⬃4.6 to 5.5 in the NTS liquids.

In this analysis, we assume a network-former role for both Ti and [5]Ti. According to this model, NTS and KTS liquids with alkali concentrations near 20 mol% will contain a maximum abundance of both Q3 and Q4 species, and are therefore expected to contain a higher concentration of [5]Ti compared to liquids with alkali concentrations ⱖ 33 mol%, in which there is little Q4. This is exactly the trend that is observed. We further propose that the reason why this trend breaks down in the NTS liquids at coordination numbers near 5.3 is because this may be the point where the population of [4]Ti drops to zero, removing a key ingredient for the reaction in Eqn. 5.

4.2. The Mechanism for Composition-Induced Ti Coordination Change

4.3. The Thermal Expansivity of the TiO2 Component

From the data presented in Figures 4 and 8, it is clear that there are two distinct compositional effects that control the average coordination of Ti in alkali silicate melts. The first is the substitution of K2O for Na2O for a given titanosilicate melt composition, which leads to an increase in V¯TiO2 of ⬃3 cm3/ mole (Fig. 4) and a corresponding decrease in the average coordination number by ⬃0.6 (Fig. 8). This effect has been discussed at length by Farges et al. (1996b) in terms of bondvalence models. For example, when Na is replaced by K, the contribution of alkalis to the bond-valence sum decreases, owing to the longer K-O distance (2.9 Å) vs. Na-O distance (2.6 Å) and the higher average coordination for K (nine-fold) vs. that for Na (six-fold). This decrease in the bond-valence sum can be compensated if the Ti-O bond length shortens, which is achieved if the Ti coordination number decreases (converting [5]Ti to [4]Ti). The second compositional control on the average Ti coordination number is the effect of increasing NBO/T (or increasing alkali concentration). The data for both the KTS and NTS liquids clearly demonstrate that as NBO/T increases (increasing alkali concentration), the average Ti coordination number decreases, at least between coordination numbers of 4.0 and 5.3

4.3.1.

⭸V¯TiO 2 and Ti coordination ⭸T

⭸V¯TiO 2 vary The results of this study show that values of ⭸T ¯ ¯ systematically with VTiO2 (Fig. 6). Because values of VTiO2 can be correlated to average Ti coordination numbers, the implica⭸V¯TiO 2 is near zero when the average Ti coordination tion is that ⭸T is close to 4 and reach a maximum of ⬃6 to 8 ⫻ 10⫺3 cm3/mol-K when the Ti coordination number is close to 5 (Fig. ⭸V¯TiO 2 6). This result strongly suggests that the magnitude of is ⭸T [5] positively correlated to the relative abundance of Ti.

4.3.2. Configurational vs. vibrational contributions to

⭸V¯TiO 2 ⭸T

The thermal expansivity of silicate liquids can be divided into a vibrational and a configurational component (Richet and Neuville, 1992). The vibrational component arises from the anharmonicity of the molecular vibrations (that increases with temperature) and is the sole contribution to the thermal expan-

The partial molar volume of TiO2 in silicate melts Table 6. Fitted values for ⭸V i /⭸T in glasses at 573 K from Eqn. 6.

Oxide SiO2 Al2U3 MgO CaO Na2O K2O TiO2

⭸V i /⭸T ⫾ 1␴ 10⫺3 cm3/mol-K (no Ti samples)

⭸V i /⭸T ⫾ 1␴ 10⫺3 cm3/mol-K (w/16 Ti samples)

⭸V i /⭸T ⫾ 1␴ 10⫺3 cm3/mol-K (w/16 Ti samples)

— — 0.76 ⫾ 0.11 1.12 ⫾ 0.07 3.31 ⫾ 0.09 3.98 ⫾ 0.21

— — 0.76 ⫾ 0.10 1.11 ⫾ 0.07 3.21 ⫾ 0.07 4.08 ⫾ 0.15 0.09 ⫾ 0.10

— — 0.76 ⫾ 0.10 0.11 ⫾ 0.07 3.24 ⫾ 0.06 4.15 ⫾ 0.13 —

All 3 regressions include the glass data on 24 samples from Lange (1996, 1997).

sion of solids. In contrast, the configurational contribution is unique to liquids and is associated with atomic and molecular motion involved with temperature-induced structural rearrangements in the liquid (e.g., Qn species exchange, coordination change, topological changes in ring size, etc.). The relative proportion of vibrational vs. configurational contributions to ⭸V¯TiO 2 can be determined by comparing its magnitude in the ⭸T glass vibrational liquid ⭸V¯TiO ⭸V¯TiO ⭸V¯TiO 2 2 2 to that in the liquid ( glass ⫽ ; the ⭸T ⭸T ⭸T configurational ¯ ⭸VTiO 2 . difference is ⭸T glass ¯ ⭸VTiO 2 can be determined by a simple linear The value of ⭸T regression of the following model equation:

冉

冊

⭸V glass ⫽ ⭸T

冘

Xi

⭸V¯ glass i ⭸T

(6)

⭸Vglass (⫽V glass ␣ glass ) is the thermal expansivity of ⭸T each glass obtained from the dilatometry experiments, Xi is the ⭸V¯glass i mole fraction of each oxide component, and is the partial ⭸T molar thermal expansivity of each oxide component in the glass. The regression includes the 24 K2O-Na2O-CaO-MgOAl2O3-SiO2 glasses of Lange (1996, 1997) as well as all 14 TiO2-bearing glasses in this study for which dilatometry runs were made. An excellent fit to the entire data set was obtained, and the results of the regression are reported in Table 6. The glass ⭸V¯TiO 2 is zero most surprising feature is that the fitted value for ⭸T glass glass ¯ ⭸V¯SiO ⭸V Al 2 O 3 2 (within error) as is also found for and . This ⭸T ⭸T liquid ⭸V¯TiO 2 means that the vibrational contribution to is zero for all ⭸T KTS and NTS liquids, including those with the largest magniliquid ⭸V¯TiO 2 . It further requires that the configurational tude of ⭸T liquid ⭸V¯TiO 2 contribution to is 100%. For comparison, the configu⭸T rational contributions (⫾2␴) to liquid values for ⭸V¯K 2O ⭸V¯Na 2O ⭸V¯CaO ⭸V¯MgO , , , and are 66 (⫾4), 57 (⫾3), 70 ⭸T ⭸T ⭸T ⭸T (⫾4), and 77 (⫾7) %, respectively (Lange, 1997). The emergwhere

2391

ing picture, therefore, is that the thermal expansivity associated with the TiO2 component in alkali silicate liquids arises primarily from [5]Ti and is caused by structural variations available to liquids and not solids.

4.3.3. The “excess” configurational

⭸V¯TiO 2 in the Supercooled ⭸T

Liquid ⭸V¯TiO 2 in the previous section was for the ⭸T ⭸V¯TiO 2 stable liquid region only. Here we explore the “excess” ⭸T in the supercooled liquid region of the TiO2-bearing liquids, which leads to the non-linear temperature dependence to volume immediately above the glass transition (Fig. 3). Although we do not know the exact form of the ⭸V/⭸T function with temperature throughout the supercooled liquid region, the data clearly show that the slope of volume vs. temperature is steeper near the glass transition and gradually shallows into the stable liquid region. The variation in ⭸V/⭸T is also strongest in those liquids with the highest TiO2 concentration. This shows that the behavior of ⭸V/⭸T is very similar to that seen for Cp in similar alkali titanosilicate liquids (Richet and Bottinga, 1985; Lange and Navrotsky, 1993; Tangeman and Lange, 1998; Bouhifd et al., 1999). The consequence of the “excess” configurational ⭸V/⭸T and Cp is to cause a rapid increase in the configurational volume and entropy, respectively, of these liquids throughout the supercooled liquid region. The net result at high temperature is that TiO2-bearing alkali silicate liquids have much higher configurational volumes and entropies than those that are TiO2-free. There is some evidence that the cause of this anomalous ⭸V/⭸T and Cp behavior in the supercooled liquid region may be related to the occurrence of [5]Ti. It is not known if the volume vs. temperature relation is strongly curved in those liquids with little [5]Ti (e.g., samples KTS-5, KTS-8, KTS-11 with Ti coordination numbers close to four) because these are the samples that were too hygroscopic (owing to their high K2O concentrations) for glass density measurements. Nonetheless, among those samples for which we do have T⬘f volume measurements, the one with the least curvature in Figure 3 is KTS-3, which contains the lowest abundance of [5]Ti. Farges et al. (1996b) argue that [5]Ti is present in alkali silicate glasses and liquids as titanyl square pyramids with one non-bridging oxygen doubly-bonded to Ti (and four alkali cations) and four bridging oxygens bonded to Si or Ti (and two other alkali cations). As a consequence of this geometry, Farges et al. (1996b) suggest that [5]Ti occurs at the interface of two domains in the glass, one that is relatively rich in alkalis (percolation domains) and the other that is rich in networkformers. In their study of the effect of temperature on melt structure, Farges et al. (1996c) suggest that it is the breakup of this domain structure with increasing temperature that is responsible for the anomalous heat capacity behavior in the supercooled liquid region (and not a change in the average Ti coordination number). However, Bouhifd et al. (1999) present a compelling case that such topological changes in intermediate-range order cannot account for such a large increase in the energetics of these melts and instead suggest the onset of Ti,Si All discussion of

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mixing as the source of the excess configurational entropy in the alkali titanosilicate liquids. Although neutron scattering (e.g., Cormier et al., 1997) and EXAFS data (Farges, 1999) suggest clustering of Ti in these melts, this does not preclude some Ti,Si mixing, perhaps at the periphery of these clusters. Although Bouhifd et al. (1991) argue that topological changes are not the source of the strong increases in configurational entropy with temperature in the alkali titanosilicate liquids, it is also true that Ti,Si mixing is equally unlikely to cause the strong increases in configurational volume with temperature that is also observed in these liquids (Fig. 3). It is more likely that the rapid change in the volume of alkali titanosilicate liquids arises from the topological changes described by Farges et al. (1996c) and Reynard and Webb (1998), namely the decrease of the percolation domain size with increasing temperature. Evidence that topological variations in network connectivity can exert a strong influence on melt density has been demonstrated by Stixrude and Bukowinski (1990a). Using Monte Carlo simulations of tetrahedrally bonded SiO2 liquid at various pressures, they show that SiO2 melt compresses by reducing the abundance of three-membered rings in favor of largersized rings. These conclusions are consistent with the strong variations in density (factor of 2) observed in crystalline frameworks as a systematic function of ring statistics (Stixrude and Bukowinski, 1990b), where decreasing ring size leads to lower density. However, the gradual increase in ring size with pressure that is seen in the simulated liquids, where Si-O bonds are constantly broken and reformed, is a compression mechanism unavailable to crystals and is thus entirely configurational in nature. It is interesting to speculate whether an analogy can be drawn between a decrease in ring size in SiO2 liquid and a decrease in domain size (that may also lead to a decrease in ring size) in alkali titanosilicate liquids, both causing a decrease in density. We caution, however, that the effect of decreasing ring size on decreasing density was illustrated by Stixrude and Bukowinski (1990a) for fully tetrahedral liquids and may not apply to those containing five-coordinated network-formers. 5. CONCLUSIONS

The results of this study show that derived values of V¯TiO2 ⭸V¯TiO 2 vary systematically with silicate melt composition and ⭸T and, in fact, are sensitive indicators of the average Ti4⫹ coordination number. A variation of ⬃1 cm3/mole in V¯TiO2 corresponds to a change of only ⬃0.2 in Ti coordination number. The data also suggest that [5]Ti plays a critical role in controlling both the anomalous, rapid increase in volume in the supercooled liquid region (perhaps owing to topological variations in domain/ring size) and also in maintaining high thermal ⭸V¯TiO 2 expansivities in the stable liquid region. This variation in ⭸T with Ti coordination has intriguing implications for the equation of state of magmatic liquids under the high pressure and temperature conditions of the deep Earth where Si4⫹ undergoes coordination change. The anticipated melt compaction accompanying the transformation to higher Si4⫹ coordination may be offset to some extent by a pronounced expansion at high

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