American Mineralogist, Volume 78, pages 710-723, 1993

Experimental rheometry of melts and supercooled liquids in the systemNaAlSiOo-SiOr: Implications for structure and dynamics

D.q.Nrnr, J. SrnrN, FnlNx J. SpenaInstitute for Crustal Studies and Department of Geological Sciences, University of California, Santa Barbara,

Santa Barbara. California 93106. U.S.A.

AssrRAcr

Viscometric data for seven compositions in the system NaAlSiOo-SiO, have been col-lected by the technique of concentric cylinder rheometry in the temperature and shear rateranges 1000-1300'C and 10 2-8ls, respectively, for single-phase melts or supercooledliquids. As a function of increasing NaAlSiO.(N) content, the compositions include thetridymite + albite eutectic (Nro, eutectic I), the thermal divide composition (Nrr, NaAl-Si3O8), the albite + nepheline solid-solution eutectic (N0,, eutectic II), jadeite composition(NJo, NaAlSirOu), and peritectic composition (Nuo). The range of experimentally accessibleshear rates is not large enough to evaluate fully the extent of pseudoplastic (non-Newto-nian) behavior across the compositional spectrum. However, a small departure from New-tonian behavior is not excluded for some of the compositions. Measured viscosities varyfrom nearly 108 to 104 Pa.s for the range of compositions and temperatures investigated.Temperature-viscosity dala are extremely well fitted by both Arrhenian (two-parameter)and Fulcher (three-parameter) expressions. In cases where the temperature range is large(e.g., NaAlSi.O, and NaAlSi,Ou melts) the Fulcher fit is statistically significant. In theFulcher fit, there is a systematic increase in Zo (the Vogel temperature) indicative ofincreasing melt fragility as the concentration of NaAlSiOo component increases. Similarly,there is a linear relationship between Arrhenian activation energy (E,) and the mole frac-tion of NaAlSiO. (X") according to the expression E, : (499 - 158)XN (with ,8, in kilo-joules per mole), which is valid across the entire NaAlSiOo-SiO, join. The increase inVogel temperature and decrease in activation energy for viscous flow and isothermal vis-cosity as NaAlSiOo is added to molten silica may be rationalized microscopically on thebasis of the increased Al-O bond length relative to Si-O, the reduction in bond energy forAI-O compared with Si-O, and the smaller mean TOT intertetrahedral bridging angle forAl-O-Si relative to Si-O-Si.

IxrnorucrroN tems. At the most fundamental level, the complex rela-tionship between the dynamics of a melt and its structure

Viscosity is among the most widely studied properties at the atomic scale must be understood in order to achieveof silicate melts, with obvious relevance to the study of a quantitative understanding of magmatic phenomena.momentum transport phenomena in magmas, and in- In order to organize the data available at the time, Bot-cludes implications for other processes such as chemical tinga and Weill (1972) and Shaw (1972) developed al-and tracer diffusion, advection of heat, and the nucleation gorithms for calculating the viscosity of silicate melts,and growth rates of solid or fluid phases in magmatic independent of shear rate, accurate to within a factor ofsystems. For some time, there has existed an extensive 5 or less for a given temperature and composition in termsbody of viscosity measurements on silicate melts, super- of oxide components at 100 kPa of total pressure. Thesecooled liquids, and glasses, spanning a considerable range strictly empirical models, although not based on analysisof temperatures and compositions of geochemical interest of any physical mechanism, are useful in estimating vis-(e.g., Bottinga and Weill, 1972; Shaw, 1972;Urbain et cosities within the range of magmatic compositions andal., 1982; Richet, 1984; Mysen, 1987, 1988). Experimen- temperatures. It has been noted that logarithmic viscositytal measurements of viscosity in molten silicates and sil- isotherms in simple binary and ternary systems of metalicate multiphase mixtures as a function of pressure, oxi- oxide and silica exhibit apparent linear variation withdation state, and deformation rate have become more silica mole fraction within restricted compositional inter-common in the last decade (e.g., Kushiro, 1976, 1978; vals; other properties show similar behavior. The bound-Dingwell and Virgo, 1987; Scarfe et al., 1987; Ryerson et aries of these intervals intersect invariant (e.g., eutectic)al., 1988; Spera et al., 1988), although a great deal re- compositions on the equilibrium phase diagram of themains to be accomplished, especially for multiphase sys- system (Babcock, 1968; Urbain et al., 1982; see Spera et

0003-004x/93l0708-07 l 0$02.00 7 r0

STEIN AND SPERA: MELTS AND SUPERCOOLED LIQUIDS 7 t l

al., 1988, their Table 2 for a summary). According toUrbain et al. (1982), this suggests that the phase transi-tions that occur along the liquidus reflect composition-dependent changes in liquid structure that persist far abovethe liquidus, resulting in the segmented linear depen-dence of the viscosity (see Figs. 2 and 8 in Urbain et al.,1982). As noted previously (Spera et al., 1988), this pat-tern is commonly observed in plots of log a vs. meanmolecular weight for organic polymer fluids such as thelinear chain polyisobutylenes. The book by Ferry (1980)documents many such examples. It is the correlation be-tween microscopic structure and its projection into themacroscopic realm that guides our understanding of theliquid state (Hansen and McDonald, 1986; Ziman, 1979;Evans and Morriss, 1990; Scamehorn and Angell, l99l)and provides a formidable challenge to experimentalistsand theoreticians alike.

Phase relations for the system NaAlSiOo-SiO, (Na-AlSiO" : N,oo) at 100 kPa (l bar) compiled from the workof Greig and Barth ( I 938) and Schairer and Bowen ( l9 5 6)are depicted in Figure I . Examination of Figure I revealsthe following liquidus phase relations as the NaAlSiOocomponent in the melt increases: a tridymite- and albite-saturated eutectic melt (Nro, eutectic I), a thermal divideat the composition albite (Nrr), an albite- and nepheline""-saturated eutectic melt (No, , eutectic II), and the peritecticcomposition (Nuo). Subscripts represent mole percent ofNaAlSiOo in the system NaAlSiO.-SiOr. Nominal com-positions in this system have the common molar ratioNa/Al: l, and in the molten state at 100 kPa all havefully polymerized network structures. An ideal opportu-nity is presented to investigate hypotheses that proposerelationships between phase equilibria behavior and thestructure and dynamics of a system well studied in termsof phase relations (Greig and Barth, 1938; Schairer andBowen, 1956), spectroscopy (Sharma et al., 1978; Taylorand Brown, 1979a, 1979b; McMillan et al., 1982; Seifertet al., 1982), and thermochemistry (Navrotsky et al., 1982;Richet and Bottinga, 1984) at 100 kPa. Furthermore, thecomposition NaAlSirOu (Nro) occurs in this system. It hasbeen noted that in crystalline NaAlSi,Ou (adeite), all Alis t6lAl. In contrast, melt of jadeite composition is dom-inated by torAl, at least at pressures <-4 GPa (Sharmaet al., 1979; Ohtani et al., 1985; Hamilton et al., 1986).

In order to understand better the connection betweenmelt structure and melt dynamics, we have undertakenan experimental study of viscosity in the system Na-AlSiO"-SiO, determined by concentric cylinder rheome-try. Rheometric data have been collected for seven com-positions in this system, over the range of temperaturesfrom 1350 to 1000 "C and with pressure at 100 kPa, atshear rates from 0.01 to 8.7/s for single-phase melts andsupercooled liquids with compositions from Nro to Nuo.For many of these compositions, no data previously ex-isted. In this investigation, we compare and combine ourdata with those of other workers, paying particular atten-tion to the compositional variation of viscosity and itstemperature derivative, and speculate on the physical sig-

1700

r f c )

100NaAlSi04

60 ^o -4o 40

WEIGHT PEFCENT

Fig. l. Phase diagram of the system NaAlSiO"-SiOr, basedon the work ofGreig and Barth (1938) and Schairer and Bowen(1956). Composition axis is in weight percent of NaAlSiO. com-ponent; note that in text compositions are referred to in molepercent of NaAlSiOo component. Temperatures are noted in de-grees Celsius, including specified invariant points. Dashed ver-tical lines represent temperature range sampled for each com-position in viscometric experiments; labels refer to samplenumbers in Table 1. Abbreviations for the various phases in thesystem are Ab : albite; Cg: carnegieite; Cg,, : carnegieite-albitesolid solution; Ne : nepheline; Ne". : nepheline solid solution;Cr : crisrobalite; L : liquid; Tr : tridymite.

nificance of the observations. In concurrent studies, the

technique of molecular dynamics is used to understandthe relationships between melt structure and the ther-modynamic and transport properties in this system (Stein

et al., 1992a, 1992b\. On the atomic scale, the molecular

dynamics studies rationalize the relationships discoveredexperimentally (see also Scamehorn and Angell, l99l)

and direct attention to further experimental studies need-

ed to elucidate the microscopic to macroscopic connec-tron.

ExprnrNlrNTAL MEASUREMENTS

Sample preparation

The viscometric data of this study were collected forcompositions along the join NaAlSiOo-SiO', denoted bythe mole fraction of NaAlSiOo (N'oo). Nominal compo-sitions include (in mole percent) ll,o (the albite-tridymiteeutectic, hereafter labeled eutectic I), Nro (near eutectic I),N33 (the albite thermal divide, ab), Nro (near albite), No'(the albite-nepheline"" eutectic, hereafter labeled eutecticII), N,o (adeite, jd), and Nuo (peritectic). Nominal andexperimental compositions are collected in Table I andare indicated on the 100-kPa phase diagram ofFigure l.Starting glasses were prepared by mixing appropriate pro-portions of reagent grade NarCO3, Al2O3, and silica.Batches were dry-mixed, ground, and decarbonated at850 'C. Decarbonated products were then fused and

152

| 500

1 400

1 300

12541 200

1 1 0 0

2 0 0si02

Pedleclic

BEutectlc I

\. \L l

t \rvI x fI z 2

C r + L

t71

N€ssl

\ :| 1 1 8

I

II lle A b + T r

7 t 2 STEIN AND SPERA: MELTS AND SUPERCOOLED LIQUIDS

TreLe 1. Nominal and analyzed compositions of viscometric samples

Viscometric Na,OSample experiment (wt%)

sio,(wt%)

Al,03(wt%) Total

N20 (eutectic l)M4N33A (ab)AE3B"- (ab)A/34A/41 (eutectic ll)A/50A 0d)N50B (jd)Nsoc-- 0d)N60A (peritectic)N60B (peritectic)A/60C (peritectic)

JS132.3JS131 . 2J S 1 1 5JS1 21JS1 29JS1 30JS1 18JS1 23JS128.2J S 1 1 7J5127.2JS127UP

8.1(8 .1) -10.3(10.6)1 2.6(12.8)

12 0(11 .8)1 3.8(14.2).1 s 9(1 5.3)15.4

18.0(17.s).t / . o

13.6(1 3.3)',17.3(17 5)20.7(21 1)

Same as JS1 1 520.1(19 4)23.1(23 4\'25 6(25.2124.3

Same as JS12327.2(28.8)-27.4

Same as J5127.2

78.1(78.6r71 .6(71 .9)66.0(66.1)

67.2(68.7)61.5(62.4)-s8.0(59.4)60.0

s3.1(53.7I53.7

99.899.299.3

99.198.4o o E9 9 7

98.398.7

Note: Nominal compositions indicated by parentheses. The compositions corresponding to albite and jadeite are abbreviated as ab and id, respectively.* Nominal composition for ternary invariant points of system NarO-AlrO3-SiO, (Schairer and Bowen, 1956).

.. Reolicate measurements.

ground in several cycles to produce homogeneous glasschips. Samples were analyzed at the end of viscometricexperiments, and compositions are within acceptable tol-erances of nominal values, which have molar Na/Al equalto unity. Quenched glasses were analyzed by electron mi-croprobe using standard techniques with special effort toavoid volatilization of Na. After viscometric measure-ments, samples were examined for bubbles and any evi-dence of specimen heterogeneity. Bubble contents weregenerally < I volo/o; bubbles when present were ratheruniformly distributed within the sample. All measure-ments were made in air at 100 kPa.

Rheometric measurements

The design, construction, and calibration of the high-torque concentric cylinder rheometer used in this studyhave been previously described (Spera et al., 1988). Pe-riodic standardization using NBS borosilicate glass 717throughout the period of investigation indicated an ac-curacy of about 0.05 in log a, slightly poorer than theNBS-quoted uncertainty of 0.03 in log a for NBS 717.Temperatures were accurate to + 3 K. The physical mea-surement consisted of a precisely determined rotor rota-tion rate paired with a measured rotor torque. A discus-sion of the experimental methodology may be foundelsewhere (Spera et al., 1988). Table 2lists the radialdimensions of the rotors (R.), cylindrical crucibles (R.),and rotor immersion depths (ft) for each experiment. Oncea given sample of bubble-free homogeneous glass wasloaded into the cup of the rheometer, isothermal mea-surements were made starting at the high-temperatureend of the desired range. At each temperature, torquedata were collected throughout the broadest possible rangein shear rate, given the limitations of the rheometer andthe high viscosity of some of the compositions. At theend of each isothermal experiment, the temperature wasraised to allow the free surface to relax viscously; thenthe temperature was dropped to a new value, and theprocedure was repeated after thermal reequilibration. Therange of temperature for each composition is indicatedby a dashed vertical line in Figure l. Each data point

(consisting ofboth a rotation rate and torque at a giventemperature for a specified composition) is an average offrom three to ten individual measurements, each of aduration of l0-100 s.

Data reduction

Experimental values of rotation rate (O) and torque (l)were analyzed independently of any assumptions regard-ing constitutive behavior of the melt or supercooled so-dium aluminosilicate liquid. By this method, details ofwhich are contained in Spera et al. (1988), unique valuesfor the shear stress (r,r) and shear rate (!,r) and theirrespective uncertainties were recovered from the raw ex-perimental data. The power law model was found to bethe most general model justified by the data, accordingto rigorous application ofthe,F statistic to a sequence ofpower series regressions oflog O against log r, r. At a giventemperature and composition, the power law model gives

r , o : t T t .Y i o ( l )

in which m and n are determined, respectively, from theintercept and slope of the linear regression of log Q vs.Iog 2,, for a set of isothermal rheometric data. That is,once the regression parameters ao and at in the expression

l o g 0 : a o + a t l o g r , o Q )

are found, the power law parameters are then computedaccording to

(3a)

(3b)

with C: (R./R.y in Equation 3a. Note that Equation 3acorrects a typographical error in Spera et al. (1988), whichalso includes a derivation ofEquation 3. A practical dif-ficulty encountered in the reduction of isothermal r7 datais that without sufficient range in shear rate, the value ofthe power law exponent n may be inaccurately deter-mined (Borgia and Spera, 1990; Stein and Spera, 1992).For silicate melts, with estimated power law exponents

STEIN AND SPERA: MELTS AND SUPERCOOLED LIQUIDS 7 1 3

TABLE 2. Rheometer dimensions

Sample F" (cm)

Nofej Sample numbers correspond to those given for viscometric ex-periments in Table 1. R. is the radius of the cytindrical crucible. B, is therotor radius The symbol h is the depth of immersion of the roror.

close to unity (0.8 = n < l), simple forward modelingcalculations show that the ratio of maximum to mini-mum shear rate ought to be at least 50-100 to recoveran accurate value of the power law exponent (n) fromconcentric cylinder rheometric data exhibiting typical ex-perimental uncertainties. Because limitations inherent inthe design of the rheometer preclude the measurement oftorque for a suitably large variation of rotation rate inthe aluminosilicate system, we chose not to incorporatethe power law parameters explicitly into the viscosity-temperature relationship. Instead, we adopted a proce-dure whereby the extracted power law parameters m andn, along with their uncertainties, were used to determinea single viscosity (rl) and a measure of its uncertainty (o,)at each temperature, allowing for instrumental errors.Viscosities were computed according to the relation

q : 1 . : m t ' ' @ )I

at each temperature from individual pairs of shear stress(z,r) and shear rate (|.r). Uncertainty in viscosity wascalculated based on propagation of errors in the powerlaw coefficients m and n. We have chosen the power lawanalysis specifically to avoid a priori assumptions regard-ing constitutive behavior. In order to test the robustnessand validity of the data reduction methodology, we usedthe raw r,,-Q data, together with the standard (Margules)expression for Newtonian viscosity, as a function of l, O,and C to compute 4 and o,. The viscosities computed byeach method were indistinguishable within the limits ofuncertainty. We observed a departure from Newtonianffow (i.e., n + l) in the few experiments for which |-,./?*' > 50, e.g., Nro at 1200'C, At, at ll25 "C, Nro" at1200 'C. In all cases the departure remained rather smalland the power law parameter n was less than or equal tounity (see Table 3).'

Dingwell and Webb (1989) and Webb and Dingwell(1990) asserted that the onset ofnon-Newtonian behav-ior in silicate melts occurs due to viscoelastic responsewhen the characteristic time scale of an experimental per-turbation (i-' in rheometry) is < - 100-300 times greaterthan the time scale of the relaxation response of the melt(defined by n/G-, where G- is the unrelaxed shear mod-ulus). From routine analysis of our experimental condi-tions, it is evident that this limit was never exceeded inour experiments because of the dynamic limitations ofthe rheometer. Unfortunately, the power law analysis be-ing presented here neither demonstrates nor excludes smalldepartures from Newtonian behavior in the relaxed meltregime. If the above examples are to be accepted, theycannot be explained by the onset of viscoelastic responsein these melts.

Results

Table 3 presents for each composition and temperaturethe number of data points in the regression of log O andlogr, u, the correlation coefficient ofthe regression definedby Equation 2, the runge of experimental shear rate andshear stress, and the derived power law parameters, in-cluding their respective uncertainties. Several importantfeatures of the data should be noted. Correlation of theraw Q-2., data by Equation 2 is generally excellent, with12 values >0.96 in most cases. The number of data pointsused in the fundamental regression varies somewhat butaverages around 20-30 individual O-r,, pairs for a givencomposition at a fixed temperature. For some composi-tions, such as NaAlSirOu melt (e.g., Nro"), as many as 75O-2., pairs were utilized in the regression, and the corre-lation at high temperature exceeds 0.98. Examination ofthe shear rate and shear stress range for specific compo-sitions along an isotherm shows a wide variance. On av-erage, measurements span a range in shear rates of abouta factor of l0- I 5, with a maximum range of 80 and min-imal values around 2. The lo uncertainties in the param-eters lzt and n collected in Table 3 refer to the precisionof the measurements and not their inherent accuracy.

Temperature dependence

Viscosity values, including lo errors, for each isother-mal experiment are given in Table 4. Sample numbersare those used in Table l. Figure 2a-29 shows the vis-cosity-inverse temperature data for each composition;when multiple measurements were made on a single com-position (e.9., ALr, Nro, and lluo), data are combined on asingle plot. Presented on each plot are the computed ac-tivation energy for viscous flow from the Arrhenian mod-el (B : E,/R)

l og4 : A +

and the range of shear rates in the entire set of rheometricdata for that composition. Error bars (+ lo) for each com-puted viscosity are shown with each point. To aid com-parison, the horizontal axes are identical and the verticalaxes employ a uniform scale for each plot. In general, the

R, (cm) h (cm)

N20N24N33AAA3BA/34N41N5OAN5OBN50CN6OAN6OBA/60C

1 . 4131.4541 .2701 .2701.5081 4571.2701.4681.4681.2701.2701.270

0 4830.4770.5000.4770.477o.477o.4730 4770.4760 4760 4760.476

2.5024.5722.8733.8864.8014 3694 j282.3294.7503.3523.3523.352

(5)BT

I Table 3 may be obtained by ordering Document AM-93-532from the Business Office, Mineralogical Society of America, I I 30Seventeenth Street NW, Suite 330, Washington, DC 20036,U.S.A. Please remit $5.00 in advance for the microfiche. Table3 is also available from the authors upon request.

( a )

EUTECTIC I ,N2o

+ i

t

r E = 4 7 0 . 6 t 1 5 . 9 k J / m o lq

0.008 s '1 < '1 , . 2 .18 s '1

7 t 4 STEIN AND SPERA: MELTS AND SUPERCOOLED LIQUIDS

8 . 5

I

7 . 5

8 . 5

8

^ L aahe 7o-7 o . s(,96

Ge 7o-; 6 . s

865 . 55 . 5

5

4 . 5

5

4 . 5

4 - 5

4

7 . 5

7

7 . 2 7 . 6 8(K)

6 . 47 . 66 . 4 6 . 8 7 . 210000/T (K)

6 . 8 7 . 210000/T (K)

6 . 8 7 . 210000/T (K)

6 . 8 7 . 210000/T (K)

6 . 81 0000/T

8

7 . 5

4 . 5

46 . 8 7 . 2

10000/ r (K)

( t )

JADEITEN s 0

t

r lI

f 'E

= 437.8 + 3 .0 kJ /moln

+ I Joo , " ' ' . i <8 .27

s ' 16 . 8

1 0000/T

Fig. 2. (a-g) Arrhenius plots of viscosity-temperature datafor each experimental composition; replicate measurements arecombined on a single plot; error bars represent la values (see

text for method of calculation). The horizontal axis is inversetemperature (in degrees Kelvin) and the vertical axis is the log-arithm (base 10) ofviscosity in Pascal-seconds. Horizontal scalesare identical in all plots; vertical scales are uniform but vary inorigin. On each plot the composition (the N number indicatesmole fraction NaAlSiO.), the Arrhenian activation energy in ki-Iojoules per mole, and the range of shear rates covered in thedata are given. Compositions representing invariant points ofthe NaAlSiOo-SiO, phase diagram are indicated by naming con-vention used in text.

I

7 . 5

7

? . .u(0g 6

R s . sJ

5

4 . 5

7o; 6 . 5Ig 6c,9 5 . s

5

7 . 66 . 47 . 66 . 4

8

7 . 5

? 6 . 5

86( , 5 . 5:1

t

7an6 o . Jo-

F 6oQ s . 5J

5

7 . 5

7

b . 5

G; oo.; 5 . 5

8s4 . 5

4 . 5

47 . 2 7 . 6 I(K)

6 . 47 . 66 . 4

4

3 . 5

( b )

N 2 4

.+,l

a

' E = 4 5 6 . 9 + 1 1 ' 5 k J / m o lr l

r .

0 . 0 1 1 s ' t . 1 . 3 . 8 4 s ' t

( c )

ALBITEN 3 3

- a' l l '

_ l l l_ I '

II

Ir E = 4 3 4 . 9 + 5 . 0 k J / m o l

t lI

| 0 .057 s '1 . i < 8 .65 s - t

( d )

N 3 4

i E = 4 4 0 . 1 1 4 . 9 k J / m o l. l'

o . o 1 o s ' t . y . 7 . 4 1 s - 1

( e )

EUTECTIC IIN 4 1

I' E = 4 1 0 . 6 1 4 . 5 k J / m o lr r t

a

o.0o8 s - t . i . 6 .79 s '1

PERITECTICN60 I+

. II

s l

+t

. t' I l E = 4 2 1 . O t 1 1 . 1 k J / m tl T n'

o . o o s - t . y < 8 . 1 3 s ' 1

7 . 6

Trsue 4. Summary of viscosity

rfc) log a (Pa s)- rcc) log 4 (Pa s)' o q

N20 ,vsoA1 300t l I C

1 2501225120011751 15011251 100

s.5335.8046.0976.3586.6306.8807.1407.4527.739

0.0390.0210.0410.0270.0800.0890.0920.148o.224

12751250122512001 15011251 1001 0751 060

0.1090.1 360.0800.0350.0650.0950.2380.1450.015

4.3914 .5194.8425.0515.7046.0036.2606.5806.702

^,508N24

1 30012751 25012251 20011751 15011251 1001075

5.103c .z5cc .czc5.7606.1026.3696.6426.8817.2547.500

,v33A

0.0410.0220.019o.0220.0270.0s30.0770.0900.1710.157

4.9285.1535.3805.5575.8076.0286.2576.4756.7816 .9157.0357.189

,vs0c

0.0160.0100 0 1 10.0080.0130.0130.0310.0260.0260.0660.0360.033

12201 2001 1801 1601 14011201 1001 0801 0601 05010401 030

1 3501 3001275125012251 20011751 1601 1501 1 4 01 1 3 0

4.3654.8164.9985 2285 5325.8356.0636.2026.32s6.427o.coo

A'338

0.0940.0480.0320.0350.0810.1380.0810.1260.1630.1940.103

125012251 20011751 15011251 1001 0801 0601 0401020

4.5624.7584.9475 .2165.495c . l 0 z

6.0556.374o.oco

6.9007.207

,v60A

0.021o.0220.0170.0170.0180.01s0.0310.0610.0690.0700.104

1 3501 3251 30012751 250122512001 1801 1601 140-1120

4 4714.6634.8485.0375 2945.5805 8596.0576.2546.5006.689

0.0360.018o.o170.0120.0120.0110 0220.0290.0330 043o o72

1 26012301 20011701 1401 1001 0601 040

0.2290.1200.0950.0890.0680.1580.3490.213

4.3024.4894.7905.0525.4125.9516.4096.63s

A'608N34

1 30012751 250122512001175'| 15011251 1001 0801 060

4.6864.8065.0785.3275.5935.8586 .1276 4476.7757.0507.317

N41

0.0230.0130.1020.0140.0160.0210.019o.o240.o740.1000.163

4.2494.5124.830s.3405.9776.505

o.1670.1510.0900.0s20.0700.160

1 2601 23012001 1501 1001 060

A'60C

1 3001275125012251 20011751 1501 1251 1001 0751 050

4.5304.7024.9455.1 075.2905.5735.8876.1 886.43167647.138

0.0230 02s0 0 1 7o.0210.0310.0280.0310.0360.045G.0590.030

12801 26012301 2001 1501 1001 060

4 .1514.2754.5754.8365.3485.9496 .518

0.0870.2820.0380.0970.0560.036o.128

- The viscosity at each temperature is an average computed by the method presented in the text.-t Standard deviation (1o value) is computed from propagation of errors in the power law parameters m and n, according to the method presented

in the text.

o o o o oo o o o o .t - o 6 F o f

I(^ 3

&ost ^ sqt"

a 9 -

NaA lS i .O ,

r ('c)

( A )

1 t 6 STEIN AND SPERA: MELTS AND SUPERCOOLED LIQUIDS

1 4

1 2

?ro(6o-; 8E )

.96

1 2

1 0

ABoo.

; 6o)54

6 7 810000/T (K)

710000/T

f c ) o oo oN O

ooo

NaAlSiO . N'Dala et al. (1984)4

o Riebting (1966)

(c)

4 4 . 5 5 5 . 5 6 6 . 5 710000/T (K)

uncertainties on the individual data points are smallestin the middle of the temperature range, where the rangeof shear rates examined for a particular temperature isgreatest (see Table 3). This condition more precisely de-termines the power law parameterc m andn, from whichthe errors in viscosity are calculated. The data are wellrepresented by the Arrhenian model in the temperaturerange studied; correlation coefficients for the 4 vs. l/Tregressions are almost always >0.998.

Fig. 3. (A) Plot of viscosity vs. inverse temperature for albitecomposition. Lower horizontal scale is inverse temperature; cor-responding temperatures in degrees Celsius are indicated on up-per horizontal scale. Symbols for Riebling (1966) represent endpoints ofRiebling's temperature range; data were reported onlyas regression parameters and a temperature range, with no in-formation on the actual number of data points nor estimates oftheir quality. Low-temperature data points from Taylor andRindone (1970), Dietz et al. (1970), and Cranmer and Uhlmann(1981b) were read from their published graphical presentations.The following symbols are used in the figure: open circles :

Urbain et al. (1982); solid circles : Riebling (1966); open squares: present study; solid triangles : Kozu and Kani (1935); + :

Scarfe and Cronin (1986); open triangles : Hummel and Arndt(1985); open diamonds : Cranmer and Uhlmann (1981b); soliddiamonds : Dietz et al. (1970); x : Taylor and Rindone (1970).(B) Plot of viscosity vs. inverse temperature for jadeite compo-sition. Lower horizontal scale is inverse temperature; core-sponding temperatures in degrees Celsius are indicated on upperhorizontal scale. Symbols for Riebling (1966) represent end pointsof Riebling's temperature range; data were reported only as re-gression parameters and a temperature range; low-temperaturedata from Taylor and Rindone (1970) were read from their pub-lished graphical presentation. Data reported by Hunold andBriickner (1980) differ considerably from the remainder ofthedata set and are not used in statistical analyses reported else-where in this paper. Symbols: open squares: present study; x: Hunold and Briickner (1980); solid circles : Riebling (1966);solid squares : Taylor and Rindone (1970). (C) Plot ofviscosityvs. inverse temperature data for nepheline composition. The re-gression published by Riebling ( I 966) for nepheline compositionis represented by the end points of the range of temperaturesreported.

As an exercise, polythermal viscometric data for eachof the seven compositions investigated were fitted to thethree-parameler Fulcher expression

1 11 0

1 0I(K)

(6)

@ 4(og

2o)q

2

l n o . : O * B

^ v P ' ' ' - T - T n

where A, B, and Io are constants for a given melt. Notsurprisingly, the quality of each of the log ri'-I fits wasimproved using the three-parameter expression as op-posed to the two-parameter Arrhenian one. Applicationof the F statistic shows that the Fulcher fit is statisticallysignificant for three of the compositions (Nro, No', andNuo), despite the rather limited temperature range (-250'C) of the viscometric data. It is also interesting (but per-haps coincidental) that Io increases as melts become moreNaAlSiO"-rich (e.g., Io values for N,o, No', and AIuo are550, 780, and 795 K, respectively). This indicates thatmelts become more non-Arrhenian as the NaAlSiO.component increases (i.e., more fragile; see Angell, 1988),which is consistent with the more irregular structure of anetwork in which intertetrahedral distortion accompaniesthe coupled substitution Na + Al : Si (see below).

The viscosity measurements span a temperature rangeof nearly 1000'when combined with those in the liter-

Eg F B r ( " c ) . .o a

a

a

( B ) J Ee E

- @ E

" B * xd B

I

x l t laA lS i O2 6

STEIN AND SPERA: MELTS AND SUPERCOOLED LIQUIDS 7 t'l

Trale 5. Arrhenian oarameters

SampleA

(log Pa-s)x"B

( l o g P a s - K ) (kJ/mol)

sio,N20N24ABBestN33N33UAN33KBN33SCN33TRDN33CUEN33HFN33DGN33RHN34N41JDBestN50N5OTRON50RHN60N67RHN79RHNaAlSiO4HNaAlSi04l

0.0000.2030 2420 3330.3330 3330.3330.3330.3330.3330.3330.3330 3330.3410.4080.5000.5000 5000.500n (aR

0.6670.7921.0001 000

7.246- 10.071-10.144-9 .123-9.603-8 606-8 686

t , t J l-12.249-7.930

- 1 1 . 9 6 2-11522-7 0861 0 . 0 1 6-9 16611.735

- 1 0.433- 13 .1 86

7.828-10 085-7 486-7 417

7.320-7.314

0.0780.5460.3980 0 1 30.1710 1 1 80.8020.1800.9950.4370.40005221.0000.1740.1 600.0350.1 090 6561.0000 4061.0001.0001.0001 0 1 1

269322458223868222732271621 589z t c v c

1 88711 0 0 t 1

20714261 032561 I1 864022989214492474322870264351 80252199417640170401622017825

150833600

1 8261205523318

1 099504468559

1 86425823648

156739

1 802581

1764170416221 950

515 .6470.6456.9426.4434.9413.3413 .5361 .3503.9396.6499 7490.5356.9440.1410 .6473.7437 I506.1345.1421.05 5 1 . t

326.3310.5341 2

2.915.91 1 . 50.35 .03.9

10.06.1

21.O

9.01 0 7J C , /

4.94.50.93.0

1 4 234.51 t . 133.832.63 1 . 137.3

Notei Sample numbers from this study are those given in Table 1. XN is the mole fraction of NaAlSiO4 component A and B are the coefficients otthe Arrhenian model of Eq. 5 (uncertainties o) Activation energy for viscous flow (in kilojoules per mole) and its uncertainty are calculated directly fromvalues of B. ABBest and JDBest are parameters for albite and jadeite, respectively, from combined data sets as described in text.

R e s u l t s f r o m p r e v i o u s l y p u b l i s h e d s t u d i e s : A : U r b a i n e t a l . ( 1 9 8 2 ) ; B : K o z u a n d K a n i ( 1 9 3 5 ) ; C : S c a r f e a n d C r o n i n ( 1 9 8 6 ) ; D : T a y l o r a n dRindone (1970); E: Cranmer and Uhlman (1981b); F: Hummel and Arndt (1985); G : Dietz et a l . (1970); H : Riebl ing (1966); | : N'Dala et a l .(1 984).

ature from Kozu and Kani (1935), Riebling (1966),Dietzet al. (1970), Taylor and Rindone (1970), Hunold andBriickner (1980), Cranmer and Uhlmann (l98lb), Ur-bain et al. (1982), N'Dala et al. (1984), and Hummel andArndt (1985) for the compositions NaAlSi,O, (albite, l/r,)and NaAlSirOu (adeite, Nro). Figure 3,{ shows the resultsfor NaAlSirO, combined with literature values and Fig-ure 38 shows results for NaAlSirOu. Figure 3C shows thelimited data available for nepheline composition (Na-AlSiO"). Figure 3A-3C portrays all relevant data knownto us lor these compositions.

The data for albite composition melt at superliquidustemperatures in the range l120-1700'C show remark-able consistency among five investigators (Fig. 3A). Ar-rhenian parameters for all individual investigators aregiven in Table 5. Arrhenian parameters for a best fit ofall available results for molten and supercooled albite inthe temperature range 800-1720 'C are also listed in thetable, in the entry labeled ABBest. Proper treatment ofthe errors, either as originally reported or estimated byus, that accounts for the methods used and their generalaccuracies has been included in the derivation ofthe Ar-rhenian parameters collected in Table 5. The data of Rie-bling (1966) for NaAlSi.O, melt yield a considerablysmaller activation energy and larger intercept and are re-stricted to a small range of relatively high temperatures.Unfortunately it is impossible to rate the quality of Rie-bling's viscometric data. Raw experimental data are notreported by Riebling; only regression (Arrhenian) param-eters are given, and no uncertainties are reported for theregression constants. In light of these omissions, we have

chosen not to include Riebling's data in f,tting the overalldata set to the Arrhenian model (ABBest), based on com-bining our data (open squares on Fig. 3,A) with those ofprevious workers.

The data for jadeite composition from the present work,combined with those of Taylor and Rindone (1970), cov-er a temperature range from 800 to nearly 1300'C (Fig.3B). The entire data set shows less consistency than thatfor albite: the results of Hunold and Briickner (1980) varyconsiderably from the remainder of the data, and wetherefore disregard their results. It is interesting to notethat Richet (1984) rejected the results of Hunold andBriickner (1980) as being inconsistent with the high-tem-perature viscometric data of Riebling (1966) and the low-temperature viscometric data of Taylor and Rindone(1970) on jadeite composition melt. Our new results onjadeite composition (Nroo, Nuou, Nro.) support Richet'sargument. The viscometric data of Hunold and Briickneron jadeite melt appear to be too low (about 0.5-1.0 inlog a) in the temperature range of our experiments (1293-1548 K; see Fig. 3B). At low temperatures (i.e., aroundthe glass transition temperature Zs) the discrepancy be-tween the results of Taylor and Rindone (1970) and Hu-nold and Briickner (1980) is greater than an order of mag-nitude. Riebling (1966) gives a significantly smalleractivation energy for NaAlSirOu melt compared with ourvalues, and, for the reasons presented above, we also choseto exclude Riebling's data in fitting the Arrhenius relationfor jadeite melt (labeled JDBest in Table 5), using onlyour data and those of Taylor and Rindone at low tem-peratures.

7 1 8 STEIN AND SPERA: MELTS AND SUPERCOOLED LIQUIDS

Eq.tn

Sample text N. Coetficients

TABLE 6. Statistical tests of Arrhenian vs. Fulcher eouations Our fits to the Fulcher equation were accomplished bystandard nonlinear regression using the Levenberg-Mar-quardt technique (Press et al., 1986) and include resultsfrom this study, which was not available to Richet (1984).We combined our results with those of Kozu and Kani(1935), Taylor and Rindone (1970), Dietz et al. (1970),Cranmer and Uhlmann (198 lb), Urbain et al. (1982),Hummel and Arndt (1985), and Scarfe and Cronin (1986)for molten NaAlSirO, and with those of Taylor and Rin-done (1970) for molten NaAlSirO6, excluding in both casesthe results of Riebling ( I 966) for reasons cited earlier. Weincluded low-temperature data from Cranmer and Uhl-mann (l98lb), which Richet (1984) chose to exclude asseeming less precise. Results of the nonlinear fitting arepresented in Table 6, which lists the sample number andcomposition, along with the equation number (either Eq.5 or Eq. 6 in the text) to which the parameters corre-spond, the values of the fit parameters and their uncer-tainties, the 12 value ofthe regression, and the results ofthe -Ftest for each regression. Both two- and three-param-eter regressions fit the data very well. Notably, our resultsindicate that for both NaAlSirO, and NaAlSirOu melts,the Fulcher model is statistically significant, given appro-priate estimates of experimental uncertainties and properweighting of individual measurements.

There are indications from the above results on N.. andNro and from the results presented earlier on AIro, llo', andN6o that melts and supercooled liquids in this system aredescribed increasingly better by the Fulcher equation ascomposition changes from SiO, toward NaAlSiOo. In Ta-ble 5, the low-temperature data of Taylor and Rindone(1970) give the highest activation energies, whereas thehigh-temperature measurements of Riebling (1966) sys-tematically yield the lowest ones, and the spread is greaterfor jadeite than for albite. As Richet (1984) found, Zo foralbite is less than that for jadeite, although we find it onlymarginally so; the magnitude of Zo is one measure of thedegree ofdeparture from Arrhenian behavior. Clearly, asIo - 0, the three-parameter Fulcher model collapses intothe two-parameter Arrhenian one.

Richet's Zo values and those found in the present studyare quite similar for NaAlSi.O, (Richet obtained 277 K,whereas we find 274 + 5 K) but rather different forNaAlSi,Ou. Richet obtained 477 K for NaAlSi,Ou, butour value is only 297 + 16 K, similar to the value forNaAlSi,Or. The difference may be explained by our in-clusion of new results on NaAlSirOu and by Richet's in-clusion of Riebling's results, which we have disregarded.The new result indicates significantly less non-Arrhenianbehavior for NaAlSirOu than was found by Richet. Figure4 shows the logarithmic viscosity results for NaAlSirO'and NaAlSirOu plotted against T"/7, using values of Z,published by Richet and Bottinga (l 984). The greater cur-vature of the data for NaAlSirOu when compared withthat for NaAlSirO, is visible evidence of the increasednon-Arrhenian character (i.e., greater fragility) of Na-AlSirO6 melt compared with NaAlSi.O, melt. Further highquality viscosity measurements, particulady at tempera-

Errorest. x"

Albite 5 95 A: -9.123B: 22273

A lb i t e 6 95 A : -5 .994B: 14219To: 273'9

Jade i t e 5 42 A : -11 .735B :24743

Jadei te 6 42 A: -7 294B : 1 4 5 6 0To: 297.1

0.013 10126 103631 8

0.058 8105 6716131 (17 .9 )4 .9 F . , , , + : 11 .9

0.035 909.4 1390648

0.245 697.5 1 1800480 (20.8)

't5.7 F.,,,+: 12.6

0.020.050.050.05

Uncertainties in log r1 for data sou.ces used in regressionsUrbain et al. (1982)Dietz et al. (1970)Scarfe and Cronin (1986)Kozu and Kani (1935)Taylor and Rindone (1970)Cranmer and Uhlmann (1981b)Hummel and Arndt (1985)

. N is the number of data points in each regression.*. F,4 is the Ftest of the overall regression.t 4dd is the result of the Ftest for the significance of the added term

in the three-oarameter model+ F",r, is the minimum value of 4do required to denote significance for

the additional term at the 0.999 level

Data for nepheline composition are quite limited. Fig-ure 3C shows that the two sets of available measurementsdiffer consistently by nearly a full log unit in viscosityand that the activation energy published by Riebling, aswith his data for NaAlSi.O, and NaAlSi,Ou melt, is sig-nificantly lower than that computed from the data ofN'Dala et al. (1984). It is clear rhat additional high- andlow-temperature measurements on NaAlSiOo and Na-AlSirO6 melts and additional low-temperature measure-ments on NaAlSirO, would be beneficial to evaluate thedegree ofdeparture from Arrhenian behavior.

The Arrhenius relation is a semiempirical correlation,known to be inadequate to model data for viscosity vs.temperature data over a wide temperature range for manysubstances. For most of the compositions examined inthe present study, the temperature range of the viscositydata was 200 "C or less, barely adequate to resolve de-partures from Arrhenian behavior. For albite andjadeitecompositions, however, the range of temperatures is > 800"C. This allowed for a more definitive testing of the three-parameter Fulcher model of temperature variation (Eq.6). Recent applications of free volume theory (Cohen andTurnbull, 1959) and the Fulcher equation in studies ofviscosity of silicate melts and supercooled liquids includethe work of Cranmer and Uhlmann (l98la) on the sys-tem albite-anorthite, Cranmer and Uhlmann (198 lb) onalbite, and a review of the literature of oxide and simplesilicate viscosities by Richet (1984). Richet (1984) ap-plied the Fulcher equation to available data on albite andjadeite compositions and published values for the threecoefficients, using data from Riebling (1966) and Taylorand Rindone (1970) for both albite and jadeite, as wellas the data of Urbain et al. (1982) for albite.

0.020.020.05

STEIN AND SPERA:MELTS AND SUPERCOOLED LTQUIDS 7 1 9

1 4

1 2

? 1 ooc

o BoJ

0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 r . 1 1 . 2T s l T ( K )

Fig. 4. Plot of log viscosity (Pascal-seconds) vs. d/?" foralbite- and jadeite-composition data (includes all data exceptRiebling, 1966, and Hunold and Brtickner, 1980; I, is calori-metric glass transition temperature reported by Richet and Bot-tinga, 1984). A plot in these coordinates allows comparison ofdegree of curvature in each data set; a larger ?", (i.e., greatercurvature) indicates greater departure from the Arrhenian tem-perature variation for NaAlSirOu melt.

tures approaching Q, and careful evaluation of experi-mental uncertainties, will be needed in order to resolvethis issue and establish unequivocally whether Zo doesincrease with increasing mole fraction of NaAlSiOo asspeculated here.

Cornposition dependence

Figure 5 is a portrayal of results in the form of anisotherm plot of log viscosity vs. composition in terms ofthe mole fraction of NaAlSiO. at 1673 K. There is asystematic decrease of viscosity with increasing NaAl-SiOo content. Most of the decrease occurs between puresilica and eutectic I, although it is clear that for XNaArsioa(hereafter X) > 0.2, there is a log-linear relationship be-tween viscosity and composition. Along the 1673-K iso-therm for example, there is a decrease by a factor of 50in the viscosity from eutectic I melt (& : 0.2) at 32000Pa's to pure NaAlSiOo melt at 2 I 90 Pa.s. There may alsobe a logJinear relationship between viscosity and com-position between pure silica (5 x 108 Pa.s) and eutecticI melt (X, : 0.2, n : 32000 Pa.s), although there are notenough data in this compositional range to determineprecisely the form of the dependence. The structural in-terpretation of the drastic reduction of viscosity by theaddition of metal oxides (e.9., NarO, KrO, etc.) to silica-rich liquids is generally given in terms of the network-modifying model as originally put forward by Zachai-asen (1932). The extent of network modification dependson the number of nonbridglng O atoms (NBO), which, ofcourse, is directly related to the concentration of the met-al oxide additive. The data presented in Figure 5 cannotbe rationalized in such a simple fashion. It is obviousfrom the stoichiometry of the coupled substitution Nat

O Cranmer and Uh lmann (1981b)

a Urba ln e l a l . (1982)

a Taylor and Blndone (1970)

O Scarfe and Cronln (1986)

o N'Dala el al. (1984)

A Kozu and Kanl (1935)

! Th ls S tudy ^ nH !

n r L . ^^'

1673 K

'|NaA lS lg

0 . 8 0 . 6 0 . 4 0 . 2 0Mole Fract lon NaAlSlO Siq

Fig. 5. Plot of viscosity (Pascal-seconds) vs. composition interms of mole fraction NaAlSiOo along the 1673 K isotherm,including results from previous studies listed in Table 5, Somepoints are extrapolations using Arrhenian parameters from Ta-ble 5.

+ tarAlr+ : I41Si4+ that the addition of NaAlSiO, does notbreak down the network structure per se. Since Al is pri-marily in fourfold coordination and Na serves to balancethe charge, NaAlSiOo-rich melt is a network fluid with Ocoordination numbers near 2 and tetrahedral cation (Alor Si) coordination numbers around 4, as in pure SiO,melt at 100 kPa (e.g., Rustad et al., l99la, l99lb, 1992).Thus the negative value of (d 1rog4/dXr)rr, as determinedexperimentally for melts in the system NaAlSiOo-SiOr, isnot caused by a significant increase in the concentrationof NBO. We speculate that topological and bond energyconsiderations must be important factors. Na-O and Al-Obond lengths are greater than Si-O lengths; similarly, theSi-O bond energy is *20o/o greater than the A1-O energy.Substitution of (Na,Al) for Si must induce some randomirregularity of the T-O Voronoi polyhedra beyond thatusually ascribed to the amorphous state and must broad-en the distribution of intertetrahedral TOT angles, as wellas displace the mean angle to lower values. Currently, weare pursuing MD simulations (Stein et al., 1992a, 1992b)to gain further insight into the characteristics ofinducednetwork distortion as NaAlO, is added to molten SiO,(see also Scamehorn and Angell, l99l).

The variation of viscous activation energy with com-position is shown in Figure 6, in which a trend of de-creasing activation energy with increasing NaAlSiOo con-tent is evident. This figure includes results from our ex-periments, from Urbain et al. (1982) for silica, and fromN'Dala et al. (1984) for nepheline melt. The silica valueis especially well determined and comes from the ex-haustive analysis of Urbain et al. (1982). The value formolten NaAlSiOo comes from N'Dala et al. (1984), whichis slightly higher than the ill-constrained value given byRiebling (1966) (not plotted). For the purpose of maxi-mizing internal consistency, all other values of E, (i.e.,for Nro, Nro, Nr., N.o, No,, Nro, and N.o) were derivedexclusively from the present study. The trend ofdecreas-

o N a A l S i O3 0

@ or NaA tS i2OG ^c1p,q

^gaB

@

o; 6

o9 4

-120

5 0 0

r Thls Stu.lytr Urbaln et al. (1982)a N'Dala et al. (1984)

- - Besl Fll-

l -_ a -l / l

. J L

/ lT r -

L" t

Fig 6 Activarion ."J;j:":i;:;,,.",'ian mode,,in kilojoules per mole) vs. composition in terms of mole fractionNaAlSiO. using results from Table 5. Error bars on data pointsrepresent uncertainties in E,(lo values). Best-fit linear regressionline includes data from the present study for intermediate com-positions, data of N'Dala et al. (1984) for NaAlSiOo, and dataof Urbain et al. (1982) for SiO,.

ing.E" in Figure 6 is approximately linear for values mea-sured in the range of magmatic temperatures, decreasingfrom 515 kJlmol at SiO, to 340 kJ/mol at NaAlSiOo.Linear regression analysis ofthe data returned the equa-tion.E, :499 - l58XN, where the activation energy.ismeasured in kilojoules per mole and X, is the mole frac-tion of the NaAlSiO4 component in the melt. The cor-relation coefficient is r'? : 0.89, which indicates that near-ly 900/o of the variation of E, can be explained in termsof a linear dependence on mole fraction NaAlSiO.. It isinteresting to note that the fractional change in -8" goingfrom SiO, to NaAlSiO" melt (-300/o) is about equal tothe difference in Si-O and Al-O bond energies. Activationenergies for the viscometric data of Taylor and Rindone(1970), measured for NaAlSirO, and NaAlSi2O6 at tem-peratures around T"appear anomalously high and are notplotted. A similar viscometric technique was used in thesame temperature range by Cranmer and Uhlmann(l98lb) for NaAlSi.OS, and their value for.E, falls nearthe range ofour values.

Compensation

An additional feature of the rheometric data for thissystem is seen in Figure 7, in which the Arrhenian pa-rameters A and B are plotted against one another in theform of a compensation plot analogous to those made fordiffusion data in silicates. There appears to be a roughcorrelation, although the problems cited earlier regardingsome of the previous studies are apparent. Again, if thedata ofRiebling (1966) and ofTaylor and Rindone (1970)are neglected, a reasonably linear compensation array re-sults (except for silica). Although we have reasons to doubtthe quality of some of Riebling's data, no such reasonsare immediately apparent for the Arrhenian parametersof Taylor and Rindone.

STEIN AND SPERA: MELTS AND SUPERCOOLED LIQUIDS

o 4 5 0

IJ

4 0 0

2 8 0 0 0

2 6 0 0 0

^ 2 4 0 0 0

g 2 2 0 o o

t 2 o o o o

1 8 0 0 0

1 6 0 0 0

s i o -

O Clanmer and Uh lmann (1981b) ! B

! Th ls S tudy -I Kozu and Kanl (1935)

O N'Dala et al. (1984)

a scarfe and cronln (1986) O

a Taylor and Flndone (1970)a Urbaln et al. (1982)

!!

- 1 4 - 1 3 . 1 2 . 1 1 . 1 0 - 9 - 8 - 7

A (Log Pa.s )

Fig. 7. Plot of A vs. B from the Arrhenian parameters ofTable 5. Perfect compensation would exhibit a linear relation-ship between the plotted values ofl and B. Note that I is pro-portional to a fictive (logarithmic) viscosity at infinite tempera-ture and that -B is proportional to the activation energy for viscousflow (i.e.. it is related to the temDerature derivative of the vis-coslty).

DrscussroN

The systematic decrease in both the isothermal viscos-ity and activation energy for viscous flow as NaAlSiOo isadded to molten silica, as depicted in Figures 5 and 6,may be semiquantitatively explained by simple topolog-ical and bonding arguments. Indeed there is a large bodyofevidence upon which to base an explanation, includingRaman spectra (Sharma etal., 1978; Mysen et al., 1980;McMillan et al.. 1982: Seifert et al.. 1982: Matson andSharma, 1985), X-ray radial distribution studies (Taylorand Brown, 1979a, 1979b; Taylor et al., 1980), molecularorbital calculations (DeJong and Brown, 1980a, 1980b;Gibbs et al., l98l), simulations of molecular dynamics(Scamehorn and Angell, 199 l; Stein et al., 1992a, 1992b),noble gas solubilities (Roselieb et al., 1992), and calori-metric studies (Navrotsky et al., 1982).

Substitution of NaAlO, for SiO, appears to expand thenetwork stmcture and introduce distortions in the TOonetwork. For example, the volume of a gram-atom ofNaAlSi,O,, NaAlSirO6, and NaAlSiOo glass at 25 "C is1.376, 1.386, and 1.422 J/bar per O atom, respectively.In summarizing data for crystalline phases in the systemNaAlSiOo-SiOr, Taylor and Brown (1979b) noted thatmean TO bond distances increase from 1.59 A for crys-talline SiO, ro 1.67 A for nepheline. There is also a de-crease in the mean intertetrahedral TOT bond angles from150 to 143'as the T site becomes half-occupied by Al.The decrease in bridging intertetrahedral TOT angles issimilar to the observed pressure-induced shift in the Si-O-Si bond-angle distribution maximum from 143 to 138"determined by magic-angle spinning nuclear magneticresonance experiments on amorphous silica. Devine etal. (1987) have explained the decrease ofbridging anglein terms of a reduction in the distance separating O andthe second nearest neighbor O from 3.12 to 2.9 A. Such

3 0 0

STEIN AND SPERA: MELTS AND SUPERCOOLED LIQUIDS 721

a steric effect may also be important in NaAlSiOo-SiO,melts as X, increases isobarically. In ultrasonic studies,Rivers and Carmichael (1987) found that longitudinalsound velocity decreased with composition from moltenNaAlSiO. to molten NaAlSi,Or. Compressibility (e.g.,governed by O-O repulsions) is inversely related to thesound velocity, so the pattern ofultrasonic velocities canbe rationalized in terms of inferred changes in intertetra-hedral angles. Potential energy curves vs. TOT intertetra-hedral bndging angle for HuSirO, and HuSiAlOr-r clus-ters in molecular orbital calculations by Meagher et al.(1980) gave minimum-energy Si-O and Al-O bond lengthsof 1.59 and 1.70 A, respectively, and minimum-energybridging angles of 142 and 131" for Si-O-Si and Al-O-Si,in agreement wrth X-ray data (Taylor et al., 1980). Ca-lorimetrically determined mixing enthalpies in the sys-tem NaAlOr-SiO, (Navrotsky et al., 1982) show thatmaximum stabilization occurs at the nepheline compo-sition (l:1 ratio of NaAlO,/SiOr). The molecular orbitalcalculations of DeJong and Brown (1980a, 1980b) foraluminosilicate clusters indicate that the exchange reac-tion TdSi-O-Si) + ydAl-O-AD : Al-O-Si is strongly exo-thermic, with an approximate enthalpy AH - -210

kJ/mol. Interestingly, this energetic stabilization is aboutequal to the experimentally observed decrease in activa-tion energy for viscous flow from SiO, (5 15 kJ/mol) toNaAlSiOo (350 kJlmol). Polarization ofbridging O atomsin the Al-O-Si network, which is caused by a greater bondlength and a larger electronegativity difference betweenmetal and O for Al-O compared with Si-O, makes for aless covalently bonded structure. The greater ionicity ofthe Al-O bond compared with Si-O, coupled with theincreasing occupancy of holes defined by six-memberedtetrahedral rings of Na atoms, leads to a smaller averageTOT intratetrahedral angle (Okuno and Marumo, 1982),a larger variance in the distribution of TOT angles, andhence smaller TO bond energies. These topological andenergetic factors give rise to a weaker network that cor-relates with a small, but measurable, increase in the de-gree of non-Arrhenian thermal behavior as NaAlSiOoconcentration increases (i.e., from NaAlSirO, to NaAl-SirOu melt), as monitored by the increase in Io in theFulcher equation. The approximate linear relation be-tween -8, and composition is consistent with the gradualweakening of the network. In recent simulations usingmolecular dynamics on aluminosilicate melts and glasses,Scamehorn and Angell (1991) showed that non-Arrheni-an behavior (termed melt fragility) can be correlated withincreasing TO length and decreasing TOT angle. If meltfragility does increase with increasing substitution of Na+ Al: Si, then one expects an increase of L,Cr/Crattheglass transition temperature as the NaAlO, content of theglass increases. One also would expect the solubility ofnoble gases to decrease at constant temperature and pres-sure upon addition of NaAlO, to SiO, melt because ofthe greater framework distortion associated with smallerTOT bridging angles and less hole volume availabilityfor a noble gas atom due to increasing occupation ofsix-

membered ring holes by Na. On the basis of available(but limited) data, these trends are indeed observed (Ri-chet, 1984; Richet and Bottinga, 1984 Roselieb et al.,r992).

In summary, viscometric data in the system NaAlSiOo-SiO, can be rationalized in terms of the reduction of thestrength of the network associated with introduction ofAl into tetrahedral sites, and Na + Al : Si has the effectof producing a weaker network structure, with an acti-vation energy for viscous flow considerably smaller thanthat for molten silica.

CoNcr,usroNs

We have performed measurements of viscosity on meltsand supercooled liquids in the system NaAlSiOo-SiOr, attemperatures from I 000 to I 300 oC at shear rates rangingfrom 0.01 to 8.7/s using concentric cylinder rheometry'Departure from Newtonian flow is difficult to detect atthe conditions of temperature and shear rate of the ex-periments. However, when measurements are performedover a sufficiently large range ofshear rates, it is not pos-sible to exclude non-Newtonian constitutive behavior(with a power law exponent n < l).Systematic compo-sitional variation of viscosity and its temperature deriv-ative are evident from our measurements; these resultsinclude data on five compositions spanning the range from20 to 60 molo/o NaAlSiO., for which no previous datawere available. Fitting of the viscosity-temperature data(including estimated uncertainties) to both the Arrhenianand Fulcher models was performed. Statistically signifi-cant fits to the three-parameter Fulcher equation resultfrom combination of our data with previously publishedliterature values for the compositions NaAlSi.O' andNaAlSi,Ou. These tests give indications that melts in thissystem exhibit increasingly non-Arrhenian behavior withincreasing concentration of NaAlSiOo component. Re-sults for NaAlSirOu melt in the temperature range 1275-1000 "C confirm that the results of Hunold and Briickner(1980) differ considerably from the remainder ofthe data,are systematically low by 0.5 to > I log unit, and shouldbe considered suspect. Properties of melts and glasses inthis binary system have been well studied by a variety oftechniques, including X-ray diffraction, infrared and Ra-man spectroscopy, thermochemistry, and computer cal-culations using molecular dynamics and quantum-chem-ical (molecular orbital) methods. Results from thesestudies strongly suggest that introduction of Na and Alwith l:1 molar ratio into molten SiO, produces irregularTOo intertetrahedral network distortion, in addition to anet reduction of intratetrahedral bond strength due toboth the greater Al-O bond length and the polarizing ef-fects of six-membered ring hole filling by Na. These mi-croscopic features give rise to the decrease both in vis-cosity and in its temperature derivative as NaAlSiOo isadded to silica liquid. Finally, the increasing Vogel tem-perature (Io in the Fulcher expression, Eq. 6), lncreasesupon addition of NaAlSiO4 component to silica melts, asign of increasing melt fragility.

'722

Acrnowr,ntcMENTS

This is contnbution 0135-29CM of the Institute for Crustal Studies,University of California, Santa Barbara. The research was completed un-der the support of grants from the National Science Foundation (NSFEAR-92-05820) and from the United States Department of Energy (DE-FG03-9lER-1421 l). The authors also wish to express their appreciationto Donald Dingwell for his review of the manuscript and to Mark Ghiorsofor editorial handling.

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MeNuscnrrr RECEIVED Aucusr 3, 1992M,c.NuscnrFr ACcEpTED Mancs 18, 1993

STEIN AND SPERA: MELTS AND SUPERCOOLED LIQUIDS