American Mineralogist, Volume 64, pages 77-85, 1979
Thermodynamicsof meltingof anorthitededucedfrom phaseequilibriumstudies
SrBveLuorNcroN
U.S. Geological
Suruey
Denuer,Colorado80225
Abstract
Applicationof freezing-pointdepression
theoryto experimentally-determined
meltingrelationsof anorthitein binarysystems
with silica,orthoclase,
leucite,albite,wollastonite,
and
diopsideyieldsresultswhichareconsistent
with an enthalpyof fusionfor anorthiteof 81000
J,/mol,the bestestimateof Robieet al. (1978).The calculationsare madeusingthe 8-oxygen
modelof silicatemeltssuggested
by Burnham(1975).They alsoincorporatesolid-solution
data among anorthite,quartz, and orthoclase.All temperatures
are convertedto the International PracticalTemperatureScaleof 1968.
The binary silicatesystemsstudieddo not appearto mix ideally,but theymay be described
by regular solution theory. The deviationsfrom ideal behavior are related to the ionic
potentialol the cations.
Introduction
Thus,
This study originatedin an attempt to definethe
enthalpyof fusion of anorthite by applicationof
freezing-point depressiontheory to experimental
phase-equilibrium
studies.Thesedata might then be
appliedto problemsinvolvingthe estimationof heat
contentsof crystal-melt
mixturesfor usein the delineation of geothermalenergyreserves.
Hopesfor successwerebasedin part on thesuggestion
by Burnham
(1975)that many silicatemeltsmight, by judicious
choiceof components
and standardstates,be viewed
as ideal mixtures.Subsequent
to initiation of the
project,calorimetricstudieson anorthitehavemore
closelydelineated
the boundson thepossiblerangeof
valuesfor its enthalpyof fusion.Thiscommunication
seeksto answersomequestionsabout the natureof
silicatemelts, given some known thermodynamic
quantitiesas boundaryconditions,and to showthat
the melting behaviorof a phasedoes not closely
constrainits enthalpyof fusion.
H rot - I1at"r: A11S: TASH
Q)
If a componentof compositionA is presentin a
solution,and a solidandliquid coexistat equilibrium
at any temperatureZ, the chemicalpotentialof A in
both phasesis equal,and we may write parsr: &n.r.
B u t p o 1 " y: G e r " r * R Z l n 4 a 1 s yo1o d & e r , : G ^ o + R T
ln aa11y.
Equating the last two expressions, we have:
AG-
:
RT ln (o661/as6)
(3)
A first approximation to the temperature and compositional dependenceof the enthalpy of fusion is to
assume that the heat capacity difference, ACo, between the liquid and solid is constant.Thus equation
(1) holds at any temperatureand, combining (l) and
(3), we have:
LH^ - T(LH^/T-)
: R7" ln (aog)/aA1n) (4)
Rearranging,we get:
AH^ : R[n (ao,";/c^o)]/[(l/T) - (l/Z-)]
(5)
More complex equations which incorporate fewer
simplifying assumptionsabout heat capacitiesmay be
The stateof a pure solid phase,A, in equilibrium made, but they can be shown to have a much
smaller
with a liquid of its own compositionat its melting
effect on calculated enthalpies or entropies than do
temperature,?-, may be describedas follows. For the uncertaintiesof the
data used in this study.
-
Thermodynamic
framework
the reaction,A(s) : A(l), AG- = Garl Gor"r: 0.
AG*, the free energyof fusion, may also be written
AS:
AG- :
Ho,, -
Ho," - I-(5o6r - So,",) (l)
0003-004x/79/0102-0077$02.00
Precision and accuracy of calculations
Adoption of the new temperature scale, Irrs-68,
reguires that accurate thermochemical data be refer77
't8
LUDINGTON: MELTING OF ANORTHITE
point. DifferencesbetweenGL-12 and lprs-68 are
strongly temperature-dependent,
and while for hydrothermalexperimentsbelow 1200K the differences
No.
IPTS-68
GL-I2
Dlfference
may perhapsbe ignored,at the high liquidustemper1
Zt
419.58
4r9.4
0 .1 8
aturesof the studiedsystemsthe differencesare sig2
s
4 4 4, 6 74
o.L24
nificant. Table I and Figure I show the difference
sb
3
6 3 0. 7 4
530.0
o.74
betweenthe two scalesas a function of temperature;
9 5 1 . 93
960.2
L.73
Figure I wasusedto convertthe temperatures
usedin
Au
LO64.43
L062.6
r.83
this
study.
6
Cu
1084.5
1082.8
L.?
Liquidus temperaturesreportedin melting experi7
Pd
t554
1 5 4 9. 5
ments are commonly bracketedby two runs any8
Pt
t7 72
Lt))
L7
where from 4 to 30 degreesapart, one in which all
The cafibtation
in the tabie
cotrespond
to the
trDints
nuntbered
sgnbols
in Figute
1.
AlL temtrEratutes
are relting
glassis obtained,and one in which somecrystalsare
exptessed
in degrees
Ce]sjus,
except
sul_fur,
Ioints,
which
point
present.Suchexperimentsareseldomreversed.Startis the boiTing
at one atrcspbere.
I?TS-5q
teftperatures
(7974).
ate ftom PowefT et aL.
GL-72 temlEratures
ate fton
ing materialsare generallycrystalline,occasionally
glass.In very few casesis a temperaturewell defined
enced to the new temperatures.Temperaturesre- above which crystals melt completely,and below
ported in phaseequilibriumstudiesaregenerallyref- which glassstartingmaterialsyield somecrystals.In
erencedin three ways: (l) Iprs-48 international this study I assumedthat reportedliquidus temper.
temperaturescale,(2) 1912CarnegieInstitutionof atureswere more likely to be too high, becauseof
Washington,GeophysicalLaboratory(hereafterGL- lack of reversal,than too low, becauseof lack of
12) temperaturescale,and (3) unspecified.The pre- equilibrium.Accordingly,the generalprocedurewas
ponderanceof the data are GL-12 temperatures, to choosean upper bracket2o higherthan the lowest
chieflybecauseof the wide acceptance
of the melting temperatureat which all glasswas obtained,and a
point of diopside(1391.5'C,GL-12) as a calibration lower bracket 7o below the upper bracket.Table 2
and Figure2 show the resultsof calculationsusedto
testthe resultantuncertainties
in enthalpiesoffusion,
given commonlyencounteredtemperatureand compositionaluncertainties
in the input data.
Equation (5) is very sensitiveto activitiesof the
solids.However,few quantitativecompositionaldata
are known about solid solutionsin silicatesystemsat
near-liquidus
temperatures.
Sincemostof the studies
consideredhereweremadewithout the benefitof the
electronmicroprobe,anorthite has been commonly
assumedto have end-membercomposition.
Figure 3 illustratesthe effectsof solid solution in
o
phaseA (Table2, Fig.2) on calculatedenthalpies
of
r
fusion
at
1750
K.
The
compositional
effects
can
be
F
relativelylarge, and may easilyovershadowtemperature uncertainties.In calculatingenthalpiesof fusion, all melt and crystalcomponentswere assumed
7
to mix ideally, and activitieswere set equal to mole
fractions.Departuresfrom ideal mixing are thus reflectedin the extracteddata.
The ability to calculatemole fractions correctly
dependscritically on understandingthe structureof
600
1000
1400
silicate melts. Such a melt consistsof an array of
T,"rr-ua, oG
cations,free oxygenions,and silicateions displaying
polymerization.Polymer theory
Fig. L The discrepancy
betweenI prs-68and GL- I 2 temperature various degreesof
has
applied
to
silicatemelts by Masson(1972),
been
scales.Numberedsymbolscorrespondto the calibrationpoints
listedin Tablel.
but the theory has not beenextendedto ternary and
Table l. Someprimary calibrationpointson the Iprs-68and GLl2 temperaturescales
444.
))
4.)
N
F
@ rv
@
F
LUDINGTON' MELTING OF ANORTHITE
Table 2. Samplecalculationto show constraintson precisionof
calculatedenthalpiesof melting
T(K)
1750
X(an)
ltquld
I650
0.720
AH2
AH3
87.49
97.95
90.08
93.93
73.30
71.?8
_to:to
85.85
74.73
61.95
90.25
87.t5
8q.04
93.89
AH4
A!5
107.65
83.E9
0,a52
_
1700
AHI
AHn
_
_
83.60
81,84
71.7A
80.08
78,4t
74.52
84.17
87.99
A6.32
87,57
90.o2
82.74
19.50
80.83
19.66
76.90
0 . 6 0 2 8 3 , 55
Nunbers 1n the !able ue re obtained aB folloest
pnase A
uas as6uned to h€ve a neltlng
tenperaiure
of 1800 (, and a
true en!haIpy of neltlng
of 83,68 KJ/mot,
lrole fractions
of A ln the nelt uere calculated
fron equatton (5), then
!he enthelpy uas rec6lculsced fron those nole fracEions.
which 6re eccurate to the nearest,00t,
AHI represents
t2 deg uncertalnty
in tenpereture, A{2 represents ! 7 aee.
AH3 represen!s !1 nol Z uncertalnty
ln conposltlon.
AH4
and All5 represent conblned naxlmun uncertalnties
of mcthods
I and 3, and 2 and 3, respectivel
LJJ ^^
YU
-J
o
-
I
E
80
higher-ordersystemswith any greatsuccess,
so I did
not attempt to apply it in the presentstudy, which
dealswith ternaryand higher-order
oxidesystems
of
appreciable
aluminacontent.
Thoughvariousmodels
were explored,the procedureadoptedwas to considerthe unit of silicatemelt to be 8 oxygenatoms
and the cations associatedwith them (Burnham,
1975).
Results
17 5 0
Preuiouswork
Bowen(1913)demonstrated
that freezing-point
depressiontheory appliedto the plagioclasephasediagram yields a value for the enthalpyof fusion of
anorthiteoflapproximately
121000
J/mol. Theresults
of Pecket al. (1977),basedon thermalmodelingof
the Alae Lava Lake, Hawaii, are consistentwith
Bowen'sestimate.Ferrier(1969)madea calorimetric
determinationof 167000J/mol for the enthalpyof
fusionof anorthite.Klein and Uhlmann(1974),using
a kinetic study of anorthitecrystallization,estimated
an enthalpyof fusionof betweenI 17000and 188000
J/mol Yoder(1975)reportedunpublished
dataof O.
J. Kleppa and T. V. Charlu, who determinedenthalpiesof solutionof anorthiteand anorthiteglassin
molten lead borate, which yield an enthalpy differenceat 973 K of 78200J/mol. Robie et al. (t978),
usingthe heatcapacities
of Krupka, Robie,and Hemingway (in preparation)and the standard enthalpiesof anorthiteand anorthiteglassmeasured
at
298 K (Kracek and Neuvonen,1952),report a value
of 81000I/mol. The apparentlack of agreement
in
the calorimetricstudiessuggests
the utility of an examinationof the phaseequilibria studies.
17 0 0
16 5 0
KELVINS
TEMPEBATURE,
Fig.2. Uncertainties
in AH- resulting
from (l) *2o temperature
uncertainty,(2) +7" temperatureuncertainty,(3) t I molepercent
(4) a combination
compositional
uncertainty,
of I and3, and(5) a
combination
of 2 and3.
Anorthite-albite
Data wereextractedfrom Bowen's(1913)studyin
the followingmanner.Bowenwasso thoroughas to
publishhis galvanometer
readings,and it was possible to converthis temperatureto Iprs-68 in a very
rigorousmanner.A graph of EMF us. temperature
was constructed,basedon a straightline betweenhis
low and high calibrationpoints of lithium metasilicate (m. p. l208oC,Irrs-68), and anorthite(m. p.
1558.5oC,Irrs-68). Reversalbracketsfor the liquidus were constructedby noting the lowesttemperature at which all glasswasobtainedfrom crystalline
starting materials(upper bracket), and the highest
temperatureat which crystalswereobservedstarting
with glass(lowerbracket).Maximumand minimum
permissibleliquidi were then drawn through the resultingbrackets.Data for discretetemperatureinter-
80
LUDINGTON: MELTING OF ANORTHITE
microprobeand X-ray diffraction analysisof the resulting feldsparsshow no more than 2 mole percent
solid solution at thosetemperatures.Probeanalyses
of the glassagree,within analyticaluncertainty,with
Schairerand Bowen's liquidus curve. Accordingly,
the solid phase in equilibrium with liquids in the
anorthitefield wasassigneda compositionof AnrrOrs
to vary linearly
at the eutectic(1641K) and assumed
with temperatureto Anrooat pure anorthite. Interpolatedvalueswerethen assignedto eachofSchairer
and Bowen'sliquiduspoints.
Data for anorthite-diopsideand anorthite-wollastonite weretakenfrom Osborn(1942).Inthe absence
of any quantitative data on solid solution among
thesephases,mole fractionsof crystallineanorthite
weretaken to be unity.
18 0 0
a"
a
z
IU
Y
F
a
=
k.
rO
\"1
090
095
MOLE FRACTION
aHm(1750K)
83.7 kJ
78.7 kJ
56.9 kJ
28.9 kJ
SOLIDUS
No ss
1
2
J
Fig. 3. Calculated enthalpies offusion for the hypothetical phase
considered in Table 2, showing the effect of different amounts of
solid solution.
valswerethen readfrom the resultingphasediagram.
The soliduswasassumedto be accurate.
Othersystems
Data for anorthite-leucite.anorthite-orthoclase.
and anorthite-silicawere taken from Schairerand
Bowen (1947),exceptfor solidusdata on anorthitesilica from Longhi and Hays (1976).Schairerand
Bowenusedthermocouplecalibrationpoints of palladium (m. p. l554oc, Irrs-68) and gold (m. p.
1064.43'C,Irrs-68) to correctthe temperatures.
For
solidus data in the systemanorthite-silica,a solid
compositionwasestimatedby interpolationfrom the
data of Longhi and Hays for each liquidus point
reported by Schairer and Bowen. Leucite was assumedto exhibit no solid solution with anorthite.
Orthoclase.however.dissolves
in anorthiteto some
extent.Somelunar feldspars(Ryder et al., 1975)are
reportedto exhibit extensiveternarysolid solution.
To test this hypothesis,two experimentswere performedwith the help of B. R. Lipin. Mixturesof 60
mole percentanorthiteand 40 mole percentorthoclase(both crystalline)wereequilibratedfor 5 hours,
one sampleat 1673K and one at 1698K. Electron
of results
Discussion
Calculatedenthalpiesare presentedin Table 3 and
plotted as a function of anorthitecontentof the melt
in Figures4 through 6. The enthalpiesdo not present
a coherentpattern nor easily lend themselvesto a
model. Particularlydisturbing is the
comprehensive
fact that someof the enthalpydata tend to approach
pure anorthitein an asymptoticmannerinsteadof
extrapolatingto a commonvaluefor the enthalpyof
fusion. High-temperaturedata might be lessreliable
for the following reasons:
( I ) Temperaturemeasurement
above1700K is less
precisethan at lower temperatures;
thermalgradients
greater
thermal conmay be larger becauseof
ductivitiesat high temperatures.
(2) Small temperatureerrorsnear ?'- have a large
effecton calculatedenthalpiesbecausethe absolute
of
temperaturevariation is a much largerpercentage
T^-7.
(3) Experimentsat high temperaturestend to be
very short and may not alwaysreachequilibrium.
Extrapolationof thesedata to pure anorthitecomposition fall into two groups. Binary systemswith
albite,leucite,and diopsideindicate aheat of fusion
near 109000J/mol, while the orthoclase,silica, and
wollastonitedatapoint to a figurenear 146000J/mol.
The large uncertaintymay be a result of poor data
or poor modeling.Probablythe uncertaintyis as
large as the uncertaintiesof the highesttemperature
points(+25000J/mol). If suchan uncertaintyis assigned,all the valuesoverlapand the "determined"
enthalpy of fusion of anorthite is approximately
J/mol, which includesall the dis126000+54000
paratecalorimetricdata reported.The conclusionis
that this methoddoesnot closelydelineateenthalpies
of fusion.
LUDINGTON: MELTING OF ANORTHITE
8l
Table 3. Calculatedenthalpyof fusionof anorthite
TEI,IP(K)
SOLID
Anorthite-atbi
1825
1823
1 E1 3
1E13
1 79 3
1793
1773
1773
1 75 3
1 75 3
1 73 3
1733
1 71 3
1 71 3
16 9 3
't693
1 6 73
1 6 73
1653
1653
1633
1633
1 6 13
1613
17 0 6
16 9 9
0 . 9 83
0 . 9 83
0.960
0 . 9 60
0 . 9 15
0.9r5
0 . 8 7/ ,
0 . 8 71
0.E36
0.836
0.799
o.7cc
0 . 76 3
0.763
0.728
o . 72 8
o.692
o 692
0.656
0.656
0 . 6 19
0.619
0.5E1
0.5E1
0.950
0.961
0.887
0.906
0.77?
0.800
0.689
1.701
0.581
0.609
0.50E
c.529
o. 1 1 ?
0.161
0.385
0.402
0.329
0.3r.8
0.279
1.298
3.231
0.?54
0.191
0 . 2 1Z
135307
89689
12E333
9 3 94 Z
12 5 3 0 0
99031
112563
104391
12 6 0 1 5
1 0 9 74 1
12 3 10 8
11 2 0 9 7
1 ? 16 1 9
11?213
120762
111658
1?0551
' l1 1 4 4 8
1 2 11 E 1
112122
1 22 6 9 1
11?348
125818
11 1 0 2 1
0.901
c.901
0.807
0.807
c.7t9
0.709
0.610
0.510
3.510
c.485
0.485
13 ? 2 E ?
98827
126535
10 9 3 9 0
142083
127760
145403
13 1 3 6 7
118610
1 3 9 71 3
' 1 5 11 7 1
1 1 2 79 1
0.900
0.900
0.800
0.800
0.70c
0.700
161112
113932
191535
1 5 2 11 E
1 6 8 3 7I
1 1 E 16 5
TEMP(K)
SOLID
LlaulD
1752
1715
1750
1723
1694
1687
1679
1672
1657
1650
't641
1634
Anorthite-si
1814
1807
1781
'1777
l. ?80
1.9E0
1.980
1.9E0
1.980
1.980
1.980
1.980
3.?70
).970
1.970
3.970
ti ca
l.?95
l . ?9 5
1.980
1.980
3.965
1.965
l . ?5 5
l.?55
1.940
c.940
1.935
l . ?3 5
l.?15
1 . 9 ' 15
0.600
0.600
0.500
0.500
0.400
0. 100
0.350
0.550
0.300
0.300
0.25C
0.250
15 7 5 7 1
1t3251
177131
151E76
159325
150E15
171192
115781
17 1 1 1 8
153573
179115
171981
0.8E6
0.886
o.776
0.776
0.668
0.66E
0.616
0.616
0.564
0.561
0.514
0.514
0.473
o.173
2 J O 11 7
r I 8595
1t 7 ? 2 6
119 1 6 7
1 1 2 2 15
t4816
??490
t 3399
96811
?1592
?77J9
?2479
)1548
?0355
0.903
0.903
0.806
0.806
0.708
0.708
0.609
0.609
0. 509
0.509
17 6JO9
1?r768
t5155
85029
3 ? 15 3
76724
78 ? 2 3
71549
f???5
70a25
1735
1 72 8
1715
1708
16 9 1
1687
1 6 73
16 6 6
16 5 1
'l617
te
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1. 0 0 0
1.000
Anorthite-orthoc
181/,
1807
1E00
1793
1776
1 76 9
aHh(J/M0L)
te
Anorthite-teuci
1 80 9
18 0 2
l784
1777
1 76 5
1758
1 71 0
1755
1 71 2
LICUID
tase
0.990
0.990
0.990
0.990
0.980
0.980
6Hh(J/rrt0L)
Anorth ite-Ci )Dsi de
1Et4
1807
1 76 9
1 76 2
1 72 0
1713
1669
16 6 2
1604
't
597
1.900
1. 0 0 0
1. 1 0 0
1.900
1.t00
1.C00
1.000
1.t00
1.300
1.000
Anorth ite-rctt as toni te
1790
1.300
0.817
1 78 3
1 71 5
1 73 8
1605
1598
t .100
1.C00
1.300
r.J00
1.900
0.817
o.722
0.722
9.s?7
0.527
1 3 75 1 7
1 1 6 56 3
1 J 1 ?1 5
?3626
695?3
5 7 13 1
Data for anorthite-aLbite
are {rOn Boyen (1915), tor anortlite-teucite,
anorthit!-orthOclase,
and anorthite-siIica
from schairer
and Bouen (1917)t for ancrtlite-diopside
and anorthite-dcl,tastonite
'sotidr
trom 0sborn ('1912>. Cotuons entitted
and . Liquid' refer to mote fractions
of alcrthite.
Our imperfectknowledgeof the structureof calcium-rich plagioclase at high temperature complicatesthe picture(seeSmith,1975).For pureanorthite, a completelydisorderedcrystal has 23.05J/
mol.K of configurationalentropy (Ulbrich and
Waldbaum, 1976).A 42000J/mol differencethus
existsbetweenthe enthalpyof fusion of completely
ordered and completelydisorderedanorthite, with
the orderedphaseexhibitinga higher value.On the
basisof TEM (transmissionelectronmicroscopy)ob(1977,oralcommuniservations,
G. L. Nord suggests
cations)that pure anorthiteformed at temperatures
higher than 1700K probably crystallizesin the disorderedCl structure.However,it is the high-temperature data in Figures 4 through 6 which suggest
anomalouslyhigh enthalpiesof fusion, and hence
crystallization as the ordered phase. This contradictionremainsunresolved.
(1952)deterGrantedthat KracekandNeuvonen's
minationof the heatof solutionof anorthitecrystals
and glassis approximatelycorrect,one is led to agree
with Robie et al. (1978) and to concludethat the
differencein enthalpy betweenanorthite glass and
crystalsat themeltingpointis verynear81000J/mol.
Data of Krupka and others(in preparation)do reqirire a long extrapolation,but the heat contentdifference,A(I1r*o - Hrr), betweenglassand crystals
must lie betweenabout 6000and 15000J/mol. An
enthalpyof fusionin the neighborhood
of 150000
J/
mol is untenablein the light of the best available
calorimetricdata.
If the enthalpyof fusionof anorthiteis near 8 1000
LUDINGTON: MELTING OF ANORTHITE
630
E
Itrrffrf
a
o
6
o
x
!
I
f
E
<25
r25_
o
E
?
f
E
100
EXPLANATION
A Albite
tr Oiopside
?
On
c
15L
10
80
06
o4
o2
XLX,iro,s,,o,
Fig. 4. Calculatedenthalpiesof fusionfor thesystemsanorthiteorthoclaseand anorthite-silica.
E
E
o
o
v
a
-
I
I
E
EXPLANATION
o Leucite
O wollastonite
8
v^ tiquid
Car.l2Si2OB
Fig. 5. Calculatedenthalpiesof fusionfor thesystems
anorthiteleuciteand anorthite-wollastonite.
Fig. 6. Calculatedenthalpiesof fusionfor the systems
anorthitealbite and anorthite-diopside.
J/mol, the discrepancies
in the enthalpiescalculated
in thispapermight be ascribedto non-idealmixingin
the silicateliquids.To assess
the natureand degreeof
this possiblenon-ideality,activitiesof anorthite in
liquid werecalculatedfor the variousbinary systems,
assumingthe enthalpyof fusion of anorthiteto be
81000J/mol. Solid activitieswere assumedto be
equal to mole fractions, and the temperatureused
was the midpoint of the temperaturerange of the
original data. The resultingactivitiesand activity coefficientsare shownin Figures7 and 8, respectively.
The activity coefficientis simply the quotient of the
calculatedactivity and the liquid composition.
Figure 8 looks remarkably like similar plots for
metalalloys(Richardson,1974,chapter4), implying
that the data are compatiblewith a regularsolution
model.The modelseemsto hold for mole fractionsof
<0.75, but the behaviorof the activity coefficients
at
mole fractions of anorthite )0.75 is very uncertain
and subject to large perturbationsas the result of
smallchangesin the assumedenthalpiesof fusionand
meltingpoint of anorthite.
The slopeof the lines in Figure 8 can be roughly
correlatedwith the ionic potential df the cationsin
the solutions, with the largest positive deviations
from ideality shown by systemscontaining potassium,the ion with the lowestpotential.
LADINGTON. MELTING OF ANORTHITE
83
10.0
8.O
0.6
o
o
a
N
.=<
t(U
;o
(!
0.4
EXPLANATION
o Orthoclase
o Leucite
a Albite
a Silica
D Diopside
O Wollastonite
o.2
o.2
o4
06
0.8
1.0
',r,liquid
^ caAlrsiro,
Fig.7. Calculatedactivity-composition
relationsusingthe assumptions
that theenthalpyoffusion ofanorthiteis 81000J/moland that
its meltingpoint is 1830K. Sizeof the symbolsfor anorthite-albitereflectsthe uncertainty.The othersymbolsareaboutonehalf the size
of their uncertainties
for clarity.The straightline represents
ideal mixing behavior.
The intent of this communicationis to suggestthat
a regularsolutionmodelmay be applicableto silicate
melts;analysisof the modelwill requiremore extensivetestingwith moredataand perhapsmoresophisticated thermodynamicmodels.The great variation
in the slopesof the linesin Figures8 and 9, however,
stronglysuggests
that a simpleabandonment
of the
assumption
of constantACowill not greatlysimplify
the situation.
An interestingimplicationof this data for experimental petrology is that valuable thermodynamic
data may be gatheredfrom close-spaced
and precise
data on liquidussurfaces.It could be very illuminating to study one of the systemsconsideredin this
study at 2 to 5 mole percentintervals,along with a
careful determinationof the melting point of anorthite. A necessityin such a study would be careful
determinationof the structural state of the calcic
84
LUDINGTON: MELTING OF ANORTHITE
Orthoclase
N
6
Albite
Leucite
@
^ ^
UJ
'i<
*6
.=
- x -. 1
02
Diopside
Wollastonite
0
01
0.2
03
0.4
A v tiquid
1z
\'-^ cantrsiror/
0.5
06
0.7
F i g 8 N a t u r a l l o g a r i t h m o f c a l c u l a t e da c t i v i t y c o e f f i c i e n t sp l o t t e d u s . t h e s q u a r eo f t h e m o l e f r a c t i o n o f t h e s o l u t e . S t r a i g h t l i n e s a r e
- , Y U F X i l " , , o(, ) 0 . 2 a r e
e y e b a l lb e s t f i t s t o t h e d a t a o v e r t h e r a n g e i n w h i c h t h e y a p p e a r t o e x h i b i t r e g u l a r s o l u t i o n b e h a v i o r .P o i n t s a t ( l
omitted for clarity
plagioclase.It might also be particularly revealingto
study the molar volume of a seriesof glassesin some
of these binary systemsto seeif such data could be
correlated with the mixine behavior deduced from
phasediagrams.
Summary and conclusions
An examination of the thermodynamicsof melting
of anorthite in binary systems suggestssome basic
conclusionsabout silicatemelts containing anorthite
as a component.
(l) Calculated enthalpies of fusion based on an
ideal solution model are not compatible in detail with
each other or with the calorimetrically-constrained
figure of 81000 J/mol suggested by Robie et al.
( 1978).
(2) Calculated activity-composition relations for
anorthite-bearing melts suggest that the binary systems under study may be describedby regular solu-
controlledby the
tion theory,with mixingparameters
ionic potentialsof the ions in the melt.
Acknowledgments
I wish to thank D. R. Wones, B. R. Lipin, J. L. Haas, G. L.
Nord, D. B. Stewart, and C. Wayne Burnham for encouragement
and stimulating discussion throughout the study. The manuscript
was read at an early stage by Herb Shaw, and reviewed by P. C.
H e s s , R . A . R o b i e , a n d J . B . M o o d y . T h e i r h e l p f u l c o m m e n t sa r e
gratefully acknowledged; the shortcomings remain my own.
References
B o w e n , N . L . ( 1 9 1 3 ) T h e c r y s t a l l i z a t i o no f t h e p l a g i o c l a s ef e l d s p a r s .A m . J . 9 c i , 3 5 , 5 7 7 - 5 9 9 .
Burnham, C. W. (1975) Water and magmas; a mixing model.
Geochim. Cosmochim Acta. 39. 1077-1084.
Ferrier, A. (1969) Etude experimentalede I'enthalpie de l'anorthite
synthetique entre 298 et 1950 K. C. R Acad Sci. (Paris), Ser. C,
269,9st-954.
K l e i n , L . a n d D . R . U h l m a n n ( 1 9 7 4 ) C r y s t a l l i z a t i o nb e h a v i o r o f
a n o r t h i t e J G e o p h y s .R e s, 7 9 , 4 8 6 9 - 4 8 7 4 .
K r a c e k , F C . a n d K . J . N e u v o n e n ( 1 9 5 2 ) T h e r m o c h e m i s t r yo f
LUDINGTON.. MELTING OF ANORTHITE
plagioclaseand alkali feldspars.Am J. Sci, Bowen Volume.
CaAl,SirO,glasses
and of anorthite.Am. Mineral .63. l0g-123.
293-3I 8.
Ryder,G., D. B. Stoeser,
U. B. Marvin and J. F. Bower(1975)
Longhi,J. and J. F. Hays (1976)Solidsolutionand phaseequiproc 6th Lunar
Lunar graniteswith uniqueternaryfeldspars.
join
fibria on the
anorthire-silica(abstr.).Am. Geophys.Union
Sci. Con"f.,Geochim.Cosmochim.Acta Supp 6, 435-449.
Trans.,57,340.
Schairer,J. F. and N. L. Bowen (19a7)The systemanorthiteMasson,C. R. (1972)Thermodynamics
and constitutionof silicate
Ieucite-silica.
Bull. Comm Geol.Finlande.140.67-87.
slags."/. Iron SteelInst.,210,89-96.
Smith,J. V. (1975)Phaseequilibriaof plagioclase.
In p, H. Ribbe,
Osborn,E. F. (1942)The systemCaSiOr-diopside-anofthite.
Am.
Ed., FeldsparMineralogy, Chapter7 Mineral. Soc. Am. Short
J . S c i . 2, 4 0 . 7 5 1 - 7 8 8 .
CourseNotes2.
Peck,D. L., M. S. Hamiltonand H. R. Shaw(1977)Numerical Sosman,R. B. (1952)Temperaturescales
and silicateresearch.
analysisof lavalakecoolingmodels.part ll, applicationto Alae
A m -J . S c i . , 2 5 0 Ap, t . 2 , 5 1 7 - 5 3 2 .
l a v al a k e ,H a w a i i A
. m . J . 9 c i , 2 7 7 , 4 1 5 - 4 3.' 1
Ulbrich,H. H. and D. R. Waldbaum(t976)Structuraland other
Powell,R. L., W. J. Hall, C. H. Hyink, Jr., L. L. Sparks,C. W.
contributionsto the thirdJaw entropiesof silicates.Geochim.
Burns,G. Scrogerand H. H. plum (1974)Thermocouplerefer_
CosmochimActa. 40. l-24.
encetables basedon the lprs-68. National Bureauof Standards Yoder,H. S., Jr. (t975) Heat of meltingof somesimple
systems
Monograph125.
relatedto basaltsand eclogites.CarnegieInst lt/ash year Book,
Richardson,F. D. (1974)PhysicalChemisrryof Melts in Meral_
74,5t5-519.
lurgy, u. /. AcademicPress,London and New york.
Robie,R. A., B. S. Hemingwayand W. H. Wilson(1978)LowManuscripl receitsed,September 22, 1977;
temperatureheat capacitiesof KAlSirOr, Na AlSirO", and
acceptedlor publication, June 16, 1978.
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