- Email: [email protected]
Heat of fusion of basaltic magma
Earth and Planetary Science Letters, 73 (1985) 407-414
407
Elsevier Science Publishers B.V., A m s t e r d a m - Printed in The Netherlands
[61
Heat of fusion of basaltic magma Hiroyuki Fukuyama * Geological Institute, University of Tokyo, Bunkyo- ku, Tokyo 113 (Japan)
Received June 27, 1984 Revised version received January 23, 1985
The heat of fusion of haplobasaltic liquids in the systems forsterite-diopside-SiO 2 and basaltic liquids in natural peridotite has been determined by high-temperature solution calorimetry. For liquids in the systems diopside-anorthite and forsterite-diopside-anorthite the heat of fusion was calculated from literature data. The heats of fusion for eutectic liquids in the system anorthite-diopside and forsterite-diopside-anorthite, for haplobasaltic liquid in equilibrium with olivine and two pyroxenes in the system forsterite-diopside-SiO 2 and for basaltic melts from natural peridotite parent, are 130.6, 121.1,157.4 and 161.5 cal/g, respectively. The heat of mixing in the liquids contributes up to about 5% of this value. The magnitude of this contribution increases when the structure of the endmember minerals is significantly different (e.g., forsterite and anorthite or quartz). The pressure effect on the heat of fusion results in a 10-20% increase in the pressure range 10-30 kbar compared with the 1-atm values. This increase results from the larger compressibility of silicate liquids compared with that of the coexisting minerals in both model and natural compositions.
I. Introduction
Both dynamic and static processes are important in the generation of magma in the upper mantle and the crust of the earth. One process of particular importance is diapiric movement of material through the mantle. The data necessary to deal quantitatively with this process and related melting phenomena frequently are not available. Rheological properties, thermal conductivity and heat of fusion of mantle materials, especially at high pressure, are not well known, for example. The heat of fusion of basaltic magma has been simulated by the heat of fusion of common rockforming minerals such as diopside [1-3]. Its value has been suggested to be approximately 100 c a l / g by Bowen [1,3] and 85.4 c a l / g by Yoder [2]. In a system with more than one component, the heat of fusion of a eutectic composition can be estimated * Deceased. 0012-821X/85/$03.30
© 1985 Elsevier Science Publishers B.V.
from the heats of fusion of the endmember phases, the heat capacities of the solids and liquid and the heat of mixing of the liquid. The heat of mixing of the liquid, which is required for accurate calculation of the heat of fusion of a eutectic composition is, however, rarely known for petrologically important compositions. The heat of fusion of a congruently-melting phase (one-component system) equals the enthalpy difference between the crystalline phase and its melt at the melting temperature. Similarly, for eutectic compositions in systems with more than one component, the heat of fusion is the enthalpy difference between the crystal mixture and its melt at the eutectic temperature. This enthalpy difference commonly cannot be measured directly at temperatures as high as that of the eutectic of most rock-forming minerals. Its value can be obtained, however, by measuring first the enthalpy difference between crystals and glass of the same composition. For calorimetric measurements where
408 the calorimetry temperature is higher than that of the glass transition temperature, the heat of fusion of the crystalline mixture at its melting temperature is:
AH=AHS°'+ fTe(CZp-Cp)dT, T~ch
(1)
where A H is the heat of fusion o f t h e crystalline mixture, A H ~°l is the difference of the heat of solution of the crystalline mixture and supercooled liquid obtained by solution calorimetry, Cpl and Cp are the heat capacities of the supercooled liquid and crystalline mixture, respectively, and T~ch and Tf are the temperatures of the solution calorimetric measurements and the melting temperature of the mixture, respectively. The enthalpy of the liquid decreases continuously with decreasing temperature even if crystals do not precipitate (supercooled liquid), and the thermodynamic properties of this liquid can be expressed with continuous functions extending from the liquid itself. At the glass transition temperature ( Tg) the slope of the enthalpy curve changes to follow that of the glass. If the calorimeter temperature is less than that of Tg, the following expression can be used to obtain the heat of fusion of the crystalline mixture:
2. Experimental techniques 2.1. Starting materials
The system forsterite-diopside-SiO 2. Liquidus phase equilibria in the system forsterite-diopside-SiO 2 have been studied extensively both at 1 atm and at high pressure [3-5J. The composition of the reaction point A (Fo20Di68(SiO2)12 , by weight) at 1 atm from Kushiro and Schairer [5] is adopted as a haplobasaltic liquid coexisting with olivine, clinopyroxene and a Ca-poor pyroxene. The glass of this composition was made from a mixture of synthetic forsterite, diopside and natural quartz by melting at 1450°C for 4 hours. The mixing and melting procedure was repeated twice. Natural peridotite. The natural peridotite composition was a spinel lherzolite from British Columbia, Canada (BC-5000). Its bulk composition, the composition of its constituent mineral (except spinel) and the composition of the peridotite reconstituted from the modal abundance of olivine, orthopyroxene and clinopyroxene ( 5 8 : 2 2 : 2 0 ) are shown in Table 1. The effect of small amounts of an aluminous (55-58 wt.% A1203, chromium-rich (11-12 wt.% Cr203) spinel (Irvine, personal com-
AH--- A H ~°' + fT~c_~dT ~, + f T ~ c ' d T - f T ' 7:,oh JT~ ~ Jr.ch (1') where Cpg is the heat capacity of the glass at T~, the glass transition temperature. Solution calorimetry can be carried out either at lower temperatures with H F as solvent or at higher temperatures with an oxide flux as solvent. Because of the uncertainties in the values of Cp, Cg and CpI in equations (1) and (1'), the heat of fusion can be estimated with greater accuracy from high-temperature solution calorimetry. This paper describes a method to determine the heat of fusion of haplobasaltic and basaltic liquids in the system forsterite-diopside-SiO 2 and in natural peridotite. The heats of fusion of haplobasaltic liquids in the systems diopside-anorthite and forsterite-diopside-anorthite have been calculated from literature data for comparison.
TABLE 1 The composition of BC-5000 lherzolite and constituent minerals Sample
1
1'
2
3
4
SiO2 TiO2 A1203 FeO MnO MgO CaO Na20 K20 Total
45.80 0.17 1.34 1.78 0.15
45.73 0.14 2.09 7.27 0.14 38.66 4.32 0.23 0.00 98.58
39.80 0.00 0.00 9.36 0.16
52.33 0.55 5.73 2.78 0.06
55.33 0.15 4.27 5.85 0.17 32.19 0.90 0.05 0.00 98.91
38.02 4.30 0.24 0.02 98.28
48.86
16.20
0.07 0.00 0.00 98.25
20.38 1.11 0.00 ~
l=spinel lherzolite BC-5000, analyst: H. Haramura; 1'= chemical composition of BC-5000 reconstituted from composition and model proportions of the constituent minerals; 2 = olivine in BC-5000; 3 = clinopyroxene in BC-5000; 4 = orthopyroxene in BC-5000.
409 TABLE 2 Bulk compositions, temperatures of fusion (Tf) and heat of fusion (Hf) of simulated basaltic liquids Sample SiO2 TiO2 AI203 Fe203 MnO MgO CaO Na 2° K 20 Total Tf (°C) Hf (cal/g)
1
2 54.14 0.53 11.19 10.54 0.19 9.69 14.24 0.49 0.01 98.29
1260 161.5
3 58.28 0.00 15.95 0.00 0.00 10.52 23.40 0.00 0.00 100.00
1274 130.6
4 49.18 0.00 15.94 0.00 0.00 13.42 21.46 0.00 0.00 100.00
1270 121.1
58.27 0.00 0.00 0.00 0.00 24.12 17.61 0.00 0.00 100.00
fled argon gas. A r g o n was i n t r o d u c e d into the silica glass tube in the c a l o r i m e t e r after passing it over t i t a n i u m p o w d e r h e a t e d at a p p r o x i m a t e l y 800°C. Both the s a m p l e c o n t a i n e r a n d the crucible c o n t a i n i n g the lead b o r a t e solvent were p l a c e d at the b o t t o m of the glass tube. The e x p e r i m e n t s were c o n d u c t e d b y s u b m e r g i n g the s a m p l e container into the solvent. N o m i n a l run d u r a t i o n was two hours. This time p e r i o d includes b o t h the time r e q u i r e d for thermal e q u i l i b r a t i o n a n d the a c t u a l solution experiment. N o o x i d a t i o n of ferrous iron to ferric i r o n of the n a t u r a l F e - b e a r i n g m a t e r i a l s was o b s e r v e d within this time period.
1390 157.4
1 = glass of BC-5000, partially melted at 1260°C and 1 atm; 2 = eutectic composition in the system diopside-anorthite; 3 = eutectic composition in the system diopside-anorthite-forsterite; 4 = eutectic-like composition in the system diopsideforsterite-SiO 2.
m u n i c a t i o n , 1984) was ignored in the c a l o r i m e t r i c e x p e r i m e n t s a n d s u b s e q u e n t calculation. Solidus t e m p e r a t u r e s a n d degree of melting as a f u n c t i o n of t e m p e r a t u r e o f this spinel lherzolite are a v a i l a b l e [6-8]. A t 1 atm, the solidus t e m p e r a t u r e is n e a r 1200°C with 15% melt f o r m e d at 1260°C. T h e b u l k c o m p o s i t i o n of this melt is given in T a b l e 2. T h e starting m a t e r i a l s for the c a l o r i m e t r i c m e a s u r e m e n t s of the liquid c o m p o s i t i o n was prep a r e d b y first a n n e a l i n g a p o w d e r e d glass at 1200°C at 2 k b a r for 2 hours in an internallyheated, g a s - m e d i a a p p a r a t u s . T h e resulting glass was d i v i d e d into two parts, each of which was h e a t e d overnight at l l 0 0 ° C a n d 1260°C, respectively, in a 1-atm, vertical quench furnace with the o x y g e n fugacity c o n t r o l l e d n e a r 10 - t ° . These m a t e r i a l s were then crushed a n d used for the calorimetric measurements.
2.2. Calorimetry T h e c a l o r i m e t e r was a C a l v e t - t y p e microc a l o r i m e t e r o p e r a t e d at 750°C [9] with 2 P b O . B20 3 as solvent. I n o r d e r to p r e v e n t o x i d a t i o n of the i r o n - b e a r i n g s a m p l e s ( n a t u r a l peridotite), the c a l o r i m e t e r a t m o s p h e r e was c o n t r o l l e d with puri-
3. Results
3.1. The system forsterite-diopside-SiO 2 T h e heat of solution ( T a b l e 3) of glass of c o m p o s i t i o n F020 Di68(SiO2)12 (reaction p o i n t A from K u s h i r o a n d Schairer [5]) is very n e a r 0 k c a l / m o l a n d the variations between i n d i v i d u a l measurem e n t s shown in T a b l e 3 result from the effect of stirring. The e n t h a l p y difference between the glass a n d the crystal m i x t u r e forsterite + d i o p s i d e + e n s t a t i t e (although at the t e m p e r a t u r e of the reaction point, n e a r 1400°C, enstatite is not stable, this difference is neglected) was calculated from p u b lished heat of solution d a t a for each m i n e r a l (for-
TABLE 3 Enthalpy of solution at 750°C in 2PbO. B203 System
Sample (mg)
//soI (cal/g)
Average
Fo-Di-SiO2 glass
31.30 42.36 50.84 32.18
- 3.49 - 2.82 - 0.70 2.62
- 1.10
57.78 40.13 58.71 41.55
80.34 72.78 68.50 79.31
75.23
38.16 40.75 38.99 36.72 34.12
59.32 52.74 67.14 60.82 58.14
59.63
BC-5000 sintered (crystalline) BC-5000 partially melted
410 TABLE 4 P a r a m e t e r s u s e d in the c a l c u l a t i o n of Cp o f m i n e r a l s
Cp=a+bxlO-3T+c×lO 6 T 2 + d x l O 2 / T + e x l 0 5 T 2
Mineral
Forsterite Fayalite Diopside Enstatite Anorthite Quartz
a
b
c
34.49 36.51 52.87 49.14 64.42 17.39
9.26 9.36 7.84 3.06 13.70 0.31
-1.32
Reference a
d
-
-7.85 - 6.70 - 15.74 2.85 - 16.89 - 9.90
5.49
1 2 2 3 2 1
" R e f e r e n c e s : 1 = S p e n c e r [32]; 2 = Kelly [33]; 3 = R o b i e et al. [34].
sterite [10], 114.5 cal/g (16.11 kcal/mol); diopside [11], 94.5 cal/g (20./78 kcal/mol); and enstatite [10]; 87.5 cal/g (8.78 kcal/mol)). This enthalpy difference at 750°C is corrected to the melting temperature with equation (1). In using equation (1), it was assumed that the temperature of the calorimeter (750°C) is higher than the glass transition temperature for the following reasons. For a
range of relevant mineral compositions [12,13] and for glasses of rhyolite to basalt composition [13-16], the glass transition temperatures at 1 atm range from about 800 ° to about 630°C. The Tg for basaltic compositions ranges between 630 ° and 730°C. Composition A is a model basalt composition, and the Tg most likely is less than 750°C. The C; was calculated from the data and the
I
H~H2, 8 (kcal/mol) 100 / 9O
/ m
/ /
80
_
Hf 4
S
70
60
/
5O
40 1200 I
I
I
I
800
[
I
1400 I
I
1000
I
(°K)
1600
1
I
I
1200
I
J
I
1400
(°C)
Temperature Fig. 1. T e m p e r a t u r e - e n t h a l p y d i a g r a m for c o m p o s i t i o n A in the s y s t e m f o r s t e r i t e - d i o p s i d e - S i O 2 (see text f o r details).
411 expression shown in Table 4. Because heat capacities for clinoenstatite are not known, the values for enstatite were used. The Cp1 was calculated by linear summation of partial molar heat capacity data of oxide components from Carmichael et al. [17]. The resulting enthalpy-temperature diagram for the model basalt composition (reaction point A in the system forsterite-diopside-SiO2 [5]) is shown in Fig. 1 where it is assumed that mutual solubilities of diopside in enstatite and enstatite in diopside do not affect the heat contents of the mixture significantly.
3.2. Natural peridotite Calorimetric measurements were carried out with samples sintered at 1000°C (crystalline) and heated at 1260°C and quenched (85% crystals + 15% glass) with the results shown in Table 3. Because of the heterogeneous distribution of the different phases (including glass) in the solution samples, the individual heat of solution data points show larger variations than those obtained for glass in the system forsterite-diopside-SiO2. The difference of heat of solution between fully crystalline and partially molten peridotite is 16.1 cal/g at 1260°C. The measured heat of fusion of the liquid with the bulk composition corresponding to that of the liquid at 15% melting of BC-5000 is 161.5 cal/g. In calculating the heat of fusion at 1260°C, equation (1) was used with the following assumptions. First, the glass transition temperature of this basaltic composition is lower than the 750°C of the solution calorimeter. Second, the proportions of olivine, clinopyroxene and orthopyroxene in the residual material do not change during partial melting. This latter assumption is not strictly true, but may not affect the results significantly for this relatively low degree of melting.
3.3. The systems diopside-anorthite and forsterite-diopside-anorthite The heats of fusion of basaltic liquids in the systems diopside-anorthite and forsterite-diopside-anorthite have been calculated from published data. The system diopside-anorthite is not, strictly speaking, binary [18]. For the model calcu-
lations carried oUt here, this non-binary nature does not pose a serious problem because the mutual solubilities of the two endmember phases in each other is small [18]. The liquidus phase diagram of this system was first determined by Bowen [19], who also calculated the heat of mixing of liquids on the join [3]. The heats of fusion reported by Bowen were 23.39 kcal/mol (108.0 cal/g) for diopside and 29.0 kcal/mol (104.2 cal/g) for anorthite. For the eutectic liquid composition (near Di65An35, by weight, [18]), the heat of mixing of the liquid is near -0.7 kcal/mol ( - 3 cal/g). The system diopside-anorthite was reinvestigated by Weill et al. [11], who found the heat of fusion of diopside to be 34.085 kcal/mol (157.4 cal/g) at 1391°C, a value also in accord with other estimates [13,20]. The reported heat of fusion values for anorthite range from 19 to 40 kcal/mol depending on the method used. It has been suggested [11] that this range results from lack of precise heat capacity data for the liquid (C~) at high temperatures. The value used in the present calculation is 32.4 kcal/mol (116.4 cal/g) [21]. The heat of mixing of the eutectic liquid composition is -1.5 kcal~/mol [11]. For the eutectic composition, the heat of fusion at the eutectic temperature (1360°C) is 31.22 kcal/mol (130.6 cal/g). The estimate of Yoder [2], based on the older thermodynamic data [1] was 20 kcal/mol (83.7 cal/g), or approximately 2/3 of the value of the present study. Heat of fusion data in the system forsterite-diopside-anorthite were also calculated by Yoder [2]. The difference between the heat of solution of the crystal mixture and a glass of the eutectic composition (Fo8,Di46 An 46, by weight [5]) is 19.0 kcal/mol (79.6 cal/g) at 750°C. By substituting the calculated C~ and C~ into equation (1), the heat of fusion of the eutectic mixture at the eutectic temperature (1270°C) is 28.9 kcal/mol (121.1 cal/g). 4. Discussion
4.1. Effect of bulk composition The heat for fusion of basaltic and haplobasaltic liquids determined and calculated here is
412 shown in Table 2. The heat of fusion of anorthitebearing model systems is always smaller than in those systems that do not contain anorthite component. This difference is due to the smaller heat of fusion of anorthite than of any of the other mineral components. For partial melts in the natural peridotite system the liquid has about 30% normative plagioclase, but its heat of fusion is the largest of those in Table 2. The feldspar component in natural partial melts from the upper mantle is derived mainly from aluminous pyroxene in the starting material. Although the effect of jadeite and tschermak's molecule solution in pyroxenes on their heats of fusion is not known, it is suggested that the explanation for the larger heat of fusion in the natural peridotite system may be because of the aluminum-bearing components in the pyroxenes. The least well known parameter in determining the heat of fusion of mineral mixtures is the heat of mixing of the liquid. In general, this contribution to the enthalpy budget is larger in systems containing structurally different phases [22]. This tendency most likely results from the observation [23] that important structural features in crystalline materials are retained in the silicate melts. Such effects have, however, only been determined accurately in the systems diopside-anorthite and diopside-albite [11], where the heat of mixing is about - 1 . 5 kcal/mol ( - 6 cal/g) at the eutectic compositions. Thus, the mixing term contributes about 5% to the heat of fusion calculated from endmembers in appropriate stoichiometric proportions.
4.2. Effect of pressure The heat of fusion of silicate materials is significantly pressure dependent [2,24]. This pressuredependence can be described with the equation:
d A H / d P = mVm(] - mo/Z),
(2)
where AVm is the volume change of fusion, Aa is the difference of thermal expansion between solid and liquid phases and T is the absolute temperature. Based on volume data at 1 atm pressure, Yoder [2] estimated a 35 c a l / g increase in heat of fusion between 1 atm and 30 kbar for basaltic
liquids. The densities of basaltic liquids at high pressure [25] increase more rapidly than those of the crystals so that AVm decreases with increasing pressure (see also [26]). With this correction for AVm, the pressure-dependent increase of heat of fusion of peridotite to produce basaltic liquid is between 19 and 27 cal/g. In summary, the heat of fusion of basaltic magma increases by at least 15% in the pressure range from near surface conditions through the pressure range of partial melting in the upper mantle.
4.3. Petrological implications Detailed studies of the melting behavior of anhydrous four-phase peridotite have shown [27] that the principal features of the melting behavior of natural peridotite are quite similar to those observed in the four-component model system CaO-MgO-A1203-SiO 2. For natural peridotite, 20-30% partial melt of basaltic composition may be obtained under isobarically near invariant conditions. The heat required for this much melting is, however, sufficient to heat up a source rock, provided that it does not melt, by about 70°C at the same pressure and temperature conditions [28]. Relationships between degree of melting, compositions of melt, temperature, pressure and enthalpy requirements for upper mantle peridotite are shown in Fig. 2. The degree of melting is shown schematically with data from [6-9,27,29]. The solidus temperatures and bulk compositions of the partial melts are from Takahashi and Kushiro [30]. Note the presence of cusps in the melting curve, a feature also found in the simple model system CaO-MgO-A1203-SIO 2 [31]. The data in Fig. 2 may be used to illustrate relationships between degree of melting and depth in an adiabatically ascending diapir or plume in the upper mantle. Depending on the heat content of the ascending diapir (see, for example the isoenthalpic lines, H1-H6; Fig. 2), the material in an ascending diapir will commence melting at different depth. This heat content may be a function of the depth in the mantle from which the diapir initially begun its ascent. Inasmuch as the bulk composition of partial melts depends on the depth
413 T .c,
r4oc-
/~i!;:.:~i~/~
~
Y
_,-:!,-,-
...
-1
H&H5 ] H3H3
1300 ......
~ ' " . . . . "'-'-':~-~'f.~......:~:.' " ~'- - '_ ~.-" ._: "--."-.iS ; - ~ ~ , ~ , /
15 . . . . .
-
HI H2 ----H1 - -
- -
"
:" ": :,~.'.'5".'-~" . ' ~ Sp-therz0hte 1200 ~
II00
'
0
f
'
~
'
'
[
5
/
'
....
J
'
I
I0
,
,
,
15 . . . . -5 ....
,
J
15'/, degree of 5 °/o rnettlng
. . . .
15
1
20
. . . .
1
25
Pressure(kb)
Fig. 2. Temperature-pressurerelationships of the solidus temperature, degree of melting and the composition of partial melts of a lherzolite composition [30]. Lines H] - H6 are isoenthalpic contour lines. Dashed and dotted areas correspond to olivine tholeiitic and alkali basaltic magmas. (Composition data from Takahashi and Kushiro [30].)
of melting [2,30,31], the source depth of the diapir itself, though deeper than that of the partial melting, may govern the composition of the initial melt in the diapir. For example, one may speculate that partial melts of alkali basaltic composition may require the temperature (and, therefore, heat content) of the diapir itself at its point of origin to be greater than that required to form olivine tholeiite. As a result of the greater heat content, initial melting will commence at greater depth in the mantle where the initial melt may be alkali basalt. Melting at shallower depth (requiring smaller heat content of the diapir) may yield olivine tholeiite melt composition. It is also noted from the data in Fig. 2 that the isoenthalpic curves and the lines depicting the pressure-temperature conditions of constant degree of melting become nearly parallel at pressures less than about 10 kbar. Thus, even though the degree of melting in an ascending diapir may increase as the diapir rises through the mantle to about 30 km depth, additional rise does not affect this degree of melting further. Thus, at depth of 30 km or less, the bulk composition of the partial melt in the diapir is strictly a function of
pressure-dependent phase equilibria, whereas at greater depth the bulk composition of partial melts depends on both the pressure-dependent phase equilibria and the degree of melting controlled by the relationship of the isoenthalpic lines to the curves of equal degree of melting.
Acknowledgements This work was carried out during a visit to the Arizona State University and was partially supported by U.S. Department of Energy (Contract DEA0280e10765 to Dr. A. Navrotsky). The author thanks Dr. A. Navrotsky for encouragement and Drs. I. Kushiro and H.S. Yoder, Jr. for reviewing the manuscript.
References 1 N.L. Bowen, The Evolution of the Igneous Rocks, 333 pp., Princeton University Press, Princeton, N.J., 1928. 2 H.S. Yoder, Generation of Basaltic Magma, 246 pp., National Academy of Sciences, Washington, D.C., 1976.
414 3 N.L. Bowen, The melting phenomena of plagioclase feldspars, Am. J. Sci., 4th Ser. 35, 577-599, 1913. 4 J.J. Schairer and H.S. Yoder, The system diopsideenstatite-silica, Carnegie lnst. Washington Yearb. 61, 75-82, 1962. 5 I. Kushiro and J.F. Schairer, New data on the system diopside-forsterite-sihca,Carnegie Inst. Washington Yearb. 62, 95-103, 1963. 6 T. Murase, I. Kushiro and T. Fujii, Electrical conductivity of partially molten peridotite, Carnegie lnst. Washington Yearb. Book, 76, 416-419, 1976. 7 T. Murase and I. Kushiro, Compressional wave velocity in partially molten peridotite at high pressures, Carnegie Inst. Washington Yearb. 78, 559-562, 1979. 8 T. Murase and H. Fukuyama, Shear wave velocity in partially molten peridotite at high pressures, Carnegie Inst. Washington Yearb. 79, 307-310, 1980. 9 A. Navrotsky, Progress and new directions in high-temperature calorimetry, Phys. Chem. Miner. 2, 89-104, 1977. 10 T.V. Charlu, R.C. Newton and O.J. Kleppa, Enthalpies of formation at 970°C of compounds in the system MgOA1203-SiO2 from high-temperature solution calorimetry, Geochim. Cosmochim. Acta 39, 1487-1497, 1975. 11 D.F. Weill, R. Hon and A. Navrotsky, The igneous system CaMgSi2Or-CaA12 Si 2Os-NaA1Si308: variations on a classic theme by Bowen, in: Physics of Magmatic Processes, R.B. Hargraves, ed., Chapter 2 Princeton University Press, Princeton, N.J., 1980. 12 J. Arndt and F. Haberle, Thermal expansion and glass transition temperature of synthetic glasses of plagioclase-like compositions, Contrib. Mineral. Petrol. 39, 175-183, 1973. 13 P.J. Vergano, D.C. Hill and D.R. Uhlmann, Thermal expansion of feldspar glasses, J. Am. Ceram. Soc. 50, 59-60, 1967. 14 C.M. Scarfe, Viscosity of some basaltic glasses at one atmosphere, Can. Mineral. 15, 190-194, 1977. 15 C.R. Bacon, High-temperature heat content and heat capacity of silicate glasses: experimental determination and a model calculation, Am. J. Sci. 277, 109-135, 1977. 16 M.P. Ryan and C.G. Sammis, The glass transition in basalt, J. Geophys. Res. 86, 9591-9535, 1981. 17 I.S.E. Carmichael, J. Nichols, E.J. Spera, B.J. Wood and S.A. Nelson, High-temperature properties of silicate liquid: application to the equilibration and ascent of basic magma, philos. Trans. R. Soc. London, Ser. A 286, 373-431, 1977. 18 E.F. Osborn, The system CaSiO3-diopside-anorthite, Am. J. Sci. 240, 751-788, 1942. 19 N.L. Bowen, The crystallization of haplobasaltic haplodioritic and related magmas, Am. J. Sci., 4th Ser. 40, 161-185, 1915.
20 A. Ferrier, Mesure de l'enthalpie du diopside synthetique entre 298 and 1885 K, C.R. Acad. Sci. Paris, Ser. C 267, 101-103, 1968. 21 D.F. Weill, J.F. Stebbins, R. Hon and I.S.E. Carmichael, The enthalpy of fusion of anorthite, Contrib. Mineral. Petrol. 74, 95-102, 1980. 22 P. Richet, Viscosity and configurational entropy of silicate melts, Geochim. Cosmochim. Acta 48, 471-485. 23 B.O. Mysen, D. Virgo and F.A. Seifert, The structure of silicate melts: implications for chemical and physical properties of natural magma, Rev. Geophys. 20, 353-383, 1982. 24 S. Maaloe, The significance of the melting interval of basaltic magmas at various pressures, Geol. Mag. 110, 103-112, 1973. 25 T. Fujii and I. Kushiro, Density, viscosity and compressibility of basaltic liquid at high pressures, Carnegie Inst. Washington Yearb. 76, 419-424, 1977. 26 E. Stolper, D. Walker, B.H. Hager and J.F. Hays, Melt segregation from partially molten source region: the importance of melt density and source region size, J. Geophys. Res. 86, 6261-6271, 1981. 27 B.O. Mysen and I. Kushiro, Compositional variations of coexisting phases with degree of melting of peridotite in the upper mantle, Am. Mineral. 62, 843-865, 1977. 28 R.G. Cawthorn, Degree of melting in mantle diapirs and the origin of ultrabasic liquids, Earth Planet. Sci. Lett. 27, 113-120, 1975. 29 A.J. Jaques and D.H. Green, Determination of liquid compositions in high pressure melting of peridotite, Am. Mineral. 64, 1312-1321, 1979. 30 E. Takahashi and 1. Kushiro, Melting of a dry peridotite at high pressures and basalt genesis, Am. Mineral. 68, 859-879, 1983. 31 D.C. Presnall, J.R. Dixon, T.H. O'Donell and S.A. Dixon, Generation of mid-ocean ridge tholeiites, J. Petrol. 20, 3-36, 1979. 32 P.J. Spencer, The thermodynamic properties of silicates, Natl. Phys. Lab., U.K. Rep. Chem. 21. 33 K.K. Kelly, Contributions to the data on theoretical metallurgy, 3. High-temperature heat content, heat capacity and entropy data for the elements and inorganic compounds, U.S. Bur. Mines Bull. 584, 232 pp., 1960. 34 R.A. Robie, B.S. Hemingway and J.R. Fisher, Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar pressure and higher temperatures, U.S. Geol. Surv. Bull. 1452, 1978.
407
Elsevier Science Publishers B.V., A m s t e r d a m - Printed in The Netherlands
[61
Heat of fusion of basaltic magma Hiroyuki Fukuyama * Geological Institute, University of Tokyo, Bunkyo- ku, Tokyo 113 (Japan)
Received June 27, 1984 Revised version received January 23, 1985
The heat of fusion of haplobasaltic liquids in the systems forsterite-diopside-SiO 2 and basaltic liquids in natural peridotite has been determined by high-temperature solution calorimetry. For liquids in the systems diopside-anorthite and forsterite-diopside-anorthite the heat of fusion was calculated from literature data. The heats of fusion for eutectic liquids in the system anorthite-diopside and forsterite-diopside-anorthite, for haplobasaltic liquid in equilibrium with olivine and two pyroxenes in the system forsterite-diopside-SiO 2 and for basaltic melts from natural peridotite parent, are 130.6, 121.1,157.4 and 161.5 cal/g, respectively. The heat of mixing in the liquids contributes up to about 5% of this value. The magnitude of this contribution increases when the structure of the endmember minerals is significantly different (e.g., forsterite and anorthite or quartz). The pressure effect on the heat of fusion results in a 10-20% increase in the pressure range 10-30 kbar compared with the 1-atm values. This increase results from the larger compressibility of silicate liquids compared with that of the coexisting minerals in both model and natural compositions.
I. Introduction
Both dynamic and static processes are important in the generation of magma in the upper mantle and the crust of the earth. One process of particular importance is diapiric movement of material through the mantle. The data necessary to deal quantitatively with this process and related melting phenomena frequently are not available. Rheological properties, thermal conductivity and heat of fusion of mantle materials, especially at high pressure, are not well known, for example. The heat of fusion of basaltic magma has been simulated by the heat of fusion of common rockforming minerals such as diopside [1-3]. Its value has been suggested to be approximately 100 c a l / g by Bowen [1,3] and 85.4 c a l / g by Yoder [2]. In a system with more than one component, the heat of fusion of a eutectic composition can be estimated * Deceased. 0012-821X/85/$03.30
© 1985 Elsevier Science Publishers B.V.
from the heats of fusion of the endmember phases, the heat capacities of the solids and liquid and the heat of mixing of the liquid. The heat of mixing of the liquid, which is required for accurate calculation of the heat of fusion of a eutectic composition is, however, rarely known for petrologically important compositions. The heat of fusion of a congruently-melting phase (one-component system) equals the enthalpy difference between the crystalline phase and its melt at the melting temperature. Similarly, for eutectic compositions in systems with more than one component, the heat of fusion is the enthalpy difference between the crystal mixture and its melt at the eutectic temperature. This enthalpy difference commonly cannot be measured directly at temperatures as high as that of the eutectic of most rock-forming minerals. Its value can be obtained, however, by measuring first the enthalpy difference between crystals and glass of the same composition. For calorimetric measurements where
408 the calorimetry temperature is higher than that of the glass transition temperature, the heat of fusion of the crystalline mixture at its melting temperature is:
AH=AHS°'+ fTe(CZp-Cp)dT, T~ch
(1)
where A H is the heat of fusion o f t h e crystalline mixture, A H ~°l is the difference of the heat of solution of the crystalline mixture and supercooled liquid obtained by solution calorimetry, Cpl and Cp are the heat capacities of the supercooled liquid and crystalline mixture, respectively, and T~ch and Tf are the temperatures of the solution calorimetric measurements and the melting temperature of the mixture, respectively. The enthalpy of the liquid decreases continuously with decreasing temperature even if crystals do not precipitate (supercooled liquid), and the thermodynamic properties of this liquid can be expressed with continuous functions extending from the liquid itself. At the glass transition temperature ( Tg) the slope of the enthalpy curve changes to follow that of the glass. If the calorimeter temperature is less than that of Tg, the following expression can be used to obtain the heat of fusion of the crystalline mixture:
2. Experimental techniques 2.1. Starting materials
The system forsterite-diopside-SiO 2. Liquidus phase equilibria in the system forsterite-diopside-SiO 2 have been studied extensively both at 1 atm and at high pressure [3-5J. The composition of the reaction point A (Fo20Di68(SiO2)12 , by weight) at 1 atm from Kushiro and Schairer [5] is adopted as a haplobasaltic liquid coexisting with olivine, clinopyroxene and a Ca-poor pyroxene. The glass of this composition was made from a mixture of synthetic forsterite, diopside and natural quartz by melting at 1450°C for 4 hours. The mixing and melting procedure was repeated twice. Natural peridotite. The natural peridotite composition was a spinel lherzolite from British Columbia, Canada (BC-5000). Its bulk composition, the composition of its constituent mineral (except spinel) and the composition of the peridotite reconstituted from the modal abundance of olivine, orthopyroxene and clinopyroxene ( 5 8 : 2 2 : 2 0 ) are shown in Table 1. The effect of small amounts of an aluminous (55-58 wt.% A1203, chromium-rich (11-12 wt.% Cr203) spinel (Irvine, personal com-
AH--- A H ~°' + fT~c_~dT ~, + f T ~ c ' d T - f T ' 7:,oh JT~ ~ Jr.ch (1') where Cpg is the heat capacity of the glass at T~, the glass transition temperature. Solution calorimetry can be carried out either at lower temperatures with H F as solvent or at higher temperatures with an oxide flux as solvent. Because of the uncertainties in the values of Cp, Cg and CpI in equations (1) and (1'), the heat of fusion can be estimated with greater accuracy from high-temperature solution calorimetry. This paper describes a method to determine the heat of fusion of haplobasaltic and basaltic liquids in the system forsterite-diopside-SiO 2 and in natural peridotite. The heats of fusion of haplobasaltic liquids in the systems diopside-anorthite and forsterite-diopside-anorthite have been calculated from literature data for comparison.
TABLE 1 The composition of BC-5000 lherzolite and constituent minerals Sample
1
1'
2
3
4
SiO2 TiO2 A1203 FeO MnO MgO CaO Na20 K20 Total
45.80 0.17 1.34 1.78 0.15
45.73 0.14 2.09 7.27 0.14 38.66 4.32 0.23 0.00 98.58
39.80 0.00 0.00 9.36 0.16
52.33 0.55 5.73 2.78 0.06
55.33 0.15 4.27 5.85 0.17 32.19 0.90 0.05 0.00 98.91
38.02 4.30 0.24 0.02 98.28
48.86
16.20
0.07 0.00 0.00 98.25
20.38 1.11 0.00 ~
l=spinel lherzolite BC-5000, analyst: H. Haramura; 1'= chemical composition of BC-5000 reconstituted from composition and model proportions of the constituent minerals; 2 = olivine in BC-5000; 3 = clinopyroxene in BC-5000; 4 = orthopyroxene in BC-5000.
409 TABLE 2 Bulk compositions, temperatures of fusion (Tf) and heat of fusion (Hf) of simulated basaltic liquids Sample SiO2 TiO2 AI203 Fe203 MnO MgO CaO Na 2° K 20 Total Tf (°C) Hf (cal/g)
1
2 54.14 0.53 11.19 10.54 0.19 9.69 14.24 0.49 0.01 98.29
1260 161.5
3 58.28 0.00 15.95 0.00 0.00 10.52 23.40 0.00 0.00 100.00
1274 130.6
4 49.18 0.00 15.94 0.00 0.00 13.42 21.46 0.00 0.00 100.00
1270 121.1
58.27 0.00 0.00 0.00 0.00 24.12 17.61 0.00 0.00 100.00
fled argon gas. A r g o n was i n t r o d u c e d into the silica glass tube in the c a l o r i m e t e r after passing it over t i t a n i u m p o w d e r h e a t e d at a p p r o x i m a t e l y 800°C. Both the s a m p l e c o n t a i n e r a n d the crucible c o n t a i n i n g the lead b o r a t e solvent were p l a c e d at the b o t t o m of the glass tube. The e x p e r i m e n t s were c o n d u c t e d b y s u b m e r g i n g the s a m p l e container into the solvent. N o m i n a l run d u r a t i o n was two hours. This time p e r i o d includes b o t h the time r e q u i r e d for thermal e q u i l i b r a t i o n a n d the a c t u a l solution experiment. N o o x i d a t i o n of ferrous iron to ferric i r o n of the n a t u r a l F e - b e a r i n g m a t e r i a l s was o b s e r v e d within this time period.
1390 157.4
1 = glass of BC-5000, partially melted at 1260°C and 1 atm; 2 = eutectic composition in the system diopside-anorthite; 3 = eutectic composition in the system diopside-anorthite-forsterite; 4 = eutectic-like composition in the system diopsideforsterite-SiO 2.
m u n i c a t i o n , 1984) was ignored in the c a l o r i m e t r i c e x p e r i m e n t s a n d s u b s e q u e n t calculation. Solidus t e m p e r a t u r e s a n d degree of melting as a f u n c t i o n of t e m p e r a t u r e o f this spinel lherzolite are a v a i l a b l e [6-8]. A t 1 atm, the solidus t e m p e r a t u r e is n e a r 1200°C with 15% melt f o r m e d at 1260°C. T h e b u l k c o m p o s i t i o n of this melt is given in T a b l e 2. T h e starting m a t e r i a l s for the c a l o r i m e t r i c m e a s u r e m e n t s of the liquid c o m p o s i t i o n was prep a r e d b y first a n n e a l i n g a p o w d e r e d glass at 1200°C at 2 k b a r for 2 hours in an internallyheated, g a s - m e d i a a p p a r a t u s . T h e resulting glass was d i v i d e d into two parts, each of which was h e a t e d overnight at l l 0 0 ° C a n d 1260°C, respectively, in a 1-atm, vertical quench furnace with the o x y g e n fugacity c o n t r o l l e d n e a r 10 - t ° . These m a t e r i a l s were then crushed a n d used for the calorimetric measurements.
2.2. Calorimetry T h e c a l o r i m e t e r was a C a l v e t - t y p e microc a l o r i m e t e r o p e r a t e d at 750°C [9] with 2 P b O . B20 3 as solvent. I n o r d e r to p r e v e n t o x i d a t i o n of the i r o n - b e a r i n g s a m p l e s ( n a t u r a l peridotite), the c a l o r i m e t e r a t m o s p h e r e was c o n t r o l l e d with puri-
3. Results
3.1. The system forsterite-diopside-SiO 2 T h e heat of solution ( T a b l e 3) of glass of c o m p o s i t i o n F020 Di68(SiO2)12 (reaction p o i n t A from K u s h i r o a n d Schairer [5]) is very n e a r 0 k c a l / m o l a n d the variations between i n d i v i d u a l measurem e n t s shown in T a b l e 3 result from the effect of stirring. The e n t h a l p y difference between the glass a n d the crystal m i x t u r e forsterite + d i o p s i d e + e n s t a t i t e (although at the t e m p e r a t u r e of the reaction point, n e a r 1400°C, enstatite is not stable, this difference is neglected) was calculated from p u b lished heat of solution d a t a for each m i n e r a l (for-
TABLE 3 Enthalpy of solution at 750°C in 2PbO. B203 System
Sample (mg)
//soI (cal/g)
Average
Fo-Di-SiO2 glass
31.30 42.36 50.84 32.18
- 3.49 - 2.82 - 0.70 2.62
- 1.10
57.78 40.13 58.71 41.55
80.34 72.78 68.50 79.31
75.23
38.16 40.75 38.99 36.72 34.12
59.32 52.74 67.14 60.82 58.14
59.63
BC-5000 sintered (crystalline) BC-5000 partially melted
410 TABLE 4 P a r a m e t e r s u s e d in the c a l c u l a t i o n of Cp o f m i n e r a l s
Cp=a+bxlO-3T+c×lO 6 T 2 + d x l O 2 / T + e x l 0 5 T 2
Mineral
Forsterite Fayalite Diopside Enstatite Anorthite Quartz
a
b
c
34.49 36.51 52.87 49.14 64.42 17.39
9.26 9.36 7.84 3.06 13.70 0.31
-1.32
Reference a
d
-
-7.85 - 6.70 - 15.74 2.85 - 16.89 - 9.90
5.49
1 2 2 3 2 1
" R e f e r e n c e s : 1 = S p e n c e r [32]; 2 = Kelly [33]; 3 = R o b i e et al. [34].
sterite [10], 114.5 cal/g (16.11 kcal/mol); diopside [11], 94.5 cal/g (20./78 kcal/mol); and enstatite [10]; 87.5 cal/g (8.78 kcal/mol)). This enthalpy difference at 750°C is corrected to the melting temperature with equation (1). In using equation (1), it was assumed that the temperature of the calorimeter (750°C) is higher than the glass transition temperature for the following reasons. For a
range of relevant mineral compositions [12,13] and for glasses of rhyolite to basalt composition [13-16], the glass transition temperatures at 1 atm range from about 800 ° to about 630°C. The Tg for basaltic compositions ranges between 630 ° and 730°C. Composition A is a model basalt composition, and the Tg most likely is less than 750°C. The C; was calculated from the data and the
I
H~H2, 8 (kcal/mol) 100 / 9O
/ m
/ /
80
_
Hf 4
S
70
60
/
5O
40 1200 I
I
I
I
800
[
I
1400 I
I
1000
I
(°K)
1600
1
I
I
1200
I
J
I
1400
(°C)
Temperature Fig. 1. T e m p e r a t u r e - e n t h a l p y d i a g r a m for c o m p o s i t i o n A in the s y s t e m f o r s t e r i t e - d i o p s i d e - S i O 2 (see text f o r details).
411 expression shown in Table 4. Because heat capacities for clinoenstatite are not known, the values for enstatite were used. The Cp1 was calculated by linear summation of partial molar heat capacity data of oxide components from Carmichael et al. [17]. The resulting enthalpy-temperature diagram for the model basalt composition (reaction point A in the system forsterite-diopside-SiO2 [5]) is shown in Fig. 1 where it is assumed that mutual solubilities of diopside in enstatite and enstatite in diopside do not affect the heat contents of the mixture significantly.
3.2. Natural peridotite Calorimetric measurements were carried out with samples sintered at 1000°C (crystalline) and heated at 1260°C and quenched (85% crystals + 15% glass) with the results shown in Table 3. Because of the heterogeneous distribution of the different phases (including glass) in the solution samples, the individual heat of solution data points show larger variations than those obtained for glass in the system forsterite-diopside-SiO2. The difference of heat of solution between fully crystalline and partially molten peridotite is 16.1 cal/g at 1260°C. The measured heat of fusion of the liquid with the bulk composition corresponding to that of the liquid at 15% melting of BC-5000 is 161.5 cal/g. In calculating the heat of fusion at 1260°C, equation (1) was used with the following assumptions. First, the glass transition temperature of this basaltic composition is lower than the 750°C of the solution calorimeter. Second, the proportions of olivine, clinopyroxene and orthopyroxene in the residual material do not change during partial melting. This latter assumption is not strictly true, but may not affect the results significantly for this relatively low degree of melting.
3.3. The systems diopside-anorthite and forsterite-diopside-anorthite The heats of fusion of basaltic liquids in the systems diopside-anorthite and forsterite-diopside-anorthite have been calculated from published data. The system diopside-anorthite is not, strictly speaking, binary [18]. For the model calcu-
lations carried oUt here, this non-binary nature does not pose a serious problem because the mutual solubilities of the two endmember phases in each other is small [18]. The liquidus phase diagram of this system was first determined by Bowen [19], who also calculated the heat of mixing of liquids on the join [3]. The heats of fusion reported by Bowen were 23.39 kcal/mol (108.0 cal/g) for diopside and 29.0 kcal/mol (104.2 cal/g) for anorthite. For the eutectic liquid composition (near Di65An35, by weight, [18]), the heat of mixing of the liquid is near -0.7 kcal/mol ( - 3 cal/g). The system diopside-anorthite was reinvestigated by Weill et al. [11], who found the heat of fusion of diopside to be 34.085 kcal/mol (157.4 cal/g) at 1391°C, a value also in accord with other estimates [13,20]. The reported heat of fusion values for anorthite range from 19 to 40 kcal/mol depending on the method used. It has been suggested [11] that this range results from lack of precise heat capacity data for the liquid (C~) at high temperatures. The value used in the present calculation is 32.4 kcal/mol (116.4 cal/g) [21]. The heat of mixing of the eutectic liquid composition is -1.5 kcal~/mol [11]. For the eutectic composition, the heat of fusion at the eutectic temperature (1360°C) is 31.22 kcal/mol (130.6 cal/g). The estimate of Yoder [2], based on the older thermodynamic data [1] was 20 kcal/mol (83.7 cal/g), or approximately 2/3 of the value of the present study. Heat of fusion data in the system forsterite-diopside-anorthite were also calculated by Yoder [2]. The difference between the heat of solution of the crystal mixture and a glass of the eutectic composition (Fo8,Di46 An 46, by weight [5]) is 19.0 kcal/mol (79.6 cal/g) at 750°C. By substituting the calculated C~ and C~ into equation (1), the heat of fusion of the eutectic mixture at the eutectic temperature (1270°C) is 28.9 kcal/mol (121.1 cal/g). 4. Discussion
4.1. Effect of bulk composition The heat for fusion of basaltic and haplobasaltic liquids determined and calculated here is
412 shown in Table 2. The heat of fusion of anorthitebearing model systems is always smaller than in those systems that do not contain anorthite component. This difference is due to the smaller heat of fusion of anorthite than of any of the other mineral components. For partial melts in the natural peridotite system the liquid has about 30% normative plagioclase, but its heat of fusion is the largest of those in Table 2. The feldspar component in natural partial melts from the upper mantle is derived mainly from aluminous pyroxene in the starting material. Although the effect of jadeite and tschermak's molecule solution in pyroxenes on their heats of fusion is not known, it is suggested that the explanation for the larger heat of fusion in the natural peridotite system may be because of the aluminum-bearing components in the pyroxenes. The least well known parameter in determining the heat of fusion of mineral mixtures is the heat of mixing of the liquid. In general, this contribution to the enthalpy budget is larger in systems containing structurally different phases [22]. This tendency most likely results from the observation [23] that important structural features in crystalline materials are retained in the silicate melts. Such effects have, however, only been determined accurately in the systems diopside-anorthite and diopside-albite [11], where the heat of mixing is about - 1 . 5 kcal/mol ( - 6 cal/g) at the eutectic compositions. Thus, the mixing term contributes about 5% to the heat of fusion calculated from endmembers in appropriate stoichiometric proportions.
4.2. Effect of pressure The heat of fusion of silicate materials is significantly pressure dependent [2,24]. This pressuredependence can be described with the equation:
d A H / d P = mVm(] - mo/Z),
(2)
where AVm is the volume change of fusion, Aa is the difference of thermal expansion between solid and liquid phases and T is the absolute temperature. Based on volume data at 1 atm pressure, Yoder [2] estimated a 35 c a l / g increase in heat of fusion between 1 atm and 30 kbar for basaltic
liquids. The densities of basaltic liquids at high pressure [25] increase more rapidly than those of the crystals so that AVm decreases with increasing pressure (see also [26]). With this correction for AVm, the pressure-dependent increase of heat of fusion of peridotite to produce basaltic liquid is between 19 and 27 cal/g. In summary, the heat of fusion of basaltic magma increases by at least 15% in the pressure range from near surface conditions through the pressure range of partial melting in the upper mantle.
4.3. Petrological implications Detailed studies of the melting behavior of anhydrous four-phase peridotite have shown [27] that the principal features of the melting behavior of natural peridotite are quite similar to those observed in the four-component model system CaO-MgO-A1203-SiO 2. For natural peridotite, 20-30% partial melt of basaltic composition may be obtained under isobarically near invariant conditions. The heat required for this much melting is, however, sufficient to heat up a source rock, provided that it does not melt, by about 70°C at the same pressure and temperature conditions [28]. Relationships between degree of melting, compositions of melt, temperature, pressure and enthalpy requirements for upper mantle peridotite are shown in Fig. 2. The degree of melting is shown schematically with data from [6-9,27,29]. The solidus temperatures and bulk compositions of the partial melts are from Takahashi and Kushiro [30]. Note the presence of cusps in the melting curve, a feature also found in the simple model system CaO-MgO-A1203-SIO 2 [31]. The data in Fig. 2 may be used to illustrate relationships between degree of melting and depth in an adiabatically ascending diapir or plume in the upper mantle. Depending on the heat content of the ascending diapir (see, for example the isoenthalpic lines, H1-H6; Fig. 2), the material in an ascending diapir will commence melting at different depth. This heat content may be a function of the depth in the mantle from which the diapir initially begun its ascent. Inasmuch as the bulk composition of partial melts depends on the depth
413 T .c,
r4oc-
/~i!;:.:~i~/~
~
Y
_,-:!,-,-
...
-1
H&H5 ] H3H3
1300 ......
~ ' " . . . . "'-'-':~-~'f.~......:~:.' " ~'- - '_ ~.-" ._: "--."-.iS ; - ~ ~ , ~ , /
15 . . . . .
-
HI H2 ----H1 - -
- -
"
:" ": :,~.'.'5".'-~" . ' ~ Sp-therz0hte 1200 ~
II00
'
0
f
'
~
'
'
[
5
/
'
....
J
'
I
I0
,
,
,
15 . . . . -5 ....
,
J
15'/, degree of 5 °/o rnettlng
. . . .
15
1
20
. . . .
1
25
Pressure(kb)
Fig. 2. Temperature-pressurerelationships of the solidus temperature, degree of melting and the composition of partial melts of a lherzolite composition [30]. Lines H] - H6 are isoenthalpic contour lines. Dashed and dotted areas correspond to olivine tholeiitic and alkali basaltic magmas. (Composition data from Takahashi and Kushiro [30].)
of melting [2,30,31], the source depth of the diapir itself, though deeper than that of the partial melting, may govern the composition of the initial melt in the diapir. For example, one may speculate that partial melts of alkali basaltic composition may require the temperature (and, therefore, heat content) of the diapir itself at its point of origin to be greater than that required to form olivine tholeiite. As a result of the greater heat content, initial melting will commence at greater depth in the mantle where the initial melt may be alkali basalt. Melting at shallower depth (requiring smaller heat content of the diapir) may yield olivine tholeiite melt composition. It is also noted from the data in Fig. 2 that the isoenthalpic curves and the lines depicting the pressure-temperature conditions of constant degree of melting become nearly parallel at pressures less than about 10 kbar. Thus, even though the degree of melting in an ascending diapir may increase as the diapir rises through the mantle to about 30 km depth, additional rise does not affect this degree of melting further. Thus, at depth of 30 km or less, the bulk composition of the partial melt in the diapir is strictly a function of
pressure-dependent phase equilibria, whereas at greater depth the bulk composition of partial melts depends on both the pressure-dependent phase equilibria and the degree of melting controlled by the relationship of the isoenthalpic lines to the curves of equal degree of melting.
Acknowledgements This work was carried out during a visit to the Arizona State University and was partially supported by U.S. Department of Energy (Contract DEA0280e10765 to Dr. A. Navrotsky). The author thanks Dr. A. Navrotsky for encouragement and Drs. I. Kushiro and H.S. Yoder, Jr. for reviewing the manuscript.
References 1 N.L. Bowen, The Evolution of the Igneous Rocks, 333 pp., Princeton University Press, Princeton, N.J., 1928. 2 H.S. Yoder, Generation of Basaltic Magma, 246 pp., National Academy of Sciences, Washington, D.C., 1976.
414 3 N.L. Bowen, The melting phenomena of plagioclase feldspars, Am. J. Sci., 4th Ser. 35, 577-599, 1913. 4 J.J. Schairer and H.S. Yoder, The system diopsideenstatite-silica, Carnegie lnst. Washington Yearb. 61, 75-82, 1962. 5 I. Kushiro and J.F. Schairer, New data on the system diopside-forsterite-sihca,Carnegie Inst. Washington Yearb. 62, 95-103, 1963. 6 T. Murase, I. Kushiro and T. Fujii, Electrical conductivity of partially molten peridotite, Carnegie lnst. Washington Yearb. Book, 76, 416-419, 1976. 7 T. Murase and I. Kushiro, Compressional wave velocity in partially molten peridotite at high pressures, Carnegie Inst. Washington Yearb. 78, 559-562, 1979. 8 T. Murase and H. Fukuyama, Shear wave velocity in partially molten peridotite at high pressures, Carnegie Inst. Washington Yearb. 79, 307-310, 1980. 9 A. Navrotsky, Progress and new directions in high-temperature calorimetry, Phys. Chem. Miner. 2, 89-104, 1977. 10 T.V. Charlu, R.C. Newton and O.J. Kleppa, Enthalpies of formation at 970°C of compounds in the system MgOA1203-SiO2 from high-temperature solution calorimetry, Geochim. Cosmochim. Acta 39, 1487-1497, 1975. 11 D.F. Weill, R. Hon and A. Navrotsky, The igneous system CaMgSi2Or-CaA12 Si 2Os-NaA1Si308: variations on a classic theme by Bowen, in: Physics of Magmatic Processes, R.B. Hargraves, ed., Chapter 2 Princeton University Press, Princeton, N.J., 1980. 12 J. Arndt and F. Haberle, Thermal expansion and glass transition temperature of synthetic glasses of plagioclase-like compositions, Contrib. Mineral. Petrol. 39, 175-183, 1973. 13 P.J. Vergano, D.C. Hill and D.R. Uhlmann, Thermal expansion of feldspar glasses, J. Am. Ceram. Soc. 50, 59-60, 1967. 14 C.M. Scarfe, Viscosity of some basaltic glasses at one atmosphere, Can. Mineral. 15, 190-194, 1977. 15 C.R. Bacon, High-temperature heat content and heat capacity of silicate glasses: experimental determination and a model calculation, Am. J. Sci. 277, 109-135, 1977. 16 M.P. Ryan and C.G. Sammis, The glass transition in basalt, J. Geophys. Res. 86, 9591-9535, 1981. 17 I.S.E. Carmichael, J. Nichols, E.J. Spera, B.J. Wood and S.A. Nelson, High-temperature properties of silicate liquid: application to the equilibration and ascent of basic magma, philos. Trans. R. Soc. London, Ser. A 286, 373-431, 1977. 18 E.F. Osborn, The system CaSiO3-diopside-anorthite, Am. J. Sci. 240, 751-788, 1942. 19 N.L. Bowen, The crystallization of haplobasaltic haplodioritic and related magmas, Am. J. Sci., 4th Ser. 40, 161-185, 1915.
20 A. Ferrier, Mesure de l'enthalpie du diopside synthetique entre 298 and 1885 K, C.R. Acad. Sci. Paris, Ser. C 267, 101-103, 1968. 21 D.F. Weill, J.F. Stebbins, R. Hon and I.S.E. Carmichael, The enthalpy of fusion of anorthite, Contrib. Mineral. Petrol. 74, 95-102, 1980. 22 P. Richet, Viscosity and configurational entropy of silicate melts, Geochim. Cosmochim. Acta 48, 471-485. 23 B.O. Mysen, D. Virgo and F.A. Seifert, The structure of silicate melts: implications for chemical and physical properties of natural magma, Rev. Geophys. 20, 353-383, 1982. 24 S. Maaloe, The significance of the melting interval of basaltic magmas at various pressures, Geol. Mag. 110, 103-112, 1973. 25 T. Fujii and I. Kushiro, Density, viscosity and compressibility of basaltic liquid at high pressures, Carnegie Inst. Washington Yearb. 76, 419-424, 1977. 26 E. Stolper, D. Walker, B.H. Hager and J.F. Hays, Melt segregation from partially molten source region: the importance of melt density and source region size, J. Geophys. Res. 86, 6261-6271, 1981. 27 B.O. Mysen and I. Kushiro, Compositional variations of coexisting phases with degree of melting of peridotite in the upper mantle, Am. Mineral. 62, 843-865, 1977. 28 R.G. Cawthorn, Degree of melting in mantle diapirs and the origin of ultrabasic liquids, Earth Planet. Sci. Lett. 27, 113-120, 1975. 29 A.J. Jaques and D.H. Green, Determination of liquid compositions in high pressure melting of peridotite, Am. Mineral. 64, 1312-1321, 1979. 30 E. Takahashi and 1. Kushiro, Melting of a dry peridotite at high pressures and basalt genesis, Am. Mineral. 68, 859-879, 1983. 31 D.C. Presnall, J.R. Dixon, T.H. O'Donell and S.A. Dixon, Generation of mid-ocean ridge tholeiites, J. Petrol. 20, 3-36, 1979. 32 P.J. Spencer, The thermodynamic properties of silicates, Natl. Phys. Lab., U.K. Rep. Chem. 21. 33 K.K. Kelly, Contributions to the data on theoretical metallurgy, 3. High-temperature heat content, heat capacity and entropy data for the elements and inorganic compounds, U.S. Bur. Mines Bull. 584, 232 pp., 1960. 34 R.A. Robie, B.S. Hemingway and J.R. Fisher, Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar pressure and higher temperatures, U.S. Geol. Surv. Bull. 1452, 1978.