American Mineralogist,Volume76, pages 1931-1939, 1991
Tremolite: New enthalpy and entropy data from a phaseequilibrium study of the
reaction tremolite : 2 diopside + 1.5 orthoenstatite+ 0-qurtz * HrO
Mlm
D. Wnr-cn,* Ausoll
R. Plwr,Bv**
Department of Geology and Geophysics,University of Edinburgh, West Mains Road, Edinburgh EH9 3Jw, United Kingdom
Ansrucr
New enthalpy and entropy data have been obtained for a natural end-member tremolite
from phaseequilibrium experimentson the high-temperaturedehydration reaction tremolite : 2 diopside + 1.5 orthoenstatite * B-quartz + HrO. Six reversed experimental
bracketswereobtainedat0.25kbar (996-1033K), 0.6 kbar (1038-1058K), I kbar (10751 1 0 4K ) , 1 . 5 k b a r ( l l 0 l - 1 1 2 5 K ) , 2 k b a r ( l l l 5 - 1 1 2 8 K ) , a n d 8 k b a r ( 1 1 7 9 - 1 2 0 9 K ) ,
from which the enthalpy of formation and the third-law entropy of tremolite have been
calculated using the internally consistent thermodynamic datasetThermocalc of Holland
and Powell (1990).The valuesobtainedare Af{(Tr) : -12299.48 + 14.84kJlmol and
S{Tr): 0.5525 + 0.0100 kJ/mol.K, which are in excellentagreementwith the values
given in Thermocalcand agreewell with the valuesof Berman et al. (1985).We use the
new thermodynamic data to calculate revised limits of tremolite stability in the system
CaO-MgO-SiOr-H,O (CMSH). We also discussthe apparent major discrepancybetween
values for AIIi(Tr) obtained from solution calorimetry (Kiseleva and Ogorodova, 1984)
and the phase equilibrium values. The difference between enthalpies for end-member
tremolite determined from phase equilibrium and calorimetric studies (36 kJ) is comparable to that observedfor talc (Kiseleva and Ogorodova, 1984),perhapssuggestinganomalous dissolution behavior of the talclike elementsof tremolite.
ria have been made in the systemsCMSH and CMSHTremolitic amphiboles are important constituents of CO, under geologically relevant conditions. These are
hydrated basic and ultrabasic rocks and siliceousmarbles summarized in Table l, from which it is evident that
in the greenschistand albite-amphibolite facies. These most of the amphiboles studied do not approach ideal
amphiboles are the first to grow in these rocks, and as tremolite composition closely.The resultsof thesestudies
such they are substratesfor a range of continuous reac- have been used as sourcesfor deriving thermodynamic
tions (most importantly coupledexchangereactions);these data for tremolite (Table l). Not surprisingly, given the
reactions can lead to zoned amphiboles of use in eluci- chemical diversity of the amphiboles used, there is poor
dating the pressure-temperature-timeevolution of meta- agreement between thermodynamic datasets. Furthermorphic rocks (cf. Holland and Richardson, 1979). The more, the microstructural statesofthese amphiboleswere
procurement of well constrainedthermodynamic data for not determined.Mareschand Czank (1988) have shown
end-member tremolite CarMgrSirOrr(OH),is thereforean that the intensity shifts in X-ray diffraction patterns used
important objective. However, despite the dozen or so to infer reaction direction in reversal experiments can
experimental studiesof tremolite stability that have been also arise from the preferential elimination of chain-mulmade over the last 30 years, good agreementon experi- tiplicity faults (Czank and Liebau, 1980) in polysomatmentally derived thermodynamic data is lacking. Some ically disordered reactant amphibole, leading to the
spurious location of amphibole equilibria in pressuresourcesofdiscrepancy are discussedbelow.
space(seealso Graham et al., 1989, p. 70).
temperature
Boyd (1959) made the first experimental study of tremThe
on synthetic tremolite deservefurther
experiments
olite stability in the syntheticsystemCaO-MgO-SiOr-HrO
(CMSH) at H,O pressuresup to 2 kbar. He found that comment. End-member tremolite is notoriously difficult
to synthesize:assemblagessuch as diopside + talc + amamphibole was stable at -800 t/0.6 kbar and -870
phibole + quartz, amphibole + diopside * enstatite,and
"C/2kbar. A number of later studies of tremolite equilibamphibole + diopside + qvartz are common synthesis
products. Complete yields of amphibole from tremolite
* Present address:Department of Earth Sciences,University
syntheseshave never been achieved, and yet end-memof Cambridge, Downing Street, Cambridge CB2 3EQ, United
tremolite, although very rare, does occur in natureber
Kingdom.
** Present address:Department of Chemistry, Arizona State the one usedin this study is one example,that of Kiseleva
University, Tempe, Arizona 85287,U.S.A.
and Ogorodova (1984) is another. Jenkins (1987) adINrnooucrroN
0003-o04x/91l1
I I 2-l 93l$02.00
l93l
1932
WELCH AND PAWLEY: ENTHALPY AND ENTROPY OF TREMOLITE
Trele 1, Tremolitestarting materialsused in experimentalstudiesof tremolitestabilityand thermochemistry
Authors
Reaction/technioue
Weeks(1956)
Hf calorimetry
Boyd (19s9)
Tr : Di + En + Qz + HrO
Robie& Stout (1963)
Low-T calorimetry(Cp)
Metz (1967,1976)
Tr + Dol : Fo + Cc + CO, +
H.O
Phl + Cc + Oz : Tr + Ksp +
CO, + H,O
Phl + Cc + Qz : Tr + Ksp +
Hoschek(1973)
Hewitt (1975)
co, + Hro
slaughtheret al. (1975)
and Eggert & Kerrick
( 19 8 1)
Tr+Cc:Dol+Di+CO,+
H.O
Dol+Qz+H,O:Tr+Cc+
CO,
Tc+Cc+Qz:Tr+CO,+
H.o
Dol+Tc+Oz:Tr+CO,
Tr+Cc+Qz:Di+CO,+
Jenkins(1983)
HrO
Tr+Fo:Di+En+HrO
Yin & Greenwood (1983)
Tr:Di+En+Qz+HrO
Skippen& McKinstry
(1985)
Kiseleva& Ogorodova
(1984)
Welch(1987)
Tr+Fo:Di+En+HrO
high-f lead borate calorimetry
Tr:Di +En+Qz+HrO
Tremolite composition
Data set
Ga/Mg
(Ca,aMno@[email protected]
Aloos)Orrlo(OH)rc
<0.40
Synthetic tremolite (oxide mix,
glass)
(Nao11Gorxca1$Mgo,oXMguoo-0.37
Feo01XSi7
*
seAlo
o8)O*(OH),
Nao,1(Ca,7sMgo27xMg4sAlo,.)-0.33
(Si7e3Aloo7)Oz(OH)1$
<0.40
Synthetic tremolite (gel)
see Table3
FallsVillage,New York
HP, BBG
Naturaltremolite,Campo Lungo
Naoos(Cale4Mgoo5NMgn."Feoor)0.385
HP
Gouverneur,New York
BBG, HP
St. Gotthard, Switzerland
<0.40
B B G ,H P
=90% synthetic amphibole yield
<0.40
BBG
(si, &Alo,o)or2(oH),,4Fo06
(Na,K)o s5(Ca1?3Mgoro[Mgr zoFeoo5Alo,sXSiT
osAlo,r)Orr(oH)osFo6
Synthetic tremolite (oxide mix)
Synthetictremolite(gel,glass,
oxide mix)
Synthetic tremolile (gel, oxide
mix)
Ca, 16(Mg4
e4Feo
o3XSi,
erAloo,)o,,(oH)roFo03
Caro,Mgo..SirorOrr(OH),"u
Naooloa, oo(MglesFeo
oJsisooorr(oH)ro
Skarn termolite,Balmat, New York
H, HP
HP, BBG
0.346
<0.40
Ca,16(Mg4e4Feo@)
(siTerAlool)or2(oH)roFoo3
R
0.437
0.437
0.404
0.400
St. Gotthard, Switzerland
Marble, Karelia
Locality unknown.
HRTEM (structurally
ordered) lR, Raman
Note.' From Graham et al. (1989). Abbreviations: Tr : tremolite, Di : diopside, En : enstatite, Qz : quartz, Dol : dolomite, Cc : calcite, Fo :
forsterite,Phl : phlogopite,Ksp : potassiumfeldspar,Tc: talc, R : Robieet al. (1978),H : Helgesonet al. (1978),HP: Hollandand Powell(1985),
BBG : Bermanet al. (1985).
dressedthe problem of tremolite synthesisand presented
a cogent case for incongruent dissolution of tremolite
(specificallythe SiO, component) in supercritical HrO as
a major control on experimental products. With increasing initial HrO contents,the incongruent dissolulion process leads to the following sequenceof assemblagesin
which the fluids are SiO, undersaturated:
that the stable amphibole was limited to within a few
mole percent of TrroMc,o;Tr,oogave Tr-Mc amphibole
* clinopyroxene. He also demonstratedfrom dissolution
and regrowth experiments that the yield of amphibole
could be increased by adding enough quartz to give a
SiOr-saturated fluid. Following from this, Jenkins attempted to synthesizetremolite at 6 kbar/850 'C (well
inside the nominal stability field calculated from therTr * H,O : Tr"" * Di + En + fluid
(l)
modynamic data sets)and obtained Tr-Mc amphibole *
Tr * HrO: Di + En + fluid
(2) clinopyroxene + qvartz, a high-temperatureassemblage
Tr * H,O: Di + Fo + En + fluid
(3) frequently encountered in previous studies. This result
is
Tr + HrO: Di + Fo + fluid.
(4) strongly suggestedthat end-member tremolite unstable
under theseconditions and starts to break down at a lowReaction I (seeAppendix I for abbreviations) involves er temperature by continuous reaction: Tr : Tr., * Cpx
a change in amphibole chemistry from tremolite to a + Qz + fluid. The end-member natural tremolite samtremolite-magnesiocummingtonite(Tr-Mc) amphibole ples are then inferred to be stable at temperaturessignif(Jenkins, 1987).Hence,changesin modal proportions and icantly below the univariant dehydration of the limiting
amphibole chemistry can occur. The quartz solubility data Mg-saturated Tr-Mc amphiboles: Tr." : Cpx + Opx +
of Andersonand Burnham (1965)imply that assemblages Qz + fluid. Amphibole composition is inferred to change
3 and 4 are restrictedto bulk compositions with very high continuously along the univariant dehydration boundary
H,O/Tr ratios (i.e., >90 wto/oHrO) at P < l0 kbar and (cf. Graham et al., 1989,their Fig. 9). An important corf < 900'C. Jenkins(1987) attemptedto synthesizeTr- ollary of the incongruent dissolution phenomenonis that
Mc amphiboles at 5 molo/ointervals from tremolite to tremolite phaseequilibria in SiOr-saturatedsystemsmay
Tr,,Mcr. at 6 kbar and l3 kbar (750-852 "C) and found be thermodynamically incompatible with those deter-
WELCH AND PAWLEY: ENTHALPY AND ENTROPY OF TREMOLITE
l 933
mined in SiOr-undersaturated (e.g., forsterite-bearing) TraLE2. Averagemicroprobeanalysisof naturaltremolite(n:
systems.
31)
A further complication with tremolite synthesesis the
2o
Atoms
rapid grofih of diopside (+ talc) in the first hour or so
(sample)
(O :24)
Wt"/"
of an experiment(Welch, 1987).When gelsare used,this
(0.52)
7.95
sio,
58.61
problem may be even worse becauseof the presenceof
(0.01)
Tio,
0.o2
0.00
(0.02)
Al,o3
0.03
0.01
diopside crystallites produced during firing of the gel at
(0.01)
CrrO"
0.01
0.00
850-900 "C. Similar crystallization behavior has been
(0.02)
FeO'
0.43
0.05
observed in some other calcic amphiboles such as eden(0.01)
MnO
0.03
0.00
(0.30)
Mgo
25.O1
5.06
ite, magnesio-hornblende,and richterite. In some cases
(0.1
13.65
8)
1.98
CaO
(e.g.,richterite), diopside can be reacted out by crushing
(0.01)
Naro
o.02
0.00
(0.01)
KrO
o.02
0.00
and re-reacting,suggestingthat the diopside in synthesis
(0.00)
F..
0.05
0.00
products is being preservedby an amphibole armor and
(0.22)
2.19
1.98
H.ot
thereby isolated from the reacting gel or oxide mix.
(1.30)
100.07
17.03
This study was undertaken to derive well-constrained
(+0.95)+
enthalpy and entropy data for end-member tremolite from
* FerO"was not detected in wet-chemicalanalysis(M.J. Saunders,anphase-equilibrium experimentson the reaction Tr : 2Di
alyst).
". Wet-chemicalanalysis (M.J. Saunders, analyst).
+ l.5En + B-Qz + HrO using a natural end-member
HrO content determined by H extraction method (see Holdaway et
tremolite sample and, if possible,to clarify the nature of a l .f, 1 9 8 6 ) .
the breakdown.
f This error is the total of analyticaluncertainties(> 2o).
ExpnnrlrnnrAr,
METHoDS
Starting materials
Diopside and orthorhombic enstatite were synthesized
hydrothermally from stoichiometric gels at 4 kbar/900
1J and 2kbar/900 "C, respectively.Pure natural a-quartz
that had been acid washed was used. The specimen of
tremolite came from the University of Edinburgh collection, but its locality is unknown. A chemical analysis(the
average of 3l microprobe analysesfor the cations and
also F and HrO analysesdetermined by other methods)
is given in Table 2, from which it can be seen that the
specimen has the ideal tremolite composition and is F
free. High-resolution transmission electron microscopy
revealedthat the amphibole is exceptionally free of polysomatic (chain-width) and polytypic (stacking)faults and
mineral inclusions. As such, this tremolite sample is the
most suitable specimen for thermodynamic analysis of
any tremolite yet studied (seeTable l).
Cleavage fragments of tremolite were removed from
the hand specimen(a tremolite-calcite-quartzrock) using
a razor blade; then they were crushed and left to stand
overnight in 30 volo/oethanoic acid to remove any carbonate residuesadhering to crystals.Examination by optical microscopy and powder X-ray diffraction showed
that calcite was absent,the sample being amphibole with
very minor amounts of quarlz. Two complimentary starting mixes were prepared: 850/oTr:150/oDi-En-Qz
and
150/oTr
: 850/oDi-En-Qz,the diopside, enstatite,and quartz
being mixed in tremolite proportions (4:3:2). All phases
were cmshed and sievedto < l5 prm.Approximately 0.02
g of mix was loaded into a Pt capsule(already welded at
one end) along with 4-10 wto/odistilled HrO, and the
capsulewas welded shut. Eachexperiment was conducted
with pairs of mixes. At the conditions of our cold-seal
experiments(0.25-2.0kbail700-930 oC),rhe data of Anderson and Burnham (1965) indicate that the hydrous
fluids have SiO, molalities of -0. I mol SiO,/kg HrO,
which correspondsto <0.01 molo/oSiO, in the fluid. With
regard to our experimentsat 8 kbar/900-940'C, we have
interpolateda SiO. molality of -1.7 at 900 "C from the
data ofAnderson and Burnham (1965,their Fig. 4), corresponding to -3 molo/oSiO, in the fluid. Therefore, we
consider the fluids in all our experimentsto be essentially
pure HrO, while acknowledgingthat high quartz solubility (and by implication incongruent dissolution) is likely
to exert an important control on tremolite stability at
higher pressuresand temperatures(> l0 kbar/>800 'C).
Apparatus
Experimentsat 700-930'C and 0.25-2.0 kbar were
performed using vertical cold-sealvessels(Nimonic 105),
and those at 8 kbar used an internally heated gas vessel
(Holloway, l97l). Ar was used as the pressuremedium.
Temperature and pressurewere recorded at least once a
day.
Temperaturesof the experimentswere measuredusing
an external PtlPtl3Rh thermocouple and are accurateto
+3 'C (Ford, 1972). Experimental temperatures in experiments were extremely stable: diurnal and long-term
variations (2o) were +2 "C. The temperature profiles of
the furnaces used in this study were measuredat I atm
and 600, 800, and 900 "C using an internal axial Ptl
Ptl3Rh thermocoupleThe isothermalhot-spot zone (35 cm long) of each furnace was located and the furnace
positioned relative to the vessel so that the charge zone
(2 cm long) coincided with the hot spot. Vessel-furnace
pairs were kept the same throughout the study. The internally heated pressure vessel was calibrated for temperature at 8 kbar using NaCl melting (detection of latent
heat) and is accurateto + 5 'C. In all experiments,sampleswereheatedisobaricallyto temperature.Sampleswere
1934
WELCH AND PAWLEY: ENTHALPY AND ENTROPY OF TREMOLITE
.t
Fig. l. Scanningelectron micrographs of experimental products. (A) Tremolite growth (TD29: 0.6 kbar, 765 "C) in which most
tremolite grains have retained their original prismatic facesand sharp outlines. Fretted terminations with protrusions can be seen
'C).
on the large tremolite grain (arrowed and inset). (B) Typical product in which dehydration has occurred (TD13: I kbar, 831
quartz
grains
seen.
can be also
The view is mostly of pyroxene bladeswith well developed sharp faces;some small equant
quenchedin a jet of compressedair. All quencheswere
isobaric.
Pressuresof the experimentswere measuredby a Heise
gaugeand are accurateto +30 bars (+ 10 guaranteedaccuracy, +20 hysteresis),although they could be read to
within 5 bars. Cold-seal pressurevesselswere closed off
from the gauge.As a check on the extent to which the
gauge + line volume buffered pressure drops, dummy
experimentswere performedat 0.5-2 kbar and 650-900
'C in which the pressurevesselwas either (1) open continuously to the gaugeor (2) shut offfrom the gauge.By
using segments of hollow filler rod it was possible to
achieve pressuredrops that were very close to those observedupon opening a vesselto the gauge.Pressuredrops
could thus be standardizedso that they correspondedto
the true vessel pressures,i.e., gauge + line volume :
vesselvolume.
The internally heatedgasvesselwas calibrated for pressure (Manganin gauge)using the freezing point of mercury at 298 K, and our quoted pressuresare accurateto
+20 bars. Pressurewas recorded by a Manganin gauge
open continuously to the vessel.
Experimental product examination
electron imaging facility; element standardswere wollastonite and periclase;a current of 20 nA and accelerating
potential of 20 kV were used. A number of products (including all those within and defining the experimental
brackets) were examined by SEM to see if reaction textures could be recognizedand correlated with the X-ray
results. SEM could also show the presenceof impurities
below the detection limit of XRD (<50/o)and indicate
whether dissolution had occurred(Jenkins, I 987). An analytical facility was used that enabled phasesto be identified and distinguished readily. Some representative
electron micrographs are shown in Figure l. Figure lA is
from an experiment at 0.6 kbar/165 "C (TD29) in which
tremolite grew (X-rays). This view is dominated by tremolite grains that have retained their original prismatic faces and sharp outlines. The relatively large grain (arrowed
and inset) showsclear ledgesand irregular sharp protruding terminations, the latter giving a "fretted" appearance.
This texture is the same as that interpreted by Jenkins
(1987, his Fie. 3b) to indicate tremolite erowth. The fretted habit is typical of experiments in which tremolite grew.
Other tremolite grains commonly show distinct en-echelon growth ledges.In all casesthe SEM observationsare
consistentwith the X-ray results.Evidently, the 250loXRD
criterion is good enough to give unequivocal microtextures. We did not observetremolite with smooth rounded
edges,such as are characteristicofpartially dissolved and
recrystallized cleavagefragments (seeJenkins, 1987, his
Fig. 3a), nor did we observe any impurities in grain
mounts (RI oils) or SEM samples.
Products were examined using the petrological microscope,powder X-ray diffraction (Ni-filtered CuKa, radiation), scanningelectron microscopy (SEM), and in some
casesthe electron microprobe. Reaction direction was inferred from changesin the intensities of certain strong
diagnostic X-ray reflections. A changein intensity of at
least 25o/orelative to starting material diffractogramswas
ANALYSTS
TrrnnuolvNAMrc
taken as evidence of reaction. Multiple repeatedsmears
We now give details of our thermodynamic treatment
were made to check for any orientational biases,but the
of the phase equilibrium data. For internal consistency
intensities of all reflections were reproducible to within
100/orelative. Microprobe analysis was performed using we have chosen a single thermodynamic dataset Thera Camebax microprobe equipped with a backscattered mocalc (Holland and Powell. 1990). This datasetwas
WELCH AND PAWLEY: ENTHALPY AND ENTROPY OF TREMOLITE
l 935
TAaLe3, Experimentalresultsfor the reactionfi : 2Di + 1.5En + B-Qz + H,O
Experiment
P(kbar)'
TD1
TD2
TD3$
TD7
TD4
TD8
TDs$
TD6
TD28
TD29$
TD34
TD3O$
TD31
TD32
TD33
TD9
TD1O
TD11$
TD15
TD12
TDl3$
TD14
TD22$
TD23
rD24
rD27
TD25$
TD26
TD16
TDl7
TD18$
TD19$
TD2O
TD21
TD35$
TD36$
0.241
0 245
0.244
o.237
o.240
0.222
o.225
0.231
0.616
0.609
0.598
0.604
0.611
0 627
0.596
0.998
1.O14
1.000
1.007
0.989
0.996
1. 0 1 0
1.487
1.472
1.476
1.419
1.477
1.473
1.974
1.986
1.990
1.982
1.985
1.956
8.020-8.060
7.960-7.990
rfc)
Duration (h)
700
713
723
606
606
/JC
746
556
746
740
748
760
780
758
/oc
778
785
800
820
839
780
802
812
818
824
831
850
828
834
843
845
852
880
820
835
842
855
880
901
911
931
5b/r
c5b
555
475
474
668
474
439
440
437
500
501
503
690
503
RNE
506
413
389
389
629
388
386
454
455
433
433
430
428
120
143
85Tr..
85Prod'-
Tr{
Tr
Tr
Tr+Pr
Tr+Pr
Tr+Pr
Tr+Pr
Pr
Tr
Tr
Tr+Pr
Tr+Pr
Tr+Pr
Pr
Pr
Tr
Tr
Tr+Pr
Tr+Pr
Tr+Pr
Tr+Pr
Tr+Pr
Pt + ?Tl
Pr
ft+?Pr
Tr+Pr
Tr+Pr
Pr + ?Tl
Directionf
H
H
H
N
N
N
D
D
H
H
N
D
D
D
D
H
H
H
N
N
Pl
Pr
Pr
Tr
ft+?Pr
Tr+Pr
Tr+Pr
Tr+Pr
Pr
Pr
Tr
Tr+Pr
Tr+Pr
Tr+Pr
Pr
Pr
Tr
Tr
Tr + ?Pr
Pr + ?Tr
Pr
Pr
Tr
Pr
Tr
Tr
Tr+Pr
Tr+Pr
Pr + ?Tr
Pr
Tr
Tt + ?Pl
Tr+Pr
Tr+Pr
Pr
Pr
Tr
Tr
Tr
Tr+Pr
Pr
Pr
tr
Pr
D
H
H
N
N
D
D
H
H
H
D
D
D
H
D
- The given pressures
are the mean for each experiment(see text).
'. Starting materials(mineral
mixes)
t Interpretationof reaction direction: H : hydration (tremolitegrowth), D : dehydration,N : no reaction.
+ Experimentalproducts: Tr: tremolite, Pr : dehydrationproducts.
$ Experimentdefining a bracket limit.
chosenover that ofBerman et al. (1985) becauseit enables the derivation of uncertainties of enthalpies to be
extracted.
Six reversed experimental brackets were obtained for
the reactionTr: 2Di + l.5En + P-Qz + HrO. Data for
all experiments are given in Table 3. Experiments lasted
120-746 h. These six brackets were used to derive enthalpy and entropy data for tremolite as follows. At each
point along the univariant reaction boundary, the following equilibrium relation holds:
AG.:0:^H?- rasg*
-T
fT(.P
* nRTlnfr"
(6)
+ nRZln/",o + Rl"ln K..
RearrangingEquation 5 gives another having a more obvious linear form:
+ f|*,wdr*
av,dp
r".
+ RZln K".
P'A(pY)
+ PAV\ + PL(aY)"(T-298)-
- ^He:
zA^te
I)"or,dr r f'"or.,, u,
f'"a,c,ar
I A c- p / T d r +Jr|
Jzge
* [)"or,dr - r f'"or.,, o,
o : Ane- z^,se
(5)
When expansivities and compressibilities are available
and P >> I bar, then Equation 5 can be expandedthus:
+ RI ln K..
nRTlnf^,o
(7)
The right hand side of Equation 7 is combined into a
single term here referred to as G'. Note that this is not
the same as the G' of Jenkins(1983, 1984).By plotting
WELCH AND PAWLEY: ENTHALPY AND ENTROPY OF TREMOLITE
l 936
4.2
85
80
Iotercept
= -AH"r = -114.23 !
Slope = ASor = 0 1640 t
11.24 kt
00100
8.O
kJ K-'
7.4
70
36s
()60
2.O
o
1100
1200
Fig.2. Plorof G' againstabsolutetemperature.
Linesof maximum and minimum slopethroughall quadrilaterals
definethe
minimum-maximumuncertainties
on 4119and AS9.Seetext.
! t.s
o
a
o
a
o
L
o 1.o
G' against absolute temperature, values for - AHI and
A,$ are obtained as the intercept and slope, respectively.
o.5
Water fugacitieswere taken from Thermocalc and are
correct to within +0.1 kJ. This uncertainty amounts to
< I 'C in the location of the tremolite dehydration reaction. The uncertainty on our 8 kbar data arising from the
Thermocalc fit is <10. I kJ. With regard to the equilibrium-constant term, K., electron microprobe data for am900
1000
800
700
phiboles and pyroxenes from the highest- and lowest('C)
Temperature
temperature experimental brackets indicate that, within
analytical error, these have end-member compositions.
Fig. 3. Experimentalbracketsfor the reactionTr : 2Di +
Hence, K. : I in all our calculations.
l.5En + p-Qz+ HrO. Alsoshownis the minimum-maximum
The Thermocalc data usedin our calculationsare given envelopecalculated
from the minimum-maximumslopedataof
in Table 4. Values for fnro and G' are given with the the G' against?Fplot.
pressuresand temperaturesof the six experimentalbrackets (expandedby uncertaintiesin pressureof +0.02-0.03
mean and is
kbar and temperature of t 5'C) in Table 5. A plot of G' The uncertainty on AIl(Tr) is 2o of the
the
enthalpies
offoron
from
the
uncertainties
calculated
against absolute temperature is shown in Figure 2. The
p-quartz, and HrO
orthoenstatite,
mation
of
diopside,
limits of the bracket data give rise to six quadrilaterals.
A,F1!above. As
Lines of maximum and minimum slope passingthrough given in Table 4 and the uncertainty on
give uncertainties on third-law ennot
Thermocalc
does
quadrilaterals
all
define an envelope within which the
tropies, the uncertainty on S0(Tr) is taken as the uncerunivariant curve must lie. Maximal uncertainties (>2o)
phaseequilibrium data
:
114.23 tainty on AS! above. These new
are derived from the two limiting slopes: MI?
+ 11.24kJ, ASP: 0.16400 + 0.0100kJ/K.The corre- for tremolite are discussedin the next section.
lation coefficient relating A11! and AS! is 0.985. These
Coup-lnrsoNs wITH PUBLISHED
data were used to calculate the position of the tremolite
DATA
THERMODYNAMIC
dehydration reaction: Figure 3 showsthe position defined
A compilation of enthalpy and entropy data for tremby the above uncertainties, along with our experimental
including our new values,is given in Table 6. There
olite,
(expanded
With
brackets
by experimental uncertainties).
is
excellent
agreement between our phase equilibrium
respectto a mean line (not shown in Fig. 3), the reaction
of Thermocalc, and good agteement with
values
and
those
is located to within + l0 "C by the experimental data.
Berman
et al. (1985). The value for AI1!(Tr)
data
of
rhe
Enthalpy and entropy data for tremolite were calculated
of Robie et al. (1978), obtained by integratingthe C" data
from Afl! and AS! as follows:
ofRobie and Stout (1963),is clearly discrepant.The caAil!(Tr) : )taaKzoi, l.5En,B-Qz,H,o) - aF19
lorimetrically derived value for AH!(Tr) obtained by Kiselevaand Ogorodova(1984) deservessome discussion
: -12299.48 + 14.84kJ/mol
(8) as there is a major difference between our value for
AHf(Tr) and theirs for a natural tremolite that is chemH,o) - a,sg
s{Tr) : ) s.1zoi,l.5En,p-Qz,
ically identical to ours in terms of cation proportions but
: 0.5525+ 0.0010kJ/mol'K.
(9) of unknown F content. To facilitate a direct, internally
WELCH AND PAWLEY: ENTHALPY AND ENTROPY OF TREMOLITE
t937
TABLe4. Thermodynamicdata used in calculatingtremoliteequilibria
QO
Phase
LH?
oAHl
(x10.)
Tremolite
Diopside
Orthoenstatite
d-quanz
B-quartz
Forsterite
Talc
H"O
-12299.48-3200.15
-3089.38
-910.80
-909.07
-2171.87
-5895.23
-241.81
7.42
1.90
2.08
0.74
0.74
1.62
3.70
0.03
552.50'
142.70
132.50
41.50
43.54
94.10
260.80
188.80
aV
BV
(x10+) (x10{)
b
Vo
27.2456.619
6.262
2.269
2.367
4.366
13.625
0.000
a
1.2144
0.3145
0.3562
0.0979
0.0979
0.2349
0.5343
0.0401
1x10
5)
2.6528
0.0041
-0.2990
-0.3350
-0.3350
0.1069
3.7416
0.8656
- 12363.0
-2745.9
596.9
-636.2
-636.2
542.9
-8805.2
487.5
-7.3885
-2.0201
-3.1853
-0.7740
-0.7740
- 1.9064
-2.1532
-0.2512
84.5
22.0
18.0
8.0
0.0
16.0
39.0
0.0
36.0
5.5
46
5.9
2.6
3.2
23.O
0.0
/Vote.'Unitsare in kJ, K, and kbar. Numbers in parenthesesare those bv which the values in the column below must be multiplied
. This study.
consistent comparison between the two studies,we have
:
recalculatedtheir AIIP(Tr) using their AI1"",,,,"".nrr"(Tr)
388.65 kJ/mol and a calorimetric cycle basedupon the
reactiontremolite:2diopside + 2periclase+ 4 B-quartz
+ brucite. Although various other reactions could have
beenchosen,this one resultsin the smallesterror on the
derived AIl*,o,.,(Tr). Solution calorimetric data for diopside (Weill et al., 1980), periclase (Davies and Navrotsky, l98l), B-quartz (Akaogi and Navrotsky, 1984),
and brucite(Clemenset al., 1987)wereusedwith the heat
capacitiesfrom Thermocalc to calculate A11g(Tr)as fotlows:
AffiTr) -- ) MI,1ZO|, 2Per, 4B-Qz, Bru)
*
Morurion.gzo*(Tr) +
re16
AG
|
df.
(10)
J 29a
From this we obtain a value for Afl!(Tr) of -12336-63
+ 13.94kJ/mol. When uncertaintiesare considered,there
is a minimum differenceof 8.37 kJ. Interestingly, an analTraue5. Valuesof G and f""ofor the experimental
brackets
P (kbao
rfc)
0.202
0.286
0.194
o.276
0.569
0.649
0.560
0.648
0.949
1.051
0.939
1.053
1.426
1.548
1.423
1.531
1.940
2.040
1.9',t7
2.O47
8.000
8.080
7.940
8.010
718
718
765
765
760
760
790
790
807
807
836
836
823
823
857
857
837
837
860
860
906
906
936
936
fH.o(kbar)
0.151
0.261
0.133
o.245
0.532
0.594
0.534
0.596
0.838
0.912
o.847
0.935
1.204
1.296
1.236
1.321
1.623
1.705
1.639
1.749
11.067
11.270
11.'102
11.284
. Valuelying
on the lineot minimumslope in d plot.
'- Value lying on the line maximum
of
slope in G plot.
G (kJ)
45.34
49.66.
46.85
51.71
57.61
58.34
59.58.60.48
63.82
64.34
65.93
oo.c/
67.10
67.49
69.80
70.18
69.67
69.89
71.53'
71.83
79.77
79.77*
82.65
82.6s
ogous calculation for talc using a value Af1,o,o,,on,nrr*(Tc)
: 207.57 + 3.49 kJ/mol taken from Kiselevaand Ogorodova (1984) gives AH!(Tc) : -5923.57 + 10.50 kJl
mol comparedwith a value of - 5895.23 + 7.40 kJ/mol
derived from phaseequilibria experiments(Thermocalc).
The difference is comparable to that observed for tremolite. The crystal-chemicalsimilarities betweentremolite
and talc (e.g.,Thompson, 198l) suggesta genuine,possibly anomalous, calorimetric effect associatedwith dissolution of the talc-like elements of the tremolite structure in lead-borate flux. However, we should also point
out that as Kiseleva and Ogorodova did not analyze for
F, their value for A.F1"o,,,,o,(Tr)
may result from a significantly higher F content than ours. In fact, their value is
slightly more endothermic than that obtained for synthetic end-member fluortremolite by Graham and Navrotsky(1986).
C.ql,cur,arroN oF THE Lrvrrrs oF
TREMOLITESTABILITYIN CMSH
Our values for the enthalpy and entropy of tremolite
derived from phase equilibrium experiments have been
used to calculate revised limits of tremolite stability in
the CMSH system to 30 kbar. These are shown in Figure
4. In the absenceof any published uncertainties on the
third-law entropies of diopside, orthoenstatite,forsterite,
quartz, and HrO and the lack of a systematic rationale
for combining uncertainties in enthalpy and entropy, we
TaBLE
of enthalpyandentropydatafor tremolite
6. Compilation
Source
Robieet al. (1978)
Helgesonet al. (1978)
Bermanet al. (1985)
Holland and Powell (1990)
Kiselevaand
Ogorodova (1984)f
This study
AHP (kJ/mol)
So (kJ/mol'K)
-12355.08
(17.32)' 0.54890',"
(0.001
3)
-12319.70
0.54890*(0.0013)
- 1231
1.30
0.5s115
-1230250 (14.121 0.55000
- 12347.s3(10.88)+
-12336.63(13.94)$
-123OO.47
(14.84) 0.55250 (0.0100)
' Uncertaintiesin brackets are 2r.
'- From Robie and Stout (1963); calorimetricallydeterminedvalue.
t High temperature solution calorimetry. Their sample was a natural
end-membertremolite (possible F) from a Karelianmarble.
+ Value given by Kiselevaand Ogorodova.
$ Valuecalculatedusing internallyconsistentdata from Thermocalcand
the heats of solutionfor diopside,periclase,brucite,and B-quartzspecified
in the text.
WELCH AND PAWLEY: ENTHALPY AND ENTROPY OF TREMOLITE
19 3 8
for tremolite give the following thermodynamic quantities:A11! : 4.0 + 0.7 kJ; A.sg: -0.0063 + 0.0010kJ/
-0.382 kJ/kbar. Hence,there will be very small
K AZ3 :
free-energydifferentials at experimental temperaturesto
drive this reaction: AG! is only about 6.5 kJ. The limits
set upon the location ofthis reaction by the uncertainty
in the enthalpy of reaction are shown in Figure 4 and
amount to + 1.5 kbar. Combining this with our envelope
for the SiOr-saturated tremolite dehydration reaction gives
the location of the invariant point as 27-31 kbar/730800 "C. In passingwe note that our +2d envelopepasses
through the bracketsdefined by some recent experiments
on this reaction by Jenkins et al. (unpublished data) using
synthetic tremolite (T. Holland, personal communication).
20
16
1, 111bar)
l2
CoNcr-usroN
700
800
r (t)
Fig. 4. Stabilityrelationsof tremolitein the CMSH system
calculatedfrom the thermodynamicdata for the naturalstoichiometrictremoliteof this study.J: Jenkins(1983)for the
reactionTr * Fo : 2Di + 2.5En+ HrO, usingsynthetictremolite. Seetext for discussion.
have chosento use the method of calculating correlated
uncertaintiesadvocatedby Powell and Holland (1985),
in which only uncertaintiesin enthalpies are considered.
The correlation matrices used were taken from Table 3a
of Holland and Powell (1985).
2Di + 1.5En + Qz + H,O
The minimum-maximum derivation of the median reaction curve from the G' vs. T plot implies that at 853
"C the uncertainty in its location is zero. Clearly, this is
unrealistic, and so we have calculatedthe uncertainty on
the reaction in the same way as we have for Tr : 2Di +
Tc and Tr * Fo : zDi + 2.5En + HrO, using only the
uncertainties on the enthalpies of formation given in
Thermocalc and our uncertainty on AIIf(Tr) (o : +7.4
kI. This reactionis locatedto t6-12'C and reachesa
thermal maximum of 925 "C at about 8 kbar.
Tr:
Tr * Fo: 2Di + 2.5En + H,O
The location ofthis reaction calculated from our data
is in good agreementwith the experimental determination of Jenkins (1983) for synthetic"tremolite" (Tr-Mc
amphibole?).We obtain an uncertainty in the position of
this reactionof + l0-13 oCover the pressurerange l-16
kbar. The position of the reaction is shown as an envelope in Figure 4.
Tr:
2Di + Tc
This is a "biopyribole" reaction(seeThompson 1981,
his Table 3) in which amphibole disproportionates into
plroxene and sheet silicate. Our phase equilibrium data
We have presentednew enthalpy and entropy data for
a natural end-member tremolite determined from phase
equilibrium experiments.The data are in excellentagreement with those of Thermocalc and agreewell with those
of Berman et al. (1985). The uncertainty on AHKTr)
(2o : + 14.84 kJ) is comparable to that of Thermocalc
(+14.12 kJ) and is necessarilyquite largebecausetremolite is a "non-anchor phase" (terminology of Holland
and Powell, 1990) in the dataset and therefore incorporates uncertainties on substituent phases. Calculations
made using the phase equilibrium values give plausible
positions for some important tremolite equilibria in
CMSH. The calculated position of the reaction Tr * Fo
: 2Di + 2.5En + HrO agreeswell with the experimental
data ofJenkins (1983). However, at P > l0 kbar and 7"
> 800'C it is likely that incongruent dissolution of tremolite will occur, stabilising Tr-Mc amphiboles and thereby displacing the univariant dehydration reaction Tr.. :
Di + En + HrO to temperaturesabove the end-member
reaction. In this respect the calculated curve for endmember tremolite servesas a referencedatum.
Acxlrowr,rncMENTS
M.D.W. and A.R.P. acknowledgefinancial support from NERC research studentships. The high-pressure and electron microprobe facilities
at University of Edinburgh are supported by NERC. We thank Peter Hill
for advice on microprobe analysis, and Colin Graham and Tim Holland
for helpful discussions. Frank Spear and David Jenkins are thanked for
very thorough and helpful revrews.
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MaNuscnrrr REcETVED
Aucusr 23, 1990
MeNuscnrsr AccEmEDJuNe 26, l99l
ApprNorx
l.
Glossary of thermodynamicterms used in this paper
P
Total pressure(kbar)
T
Temperature ('C, K)
VP
Volume of a solid phase(U/kbar)
R
Universal gas constant (0.008314 kJlK)
4113 Molar enthalpy of formation of a phase from the elements at 298.15 K and I bar (kJ/mol)
So
Molar thirdJaw entropy of a phase at 298.15 K and I
bar (kJlmol.K)
AHP Enthalpy of reaction at 298.15 K and I bar (kJ)
A,SP Entropy of reaction at 298.15 K and I bar (kJlK)
C,
Molar heat capacityof a phaseat constant P (kJlmol'K),
formulated as a polynomial in temperatureiCp: a + bT'
+ CT-2+ dTt/z
aV
Product of volume and isobaric expansivity for a solid
phaseftJ/K.kbar)
Product of volume and isothermal compressibility for a
0V
solid phase(kJ/kbar)
List of formulae and abbreviationsusedin this paper
tremolite (Tr)
CarMgrSirOrr(OH),
Magnesiocummingtonite(Mc)
Mg,Si,O,,(OH),
Diopside (Di)
CaMgSi,Ou
Orthoenstatite (En)
MgrSirOu
sio,
Quartz (a, B) (Qz)
Forsterite (Fo)
MgrSiOn
Talc (Tc)
MgrSioO,o(OH),
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