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Thermochemistry of some pyroxenes and related compounds
Geochlmica
et Cosmochimica
Acta, 1976, Vol. 40. pp. 1281 to 1288. Pergamon
Press. Printed
in Great Britain
Thermochemistry of some pyroxenes and related compounds ALEXANDRANAVROTSKYand WILLIAM E. COONS Department of Chemistry and Center for Solid State Science, Arizona State University, Tempe, Arizona 85281, U.S.A. (Received 4 February
1976; accepted in revised form 26 April 1976)
Abstract-The enthalpies of formation of a number of crystalline silicates from the oxides at 986 K were determined by oxide melt solution calorimetry. The values of A\H;,as6, in kcal/mol, are as follows: MgCaSi,O,, -34.3 f 0.4; CoCaSi,O,, - 26.7 $ 0.5; NiCaSi,O,, -27.1 + 0.5; MnSiO,, -6.3 k 0.3; Mn,SiO,, - 12.2 f 0.3. In addition, for MnStO, (rhodonite)+ MnSiO, (pyroxmangite), AH;,, = +0.06 f 0.3, kcal/mol and for MgCaSi,O, (diopside) = MgCaSi,O, (glass), AH&,, = f21.0 f 0.3 kcal/ mol. For hedenbergite, FeCaSi,O,, AGT,,, = -25.6 f 1.5 kcal/mol. In terms of pyroxene phase equilibria and crystal chemistry, our thermochemical data support the generally accepted crystallographic arguments that (a) the C2/c clinopyroxene structure increases in stability with decreasing size of the ion occupying the Ml site in the MCaSi,O, series, and (b) the energy (and enthalpy) differences between orthopyroxene, clinopyroxene, and pyroxenoid structures are generally quite small and often less than 5OOcal/mol in magnitude.
1. INTRODUCITON
end-member pyroxenes would provide information to complement such crystallographic data. We have chosen to begin such a study with an attempt to resolve the discrepancy in the thermochemical data for diopside, and with measurements of the enthalpies of formation of the cobalt and nickel analogues of diopside, CoCaSi,O, and NiCaSi,O,. Equilibrium data already in the literature permit us to estimate the free energy of formation of hedenbergite, FeCaSizO,. We have also measured the enthalpy of formation of Mn,SiO, and of the rhodonite and pyroxmangite polymorphs of MnSiOJ. In this paper we report these results and discuss their significance in terms of crystal chemistry. In addition, we report a new measurement of the enthalpy difference between glass and crystals of the diopside composition.
ALTHOUGH the crystallography (CAMERON et al., 1973a, b; PREWITT and PEACOR, 1964) and phase relationships (BIGGAR and CLARKE, 1971; TURNCZK et al., 1973) of pyroxenes are being actively studied, these investigations are largely limited to the gathering of information relating pyroxene composition to the cooling rates and temperatures and pressures of formation of igneous rocks (PAPIKE and BENCE, 1972; BOYD, 1973; VIRC~ and HAF~\IER,1969). Because the emphasis has been shifted in this direction, surprisingly little is known of the thermodynamics of formation of even the end-member pyroxenes. Until recently, thermochemical data on pyroxene and pyroxenoids have been confined to low temperature heat capacity measurements and enthalpies of formation obtained by hydrofluoric acid solution calorimetry for 2. EXPERIMENTAL TECHNIQUES AND MnSiO, and CaSiO, (TORGFXIN and SAHAMA, 1948) SAMPLE CHARACTERIZATION MnSiO, (KING, 1952) and CaMgSi,O, (NEUVONEN, 2.1 Sample preparation 1952; KRACEK, 1953). These latter measurements are 2.1.1 Binary oxides. SiOz was pulverized Brazilian subject to considerable uncertainty; for example, the quartz crystal, provided by the Thermal American Fused two separate determinations of the enthalpy of formaQuartz Company. This had been acid leached and ground tion of diopside from the component oxides differ by to -200mesh. Prior to calorimetry, the batch to be used was fired at 1OGO”Cfor 48 hr. 2.5 kcal/mol. More recently, the enthalpy of formation MgO was reagent grade magnesium oxide (Baker), of enstatite (SHEARER and KLEPPA, 1973; CHARLU et ignited for 18 hr at 1250°C and sifted to -325 mesh. al., 1975) and of an aluminous enstatite (CHARLU et - CaO was prepared from reagent grade CaCO, by ignital., 1975) have been measured by calorimetry in a ine at 1350°C for a total of 72 hr. Since this material dismolten oxide solvent at 692°C. soives readily, it was left in the form of coarse sintered powder to minimize pickup of Hz0 and CO*. The thrust of pyroxene crystal chemistry has been NiO was reagent grade nickel oxide (Clico) ignited 48 hr to correlate the observed space group, silicate chain at 1000°C and sifted to - 200 mesh. configuration, and cation distribution among Ml and Co0 was prepared from reagent grade ‘cobaltic oxide’ M2 sites with atomic parameters such as ionic radius (Alfa Inorganics). This oxide was first annealed in air at (CLARK et al., 1969), ligand field stabilization (BURNS, &WC for-48 hr’ to convert it to stoichiometric Co,O,. 1969) and tendency toward covalent bonding (GHOSE That material was then reduced at 1000°C under nitrogen and cooled in the inert atmosphere. The sample was et al., in press). Because the thermodynamic stability ground and put back for further reduction until constant of a given pyroxene is a function of these same parweight was reached, a total of - 30 hr being required. The ameters, systematic calorimetric study of a series of total weight loss on a 7g sample was within 1 mg of that 1281 c.c.*. 40/1lsJ
A. NAVROTSKY and W. E. C(X)NS
1282
theoretically required for stoichiometric reduction of Co304 to COO. For calorimetry, two separately prepared batches of Co0 were used, giving essentially identical heats of solution. MnO was prepared from reagent grade Mn,O, (Baker Analyzed Reagent) by heating for 5 days at 800°C under a flowing atmosphere of CO:CO, = 3: I. This low-temperature anneal in the stability field of MnO was chosen to yield a product with a very small deviation from stoichiometry. The powder produced was uniformly bright green in color and single phase MnO to X-ray and microscopic investigation. All sample anneals were carried out in platinum crucibles. All samples used in calorimetry were stored in desiccators with ‘drierite’. The total impurity levels in all materials used were well below 0.1%. 2.12. Silicates.Two types of diopside samples, MgCaSi,O,, were used. One was a natural diopside from Twin Lakes, California, provided by Dr. H. S. Yoder of the Geophysical Laboratory. The sample used came from a larger batch which had been ground and analyzed. This is indeed an exceptionally pure and stoichiometric metamorphic diopside, see Table 1. Heat-treatment of this sample was performed in air in Pt crucibles in appropriate furnaces with temperature control to *5”C, see below. The second sample used was a synthetic diopside made from the MgO, CaCO,, and SiOz described above. After thorough grinding, the oxide mix was melted at _ 1450°C for 6 hr. then cooled in the furnace to 800°C and removed. The product, a mixture of diopside crystals and glass, was ground to -200 mesh and then annealed for 4 days at _ 1275°C. The resulting material was fully crystalline and single phase to both microscopic and X-ray investigation. Glass of the diopside composition was given to us by Dr. D. F. Weill. It has been prepared by melting an oxide mix at 1450°C for I8 hr. Two batches of this glass were used, one rapidly quenched from 1450°C. one more slowly cooled. They gave identical heats of solution, within experimental error, and the average of all solution experiments on diopside glass is given in Table 2. CoCaSi,O, was prepared from previously dried CaCO,, COj04, and SiO, (materials described above). The oxide mix was ground in an agate ball mill, dried, and then fired in air at 1460°C in a platinum crucible. After 2 hr, furnace temperature was dropped abruptly to 85O’C. the charge removed. crushed, refired at 1460°C for an additional 4 hr. quenched to 850°C. and removed. The product consisted Table
Niesi,Oa synthetic
1. Analytical
data for MgCaSi,O,, NiCaSi,O,
29.29
22.50
CoCaSi,O,,
48.47
and
100.26
Table
2. Enthalpies
of solution of oxides 2Pb0.BzOi at 713°C
and silicates
in
Compound cao
-13.03
MgO
+ 1.1’1
* 0.14
(5)
t&IO
+ 1.59
+ 0.17
(5)
coo
+ 5.38
i 0.26
(10)
NiO
t 8.56
-c 0.35
0;)
Si@
- 0.76
f 0.10
(6)
MgCaSi,OG(natural)
+20.95
t 0.25
(13)
MgCaSi,O,(synthetic)
+20.82
f 0.28
(8)
M$aSi,O,(all)
+20.30
+ 0.26
(21)
MgCaSiBOs(glass)
- 0.111
+ 0.085, (7)
CoCaSizOB
+li.il
+ 0.33
(10)
NiCaSi,?O,.
+21.08
f 0.33
(9)
Mn,SiO,
b14.2’1 * 0.20
(4) (6)
(i-,)
+ 0.22
tiSiO,(rhodonite)
+ 6.90
* 0.26
i%SiO,(pyrmmmgite)
+ 6.~2
i 0.19
MnSiO,(all)
l
6.95
i 0.22
(a) Error given is standard
theses is number
deviation, number of experiments performed.
(6)a
(12)
in paren-
of a mixture of fairly large pink crystals of cobalt diopside, and some deep blue glass. The sample was then ground, sieved to -2OOmesh, and the fine fraction was annealed near 1125°C for 11 days in a platinum crucible in air. The product contained no glass and was found to be single-phase cobalt diopside by both microscopic and X-ray investigation. The nickel analogue of diopside, NiCaSi,Oh, melts near 1340°C at 1 atm (HIGGINS and GILBERT, 1973). We prepared this compound by melting a mix of NiO, CaCO,. and SiOZ. Because nickel-bearing systems, in our experience, react quite sluggishly, we chose a higher initial melting temperature, - 1525°C. After 6 hr at this temperature and rapid cooling to 850°C. the sample consisted of yellowgreen diopside crystals, a minor amount ( - 10%) of yellowbrown glass. and few specks of dark green nickel oxide. The sample was ground and then annealed at 1250°C for 14 days. The product appeared to be single phase nickel diopside by both X-ray and microscopic examination. Mn,SiO, was prepared hydrothermally from MnO and SiOz by heating for 10 days at 900°C and 0.5 kbar. The sample was then heated under a 1: 1 CO-~C02 atmosphere at 1050°C for 24 hr to insure complete dryness. The product was well crystallized homogeneous tephroite. The rhodonite and pyroxmangite forms of MnSiOA were given to us by Dr. Jon Ito. They have been prepared hydrothermally in silver foil containers from a starting mixture of MnCO, and H,Si03. Pyroxmangite was crystallized for 72 hr at 3 kbar water pressure at 650°C. rhodonite for 48 hr at 780°C and 0.5 kbar. Preparation conditions for the two polymorphs of MnSiO, have been discussed by ITO (1972a. b).
Table I shows analytical data for the diopside samples. The Twin Lakes diopside analysis was given to us by H. S. Yoder. The other analyses were done at Arizona State University by Sharon Ode using X-ray fluorescence. The
Thermochemistry
of some pyroxenes and related compounds
1283
involving disordering, in the heat-treated samples, Further experiments showed this to be unlikely for several reasons. Firstly, an X-ray structure refinement 2.3 Cu~~rj~ier~~~ by L. Finger on untreated and heated natural diopThe Calvet-type twin microcalorimeter and sample side samples showed no change in lattice parameters, assembly have been described previously (NAVROT~KY and KLEPPA,1968; NAVROTSKY, 1973).The only modification bond distances or thermal parameters. Secondly, 0. was in the design of a new platinum sample holder for J. Kleppa (personal communication) reports no differoxides, such as MgO, which tend to dissolve relatively ence in the heat of solution in 2PbO.B,0, of heated slowly in the lead borate solvent, 2PbO,B,O,. Rather and unheated natural Twin Lakes diopside, even than a hemispherical solid cup, the sample holder consisted of a cylinder of heavy Pt foil to which a thin Pt bottom when the sample was heated at 1420°C and 20 kbar. (O.~in. thick foil) was welded. At the start of an experSignificantly, our data for the heat-treated samples iment, the sample cup was lowered into the melt and the coincides with the values obtained by Kleppa for both Pt bottom torn with a Pt tipped plunger which had been heated and unheated samples. This correspondence positioned above the sample. This arrangement has the implies some difference between our materials and advantage of bringing the entire solid sample into contact with the solvent at the start of a run, of eliminating the those used by Kleppa. Although the two samples were need for a large number of stirrings (with concomitant furnished from the same bottle of ground Twin Lakes small heat effects that would need to be taken into diopside by Dr. H. S. Yoder, it may be possible that account), and of providing good mechanical stability for slight differences exist between them due to the presthe sample assembiy during loading and equilibration. This new sample assembly was used for MgO, MnO, ence of trace amounts of amp~bole, observed as a MgCaSi,O,, NiO, and NiCaSi20,, while COO, CaO, coherently intergrown phase during very careful SiO,, CoCaSizO,, Mn,SiO,, and MnSiO, were found to microscopic examination. This is not detectable by dissolve readily with the solid-cup assembly. X-rays or by casual microscopic examination. When The sample size per run averaged 50mg. Throughout this series of experiments, the temperature of the calorisuch a sample is dissolved in molten lead borate at meter remained constant at 713.O”C and the calibration 713”C, the small amount of water liberated can generfactors remained constant. ate a significant heat effect if it all vaporizes into the Calorimetry of cobalt-containing samples was done unatmosphere. On the other hand, if the amphibole is der a protective atmosphere of nitrogen or carbon dioxide to prevent oxidation, as previously described (NAVROTSKYfirst converted to anhydrous silicates by preheating and KLEPPA,1968). Calorimetry of MnO and manganese the sample above lOOO”C, the heat of solution of silicates was done under an atmosphere of purified Cot, diopside wifl not be measurably affected by the preswith special care taken to flush out the system with gas ence of a small amount (co.1 wt ‘A) of other silicates before lowering the samples into the hot zone. By taking produced by amphibole dehydration. We surmise that appropriate care, oxidation of MnO during an equilibration period of 2-3 hr in the calorimeter could be entirely our initial sample contained more amphibole than prevented. Kleppa’s sample and thus we saw a spurious endoSamples of MgCaSi,O, glass were dissolved after a thermic heat effect associated with the solution of the minimum time of pre-equilibration (223 hr instead of overuntreated diopside sample. night). Recrystalli~tion of the glass did not appear to be For the reaction: a sibilant problem under these conditions.
analysis confirms that the samples are indeed close to stoichiometric in terms of oxide components.
MgO + CaO + 2Si02 = MgCaSi,O, 3. RESIJLTS AND DISCUSSION 3.1 Enthalpies
of solution
of binary
AH& = -34.3 &-0.4 kcal/mol
oxides
data are given in Table 2. Our data are consistent with those collected over the last several years by Kieppa and co-workers (NAVROTSKY and KLEPPA, 1968; NAVROTSKY,197la; SHEARERand KLEPPA, 1973; M~~LLI~Rand KLEPPA, 1973; CHARLU et al., 1975). According to the above studies, the enthalpies of solution in 2PbO’B,Oa of CaO, MgO, SiO,, NiO, CuO, and ZnO are more endothermic at 900°C than at 692°C and our data at 713°C fit this general trend. The
3.2 Enthalpy
and jkr
cnrrqy
qf’,fonnation
qj’ diopsidic
clinopyroxmes 3.2.1 ~~o~s~de, MgCaSi*O,. Initial ~lo~metric experiments on the Twin Lakes natural diopside gave values of the heat of solution which were about I kcal/mol more endothermic than those for the synthetic sample. These values also showed considerably more scatter than those for the synthetic diopside or the heated natural samples. Although we initially suspected the possibility of a structural change, possibly
AH&s = -33.6 + 0.7 kcal/mol,
(1)
where the heat contents given in ROBIEand WALDBAUM(1968) are used to correct our data to room temperature. We have not attempted to correct our heats of formation for the small deviations from stoichiometry detected in the analyses. We feel that the uncertainties inherent in the analytical methods and the uncertainties in assigning the excess oxides to solid solutions or second phases make the validity of such a correction doubtful. In any case, depending on the model chosen, the correction would make the calculated enthalpy of fo~ation of diopside more exothermic by %200 cal/mol. There are two determinations by acid calorimetry of the enthalpy of formation of diopside (KRACEK, 1953; NEUVONEN,1952). The value in ROBIE and WALDBAUM (1968) is an average of these. Kracek used a ‘synthetic diopside’, not further characterized, and obtained AH&s = - 37.76 kcal/mol. Neuvonen used
I784
A.
NAVROTSKYand
a natural diopside from Juva, Finland, which was analyzed to contain 49.22mol y,:, Casio,, 49.74% MgSiO,. 1.01*:, FeSiO,, and 0.031;: MnSiO,. After correction terms were applied for the impurities and slightly no~stoichiometric composition, Neuvonen obtained AH>ox = - 35.25 i 0.22 kcaI,imol. Kracek’s value is clearly too exothermic, possibly because of gross compositional errors in the synthetic sample. whereas Neuvonen’s value depends somewhat on the exact corrections to be made for the presence of the impurities. especially iron. Hemingway (1976. personal communication) suggests that Neuvonen’s value for the heat of solution of quartz should be corrected by + 300 to the + 400 cal/mol because of the fine particle size of the sample used. The corrected heat of formation of diopside from the oxides would then be AH 2u8 = -33.55 i: 0.25 kcal/mol. in better agreement with our dat;I. H~L~;Ix)N 1’1LI/.(in preparation) has been developing a set of self-consistent free energies of formation of minerals which satisfy the reversed phase boundaries for mineral equilibria (mostly below 600°C). If one accepts the calorimetric entropies, S&s of diopside, MgO, CaO. and SiOZ (from low temperature heat capacity measurements) as being correct as listed in ROHIEand WALDBAUM(1968), then Helgeson’s data (personal co~nm~lnic~tion) suggest for diopside, AH& = - 34.7 kcal/mol (formation from the oxides). Our vnluc of - 33.6 & 0.7 kcalimol is in fair agreement with this estimate. We believe our determination of the enti~~tl~~/ of forn~ation of diopside to be more reliable than the curly hydro~uoric acid solution calorimetric work. although modern techniques of acid-solution calorimetry clearly can and do provide accurate thermochemical data, especially for hydrous minerals. 3.X C’oCaSi,O,, and NiCaSi,O,. From the calorimetric data, we have. for the reaction: Co0
+ CaO -t 2SiOZ = CoCaSi,O,
AH,,,,, = - 26.7 _t 0.5 kcal/mole.
(2)
and for NiO -t- CaO + 2Si02 = NiCaSi,O, AHux<, = - 27. I rtr 0.5 kcaljmol.
(3)
These data are consistent with the pattern observed for other silicates and germanates (NAVROTSKY, 1971a). in which the magnesian end-members are substantially more stable than those containing Fe, Ni and Co. However, it is interesting to note that. whereas Ni$iO, is considerably less stable than Co,SiO, or Fe,Si04. NiSiO, is less stable than FeSiO, or CoSiO,, and Ni,GeO, is less stable than Co,GeO, (NA~ROTSK~. 197 la), the three cal~um-containing pyroxenes. FeC’aSi,O,. CoCaSi,O,, and NiCaSizO, all have very similar enthalpies of formation from the oxides. That is. nickel diopside is relatively more stable than other nickel silicates. This is probably due to the competition of two factors (a) the genera1 trend
W. E.
&INS
toward decreasing silicate stability in the series Mg, Mn, Fe, Co. Ni. Cu discussed by NAVROTSKY(1971). and (b) the stabifization of the diopside structure by small cations in M 1. Since cation size decreases in the order Mn, Fe, Co, Ni, the two effects balance and result in very similar enthalpies for FeCaSi,O,. CoCaSi,O,. NiCaSi,O, . GHOX and WAN (1975) observe that in MCaSizO, clinopyroxenes the average M2-0 distance increases approximately linearty with increasing M 1-O distance. The thermochemical trend is consistent with optimum Ca-0 distances being possible in clinopyroxencs with the smalleI cations. Mg” and Ca” ‘. The transformations to the bustamite structure of MnCaSi,O, (johannsenite) above -400°C (LAMB and LINDSL~-:Y,1972), and of FeCaSi,O, above z i ooo‘c (LINDSLI:Yand MUNOZ. 1969), compared to the stability to the temperature of melting of CoCaSizO,, MgCaSizO, and NiCaSi,O, are further manifestations of the decreasing stability of the diopside structure relative to other phase assemblages as the radius of the M’+ cation increases. 3.2.3 FeCaSi,O, hrdenheryite. We did not determine the heat of formation of hedenbergite, although we are currently developing calorimetric techniques under atmospheres of controlled oxygen fugacity. However, data in the literature permit an estimate of the free energy of formation of FeCaSi,O, from its oxide components as follows. FeCaSi,O, is stable in the hedenbergite structure only at relatively low tem~mture (LINIXLEY and MLINOZ. 1969). At 1080°C and atmospheric pressure. the composition FeCaSi,O, exists as a phase initially described as a wollastonitc solid solution (JOEIIVSONand MUAN. 1967) or. more correctly, as a phase with a bustamite-related structure (RUTSTEIN, 1971 ; RAPOPOKTand BURNHAM. 1973). Although, strictly speaking. structural relations along the Fe,&, _,Si03 join (0
where the free energies of formation are from the component oxides and the logarithmic term comes from the assumed ideal mixing of the 2 mols of cations. At 1350 K, AG’:. - 21. I kcal/mol CsS~O~~woli.~~~ositc) 1. (RoBII: and WALDBAUM, 1968) and AG~eSior(I~rra,i,it~i = - 1.5 kcal/mol (NAVKOTSKY, 1971a). Thus AC~cCPSiPh(h,~rtami,c) = - 26.4 kcat/moi. Since hedenbergite is unstable with respect to the bustamite structure at 1350 K. its free energy of formation from the oxides must be somewhat fess cxothermic than the above value. LINIXLEY and Mr;~oz (1969) report that the transition FeCaSi,O, (heden-
Thermochemistry
bergite+ bustamite) occurs reversibly near 5 kbar at 1350 K. Crystallographic data for the bustamite form of FeCaSi,O, are given by RAPOFQRTand BURNHAM (1973), and their calculated cell volume is 727.2 A3 = 73.00cm3/mol. Taking the known molar volume of hedenbergite, 452.2 A3 = 68.30 cm3/mol (ROBIE et al., 1967), we have
heat contents reported by MAH (1960). When the tabulated heat contents are used to correct our calorimetric values to 298 K, we get AH&(MnSi03) = - 5.86 kcal/mol and AH’&,(MnSiO,) = - Il.59 kcal/mol. Thus our data confirm the earlier calorimetric work. For the reaction 2MnSi0,
AG~,c,sip,(bustamile) = AG~ecasi206(hedenbergitc) - PAV,
(5)
where AV = Vhedenbergite - Vbus,ami,e= -4.70 cm3/mol AG;,c,si,o,(hedrnbergite) = - 25.8 kcal/mol.
(6)
The estimated uncertainty in this final value is 5 f 1.5 kcal/mol. One should note that the PAV correction term is less than 1 kcal, so that even a factor of two in the uncertainty would lead to only about 500 cal uncertainty in AGPeCaSiZo6. Recently, KURSHAKOVA and AVETISYAN (1974) determined the equilibrium oxygen fugacity as a function of temperature for the phase assemblage hedenbergite, wollastonite, quartz, metallic iron. They calculated the free energy of formation of FeCaSi,O, in the temperature range 50&1300K and obtained values of AGT from the oxides which decreased in magnitude from - 29.7 kcal/mol at 500 K to - 22.4 kcal/mol at 1300 K. This would imply an entropy of formation of some -9 cal/deg mol, which does not seem reasonable. The probable major source of error in their analysis of the data is the assumption that the wollastonite phase exists as pure Casio,. Rather, reduction of hedenbergite will probably produce an iron-containing wollastonite or an iron-containing phase of bustamite structure, as the phase equilibrium data of RUTSTEIN (1971) imply. Then the activity of CaSiO, in the wollastonite phase will not be unity. This error will be magnified in deriving enthalpy and entropy terms from the temperature dependence of the free energy. However, the values of AGY that Kurshakova and Avetisyan calculate bracket our estimated value of -25.6 kcal. 3.3 Manganese silicates From the data in Table 2, we have, for reactions at 986 K MnO + SiO, = MnSiO,
1285
of some pyroxenes and related compounds
AH” = 6.32 + 0.30 kcal/mol
2MnO + SiOz = Mn,SiO,AH” = 12.23 + 0.33 kcal/mol.
(8)
Using tabulated values from ROBIE and WALDBAUM (1968), one gets, for the formation of rhodonite and tephroite from the oxides at 1000 K, AH” = -6.38 and - 12.41 kcal/mol, respectively, in excellent agreement with our data. These tabulated values are based on hydrofluoric acid solution calorimetry by KING (1952) [AH&,(MnSi03) = -5.92 f 0.17 kcal/ mol] and by JEFFES rt al. (1954) [AH&,(Mn,Si04) = - 11.75 k 0.56 kcal/mol] and high temperature
+ SiO,,
(9)
our data give AH& = +0.41 f 0.38 and AH&,, = f0.13 kcal/mol. Rhodonite is, of course, a stable phase with respect to tephroite and quartz, and our data suggest that the enthalpy, as well as the free energy, of reaction (9) is positive at atmospheric pressure. The free energies of formation from the oxides at 1423 K of MnSiO, and Mn,SiO, have been determined by SCHWERDTFEGERand MUAN (1965) to be - 5.9 + 0.3 and - 10.4 f 0.4 kcal/mol, respectively. Combined with our calorimetric data, these give entropies of formation from the oxides at 1423 K of - 0.30 cal/deg mol for MnSiO, and - 1.3 cal/deg mol for Mn,Si04. These are in reasonable agreement with the values obtained from heat capacity measurements as calculated from the ROBIE and WALDBAUM (1968) mol tabulations: AS;15,,0 = -0.17 and -0.84cal/deg for MnSiO, and MnSiO,, respectively. Thus the thermochemical data for Mn,Si04 and MnSiO, show very good agreement among several measurements using different techniques. Our heats of solution of the two polymorphs of MnSiO,, rhodonite and pyroxmangite, are very similar. From our data, for the reaction MnSiO,
(rhodonite) AH&
= MnSiO,
(pyroxmangite)
= +0.06 i 0.33 kcal/mol.
(10)
AKIMOTOand SYONO (1972) in a high pressure study of MnSiO,, report a transformation from rhodonite to pyroxmangite structures at P(in kbar) = 10 + 0.026 T (in “C).
(11)
Using the molar volumes given by these authors, one gets AV” = -0.391 cm3/mol, and, through the Clausius_(=lapeyron equation, AS” = -0.246cal/mol K. At looo”C, the transformation occurs at 36 kbar, thus AG” = -PAL’”
(7)
= Mn,Si04
= +336.4cal = AH’ - TAS’,
(12)
or AH” = +23 cal. Because the volume change associated with this transition is small, neglect of differences in compressibilities and thermal expansion factors for the two polymorphs may introduce significant errors. However, both our data and that of Akimoto and Syono indicate that the difference in enthalpy between the two polymorphs is extremely small. According to the data of AKIMOTOand SYONO (1972) and in agreement with our AH” value, the pyroxmangite polymorph of MnSiO, below about 10 kbar is unlikely to be stable at any temperature. However, the hydrothermal synthesis at 3 kbar and 650°C by
A. NAVR~TSKYand W. E. Coot~s
1286
ITO (1972a, b; personal communication) and at 2 kbar below about 700°C (PETERS, 1971; ALBRECHT and PETERS, 1975) and similar hydrothermal syntheses by MOMOI (1974) suggest a stability of pyroxmangite at or near atmospheric pressures at temperatures below 500°C. With such comparable energies for the silicate chains with a 5 unit repeat (rhodonite) and a 7 unit repeat (pyroxmangite), the effects of surface energies, coherent intergrowths, and possible defects or ‘mistakes’ in stacking sequences may affect the observed equilibria to an observable extent. IRMA and BUSECK (1975) have observed by electron microscopy the intergrowth of ortho- and clinoenstatite on a unit cell level, while BURNHAM (1966) has suggested a pyroxenoid with a 9 unit silicate chain repeat in the structure of ferrosilite III. The close similarity between pyroxene and pyroxenoid structures may verge on continuous gradation between idealized end-member structures through the incorporation of lattice defects. The experimental data support this thesis through the small energy differences observed between: (a) rhodonite and pyroxmangite (< 100 Cal), and (b) orthoand clinoenstatite; less than 500, 100 and lOOcal for MgSi03, CoSiO, and FeSiO,. respectively (NAVROTSKY, 1976; AKIMOTO et ul., 1965). Note that the enthalpy difference between wurtzite and sphalerite forms of ZnS and ZnSe, in which polytypism and stacking disorder are well-known, is of the same order of magnitude, namely 63 and 229 cal/mol (NEUHAUS and STEFFEN, 1970; CEMIC and NEUHAUS. 1974). In addition. the data of AKIM~TO and SY~N~ (1972) also permit an estimate of AC“, AH”. and A.S’ for the reaction MnSiO,
(pyroxmangite) = MnSiO,
(clinopyroxene).
( 13)
For that reaction P(kbar) = 19 + 0.057 T(“C) (800~14OO’C).
(14)
Using their reported unit cell volume for the clinopyroxene of 455.6 A3 and calculating as before, we get: AS” = -0.635 cal/mol K, and W273 = 846 cal/mol, AH” = -211 cal/mol K. Although these values are again subject to considerable uncertainty, they suggest that the actual differences in enthalpy and entropy between pyroxene and pyroxenoid structures are rather small. 3.4 Melting of’ clinopyroxenes and enthalpy oj’,fkion of diopside The incongruent melting at atmospheric pressure of MgCaSi*O, over a temperature range of z 1340-1391 “C is well established (KUSHIRO, 1973). The products of incongruent melting appear to be a diopside solid solution with Mg/(Mg x Ca) > 1 and Si/(Mg + Ca) < 1 and a silica-enriched liquid. HIGGINS and GILBERT (1973) report that at atmospheric pressure NiCaSi,O, melts incongruently near 1340°C.
producing nickel olivine (Ni$iO,). possibly some pseudowollastonite, and liquid. At higher pressures. NiCaSi,O, may melt congruently. We have found that CoCaSizO, melts incongruently at atmospheric pressure in the temperature range Il5&1205’~C to yield a slightly Ca- and Si-deficient clinopyroxenc. a slightly Si-enriched melt. and a small amount of a very G-rich pyroxenoid. having either a wollastonite or bustamite structure. We \vill report these results more fully when we complctc a stud) of phase equilibria in the CaSiO,~CoSiO, system. However. together these studies definitely cstnblish the incongruent melting of the MC’aSizO,, clinopyroxenes as a general phenomenon. LINI)SI,L.\.and M~N~z (I 969) report that FeCaSi,O(, bustamitc melts incongruently. Our calorimetric data show that for the reaction: CaMgSizO,
(diopside)
= C‘aMgSi,O,
AHq8(, = + 21 .(I & 0.3 kcal,mol.
(glass) (15)
Using the heat contents given hq KI LI.I.Y (1960). WC get at room temperature. AH,,,, = +_‘I ._3 _+ 0.5 kcal, mol. The heats of solution in HF near room temperature have been measured. yielding. for reaction (15). AH,,, = 22.1 kcal’mol (FI KRIEK. 1971). In addition. the enthalpy of fusion at the ‘melting point’. 1665 K is reported to be 22.0 hcal!mol (Kr:r.~~r:u. 1962) 18.5 kcal/mol (Roen and WAI.I)RAI~M, 1968) and 30.6 kcal/mol (FFRRIER. 1971). The value we obtained is in general agreement with the reported values of the heat of vitrification cited above and is, we believe, a reliable measurement of the difference in cnthalpy between glass and crystals. Perhaps :I more serious question is the relationship between the cnthalpy of fusion (solidliquid) at the melting point and the cnthalpy of vitrification (solid + glass) at lower temperatures. For diopside. there arc two problems; (:I) incongruent melting of the solid, and (b) the gloss Iransitlon in the supercooled liquid. Fcrricr’s work. in particular. shows the nature of thcsc problems. Hc reports values of the heat of solution of glass :uld crqstalh at room tcmperature (HF calorimetry) and of the heat contents of glass and crystals to above the melting point (drop calorimetry). However. ths heat content of the glass cannot be measured bctlvcen _ II00 K and the melting point because of rapid r~crystalli/atiotl. Therefore the two portions of the cur\;c :Irc‘ connected by a line, thus masking the true nature of the glass-transition region. For crystalline diopside. the heat content curve does not show :I CIGIII break at the ‘melting point’, but shows an additional contribution to the enthalpy at temperatures from 100 hclow the ‘melting point’ up to the liquidus. This deviation may be caused by incongruent melting (KI’SHIKO, 1973) or by other premelting phenomena. Fr RKILR ( I97 I ) has drawn his curve so that it gives ;I maximum possible value for the heat of fusion at the melting point. a value I .5 times the cnthalp) of vitrilication. He obtains similar results for anorthite. The glass transi-
Thermochemistry
1287
of some pyroxenes and related compounds
~ck~w~e~e~nents-This work was supported by the tion will act to ‘anomalously’ increase the enthalpy National Science Foundation and the Alfred P. Sloan of the noncrystalline state with increasing temperaFoundation. We thank Dr. E. HAUSW,Dr. J. ITO. Dr. D. ture, thus making the value of the enthalpy of fusion F. WEILL and Dr. H. S. YODER,JR. for samples, and these more positive than the enthalpy of vitrification. Howneoob 01~s Dr. L. FINGER. Dr. H. C. HBLGE~ON,Dr. B. Dr. 0. J. KLI%PA, Dr. R. MCCALL~ST~R, Dr. ever, we believe that the effects seen by Ferrier (a HEMINGWAY, factor of 1.5) are too large to be reasonable. It is R. C. NEWTONand Dr. R. YL~D for stimulating discussion. interesting to note that estimates of the enthalpy of REFERENCES fusion of diopside from a freezing point depression ALBRECHTJ. and PETERST. J. (1975) Hydrothermal synanalysis of phase diagrams tend to fall in the same thesis of pyroxenoids in the system MnSiO,--CaSiOi at range (20 & 2 kcal/molf as the reported enthalpies of Pf = 2 kb. Contrib. Mineral. Petrol. 50. 241-246. vitrification (KELLEY, 1962; ROBIE and WALDBAUM AKIMOTOS. and SYONOY. (1972) High pressure transformations in MnSiOs. Amer. Mj~eru~. 5$. 7684. 196X; BURNHAM, in press; this work) rather than in BIGGARG. M. and CLARKED. B. (1971) Asnects of chase the range given by Ferrier for the enthalpy of fusion equilibria in the inversion and exsolution of pyroxenes. (30 kcal/mol). Clearly more work must be done to lndian Mineral. 12, l-13. Bovo F. R. (1973) A pyroxene geotherm. Geochim. Cosmoanswer these questions. It is of interest to note that chim. Acta 37, 2533-2546. for SiO, and Ge02, there does not appear to be a BURNHAMC. W. (1966) Ferrosilite III: a triclinic pyroxsignificant difference between the enthalpy of fusion enoid-type polymorph of ferrous metasilicate. Science and of vitrification (HOLM et al., 1967; NAVROTSKY, 154, 513-516. 1971b). BURNH~ C. W. (in press) ~erm~ynamics of melting in 1
4. CONCLUSIONS The present investigation provides new themechemical data for several pyroxenes and pyroxenoids. The enthalpy of fo~ation data may be used in several ways to generate complete the~~ynamic data for the phases in question. The enthalpies of formation may be combined with standard entropies obtained from heat capacity measurements to produce the free energy of formation as a function of tem~rature. Un~rta~nties in the calorimetric entropies of silicates, which arise from uncertainties in cation ordering, defect structure, and magnetic ordering have been discussed in detail in a recent paper by ULBRICHand WALDBAUM(1976). We feel that the enthalpy of formation data can be put to good use to partially overcome these di~culties as follows. High temperature equilibrium data are available for a number of silicates, with values of their free energies of formation at temperatures of 1000 K and above. When both equilibrium work and high temperature solution calorimetry have been performed on wellequilibrated samples, preferably of characterized structural state, then the entropy of the fo~ation can accurately be calculated as Ails”= (AH0 - AG”)/T. This can provide a more accurate estimate of the entropy of formation than one can get either from heat capacity measurements alone (because of the difficulties mentioned above) or from the temperature dependence of the equilib~~ data (taking a slope over a small temperature interval can lead to large errors). Then, if the standard entropy of some phases is well known, that of others involved in the equilibria can be computed. We are currently analyzing the available data for anhydrous transition-metal oxides and silicates in order to produce a ‘best set’ of enthalpy, entropy, and free energy values. We plan to report those data and their application to some geochemical calculations in a subsequent communication.
silicate-volatile systems: Fortsch. &f&era!. BURNTR. G. (1969) Site ureference of transition metal ions in silicate irystal strudtures. Chem. Geol. 5, 275-283. CAMERONM. E., PAPIKE J. J., PREWITTC. T. and SUENO S. (1973a) Pyroxenes-comparisons of real and ideal structural topologies. Z. Krist. 138. 254-273. CAMERONM. E., S&NO S., PREWXTT’C. T. and PAPIKE J. J. (1973b) High temperature crystal chemistry of acmite, diopside, hedenbergite, spodumene and ureyite. Amer. Mineral. 58, 594-618.
CEM~CL. and NEUHAUSA. (1974) Untersuchungen zum Mischbarkeits-, Zustands- und Strukterverhalten im System ZnSe-MnSe bei Drticken bis 125 Kbar und Temperaturen Von 5~1100°C. Nigh ~tn~~igh Pres. 6, 203-2 15.
CHARLUT. V., KLEPPA 0. J. and NEWTONR. C. (1975) Enthalpies of formation at 970K of compounds in the system MgO-Al,Os-SiO, from high temperature solution calorimetry. Geochim. Cosmochim. Acta 39, 1487-1498.
CLARKJ. R., APPLEMAN D. E. and PAPIKEJ. J. (1969) Crystal-chemical characteristics of clinopyroxenes based on eight new structure refinements. Mineraf Sot. Amer. Spec. Paper 2, 31-50.
FERRIERA. (1971) Etude experimentale de l’enthalpie de cristallisation du diopside et de l’amorthite synthttiques. Rev. Int. Hautes Temper. Refract. 8, 31-36.
GHOSES. and WAN C. (1975) Crystal structure of CaCoSi,O, and CaNiSi,O,: crystal chemical relations in C2/c pyroxenes. EOS 56, 1076. GHOSES., WAN C. and OKAMURAF. (in press) Site preference of transition metal ions in pyroxenes and olivines, a new model. HELGE~~NH. C., DELANYJ. and NE~BITTH. W. (in preparation) Summary and critique of the thermodynamic properties of the rock-forming minerals. HIGGINSB. and GILBERTM. C. (1973) High pressure stability of nickel diopside. Amer. J. Sci. 273A, 51l-521. HOLM J. L., KLEPPA 0. J. and WESTRUME. F. JR. (1967) ~erm~ynamics of ~lymorphic transformations in silica. Thermal properties from 5 to 1070°K and pressure -temperature stability fields for coesite and stishovite. Geochim. Cosmochim. Acfa 31, 2289-2307.
IIJIMAS. and BUSECKP. R. (1975) High resolution electron microscopy of enstatite I: twinning, ~ivmorphism and polytypism. Amer. Mineral. 60, ?5&-$70: . ITOJ. (1972a) Rhodonite-ovroxmanaite aeritectic alone the join‘MnSib,-MgSiO,.‘kmer. Mkerdl. 57, 865-876: ITO J. (1972b) Synthesis and crystal chemistry of Li-hydropyroxenoids. Mineral J. 7, 45-65.
1288
A. NAVROT~KY and W. E. COONS
JEFFES J. H., RICHARDSON F. D. and PEAKSON J. (1954) The heats of formation of manganous orthosilicate and manganous sulfide. Trans. Faraday Sot. SO, 364-370. JOHNSON R. E. and MUAN A. (1967) Activity-composition relations in solid solutions in the system CaO-“FeO”SiOz in contact with metallic iron at 1080°C. Trans. Met. Sot. AIME 239, 1931-1939. KELLEY K. K. (1960) Contributions to the data on theoretical metallurgy XIII. High temperature heat capacity and entropy data for the elements and inorganic compound& U.S. Bur. Mines Bull. 584. KELLEY K. K. (1962) Heats and free energies of formation of anhydrous silicates. U.S. Bur. Mines Rep. Invest. 5901. KING E. G. (1952) Heats of formation of manganous metasilicate (rhodonite) and ferrous orthosilicate (fayalite). J. Amer. Chem. Sot. 74, 444&4448. KRACEK F. C. (1953) Contributions of thermochemical and X-ray data to the problem of mineral stability. Carnegie Inst. Wash. Yearh. 52. 69-75. KURSHAKOVA L. D. and AVETISYAN E. I. (1974) Stability and properties of synthetic hedenbergite. Geokhimiya No. 3. 444453. KLISHIRU I. (1973) Incongruent melting of Dure diopside. . Carnegie Inst. Wash. fearh. 72, 7081709.’ LAMP C. and LINDSLEY D. H. (1972) Johannseniteebustamite: inversion and stability range. Geol. Sot. Amer. Abstr. Programs, Annual Mketingr p. 571. LINDSLEY D. H. and MUNOZ S. L. 11969) Subsolidus reiations along the join hedenbergite-ferrosilite. Amer. J. Sri. 26lA. 295-324. MAH A. D. (1960) Thermodynamic properties of manganese and its compounds. U.S. Eur. Mines Rep. Invest. 5600. M~LL~:R F. and KL~,P~A 0. J. (1973) Thermodynamics of formation of chromite spinels. J. Inorg. Nucl. Chem. 35. 2673 -2678. M~MOI H. (1974) Hydrothermal crystallization of MnSiO, polymorphs. Mineral. 1. 7. 359.-373. NAVKODKY A. (197la) Thermodynamics of formation of the silicates and germanates of some divalent transition metals and of magnesium. J. fnorg. Nucl. Chem. 33. 4033 -4050. NAVKOTSKY A. (1971 b) Enthalpies of transformation among the tctragonal, hexagonal and glassy modifications of GeO,. J. Inorg. Nucl. Chem. 33, 1119-l 124. NAVKOTSKY A. (1973) Ni,SiO,+nthalpy of the olivinespine1 transition by solution calorimetry at 713’ C. Earth Planet. Sri. Lett. 19, 471-475. NAVROTSKY A. (1976) Silicates and related minerals; solid state chemistry and thermodynamics applied to gcothermometry and geobarometry. bog. Solid State Chem. 11. in press. NAVROTSKY A. and KLEPPA 0. J. (1968) Thermodynamics
of formation of simple spinels. J. Inorg. .&‘a~/.Chrm. 30. 479498. NEUHAUS A. and STEFFEN R. (1970) uber das Zustandsund Mischbardeitsverhalten des Systems ZnS-MnS im Druckbereich bis 140 kbar. Z. Phys. Chem. N. F. 73, 188-214. NEUVONEN K. J. (1952) Thermochemical investigation of the akermanite-gehlenite series. Bull. Cornm. Grol. Finlande No. 158. 4--50. PAPIKE J. J. and BENCE A. E. (1972) Pyroxenes as recorders of lunar basalt petrogenesis; chemical trends due to crystal-liquid interactions. Geochim. Cosmochim. Acta 8. 43 I -469. PETERS T. J. (1971) Pyroxmangite: stability in H+C02 mixtures at a total pressure of 2ooO bars. Contrih. Mineral. Petrol. 32, 267-273. PREWITT C. T. and PEACOK D. R. (1964) Crystal chemistry of the pyroxenes and pyroxenoids. Amer. Mineral. 49. 1527-1542. RAPOPORJ. P. A. and BUKNHAM C. W. (1973) Ferrobustamite; the crystal structure of two Ca, Fe bustamite type pyroxenoids. Z. Krist. 138, 419438. Roan R. A., BETHK~ P. M. and B~AKDSL~Y K. M. (1967) Selected X-ray crystallographic data, molar volumes. and densities of minerals and related substances. U.S. Grol. Surv. Bull. 1248. RORIE R. A. and WALDBAUM D. R. (196X) Thermodynamic properties of minerals and related substances at 298.15’K (25.O”C) and one atmosphere (1.013 bars) pressure and at higher temperatures. C’S. Creel. Sure. Bull. 2159. RUTSTEIN M. S. (1971) Reexamination of the wollastonitehedenbergite equilibria. Amer. MirIeral. 56. 2040-2052. SCHWEKDTFEGER K. and MUAN A. (1965) Activities in olivine and pyroxenoid solid solutions of the system Fen Mn-Sip0 at 1150°C. Traw. Met Sot. AIME 236. 201 211.
SHI:AK~K J. A. and KLEPPA 0. J. (1973) The enthalpies of formation of MgAIZO,, MgSiO,. Mg,SiO, and AIZSiO, by oxide melt solution calorimetry. J. Itrorg. Nucl. Chem. 35. 1073~1078. T~KGESON D. R. and SAHAMA T. G. (I 948) A hydrofluoric acid solution calorimeter and the determination of the heats of formation of Mg$iO,, MgSiO,. and Casio,. .I. Amer: Chem. Sot. 70, 2 156~2160. TURNOC.K A. E., LINUSL~V D. H. and GKOVER J. E. (1973) Synthesis and unit cell parameters of Cam-Fe-Mg pyroxenes. Amer. Mineral. 58. 50~59. UI.BRICH H. H. and WAI.I)BAIIM D. R. (1976) Structural and other contributions to the third-law entropies of silicates. Geochirn. Cosmochim. Acta 40, I- 24. VIRGO D. and HAFNER S. S. (1969) Fe” Mg order disorder in heated orthopyroxenes. Mineral Sot. ,4mer. Spec. Paper 2, 27--81.
et Cosmochimica
Acta, 1976, Vol. 40. pp. 1281 to 1288. Pergamon
Press. Printed
in Great Britain
Thermochemistry of some pyroxenes and related compounds ALEXANDRANAVROTSKYand WILLIAM E. COONS Department of Chemistry and Center for Solid State Science, Arizona State University, Tempe, Arizona 85281, U.S.A. (Received 4 February
1976; accepted in revised form 26 April 1976)
Abstract-The enthalpies of formation of a number of crystalline silicates from the oxides at 986 K were determined by oxide melt solution calorimetry. The values of A\H;,as6, in kcal/mol, are as follows: MgCaSi,O,, -34.3 f 0.4; CoCaSi,O,, - 26.7 $ 0.5; NiCaSi,O,, -27.1 + 0.5; MnSiO,, -6.3 k 0.3; Mn,SiO,, - 12.2 f 0.3. In addition, for MnStO, (rhodonite)+ MnSiO, (pyroxmangite), AH;,, = +0.06 f 0.3, kcal/mol and for MgCaSi,O, (diopside) = MgCaSi,O, (glass), AH&,, = f21.0 f 0.3 kcal/ mol. For hedenbergite, FeCaSi,O,, AGT,,, = -25.6 f 1.5 kcal/mol. In terms of pyroxene phase equilibria and crystal chemistry, our thermochemical data support the generally accepted crystallographic arguments that (a) the C2/c clinopyroxene structure increases in stability with decreasing size of the ion occupying the Ml site in the MCaSi,O, series, and (b) the energy (and enthalpy) differences between orthopyroxene, clinopyroxene, and pyroxenoid structures are generally quite small and often less than 5OOcal/mol in magnitude.
1. INTRODUCITON
end-member pyroxenes would provide information to complement such crystallographic data. We have chosen to begin such a study with an attempt to resolve the discrepancy in the thermochemical data for diopside, and with measurements of the enthalpies of formation of the cobalt and nickel analogues of diopside, CoCaSi,O, and NiCaSi,O,. Equilibrium data already in the literature permit us to estimate the free energy of formation of hedenbergite, FeCaSizO,. We have also measured the enthalpy of formation of Mn,SiO, and of the rhodonite and pyroxmangite polymorphs of MnSiOJ. In this paper we report these results and discuss their significance in terms of crystal chemistry. In addition, we report a new measurement of the enthalpy difference between glass and crystals of the diopside composition.
ALTHOUGH the crystallography (CAMERON et al., 1973a, b; PREWITT and PEACOR, 1964) and phase relationships (BIGGAR and CLARKE, 1971; TURNCZK et al., 1973) of pyroxenes are being actively studied, these investigations are largely limited to the gathering of information relating pyroxene composition to the cooling rates and temperatures and pressures of formation of igneous rocks (PAPIKE and BENCE, 1972; BOYD, 1973; VIRC~ and HAF~\IER,1969). Because the emphasis has been shifted in this direction, surprisingly little is known of the thermodynamics of formation of even the end-member pyroxenes. Until recently, thermochemical data on pyroxene and pyroxenoids have been confined to low temperature heat capacity measurements and enthalpies of formation obtained by hydrofluoric acid solution calorimetry for 2. EXPERIMENTAL TECHNIQUES AND MnSiO, and CaSiO, (TORGFXIN and SAHAMA, 1948) SAMPLE CHARACTERIZATION MnSiO, (KING, 1952) and CaMgSi,O, (NEUVONEN, 2.1 Sample preparation 1952; KRACEK, 1953). These latter measurements are 2.1.1 Binary oxides. SiOz was pulverized Brazilian subject to considerable uncertainty; for example, the quartz crystal, provided by the Thermal American Fused two separate determinations of the enthalpy of formaQuartz Company. This had been acid leached and ground tion of diopside from the component oxides differ by to -200mesh. Prior to calorimetry, the batch to be used was fired at 1OGO”Cfor 48 hr. 2.5 kcal/mol. More recently, the enthalpy of formation MgO was reagent grade magnesium oxide (Baker), of enstatite (SHEARER and KLEPPA, 1973; CHARLU et ignited for 18 hr at 1250°C and sifted to -325 mesh. al., 1975) and of an aluminous enstatite (CHARLU et - CaO was prepared from reagent grade CaCO, by ignital., 1975) have been measured by calorimetry in a ine at 1350°C for a total of 72 hr. Since this material dismolten oxide solvent at 692°C. soives readily, it was left in the form of coarse sintered powder to minimize pickup of Hz0 and CO*. The thrust of pyroxene crystal chemistry has been NiO was reagent grade nickel oxide (Clico) ignited 48 hr to correlate the observed space group, silicate chain at 1000°C and sifted to - 200 mesh. configuration, and cation distribution among Ml and Co0 was prepared from reagent grade ‘cobaltic oxide’ M2 sites with atomic parameters such as ionic radius (Alfa Inorganics). This oxide was first annealed in air at (CLARK et al., 1969), ligand field stabilization (BURNS, &WC for-48 hr’ to convert it to stoichiometric Co,O,. 1969) and tendency toward covalent bonding (GHOSE That material was then reduced at 1000°C under nitrogen and cooled in the inert atmosphere. The sample was et al., in press). Because the thermodynamic stability ground and put back for further reduction until constant of a given pyroxene is a function of these same parweight was reached, a total of - 30 hr being required. The ameters, systematic calorimetric study of a series of total weight loss on a 7g sample was within 1 mg of that 1281 c.c.*. 40/1lsJ
A. NAVROTSKY and W. E. C(X)NS
1282
theoretically required for stoichiometric reduction of Co304 to COO. For calorimetry, two separately prepared batches of Co0 were used, giving essentially identical heats of solution. MnO was prepared from reagent grade Mn,O, (Baker Analyzed Reagent) by heating for 5 days at 800°C under a flowing atmosphere of CO:CO, = 3: I. This low-temperature anneal in the stability field of MnO was chosen to yield a product with a very small deviation from stoichiometry. The powder produced was uniformly bright green in color and single phase MnO to X-ray and microscopic investigation. All sample anneals were carried out in platinum crucibles. All samples used in calorimetry were stored in desiccators with ‘drierite’. The total impurity levels in all materials used were well below 0.1%. 2.12. Silicates.Two types of diopside samples, MgCaSi,O,, were used. One was a natural diopside from Twin Lakes, California, provided by Dr. H. S. Yoder of the Geophysical Laboratory. The sample used came from a larger batch which had been ground and analyzed. This is indeed an exceptionally pure and stoichiometric metamorphic diopside, see Table 1. Heat-treatment of this sample was performed in air in Pt crucibles in appropriate furnaces with temperature control to *5”C, see below. The second sample used was a synthetic diopside made from the MgO, CaCO,, and SiOz described above. After thorough grinding, the oxide mix was melted at _ 1450°C for 6 hr. then cooled in the furnace to 800°C and removed. The product, a mixture of diopside crystals and glass, was ground to -200 mesh and then annealed for 4 days at _ 1275°C. The resulting material was fully crystalline and single phase to both microscopic and X-ray investigation. Glass of the diopside composition was given to us by Dr. D. F. Weill. It has been prepared by melting an oxide mix at 1450°C for I8 hr. Two batches of this glass were used, one rapidly quenched from 1450°C. one more slowly cooled. They gave identical heats of solution, within experimental error, and the average of all solution experiments on diopside glass is given in Table 2. CoCaSi,O, was prepared from previously dried CaCO,, COj04, and SiO, (materials described above). The oxide mix was ground in an agate ball mill, dried, and then fired in air at 1460°C in a platinum crucible. After 2 hr, furnace temperature was dropped abruptly to 85O’C. the charge removed. crushed, refired at 1460°C for an additional 4 hr. quenched to 850°C. and removed. The product consisted Table
Niesi,Oa synthetic
1. Analytical
data for MgCaSi,O,, NiCaSi,O,
29.29
22.50
CoCaSi,O,,
48.47
and
100.26
Table
2. Enthalpies
of solution of oxides 2Pb0.BzOi at 713°C
and silicates
in
Compound cao
-13.03
MgO
+ 1.1’1
* 0.14
(5)
t&IO
+ 1.59
+ 0.17
(5)
coo
+ 5.38
i 0.26
(10)
NiO
t 8.56
-c 0.35
0;)
Si@
- 0.76
f 0.10
(6)
MgCaSi,OG(natural)
+20.95
t 0.25
(13)
MgCaSi,O,(synthetic)
+20.82
f 0.28
(8)
M$aSi,O,(all)
+20.30
+ 0.26
(21)
MgCaSiBOs(glass)
- 0.111
+ 0.085, (7)
CoCaSizOB
+li.il
+ 0.33
(10)
NiCaSi,?O,.
+21.08
f 0.33
(9)
Mn,SiO,
b14.2’1 * 0.20
(4) (6)
(i-,)
+ 0.22
tiSiO,(rhodonite)
+ 6.90
* 0.26
i%SiO,(pyrmmmgite)
+ 6.~2
i 0.19
MnSiO,(all)
l
6.95
i 0.22
(a) Error given is standard
theses is number
deviation, number of experiments performed.
(6)a
(12)
in paren-
of a mixture of fairly large pink crystals of cobalt diopside, and some deep blue glass. The sample was then ground, sieved to -2OOmesh, and the fine fraction was annealed near 1125°C for 11 days in a platinum crucible in air. The product contained no glass and was found to be single-phase cobalt diopside by both microscopic and X-ray investigation. The nickel analogue of diopside, NiCaSi,Oh, melts near 1340°C at 1 atm (HIGGINS and GILBERT, 1973). We prepared this compound by melting a mix of NiO, CaCO,. and SiOZ. Because nickel-bearing systems, in our experience, react quite sluggishly, we chose a higher initial melting temperature, - 1525°C. After 6 hr at this temperature and rapid cooling to 850°C. the sample consisted of yellowgreen diopside crystals, a minor amount ( - 10%) of yellowbrown glass. and few specks of dark green nickel oxide. The sample was ground and then annealed at 1250°C for 14 days. The product appeared to be single phase nickel diopside by both X-ray and microscopic examination. Mn,SiO, was prepared hydrothermally from MnO and SiOz by heating for 10 days at 900°C and 0.5 kbar. The sample was then heated under a 1: 1 CO-~C02 atmosphere at 1050°C for 24 hr to insure complete dryness. The product was well crystallized homogeneous tephroite. The rhodonite and pyroxmangite forms of MnSiOA were given to us by Dr. Jon Ito. They have been prepared hydrothermally in silver foil containers from a starting mixture of MnCO, and H,Si03. Pyroxmangite was crystallized for 72 hr at 3 kbar water pressure at 650°C. rhodonite for 48 hr at 780°C and 0.5 kbar. Preparation conditions for the two polymorphs of MnSiO, have been discussed by ITO (1972a. b).
Table I shows analytical data for the diopside samples. The Twin Lakes diopside analysis was given to us by H. S. Yoder. The other analyses were done at Arizona State University by Sharon Ode using X-ray fluorescence. The
Thermochemistry
of some pyroxenes and related compounds
1283
involving disordering, in the heat-treated samples, Further experiments showed this to be unlikely for several reasons. Firstly, an X-ray structure refinement 2.3 Cu~~rj~ier~~~ by L. Finger on untreated and heated natural diopThe Calvet-type twin microcalorimeter and sample side samples showed no change in lattice parameters, assembly have been described previously (NAVROT~KY and KLEPPA,1968; NAVROTSKY, 1973).The only modification bond distances or thermal parameters. Secondly, 0. was in the design of a new platinum sample holder for J. Kleppa (personal communication) reports no differoxides, such as MgO, which tend to dissolve relatively ence in the heat of solution in 2PbO.B,0, of heated slowly in the lead borate solvent, 2PbO,B,O,. Rather and unheated natural Twin Lakes diopside, even than a hemispherical solid cup, the sample holder consisted of a cylinder of heavy Pt foil to which a thin Pt bottom when the sample was heated at 1420°C and 20 kbar. (O.~in. thick foil) was welded. At the start of an experSignificantly, our data for the heat-treated samples iment, the sample cup was lowered into the melt and the coincides with the values obtained by Kleppa for both Pt bottom torn with a Pt tipped plunger which had been heated and unheated samples. This correspondence positioned above the sample. This arrangement has the implies some difference between our materials and advantage of bringing the entire solid sample into contact with the solvent at the start of a run, of eliminating the those used by Kleppa. Although the two samples were need for a large number of stirrings (with concomitant furnished from the same bottle of ground Twin Lakes small heat effects that would need to be taken into diopside by Dr. H. S. Yoder, it may be possible that account), and of providing good mechanical stability for slight differences exist between them due to the presthe sample assembiy during loading and equilibration. This new sample assembly was used for MgO, MnO, ence of trace amounts of amp~bole, observed as a MgCaSi,O,, NiO, and NiCaSi20,, while COO, CaO, coherently intergrown phase during very careful SiO,, CoCaSizO,, Mn,SiO,, and MnSiO, were found to microscopic examination. This is not detectable by dissolve readily with the solid-cup assembly. X-rays or by casual microscopic examination. When The sample size per run averaged 50mg. Throughout this series of experiments, the temperature of the calorisuch a sample is dissolved in molten lead borate at meter remained constant at 713.O”C and the calibration 713”C, the small amount of water liberated can generfactors remained constant. ate a significant heat effect if it all vaporizes into the Calorimetry of cobalt-containing samples was done unatmosphere. On the other hand, if the amphibole is der a protective atmosphere of nitrogen or carbon dioxide to prevent oxidation, as previously described (NAVROTSKYfirst converted to anhydrous silicates by preheating and KLEPPA,1968). Calorimetry of MnO and manganese the sample above lOOO”C, the heat of solution of silicates was done under an atmosphere of purified Cot, diopside wifl not be measurably affected by the preswith special care taken to flush out the system with gas ence of a small amount (co.1 wt ‘A) of other silicates before lowering the samples into the hot zone. By taking produced by amphibole dehydration. We surmise that appropriate care, oxidation of MnO during an equilibration period of 2-3 hr in the calorimeter could be entirely our initial sample contained more amphibole than prevented. Kleppa’s sample and thus we saw a spurious endoSamples of MgCaSi,O, glass were dissolved after a thermic heat effect associated with the solution of the minimum time of pre-equilibration (223 hr instead of overuntreated diopside sample. night). Recrystalli~tion of the glass did not appear to be For the reaction: a sibilant problem under these conditions.
analysis confirms that the samples are indeed close to stoichiometric in terms of oxide components.
MgO + CaO + 2Si02 = MgCaSi,O, 3. RESIJLTS AND DISCUSSION 3.1 Enthalpies
of solution
of binary
AH& = -34.3 &-0.4 kcal/mol
oxides
data are given in Table 2. Our data are consistent with those collected over the last several years by Kieppa and co-workers (NAVROTSKY and KLEPPA, 1968; NAVROTSKY,197la; SHEARERand KLEPPA, 1973; M~~LLI~Rand KLEPPA, 1973; CHARLU et al., 1975). According to the above studies, the enthalpies of solution in 2PbO’B,Oa of CaO, MgO, SiO,, NiO, CuO, and ZnO are more endothermic at 900°C than at 692°C and our data at 713°C fit this general trend. The
3.2 Enthalpy
and jkr
cnrrqy
qf’,fonnation
qj’ diopsidic
clinopyroxmes 3.2.1 ~~o~s~de, MgCaSi*O,. Initial ~lo~metric experiments on the Twin Lakes natural diopside gave values of the heat of solution which were about I kcal/mol more endothermic than those for the synthetic sample. These values also showed considerably more scatter than those for the synthetic diopside or the heated natural samples. Although we initially suspected the possibility of a structural change, possibly
AH&s = -33.6 + 0.7 kcal/mol,
(1)
where the heat contents given in ROBIEand WALDBAUM(1968) are used to correct our data to room temperature. We have not attempted to correct our heats of formation for the small deviations from stoichiometry detected in the analyses. We feel that the uncertainties inherent in the analytical methods and the uncertainties in assigning the excess oxides to solid solutions or second phases make the validity of such a correction doubtful. In any case, depending on the model chosen, the correction would make the calculated enthalpy of fo~ation of diopside more exothermic by %200 cal/mol. There are two determinations by acid calorimetry of the enthalpy of formation of diopside (KRACEK, 1953; NEUVONEN,1952). The value in ROBIE and WALDBAUM (1968) is an average of these. Kracek used a ‘synthetic diopside’, not further characterized, and obtained AH&s = - 37.76 kcal/mol. Neuvonen used
I784
A.
NAVROTSKYand
a natural diopside from Juva, Finland, which was analyzed to contain 49.22mol y,:, Casio,, 49.74% MgSiO,. 1.01*:, FeSiO,, and 0.031;: MnSiO,. After correction terms were applied for the impurities and slightly no~stoichiometric composition, Neuvonen obtained AH>ox = - 35.25 i 0.22 kcaI,imol. Kracek’s value is clearly too exothermic, possibly because of gross compositional errors in the synthetic sample. whereas Neuvonen’s value depends somewhat on the exact corrections to be made for the presence of the impurities. especially iron. Hemingway (1976. personal communication) suggests that Neuvonen’s value for the heat of solution of quartz should be corrected by + 300 to the + 400 cal/mol because of the fine particle size of the sample used. The corrected heat of formation of diopside from the oxides would then be AH 2u8 = -33.55 i: 0.25 kcal/mol. in better agreement with our dat;I. H~L~;Ix)N 1’1LI/.(in preparation) has been developing a set of self-consistent free energies of formation of minerals which satisfy the reversed phase boundaries for mineral equilibria (mostly below 600°C). If one accepts the calorimetric entropies, S&s of diopside, MgO, CaO. and SiOZ (from low temperature heat capacity measurements) as being correct as listed in ROHIEand WALDBAUM(1968), then Helgeson’s data (personal co~nm~lnic~tion) suggest for diopside, AH& = - 34.7 kcal/mol (formation from the oxides). Our vnluc of - 33.6 & 0.7 kcalimol is in fair agreement with this estimate. We believe our determination of the enti~~tl~~/ of forn~ation of diopside to be more reliable than the curly hydro~uoric acid solution calorimetric work. although modern techniques of acid-solution calorimetry clearly can and do provide accurate thermochemical data, especially for hydrous minerals. 3.X C’oCaSi,O,, and NiCaSi,O,. From the calorimetric data, we have. for the reaction: Co0
+ CaO -t 2SiOZ = CoCaSi,O,
AH,,,,, = - 26.7 _t 0.5 kcal/mole.
(2)
and for NiO -t- CaO + 2Si02 = NiCaSi,O, AHux<, = - 27. I rtr 0.5 kcaljmol.
(3)
These data are consistent with the pattern observed for other silicates and germanates (NAVROTSKY, 1971a). in which the magnesian end-members are substantially more stable than those containing Fe, Ni and Co. However, it is interesting to note that. whereas Ni$iO, is considerably less stable than Co,SiO, or Fe,Si04. NiSiO, is less stable than FeSiO, or CoSiO,, and Ni,GeO, is less stable than Co,GeO, (NA~ROTSK~. 197 la), the three cal~um-containing pyroxenes. FeC’aSi,O,. CoCaSi,O,, and NiCaSizO, all have very similar enthalpies of formation from the oxides. That is. nickel diopside is relatively more stable than other nickel silicates. This is probably due to the competition of two factors (a) the genera1 trend
W. E.
&INS
toward decreasing silicate stability in the series Mg, Mn, Fe, Co. Ni. Cu discussed by NAVROTSKY(1971). and (b) the stabifization of the diopside structure by small cations in M 1. Since cation size decreases in the order Mn, Fe, Co, Ni, the two effects balance and result in very similar enthalpies for FeCaSi,O,. CoCaSi,O,. NiCaSi,O, . GHOX and WAN (1975) observe that in MCaSizO, clinopyroxenes the average M2-0 distance increases approximately linearty with increasing M 1-O distance. The thermochemical trend is consistent with optimum Ca-0 distances being possible in clinopyroxencs with the smalleI cations. Mg” and Ca” ‘. The transformations to the bustamite structure of MnCaSi,O, (johannsenite) above -400°C (LAMB and LINDSL~-:Y,1972), and of FeCaSi,O, above z i ooo‘c (LINDSLI:Yand MUNOZ. 1969), compared to the stability to the temperature of melting of CoCaSizO,, MgCaSizO, and NiCaSi,O, are further manifestations of the decreasing stability of the diopside structure relative to other phase assemblages as the radius of the M’+ cation increases. 3.2.3 FeCaSi,O, hrdenheryite. We did not determine the heat of formation of hedenbergite, although we are currently developing calorimetric techniques under atmospheres of controlled oxygen fugacity. However, data in the literature permit an estimate of the free energy of formation of FeCaSi,O, from its oxide components as follows. FeCaSi,O, is stable in the hedenbergite structure only at relatively low tem~mture (LINIXLEY and MLINOZ. 1969). At 1080°C and atmospheric pressure. the composition FeCaSi,O, exists as a phase initially described as a wollastonitc solid solution (JOEIIVSONand MUAN. 1967) or. more correctly, as a phase with a bustamite-related structure (RUTSTEIN, 1971 ; RAPOPOKTand BURNHAM. 1973). Although, strictly speaking. structural relations along the Fe,&, _,Si03 join (0
where the free energies of formation are from the component oxides and the logarithmic term comes from the assumed ideal mixing of the 2 mols of cations. At 1350 K, AG’:. - 21. I kcal/mol CsS~O~~woli.~~~ositc) 1. (RoBII: and WALDBAUM, 1968) and AG~eSior(I~rra,i,it~i = - 1.5 kcal/mol (NAVKOTSKY, 1971a). Thus AC~cCPSiPh(h,~rtami,c) = - 26.4 kcat/moi. Since hedenbergite is unstable with respect to the bustamite structure at 1350 K. its free energy of formation from the oxides must be somewhat fess cxothermic than the above value. LINIXLEY and Mr;~oz (1969) report that the transition FeCaSi,O, (heden-
Thermochemistry
bergite+ bustamite) occurs reversibly near 5 kbar at 1350 K. Crystallographic data for the bustamite form of FeCaSi,O, are given by RAPOFQRTand BURNHAM (1973), and their calculated cell volume is 727.2 A3 = 73.00cm3/mol. Taking the known molar volume of hedenbergite, 452.2 A3 = 68.30 cm3/mol (ROBIE et al., 1967), we have
heat contents reported by MAH (1960). When the tabulated heat contents are used to correct our calorimetric values to 298 K, we get AH&(MnSi03) = - 5.86 kcal/mol and AH’&,(MnSiO,) = - Il.59 kcal/mol. Thus our data confirm the earlier calorimetric work. For the reaction 2MnSi0,
AG~,c,sip,(bustamile) = AG~ecasi206(hedenbergitc) - PAV,
(5)
where AV = Vhedenbergite - Vbus,ami,e= -4.70 cm3/mol AG;,c,si,o,(hedrnbergite) = - 25.8 kcal/mol.
(6)
The estimated uncertainty in this final value is 5 f 1.5 kcal/mol. One should note that the PAV correction term is less than 1 kcal, so that even a factor of two in the uncertainty would lead to only about 500 cal uncertainty in AGPeCaSiZo6. Recently, KURSHAKOVA and AVETISYAN (1974) determined the equilibrium oxygen fugacity as a function of temperature for the phase assemblage hedenbergite, wollastonite, quartz, metallic iron. They calculated the free energy of formation of FeCaSi,O, in the temperature range 50&1300K and obtained values of AGT from the oxides which decreased in magnitude from - 29.7 kcal/mol at 500 K to - 22.4 kcal/mol at 1300 K. This would imply an entropy of formation of some -9 cal/deg mol, which does not seem reasonable. The probable major source of error in their analysis of the data is the assumption that the wollastonite phase exists as pure Casio,. Rather, reduction of hedenbergite will probably produce an iron-containing wollastonite or an iron-containing phase of bustamite structure, as the phase equilibrium data of RUTSTEIN (1971) imply. Then the activity of CaSiO, in the wollastonite phase will not be unity. This error will be magnified in deriving enthalpy and entropy terms from the temperature dependence of the free energy. However, the values of AGY that Kurshakova and Avetisyan calculate bracket our estimated value of -25.6 kcal. 3.3 Manganese silicates From the data in Table 2, we have, for reactions at 986 K MnO + SiO, = MnSiO,
1285
of some pyroxenes and related compounds
AH” = 6.32 + 0.30 kcal/mol
2MnO + SiOz = Mn,SiO,AH” = 12.23 + 0.33 kcal/mol.
(8)
Using tabulated values from ROBIE and WALDBAUM (1968), one gets, for the formation of rhodonite and tephroite from the oxides at 1000 K, AH” = -6.38 and - 12.41 kcal/mol, respectively, in excellent agreement with our data. These tabulated values are based on hydrofluoric acid solution calorimetry by KING (1952) [AH&,(MnSi03) = -5.92 f 0.17 kcal/ mol] and by JEFFES rt al. (1954) [AH&,(Mn,Si04) = - 11.75 k 0.56 kcal/mol] and high temperature
+ SiO,,
(9)
our data give AH& = +0.41 f 0.38 and AH&,, = f0.13 kcal/mol. Rhodonite is, of course, a stable phase with respect to tephroite and quartz, and our data suggest that the enthalpy, as well as the free energy, of reaction (9) is positive at atmospheric pressure. The free energies of formation from the oxides at 1423 K of MnSiO, and Mn,SiO, have been determined by SCHWERDTFEGERand MUAN (1965) to be - 5.9 + 0.3 and - 10.4 f 0.4 kcal/mol, respectively. Combined with our calorimetric data, these give entropies of formation from the oxides at 1423 K of - 0.30 cal/deg mol for MnSiO, and - 1.3 cal/deg mol for Mn,Si04. These are in reasonable agreement with the values obtained from heat capacity measurements as calculated from the ROBIE and WALDBAUM (1968) mol tabulations: AS;15,,0 = -0.17 and -0.84cal/deg for MnSiO, and MnSiO,, respectively. Thus the thermochemical data for Mn,Si04 and MnSiO, show very good agreement among several measurements using different techniques. Our heats of solution of the two polymorphs of MnSiO,, rhodonite and pyroxmangite, are very similar. From our data, for the reaction MnSiO,
(rhodonite) AH&
= MnSiO,
(pyroxmangite)
= +0.06 i 0.33 kcal/mol.
(10)
AKIMOTOand SYONO (1972) in a high pressure study of MnSiO,, report a transformation from rhodonite to pyroxmangite structures at P(in kbar) = 10 + 0.026 T (in “C).
(11)
Using the molar volumes given by these authors, one gets AV” = -0.391 cm3/mol, and, through the Clausius_(=lapeyron equation, AS” = -0.246cal/mol K. At looo”C, the transformation occurs at 36 kbar, thus AG” = -PAL’”
(7)
= Mn,Si04
= +336.4cal = AH’ - TAS’,
(12)
or AH” = +23 cal. Because the volume change associated with this transition is small, neglect of differences in compressibilities and thermal expansion factors for the two polymorphs may introduce significant errors. However, both our data and that of Akimoto and Syono indicate that the difference in enthalpy between the two polymorphs is extremely small. According to the data of AKIMOTOand SYONO (1972) and in agreement with our AH” value, the pyroxmangite polymorph of MnSiO, below about 10 kbar is unlikely to be stable at any temperature. However, the hydrothermal synthesis at 3 kbar and 650°C by
A. NAVR~TSKYand W. E. Coot~s
1286
ITO (1972a, b; personal communication) and at 2 kbar below about 700°C (PETERS, 1971; ALBRECHT and PETERS, 1975) and similar hydrothermal syntheses by MOMOI (1974) suggest a stability of pyroxmangite at or near atmospheric pressures at temperatures below 500°C. With such comparable energies for the silicate chains with a 5 unit repeat (rhodonite) and a 7 unit repeat (pyroxmangite), the effects of surface energies, coherent intergrowths, and possible defects or ‘mistakes’ in stacking sequences may affect the observed equilibria to an observable extent. IRMA and BUSECK (1975) have observed by electron microscopy the intergrowth of ortho- and clinoenstatite on a unit cell level, while BURNHAM (1966) has suggested a pyroxenoid with a 9 unit silicate chain repeat in the structure of ferrosilite III. The close similarity between pyroxene and pyroxenoid structures may verge on continuous gradation between idealized end-member structures through the incorporation of lattice defects. The experimental data support this thesis through the small energy differences observed between: (a) rhodonite and pyroxmangite (< 100 Cal), and (b) orthoand clinoenstatite; less than 500, 100 and lOOcal for MgSi03, CoSiO, and FeSiO,. respectively (NAVROTSKY, 1976; AKIMOTO et ul., 1965). Note that the enthalpy difference between wurtzite and sphalerite forms of ZnS and ZnSe, in which polytypism and stacking disorder are well-known, is of the same order of magnitude, namely 63 and 229 cal/mol (NEUHAUS and STEFFEN, 1970; CEMIC and NEUHAUS. 1974). In addition. the data of AKIM~TO and SY~N~ (1972) also permit an estimate of AC“, AH”. and A.S’ for the reaction MnSiO,
(pyroxmangite) = MnSiO,
(clinopyroxene).
( 13)
For that reaction P(kbar) = 19 + 0.057 T(“C) (800~14OO’C).
(14)
Using their reported unit cell volume for the clinopyroxene of 455.6 A3 and calculating as before, we get: AS” = -0.635 cal/mol K, and W273 = 846 cal/mol, AH” = -211 cal/mol K. Although these values are again subject to considerable uncertainty, they suggest that the actual differences in enthalpy and entropy between pyroxene and pyroxenoid structures are rather small. 3.4 Melting of’ clinopyroxenes and enthalpy oj’,fkion of diopside The incongruent melting at atmospheric pressure of MgCaSi*O, over a temperature range of z 1340-1391 “C is well established (KUSHIRO, 1973). The products of incongruent melting appear to be a diopside solid solution with Mg/(Mg x Ca) > 1 and Si/(Mg + Ca) < 1 and a silica-enriched liquid. HIGGINS and GILBERT (1973) report that at atmospheric pressure NiCaSi,O, melts incongruently near 1340°C.
producing nickel olivine (Ni$iO,). possibly some pseudowollastonite, and liquid. At higher pressures. NiCaSi,O, may melt congruently. We have found that CoCaSizO, melts incongruently at atmospheric pressure in the temperature range Il5&1205’~C to yield a slightly Ca- and Si-deficient clinopyroxenc. a slightly Si-enriched melt. and a small amount of a very G-rich pyroxenoid. having either a wollastonite or bustamite structure. We \vill report these results more fully when we complctc a stud) of phase equilibria in the CaSiO,~CoSiO, system. However. together these studies definitely cstnblish the incongruent melting of the MC’aSizO,, clinopyroxenes as a general phenomenon. LINI)SI,L.\.and M~N~z (I 969) report that FeCaSi,O(, bustamitc melts incongruently. Our calorimetric data show that for the reaction: CaMgSizO,
(diopside)
= C‘aMgSi,O,
AHq8(, = + 21 .(I & 0.3 kcal,mol.
(glass) (15)
Using the heat contents given hq KI LI.I.Y (1960). WC get at room temperature. AH,,,, = +_‘I ._3 _+ 0.5 kcal, mol. The heats of solution in HF near room temperature have been measured. yielding. for reaction (15). AH,,, = 22.1 kcal’mol (FI KRIEK. 1971). In addition. the enthalpy of fusion at the ‘melting point’. 1665 K is reported to be 22.0 hcal!mol (Kr:r.~~r:u. 1962) 18.5 kcal/mol (Roen and WAI.I)RAI~M, 1968) and 30.6 kcal/mol (FFRRIER. 1971). The value we obtained is in general agreement with the reported values of the heat of vitrification cited above and is, we believe, a reliable measurement of the difference in cnthalpy between glass and crystals. Perhaps :I more serious question is the relationship between the cnthalpy of fusion (solidliquid) at the melting point and the cnthalpy of vitrification (solid + glass) at lower temperatures. For diopside. there arc two problems; (:I) incongruent melting of the solid, and (b) the gloss Iransitlon in the supercooled liquid. Fcrricr’s work. in particular. shows the nature of thcsc problems. Hc reports values of the heat of solution of glass :uld crqstalh at room tcmperature (HF calorimetry) and of the heat contents of glass and crystals to above the melting point (drop calorimetry). However. ths heat content of the glass cannot be measured bctlvcen _ II00 K and the melting point because of rapid r~crystalli/atiotl. Therefore the two portions of the cur\;c :Irc‘ connected by a line, thus masking the true nature of the glass-transition region. For crystalline diopside. the heat content curve does not show :I CIGIII break at the ‘melting point’, but shows an additional contribution to the enthalpy at temperatures from 100 hclow the ‘melting point’ up to the liquidus. This deviation may be caused by incongruent melting (KI’SHIKO, 1973) or by other premelting phenomena. Fr RKILR ( I97 I ) has drawn his curve so that it gives ;I maximum possible value for the heat of fusion at the melting point. a value I .5 times the cnthalp) of vitrilication. He obtains similar results for anorthite. The glass transi-
Thermochemistry
1287
of some pyroxenes and related compounds
~ck~w~e~e~nents-This work was supported by the tion will act to ‘anomalously’ increase the enthalpy National Science Foundation and the Alfred P. Sloan of the noncrystalline state with increasing temperaFoundation. We thank Dr. E. HAUSW,Dr. J. ITO. Dr. D. ture, thus making the value of the enthalpy of fusion F. WEILL and Dr. H. S. YODER,JR. for samples, and these more positive than the enthalpy of vitrification. Howneoob 01~s Dr. L. FINGER. Dr. H. C. HBLGE~ON,Dr. B. Dr. 0. J. KLI%PA, Dr. R. MCCALL~ST~R, Dr. ever, we believe that the effects seen by Ferrier (a HEMINGWAY, factor of 1.5) are too large to be reasonable. It is R. C. NEWTONand Dr. R. YL~D for stimulating discussion. interesting to note that estimates of the enthalpy of REFERENCES fusion of diopside from a freezing point depression ALBRECHTJ. and PETERST. J. (1975) Hydrothermal synanalysis of phase diagrams tend to fall in the same thesis of pyroxenoids in the system MnSiO,--CaSiOi at range (20 & 2 kcal/molf as the reported enthalpies of Pf = 2 kb. Contrib. Mineral. Petrol. 50. 241-246. vitrification (KELLEY, 1962; ROBIE and WALDBAUM AKIMOTOS. and SYONOY. (1972) High pressure transformations in MnSiOs. Amer. Mj~eru~. 5$. 7684. 196X; BURNHAM, in press; this work) rather than in BIGGARG. M. and CLARKED. B. (1971) Asnects of chase the range given by Ferrier for the enthalpy of fusion equilibria in the inversion and exsolution of pyroxenes. (30 kcal/mol). Clearly more work must be done to lndian Mineral. 12, l-13. Bovo F. R. (1973) A pyroxene geotherm. Geochim. Cosmoanswer these questions. It is of interest to note that chim. Acta 37, 2533-2546. for SiO, and Ge02, there does not appear to be a BURNHAMC. W. (1966) Ferrosilite III: a triclinic pyroxsignificant difference between the enthalpy of fusion enoid-type polymorph of ferrous metasilicate. Science and of vitrification (HOLM et al., 1967; NAVROTSKY, 154, 513-516. 1971b). BURNH~ C. W. (in press) ~erm~ynamics of melting in 1
4. CONCLUSIONS The present investigation provides new themechemical data for several pyroxenes and pyroxenoids. The enthalpy of fo~ation data may be used in several ways to generate complete the~~ynamic data for the phases in question. The enthalpies of formation may be combined with standard entropies obtained from heat capacity measurements to produce the free energy of formation as a function of tem~rature. Un~rta~nties in the calorimetric entropies of silicates, which arise from uncertainties in cation ordering, defect structure, and magnetic ordering have been discussed in detail in a recent paper by ULBRICHand WALDBAUM(1976). We feel that the enthalpy of formation data can be put to good use to partially overcome these di~culties as follows. High temperature equilibrium data are available for a number of silicates, with values of their free energies of formation at temperatures of 1000 K and above. When both equilibrium work and high temperature solution calorimetry have been performed on wellequilibrated samples, preferably of characterized structural state, then the entropy of the fo~ation can accurately be calculated as Ails”= (AH0 - AG”)/T. This can provide a more accurate estimate of the entropy of formation than one can get either from heat capacity measurements alone (because of the difficulties mentioned above) or from the temperature dependence of the equilib~~ data (taking a slope over a small temperature interval can lead to large errors). Then, if the standard entropy of some phases is well known, that of others involved in the equilibria can be computed. We are currently analyzing the available data for anhydrous transition-metal oxides and silicates in order to produce a ‘best set’ of enthalpy, entropy, and free energy values. We plan to report those data and their application to some geochemical calculations in a subsequent communication.
silicate-volatile systems: Fortsch. &f&era!. BURNTR. G. (1969) Site ureference of transition metal ions in silicate irystal strudtures. Chem. Geol. 5, 275-283. CAMERONM. E., PAPIKE J. J., PREWITTC. T. and SUENO S. (1973a) Pyroxenes-comparisons of real and ideal structural topologies. Z. Krist. 138. 254-273. CAMERONM. E., S&NO S., PREWXTT’C. T. and PAPIKE J. J. (1973b) High temperature crystal chemistry of acmite, diopside, hedenbergite, spodumene and ureyite. Amer. Mineral. 58, 594-618.
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