Compressibility of melts in the CaO-Al2O3-SiO2 system

Geochimica et Cosmochtmtca Pergamon

Acta. Vol. 60, No. I, pp. 75-86, 1996 Copyright 0 1996 Elsewer Science Ltd Printed in the USA. All rights reserved 0016-7037/96 $15.00 + 00

0016-7037( 95 ) 00381-9

Compressibility

of melts in the CaO-Al,O,-SiO,

system

SHARON WEBB and F%ILIPPE COURTIAI~ Bayerisches Geoinstitut, 95440 Bayreuth, Germany (Received

March

28, 1995; accepted

in revised fotm

October

3, 1995 )

Abstract-The effect of composition and temperature on the compressibility of melts in the CaO-Al,O?SiOZ system has been investigated. The relaxed bulk moduli were measured using ultrasonic interferometric methods at frequencies of 3, 5, and 7 MHz. The measurements were carried out in the temperature range of 1350- 1600°C. For these melts, the bulk modulus increases with the addition of CaO and decreases with addition of SiO* and A1203. The bulk moduli of the present alkaline-earth aluminosilicate melts are -50% larger than the adiabatic bulk moduli of the sodium-aluminosilicate melts of Kress et al. ( 1988). The present data, together with literature data on the bulk moduli of silicate melts show that different structural mechanisms are responsible for the observed compressibility of CaO-AlZ03-SiOz and Na,O-A1,O1-SiO, melts. 1.

INTRODUCTION

A general equation of stateS( P, V, X, 7’) is one of the major goals of the study of the physical, chemical, and thermal properties of silicate melts. Data on the temperature and composition dependence of density and compressibility of silicate melts give access to a wide range of information about the rheology of melts at different conditions; from lava flows, to magma bodies, to sinking or floating of crystals in magmas, to the movement of melt through rocks. Compressibility and volume data are also required for determining solid-liquid phase equilibria at the high pressures necessary for understanding igneous petrology. Extensive investigations of the temperature and composition dependence of the molar volumes of silicate melts at superliquidus temperatures via density determinations have yielded equation of state models for silicate melt densities at high temperatures and one atmosphere pressure, i.e.f( V, X, 7’) (e.g., Stein et al., 1986; Lange and Carmichael, 1987; Dingwell and Brearley, 1988; Lange and Carmichael, 1990; Courtial and Dingwell, 1995 ) . The pressure dependence of melt volume has been addressed via high pressure density measurements (e.g., Fujii and Kushiro, 1977; Agee and Walker, 1988), shock wave measurements (e.g., Rigden et al., 1984; Miller et al., 1991), and ultrasonic determinations of the melt compressibility at ambient pressure (e.g., Manghnani et al., 1981; Rivers and Carmichael, 1987; Kress et al., 1988; Kress and Carmichael, 1991; Webb and Dingwell, 1994). Ultrasonic studies have resulted in the determination of the compressibility of a large number of binary silicate melts as a function of temperature and composition (see Rivers and Carmichael ( 1987) for a review). In addition, there have been similar studies of the compressibilities of small number of ternary (Rivers and Carmichael, 1987; Kress et al., 1988; Webb and Dingwell, 1994) and more complex multi-component silicate melts (see, Kress and Carmichael, 1991; Secco et al., 1991; Sate and Manghnani, 1985). The majority of silicate melt compositions have a bulk modulus in the range 5-20 GPa at 10’ Pa. The alkaline-earth bearing melts have much higher bulk moduli, from 20-30 GPa. That is, they are not as compressible as the alkali-rich (alkaline-earth poor) silicate melts studied to date. Further-

more, as shown by Rivers and Carmichael ( 1987) and illustrated in Fig. 1, the bulk moduli of CaO-bearing silicate melts (and alkaline earth-bearing melts in general) do not follow the simple empirical trends observed as a function of molar volume for most silicate melts. Herzberg ( 1987) also pointed out that the alkaline-earth rich silicate melts do not follow the Law of Corresponding States which relates the bulk modulus to the volume-per-atom of the melt. Given the large effect alkaline-earth oxides have on decreasing the compressibility of silicate melts (and, therefore, reducing the density increase with increasing pressure) and the ubiquitous nature of these components in natural magmatic systems, the equation of state of alkaline-earth aluminosilicate melts needs to be investigated in more detail. In this paper, we present data on the compressibility of melts as a function of temperature and composition at ambient pressure in the ternary CaOA1201-SiOZ system. 2. EXPERIMENTAL 2.1. Sample

Preparation

TECHNIQUE

and Character&&ion

The starting materials for these melts were powders of A1?O1 (Merck-y alumina), CaCOx (Merck extrapure), and SiO, (Fluka Quartz-Ign. loss < 0.3%). The starting materials were dried at 120°C for 24 h before use. The powder mixtures were weighed in batches equivalent

to 0.1 kg melt. The mixed

period of one hour in a platinum 1550°C depending the sample. The

upon the melting

crucible

powders at

temperature

were

melted

for a

temperatures of 150& and the viscosity

of

melts were then poured onto a stainless steel plate and allowed to cool. For the more viscous melts, a cycle of grinding of the glass and remelting was performed three times. Each melt was finally poured from the platinum crucible info a cylindrical stainlesssteel form, with the resulting 0.02 kg glass patty fitting into the molybdenum crucible used for the ultrasonic measurements. The quenched

glasses were

analysed

by electron

microprobe

to

check the composition and homogeneity. Some of these liquids are not good glass formers. In these cases, the glasses which were analysed were obtained by rapid quenching of a small amount of the melt. The results of these analyses (all within error of the nominal compositions) are presented in Table 1. The melts are labelled Y .X where Y and X are the mole fractions of SiOz and Al,O,,

Ca re-

spectively. The composition range investigated is controlled by the temperature of the Iiquidus surface and by the immiscibility area (e.g., Levin et al., 1964). The present compositions are plotted in Fig. 2; they were selected to lie on pseudobinary joins to SiOz.

S. Webb

loglo VOLUME 0.71 3

PER ATOM

0.85 I

0.95

I

I

I

I 04 I

I

equal to the relaxed bulk modulus (G) is zero (Herzfeld and Litovitz,

(cm’) 1.11 I

L

and P. Courtial

11 8

F

25

1.40

The compressibility

”

1.30

1.18

8

1.00

5 2

0 70

and the bulk modulus describes the variation tion of pressure P at constant entropy.

3. RESULTS AND 3.1. Experimental

5 2

FIG. 1. Bulk modulus of alkali- and alkaline earth-bearing silicate melts as a function of volume-per-atom-pair of the melt (redrawn after Rivers and Carmichael, 1987). The second scale is in units of log,, bulk modulus (GPa) and log,, volume-per-atom (cm’) to allow

comparison with Figs. 7 and 8. Measurements

The velocities of longitudinal waves propagating through these melts were determined at ultrasonic frequencies using the furnace and twin-molybdenum buffer-rod apparatus of Webb ( 199 1) There is a constant flow of forming gas ( 95%NZ-5%HZ) across the molybdenum furnace elements and the molybdenum crucible and bufferrods. Chrome-gold, coaxially-plated, 2 MHz quartz X-cut compressional wave transducers were used at the first, third, and fifth harmonic frequency. The interferometric measurements are performed in the reflection mode, with the transducer acting as both sender and

receiver. Pulsed sinusoidal signals of 80 ps duration were propagated through the melt and the change in amplitude of the returned signal was monitored as the upper buffer-rod was moved. The amplitude of

IArI’

=

R’lexp(4oL) exp(hl)

1985)

- 2 exp(2aL) - 2R' exp(2aL)

cos (47rLflu) cos (47rLflu)

+ I] + R4 ’

(1)

where (Y is the attenuation coefficient, L the melt thickness, u the wave velocity, and R is the reflection coefficient at the buffer rod-melt

interface. The buffer rods are aligned using acetone as the sample. The average of the three (3, 5, and 7 MHz) velocity determinations at 10°C for acetone is 1237 (0 = 9) m s-’ in comparison to the

literature p-wave velocity of 1238 2 4 m s-’ (Kaye and Laby, 1986). As an example, the fit to the data for melt Ca 53.12 for a frequency of 3.025 MHz at temperature 1450°C is illustrated in Fig. 3. Measurements

were performed

over

a temperature

range

were determined

with a standard

in volume

V as a func-

DISCUSSION

Results velocities

and bulk

moduli

for the five melts

in the temperature range 1350- 1600°C are listed in Table 2. The lowest temperature for each composition is limited by the onset of crystal growth within the melt. The presence of crystals in the melt results in the ultrasonic interference pattern becoming nonsymmetric and nonreproducible. The upper temperature of 1600°C is the limit of the furnace. The velocity data as a function of temperature are plotted in Fig. 4. The longitudinal wave velocities for the melts investigated range from 2950-3650 m s-’ as a function of composition in the 1350- 1600°C temperature range, with the CaO-rich (SiOzpoor) melts having the higher velocities. The temperature dependence of the relaxed longitudinal wave velocities through these melts ranges from -0.03 to -0.59 m s -’ “C- ’ , in agreement with the 0 to -0.35 m s ’ “C - ’ temperature dependence observed by Baidov and Kunin (1968) and Sokolov et al. ( 197 1) , and also within the range of temperature dependence measured for a wide range of binary, ternary, and complex silicate melt compositions by Rivers and Carmichael ( 1987), Kress and Carmichael ( 1991), and Webb and Dingwell ( 1994). The temperature dependence of the present velocities is larger for the SiOz-poor melts (see Table 3) as observed by Baidov and Kunin ( 1968) and Sokolov et al. ( 1971) for CaO-Alz03SiOz melts. The temperature dependence of the bulk moduli of the present compositions are listed in Table 3, together with the calculated densities of the present melt compositions. The densities were calculated from the model of Courtial and Dingwell (1995) for CaG-A120x-Si02 melts. The linear temperature dependence of the bulk moduli range from - 1 to - 12 X 10 -’ GPa “C -‘, in genera1 agreement with the values in the literature for other silicate melt compositions (see Rivers and Carmichael, 1987). The CaO-rich (SiO,-poor)

1350-16OO”C,

dependent upon the melting temperature for each composition. The velocities

bulk

(4)

The calculated

signal is (Rivers,

of the adiabatic

5 :

the reflected

OS of the melt is the inverse

modulus,

s

2.2. Ultrasonic

of the melt as the shear modulus 1959),

error of ~0.3%.

The cal-

Table I Measured composition

ofthe mverlugated melts (wt% )

culated adiabatic bulk moduli

(2)

K, = pv’,

for density p and velocity v, have a standard error of less than 1%. For all of these melts, no frequency dependence of the measured

velocities was observed. This indicates that the viscosities of these melts are low enough

(i.e.,

<6 Pa s; Webb

and Dingwell,

1994)

in

the investigated temperature ranges, that the relaxed bulk moduli of the melts are determined in the 3-7 MHz range. In the relaxed for each melt composition, the relaxed longitudinal modulus

regime (M) is

’ analyses from Comm

and DINGWELL (1995)

Analyses were made with a Cameca electron microprobe

operated at 15 kV and 15 nA

Compressibility of Ca-Al-silicate melts

77

SiO,

CaO

FIG. 2. The five CaO-Al,O,-SiO, melt compositions studied here (solid squares), together with the CaO-SiO, melt compositions of Baidov and Kunin (1968) [BKx, hollow circles], the melt compositions of Rivers and Carmichael (1987) [RCx, hollow squares] and the CaO-A1207-Si02 melt compositions of Sokolov et al. (197 1) [Sx, hollow squares] as mole fractions. The solid lines indicate the pseudobinaries with SiOz. and the shaded area and the dashed lines indicate the compositions of constant CaO-content discussed in Fig. 8.

melts have the largest temperature dependence of the bulk modulus. A compilation of the ultrasonically determined bulk moduli for melts in the Ca0-A120-r-Si02 system at 1500°C are shown in Fig. 5 as a function of mole fraction of the oxide components. This includes the present data together with that of Baidov and Kunin ( 1968) and Sokolov et al. ( 1971) at 1500°C and also that of Rivers and Carmichael (1987) at - 1560°C. The bulk modulus of the present melt compositions increases from 23-34 GPa at 1500°C with increasing CaO content. It can be seen from Fig. 5 that the bulk modulus for

melts in this ternary system increases with increasing CaO content and decreases with increasing the content of either SiO, or AllO?. This behaviour is contrary to that observed for the bulk modulus of melts in the Na20-A&OX-Si02 system. As shown by Kress et al. (1988) for Na*O-Al@SiO, melts in a restricted composition range ( see Fig. 6), the bulk modulus tends to increase with increasing A&O1 content for large mole fractions of SiOz and does not seem to vary as a function of NazO-SiO, ratio for a constant mol% Al,O,. This opposite effect of the addition of A1203 on the bulk moduli in these two systems, for the compositional ranges inves-

3.025 MHz 1450°C

MELT

THICKNESS

(mm)

3. The ultrasonic signal amplitude data as a function of melt thickness for the Ca 53.12 melt composition for a frequency of 3.025 MHz at 1450°C. The points are the measured amplitude of the signal, and the line is the curve fit using Eqn. 1. FIG.

78

S. Webb Table 2. Relaxed temperature

T “C -

longitudinal

(T), together

‘a 53.12 1350

2.615

1375

2.612

1400

rn-’

2.604

1450

2.600

1475

2 596

1500

2.592

1525 1550

2.588 2.584

:a 36.16 1475

2.691

1525

2.689

1550

2.677

1575

2 673

1600

2.668

- densities

”

MHz

m s-l

(v), average

are calculated

velocity

v

m s-’

GPa

“C Ca 09.23 1450

2978+3

23.20M.03

296935

23 02M.08

3.025 5.040 6.950 3.025 5.040 6.950 3.025 5.040 6.950 3.025 5.040 6.950 3.025 5.040 6.950

3257 3295 3219 3263 3271 3300 3259 3274 3284 3254 3261 3275 3254 3255 3267

3277*9

28.9W3.16

3278?9

28.74M.14

327225

28.67Ho.

3263i5

28.39tO.09

3259*4

28.33io

2956f3

T

~

2917 2974 2983 2976 2972 2948 2971 2987 2958 2957 2959 2958 2954 2944 2963 2957 2969 2963 2956 2968 2968 2938 2951 2953 2947 2964 2950 2957 2947 2956 2926 2954 2968 2963 2957 2944

22 86M.04

2955i4

22 69M.06

IO’ kg -

m-3

2.776

1475

2 769

1500

2 762

1525

2 756

1550

2.149

Ca 11.39 1525 2957f4

22.7OM

2952m

22.59M.09

and DINGWELL

f

c’

22.78M.04

2963C3

2957 2944

adiabatic bulk moduli (Ks) as a function

signal and the density (p) of the melt. (Errors

KS

3 025 5.045 6 950 3.025 3.025 5.045 5.045 6.950 6.950 3 025 3.025 5 045 5.045 6 950 6 950 3 025 5.045 6 950 3 025 3 025 3 025 5045 s.045 6.950 6.950 3 025 5 045 6 950 3.025 3.025 5.045 5.045 6.950 6.950 6.950 6.950

from COURTIAL

(V), and relaxed

(f) of the propagating

-

2608

1425

with the frequency

f

Pa IO’kg -

wave velocities

and P. Courtial

2 748

05 1550

2 7-14

1575

2.741

22.62 22.40

(1995)

Ca 38.27 1400

2.665

1425

2.662

1450

2.659

1475

2.656

1500

2.654

1525

2.651

I550

2.648

10

06

model for CaO-Al20&02

-

MHz

-

are standard

errors)

\’

v

KS

m s-’

m s-’

GPa

3.050 5.025 6.950 3.025 5.025 6.950 3.035 3.035 5.025 6.950 6.950 3 050 5.015 5.025 6.950 3 025 3.015 3.015 5.025 5.025 6.950

3599 3615 3634 3602 3593 3633 3589 3587 3600 3605 3614 3575 3587 3587 3582 3555 35718 3586 3586 3570 3577

3 015 5.040 5.040 6.950 3.015 5.040 s.040 6.950 3.015 5.040 5.040 6 950 6 950

3 015 5 040 6 950 3 015 3 015 5.040 6 950 6 950 3 015 5.040 6.950 3.015 5.040 6.950 3.015 3.015 5.040 5 040 6.950 3 015 3 015 5 040 6 950 6 950 3 015 5 040 6 950

melts

of composition

3616ilO

36.3010.17

3609*12

36.08W.20

3599*

5

35.78%..09

3583-t

3

35.37M

3574*

5

35.12M.09

337s 3 360 3358 3366 3368 3355 3356 3365 3346 3348 3339 3326 3323

3365f

4

31.llM.06

3361i

3

31.00*

3336zt

5

30 5M.08

3037 3043 3032 3027 3027 3028 3020 3031 3033 3027 3035 3030 3032 3036 303 1 3023 3043 3019 3026 3038 3015 3025 3045 3029 3032 3014 3030

30383&

3

05

0.05

24.5810.04

3027&

2

24.38M.03

3032f

3

24.44M.03

3033f

2

24.43dzO.02

3028~t

4

24.34ti.06

303oi

5

24.34M.08

3025i

5

24.23*0

08

and

Compressibility of Ca-Al-silicate melts tigated, indicates that the structure of these melts responds differently to pressure as a function of the CaO and Na,O content, with the corollary that the geometry and strength of the inter-atomic bonding in the CaO-aluminosilicate melts is different to that in the Na20-aluminosilicate melts.

Table 3 Temperature

KS(T) = a - bxl0’

Ca 53 Ca36 Ca 09 Call39 Ca 38

There are a number of possible numerical treatments to compute the contributions of the individual oxide components to the observed compressibility of a melt discussed in the literature (see Rivers and Carmichael, 1987 ) . The most commonly used semi-empirical method is based upon the successful (e.g., Lange and Carmichael, 1987) description of the partial molar volumes ( v, ) of the oxide components of silicate melts as a function of the mole fractions (X, ), for each oxide component ‘3”; = i X,V,(T) I= I

n + c X,X,q,(T). r.,=t

dependence

of the adnbatx

bulk modulus (K,). molar volume (V)

velocity (v) and density (p) of the present CaO-.&OX-SIOZ

3.2. CompressibilityModel

V(T)

79

12 16 23 27

V(T)’ = a + bxl0’

a

b

1

GPa

GPa “C-’

1 O* m’ mol.’

27.5iO 2 36li-02 542M3 499M2 267MI v(T)==-

/

T (“C)

melts (errors are lo )

33*os 4 811.4 12.3il 6 123+15 16M5 bxlO’T

a

22 21 20 24 24

(“C)

I Voiume and densq

calculated

b IO4 nl’ InoI.’ T’

33 62 66 97 74

p(T)’ = a - bxl0”

b

T (“C)

I 49 1 70 2 39 1 35 I II T (“C)

a

b

from Cor~~nn~, and DWGWELL (1995)

(5)

The second summation in Eqn. 5 represents an excess volume term ( vG) as a function of the mole fraction of the oxide components i and j. This form of the excess term is chosen as it has been used successfully by Lange and Carmichael ( 1987) to describe the excess between NazO and TiOz. The derivative of Eqn. 5 with respect to pressure is related to the compressibility & = -dVIdP.V-’ of the melt (Rivers and Carmichael, 1987; Kress et al., 1988),

K;’ =pjs= -v

pressure dependences of the partial molar volumes

2 ( I) of the oxides SiOz, A1203, and CaO at a temperature “of 1500°C. The temperature dependence of these parameters at 1500°C was calculated simultaneously, and the results are shown in Table 5. This fitting procedure involves the combination of three independent sets of data. The data of Baidov and Kunin ( 1968) and Sokolov et al. ( 1971) are for the batch compositions of their melts and, therefore, a standard deviation of ?0.5% in molar volume is assumed. A comparison of the bulk moduli of identical melt compositions measured as a function of temperature by different authors (Na,Si,O, : Rivers and Carmichael (1987) and Webb (1991); CaSi03, Li2Si20s and K2Si205; Baidov and Kunin (1968) and Rivers and Carmichael ( 1987); CaTiSiOs and BaSi205; Rivers and Carmichael ( 1987) and Webb and Dingwell ( 1994); A1203Na2Si03 melt: The Kress et al. ( 1988) model and Webb and Courtial ( 1995); see also Table 6 of Rivers and Carmichael,

1 .-S(T) ap s + i X,X,L r..,=I

av(T) 3P

II

s ’

(6)

for the oxide components i and j. The bulk moduli of the present data, together with the literature data presented in Table 4, were used to calculate the

d cnw 23

3600

q

L z c g P

1

3500 Call

3400

39

3300 3200 Ca38.27

3100 3000 2900

31300

1340

Ca53

1380

1420

1460

TEh4PERATURE

1500

1540

12

1.580

(“C)

FIG. 4. The relaxed longitudinal velocity data as a function of temperature for the five CaO-A1201-Si02 compositions investigated.

melt

S. Webb and P. Counial

80

SiO,

mole fraction

28.9,

, I

CaO FIG. 5. Bulk moduti (GPa) for the CaO-A1201-Si02 system at 15WC as a function of mole fraction. The data are listed in Table 4. The SiQ datum is from Krol et al. (1986). The A&O3 datum is extrapolated from the high temperature data of Slagle and Nelson (1970).

1987) shows that a 2-10% difference in bulk modulus between different studies is to be expected. The quality of the multi-linear fit presented here is based upon an assumed standard deviation of +2% for the bulk moduli. The ideal (linear) model can be seen in Table 5 to provide a relatively good fit to the data; the R* value is close to 1.OOO, and the x t value is low. As the xz value is not less than 1.0, it is of interest to investigate the effect of adding an excess term of the form

presented in Eqn. 6. As can be seen from the F, test, the ideal model fit to the data is improved significantly by the addition of a positive excess term between SiOz and CaO (the F, term is large). The addition of an excess term between SiO, and Alz03 or CaO and AlzOl does not improve the fit to the data (the F, term is small for both of these fits). The xz value for the fit including the CaO-SiOz excess term is less than 1.0, indicating that the assumed standard deviation for the av, I&’

SiO,

FIG. 6. Bulk moduli (GPa) for the Na>O-Al@-Si02 system at 1500°C as a function of mole fraction. The data are listed in Table 4. The SiOz datum is from Krol et al. (1986). The AlzO, datum is extrapolated from the high temperature data of Slagle and Nelson (1970).

Compressibility Table 4 Composition

of the present melts, together

adiabatic bulk modulus

Ks calculated

SiOz and NazO-Alz03-Si02

r

15OOT

of Ca-Al-silicate

81

melts

with the molar volume

at 15OO”C, in addition

to literature

V, density

systems.

V

1 w6 In3 mol ’

GPa

Ca 53.12 Ca 36.16 Ca 09.23

24.57 24.06 24 09

-1.089 -0.834 -0.675

2.592

22.57 28 86 35 69

52.54

2.687 2 760

36 29 9 24

12 II 15 16 21 92

Ca 3X.27 Ca I1 39

26.26 26.15

-1078 -0 850

2 654 2.751

24.36 3148

37.80 11.59

26 46 37 13

BKl BK2 BK3 BK? BK5 BK6 BK7 BKX BK9 BKlO Sl S2 s3 s4 s5 Sb Sl

24 07 23 45 23 17 22 89 22.55 22.15 21 93 21.67 2142 2131 30.32 28 49 28.03 27 48 27 II 2121 24 45

-I 346 -1.222 -1 147 -I 073 -0 9x0 -0.855 -0.804 -0.747 -0.695 -0.677 -1419 -0 888 -0 972 -1 058 -1.174 -0 673 -0 665

2 453 2 507 2 533 2 5% 2 590 2.627 2 648 2.673 2 696 2.707 2 649 2.774 2 752 2 703 2 635 2 759 2 763

17 88 19 19 2tl 19 21 34 23 00 25 90 27 27 29 02 30 85 31.46 21 37 32 ox 28 84 25 98 23 09 ii 96 36 75

74 6X 65 62 58 53 50 46 42 40 32 5

RCl RC2

21.74 26 91

-0 813 -1.299

2.635 2 574

27 0 20 7

48 4 50 0

RC3 RC4 Kl K2 K3 K-l K5 KG Kl KS WC

27 X4 28.13 28 99 29 27 2961 29 22 28.88 2x.32 28.10 27.81 29.07

-2 078 -2 099 -I 720 -1 587 -I 367 -1 532 -1668 -1.868 -I 748 -2 046 -1 763

2 18 2.17 2 265 2.230 2 347 2 312 2 280 2 232 2.267 2.184 2 230

13 1 13 -l 16 X6 18 44 2166 1908 17 32 15.16 16 OX 13 59 16 19

6X 8 49.5 55 82 56.95 61 05 60 99 62 2-l 63 ‘)I 7X.18 65.34 45 50

BK

-

B~ioov theu

and KLNI~ temperature

(1968)

used to calculate -

wscosity

dependences

-

RC2

RIVERS and CARMICHAEL

of CUJR?lU.

velocltles

were calculated

which

were determined

the densities

from the parameters

\rere calculated

usmg the tabulated

were determmed

~1 the

range

and DIR~YCI.L

24 6

I1 88 15 X0 2 I x0 I6 XX I? 67 6 IO 8 05 9 IO

rela\ed

1450 . 196YC (1995)

111~won1c veloc~tuzr dependmg

for 00.AI:O,-SIO:

and the shc:i~

npon

melts i\cx

of these melts

of the melt. The parameters

used to calculate RCl

whxh

The parameters

the dewties

SOKULOV et al. (1971) temperature

velocmes

dependences

\~lSCoslty Of the mell

s

p. and

data for the CaO-AlzO:-

of COURTIAL

usmg the tabulated m the range

rcla\ed

1500 - 1927’C

and DINGWELL

ultrasonic dependmg

\cIoci~~cs

:md \~CII

upon the shear

(1995) for Ca0-A120G0z

melts were

of these melts.

(1987)

of COURTML

at 1563’C

and 1560°C,

and DINGWELL

respectively;

(1995).

recalculated

for the dewties

These data were not used in the calculation

calculated of the

partial molar compresslbilities. RC3

-

RIVERS and CARMICHAEL

(1987)

at 1500°C

K

-

KRESS et al. (1988); adiabatic moduli were calculated from the velocity model of KRESS et al Na>O-A120,-SiOz vstem and the density model presented in LA?XX and CARMICHAEL. (1990)

WC

-

WEBB

RC4

and

COURTIAL

(1995):

measured

adiabatic

values from the three combined datasets is realistic and that Eqn. 6 provides a good description of the data. The need for an excess term between Si02 and CaO points to the compress-

(1988)

for the

modulus

ibility of the CaO-AllOT-Si02 melts being a complex funcof the changes in structure and bonding in the melt controlled by CaO together with the contribution of the Ca-O-

tion

S. Webb Table 5 Partial mol?.r aV, / aP (adiabatic)

and P. Courtial

and thar temperature dependence

for the CaO-A120,-Si02

melt system at 1500°C

Errors are Io The

av, i dp OfKRESS et al (1988) and KREsS and CARI*IICHAEL (1991) are isothermal I5Oo"C

10 ” m” molP Pa’ ideal model Si02 A1203 cao xs Na,O

-1 61s 02 [-0 7~2 0] -1.70%003 [ I 753 O] -0 13% 02 [-4 713 O]

XS[Si02 -2.22+002 -1.41?001 -0 4Ofo 01 197io 06

CaO]

[-0 6s 01’ [ I7?10] c-4 6*, 01’ [-04t7 01’

xs[slo*

AhO,]

ideal modelb

xs[cao.Al,o3]

-166iOO2 [-I 1U 0] -I 83M 05 [ 0 726 0] -009io 03 [-4 3+3 O] 0 55M 19 [4+22]

-I 73HO3 -131M08 002+003 -1 23M22

[-12r3 O] [33*80] [-40~40] [-5ti5]

-I 9Offloz I79AOO8

-234mo4

R’ err2

0929 0479

x2 XS FZ

11975 96

0993 0045

132 data at temperaturer

’ temperature

0945 0376

11225 91 82

9400 76 33 9

dependence

xs[Na,o

Al*011 *

-2OZHO2 -253HO6 063foO5 IO l8H50 -I 74M 05 0999

in ?X, /aP).

from 1350 to 1600°C were tilted simultaneously

to an equatmn of the form

ofthe dV, /dP terms at 1500°C are Indicated [x xx IO-l9 m’ maI-’ Pa’ “C”]

b - KRESS et al (1988). Ks=Kfil+ayT) temperature

0935 0449

112 5 09 I206

assumed et’rors: m(K,) = 2%. o(V) = 0.5%, 0, = 0 02 (standard deviation

and T

IO” m’ mol.’ Pa-’

for K, - admbatic bulk modulus, Kr

isothermal bulk modulus, a

volume thermal expansion,

y. Gruneisen ratio

in K

’ ICRESS and CARMICHAEL (1991)

R’ is the square of the multiple wrrelation coefficient and it characterizes function; and approaches I for a good fit of the data to the function,

the fit ofthe data to the chosen

xt is less than I 0 for a good fit ofthe data to the chosen function,

x2Y =x21(N-n-l) for N - number of measurements n number of fit parameters

F = x*(n-1)-x2(n) ’ x*(n)/(N-n-1)

Ax2 xt

F, is large when the extra term added to the fitting equatmn IS statistically justdied, and small when the extra tern IS not stattsttcally justified (BEVDGTON, 1969)

Si bonding interaction; with the A1203 in the present compositions acting to increase the compressibility in a linear manner. The densities and molar volume of melts in the CaOAl,03-SiO, system have been reported recently by Courtial and Dingwell ( 1995 ). They fit the volume data in this system as a function of the mole fraction and partial molar volume of the oxide components (Eqn. 5) and found that an excess term between Si02 and CaO was required to fit the volume data in this composition range, with the suggestion that excess terms for SiO,-Al,O, and CaO-A1203 interactions were also possible. The fits of the volume and compressibility data for melts in the CaO-A1203-Si02 system with Eqns. 5 and 6 both require an excess term between Si02 and CaO of the opposite sign to the v, and aq l8P parameters. These fit parameters indicate that for these melts, the variations in volume and compressibility as a function of composition are linked

to the same structural features of the melts, and that the Ca0-Si bonding acts to reduce the volume of the melts and to reduce the compressibility of the melts. Comparing the partial molar @,ldPs calculated for the present system with those calculated by Kress et al. ( 1988) for the Na20-Al@-Si02 system, it can be seen that a positive i3v, l13P for the A&O3 component is required to fit the Na20-A1203-Si02 data while a negative value is required for the present CaO-Al,O1-Si02 system. Kress and Carmichael ( 1991) used the same equation as here to calculate the partial molar av, li?P for their complex Li,O-K20-Na20-CaOMgO-FeO-Fe20~-A1207-Ti02-Si02 melts. They required a positive value of c%,ltlP for the CaO component, and a negative value for the A&O3 component together with a positive excess term between A&O, and Na20. The observation of fit parameters of opposite sign obtained for CaO-rich and CaO-poor melt compositions suggests that different compres-

Compressibility

of Ca-Al-silicate

sion mechanisms are responsible for the compressibility of the melts in these two different compositional ranges. It is, therefore, not advisable to use partial molar av, /L?Pdata to extrapolate outside the composition ranges investigated, but the calculated partial molar av, /i?lPsappear to give a reasonable interpolation of the bulk moduli of melts within the composition range investigated (Kress et al., 1988; Kress and Carmichael, 199 1) 3.3. Melt Structure

and the Bulk Moduli

Bridgman ( 1923 ) calculated that there should be a simple relationship between the bulk modulus and the volume-peratom [Va,,, = (volume per mole)/( number of atoms per mole)] for ionic crystalline materials with the same structure: log,o K = Y log,, Vm,,, + K,

(7)

where y = -413. This relationship is known as the Law of Corresponding States (Herzberg, 1987). As shown by Anderson and Nafe ( 1965), this relationship does describe the systematic behaviour of isostructural ionic crystalline materials. They observed, however, that -4 5 y ZG -3 for isostructural covalent crystals. The value of the term y is found to range from - 1 for silicate melts in general (Rivers and Carmichael, 1987) to - 1.3 for alkali-silicate melts (Webb and Dingwell, 1994), to - 1.8 for liquid oxides (Herzberg, 1987). Rivers and Carmichael ( 1987) pointed out that alkaline-earth silicate melts do not follow their general Law of Corresponding States for silicate melts in which y = 1, there being a large change in bulk modulus in these melts for almost no change in the specific volume (volume-per-atom). The bulk moduli of alkaline-earth silicate melts plot as almost vertical trends on the log,, K/log,,, volume plot of Rivers and Carmichael ( 1987) (see Fig. 1). Figure 7 illustrates log,, K as a function of log,0 V,,,, at 15OO”C, for the CaO-Al,02-SiO, melts of the present study,

83

melts

together with the CaO-Al@-Si02 data of Sokolov et al. ( 1971) and the CaO-SiO, data of Baidov and Kunin ( 1968) (and the data of Rivers and Carmichael ( 1987), CaSiO, at 1563°C and CaAl,Si,O, at 1560°C). The CaO-bearing melts form essentially vertical trends as a function of volume-peratom in contrast to the empirical behaviour (for ionic materials) which is illustrated by the dotted line with a slope of -4/3. Melts with constant Ca0:A120X ratio (data connected by solid lines) form separate vertical trends in Fig. 7; that is, the volume-per-atom of the melt does not change appreciably as Si02 is replaced by zCa0 + xA120T for x/z = constant (compare Fig. 7 with Fig. 1). With increasing amounts of Si02 (along lines of constant Ca0:Al,07), the volume-peratom at first decreases and then increases while the bulk modulus decreases monotonically. This behaviour illustrated in Fig. 7 is in contrast to the behaviour of alkaline-earth poor silicate melts (e.g., Fig. 1) in which volume-per-atom increases while the bulk modulus decreases and it is, therefore, expected that anomalously large structural changes occur in these melts as the composition is varied within the CaOA1207-Si02 system. Figure 8 illustrates the KVY relationship for the present melts at all temperatures, together with melts at 1500°C with a constant CaO content (see Fig. 2 for an illustration of the melt compositions with constant CaO-content). A straight line with a slope of -2.3 can be fit to the constant CaOcontent data. This KVY trend, together with the variation in bulk modulus as a function of CaO-content seen in Fig. 5, points to the structure (bond lengths and strengths) and compressibility (and volume) being controlled by the CaO-content of the melt. In a further attempt to understand the relationship between structural geometry, volume and compressibility in the present calcium-aluminosilicate melts, the bulk modulus at 1500°C has been plotted as a function of the number of cations-per-oxygen (Fig. 9) and the number of aluminum-

15

1.4

1.3

loglo VOLW

PER ATOM

(cm3 )

melts of the FIG. 7. Law of Corresponding States (log,, K as a function of log,, V,,,,,,) for the CaO-A1201-Si02 present study, together with the CaO-AlgO?-Si02 data of Sokolov et al. (1971), and the CaO-SiOz data of Baidov and Kunin (1968) at 1500°C; and the data of Rivers and Carmichael (1987) (Casio, at 1563°C and CaA1,Si,OR at 1560°C).

The dotted

line is for y = -4/3;

data for constant

CaO:AlzOY

ratio compositions

are connected

by solid lines.

S. Webb and P. Courtial

84

0 89

091

logi

0 93

VOLUME

0 95

PER ATOM

(cm3 )

FIG. 8. log,, K as a function of log,, V,,,, for the for the CaO-AlTOT-Si02 melts of the present study at all temperatures investigated. The CaO-AIZOz-SiOz data from Table 4 at 1500°C which have constant CaO-contents (as shown in Fig. 2) are indicated by the hatched areas. Straight lines fitted to the constant CaO-content data require a slope of -2.3.

per-oxygen (Fig. 10). The bulk modulus data for the CaOA1203-Si02 system fall upon a single smooth curve when plotted as a function of the number of cations-peroxygen in the melt. The data for the binary systems CaO-SiO, and Li,O-Si02 of Baidov and Kunin (1968) also follow smooth curves. The behaviour of the ternary CaO-. A120,-Si02 melts points to the variation in compressibility being a function of the average number of cations which need to fit around an oxygen. As the A1203-bearing data fall on the same curve as the Al,O,-free data it is the CaO which controls the packing of the metal cation around the oxygens. The CaO content also controls the magnitude of the bulk modulus with the A&O3 content having a secondary effect on the bulk modulus of the melt. The bulk moduli of melts in the Na,OA1203-Si02 system do not follow a smooth variation as a

function of the average number of cations around an oxygen. The bulk moduli form a smooth trend, however, as a function of the number of aluminiums-per-oxygen (see Fig. 10). The CaO-Al@-Si02 data fall on separate curves of constant Ca0:A1201 ratio as a function of the number of aluminiumsper-oxygen. The complex behaviour of the CaO-A1203-Si02 melts and the Na20-Al@-Si02, melts discussed here shows that the melt structures have different internal degrees of structural freedom. Studies of the structure and thermodynamics of melts on the join CaA1204-Si02 and NaA102-Si02 indicate that the role of Al?+ in these melts is dependent upon the charge balancing cation. The structures of quenched glasses inferred from Raman spectroscopy consist of homogeneous distribution of interconnected Al- and Si-bearing tetrahedra for melts

I 1500°C

0

cao9.23

METAL

n

CaO-AI,03-S102

0

CaO-S10,

PER OXYGEN

FIG. 9. Bulk modulus at 1500°C as a function of the number of cations-per-oxygen SiOl (solid symbols, present data; hollow symbols, literature data) and Na>O-A120T-SiOZ Table 4.

for melts in the CaO-Al@systems. Data are listed in

Compressibility

present

n

melts

85

data

CaO-A1,03-SiO,

S!

Ilterahw

0K4

18 -

KS

16 14 12

of Ca-Al-silicate

I

~3 RC4

0

0

K2

l

K6 I 004

I

I 0.08

I

/ 0 12

,

, 0 16

,

o , 02

data

CaO-A&O,-SiO, Na?O-AI?O,-SiO, Na,O-SiQ_ , 0 24

I 0.28

Al per oxygen FIG. 10. Bulk modulus at 1500°C A1203-Si02 and NazO-AlzO,-SiOz Table 4.

as a function of the number of aluminiums-per-oxygen systems. Data of constant Ca:Al are joined by solid .

in the NaA102-Si02 system (Seifert et al., 1982; McMillan et al., 1982). It is suggested, however, that quenched aluminosilicate melts with divalent Ca’+ to charge-balance the Al” in tetrahedral coordination may display a clustering effect of Al-0-Si-O-Al groups controlled by the presence of Ca*+ (McMillan et al., 1982). (Seifert et al., 1982 interpret their spectra in terms of six membered SiO, rings, six membered A120i- rings, and four membered rings with Al/Si = 1). Although the interpretation of the Raman spectra is variable, the spectroscopic (Seifert et al., 1982; McMillan et al., 1982) and thermodynamic (Navrotsky et al., 1982) evidence agree with the interpretation that the Al-O-Al, Si-O-Al and Si-0-Si linkages are affected by the increasing cation size and ionicity in going from Ca to Na in the aluminosilicate melts. The degree of stabilization of Al-0-Si bonding being dependent upon the cation present with the effect being largest for small divalent cations (e.g., Ca*+) and smallest for large monovalent cations (e.g., Na’) (Navrotsky et al., 1982). Based on their thermodynamic data Navrotsky et al. ( 1982) concluded that at a given silica content, the distribution of aluminosilicate molecular groups could be expressed by the relation 2(=SiOAl) * =Si + -Si(OA1)2 where “-” denotes an Si-0-Si linkage. The right-hand side of this equilibrium is favoured by small, divalent cations, the left by large monovalent cations. This interpretation is consistent with the interpretation of the Raman data by McMillan et al. ( 1982). As the above equilibrium moves to the right, the site distribution in the melt becomes less homogeneous with clusters of =Si( OA1)2 sites around more electropositive cations, and =Si= regions with no associated cations. In view of the structural interpretation of the spectroscopic (McMillan et al., 1982; Seifert et al., 1982) and thermodynamic (Navrotsky et al., 1982) evidence, it is to be expected that the compressibility of alkaline-earth aluminosilicate melts is different to that of alkali-aluminosilicate melt. The outstanding feature of the comparison of bulk moduli data is, however, that the bulk moduli of both CaO-SiO* and also

for melts in the CaOlines. Data are listed in

CaO-AlZ03-SiOz melts (and X0-SiOL + AllO melts in general; for X=Mg, Ca, Sr, Ba) tend to be higher than those of X20-Si02 ? A&O3 melts (X=Li, Na, K, Rb, Cs), as seen here in Figs. 9 and 10. Figure 9 illustrates that the addition of A1207 to CaO-SiOz melts does not change the bulk modulus/ metal-per-cation trend of the data (see also Fig. 7). Therefore, in the compositions presented here, the influence of the Ca2+ ions controls the compressibility of CaO-rich silicate melts overwhelming the effect of the A13’ ions and the resulting clustering within the CaO-aluminosilicate melts, with there being a smooth decrease in modulus with decreasing A1203 content at a constant CaO-content (Fig. 9) and a smooth decrease in modulus with increasing SiO, content (Fig. 8). The sodium- and calcium-aluminosilicate melts, however, further show different bulk modulus behaviour as a function of the ratio of cations to oxygen in the melt. The CaO-silicate and CaO-aluminosilicate melts show a smooth increase in modulus with increasing number of metals per oxygens, while the Na,O-aluminosilicates show such a trend as a function of the number of aluminiums per oxygen (Figs. 9 and 10). This points to the Al” being the controlling factor in the variation of bulk modulus of the homogeneous Na20-Al&-Si02 melts, with the number of Al” per oxygen determining the magnitude of the bulk modulus. In the CaO-aluminosilicate melts with the clusters of Al-Si-Al bonding and the resulting regions of alumina-free =Si= bonding, the bulk modulus varies smoothly as a function of the averaged effect of the total number of cations per oxygen, with the CaO-content controlling the magnitude of the modulus. The effect of the addition of A&O3 on the bulk modulus of CaO-SiO, melts can be seen in Fig. 10 as a function of number of Al?‘-peroxygen. 4. CONCLUSION

The compressibility of CaO-SiO, and CaO-AlZ03-Si02 melts is lower than that of NaZO-Al,O?-SiO, and binary

86

S. Webb

alkali-silicate melts in general. This difference in compressibility between CaO-rich and Na*O-rich aluminosilicate melts needs to be taken into account in models of the compressibility of melts in the Earth’s crust and the density of magma chambers and the rising or sinking of magmas at pressure in the Earth’s crust. It appears that the mechanism of compression of CaO-A&O?-SiO, melts is different to that of Na,OA&O,-SiO, melts, with the compressibility of CaO-A&O?SiOa melts being a complex function of the structural geometry variations due to the presence of CaO, the Ca-0-Si bond interaction, and the packing of cations around the anions in a melt with clusters of preferred Al-Si-Al bonding, whereas

the compressibility

of the Na20-Al@-Si02

appears to be mainly a function of the Al-O a homogeneous melt.

melts

interactions

in

Acknowledgments-We ing and programming technical assistance.

thank Kurt Klasinski for electronic interfacas well as G. Gollner and H. Schulze for further Detlef KrauDe did the microprobe analyses.

Editorial

F. .I. Ryerson

handling:

REFERENCES Agee C. B. and Walker D. ( 1988) Static compression and olivine floatation in ultrabasic silicate liquid. J. Geophys. Res. 93, 34373449. Anderson 0. L. and Nafe J. E. ( 1965) The bulk modulus-volume relationship for oxide compounds and related geophysical problems. J. Geophys. Res. 70, 395 1-3963. Baidov V. V. and Kunin L. L. ( 1968) Speed of ultrasound and compressibility of molten silica. Sov. Phys. Dok. 13, 6465. Bevington P. R. ( 1969) Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill. Bridgman P. W. ( 1923) The compressibility of thirty metals as a function of pressure and temperature Proc. Amer. Acad. Arts Sci. 58, 165-242. Courtial P. and Dingwell D. B. ( 1995) Nonlinear composition dependence of molar volume of melts in the CaO-Al,O,-SiO, system. Geochim. Cosmochim. Acta 59,3685-3695. Dingwell D. B. and Brearley M. (1988) Melt densities in the CaO-FeO-Fe@-Si02 system and the composition dependence of the partial molar volume of ferric iron. Geochim. Cosmochim. Acta 52,2815-2825. Fujii T. and Kushiro I. ( 1977) Density, viscosity, and compressibility of basaltic liquid at high pressures. Carnegie Inst. Washington Yearb. 76,419-424. Her&erg C. T. (1987) Magma density at high pressure Part 1: The effect of composition on the elastic properties of silicate liquids. In Magmatic Processes: Physicochemical Principles (ed. B. 0. Mysen); Geochem. Sot. Spec. Publ. 1, 25-46. Herzfeld K. F. and Litovitz T. A. ( 1959) Absorption and Dispersion of Ultrasonic Waves. Acad. Press. Kaye G. W. C. and Laby T. H. ( 1986) Tables ofphysical and Chemical Constants. Longman. Kress V. C. and Carmichael I. S. E. ( 1991) The compressibility of silicate liquids containing Fe,Oi and the effect of composition, temperature, oxygen fugacity and pressure on their redox states. Contrib. Mineral. Petrol. 108, 82-92.

and P. Courtial Kress V. C., Williams Q., and Carmichael I. S. E. (1988) Ultrasonic investigation of melts in the system Na,O--Al@-SiO?. Geochim. Cosmochim. Acta 52,283-293. Krol D. M., Lyons K. B., Brawer S. A., and Kurkjian C. R. ( 1986) High-temperature light scattering and the glass transition in vitreous silica. Phys. Rev. B 33, 4196-4202. Lange R. L. and Carmichael I. S. E. (1987) Densities of NaZOKzO-CaO-MgC-F~-F~O,-Al~O~-TiO~-SiO~ liquids: new measurements and derived partial molar properties. Geochim. Cosmochim. Acta 51,293 l-2946. Lange R. L. and Carmichael I. S. E. ( 1990) Thermodynamic properties of silicate liquids with emphasis on density, thermal expansion and compressibility. Rev. Mineral. 24, 25-64. Levin E. M., Robbins C. R., and McMurdie H. F. (1964) Phase Diagrams for Ceramists, 2nd ed. Amer. Ceram. Sot. Manghnani M. H., Rai C. S., Katahara K. W., and Olhoeft G. R. ( 1981) Ultrasonic velocity and attenuation in basalt melts. In Anelastic@ in the Earth (ed. F. D. Stacey et al.); Geodynam. Ser. 4, 118-122. McMillan P., Piriou B., and Navrotsky A. ( 1982) A Raman spectroscopic study of glasses along the joins silica-calcium aluminate, silica-sodium aluminate, and silica-potassium aluminate. Geochim. Cosmochim. Acta 46,2021-2037. Miller G. H., Stolper E. M., and Ahrens T. J. (1991) The equation of state of a molten komatiite, I : Shock wave compression to 36 GPa. J. Geophys. Res. 96, 11831- 11848. Navrotsky A., Peraudeau Cl., McMillan P., and Coutures J-P. ( 1982) A thermochemical study of glasses and crystals along the joins silica-calcium aluminate and silica-sodium aluminate. Geochim. Cosmochim. Acta 44,2039-2047. Rigden S. M., Ahrens T. J., and Stolper E. M. ( 1984) Densities of liquid silicates at high pressures, Science 226, 107 1- 1074. Rivers M. L. ( 1985) Ultrasonic studies of silicate melts. PhD Thesis Univ. California. Rivers M. L. and Carmichael I. S. E. (1987) Ultrasonic studies of silicate melts. J. Geophys. Res. 92, 9247-9270. Sato H. and Manghnani M. H. ( 1985) Ultrasonic measurements of V,, and Q,,: Relaxation spectrum of complex modulus of basalt melts. Phys. Earth Planet. Int. 41, 18-33. Secco R. A., Manghnani M. H., and Liu T. C. (1991) Velocities and compressibilities of komatiitic melts. Geophys. Res. L&t. 18, 1397-1400. Seifert F., Mysen B. O., and Virgo D. (1982) Three-dimensional network of quenched melts (glass) in the systems SiOz-NaAIOz, SiO,-CaAl?O, and SiO>-MgAl,04, Amer. Mineral. 67, 696717. Slagle 0. D. and Nelson R. P. ( 1970) Adiabatic compressibility of molten alumina. J. Amer. Ceram. Sot. 53,637-638. Sokolov L. N., Baidov V. V., Kunin K. K., and Dymov V. V. ( 1971) Surface and volume characteristics of melted slags of the CaO-AlZ03-SiOZ systems. Sb. Tr. Tsentr. Naocho Issled Inst. Chern. Metall. 75,53-61. Stein D. J., Stebbins J. F., and Carmichael I. S. E. (1986) Density of molten sodium aluminosilicates, J. Amer. Ceram. Sot. 69, 396399. Webb S. L. ( 1991) Shear and volume relaxation in NazSi20s. Amer. Mineral. 76, 1449- 1454. Webb S L., and Courtial P. ( 1995) Compressibility of P10s-A120~-Na2Si0; melts. Phys. Chem. Mineral. (submitted). Webb S. L. and Dingwell D. B. ( 1994) Compressibility of titanosilicate melts. Contrib. Mineral. Petrol. 118, 157- 168.