American Mineralogist, Volume 73, pages 1-19, 1988
Condensation,evaporation,melting, and crystallization in the primitive solar nebula:
Experimental data in the systemMgO-SiOr-Hrto 1.0 X 10-ebar and
1870 "C with variable oxygen fugacity
Bronu O. MvsnN,Ixuo Kusnrno*
GeophysicalLaboratory, CarnegieInstitution of Washington, 2801 Upton Street,N.W., Washington, D.C. 20008, U.S.A.
ABSTRACT
Crystal-vapor, melt-vapor, and crystal-melt-vapor phase relations in the system MgOSiOr-H, have been determined at low pressures(10-a to lO-e bar) and high temperature
(1400 to 1870 'C) from vapor-pressuredeterminations of periclase,forsterite, silica minerals, enstatite,and liquid compositions in the system and from conventional phase-equilibrium measurementtechniques.In addition to pressure,temperature, and bulk-composition variables, the oxygen fugacity was varied from 1.5 orders of magnitude above that
of the iron-wiistite oxygen buffer to about 2.5 orders of magnitude below.
In this system, periclase, forsterite, and silica (tridymite and cristobalite) evaporate
congruently to a gas phaseconsisting of MgO, SiOr, SiO, Si, and oxygen species,whereas
enstatite (most likely protoenstatite) evaporatesincongruently to forsterite plus a silicarich vapor. Liquid is unstable at silicate vapor pressuresbelow l0-5 to 10-6 bar. The
temperaturesof the triple points where crystals, liquid, and gas coexist range from 1550
"C for enstatite, to 1600'C for silica and 1700 "C for forsterite. The temperature of the
triple point for periclasewas not determined,but is likely to be near 2800 "C. The pressures
of the triple points increaseby several orders of magnitude upon dilution of the vapor
phaseto hydrogen/silicatemolar ratios relevant to condensationin the solar nebula (e.g.,
l0a), and the temperaturesdecreaseby severalhundred degrees.
Vaporous diagrams in the systemsMgO-SiO, and MgO-SiOr-Fe show that at pressures
and hydrogen/silicateratios appropriate for the solar nebula, the vaporous phase is forsterite with a vaporous freld extending from about 95-99 molo/oMgO (forsterite-periclase
vaporous boundary) to lessthan l0 mol0/0,where the enstatiteand forsterite coexist.These
relations are consistent with extensive Mg-Si fractionation by fractional condensationof
forsterite during cooling in the early solar nebula. In the Fe-bearing,ternary system the
forsterite vaporous extends to nearly 1000/oFe, thus suggestingthat very extensive magnesiosilicatefractional condensation(and temperature reduction-at least 400 "C) is necessarybefore Fe metal will condensefrom the early solar nebula.
INrnonucttotrr
Chemical, isotopic, and petrographicevidence,in particular from carbonaceouschondrites, indicates that the
formation of rock-forming minerals in the solar nebula
was the result of processesthat include evaporation to
and condensationof liquid and crystalsfrom a vapor phase
(Grossman,1980;Wood, 1984;Grossmanand Larimer,
1974; MacPherson and Grossman, 1979; Lattimer and
Grossman,1978;Cameronand Fegley,1982;Onuma et
aI., 1979; Nagahara, 1984). Both evaporation-condensation and melting-crystallizatibn may have occurred repeatedlyboth locally and regionally (Herndon, 1978;Nagahara,1981; Wood, I 984; Niederer and Papanastassiou,
1984;Chou eI al., 1976; Clayron et al., 1977).The bulk
compositions of individual grains and agglomeratesthat
* Also at Geological Institute, University of Tokyo, Hongo
Tokyo, Japan.
0003-o04x/88/0 102-000I $02.00
accretedto form meteorite parent bodies and terrestrial
planetsdependcritically, however, on the extent to which
their early nebula-formation processeswere governedby
vapor-crystal equilibria or vapor-liquid-crystal equilibria
and also on the extent to which these were equilibrium
processes.Whether or not condensationand evaporation
processesinclude formation of liquids dependson pressure, temperature, and bulk composition of the system
(for data on commonly cited models, see for example,
Cameron, 1973, 1978 Cameronand Fegley,1982; Wood,
1981, 1984; Ahrrenius and Alfven, l97l). For a given
bulk composition, there is a minimum pressureabove
which a crystalline phasecannot condensedirectly from
a gas phase or evaporate directly to a gas without an
intervening liquid field. Liquid, crystal(s),and gascoexist
at triple points. It is important, therefore,to establishthe
pressure-temperatureconditions of the triple point (as
well as other invariant points) for relevant nebular materials.
MYSEN AND KUSHIRO: MgO-SiO'.H, AND THE PRIMITIVE SOLAR NEBULA
The oxygenfugacity in the nebula most likely was governed by C-O-H gas equilibria and can be calculated as
a function of gas composition and temperature. Redox
equilibria involving major elements such as Fe, Si, and
less abundant Ti, P, and Cr may be influenced by the
oxygen fugacity in the f, ranges suggestedfor the early
history of the solar nebula. Moreover, the pressure-temperature-composition stability relations of oxides, metals, and silicatesmay be functions of the oxygen fugacity
of the system. Estimates of the fo, range from about 56 orders of magnitude below that of the iron wiistite (IW)
buffer for the nebular gas (Fegley, 1985) to l-2 orders of
magnitude above the IW bufer for "whole-rock" CAI
inclusions from Allende as recorded with measurements
of intrinsic oxygen fugacity (Kozul et a1., 1986). Ihinger
and Stolper(1986)from spectroscopic
studiesofhibonite
from CAIs suggested
/o, values during crystallization of
hibonite from - 5 orders of magnitude below that of the
IW buffer to values slightly above those of the magnetitewiistire (MW) buffer.
Pressure,temperature,and oxygen-fugacityconditions
during formation of the mineral assemblagesin the matrix, chondrules, and inclusions in chondritic meteorites
reflect conditions in the early solar nebula. This pressure,
temperature, and oxygen-fugacity environment can be
characterizedprovided that crystal-liquid, liquid-vapor,
and crystal-vapor phase-equilibrium data for the relevant
mineral assemblageshave been experimentally obtained
under realistic pressure,temperature, and bulk-composition conditions. These calculations also require knowledgeof which phaseswere involved in the nebular condensationhistory. From data on free energiesof formation
of relevant phases, condensation sequenceshave been
calculated (e.g., Grossman and Larimer, 1974;,Laltimer
and Grossman, 1978).Those calculationsrely on accurate thermochemicaldata and on a knowledgeof the speciation in the gas phase under appropriate conditions.
The thermodynamic data are not always available. In
particular, thermochemical data for the most refractory
oxides as well as liquids are rare. Characteization of the
speciesofthe gas phase has been reported for only very
Iimited chemical compositions and under restrictedpressure, temperature, and oxygen-fugacityconditions. The
types of crystalline phasesincluded in the calculations
depend on their detection in extraterrestrial materials.
Experimental determination of phase relations of individual minerals and mineral assemblagesdoes not rely
on the above information. Experimental determination
of evaporation-condensation behavior in appropriate
compositions has been reported only for a few systems
(Sataet al., I 978;Masudaand Tanaka,I 979;Hashimoto,
1983;King, 1982;Hashimotoet al., 1979;Mysen et al.,
1985) under restricted conditions. The oxygen fugacity
was not a controlled variable in these studies.
In order to provide a framework for phaserelations in
the nebular environment, it is necessaryto determine systematically the phase relations in relevant simple oxide
and silicate systemsand then proceedwith more complex
systems before an adequate description ofphase relations
among gas, liquid, and crystalline phases in the solar nebula is feasible. The system MgO-SiO, contains the important phases forsterite and enstatite in addition to periclase and one or more silica polymorphs (depending on
the temperature range; Fenner, 1913). Characterization
of the phase relations in this system will provide, for
example, data relevant to understanding the systematic
variations in Mg/Si among chondrites (e.9., Urey, 1961;
Ahrens, 1964,1965; Wasson, 1974) as well as differences
in Mg/Si between inclusions, chondrules, and matrix
within individual chondrites (Huss et al., l98l; Nagahara, 1984). The bulk Mg/Si of the terrestrial planets also
differs (Weidenschilling, 1976; Turekian and Clark, 1969).
There is also evidence that the Earth's upper mantle is
not chondritic (Palme and Nickel, 1985). Furthermore,
detailed information on phase relations along this join is
necessary to develop the phase relationships in the more
complex, and more realistic, systems MgO-AlrOr-SiO, and
CaO-MgO-AIrO3-Sior.
ExpBnrnmNTAL
METHoDS
Starting materials were (l) finely ground (1-3 pm) synthetic
forsteritecrystallizedat 1000'C and 15 kbar for 24 h from a
spectroscopicallypure mixture of MgO + SiO, with about 5 wt0/0
reaction and produces 20-50HrO (this procedure yields 1000/o
pm euhedral forsterite crystals);(2) synthetic, spectroscopically
pure tridymite for SiOr; and (3) spectroscopicallypure MgO.
All experimentswere conductedin a high-temperature(-2000
'C), high-vacuum (P < l0-" bar) furnace describedby Mysen
et al. (1985).Briefly, the experimentswere conductedin a 5.0cm-long and I -cm-diameter,W-wound furnacecoaxially located
in a cylindrical, 35-cm-long by lS-cm-diameter vacuum chamber. The temperature was measured with a W-W74Reruthermocouple interfacedwith a programmabletemperaturecontrolIer (Hadidiacos, 1979). The temperature,calibrated against the
meltingpoint of Pt(1772 'C) and Fe (1535'C), is accurateto +5
'C. The temperaturegradient
"C. The precisionis better than + 2
oC.
along a 0.5-cm vertical zone in the fuinace is less than 10
The sampleswere contained in 2-mm-diameter (inside diameter) by 2-mm-deepMo, W, and C containerswith a 0.5-mmthick tight-fitting lid. These containers were suspendedin the
furnacewith a 0.25-mm-diameterwire fed throughtwo 0.5-mmdiameter holes drilled in the side ofthe containers.The container was placed within 1-mm of the thermocouplejunctron.
The three different sample container materials were used so
that the oxygenfugacity could be buffered at different values by
interaction between oxygen in the sample and the metal container with the following possiblereactions:
W+1.50,=WOr,
w+Or=WOr,
Mo*Or=MoOz,
3C + 2O2= 2CO + COz.
(l)
(2)
(3)
(4)
The temperaturetrajectoriesof thefo, definedby thesereactions
are shown in Figure l. Although it is not altogetherclearwhether
the W-containing buffer is that describedby Reaction I or Reaction 2 becausetheir AG values are nearly identical (Robie et
al., 1978), it is clear that these bufer assemblagescover an /o,
range from about 1.5 order ofmagnitude above to about two
orders of magnitude below that of the iron-wiistite buffer.
MYSEN AND KUSHIRO: MgO-SiO,-H, AND THE PRIMITIVE SOLAR NEBULA
For experimentsinvolving liquid = vapor equilibria (seealso
below), it was desirableto control the pressurein the vacuum
chamber. BecauseH. was the principal component in the solar
nebula, H2 was used for this purpose. P", inside the vacuum
chamber (but not necessarilywithin the sample containers;see
discussionbelow) were measuredwith a Varian Ratiomatic 842
ionization gauge.The pressurewas maintained by bleeding H,
into the vacuum chamber through a valve placedin front ofone
of the ports into the main vacuum chamber.The measuredpressure, P,",, is, therefore, equal to PHz + P-., where P",. is the
pressurein the vacuum chamber with the H, valve closed. In
the experimentsrepolted here, P""" was 1.0 x 10 '0 bar or less,
so that with the P", above 1.0 x 10 e bar, the measuredP,".
values are near the P", values in the vacuum chamber. Except
at PH2> 1.0 x 10-6bar, wherethe P..,fluctuatedby as much as
2o/oduring experimentslasting severalhours (probably owing to
convection inside the vacuum chamber),the P", is preciseto at
least 1ol0.
The experimentswere terminated by turning off the power to
the furnace. Although the quenching rate dependson the temperature,ratesnear 10-20'C/s between1500'C and 1000'C
were obtained. Becausecooling was principally by radiative
transfer, cooling to lower temperatureswas significantly slower.
Chemical analysis and petrographic studies were performed
with optical microscopy and with a JEoL-35scanning-electron
microscopeequipped with both wavelength-and energy-dispersive detection systems for quantitative analysis. Analyses of
quenchedliquids were conductedwith a l0 pm x 10 pm square
raster, and averagesof 5 to l0 such analyzed squaresare reported.
The pressureinside the sample containers is not necessarily
the sameas in the vacuum chamber (outside the capsule).With
the outside pressuresignificantly lower than the vapor pressure
of the samples,the Knudsen method (Knudsen, 1909) can be
used to determine the vapor pressureof the samples.Two 0.5mm-diameter holes were drilled in the sides of the container
walls to generatea Kludsen cell (Knudsen, 1909).Becausethese
two holes also facilitate suspensionof the containers from the
sample-suspension
wire insertedin the furnace,the effectiveorifice area, after subtraction of Mo wire cross-section,is 2.95 x
l0-3 cm2.
With the Knudsen method, the vapor pressureof a substance,
P- (bar), can be determined by measuringthe evaporation rate,
dw/dt (g/s) (Pauleand Margrave, 1967);
,
-L0w
Ac 3t
2rRT
M
(5)
where -4 is the area of the orifice (cm,), c is the Clausing factor,
M is the molecular weight of the etrusingvapor, Z is absolute
temperature,and R is the gas constant.
Equation 5 is strictly valid only under the following conditions. (l) The sample surface is infinitely large compared with
the orifice arca. (2) The evaporation constant is unity. (3) The
length of the orifice is negligible. (4) The ambient pressureis
suchthat there is no interaction betweenthe gasmolecules("free
molecule regime"). Becausethese conditions cannot be strictly
met experimentally,the P- in Equation 5 is not the equilibrium
vapor pressure,P,, but can be related to P" by the relationship
(Motzfeldt, 1955)
&: {1 + fl(r/a) + (r/w) - 2ltP^.
(6)
In this equation,f : cA/Ao, where lo is the evaporation surface
area,a is the evaporation constant, and,W is the Clausingfactor
Temperature."c
I 500
r 700 I 600
t-7
o
-10
46
48
s0 s.2 54 s6
l/T x lo{(K-r)
58
6.0
Fig. l. Oxygen fugacity-temperature trajectories for MW
(magnetite-wustite),Iw (iron-wiistite), w-wo3, w-wo', MoMoOr, and C-CO-CO, oxygenbuffers.The tungstenand molybdenum buffer curyes were calculatedfrom Robie et aI. (1978).
Other curvesare from Huebner(1971).
for a container with orifice and evaporation surfaceareasequal.
In the presentexperiments,an empirical factor that includesthe
entiry { 1 + f[(l/q) + (l/ W) - 2]] was calibratedby usingknown
substanceswith well-characterizedpressureversus temperature
relationships.The presentsystemwas calibrated with liquid Cu
and Ag (Joneset al., 1927). Results of rate studies at different
temperaturesand different run durations are given in Table 1.
The empirical pressure-correctionfactor obtained from those
data(4.0 + 1.0 x 10a)was used to compare results for vapor
pressuresof SiOzwith thermodynamic data from the literature.
The experimentalP" data from SiO, were obtained with a range
ofweight losses(8.4-860/o;see Table 2). Thus, despite the fact
that in principle there might be a changein pressureas a function
ofthe extent ofweight loss due to the open-systemnature ofthe
present experiments,this effect is small and is neglected.With
this proviso, the heat and entropy ofevaporation (AtI" and AS",
respectively)can then be relatedto the vapor pressureas follows:
ln P, : (-aG"/R7"):
(-LH"/R7)
+ (AS"/R).
(7)
Porter et al. (1955) used alumina Knudsen cells and obtained
A1/" for SiO, near 570 kJlmol. Although thoseexperimentswere
reported to have been conductedunder "neutral/o, conditions,"
possible contamination of the silica by AlrO, at the high temperaturesofthose experiments(up to 1900 K) was not consid-
Tnaue1. Experimentalresultsfor Cu and Ag metal
Starting
material
Ag
Ag
Cu
f rc)
1200
1100
1327
PF"(batl
Time
(min)
Phases
present
Loss Loss
(mS) (wt%)
1.0 x 10 s
1 . 0x 1 0 ' g
1.0 x 10'g
20
120
120
Ag(Liq)
Ag(Liq)
Cu(Liq)
4.60
5.72
3.83
/VofeiAll samDlecontainers were of Mo.
29.3
36.6
43.8
MYSEN AND KUSHIRO: MgO-SiO,-H, AND THE PRIMITIVE SOLAR NEBULA
TaaLe2. Experimentalresults
Starting
material
Tr
Tr
Tr
Tr
Tr
tr
Tr
Tr
Tr
Tr
Tr
tr
tr
Tr
tr
Tr
fl
fr
tr
Tr
Tr
tr
tr
Tr
fr
Tr
It
Pe
Pe
Pe
Pe
Pe
Pe
Pe
Pe
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
FO
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
Fo
f rc)
1400
1400
1450
1450
1500
1500
1500
1595
1595
161
I
161
8
1640
1640
1640
1661
1661
1678
1708
'1752
1500
1550
1600
1400
1500
1500
1550
1600
1750
1700
1650
1650
1600
1550
1500
1450
1400
1500
1500
1500
1595
1595
1680
1680
1680
1702
1702
1724
1724
1746
1769
1769
1769
1769
1769
1769
1869
1700
1600
1675
1600
1540
1600
1650
PH. (bad
1.8 x 10-e
1.8 x 10-"
1.8 x 10-e
1.8x10e
1.8x 10-e
1.8 x 10-e
1.8 x 10-d
1.8 x 10-e
1.8 x 10-"
5.0 x 10-5'
1.8x104
5.0 x 10-s.
1'8 x 1o-'
1.8x10e
5.0 x 10 5'
1'8 x 1o-n
1.8x 10-o
' 1 . 8x
1o-'
1.8x10s
1.8x 10-6
2.2 x 10-8
1.8x100
1 . 0x 1 0 , ' 1.0 x 1o-*1.0 x 10-*1.0 x 1o-r1 . 0x 1 0 , . '
1.8x10,
1.8x l0-,
1.8x 10-'
1.8x 10-'
1.8x100
1.8x 10-o
1.8 x 10-,
1.8x10,
1.8x10,
1.8 x 10-'
1.8x 10-,
1 8 x 1 0s
1.8x 10-t
1.8x10,
1.8x10,
1.8x10,
1.8x 10-,
1.8x 10-'
1.8x10a
1.8x 10-4
1.8x 10-?
1.8x 10-'
1.8x10'
1.8x10,
1.8x107
1.8x 10-'
1.8x10?
1 . 8x 1 0 1.8x104
1'8 x 10-n
1.8x 10-'
1.8x100
1.0x 10-*1.0x 10-,1 . 0x 1 0 , *
1 . 0x 1 0 ' g -
Time
(min)
Capsule
3800
1600
3975
9900
360
1440
1440
400
1020
120
120
120
150
300
120
12O
12O
120
60
1080
2880
120
4080
360
240
60c
20c
120
300
4100
105
360
360
1385
940
14400
3970
5760
11424
72O
1440
180
300
870
30
20
15
15
15
30
15
1Mo
5Mo
15
5Mo
5Mo
30
900
't20
330
850
260
180
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
w
W
W
c
C
C
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
Mo
w
w
C
C
C
C
Phases present
Loss
(mg)
Loss
(wt%)
Tr+Oz+V
Tr+Oz+V
Tr+Qz+V
Tr+Oz+V
Cr+Qz+V
Cr+V
Cr+V
Cr+V
Cr+V
Cr+L+V
Cr+L+V
Cr+L+V
Cr+L+V
Cr+L+V
Cr+L+V
Cr+L+V
Cr+L+V
Cr+L+V
L+V
Cr+V
Cr+V
Cr+V
Tr+V
Cr+V
Cr+V
Cr+V
Cr+V
Pe+V
Pe+V
E
Pe+V
Pe+V
Pe+V
Pe+V
Pe+V
Fo+V
Fo+V
Fo+V
Fo+V
Fo+V
Fo+V
Fo+V
Fo+V
E
Fo+L(q-Fo)+V
Fo+L(q-Fo)+V
Fo+L(q-Fo)+V
Fo+L(q-Fo)+V
Fo+L(q-Fo)+V
E
E
Fo+L(q-Fo)+V
Fo+L(q-Fo)+V
E
Fo+L(q-Fo)+V
L (q-Fo)+ V
Fo+L(q-Fo)+V
Fo+V
Fo+V
Fo+V
Fo+V
Fo+V
Fo+V
o.87
0.60
1.50
3.76
0.45
1.84
2.12
1.88
4.17
<2.33
1.26
1.28
1.25
2.90
1.68
0.66
1.71
3.62
2.57
0.56
2.4't
0.33
3,89
4.91
3.90
1.69
1.83
2.05
2.02
- 1.73
0.69
0.68
0.60
1.25
0.60
1.17
1.O2
1.'t4
2.85
1.16
2.05
2.28
3.32
n.r.
1. 1 6
0.43
0.23
1.29
2.85
n.r.
n.r.
1.27
4.30
n.r.
0.17
2.06
0.80
1.93
2.92
1.141
o.44
1.47
1.10
18.9
1't.2
25.4
57.7
8.4
30.8
43.2
37.2
86.0
<40.7
40.6
21.8
28.4
58.8
25.1
12.8
31.3
68.2
55.9
14.0
7'1.9
6.4
97.3
92.6
67.9
45.1
51.0
91.1
92.7
100.0
39.0
35.1
29.6
64.4
22.7
20.3
15.8
25.1
56.2
22s
34.5
41.2
63.4
100.0
1 7. 5
8.9
4.8
20.3
57.8
100.0
100.0
25.5
76.'l
100.0
3.5
50.5
17.7
42.2
78.1
34.4
11.3
27.5
33.6
N o f e j T r : t r i d y m i t e ; C r : c r i s t o b a l i t e ;Q z : q u a r t z ; F o : f o r s t e r i t e ; P e : p e r i c l a s e ; L : l i q u i d ; V : v a p o r ;
q-Fo: quench forsterite; n.d : not determined;n.r : not resolved; E : capsule empty atter experiment.
* Ar used as pressure medium. .. No
H. t Incompletesample recovery.
ered. Hidalgo (1960) reported this relationship betweentemperature and vapor pressure:
ln P" : (-57 800/0 + 18.4,
(8)
which is shown as the line marked "H" in Fisure 2. Zis absolute
temperature.As can be seenfrom those data, there is agreement
betweenthe two data sets.All calculationsofequilibrium vapor
pressure from the observed weight-loss data were, therefore,
conducted with Equation 5 with an empirical correction factor
obtained from the weightJossdata for liquid Cu and Ag.
MYSEN AND KUSHIRO: MgO-SiO,-H, AND THE PRIMITIVE SOLAR NEBULA
-9
-19
SiO2- H2
-10
- 1 8 W : t n e $ a l : - 5 ? 5 4 6 g 1 4 8 0 '5 1 7 . 5! 8 . 1
-11
-12
o
o
o
c
M o , t n p {v } a l = - - s 8 3 o i r s 1 s 2 . 1 8 . 6! 3 . 0
-17
_1?
C:
tn P{}al : -68826t4971 , 27.o x 2.8
-/
-16
-14
o
-15
C
-14
L
-tf,
I
-to
-11
6.0
5.5
5.0
l/T x lo4(K-r)
4.
Fig. 2. Observed vapor pressure(P") of silica as a function
of temperature.Curve H is from Hidalgo (1960).
-13
-12
-tl
Rrsur,rs
The systemSiOr-H,
Experiments in the system SiOr-H, were conducted in
the P", rangebetween 1.8 x l0 a and 1.8 x l0-, bar
and in the I range between 1400 and 1752 "C with all
experimental data shown in Table 2. Most of the experiments were carried out in Mo containers with the /o,
buffered along the Mo-MoO, curve (Fig. l). In all subsolidus experiments, l0-30-pm euhedral cristobalite and
tridymite crystals were formed. At the lowest temperatures, quartz is also present (Table 2). Most likely, the
quartz was formed during the relatively slow quenching.
The observed vapor pressuresin the subsolidus region
(Fig. 3) were fitted to a linear expressionof the form of
equation (7),
l n P , : K - 5 8 3 0 7 + 5 1 5 2 ) / 7 1 + 1 8 . 6+ 3 . 0 , ( 9 )
where Z is absolute temperature. The data are insufficiently precise to discriminate between evaporation of
tridymite and cristobalite. The experimental data with W
containers(Fig. 3) showed significantly more scatter and
can be describedwith the expression
ln P" : l(-57 546 + v803)/71+ r7.3 + 8.2. (10)
The two curyes cannot be separatedwithin experimental
uncertainty.
There is a distinct differencein slope and intercept for
the vapor-pressurecurves obtained with experiments in
graphite capsules(C-CO-COr-O2oxygen buffer) (Fig. 3),
as expressednumerically with the expression
ln P" : K-68 826 + 4871)/71+ 27.0 + 2.8, (l l)
comparedwith the results obtained with Mo and W sample containers.This significantly steeperslope and larger
value at the intercept is a function of the 2.5-3.5 orders
of magnitude decreaseinf, resulting from using graphite
rather than Mo or W containers.
-9
5.5 5.6 5.7 5.8 5.9 6.0
l/T x 101(K-1)
of crystallinesilica(cristoFig. 3. Observedvaporpressure
baliteand tridymite)with differentcontainermaterialsas indiis mostprobablyinaccurate
becated.The point in parentheses
causeof partialblockageof the holesin the W containerin that
experiment.
s.3
5.4
Liquid, which quenchesto a clear, bubble-free glass,
was found to coexist with euhedral l0-30-pm cristobalite
at temperaturesabove 1600 "C, and only liquid (glass)
existsin experimentsat temperaturesabove 1700"C (Fig.
4). This observation contrasts with that for phase relations in the SiO, systemat I bar, where cristobalite melts
congruentlyat 1713 oC (Fenner, 19I 3). This melting interval, therefore, (l) either results from chemical impurity (contamination), (2) a - 100 oC temperature gradient
vertically along 3 mm in the furnace, (3) or the phase
relations cannot be describedsimply in terms of the una.
ry system SiOr. A solidus depressionresulting from H,
solution in the melt is ruled out as unlikely in view of the
fact that this depressionrequires about 25 molo/oH, in
solution.
Although not detectedexperimentally, the topology of
the phaserelations depicted in Figure 4 requires that there
should be a phase field between Cr + L + V and V
involving vapor and another phase, possibly a liquid of
different composition than the liquid coexistingwith vapor at temperaturesabove about 1700 "C.
Electron-microprobe analysesof quenchedglassesand
coexistingcristobalite show at most 0.4 wto/oAlrO, in the
quenchedglass (Table 3), possibly resulting from vapor
transport of AlrO, from the alumina furnace tube. Onebar liquidus phaserelations on the join SiOr-AIrO, (Ara-
MYSEN AND KUSHIRO: MgO-SiO,-H, AND THE PRIMITIVE SOLAR NEBULA
-13
10 - 3
s i o 2- H 2
o
Mocontainer
r/
l n P.i-.-=- -- -5-0- -0-1- -t =6 -2 1 6 . 14 . 2 t . 3 . 2
Otr
I O-1
ootr
L*V
-12
C r * L +V
tG'
1o-s
o
o
-o
Cr*V
Tr.V
f
a
@
(l)
o_
S i O 2- H 2
C
I O-6
-11
1o - 7
-10
4.9 s.0
I O-8
14 0 0
15 0 0
16 0 0
17 0 0
Temperature,'C
18 0 0
5.2
5.1
5.3
s.4
i/r x 104(K-1)
of moltensilica(P")asa functionof
Fig. 5. Vaporpressure
with Mo samplecontarners'
temperature
Fig. 4. Pressure-temperaturephase relations in the system
SiOr-H, at the oxygenfugacity of the Mo-MoO, buffer. The pressure axis is total pressure(silicate vapor pressure + hydrogen
pressure).In experimentsalong the vaporous, the silicate vapor
pressureis approximately equal to total pressurebecauseP", is
one or more order of magnitude lessthan the silicate vapor pressure. Closed symbols, no liquid present;half-open symbols, liquid and crystals present; open symbols, liquid and no crystals
present.Circles denote experimentsused for vapor-pressuredetermination. Squaresrepresent experiments at imposed pressuresgreaterthat vapor pressure.Note that although there must
be an additional phase field between the Cr + L + V and V
fields, this is not indicated becauseof lack of experimental information.
nation is ruled out to explain the existenceof a melting
interval below the l-bar liquidus of SiOr. As indicated
above, the temperaturegradient along a 3-mm section of
the furnacesis less than l0'C, and explanation 2, requiring a -100 'C gradientis, therefore,implausible.It
appears,therefore, that the only viable explanation for
the temperature depressionof the solidus and the existence of a melting interval is that the melt is partially
dissociatedinto SiOr, SiO (and possibly Si), and oxygen,
where oxygen may combine with ambient H, to form
water. Sosman(1965) suggested
that addition of 5 wto/o
Si to SiO, might result in a > 100 "C liquidus depression
on this join, which is in general accord with results of
maki and Roy, 1959) indicate, however, that about 5 wto/o preliminary experiments on this join shown in Table 4.
The suggestedpartial dissociation of SiO, in the melt
AlrO, is required for a 100 'C liquidus temperature
is also consistent with the magnitude of the change in
depression along the join at I bar. There is no other
slope ofthe vaporous curves when liquid appearson the
chemical contamination of the system, and this explaregressionofthe vaporvaporous(Fig. a). Least-squares
pressuredata for liquid SiO, (Fig. 5) obtained with Mo
Teele 3. Chemicalcompositions,SiO, system
containersresultsin the expression
P H " : 1 . 8 x 1 0 - 4b a r ,
1670.C
r:
Cristobalite
Si
AI
Mg
Total
JI
AI
Mg
U
47.51
0.20
001
53.74
1 0 1. 1 6
P " . : 1 . 8 x 1 0 - 1b a r ,
7: 1650.C
Cristobalite
46.83
0.16
0.00
53.03
100.03
47.13
0.16
0.00
53.19
100.73
Atomic proportions (O : 2)
1.006
0.006
0.000
2.000
1.006
0.006
0.000
2.000
1.013
0.006
0 000
2.000
47.35
0.18
0.00
53.33
100.86
1. 0 1 3
0.006
0.000
2.000
l n P " : ( - 5 0 0 1 | + 6 2 1 6 / 7 )+ 1 4 . 2+ 3 . 2 . ( 1 2 )
results,SiO"-Sisystem
TneLe4. Preliminary
Run no.
2882'
2883.
2892*
2894*
Starting
material
T
fC)
1Si 3SiO,
1Si gSiO,
1Si gSiO,
1Si gSiO,
1624
1624
1002
1669
P
(bar)
1.0 x
1.0 x
9.0 x
9.0 x
10 e
10 I
10'a
10 8
Time
(min) Phases presentt
24O
90
24O
90
Cr
Cr
Cr
Cr
+
+
+
+
2liquids
liquid
SiO
liquid
. SealedPt containers.'* Mo Knudsencellswith H, as pressuremedium.
t Cr : cristobalite.
MYSEN AND KUSHIRO: MgO-SiO,-H, AND THE PRIMITIVE SOLAR NEBULA
10-r
225
si02-H2
o
E
--)
U I.\J,
L*V
175
\Z
10 - r
(n
Cr*L'V
si02
I600'c
125
(('
L
-tz
-l
-i0
-9
-B
-7
-6
1o - s
-o
/l
Tr*V
q.)
L
f
a
W-WO2
o
550
o
o_
I 0-6
o
E
Mo+MoO2
--)
Y
500
-
1o - 7
si02
16 0 0 ' c
-B
12 -11 -10 -9
log fo2
-f
-6
Fig. 6. Enthalpy and entropy ofvaporization (A11"and A,S",
respectively)of silica at I 600 "C as a function of oxygenfugacity
(f",).
The ambient Pr, in the experiments used to obtain the
coemcientsin Equation 12 ranged from 1.8 x l0 8 to
1.8 x l0 o bar. In this Pr, range,no effectof the ambient
pressureon the observedvapor pressureswas observed.
The enthalpiesand entropiesof vaporization,derived
from the data in Figure 3, are shown in Table 5. The
differencesbetweenA,FI"and AS" for the Cr = V and the
L + V curves,are the enthalpiesand entropiesassociated
with the melting and other possible processessuch as
partial dissociationof SiO, in the liquid, for example (see
alsobelow for further discussionofthis possibility).Both
values[-72 kJ/mol and -37 J/(mol.K)]are significantly
greater than the enthalpy and entropy of fusion of cristobalite at I bar [8.9 U/mol and 4.5 J/(mol.K), respec-
TneLe5. Thermochemical
data
Reactiont
Container
AH" (kJ/mol)
AS" [J/(K mol)]
sio,
sio,
sio,
sio,
x,v
x,v
x,v
L,v
Mg,SiOo
MgrSiO4
Mg,SiOo
MgO
X,V
X,V
L,V
X,V
W
Mo
C
Mo
C
Mo
Mo
Mo
478 + 123
484 + 43
572+41
416+ 52
667 + 206
640 + 36
550 + 110
321+32
143 + 68
155 + 25
224+23
1 1 8+ 2 6
241 + 110
21O+ 54
179+ 54
63+17
Material
. ReactionX,V denotes evaporationof crystallinematerial.ReactionL,V
denotes evaporationof liquid
I O-8
r 400
1s 0 0
I 600
oC
Temperature,
17 0 0
18 0 0
Fig. 7. Pressure-temperaturephase relations in the system
SiOr-Hzat diferent oxygenfugacities(asindicated on the figure).
The pressure axis is total pressure (silicate vapor pressure +
hydrogen pressure).In experimentsalong the vaporous, the silicate vapor pressureis approximately equal to total pressurebecauseP", is one or more orders of magnitude less than the silicate vapor pressure. Note that although there must be an
additional phasefield betweenthe Cr + L + V and V fields, this
is not indicated becauseof lack of experimental information.
tively; Richet and Bottinga, 19861.The Ail and A,S of the
reaction (Robie et al.. 1978)
V2O2+SiO+SiOu,
(l 3)
are about -780 kJlmol a\d244 J/(mol'K), respectively.
Although the thermodynamic data for Equation 13 are
for crystalline materials, it would seem that partial dissociation of SiO, in the liquid would more readily account for the differencebetween A,Il and AS from Equations 9 and 12 than simply those associatedwith melting.
The use of graphite capsulesrather than Mo or W results in a lowering of the /o, of between three and four
orders of magnitude.This/"2 reduction resultsin the 190/o
increasein the slope ofthe vapor-pressurecurve and also
a changein the intercept(Fig. 3; seealso Eqs.9-l l). This
changein slope, expressedin terms of LH" and AS" (Fig.
6), results in a significant increasein both enthalpy and
entropy [from 480 to 570 kJ/mol and 155 to 224 J/(mol'
K), respectively].These increasesare consistentwith increaseddegreeof dissociation of SiOy" to SiOu* + O9*.
From the thermodynamicdata of Stull and Prophet( I 97 1),
complete dissociation of SiOry would result in a I l0 kJ/
MYSEN AND KUSHIRO: MgO-SiO,.H, AND THE PRIMITIVE SOLAR NEBULA
-t5
M g o- H 2
-20
-1?
-19
o
.
I
c
-
a Mo container
O C container
l n P i t " r = - 7 7 9 5 5 ! 14 9 5 5 * 2 7 . 7 t 2 . 6
-12
-11
-10
M g 2 S i 0 -4 H 2
-17
ln Pu = -3_951633991* 76 t 2 1
G
o
5.0
5.5
1/ T x r 0 4 ( -K1 )
6.0
(P")of crystallineMgO (periclase)
Fig. 8. Vaporpressure
as
(Mo samplecontainers).
a functionof temperature
-to
o->
c
-14
-1<
-tz
mol increasein A.FI".Within the uncertainty of the data
reported here, the calculated changeis similar to the observed value. It appears,therefore, that the reduction of
/o, from that of Mo-MoO, (or the lessaccuratetungstentungstenoxide buffer) to that of the C-CO-CO, bufer may
have resulted in substantial,perhaps complete, dissociation of SiOy' to SiOg"'+ OF". Further dissociation to elemental Si is likely only if a significant proportion of the
gasspeciesformed in equilibrium with the Mo-MoO, oxygen buffer include SiO and Or.
From the thermodynamic data summarized in Table
5, a phase diagram for SiO, as a function of pressure,
temperature,and oxygenfugacity is suggested(Fig. 7). In
constructing this diagram, it was assumed that the A11
and A,Sof melting derived from the results with the MoMoO, buffer are not significantly affectedby the lowering
of fo, to that of the C-CO-CO, buffer. The reduction of
the oxygen fugacity has a very substantial influence on
the minimum pressurebelow which liquid cannot exist
in this system (about 2.5 orders of magnitude). This differenceis a consequenceof the paftial (or complete?)reduction of SiO, in the gas to SiO and O, and perhaps
even Si.
The system MgO-H,
The vapor pressuresabove crystalline MgO under appropriate temperature-oxygen fugacity conditions are
neededin order fully to characterizethe phaserelations
on the join MgO-SiO, even though periclase itself may
not have been an important phase in the petrogenetic
history ofthe early solar nebula.
Becausethe oxygen fugacities necessaryto dissociate
MgO to Mg and O, (Lou et al., 1985)are far below those
attainable with the experimental design used here, the
vapor pressuresabove MgO were determined only with
Mo containers (Fig. 8; see also Table 2). Furthermore,
this /", is so low that equilibria involving oxygen and
metallic Mg are not relevant to petrogeneticprocessesin
the early solar nebula.
-11
4.6 4.8
s.0
s.2
s.4
s.6
5.8 6.0
1lf x 101(K-1)
Fig. 9. Vapor pressureof crystalline forsterite (P") as a function of temperature with Mo (filled circles) and C (open hexagons)containers.
The vapor-pressure data were fitted to a straight line,
ln P" : (-38676 + 3881/D + 7.6+ 2.1,
(14)
with the derived enthalpy, entropy, and free energy of
evaporation shown in Table 5. The free energy of evaporation from Equation 14 at 1900K, for example,is 202
kJ/mol as compared with 250 kJlmol as calculatedfrom
the JANAF tables(Stull and Prophet, l97l). The AG" for
the reaction
MgQ^,ut: Mgt^ + OF'
(15)
at the sametemperatureis774kl/mol. This much higher
value thus lends further support to a suggestionthat in
these experiments, most likely periclase evaporates to
MgO gas.
The system MgrSiOo-H,
Evaporation behavior and phase relations in the system MgrSiOo-H, are shown in Figures 9-l I with experimental resultsin Table 2. Sataet al. (1978) suggestedthat
forsterite might evaporate incongruently to periclase *
vapor. Despite extensive search and very long experimental run duration (Table 2), no evidence for the proposed incongruencywas found. The forsterite is pure or
nearly pure (Table 6) Mg,SiOo with no evidence of significant contamination from the furnace(Al from the furnace tube or Mo from the sample container) as would be
expectedbecauseof the many orders of magnitude lower
vapor pressuresof Mo and Al (or AlrO.) (e.9., Jones et
aI., 19271,
Stull and Prophet, 1971)comparedwith those
of forsterite.
MYSEN AND KUSHIRO: MgO-SiO,-H, AND THE PRIMITM
I O-2
forsterite
TneLe6. Chemicalcompositions,
Mg2Sio4-H2
FlMocontainer
10 - J 6- c container
a W container,
P".(bao: 1.8x10-t
1500
r (€):
iotr
1o - 1
o
o
a
SOLAR NEBULA
I O-s
o
L
sio,
1.9x10'
1769
1.3x107
1746
41.74
0.94
57.94
100.62
42.81
0.84
57.96
101.61
Alroo
Mgo
Total
41.56
0.58
58.48
100.62
Si
AI
Mg
(O : 4)
Atomicproportions
0.969
0.973
0.016
0.027
2.035
2.016
0.988
0.023
1.992
c
I O-6
I O-7
ivine (Table 2). The temperature of the onset of melting
is 170-190 "C below the suggestedliquidus temperature
I O-8
of forsteriteat lbar (1890 + 20 "C; Bowenand Andersen,
1e002000
r 400r s00r600
l9l3: Bowen and Schairer,1936)where forsteritemelts
J.tT"lq.
congruently. The 1870 oC phase boundary between forFig. 10. Pressure-temperaturephase relations in the system sterite * liquid + vapor and liquid + vapor (Fig. l0)
MgrSiOo-H, at different oxygen fugacities (as indicated by difaccords, within experimental error, with the suggested
ferent symbols in the figure). The pressureaxis is total pressure
l-bar liquidus temperature for forsterite (note, however,
(silicate vapor pressure f hydrogen pressure).In experiments
that
the l-bar liquidus temperature of forsterite is an expressure
is approximately
along the vaporous, the silicate vapor
value from data along the joins MgrSiOotrapolated
equal to total pressurebecauseP", is one or more orders of
MgrSiOo-SiOr).
Fe,SiOo
and
pressure.
magnitude lessthan the silicate vapor
Closed symbols,
The phaserelations in the systemMgrSiOo-H, (Fig. 10)
no liquid present;half-open symbols,liquid and crystalspresent;
open symbols,liquid and no crystalspresent.Note that although are topologically similar to those of the system SiO2-H2,
there must be an additional phase field between the Fo + L +
in which case there is a melting interval between 1600
V and V fields, this is not indicated becauseof lack of experi- and 1700 oC where cristobalite coexists with liquid and
mental information.
vapor. As for the silica system there is no evidence of
contamination and thermal gradientswithin the furnace,
and it is suggested,therefore, that the melting interval is
The vapor pressure above crystalline forsterite was dethe result ofpartial dissociation ofsilica in the liquid and
termined as a function of temperature in Mo and C conthe system is MgO-SiOr-SiO-O, rather than MgrSiOo.It
tainers (Fig. 9), but within experimental uncertainty (5should also be noted that the topology ofthe diagram in
100/o),no effect of different container material could be
Figure l0 also requires an additional phasefield between
discerned. Linear regression ofall the data points results
that offorsterite + liquid * vapor and that ofvapor only.
in the expression
This field has not beendetectedexperimentally,however,
and is not included in the figure.
l n P " : ( - 7 7 9 5 5 + 4 9 5 5 / D + 2 7 . ' 7! 2 . 6 , ( 1 6 )
Two vapor pressure-temperaturecurves in the temwith the entropy and enthalpy of evaporation derived perature range of liquid have been determined (Fig. I l).
from Equation 16 in Table 5. The absenceof discernible There is a steepcurve that is defined by the weight-loss
fr-dependence differs from the behavior of pure SiO, data at an imposedP", of 1.8 x l0-8 bar,
(Fig. 3), where a 190/oincreasein the At1" was observed.
tn P" : K- 185390 + 14365)/71+ 82.7 ! 7.2, (r7)
This difference in behavior most likely results from the
fact that the mole fraction of SiO, in the MgrSiO4system and there is a curve with a much less steepslope at P"" :
is 0.333. Becauseonly the SiO, component in the gas 1 . 8 x l 0 a b a r ,
phase undergoesreduction with decreasing/o, resulting
l n P " : l ( - 6 6 r 7 3 + 1 3 3 4 2 ) / 7 1+ 2 t . 5 + 6 . 6 . ( 1 8 )
in a l9o/oincrease in the slope of the SiO, evaporation
curve, only about a 60/oeffect would be expectedin the The curve defined by Equation 17 correspondsto A,F1":
MgrSiOo system. A 60/ochangein slope and intercept is 1540 kJ/mol and AS, : 687 J/(mol'K). This curve is
within the uncertainty of the MgrSiO4vapor-pressuredata physically implausible becauseit implies that the heat of
in Figure 9.
evaporation of MgrSiOo liquid is 2.4 limes greater-not
Small amounts of interstitial melt were detected at less-than that of crystalline forsterite at the same temtemperaturesnear 1700 'C (Fig. l0). The liquid does not perature. This behavior may be related to the fact that
quench to glass,but exists as fibrous, quench forsterite the ambient pressureused during acquisition of the data
along grain boundaries to temperatures near 1870 'C, behind Equation l7 is significantly less than the vapor
where the experimental chargesconsist ofall quench ol- pressureitself. Melt near forsterite composition is very
l0
MYSEN AND KUSHIRO: MgO-SiO,-H, AND THE PRIMITIVE SOLAR NEBULA
-14
-13
P H z = i . 8 x 1 o - 4b a r t
l n Pv - . = - 6 6 1 7 3 t 1 3 3 4 2* 2 1 . 5 t 6 . 6
T
=
1
.
8
x
.
|
0
8
PHz
bar:
ln P = -185390t14565 * 82.7t7.2
-12
-11
8 x 10 - a b a r
t(U
-o
u-
-10
\
c
-9
-8bar
(1)
\r
-8
MgzSi0l
H2
Q)
-7
4.s
4.6
4.7 4.8 4.9 5.0
1/T x 104(K-r)
s.1
s.2
Fig. I l. Vapor pressurecurves in the ternperatureregime of liquid present in the MgrSiO4system at two different PH2values as
indicated. Note that whereascurve I was obtained with P", > P", curve 2 was determined with P", . P".See text for detailed
discussionof the relationships.All experimentswere conductedwith Mo containers.
fluid (on the order of I poise or less at these temperatures). This environment is, therefore,conducive to boiling, in which casethe weightJoss determinations can be
too high by severalorders of magnitude (Centolanzi and
Chapman,1966).This phenomenonmay explainthe implausiblyhigh valuesof the coefficientsin Equation 17.
The other curve in Figure I I (Eq. 18) resultsin slightly
smaller values of AI1" and A,S"than for crystalline forsterite [640 and 550 kJlmol and 2 I 0 and l] 9 J/(mol . K),
respectivelyl. The latter two sets of data correspond to
AfI, and AS- of 90 kJ/mol and 3l J/(mol.K), respectively, at the temperature of onset of melting (1700 "C).
Values for enthalpy offusion offorsterite have been suggestedin the range 7 | to 235 kJlmol (Stull and Prophet,
l97l;Bottinga and Richet, 1978)with most valuesnear
the lower end ofthis range. The value derived from the
vaporization curve defined by Equation l8 also falls in
the lower part ofthis range.This curve is, therefore,consistent with available thermodynamic data.
DrscussroN
Isothermal and isobaric sections
From data presentedabove as well as data for thejoin
MgSiOr-H, (Kushiro and Mysen, 1987),partly schematic, isobaric, isothermal sectionsin the systemMgO-SiOrH, have been constructed (Figs. 12, l3). As discussed
above,neither the liquid nor the vapor compositions may
be describedwithin this system,and in the absenceof all
but qualitative inferenceson this subject, these considerations are left out. The portions of the system where
this situation may afect the topology of the sectionsare
dashedin Figure 13.
The molar ratios of hydrogen to oxide corresponding
to some of the phasechangesare shown as Xrr/X*"o, elc.
Those ratios were calculated from the thermodynamic
data summarized in Table 5 under the assumption that
the gas phasecan be treated as an ideal gas.None ofthe
ll
MYSEN AND KUSHIRO: MgO-SiO,.H, AND THE PRIMITIVE SOLAR NEBULA
P=I 0-6 bar
Weight percent
- | 450"C
X,H.
-sxro.
Xngo
X'r'
- z . l s *t o ,
e+v
llgO
Xg251Oq flgSi03
o+v
5 i02
5 i02
F o * E n *V
< | 3000c
- | 300oC
P e * F o +V
MnA
1 1 g 2 5 r Of4l g S r O g
5i o z
llgO
H g 2 5 i O 4m g S i O 3
5 i02
Fig. 12. Isobaric (1.0 x 10-6 bar), isothermal(1625, 1450, 1300, and <1300'C), partially schematicsectionsof the system
MgO-SiOr-Hr. Note that the individual joins are not to scalein order better to illusfiate the relationships. The ratios XHz/XMeo,
etc., representthe moles ratios ofhydrogen to oxide indicated in the vapor at the intersection ofa particularjoin and a vaporous
curve.
joins are drawn to scale in order to better show the relations.
At a total pressureof 1.0 x I 0-6 bar, liquid is not stable
in the system MgO-SiO, and periclase is the first phase
to condensefor compositions frsm MgO to somewhere
between MgO and MgrSiOn. The exact value of X.rol
XMg2sioa
is not known. For all phasefields, the hydrogen/
oxide ratio governs the phase relations at constant temperature and pressure.For periclase,forsterite, and silica
compositions, the only phasefields in question are those
of oxide + vapor and vapor becausethese phasesevaporate congruently.In those cases,evaporation can be accomplished isothermally and isobarically by increasing
the hydrogen/oxide ratio. The behavior of these phases
contrasts,however, with enstatite, which evaporatesincongruently(Sataet al., 1978;Kushiro and Mysen, 1987;
seealso discussionbelow). At 1450 oC,for example (Fig.
l2B). in the absenceof H,. enstatite (or clinoenstatite)is
MYSEN AND KUSHIRO: MgO-SiO,-H, AND THE PRIMITIVE SOLAR NEBULA
tz
P=10-t bar
Weight percent
.t.n'o'
Jtt
^Hgo
\
Mgo
|
',.i{!lHill\l
IL[1,-:Y-l-tt
t"*t'rnrrioq
Mgsio5t
c
MgSior
I 625'C
XHz ^,rxto,
L cr.tMg2sio-{/LHBsios
M g 2 5 i o l/ M g S i 0 3
p-'.r.,ot
Illz-^,sxroa
^Mgo
Pe*Fo*V
Mg2SiO{MgSiO5
Pe*Fo*V
M g 2 S i O qM g S i O g
si02
resultsin the appearancefirst
stable.IncreasingXrr/ X",,,"u,"
of forsterite followed by the disappearanceof enstatite
and, finally, the disappearanceofforsterite as well.
The phaserelationsat a tolal pressureof 1.0 x 10-'
bar (Fig. 13) are more complex becauseliquid is also
stable. Becausethe liquids may be partially dissociated
into reducedsilicon oxide components,the liquid-present
fields in Figure 13 are dashed.These dashedtie lines are
meant for illustrative purposes only. In this figure, the
narrow field near the MgO-SiO, join is marked "Liquid."
This field is included becausesome H, dissolves in the
liquid (see also Luth and Boettcher, 1986; Luth et al.,
1987, for discussionof H, solubility behavior in silicate
melts), thus resulting in a vapor-absentfield.
In the absenceof Hr, vapor along all but the MgO-H,
join will condenseto liquid prior to crystallization at l0-3
bar. Increasinghydrogen/oxide results, however, in
shrinkage of the liquid fields and their eventual disappearance.This feature is further illustrated in Figure 14,
showing the minimum pressurebelow which liquid is not
stable in the systems SiOr-H, (A) and MgrSiOo-H, (B).
Silica data from both Mo-MoO, and C-CO-CO, are shown
(Fig. laA), illustratingthat decreasingoxygenfugacity results in shrinking pressure-temperaturestability of liquid
silica.
The data in Figure I 3 also show that increasinghydrogenloxide ratio in some casescan result in solidification
of liquid (Fig. l3D). At temperaturesnear 1550'C, for a
rangeof compositionsbetweenMgrSiO. and Mg/Si slightly
greaterthan I (MgSiO, composition), either forsterite *
liquid or liquid only (dependingon the Mg/Si) are stable.
By diluting the vapor with Hr, forsterite and vapor will
be stabilized together with the liquid. The width of this
field rangesIo Xrr/X,,,,.onnear 1000 for the most siliceous
compositions. As even more H, is added to the system,
the liquid will solidifu with the formation of forsterite
coexisting with a more magnesianvapor than that coexisting with both liquid and forsterite.
Isobaric, polythermal sections
From the AH" data derived from the vapor-pressure
curves in Figures 3 and 9 combined with similar data for
MgSiO, bulk compositionby Kushiro and Mysen (1987),
the vaporous phase relations on the join MgrSiOo-SiO,
can be calculated as a function of temperature, oxygen
fugacity, and hydrogen/silicateratio (Fig. l5). Becauseof
the uncertainty regardingthe possibledissociation ofsilica in the vapor phase,the compositions are not strictly
on the join MgrSiOo-SiO2,but the diagrams accurately
depict the relationships ofthe silicate phases.
13
SOLAR NEBULA
MYSEN AND KUSHIRO: MgO-SiO,-H, AND THE PRIMITM
lo0
sio2-H2
I O-r
Cr*L.V
v tn-2
c-co-co2
o
i
l l
o
i
/
Vo_UoO2
to-1
Cr.V
g-s
L10u
1n - 6
A
1Or l02 IOJ 101 1os
x H 2 l xs i l i c a t e
100
Mg2si04-H2
1o - r
L
1n-2
F O * LV
T
9= 10-r
o
c
tu
r n-5
'"
tO0 1Ol 102 lOJ l01
lOs
of liquid stabilityas a function
Fig. 14. Minimum pressure
of mole fractionof H' in the gasphasefor SiO, (A) at oxygen
indicatedand for Mg,SiO.(B).
fugacities
The diagrams (Fig. 15) were constructed as follows.
The temperatures of the vaporous of the end-member
compositions are from the experimental data. The topology of the phase boundaries between forsterite + vapor
and vapor and between silica * vapor and vapor is calculated from the Van't Hoff equation,
TE: l/l(l/TJ - (R ln X,/A'H")1,
(19)
where 7u is the temperature (K) of the vaporous at mole
fraction X, of component i, To is the vaporous temperature ofthe pure phase,R is the gas constant, and AI1" is
the heat of evaporation. Equation 19 is a simplification
as it does not take into account dissociation in the vapor
phase. The principal consequencefor the vaporous diagrams of this simplification is that the forsterite vaporous
surfaceswill exhibit slightly less curvature in temperature-composition spacethan would otherwisebe the case.
The join MgrSiOo-SiO, includes enstatite, which has
ts
Fig. 13. Isobaric(1.0 x l0-3 bar), isothermal(1900, 1800, 1625, 1550, 1525,and 1300"C), partially schematicsectionsofthe
systemMgO-SiOr-Hr. Note that the individual joins are not to scalein order better to illustrate the relationships.The ratios X^r/
X"ro, etc., representthe molar ratios of hydrogen to oxide indicated in the vapor at the intersection of a particular join and a
vaporous curve. Dashed phase fields representcompositions where most likely the composition of the liquid phase is not within
the ternarv svstem.
MYSEN AND KUSHIRO: MgO-SiO,-H, AND THE PRIMITIVE SOLAR NEBULA
A
been shown to evaporate incongruently to forsterite +
silica-rich vapor (Kushiro and Mysen, 1987) along a line
definedby the expression
P = l0 - s b a r
c-co-co2
(J1600
l n P , : [ ( - 6 8 9 0 8 + 8 7 7 3 ) / 7 1 +2 4 . 3+ 5 . 0 . ( 2 0 )
There is, thus, a compositional rangealong the join where
clinoenstatite(or possibly protoenstatite)is the vaporous
phase. Note, however, that becauseof uncertainty in
structural characteization of the MgSiO, phase,this phase
is simply referred to as enstatite (En). The compositional
range extends from the intersection of the univariant
equilibrium clinoenstatite + forsterite + vapor with the
forsterite vaporous to the intersection with the silica vaporous(Fig. l5). The slopeofthis vaporousis calculated
from Equation 19 with the AfI" value (572 kJlmol) from
the least-square-fittedexpression(Eq. 20) (Kushiro and
Mysen, 1987).
As can be seenin Figure 15, forsterite is the dominant
vaporous phase in the system MgrSiOo-SiO, under all
conditions investigated.Clinoenstatiteappearson the vaporous near 82 molo/oSiOr, with a clinoenstatite-cristobalite eutecticat about 93 mol0/oSiO, at 1508'C. The
vaporous surfacesofthe individual phasesin this system
are distinct, but different functions of P",/P.,,,"","in the gas
phase:
c
o
J
|g
b
rsoo
ct
E
o
F
,,,lSiOZ'V
1.t00
0
.t0
20
80
Mg25iOlMgSiOg
80
100
si02
mo l g
M o - M o O '2 P = 1 0 - eb a r
B
=0
ft2 /Ps111s616
I 600
(J
o
o
J
|E
1s00
lftatttarlrtrt
\\\\\\r
T:
t
sio21v:
i1;1;1i1i1j1;
o
ct
E
o
En*sioz l;l1l;l;
;l:
r'*..--r;.\'\'\'.'
\ f\t\t \t f\t\t \t t\t\t \t l\ \ \
I 400
f
f.t
I
20
40
M 9 2 S i o qM g S i O s
0
I
4, I
E0
a
a
I
t
E0
t
I
100
SiO2
mol tr
c
M o - M o O 2$,
,l=10-
=I
/P3111s61e
()
a
o
5
1200
G'
o
6.
E
o
F
(21)
where Xr, is the PrrlP.,,,"",.and P,., is the total pressure.
With XH, : lOa(Fig. l5C), the forsteritevaporoustemperature is lowered by about 300 'C, the forsterite-enstatite peritectic by about 340 "C, the silica vaporous by
about 390'C (wheretridymite is now the vaporousphase),
and the tridymite-enstatite eutecticby about 390'C compared with the H.-free vaporous surfaces.Notably, the
temperature range over which both forsterite and enstatite occur on the vaporous is wider with the diluted gas
phasethan in the absenceof Hr.
As discussedabove, an effect off, on the slope of the
vaporous could be discerned,within experimental uncertainty, for pure SiO, (Fig. 3 and 9). Thus, at given pressure, both the vaporous temperature and the heat of
evaporation of SiO, (regardlessof whether this is cristobalite, tridymite, or liquid) are affected.The influence of
these changeson the vaporous relations along the join
Mg,SiOo-SiO,is illustratedin Figuresl5.A and l58 for a
total pressureof 1.0 x l0 6 bar. At this pressure,the
most dramatic effect of reduction of /", (by about 3 log
units) is in the vaporous temperature(seealso Figs. 3 and
\\\a\\r
ffltttttttaatl
F
AH"/\LS" - [R ln(P,.,/(l + X",)]],
I 100
F
rV
I 000
02040
Mg2SiOl MgSiO5
60
mols
80
100
SiO2
Fig. 15. Temperature-composition relations along the join
MgrSiOo-SiO,at total pressure= 1.0 x l0 6 bar in a Hr-free
atmosphereat thefo, of the C-CO-CO, buffer (A), and at thefo,
of the IUo-MoO, buffer (B), both in a Hr-free atmosphere,and
at the fo, of the Mo-MoO, bufer with hydrogen/silicate: 10a
(C). The hachured area in Figure 15C is presentedin the insert
to show detail.
15
MYSEN AND KUSHIRO: MgO-SiO'-H, AND THE PRIMITIVE SOLAR NEBULA
9). As a result, the SiO, phase is tridymite (rather than
cristobalite), and the compositional width of the tridymite vaporousis lessthan 1 molo/owith an enstatite-tridymite eutectic temperature near l4l0 "C andfo, at the CCO-CO, buffer compared with the cristobalite-enstatite
eutecticnear 1510"C andforat the Mo-MoO, buffer.As
a result of this temperature depression,the enstatite vaporous surface is significantly wider (82-99 molo/oSiO'
for the
of the C-CO-CO, oxygen buffer and 82-94
"f",
molo/oSiO, for the /", of the Mo-MoO, oxygen buffer),
and the temperaturerange over which enstatite will condensefrom a gas phase has increasedfrom about 20 "C
at the highest"fo,Gvto-MoO,; seeFig. l) to about I l0 'C
at the lowestf, (C-CO-CO,;seeFig. l).
On the Mg.SiO.-MgO join, the phaserelations are controlled by a simple eutectic between periclase and forsterite becauseboth phasesevaporate congruently. The
position of this eutectic is, however, quite sensitive to
total pressureand dilution of the gas phase becauseof
the large differencein AH" for the two phases(seeTable
5). These effectsare illustrated in Figure 16. Increasing
Psr/P"i1;"or"results
in very rapid expansionof the forsterite
vaporousfield at the expenseofpericlase(Fig. l6A). Conversely, with constant PH2/P"it'.u.
or with no H, presentat
all (Fig. 16B), a very strong pressureeffect is observedas
decreasingpressureresults in rapid expansionofthe forsterite vaporous field. As a result of thesetwo effects,the
eutectic between forsterite and periclasewith P"r/P.,,,.u..
appropriate for the solar nebula (e.g., 10"), the mole percent MgO at the eutecticis very low (0.19 molo/oat P,",:
1.0 x 10-o bar, 1.9 molo/oat 1.0 x l0 3 bar, and 7.9
molo/oat 1.0 x l0-, bar).
Appr-rclrroNs
Stability of liquid silicate
Determination of the pressure-temperature-composition trajectories of liquid silicates in the solar nebula is
important becausecrystal-liquid equilibria will result in
different chemical trends compared with vapor-crystal
equilibria. Textural evidence from chondrules and also
some inclusions in chondritic meteorites point to the existence of liquid at some stage(s)during the time of formation of these materials (e.g.,Wood, 1963; Wasson,
1972;Grossman,1980;Dodd, l98l; Nagahara,1981).
In the MgrSiO4system(Fig. l4), liquid is stableto L0 x
l0-s bar at 1700'C. Below 1.9 x l0 5 bar, crystalline
forsterite will condensedirectly from a gas of forsterite
composition. In a more realistic environment with Mg/
Si : I (MgSiO,), liquid is stableto lower pressures(2.0 x
10-6 bar) at about 1550 "C (Kushiro and Mysen, 1987).
Mysen et al. (1985) found that for CaMgSirOucomposition, liquid will condensefrom the vapor down to pressuresnear I x l0 7 bar ar I 385 'C. Important ferromagnesianmineralswould not condensedirectly from an early
solar-nebula gas that contained only metal + oxygen
components (no dilution of the gas phase with Hr, for
example). Liquid would form first, and the crystalline
materials would form upon cooling of this liquid.
f l g O - 1 1 g 2i O
S4 e u t e c t i c
l024
3
ar
P 1 e 1 = 5 x 1 0b- b
to2
iol
ri
too
0
Fo*PerV
0
20
flgO
4A
60
mol %
80
100
r q ? Si 0 4
to-s
-o
lo-5
o)
=
a
L
io-7
a
c)
No lrudrogen
L
L
Io-8
a
2a
40
60
B0
100
f1g2SiO4
l'1qO
mot )6
eutectic
Fig. 16. The compositionofthe periclase-forsterite
ratto
asa functionof hydrogen/silicate
on thejoin MgO-MgrSiOo
(A) at 5 x 10-6bar total pressureand as a functionof total
(B).
pressure
in a H.-freeatmosphere
The nebular gas most likely had, however, P"r/
near l0a. The total pressurebelow which liquid
Po*iae+merar
is not stable increasesrapidly as the gas phaseis diluted
by H. so that at 1.9 x 10abars,the triple point is near 2
x l0 2 bar for enstatite composition (Kushiro and Mysen, 1987).For SiOr, the pressureof the triple point dependson fo,(Fig. 14A) and occursbetwe"n 1'g x l0-'
and l:0 x l0-2 bar. As discussedabove, this oxygenfugacity effect diminishes in importance with decreasing
SiO, content of a system.The pressureof the triple point
in the MgrSiO*-H, systemis about 5.0 x l0-z bar (Fig'
l4B) and is insensitive tof, within the experimental uncertainty. From the experimental data of Mysen et al.
(1985),the tripte point for diopsidecompositionwith P",/
: 10ais about 2.0 x l0 2 bar, thus resembling
P.nrr.,rou
pressure
for MgSiO' composition. The textural evithe
dence for liquid having existed during formation of at
leastportions of chondritic meteoritesrequires,therefore,
that under equilibrium conditions, pressuresmust have
been equal to or greater than l0 2 to l0-' bar. Alternatively, melting may not have been an equilibrium process.Blander and Katz (1967) suggestedthat metastable
tiquid could form directly from a gas below the solidus
and vaporousof minerals.Mysen et al. (1985) and Kushiro and Mysen (1987) in their melting and evaporation
experimentsin the systemsCaMgSirOr-H, and MgSiOrHr, respectively,noted that liquid apparently formed almost instantly at pressure and temperature conditions
corresponding to the vapor regions for those compositions. This liquid evaporated quite rapidly under such
conditions. For CaMgSitO, compositions, evaporation
ratesin the vapor stability field were on the order of 10-3
t6
MYSEN AND KUSHIRO: MgO-SiO,-H, AND THE PRIMITIVE SOLAR NEBULA
Io-"
P,o,=10
bar
PH .etat*orygen=1
o
2/P
3 ro-'
I
-a
rn-s
Fe metal
l0-'
10 - 5
Io-.
1.ox1o-8
/835"C
1.Bi1o-s/805"c
XFo
Fig. 17. Mole fractionof MgrSiOocomponent(X".) of the
forsterite-Fe
metaleutecticon thejoin Fe-MgrSiOo
asa function
of total pressure
in the absence
of Hr. Thermodynamic
datafor
Fe from StullandProphet(1971).
Forsterite
'€nstatite
MgrSiOo MgSiOa
g/(s.cm'z)in the vapor stability field, whereasthe evaporation rates at similar temperatures but at pressureswhere
liquid or crystalline diopside was stable, the rates were
on the order of l0-8 g/(sec.cmr).Similar observations
were made for the MgSiO.-H, system. Quenchedglasses
obtained from experimentsof I to 2 min in the pressure
range l0-e to 10-8 bar showed extensivetextural evidence of bubble formation. Melting of precursor materials by, for example, lightning or impact (see, for example, Wood, 1967; Nagahara,l98l) could, therefore,
occur at pressuresand temperatureswell within the vapor
stability field of the materials. In order to preserve the
liquid, these melts could only have experienced these
temperature conditions for periods on the order of minutes. This order of magnitude for the time of melting
accordswith experimental results on Na evaporation from
chondrule-likespheresby Tsuchiyamaet al. (1981).
Fractional condensationand chemical trends in the
solar nebula
The rangein compositions where forsterite is a vaporous phasein the MgO-SiO, systemwas quantified in Figure 15. Those resultsindicate that forsterite is the vaporous phaseover the entire rangeof Mg/Si suggestedfor the
solar systemfrom the composition ofcarbonaceouschondrites (e.g.,Larimer and Anders, 1970; Wasson, 1974;
Van Schmusand Wood, 1967;Mason,1976), regardless
of total pressureand hydrogen/(oxide + metal).
In view of the fact that the solar Mg/Si is near I and
the forsterite MglSi is 2, condensationof forsterite shifts
the Mg/Si of the residual gasphaseto values lessthan l.
The Mg/Si of carbonaceouschondrites rangesfrom 1.04
to 0.93. Limited forsterite fractionational condensation
or, perhaps, simple equilibrium forsterite condensation
may have resulted in this variation in Mg/Si. Enstatite
chondrites have Mg/Si averagingnear 0.78 (e.g.,Wasson,
1974).This lower Mg/Si ratio is consistentwith a process
of formation that involves significantly more pervasive
fractional or equilibrium condensationof forsterite compared with that required to explain the variations in Mg/
Si in carbonaceouschondrites. In these proposed processesof chondrite formation, fractional condensation
would fractionate the Mg/Si of the residual gas more ef-
SiO2
phaserelationsnearsilicate-FemetalvaFig. I 8. Calculated
porousboundariesthat total pressureof 1.0 x l0-4 bar with
ratioat lOa.Thepairednumbers,2.9x l0-e/
hydrogen/silicate
912"C etc.,represent
molefractionof forsteritein the gasrelative to Fe at a particularinvariantpoint andthe temperature
of
this point. Note that thejoins arenot drawnto scalefor clarity
althoughthe relativepositionsofpoints (5, a-e) arecorrect.
ficiently than equilibrium condensation, as will be discussedfurther below. Fractionalevaporationis a lesslikely
mechanism to explain this trend as this would require
that the starting material (the most primitive composition) has the lowest Mg/Si and that this MglSi is lessthan
the solar abundance.
The experimental data reported here may be combined
with available thermodynamic data for Fe metal (Stull
and Prophet, 1971) to place constraintson the relative
stabilities of metallic Fe, silica, enstatite, and forsterite
during condensation in the solar nebula. The composition of the forsterite-metallic Fe eutectic in the /o, range
of metallic Fe stability is shown as a function of pressure
in Figure I 7. Those resultsindicate that regardlessoftotal
pressure [calculations with variable hydrogen/(oxide +
silicate) will not affect these relations substantiallyl, Fe/
MgrSiOoratios in the gas in the range 105to l0? are required for Fe to condensebefore forsterite in a Hr-free
environment.
Some of the principles involved in these condensation
processesare illustrated in the partially schematic vaporous diagram in Figure 18. This diagram illustrates the
overall vaporous topology in the system MgrSiOo-SiO1
Fe under most realistic pressureconditions and provides
some specific data for P,. : 1.0 x l0 4 bar wilh Prr/
: lOa. Becauseof the extreme compositional
Pmerar+o,yg",
variations in the system,the geometric representationin
Figure 18 is not correct. However, the mole fractions of
silicate componentsand temperaturesof the points d and
: l.Q x lQ-s
c (Xwezsiot:
2,9 x lO-e at 912"C,and Xsio2
at 835 "C) as well as of the reaction point, a (Xro,o, :
1.8 x l0-'at 805'C), stemfrom the presentexperimental results. In terms of realistic positioning of q and b
relative to MgrSiOoand SiO, corners, the mole fraction
MYSEN AND KUSHIRO: MgO-SiO,-H, AND THE PRIMITIVE SOLAR NEBULA
of MgrSiOocomponent relative to SiO, component at d
is about 90 molo/oand at b more than 99 mol0/0.
Figure l8 can be used to illustrate some of the consequencesoffractional and equilibrium condensation.The
bulk compositions of all chondritic meteoritesfall within
the forsterite vaporous field with carbonaceouschondrites near or slightly to the left of the MgSiOr-Fe join
and enstatite chondrites significantly to the right. The solar abundance(Mg/Si : 1.06) plots slightly to the left of
the join.
,Asin crystallization in analogoussilicate melt-mineral
systems,the position of the starting compositions relative
to enstatite is important for the phase assemblagesand
compositions of the final product. For example, a bulk
composition S will begin to condenseforsterite, and as a
resiultthe vapor composition shifts toward the forsteriteenstatite vaporous boundary (intersection illustrated as e
in Figure 18. In reality, the location ofe is on the intersection between a line from the MgrSiOocorner through
S and the forsterite-enstatitevaporous boundary). Further cooling of the system results in coprecipitation of
forsterite and enstatite until the vapor reachespoint a
wtrere Fe metal begins to precipitate and forsterite reacts
with the vapor to produce enstatite. For starting composition S on the MgSiO.-Fe join, the final phaseswill
be enstatite and Fe metal. With Mg/Si of the starting
composition greater than I (to the left of the MgSiO3-Fe
join), some forsterite will be left in the assemblageafter
final crystallization with a final phaseassemblageof forsterite + enstatite * metallic Fe. with Mg/si < 1.0, all
forsterite will be consumedat a, and further cooling shifts
the vapor composition along the Fe metal--enstatitevaporous boundary and may finally reach the eutectic, b,
where enstatite + silica * Fe metal will condenseand
only H, is left in the gasphase.
The vaporous relations in Figure l8 lead to the suggerstionthat under equilibrium condensationconditions,
compositions such as those representedby carbonaceous
chondrites or the solar abundance can change only to
po,int a. There is extensive evidence among unequilibrated chondrites,however, that the re-equilibration during cooling was not complete. Mg- and Fe-rich olivines
coexist, sometimes in near contact, in the fine-grained
matrix and where there are substantialcompositional differencesbetween the fine-grained matrix and the chondrules (e.g.,Huss et al., l98l; Grossmanand Wasson,
1982;Nagahara,l98l). The matrix is often very substantially enriched in Fe and Si over the chondrules and is
also richer than the bulk chondrite in these components.
These observationsmay be explained with the aid of the
vaporous diagram (Fig. 18) by invoking fractional condensation (either partial or complete). Under such conditions, the condensedphase (or phases)does not reequilibrate with the gas, and the composition of the gas
phase may exhibit more extreme compositional change.
If, for example, the forsterite and enstatite that crystallized betweenS and a in Figure l8 did not re-equilibrate
with the gasphase,further cooling ofa gasthat has reached
L7
point a from S by fractional condensationwill move to
the eutecticat point Dwhere enstatite,silica, and metallic
Fe will crystallize at the eutectic temperature (<800 "C)
until there is only H, left in the gas phase.
It is suggestedthat the compositional variability exhibited both within a single chondritic meteorite as well as
between different meteorite groups (e.g., carbonaceous
chondrite, enstatite chondrite, and so forth) may reflect
condensation from the early nebular gas with variable,
but incomplete degreesof re-equilibration during condensation. Chondrule materials may representthe early
stagesof this processes(e.g.,betweenS and a point between e and a in the schematicrepresentationin Fig. 18).
Chondrules also show evidence of melting that perhaps
occurred under nonequilibrium conditions (e.g., Wood,
1967; Nagahara,1981),thus further complicatingcharacterization of the petrogenetichistory of thesematerials.
The dark, fine-grained, silica- and Fe-rich matrix may
representlate condensatesrepresentedby condensation
along the Fe metal-enstatite vaporous boundary and at
the Fe metal-enstatite-silica eutectic.
Acxr.{owLrocMENTS
Critical review by R. J Arculus, R W. Luth, G. M Muncill, and C. T'
Prewitt are gratefully acknowledged.
RnnnnnNcns cltgo
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MYSEN AND KUSHIRO: MgO-SiO1H, AND THE PRIMITIVE SOLAR NEBULA
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