American Mineralogist, Volume 64, pages 86-101, 1979
periclase,
anorthite,Q1{lrSirO,glass,
heatcapacities
of corundum,
High-temperature
glass,
grossular'
andNaAlSirOrglass
pyrophtllite,
KAISisOB
muscovite,
K B N N n r uM . K n u p r e , R l c H n R DA . R o e I r n N p B R u c r S . H r u t N c w e v
U.S. GeologicalSuruey
Reston, Virginia 22092
Abstract
(CF)of corundum,periclase,
anorthite,CaAlrSirO,glass,muscovite,
The heatcapacities
to an
pyrophyllite,KAlsi3os glass,grossular,and NaAlSirO,glasshavebeendetermined
K.
Our
and
1000
350
between
percent
calorimetry
differential
scanning
by
accuracyof *1.0
heat capacityand enresultshavebeencombinedsmoothlywith existinglow-temperature
tropy data, and fitted by leastsquaresto the followingequations(I in Kelvin and CP in
J/mol.K):
- 1.408
) 16.8 -0.092497
X l 0 8 T - 2- 4 5 8 8 T 1 / 2 + 4 . 1 8X8 l 0 ' r
c f ( a n o r t h i t e: 5
(298-r800
K)
- 2 . 8 1 5X l 0 6 1 2 - 2 4 5 9 7 - t / 2
C F ( C a A l , S i , O , g l a s=s )3 7 5 . 2+ 0 . 0 3 1 9 7 7
(298-rs00
K)
Cf(muscovite):917.7-0.08lllT+2.834x1067-2-103487-t/2
( 2 9 8 - r 0 0K
0)
c3(pyrophvllitel=679.r-0.064127-69027-1/2-5.997x106T'z
(2e8-800K)
+ 1 . 9 2 8x l 0 u T '
C P ( K A l S i 3 O 8 g l a s: s )6 2 9 . 5- 0 . 1 0 8 4 f+ 2 . 4 9 6x l 0 6 f - 2 - 7 2 1 0 7 - t / 2
(298-r30K
0)
+ 2.669x 10-17'
Cf (grossular): 1633.3- 0.75997+ 9.1l3 X 106?'2 - 207837-t/2
( 2 9 8 - 1 2 0K0)
/2 1.476x10-lT'z
C 3 ( N a A l S i , O , g l a s:s9)3 4 . 4 - 0 . 3 8 9 1 7 +5 . 5 9 4X l 0 6 I - ' z- 1 1 8 2 0 7 - t +
(298-r200
K)
the heat
The accuracyof the differentialscanningcalorimeterwas checkedby measuring
andcomparingtheseresultswith thosepublishedby the
capacities
ofcorundumand periclase
datafor muscovite,
We havecombinedour calorimetric
U. S. NationalBureauof Standards.
pyrophyllite,and grossularwith data from recentequilibriumstudiesto deriveimproved
valuesfor LH?.r* and AGf,r* for muscovite,pyrophyllite,and grossular.Our valuesfor
for
J/mol respectively
are -597160045180J/mol and -5595500+5190
LH?.""and AGP.,,s
J,/molrespectively
J/mol and -5265900+3960
disordered2M, muscovite,-5639800+3950
for
J/mol and -6295300+4730J,/molrespectively
for pyrophyllite,and -6657100+.4720
grossular.
Introduction
Heat capacity values above 300 K are of fundamental importance for thermodynamic calculations
of mineral equilibrium at high temperatures.Until
recently the principal method of determining these
0003-o04x/79/0102-0086$02.00
86
data has been drop calorimetry. In this method, the
sample is held at d constant (elevated)temperature,
I, within a flurnaceand is then dropped into a receiver (calorimeter) maintained at some reflerence
commonly 298 K. The quantity actemperature,Tno,
tually measuredis
KRUPKA ET AL.: HEAT CAPACITIES
H 3- H 3 " :
fT
I cfar
87
and NaAlSirO, glass.Using thesenew valueswith
ancillary thermodynamicdata from Robie el a/.
The true differentialheat capacity,C3, is derived (1978a),
we havederivedimprovedvaluesof AHl.r,
from theseheat.contentmeasurements
and
LGl,r"t
for 2Mt disordered
pyrophylmuscovite,
by graphical
differentiation
of the experimental
Hf - f1f ovalues, lite, and grossular.
or by fittingthe heatcontentdatato an equationand
Apparatus
then differentiating
the equation.In eithercase,differentiationof the experimental
The calorimeterwasa Perkin-Elmer
Hf - H9""data inModel DSC-2
troducesuncertaintyin the derivedvalueof Cf which differentialscanningcalorimetersimilar to that deis approximatelyan order of magnitudelargerthan scribed
by O'NeillandFyans(1971).
Our heatcapacthe uncertaintyoflthe measurements.
weremadeat a heatingrate of l0
Thus,although ity measurements
Hf - Hg""can with care be measuredto *0.1 per- K/min with a rangesettingof 1.25J/min (5 mcal/
cent,the Cf valuesderivedfrom themhavean uncer- sec).All sampleswereencapsulated
in gold pansand
tainty of the order of * L0 percent.The accuracyof
weighedby meansof eithera Mettler M-5A microthe derivedCp valuesdependsboth upon the accu- balanceor a Cahn Model 4100electrobalance.
Temracyof the heatcontentmeasurements
and upon the peraturecalibrationof the calorimeterwas checked
temperature
spacingof the measurements
whichcon- by measuringthe transitiontemperature(extrapotrol the accuracyof the smoothingfunction.Except lated onset temperature)of the inorganic comfor the highly accurateand closelyspacedmeasure- poundssuppliedin the thermalstandardsets,Nnsmentsof Ditmarsand Douglas(1971)on a-AlrO3 Icrn Standard ReferenceMaterials 758 and 759
(corundum),thereareprobablyno heatcapacityval- (McAdie et al., 1972).
ues, derived from Hf - H9""studies,that have an
In order to checkthe accuracyof the differential
uncertaintyof lessthan 1.0percent.Seefor example, scanningcalorimeter,
we havemeasured
the heatcaFigure7 of Ditmarsand Douglasfor an overallpic- pacitiesof a-AlrOs(corundum)both in the form of
ture of the stateof H,f - .Ffir,calorimetricmeasure- single-crystal
discsand in powder florm,and comments.
paredour resultswith the valuesreportedby Ditmars
Heat capacities
can be directlymeasured
by adia- and Douglas(1971).We havealsomadea lessextenbatic calorimetry,but are not routinelydetermined siveseriesof measurements
on MgO (periclase)
for
by this method above400 K becauseoflgreatlyin- comparisonwith the data of Victor and Douglas
creased
experimental
difficulties.
At the presenttime, ( 1 9 6 3 ) .
only the adiabaticcalorimetersdescribedby Gronvold (1967)(with an upperlimit of 1050K), and by
Materials
TrowbridgeandWestrum(1963)(with an upperlimit
(a-Alzos)
of 800K) areoperational.
Westand Westrum(1963) Corundum
havediscussed
the problemsof instrumentation
conThe sampleof single-crystal
corundumwasa disc
nectedwith the constructionand operationof adia- of Linde syntheticsapphire6.3 mm in diameterby
batic heatcapacitycalorimeters
for temperatures
as 0.25mm thick and weighed30.20mg. The chemical
highas 1000K.
given by Ditmarsand Douglas(1971)inanalyses
Watsonet al. (1964)introduceda new methodof dicatethat the purity of Linde syntheticsapphireis
thermalanalysiswhich they calleddifferentialscan- 99.98percent.Unit-cell dimensionswere measured
ningcalorimetry,
and O'Neill and Fyans(1971)de- by meansof an X-ray diffractometerat 296+l K
scribeda much improvedversionof the differential usingCurKa,radiationand a scanningrate of lo /
scanningcalorimeter(DSC). In contrastto the drop min. The cell constants
werea: 0.4760t0.0003
and
method, the differentialscanningcalorimetermea- c = 1.2993L0.0019
nm (l nm = l0A).The powdered
suresCp directlyand has an accuracycomparable corundumwas FisherScientificCo. reagentNo. 591
with that obtainedin all but a veryfewinvestigations (anhydrous
aluminumoxide),and it weighed28.59
wherea drop calorimeteris used.
mg. Chemicalanalysesby Fisher ScientificCo. inUsing this method,we havedeterminedthe high- dicatethat its purity is 99.4percentor better.Unittemperature
heatcapacities
between350and 1000K
celldimensions
weremeasured
underthesamecondifor corundum,periclase,
anorthite,CaAlrSi2O,
glass, tionsas thoseof the Lindesapphire,and they wetea
muscovite,pyrophyllite,KAlsiso8 glass,grossular, : 0.4758+0.0006
and c : 1.2992L0.0023
nm.
KRUPKA ET AL
HEAT CAPACITIES
mental Cf values in Tables I through t have been
Periclase(MSO)
from Figures I through 3. Our measured
omitted
periclasesamplewas furnished
The single-crystal
of anorthite, CaAlrsirOr glass, and
capacities
heat
by G. Weber (Pennsylvania
StateUniversity)from
grossularwere not included, becauseof the
synthetic
Its purmaterialproducedby an arc growthprocess.
thesedata and those in Figures2
ity was comparablewith commerciallyavailable similaritiesbetween
gram-formula weights were calculated
The
3.
and
high-purityMgO (Weber, 1975).The single-crystal
weights (Commission on
samplewas squarein crosssection(4.4mm) by 0.36 using the 1973 atomic
1974).Calorimetric unit conversion
Weights,
Atomic
Theunit-celldimenmm thickandweighed
26.92m9.
was made using I cal : 4.184 J. The experimental
nm.
sion wasa = 0.421210.0002
data for muscovite,pyrophyllite, KAlSi3O. glass,and
NaAlSi'O" glass,KAISi'O" glass, CaAlrSirO"glass, NaAlSieOaglasshave beencorrectedfor deviationsof
the samplesfrom their ideal chemicalformulae using
and anort.hite
The materialsusedwere portionsof the samples
heat
usedby Robieet al. (1978b)for low-temperature
capacitystudies.The NaAlSi3O'glassand KAlSirO.
glasswerediscs6.3 mm in diameterby 0"81mm thick
The
and weighed62.38 and 57.60mg respectively.
CaAlrSirO,glassand anorthitesampleswere - 100
mesh powders,which weighed30.37and 29.81mg
respectively.
2M, muscouite
I KAI,(AlSirO*)(OH)z] and
pyrophyllit e I A l2Si4O
n( OH )z]
The materialswereportionsof thesamplesusedby
Robieet al. (1976)for low-temperature
heatcapacity
The 2M, muscovitewasa single-crysmeasurements.
tal disc,6.3 mm in diameterby 0.35mm thick,and
weighed31.20mg.The pyrophyllite
was-100 mesh
powder. Two samplesof the pyrophyllitepowder
wereused,and they weighed20.80and 24.80mg.
Grossulqr( Cay4lzSi"Op)
were made on both
Heat capacitymeasurements
natural and syntheticgrossular.Two samplesof
grossularfrom the JeffreyMine, Asbestos,Quebec
(NMNH 123106)were used, weighing24.11 and
16.95mg.The unit-celldimensionof thisgrossularis
nm. The syntheticgrossularwas
c : 1.1850t0.0002
preparedby J. J. Hemley of the U.S. Geological
Surveyfrom a gelat923 K and 517bars(l bar : 105
pascals).
Two samplesweighing17.12and 19.88mg
were used.The unit-celldimensionof the synthetic
grossular
nm.
is c : 1.1853t0.0002
Experimental results
Our measuredvalues of the molar heat capacities
of corundum, periclase,anorthite, CaAlrSizO. glass,
muscovite, pyrophyllite, KAlsisos glass, grossular,
and NaAlSirOs glassare listed in Tables I through 9
respectively and shown graphically in Figures I
through 3. For the sake of clarity, some of the experi-
the same approximationsused by Robie et al. (1976,
1978b).
Our experimental Cf values are believed to be accurate to tl.0 percent,basedupon: (l) a comparison
of our heat capacity measurementson corundum and
periclaseby differential scanning calorimetry with the
Table l
Experimental heat capacities for corundum, a-AlrOg
l{eat
capacity
Tenp.
lleat
capacity
Teop.
Heat
capacity
K
J/(ool.K)
K
J/(no1.K)
K
J/(nol.K)
350.2
370.1
390.0
4I0.0
4r9.9
4 2 9. 9
419.9
4 3 9. 9
459.8
479.7
4 8 9. 7
499.'t
509.6
5 0 4. 7
509.7
eo
99.7
98.3
1 0 0 .r
102.6
104.3
105.4
106.2
107.5
to7 .4
108.0
3 4 9. 1
359.1
369.1
379.1
389.r
399.1
409.I
4 L 9. 1
429,L
4L9.2
4 2 9. 2
439.2
449.2
459.2
4 6 9. 2
88.5
90.r
91.6
93.0
94.6
96.0
96.8
98.5
9 9. 5
98.2
98.8
t00.0
101.5
102.2
1 0 3. 6
3 9 9. 5
409.5
4L9.5
439,5
459.5
479.5
484.5
474.5
484.5
499.5
519.5
539.5
549.5
559.5
549.5
96.0
9 7. 5
98.8
101.3
rO2.9
105.2
105.3
r03.6
I 04. r
105.6
106.6
108.4
109.0
110.0
r09. I
4 7 9. 2
4 8 9. 2
4 9 9. 2
509.2
504.2
509.2
5r9.2
529.2
539.2
549.2
559.2
569.2
519.2
589.2
599.2
L04.4
I 05.2
106.3
107.4
106,2
r06.4
I 0 7. 3
r08.2
109.0
109.8
110.3
111.1
111.2
112.1
113.0
559.s
609.7
629.7
649.6
659.6
6 5 9. 6
679,6
8 4 9. 5
r08.4
r10.1
111.1
llr.6
112.r
1L2.6
112.3
112.5
r13.2
112.9
114.1
r t4. )
1r5.2
1r6.4
12t.2
109.5
rl1.l
111.8
1t2.9
113.4
114.r
113.0
113.6
114.5
709.2
16.3
16.5
r6.9
17.2
16.9
859.3
874.0
898.5
908.3
918.1
923.0
9 5 9. 6
969.6
9 7 9. 6
989.6
999.5
903.4
918.1
r21.2
12r.5
122.O
122.7
r22.8
I 23.3
1 2 3. 5
124.0
r24,2
124.3
r25.O
122.2
r23.4
674.0
679.0
689.0
699.0
709.0
719.0
729.0
739,0
149.0
759.0
764.0
349.8
I16.1
II6.4
1r5.4
1I7.1
r17.0
17.6
r7.9
18.5
18.3
18.9
19.5
89.3
72 9. 2
749.2
769,2
774.2
354.8
374.7
394.7
409.6
9 2 7, 9
9 3 7. 7
9 4 7. 5
9 5 7. 3
L r 7. 6
118.3
119.3
119.7
90.0
92.5
95.8
9 7. 8
1 2 3. 7
123.4
r24.0
124.5
Tenp.
5 1 9. 7
539.7
559.6
579.6
589.6
599.6
5 9 4. 7
?
9r.8
9 4. 4
9 7. 1
oc
1
)tv.)
599.5
6t4.5
624,5
6 3 4. 5
6 2 4. 5
634.5
5 4 9. 5
6 6 9. 5
689.4
699.4
709.4
KRUPKA ET AL.: HEAT CAPACITIES
Table 2. Experimental heat capacities for periclase, MgO
Tenp.
Heat
capaclEy
Tenp.
Heat
capacity
K
J/(nol.K)
K,
J/(no1.K)
350.1
370.0
390.0
4 0 9. 9
4r9.9
429.9
419.9
439.9
459.8
479.8
489.8
40.4
41.3
42.r
42.8
499.8
509.7
594.8
599.8
609.7
6 2 9. 7
649.7
659.6
6 6 9. 6
679.6
45.7
46.1
47.5
47.7
47.6
48.0
48.3
48.4
48.5
48.7
+J.
J
43.6
43.6
43.9
44.5
45.2
45.4
valuesof Cf calculatedfrom the heatcontentdata of
Ditmars and Douglas(1971)for corundum,and of
Victor and Douglas(1963)for periclase;and (2) a
comparisonof our measurements
in the temperature
range 350-380K for muscovite,pyrophyllite,the
threefeldsparglasses,
and anorthitewith the values
of Cf determinedby Robie el al. (1976,1978b)by
low-temperature adiabatic calorimetry (accuracy
t0. I percent)on the samematerials.
Our heatcapacTable 3. Experimental heat capacities for anorthite, CaAlzSLOs
Tenp.
K
Heat
capacity
J/(mo1.K)
Tenp.
Heat
capacity
TeEp.
Heat
capacity
K
J/(nol.K)
K
J/(uol.K)
349.0
359.0
369.0
37 9. 0
389.0
399.0
409.0
419.1
23t,9
234,5
2 3 7. 9
2 4 1. 2
243.7
246.4
2 4 9. O
253.3
679.1
689.1
6 9 9. 1
709.1
719.1
729.1
739.1
749.t
295.2
4 2 9. 1
414.0
4I9.I
4 2 9. 1
439 .
449.
459.
469.
479.
489.
499.
509.
504.2
5 0 9. 2
255.5
2 5 2. 4
252.4
255.6
258.2
259.8
26I.7
2 6 3. 5
266.O
267.2
2 6 9. 1
270.5
2 71 . 2
2 72 . 4
5r9.2
5 2 9. 2
274.7
2 76 . 0
<?o
t
549.2
559.2
569.2
579.2
589.2
5 9 9. 2
674,L
777
\
279.5
279.6
282.0
281.8
2 8 3 .I
284.3
294.4
298.2
299.2
300.7
669.5
689.4
699.4
109.4
699.5
709.5
7 2 9. 5
7 4 9. 5
292.9
295.6
296.7
298.2
298.3
299.7
30t.4
3 0 2 .r
759.t
76 4 . I
349.5
354.5
3 74 . 5
394.5
409.5
399.5
4 0 9. 5
4l 9.5
439.5
459.5
4 7 9. 5
484.5
302.7
304.3
233.3
234.0
24t.2
248.4
252.8
247.7
250.6
252.7
258.0
262,7
2 6 5, 6
266.9
769.5
774.5
764,5
74 4 ; 5
789.5
809.5
829.5
839.5
844.8
859.5
879.1
898.7
908.5
918.3
304.2
305.0
304.4
3 0 4. 7
305.9
3 0 7. 2
308.6
309.6
3 0 7. 5
308.1
308.3
309.4
310.2
313.8
4 74 . 5
4 8 4. 5
4 9 9. 5
519.5
539.5
549.5
559.5
624.5
634.5
649.5
265.2
2 6 7. 3
270.r
275.1
218.2
279.7
24r.5
289.0
290.3
291.1
923.2
9r3.4
923.2
9 3 7. 9
9 5 7. 4
967.2
917.O
9 8 6. 8
965.5
3r5.4
311.0
31r.2
3t2.4
3L6.4
316.3
3I5.8
320.4
319.7
2 9 5. 7
296.8
Table 4. Experimental heat capacities for CaAlrSirOr glass
TeEp.
K
l{eat
capacity
Temp.
J/(nol.K)
K
lleat
capactty
Teep.
J/(nol.K)
K
H ee t
L d y o r r L ,
J/(no1.K)
349.1
359,1
369.1
379.
389.
399.
409.
419.
429.
414.
419 .
230.9
233.6
238.0
24r.2
2 4 3, 7
2 4 6. 5
250.I
252.5
254.7
25r.7
252.4
6 9 9. L
7 0 9 .I
719.t
729.1
739.1
749.r
759.r
764.t
349.5
354.5
374.5
298.3
2 9 9. 6
299-8
30r.4
302.0
302.7
304.4
306.4
232.8
234.5
240.O
6 2 4. 5
634.5
6 4 9. 5
669.5
689.4
699.4
709.4
699.5
709.5
729.5
749.5
2 9 0. 3
292.2
292.8
294.4
2 9 8. 4
299.1
300.3
298.9
301.3
303.3
305.2
429 .
439.
449.
459.
469 .
479.
489 .
499.
509.
504.
255.5
258.5
260.0
261,8
264.O
266.O
267.9
270.3
2 72 . 0
270.7
272.O
394.5
409.5
399.5
409.5
4 L 9. 5
439.5
459.5
4 79 . 5
484.5
414.5
484.5
246.5
2 5l . I
246.2
249.O
2 51 . 5
2 5 7. O
262.5
266.2
2 6 7. 5
263.5
265.8
769.5
774.5
764.5
774.5
789.5
809.5
829.5
839.5
844.8
859.5
898.7
307.0
3 0 7. 6
3 0 7. 6
305.9
308.0
312.1
313.1
314.2
3Lt.2
3r2.8
315.0
519.
529.
213.8
276.4
277.4
280.8
281.8
283.1
4 9 9. 5
5r9.5
539.5
5 4 9. 5
5 59 . 5
549.6
559.5
579.6
599.6
514.5
624.5
634.5
268.0
272.9
276.8
2 78 . 5
2 1 9- 6
278.6
280.0
283.7
2 8 ' l. 6
289.4
2 9 0- 6
292.r
908.5
918.3
923.2
913.4
923.2
937.9
996.6
957.4
967.2
977.0
985.8
996.5
3r5.7
318.5
317.6
3L5.7
3 1 7. 2
319.0
322.4
3r9.9
318.8
321.9
3 2 5. 6
323.8
549 .
559.
569.
579.
589.
599.
679.
689.
ral
o
286.0
286.7
295.2
295.3
296.5
ity measurements
on corundumagreewith the values
reportedby Ditmarsand Douglas(1971)for the certificationof StandardReference
Material 720with an
averagedeviationof 0.3 percent.
Previousstudies
Pankratz (1964) measuredthe relative enthalpy
Hf - H9""of a muscovitesampleat approximately
100K intervalsbetween400 and 903K. Heat capacities calculatedfrom his derived Cf equation are
smallerthan thoseobtaineddirectlyin this investigation by l 2 percentat 500K and 1.8percentat 900K.
Although hismuscovitesamplewaslesspure than the
muscovitesamplewe used,his data were not correctedfor the deviationof the samplefrom the exact
stoichiometricformula KAlr(AlSiaOroXOH),aswere
our data.
White (1919)measuredHF - Hlr, of anorthite,
NaAlSi'O, glass, CaAl2Si2O,glass, and KAlSirO,
glassat 200 K intervalsto 1673K, ll73 K,973 K,
and 1373 K respectively.From these data Kelley
(1960)derivedapproximateheat capacityequations
for eachcompoundwhich give valuesagreeingwith
KRIJPKA ET AL.: HEAT CAPACITIES
T a b l e 5 . E x p e r i m e n t a l h e a t c a p a c i t i e s f o r muscovite, rophyllite, and his heat capacity values show a large
KAl,(AlsisoroxoH),
scatter.
Tenp.
Heet
capec ity
Tenp,
Ileat
capacity
K
J/(nol.K)
K
J/(nol.K)
332.5
342.5
3 6 2. 5
382.6
392.6
397.6
374.6
384.6
394.6
4 0 9. 6
349.5
354.5
364.3
37r.9
379.9
383.1
37 0 . 0
376.7
382.4
390,4
639.6
659.6
679.7
674.7
679.7
6 9 9. 7
719.7
739.7
759.7
779.7
4 6 4. 7
4 7I . l
4 2 9. 5
449.6
469.6
4 3 9. 6
449.6
4 5 9, 6
474.7
4 8 9. 7
509.7
5 2 9. 7
524.7
400.I
409.1
689 .7.
699.7
7 1 9. 7
739.7
75 9. 7
769.6
779.6
759.6
769.6
789.6
819.6
475.3
4 75 . 3
478.7
4 8 3, 7
486.6
4 8 9. 0
493.8
4 8 2. 3
4 8 2. 3
483.3
490.8
529.7
539.7
559.7
579.8
5 9 9. 8
619.8
5 8 4, 6
5 9 4. 6
599.6
619.6
437.t
439.0
443.0
4 4 9. 2
453.3
4 5 9. 7
461.5
454.7
453.8
4 5 9. 6
8 2 9. 6
869.3
879.2
4 9 4, 9
499.5
495.5
4 9 9. 5
5 0 6. 6
5 0 7. 6
500.2
504.0
513.5
5 2 0. 6
404.2
4 0 7. 1
411.6
4t8.7
4 2 3. O
428.8
433.4
435.0
coo
n
9 0 8. 9
923.3
933.r
9 4 2. 8
957.6
967.4
4/r.6
469.4
469.3
475.1
419-t
483.0
485.3
4 8 9. 7
functions
Thermodynamic
Our resultsfor anorthite, CaAlrSirOsglass,muscovite, KAlSisOsglass,grossular,and NaAlSigOe
glassbetween350 and 1000K, and for pyrophyllite
between350and 650K werecombinedwith the lowtemperatureheat capacity values of Robie el a/.
(1976,1978b)and Westrumet al. (1978),and werefit
by leastsquaresto the equation
Cf : A + Bf + CT-2 + DT-t/2 + ET'z
suggestedby Haas and Fisher (1976). Only four
terms were used if a fifth term made no significant
contribution to the statisticalfit, i.e., no sfgnificant
decreasein the root mean squarepercentdeviation'
The curve fitting was accomplishedby meansof the
computerprogramHINc written by D. W. Osborne
of Argonne National Laboratoryand modifiedby
to
B. S. Hemingway.The equationswereconstrained
join smoothlywith the Cf valuesbetween300 and
T a b l e 6 . E x p e r i m e n t a lh e a t c a p a c i t i e sf o r p y r o p h y l l i t e ,
Alrsi.o,o(oH),
TeEp.
Heat
capacity
Tenp.
J/(no1.K)
.l/(mol.K)
to within 12.5 percentup to 1000
our measurements
K. Ferrier (1969) measuredHf - H9""of synthetic
glassto 1500K
anorthiteto 1850K and CaAIzSizOe
with a precisionof approximately2.0 percent.Ferrier, unfortunately,presentedhis data only in the
form of graphsand equations.
Westrum et al. (1978)have measuredthe heat capacity of grossularfrom Asbestos,Quebecbetween5
and 600 K by preciseadiabaticcalorimetry.Their
results were corrected for deviation of the sample
from the exactformula CasAlrSirOtr.Our measured
heat capacitieson syntheticgrossularare in agreement with these smoothed,composition-corrected
valuesto within an averagedeviationof 1.0percent
between350 and 600 K.
Kushov ( I 973) determinedthe specificheat of nat=
ural pyrophyllite over the range of 298-773K by
thermalanalysis.Kushov'sheatcapacityvalueswere
not used in this study, becausehis pyrophyllite
sampledeviatessignificantlywith respectto silicon
and aluminum from the ideal compositionof py-
Heat
capacity
335.9
355.8
375.7
395.6
415.6
320.5
3 2 9. 6
3 3 9. 7
3 4 7. 6
354.3
3 8 2. 6
392.6
374.5
384.6
lstr.d
3 4I . 0
3 4 5. 8
338.9
344.O
348.4
4 3 5. 5
4)).+
475.3
495.2
515.1
3 6 2. 3
370.2
374.3
384.8
393.3
409.6
429.6
449.5
469.6
4 3 9. 6
354.9
363.4
371.9
381.4
364.9
335.9
355.8
375.7
395.6
415.6
317.I
328.6
3 3 7. 6
347.4
356.7
449.6
459.6
474.6
4 8 9. 7
5 0 9. 7
371.6
375.E
382.6
3 86 . 5
388.8
4 3 4. 4
5 2 9. 7
524.7
529.7
392.4
395.6
3 9 7. 2
495.2
515.r
3 65 . r
37r.9
380.4
386.6
39t.9
s 3 s. 7
j*fl.2
559.8
404.0
332.5
3 4 2. 5
362.6
3 1 4. 4
3 2 1. 4
3 3r . 5
57g.8
599.8
619.8
659.6
6 7 9. 6
40g.2
4r5.4
420.8
429.r
429.7
4J).4
4T).J
KRUPKA ET AL.: HEAT CAPACITIES
370 K obtained by accuratelow-temperatureadiabaticcalorimetry.
For anorthite,CaAlrSirO,glass,KAlSirO, glass,
and NaAlSirO, glass,the curve-fittingprocesses
were
extendedto 1800K, 1500K, 1300K, and 1200K
respectively,using the heat content data of White
(1919)and Ferrier(1969).White'sHf - Hgr"data
were corrected to the 1973 values of the atomic
weights,recalculatedto H,f - .Ffir,values,and fitted
by leastsquaresto the equation
Hf -
H3"": c + Ar +]
7"
- CT-t + 2DTi2 *4 r,
with the constraintsthatHi - H3"":0 at Zqg.fS f
and that Cf at 298.15K is equalto thevaluegivenby
Robie er al. (1978b).Heat capacity valuesderived
from this equationwere addedto the heat capacities
obtainedby differentialscanningcalorimetry.
Ferrier (1969) only gave four-term polynomial
equations for Hf - Hg", values of anorthite and
Table 7. Experimental heat capacities for KAlSisO, glass
Tenp.
Ileat
capacity
K
J/ (not. K)
350.2
3 7 0 .r
390.0
4r0.0
4 1 9. 9
4 2 9. 9
419.9
439.9
459.8
479.8
228.6
489.8
4 9 9. 8
s09. l
504.7
5 0 9. 7
5 1 9. 7
5 3 9. 7
559.6
5 79 . 6
589.6
5 9 9. 6
594.8
599.7
6 0 9. 7
6 2 9. 7
6 4 9. 7
659.6
6t4.h
679.6
6t9.7
629.7
Tenp.
lleat
capaclty
298.4
2 9 7. 7
298.5
2 9 5. 8
296.6
2 9 7. 4
299.4
302.3
304.4
2 6 9. 0
2 72 . 8
2t 5.0
277.6
2 78 . 0
780.0
759.9
770.0
790.0
810.0
8 2 0 .0
830.1
864.7
874.6
888.0
3 0 5 .3
30r.7
302.9
3 0 4 .3
305.7
306.1
306.1
306.7
3 0 7. 9
310.3
282.5
2 8 3. 7
284.0
285.0
286.8
288.1
289.0
291.2
2 9 1. 5
286.8
290.0
293.8
9 0 8 .9
9r8.7
899.r
9 0 8 .9
928.6
938.4
948.2
923.7
933.5
948.2
958.0
9 6 7. 9
309.6
308.6
3 0 7. 9
z )4.
6
259.3
2 6 4 .r
2 6 4. 8
269.4
267.2
Table 8a. Experimental heat capacities for synthetic grossular,
CarAlrSisO,,
Tenp.
K
Heat
capaclty
J/(no1.K)
TeEp.
Heat
capaclty
K
J/(Eol.K)
350.2
37 0 .I
390.0
4 1 0 .0
419.9
429.9
419.9
439.9
459.8
371.1
3 79 . 9
392.6
401.0
403.8
408.7
401.8
4r0.0
4r9.6
669.6
6 79 . 6
619.8
629.8
649.7
669.7
689.7
699.7
70 9. 7
464.0
4 6 7. 9
453.6
454.5
458.3
460.4
462.3
462.8
4 6 5 .4
4 8 9. 7
499.7
509.6
504.7
5 0 9. 7
5t9.7
s 3 9. 7
559.6
424.9
424.4
4 2 9. 7
430.8
434.4
438.8
440.5
4 4 6. 9
450.7
759.7
76 9. 7
78 9. 6
819.6
829.6
869.3
8 79 . 2
899.0
9 08 . 9
468.0
4 6 3 .4
465.7
472.9
4 7 7. 6
494.8
49L.4
495.7
4 9 7. 2
452.7
452.9
918.8
9 0 3. 7
918.4
9 3 8 .0
9 4 7. 8
9 5 2. 7
962.5
9 77 . 2
987.r
492.1
4 8 0 .r
480.5
48L.2
4 8 5 .4
4 8 2. Z
481,8
4 8 9. 7
485.6
579.6
589.6
5 9 9. 6
594.7
5 9 9. 7
6 0 9. 7
629.7
649.6
6 5 9. 6
4)1.
o
456.7
c)d.
)
4 5 7. 9
459.9
462.4
4 6 2 .L
J/(no1.K)
6 6 9. 7
6 8 9. 7
699.7
709.7
6 8 9 .8
6 9 9 .8
71 9 . 9
73 9 . 9
75 9 . 9
770.O
248.7
2 5 1 .0
253.4
249.6
9l
JU/.O
309.4
310.8
312.4
JIJ.
)
JIJ.O
313.5
314.0
CaAlrSirO,glasswhich reportedlyfit his data to *2
percent.Valuescalculatedfrom his equationswere
includedwith the data setsfrom our measurements
and thoseof White for the final curvefitting.
Our resultsfor syntheticgrossularand natural
grossular from Asbestos,Quebec,were separately
combinedwith low-temperatureheat capacityvalues
of Westrumet al. (1978)and fittedby leastsquares
to
the generalCf equation.Becauseof the greateraccuracy of the data by Westrum et al. (1978),their Cf
valueswereweightedby a factor of threein the curvefitting process.The equationfor the naturalgrossular
wasnot usedfor the derivationof the thermodynamic
functionsbecause
thesamplelackedchemicalcharacterization.
The final Cf equationsfor anorthite, CaAl2Si2O8
glass, muscovite, pyrophyllite, KAlSisos glass,
grossular,
and NaAlSieO,glassarelistedin Table 10.
The errorsin the derivedthermodynamic
functions
are estimatedto be t0.7 percentin Cf and (Hf Hg"")/T,and a0.3 percentin Sf and (Gf - H9"")/T
between300 and 1000K. Tabulatedvaluesof the
thermodynamicfunctionsCf, (Hf - H3")/7, 53,
KRUPKA ET AL, HEAT CAPACITIES
92
Table 8b. Experimental heat capacities for grossular from Jeffrey
m i n e , A s b e s t o s ,Q u e b e c
Tenp.
Heat
capaciEy
Tenp.
Heat
capacity
K
J/ (nol.K)
K
J/(mol.K)
3 4 9. 1
?qo
I
3 6 9 .r
379.1
3 8 9. l
?oo
I
4 0 9 .r
419.r
4 2 9. 1
5 0 4. 2
509.2
519.2
qro 2
q?o
,
549.2
559.2
569.2
579.2
589.2
599.2
378.7
384.0
388,5
3 9 1. 8
427.9
4 8 4. 5
499.5
5r9.5
5 3 9. 5
549.5
559.5
549.5
559.5
579.5
599.5
415.1
418.4
4 2 2, 7
429.9
432.9
435.7
430.9
433.0
4 3 7. O
4 4 1. 3
4 2 2. 4
4 2 6. 7
4 2 9. 3
4 3 2. 4
434.6
436.2
4 3 7. 6
440.9
4 4 4. 1
6t4.5
6 2 4. 5
6 3 4. 5
6 2 4. 5
6 3 4. 5
649.5
6 6 9. 5
689.4
699.4
709.4
4 4 4. 6
445.8
4 4 8. 3
443.2
445.4
4 4 8. 7
451.6
456.0
457.7
459.5
354.9
361.1
365.1
3 6 9. 2
JT).1
594.0
599.0
609.0
6 1 9. 0
629.O
639.0
6 4 9. 0
659.0
669.0
679.0
442.2
349.8
354.7
358.5
361.0
371.4
3 8 3 .r
387,3
3 8 4 .r
388.6
393.5
402.2
408.0
474.3
4t6.4
4 7 2. 4
3 9 4. 7
4 0 9. 6
409.5
4r9.5
4 3 9. 5
4 5 9. 5
479.5
4 8 4. 5 ,
4t4-)
448.2
450.7
453.0
454.9
456.0
456.8
458.5
457.9
699.2
709.2
729.2
749.2
769.2
774.2
763.6
714.6
789.6
809.6
829.7
839.7
959.6
969.6
979.6
9 8 9. 6
ooo q
903.4
918.1
927.9
937.7
9 4 7. 5
9)t.5
46r.5
460.7
4 6 4 .r
461.8
470.6
467.5
468.3
4 6 9. 7
473.7
4 76 . r
476.3
493.3
495.0
4 8 9. 5
495.5
4 9 8. 0
488.7
4 9 7. 3
492.3
493.1
495.8
494.9
on a knowledge of the entropiesand heat capacities
(as a function of temperature)for all the phasesinvolved in the equilibrium. For a reaction like the
dehydration of muscovite or pyrophyllite, in which
none of the phasesis a solid solution, a value of the
enthafpy of reaction at 298.15 K, LHypsB,can be
calculated from each equilibrium bracket using the
relation
-LH|,,"":
fA [(Cf - H|")/n+
I.PLVSdP
where A Zf is the difference in the molar volumes of
the solid phases in the reaction. For the pressure
range over which equilibrium measurementsexist for
the dehydration of muscovite and pyrophyllite, the
approximation can be made that
I,,LVfdP
Table 9
It has been shown (for example, Darken and
Gurry, 1953;Lewis and Randall, 1961,p. 177;Robie,
1965;Stull and Prophet,1971,p. 5) that the so-called
third-law method provides a rigorous means of extracting values of the enthalpy of reaction at298.15
from equilibrium measurements.It also
K, A1l1,2e8,
simultaneously furnishes a critical test of the accuracy of the equilibrium data. This approach is based
l) LWsa
Experimental heat capacities for NaAlSirOr glass
Heat
capacity
Tenp.
Heat
capacity
K
J/(nol.K)
K
J/(nol,K)
350.2
370.1
390.0
410.0
4t9.9
429.9
4r9.9
439.9
459.8
479.8
2 2 8. 3
236.r
2 4 3. 3
2 4 9. 0
2 5 1. 4
2 5 3. 9
249.0
2 5 4 .r
489.8
499,8
509.7
504.7
509.7
2 6 4. 0
ql
o
) Jt
7
. I
5 5 9. 6
589.6
and AGl,z'. for musThirdlaw derivation of AH?,2s8
covite, pyrophyllite, and grossular
= (P -
Temp.
)ti.o
and (Gf - H3,,)/T derived from the Cf equationsin
Table l0 are given in Robie et al. (1978a).
(l)
* RZlnlZ,H,O)
?se
q
2 6 3. 3
zoo.o
2 6 8. 5
267.r
267.6
2 6 8. 8
272.5
274.5
276.9
279.3
599.6
594.8
599.8
609.7
6 2 9. 1
649.1
659.6
2 8 1. 7
2 8 2. 9
2 8 3. 3
284.2
286,I
2 8 6. 6
o/4.o
679.6
674:6
290.5
290.9
286.r
679.6
689.6
709.6
729.6
749.6
294.3
297.4
2 9 9. 3
302.9
3 0 5. 9
rao
?
7 5 9. 6
764.6
619.1
6 2 9. 7
6 4 9. 7
669.7
6 8 9. 7
699.7
709.7
689.8
3 0 5. 3
305.3
289.8
2 9 1 .r
294.3
296.6
298.2
2 9 9. 9
3 0 1. 9
297.6
699.8
719.9
739.9
760.0
770.0
780.0
760.0
770.0
810,0
8 2 0 .r
298.9
298.8
300.5
304,3
306.9
307.1
3 03 . 5
304.2
3 0 9. 2
310.2
830.I
8 6 4. 7
874.6
889.3
908.9
9r8,8
899.0
908.9
928.6
938.9
310.9
948.2
318.6
317.1
318.6
320.1
3 2 0. 7
3 2 1. 4
ot1
7
933.5
948.2
958.0
967.9
1l?
c
3r3.1
JL4.'
3r6.2
377.4
) \4.
JI
I
I . J
319.5
318.2
KRUPKAET AL
The value of A,Hl,"r"calculatedby this method is
independentof the enthalpiesof formation and their
associatederrors for the reacting phases.The thirdlaw method usesthe differenceof Gibbs free-energy
functions, At(Gf - Hg"r)/Tf, which is derived solely
from heat capacitydata, usually the most accurateof
the data used in a thermodynamic calculation. The
difference of Gibbs free-energy functions, which are
given in most tabulations of thermodynamic properties, is a continuous, monotonically changing function of temperatureand variesnearly linearly at high
temperatures.Figure 4 shows the variation of the
differences of the Gibbs free-energy functions with
respectto temperaturefor two mineral reactionsdiscussedlater. Values of the Gibbs free-energyfunction
can be easily interpolated, which results in an accurate integration of the entropy contribution of a reactron.
Values of the enthalpy of formation, LHo,.r"r,are
derived for muscovite, pyrophyllite, and grossular,
basedon: (1) recentequilibrium studies,(2) valuesof
the Gibbs energy function, (G+ - H|,J/ 7, calculated
130
120
HEAT CAPACITIES
150
5ro
=r0
t50
50
IEMPERATURE
IN ItLVINS
F i g . 2 . E x p e r i m e n t a l m o l a r h e a t c a p a c i t i e s ,C B , o f m u s c o v i t e
[KAl,(AlSi.O,o)(OH),], pyrophyllite [Al,SinO,o(OH),], and
K A l S i . O , g l a s s f r o m T a b l e s 5 , 6 a n d 7 , r e s p e c t i v e l yo, b t a i n e d b y
DSC Above 298 K, the solid curves are generated from the C!
e q u a t i o n sg i v e n f o r m u s c o v i t e ,p y r o p h y l l i t e ,a n d K A l S i . O , g l a s si n
Table 10. Below 298 K, the curves are from the data of Robie el a/
( 1 9 7 6 )f o r m u s c o v i t ea n d p y r o p h y l l i t e ,a n d f r o m t h e d a t a o f R o b i e
et al (1978b) for KAISi'O' glass.
0
/
(f
dlfr
,n
-lm
r
I
I
lt
r NaArS,r(
/t
0
Ga s s
//
Coiundum,!nsb cryild
/
0
r00
200
r00
r00
800
rll*lr,*rJi'* *r,J,',i,
0
r00
200
300
700
ifi**J:t,,
E00
e00
1000
*;t:
F i g . l . E x p e r i m e n t a lm o l a r h e a t c a p a c i t i e sC
, p,ofcorundum (aAlrOr) and periclase (MgO) obtained by differential scanning
calorimetry (DSC). For corundum, the solid curve is from the
v a l u e s g i v e n b y D i t m a r s a n d D o u g l a s ( 1 9 7 1 ) . F o r p e r i c l a s e ,t h e
solid curve is from the work of Victor and Douglas (1963)above
2 7 3 . 1 5 K , a n d B a r r o n e t a l ( 1 9 5 9 ) b e l o w 2 7 3 . 1 5K .
Fig. 3. Experimental molar heat capacities, C?, of grossular
(CarAlrSirO,r) from Jeffrey mine, Asbestos, Quebec, and of
N a A l S i s O eg l a s sf r o m T a b l e 9 o b t a i n e d b y D S C . F o r g r o s s u l a r ,t h e
solid curve is the least-squaresfit of the results of Westrum e, a/.
(1978) and the experimental data listed in Table 88. For
NaAISirOe glass,the solid curve above 298 K is generatedfrom the
C! equation given for NaAISLO, glass in Table 10. The solid curve
below 298 K is from the data of Robie et al. (1978b) on the same
sample of NaAlSirO, glass.
94
KRUPKA
ET AL.
HEAT
CAPACITIES
Table10. Molar heat capacity equations obtained by a leaslsquares fit to the experimental CE data for anorthite, CaAl,SirO" glass,
muscovite, pyrophyllite, KAISiBOBglass, grossular, and NaAlSi3Os glass
Temperature
range
of equation
Conpound
Aver. t
deviation
between data
and equation
Equations
for
ci
in
J,z(moI.K)
c $ = s r e . e - o . o 9 2 4 9 r - r.4oaxto6r-2- nsrer-L + 4.rBBxro-5T2
Anorthite
caAl2Si20g
(298 - 1800 K)
CaAI2Si2OS 91ass
(298 - rsoo K)
o.7
- ,+ugr-\
c f l = s l s . z + 0 . 0 3 1 9 7 T- 2.815x10fo-2
(2M1)
Muscovite
K A 1 2( A 1 s i 3 0 1 2 ) ( O H )
2
(298 - 1000 K)
o.4
cF=9L7.7 -
Pyrophyllite
A12Si40rO (OH)
2
(298 - 800 K)
0.3
cfi = elg.l
(298 - 1300 K)
o.4
c l = 6 2 9 . 5 - 0 . I 0 8 4 r + z.ag6xLo6,r-2 - rzto*-\
(298 -
1200 K)
1.0
ci*= r0::.:
(298 -
1000 K)
0.6
c i * * = 6 3 0 . 4 + O . 1 3 O O T- 3.6g5xto6r-2 - eslqr-\
n?
c i = s s a . a - o . 3 8 9 1 r + 5.59axto6r-2 - ttezor-L
KAISi308
glass
Grossular*
c"3ol2Si3o12
Grossular**
(Asbestos,
equation
** The C; data
equation
- 0 . 0 6 4 1 2 r - egozr-\ - 5.99zxro5r2
- o . 7 5 9 9 T+ g.ttgxto6r-2
+ r.928x10-5T2
- zozazr-b + 2.66gxLo-4r2
Quebec)
(298 - 1200 K)
NaAISi3OS 91ass
* ci
o . 0 8 1 1 1+
r 2.834x106r-2 - IOSAST-L
used to
derive
for
grossular
the
was used onfy
the
themodynmic
sanple
to derive
the
functions
from Asbestos,
smooth curve
listed
euebec,
for
in
from preciseheat capacity measurements,
and (3)
previously-published
valuesfor the enthalpies
of formation at 298.15K of the ancillaryreactants.The
Gibbs energyfunctionsof muscovite,pyrophyllite,
grossular,and anorthite are derived from the Cf
equationsobtainedin this study;thoseof corundum
are from Ditmarsand Douglas(1971);thoseof wollastonite,quartz,andalusite,
and steamaretabulated
in Robieet al. (1978a);and thoseof highsanidineare
from valuesgivenby Hemingway,Krupka and Robie
(unpublisheddata, 1976).Valuesfor the fugacityof
water, J(T,HrO), were taken from Burnham et al.
(1969).The molar volumes,VBrr,of the solid phases
at 298.15K and I bar pressurewere taken from
severalsources.We have used 22.688t0.001cm3,
25.575+0.007
cm3,and 51.53t0.04cmsasthe molar
volumesfor low quartz,corundum, and andalusite,
respectively,taken from the compilationof Robie el
al. (1967).For the molar volumeof 2M1 muscovite,
we used140.73+0.20cm3,which is the averageof the
volumesobtainedfrom the cell parametersof Chatterjeeand Johannes(1974),Robie et al. (1976),and
Giiven (1971). For pyrophyllite,we averagedthe
unit-cellvolumedata of Wardle and Brindley(1972)
Table 15.
were not
grossular
+ L.4z6xlo-4t2
i h
Fi
corrected
d'rr6
for
conposition.
The Ci
q
and Taylor and Bell(1971)to obtaina molarvolume
of 127.82+0.29cml. For high sanidine,we used a
molar volumeof 108.91t0.04cm3,which is an average calculatedfrom the unit-cell volumesof Openshaw e, al. (1976),Stewartand Wright (1974\, and
Chatterjeeand Johannes(1974).
Chatterjeeand Johannes(1974) investigatedthe
reactions
muscovite= high sanidine
* corundum+ steam
(2)
and
muscovite * quartz a high sanidine
* andalusitef steam
(3)
Reaction(2) was studiedin the PHrO rangeof 1000
to 8000bars, at temperaturesbetween873 and 1073
K. They gave the uncertaintiesfor the experimental
pressuresand temperatures
obtainedfor reaction(2)
as tl00 barsand 16 K at PH,O < 8000bars,and
tl00 barsand +10 K at PH,O : 8000bars.Reaction (3) wasstudiedin the PH,O rangeof 500to 5000
bars, at temperaturesbetween793 and 973 K. For
KRUPKA ET AL.' HEAT CAPACITIES
95
termsof LG',,, and thendifferentiatedwith respectto
temperatureto obtain the entropy changefor the
reaction,AS?,r usingthe relation
- AS?,r
QLGI/a7)p:
=
Y
163
.R
t.".
I
Dehydralionof muscovite
D e h y d r a t i oonJ p y r o p h y l l r t e
155
200
400
600
800
1000
1200
TEIIIPERATURE.
IN KELVINS
Fig. 4. Plot of the difference of the Gibbs free-energy functions,
-A(C? - H"""")/71,with respectto temperature
for two reactions
studied in this paper. The trianglesrepresentthe dehydration
reactionmuscovite= high sanidine* corundum * HrO. The
squares represent the dehydration reaction pyrophyllite e
andalusite
+ 3 quartz+ HrO.
The value calculatedfrom Chatterjeeand Johannes'
equationsfor AS?,,ooo
of reaction(2) is fta.2 J/K and
for AS?,,00
of reaction(3) is 159.6J/K. Valuesof
AS?,r can also be calculatedusingthe value for Sor*
and Johannes
and the
of sanidinegivenby Chatterjee
auxiliaryentropydata from the samesourceusedby
Chatterjeeand Johannes,
i.e. Robie and Waldbaum
(1968).From thesedata, AS?,rooo
of reaction(2) is
155.4J/K and AS?,,00
of reaction(3) is 155.0J/K.
However,Hemingwayand Robie (1977)point out
that Chatterjeeand Johannesusedan incorrectvalue
for S?r,of sanidine.Thevalueof AS?,rooo
for reaction
(2) is 137.2J/K and AS?,'oo
for reaction(3) is 139.0
J/K, basedon: (1) ,Sor*valuesfor sanidinefrom
Openshaw
et al. (1976)andfor muscovitefrom Robie
et al. (1976);(2) Si valuesfor sanidinefrom Hemingway, Krupka and Robie (unpublisheddata, 1976)
and for muscovitefrom this study;and (3) S?geand
Si values for andalusite,corundum, quartz, and
steam from Robie e/ al. (1978a).Thesevalues are
very different from thosecalculatedfrom the equationsof the equilibriumconstants.
The reasonfor thesediscrepancies
is not clear.The
considers
modelchosenfor the third-lawcalculations
Table ll.
Calculation of AH"..r"" for reaction (2)*, muscovite e
high sanidine * corundum * HrO
reaction(3), the uncertainties
are givenas 450 bars
and +6 K at P < 2000bars,and f 100barsand +6 K
(P-r-)^vies rr,n.o ro'rr,n^o ^"i,zgs
u [fc;-Hie8)l
----T--]__-.--z.z
at P > 2000bars.Our calculations
of the enthalpies
K
bars
J/K
bars
J/K
J/K
J
of reactions(2) and (3) at 298.15K, basedon the
equilibrium results of Chatterjeeand Johannes 873 1000 - 1 5 8 . 4
-0.7336
631.0
53.61
92L20
-0.7252
646.0
53,80
92830
(1974),are shownin Tablesl1 and 12 respectively. 883 1000 - 1 5 8 . 2
-L.404
The uncertaintiesfor the averagevaluesof LHo,.2s8 913 2000 - L 5 7 . 6
LLTL
58.75
91530
-r57 .2
-L.373
933 2000
1230
59,L6
92750
representtwo standard errors (twice the standard
- 1 5 7. 0
943 3000
62.59
1859
90950
deviationof the mean).
-156.8
-2 .OL7
953 3000
1903
62.79
91510
The calculatedvaluesof LHo,,zs8,
especiallyfor re-r)o.b
-2,662
2736
953 4000
65,80
90000
-2.608
2456
65.16
91070
action (2), show a drift with temperature
and pres- 983 4000 -L56.2
-3.221
sure. Calculationsby Zen (1977),using the same 9 9 3 5 0 0 0 - 1 5 6 . 0
68,89
89700
3964
- 1 5 5. 8
-3,L95
4040
69,O4
90220
experimentaldata, show a similar variation in the 1003 5000
- 1 5 5. 6
-3.796
6000
5474
7r.57
88970
valuesof AG?,zgs
of muscovitecalculatedby the 1013
- 3 . 75 9
1023 6000
5576
7L.72
89450
method describedby Fisher and Zen (1971).This
- r 5 4. 8
-4.870
1053 8000
76.42
87660
9813
-4.779
suggests
an error with eitherthe modelchosenfor the 1073 8000 -L54,4
10096
76.66
88540
third-law calculation and/or the experimentaldata.
AveraCe AIt;,298 = 90520 t 840 J
(1974,p. 89)giveequations
Chatterjeeand Johannes
for the equilibriumconstants
(2) and(3)
for reactions
*The experinental
(2) are froE the data
brackets
fo! reactl.on
obtainedby a linear least-squares
fit to their experi- of Chatterjee ad Johanes (1974).
mentalbrackets.Theseequationsmay be rewrittenin
-r5f.c
KRUPKA ET AL.,' HEAT CAPACITIES
Table 12. Calculation of LH",.2" for reaction (3)*, muscovite *
quartz a high sanidine * andalusite * H,O
t
K
" ^fti-*isal
"L--r
J
bars
(P-r)^vie8rr,rr"o n'rr,"^o ^"l,zgs
r
J/K
J/K
J/K
bars
J
500
500
-160.2
-759 .4
-o.1924
-0.1831
340.0
369.0
48.47
4 9. r s
887s0
91990
823 1000
843 1000
-r59.6
-0 .3711
-o,3623
550.5
585.0
s2.47
s2.98
88470
89850
863
878
2000
2000
-158.8
-158.4
-0.7081
-0.6960
1015
1062
57.56
57.93
87980
88820
893
912
3000
3000
-158.1
-1.O27
-1.004
1630
1724
6r.50
6t.96
87180
88330
933 4000
943 4000
-1s7.3
-r57.1
-1. 310
-L.296
255L
26L2
6s.22
65.42
87130
87680
963 5000
978 5000
-156.6
-L.587
-r.562
3728
3849
68.38
68.64
86480
87260
793
833
-a)o.
J
Average AIt;,298 = 88330 t 850 J
*The experiEental
of
Chatterjee
brackets
dd
Johannes
for
reactlon
(3)
are
froo
the
data
(1974).
muscoviteand sanidineto be completelydisordered
with respectto AllSi. The crystalstructuredeterminationsfor 2M, muscoviteby Giiven(1971)usingXray diffractionand by Rothbauer(1971)usingneutron diffractionindicatecompletedisorderof the Al
and Si atomsin the 2M, muscovitestructure.Because
theAllSi disordermightbe an artifactof the symmetry restrictions
usedin the data reductionby Giiven
(1971),Guggenheim
and Bailey(1975)re-refined
the
2M, muscovitestructurein the subgroupsymmetry
Cc usingRothbauer'sintensitydata.Their subgroup
refinementalso showsan Al/Si disorderin the 2M'
muscovitestructure.Without structuraldata on the
muscoviteproducedby Chatterjeeand Johannesin
their run products,we had to assumethat their muscoviteis a 2M' muscovitewith completeAllSi disorder.
Chatterjeeand Johannesalsoreport the cell dimenZ (Thomporderparameter
sionsand the long-range
produced
son, 1969;Hovis, 1974)for four sanidines
(2).
The narrow range of thesevalues
by reaction
with
arecompletelydisordered
suggests
the sanidines
range
of
their
experito
Al/Si
over
the
entire
respect
ments.
The experimentalrun timesusedby Chatterjeeand
Johannesdecreasesignificantlyas the temperatures
Experiincrease.
and pressures
of their experiments
mentalrun times,however,can be an important factor in interpretingthe final resultsas recentlyshown
in a studyon ferrieritesby Cormier and Sand(1976).
Velde(1965)hasalso shownthat the stabilityof the
differentmuscovitepolytypesis a functionof temperature, pressure,and time. Chatterjeeand Johannes
usedX-ray diffraction to identify the phasesin the
run productsand to establishthe directionof the
reaction.It would be almostimpossibleto identifya
muscovitepolytypeother than 2M, muscoviteif it
comprises
only l0 or 20 percentof the total amount
of muscovitein an X-ray diffractogramwhich also
containsall of the phasesin reaction(2) or (3).
If one considersmuscoviteasan orderedphase(for
example,3T muscovite)and subtractsout the configurational-entropycontribution for the AllSi disvaluesfor reactions(2)
order, the calculatedLHor,zse
and (3) show little or no variationwith respectto
temperature.The slopesof the calculatedreaction
curvesare then consistentwith the experimentalresults. However,theseLHo,,r" valuesresult in two
different LHor.r""values for muscovite,which are
than the valuegiven
morenegative
both considerably
by Hemingwayand Robie (1977)for a 2M' muscovite.Until a detailedstructureanalysisis madeon
the final syntheticmuscoviteproducedin the equilibwe submitthat the only logical
rium investigations,
calculationis that
modelto usein thethermodynamic
of the AllSi-disordered2M' muscovite.
The meanvalueof AHo,,",for reaction(3) (Table
l2), 88330+850J, was combinedwith the valuesof
and steamfrom Robie
for quartz,andalusite,
A,Ifs,ze
et al. (l'978a),and for sanidine(Z : 0.12+0.02)from
Hemingwayand Robie (1977)to yield a value of
-5966500+4040J/mol for the L,Ho1.ze
of muscovite
Hemingwayand Robieobtaineda
from the elements.
of
value of -5976700+3240J/mol for the LH"1.2"s
of the solutioncalomuscovite,from a recalculation
rimetry of Barany (1964),basedon their new meaof formationof gibbsite,
of the enthalpies
surements
and the heatof solutionof quartz.
The mean of the calorimetricvalue of LHor.r"
for muscovite(Hemingway and Robie, 1977) and
the AH].2rsvalue calculatedfrom reaction (3) is
-5971600+5180J/mol. We believethat this represents the best value now available for AH].rr. of
disordered2M' muscovite.The equilibriumcurves
for reactions(2) and(3), calculatedfrom this valueof
valuesof theGibbs
LHo,.""andthe high-temperature
energyfunctions(Figs.5 and 6), are in ratherpoor
agreementwith the experimentaldata of Chatterjee
and Johannes(1974) for reaction(2) and in fair
agreementwith their data for reaction(3). Montoya
of 873 K at
and Hemley(1975)give a temperature
1000barsfor the breakdownof 2M' muscovitein the
equipresence
of quartz[reaction(3)].Our calculated
K R U P K A E T A L . HEAT CAPACITIES
TEIV]PERATURE,
IN DEGRI€SCTLSIUS
600
roo
Gibbs energy functions for pyrophyllite from this
study and for andalusite,quartz,and steam(Robie el
al., 1978a)were combined with the experimentaldata
in a third-law calculation to obtain LHo,,"n,for the
reaction (Table l3). Two distinct setsof L,H",,rrvalues can be calculated from the three sets of experivaluesshows any
mental data. Neither set of LHo,.zss
significant variation with temperature.The average
value of LHo,,r, derived from the data of Hemley
(1967) and Kerrick ( 1968)is 79670i I 100 J, whereas
that calculated from results of Haas and Holdaway
(1973)is77440t370 J. The set ofexperimental brackets from Hemley and Kerrick and the set from Haas
and Holdaway are each internally consistent As Kerrick and Haas and Holdaway used the same experimental technique,we have no basis for favoring either set of experimental values. Equilibrium curves
for reaction (4) calculatedfrom each averagevalue of
we determinedare shown in Figure 7.
LHo,.zge
500
\ \ !
I\4uscovile
\*
\
-9
?a
Hrghsanrdrne+corundum+Hzo
-
05
80
90
100
(19/4)
Chatleriee
andJohannes
ilo
.
'
IO','TlN KELVINS
120
130
l4o
F i g . 5 . P l o t o f l o g l T ' , H r O ) u s . 7 ' f o r t h e r e a c t i o n m u s c o v i r e=
high sanidine * corundum + HrO. The equilibrium curve was
calculated from the AH?.r", of muscovite as determined in this
study The stippled area representsthe uncertainty contributed by
t h e t h e r m o d y n a m i c f u n c t i o n s i n t h e c a l c u l a t i o no f t h e c u r v e . T h e
experimental brackets are from the data of Chatterjee and
J o h a n n e s( 1 9 7 4 ) .
librium curve for reaction (3) (Fig. 6) is in agreement
with this value.
The mean value of LHor,n"of muscovite was combined with the valuesfor the entropiesof muscovite
(Table 12) and its constituentelements(Robie er a/.,
1978a) to obtain -5595500+5190 J/mol for the
Gibbs free energy of formation, LGoy.2ss,
for disordered 2M, muscovite.The range of LGo,.rn"
values
for muscovite calculatedby Zen (1977) from the experimental data of Chatterjee and Johannes agree
very well with the value obtained in this study.
Zen's L,G],2s8values for muscovite vary between
-5597500+4600 J/mol and -5600300+5900 J/mol.
Hemley (1967), Kerrick (1968), and Haas and
Holdaway (1913) have studied the equilibrium
pyrophyllite = andalusite I 3 quartz * steam (4)
at temperaturesbetween 638 and 736 K and in the
PH,O range of 1000 to 7000 bars. Values of the
l-{
I
(1971)
Chattdieeond.lohannes
itontDya
and Hemle,(1975)
Fig. 6. Plot of loglI,HrO)us.7-'
f o r t h e r e a c t i o nm u s c o v i t e *
quartz = high sanidine * andalusite + H,O. The equilibrium
curve was calculated from the Al1?.r* of muscovite determined in
this study. The stippled area representsthe uncertainty contributed
by the thermodynamic functions in the calculation of the curve
The experimental brackets are from the data of Chatterjee and
Johannes (1974). The solid square represents the experimental
point taken from Montoya and Hemley (1975).
KRUPKA ET AL.: HEAT CAPACITIES
Table 13. Calculation of LH",.", for reaction(4), pyrophyllite =
andalusite * 3 quartz * HrO
t
K
t
.^["i-"ig-dl
L
T I
bars
J lK
(P-1)^v;e8 rr,n"0
.
T
J/K
Rl'rr,u"o ^Ei,zes
bers
J/K
J
638 1 0 0 0 *
5 6 8 1000*
-L65.44
-165.23
-L322
-L.263
r99.5
252,8
44.O3
46.00
78300
80490
668 1800**
698 1800**
-165.23
- L 6 5. O 2
-2.274
-2.L16
358.0
440.3
48.90
50,61
79230
81380
6 8 8 3900**
718 3900**
-165.09
-164.88
-4.785
-4.585
919.0
1098.3
56.73
58.22
77840
79870
= 79520 !
IO9O J
Average
AH;.298
-L65.4L
-L55.25
-3.150
_3.046
3 7 6. 5
446.6
4 9. 3 1
50.73
76680
78180
668 3500***
678 3500***
-165.23
_165.16
-4,423
_4.358
6 9 4. 8
744.5
5 4. 4 L
54.98
7694O
77660
687 4 8 0 0 * * *
697 4 8 0 0 * * *
-165.10
-165.03
-5.898
-5.814
r252
1329
5 9. 3 0
s9.80
76740
77400
728 7 0 0 0 * * *
736 7000***
- 1 6 4. 8 1
-164.75
-8 ,I18
_8.030
3203
3323
6 7, 7 r
67.42
77040
77 5 4 0
*Experlmental
comuD.,
bracket
Is
1976) for rhar
**Experimental
***Experinental
blackets
brackets
a revised
value by Ilenley
given tn Henley (1967).
from Kerrick
from llaas
dP/dT:
AS?oolAZ?oo
: ( 6 8 . 5J / m o l ' K ) / ( 3 2 . 1 c m 3 ) : 2 l t 4 b a r / K
643 2 4 O O * * *
665 2 4 O O * * *
Average AHo,29g = 77280 !
we calculate LHo,,"n"
equal to 54300+1800J/mol for
the enthalpy changefor reaction(5). This value, combined with the enthalpiesof formation at 298.15 K
for woflastoniteand quartz (Robie et al.,1978a) and
anorthite (Hemingway and Robie, 1977) yields
-6657100+4720 J/mol for L,H],n" of grossular.
From the entropiesand molar volumes of the phases
at 800 K (Table l4), the initial slope of the equilibrium curve (i.e., at I bar pressure)was calculated
using the relation
This value agrees,within the combined experimental
uncertainty, with the line drawn through the experimental P-T data,26t2bar/K. Combining this result
with the entropiesof the elements,wollastonite,and
360
(personal
(1968).
and Holdaway
(1973).
The mean of the two averagevaluesof A//o",rn,for
r e a c t i o n ( 4 ) i s 7 8 4 0 0 t 1 8 5 0 J . W e b e l i e v et h a t t h i s
representsthe best value for LHo,,zge
for reaction (4)
and is a fair representationof the state of the art of
phase equilibrium measurementsfor pyrophyllite.
Combiningthis valuewith the AHo7,rn"valuesadopted
by Robie et al. (1978a) for quartz, andalusite,and
steam, the enthalpy of formation of pyrophyllite
f r o m t h e e l e m e n t si s - 5 6 3 9 8 0 0 + 3 9 5 0 J / m o l . T h e
enthalpy of formation of pyrophyllite was combined
with the entropiesfor pyrophyllite and its constituent
efements(Robie et al., 1978a) to obtain a value of
-526900+3960 J/mol for AG"1'""of pyrophyllite.
Newton ( 1966)H
, ays ( 1967)B
, o e t t c h e r( 1 9 7 0 ) a
, nd
Windom and Boettcher (1976) have determined the
equilibrium curve shown in Figure 8 for the reaction
g r o s s u l a r* q u a r t z a a n o r t h i t e* 2 w o l l a s t o n i t e ( 5 )
at temperaturesbetween875 and 1575K, and in the
pressurerange of 2000 to 19500 bars. Extension of
the equilibrium curve to a pressureofone bar passes
through 800+15 K. From this extrapolation and the
relation
L G " , . r : L H o , . r " " + Z A I ( G A- H " r " ) / 7 1
(1973)
o HaasandHoldaway
r
a
(1967,1976)
Hemley
(1968)
Kemck
'
10.4, IN KELVINS
Fig. 7. Plot of log/(Z,H,O)us 7 ' for the reaction pyrophyllite
= andalusite f 3 quartz + HrO. The equilibrium curve at the
lower temperatureswas calculated from the averageA.F1'..r""
for the
dehydration of pyrophyllite determined from the experimental
d a t a o f H a a s a n d H o l d a w a y ( 1 9 7 3 ) .T h e o t h e r e q u i l i b r i u m c u r v e
was calculated from the average Af1',.r* for the same reaction
u s i n g t h e d a t a o f H e m l e y ( 1 9 6 7 ;p e r s o n a lc o m m u n i c a t i o n , 1 9 7 6 )
and Kerrick (1968)
KRUPKA ET AL: HEAT CAPACITIES
quartz (Robie et al., 1978a)and our new entropy and
enthalpy values for anorthite and grossular yields
L,Go1.zse
equal to -6295300+4730 J/mol for grossular.
Summary
l6
(1966)
Newion
A
lays (19671
O
Eodths (19/0)
n
W L f l d oamn d B o e t l c h e{ 1r 9 / 6 )
J/ (mo1.K)
quadz
Grossular+
-10
E
A n o d h r t e +2 W o l l a s l o n
te
0L
600
1200
iENIPERATIJRE,
IN KITVINS
Fig 8 Plot of the P-I conditions for the reaction grossular *
q u a r t z c a n o r t h i t e * 2 w o l l a s t o n i t e .T h e o q u i l i b r i u m c u r v e w a s
e x t r a p o l a t e dt o 8 0 0 + l 5 K a n d I b a r u s i n gt h e e x p e r i m e n t a ld a t a o f
N e w t o n ( 1 9 6 6 ) , H a y s ( 1 9 6 7 ) , B o e t t c h e r( 1 9 7 0 ) , a n d W i n d o m a n d
B o e t t c h e r( 1 9 7 6 ) .
J/(m1'r)
"r3
101.4
4 6 0. 7
-290.0
caA-l25i208
-r18.4
4 0. 3 8
1 8 6. 3
Wo11s tonite
CaSi0a
6 6 5. 3
Grossular
Ca3A12Si301
- 3 9 7. 7
!26.7
2
23.36
99.58
s i02
*Ihe
themal
--
s-Quartz
---
which
czank and Schulz
--
wollastonlte
Grossular
data
expaosion
Anorthite
H.
Skinner
Skinner
was ued
are
fron:
(197I)
T. Evans, Jr.
(unpub.
data'
1977)
(1956)
(1966)
Acknowledgments
T h e a u t h o r s t h a n k E . F . W e s t r u m , J r . , E . J . E s s e n ea n d D .
P e r k i n so f t h e U n i v e r s i t y o f M i c h i g a n f o r a c o p y o f t h e i r u n p u b l i s h e d l o w - t e m p e r a t u r eh e a t c a p a c i t yv a l u e sf o r g r o s s u l a r ,a n d J . J .
Hemley of the U.S Geological Survey for valuable discussions
c o n c e r n i n ge x p e r i m e n t a lp h a s e - e q u i l i b r i as t u d i e s T h e a u t h o r s a r e
particularly grateful to H T. Evans,Jr. of the U S Geological
Survey for measuring the unit-cell parameters of wollastonite
between303 and 873 K We also thank E-an Zen and S Ludington of the U S. Geological Survey for critically reviewingthe
manuscript and for their helpful comments.
I
I
ll
512
9
- rues)/r
(c400
viOO*
S|OO
Compound
Ano r thi Ee
By combining data from recentequilibrium studies
with new heat capacity values for anorthite, muscovite, pyrophyllite, and grossular,improved values
of LH"r,rsaand AG?,zgafor muscovite, pyrophyllite,
and grossularwere calculatedby means of the thirdlaw method. The best value for AH}.""" of disordered
2 M , m u s c o v i t ef r o m t h e e l e m e n t si s - 5 9 7 1 6 0 0 + 5 1 8 0
J /mol, which is the mean of the calorimetric value of
LHol.zssfor muscovite given by Hemingway and
R o b i e ( 1 9 7 7 )a n d t h e v a l u e o f L H o , . r " d e r i v e df r o m
reaction (3). The new value of AH",."u of muscovite
yields a value of -5595500+5190 J/mol for the
for disGibbs free energy of formation, L,Gor,zse,
ordered 2M, muscovite.Similarly, an improved value
for LH"1,2""
of pyrophyllite is -5639800+3950 I/mol.
This value and the appropriate entropy data were
combined to obtain a value of -5265900Xj960 J/
mol for L,G",."reof pyrophyllite. A new value of
-6657100+4720 J/mol was determined for LH",.,r"
of grossular. The value of L,G"r,"""of grossular was
calculatedto be -6295300+4730 J/mol.
v
T a b l e 1 4 . T h e r m o d y n a m i c c o n s t a n t su s e d i n d e t e r m i n i n gA l l ? , 2 " e
of srossular
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