Anerican Mineralogist, Volume 70, pages 249-260, I9B5
Low-temperature_heat-capacitiesand derivedthermodynamic properties of anthophyllite,diofside, enstatite,bronzite, and wollast'onitt
Kn.nrern M. Knupr,ll D ep artment of Ge o scienc e s The Pennsylaania State Unioersity U niuersity P ark, Pennsyluania I 6802
RIcnc,RD A. Ronn, Bnucn S. HnMrNcw,qy U.S. Geological Suruey Reston, Virginia 22092
Dnnnrr,r, M. Knnnrcr
D ep ar tment of Ge o scienc es The Pennsyloania State Uniuersity U niuersity P ark, P ennsyluania I 6802
,c.NDJUN Iro2 The James Franck Institute The Uniuersity of Chicago Chicago, Illinois 6063 7
Abstract
The heat capacitiesfor magnesio-anthophyllite,diopside, synthetic enstatite, bronzite, and wollastonite were measuredbetween 5 and 385 K by use of an adiabatic calorimeter.The entropy change si* - s3, in f(mol' K), is 538.9+2-7 for magnesio-anthophyllite [Mgu..Feo.rsiEo22(oH)2], 142.7+o.2 for diopside, 66.27+o.ro for synthetic ensiatite (MgSior), 69.04+0.10for bronzite(Mgo.rrFeo.rrSior), and 8r.69+0.r2 for wollastonite.The heat capacity, ci, for magnesio-anthophyllite,corrected to a composition of pure Mg- anthophyllite [Mgrsiroz(oH)r], resultsin a sles - sfi valueof 537.o*2.7/(mol.K). These resultsrepresent only the entropy calculatedfrom the measuredheat capacities.No configu- rational entropy wasadded. Although our Ci values for diopside and wollastonite differ significantly from those of previousstudies, especially at cryogenictemperatures, our entropiesat 298.15K are in close agreementwith the commonly acceptedvalues. Schottky heat capacity anomalieswere ob- servedbelow 25 K for magnesio-anthophyllite,diopside, and bronzite. The contribution of the magneticentropy arising from the interaction of Fe2+ with the ligand ficld of the crystals is discussed.
Introduction (1932)also measuredthe Cfi of wollastonite over several, The previouslyaccepted entropies for diopsideand wol- often narrow, temp€ratureintervals between9 and 3(X K. lastonite at 298.15K were basedon a limited number of Prior to this study,low-temperature Ci data for magnesio- low-temperature Cfl measurements.King (1957) and anthophyllite and enstatitewere nonexistent,and heat ca- Wagner (1932)reported Ci valuesfor diopsidebetween 50 pacity measurementsby Kelley (1943)between 52 and 296 and 300 K and between20 and 40 K, respectively.Wagner K for a poorly characterizedsample of clinoenstatitewere usedto estimatethe thermodynamicproperties of enstatite. r Present address: GeosciencesResearch and Engineering De- Reliable valuesfor the entropiesof thesephases are criti- partrnent, Battelle, Pacific Northwest Laboratories, Richland, cally important to calculatingthe high-temperaturestabili- Washington99352. ty of these minerals and the metamorphic and igneous 2 Deceased. equilibriainvolving them. 0003-{04xl85/03O44249$02.W 249 250 KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES
and Burn- Table 1. Chemical analyses of samples used in low-temperature hydrouspyribole structures(Veblen et al., 19'17; Veblen of heat capacity measurements ham, l978a,b).The magnesio-anthophyllitesample is composed at least95 percent(by volume)double chain material and approxi- Hotlastonited percent wider chains (Veblen, wdtten communication, flagnesio- - Diopsided -Enstatite.* Bronzite mately 5 anthophyllited (synthetlc)" (natural )c 1978).The distribution of disordered,wider chain material is not homogeneousin the sample. A description of the intergrowth 59.4 59.2n 55.86 51.8 Si 02 structuresin this anthophyllite samplewas given by Veblen and Ti 02 0.I 0.00 0.00 Buseck(1979). 0.00 <0.05 Al 203 0.95 0.20 CrZ03 0.1r 0.10 Diopside, CaMg(SiO) 2 0.05" Fe203 0.57 0.09 The white diopside samplewas collectedby one of us (DMK) (1970), Fe0 5.7 0,48 o.l2e 10.1 1e from an area near Zermztt, Switzerlandstudied by Bearth in the experimentalstudy of Slaughteret al' (1975)' fi90 30.2 18.0 40.80 3I.61 0.t2 and was used Examinationsby meansof X-ray diffraction and a petrogaphic Mn0 0.12 0.04 0,l9 0.00 microscopedid not reveal any impurities in the powdereddiop- Ni0 0.12 side.The chemicalcomposition given in Table I is in closeagree' Ca0 25,2 0.00 0.29 48.5 ment with the analysespresented by Slaughteret al. (1975)'The Na20 0.20 0.01 0.01 cell dimensionsgiven in Table 2 are in excellentagreernent with and Smith (1969)and in Kzo 0.07 0.02 0.0I the valuesfor diopsidepresentd by Borg the Joint Committeeof Powder Diffraction Standards(rcros) file Pzos 0.03 0,03 0.00 lI-654. coz 0,01 0.01 0.00 (0.01 H2o* 2.t 0.64 Bronzite, M g s.s5F es., 5SiOg Hzo- 0.22 0.08 The bronzite sample was describedby Huebner et al. (1979)' The calorimetricsample consisted of 3l pale-brown,single-crystal 1 : 100.52 100.I 0 100.20 98.82 100,49 Tota chips,that ranged in massfrom 0.19 to 1.65g. Optical examina- tion of each chip did not reveal any impurities.The composition aAnalyses completed by conbination of atomic absorption sPect'oscopy and of each chip was determined by electron-rnicroprobeanalysis stanlard wet-chemicaltechniques. See Shapi.o (1975) for a description of these analYtical techniques. using the method of Benceand Albee(1968). Multiple spot analy- DAveraqeof 84 spot probe analyses. gi,iiiqhiia-i"i-9i'ot'a totat oi 55 spot probe analvses fo.31 bronzite chips' sesof eachchip revealedno chemicalinhomogeneities within any dTotal iron as Fe20?. chemical composition for this eTotal iron as Feo,- single chip. A weighted-average sampleis givenin Table 1. Unit-cell dimensionswere measured for the most Mg- and Fe-rich bronzite chips, designatedK30 and K3l, respectively.The refinedcell constants(Table 2) are in good Minerals agreementwith those for bronzite as given in JCPDS patterns 19-605and 26-876. M agnesio -antho ph yllit e, M g6.sF e 6. 1 Si BO 2 z ( OH ) 2 gSiO The anthophyllite sample, designated'1.3.71.10, was collected by Synthetic enstotite, M 3 Prof. Peter Misch in the North Cascades at mile-marker 132.5 Enstatite crystals were prepared by growth from a lithium- along the North Cascades Highway (Washington Route 20) north vanadomolybdateflux using the method of Ito {1975).Residual of the eastern part of Lake Diablo. A small vein of light-green' flux was removedby solution with H2O in a sonic cleanerafter coarse-bladed anthophyllite was cut from the specimen, crushed, gentle crushing of the crystals. Further details are given by and sieved to the range of -35 to +100 mesh. Impurities were Kiupka (1984).Semi-quantitative emission spectroscopy analysis removed from the sample by using a Franz3 magnetic separator detected (maximal values): Li: 1100 ppm, Mo : 1200 ppm' : and heavyJiquid techniques. X-ray powder-diffraction methods Ni : 100 ppm, P : 910 ppm, V : 1500Ppm, and Zr l2O ppm' showed that the separated anthophyllite contained talc (<5%) as Microprobe results(Table 1) show that the syntheticenstatite is the only impurity. essentially pure, stoichiometric MgSiO3. Unit-cell dimensions The chemical analysis given in Table I is in close agreement weremeasured for two samplesof syntheticMgSiOr and are given with unpublished electron probe analyses provided by Prof. Misch in Table 2. Cell dimensionsof the calorimetricsample are in excel- and with other probe analyses completed during this study. Or- lent agreementwith those given by Ito (1975)for a similarly syn- thorhombic symmetry for the sample was confirmed by use of a thesizedenstatite. petrographic microscope. The unit-cell dimensions for the calori- given T,able 2, are in good agreement with the metric sample, in Wollastonite, CaSiOg values for synthetic, pure-Mg anthophyllite (Chernosky and sample from Willsboro, EssexCounty, New Autio, 1979) and for natural anthophyllite (Finger, 1970). The wollastonite Natural ScienceEstablishment' The anthophyllite sample was also tnalyznd for the presence of York, was purchasedfrom Wards The specimenwas crushed,sieved to the range of -35 to +100 mesh,and separatedby heavyJiquid techniques.X-ray diffraction and optical measurementson the final sampledid not reveal any 3 The use of trade namesis for descriptivepurposes only and impurities. Chemical analysesof the separatedwollastonite are doesnot imply endorsementby Battelle,Pacific Northwest Labo- given in Table 1. The refinedcell constants(Table 2) are in close ratories,U.S. GeologicSurvey, or The PennsylvaniaState Univer' agreementwith the valuesfor wollastonitegiven by Buergerand srty. Prewitt(1961). KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES 251
Table 2. Cell constantsfor samplesused in heat capacitymeasurements
Magnesi o- Diopside ------Bronzite------Enstatite------tlol I astoni te anthophylI ite (natural) (synthetic) K30 K31 Ito-l lto-7
a (nm) 1.8536(3) 0.e749(1) 1.8250(3) 7.824e(2) r.8228(?l r.82re(2) 0.7e2s(1)
b (nm) 1 TAAOr2\ 0.8925(I ) 0.8837(1) 0.8843(1) 0.8816(1) 0.8814(l) 0.7322(2) c (nn) o.5277(r) 0.52511(9) 0.5190(1) 0.51e3(l) 0.5180(1) 0.s178(1) 0.7069( r ) 90. 90' 90" 90" 90" 90. eo" 4'(2)
B 90' rOso48.2,(e) 90' 90" 90' 90. 9s' 13.8'(e) 90' 90" 90' 90" 90' 90" 103"le'(l) v (nm3) 1.7606(4) 0.43966(8 ) 0.8370(2) 0.8380(2) 0.8325(2) 0.8316(2) 0.3e74(1) N 38 32 29 30 28 34 23
Note: Cell dimensionsgiven in nanometers(1 nm = l0 A). Numberin parenthesesis uncertainty in last digit. Cell dimensionswere measuredusing CuKcradiation. a N.ifilter, a scanning rate of 0.25o 20lmin, and BaFz (a = 0.61971t 0.0001 nm) as an internal standard. = N Numberof reflections used in'least-squares refinement program written by Applemanand Evans (1973).
Apparatus and procedures [Mgu..Feo.rSi8O22(OH)2]by assumingthat 848.382g of Low-temperatureCi measurementswere made using the impure anthophyllite consist of I mole of magnesio- apparatusand techniquesdescribed by Robie and Heming- anthophyllite (802.900g) and 14.239g NaAlSi.O, glass, way (1972)and Robie et al. (1976).The observedheat ca- 10.838g CaSiO. (wollastonite),5.711g FerO, (hematite), pacitieswere correctedfor curvature (Robie and Heming- 4.629 g AlrO. (corundum),4.350 g SiO, (quartz), 3.535g way, 1972)and for small quantities of He gas, generally KAlSi3Oe glass,2.552 g Feo.rS(pyrrhotite), and 1.O22g between9.6 x 10-s and 8.4 x 10-4 moles of gas, which MnO (manganosite).The low-temperature Ci data for wereintroduced into the calorimeterduring the loading in NaAlSi.O' and KAlSi.O, glasseswere from Robie et al. order to promote thermal equilibration at cryogenictem- (1978),CaSiO, from this study, FerO. from Gronvold and peratures (Robie et al., 1976).The 1975 atomic weights Westrum(1959), AlrO3 from Furukawaet al. (1956),SiO2 (Commissionon Atomic Weights, 1976),were used to cal- from unpublisheddata by Prof. E. F. Westrum,Jr. (Univer- culate the gram-formula weights of the measuredcom- sity of Michigan), Feo.rS from Gronvold et al. (1959), pounds. amositefrom Bennington et al. (1978),and the remainder of the Ci data were taken from Kelley and King (1961). Experimental results The selectionof thesephases for impurity correctionswas The experimental specific heats of magnesio- basedon the availability of accurateC[ data for the con- anthophyllite, diopside, bronzite, synthetic enstatite, and stituents.The differencebetween the uncorrectedCfi values wollastonite are listed in their chronological order of and thosecalculated for Mgu.. Feo.rSirOrr(OH),is 3.8% measurementin Tables 3 through 7, respectively.The at 50 K, and Table 3. Low-ternperature, experimental specific heats of 20 K, 0.08% at 100 K, and lessthan 0.03% at all temper- magresio-anthophyllite.(Sample mass was 22.lll g (in vacuo). aturesgreater than 150K. Data for magnesio-anthophylliteconsist of 94 measurementsbe- Below 25 K, the specific heats for magn€sio- twcen5.4 and 386.0K.) anthophyllito, diopside, and bronzite are significantly larger than those for wollastonite and synthetic enstatite. Temp. Speclfi c Temp. Specific Temp. Specific This differenceis presumablydue to a Schottky-typecon- heat heat heat tribution (Gopal, 1966) to the heat capacity at very low K U(g.K) K J/ (g.K) K J/(g.K) temperaturesarising from the small amount of Fe2+ in solid solution. Becausethe Schottky contributions are sig- SeriesI Series4 Series 7 nificant for the magnesio-anthophylliteand bronzite sam- "plateaus" 305.29 0.8379 140.17 0.4013 5.43 0.001148 ples, their heat capacitiesexhibit anomalous 311.12 0.8476 145.11 0.4195 6.00 0.001523 near 15 K. The C! anomaliesare especiallyapparent when 317.34 0.8584 150.13 0.4376 6.61 0.001907 f2, whero 323.41 0.8685 155.18 0.4552 7.35 0.002399 the data are plotted in the form of CS|T versus 329.43 0.8782 160.?2 0.4727 8.2t 9.002922 the anomaliesare seento have a maximum value near 100 335.40 0.8882 165.26 0.4897 9.07 0.003410 170.30 0.5064 9.95 0.003911 K2 (Fig. 5). The evaluation of the entropy contribution Series2 175.35 0.5228 10.97 0.004462 from the Schottky effectsfor bronzite will be discussedin a 180.41 0.5392 12.13 0.004998 341.71 0.8981 185.48 0.5547 13.38 0.005430 later section. 347.70 0.9069 190.57 0.5702 14.72 0.005880 353.66 0.9159 195.68 0.5852 16.19 0.006361 359.57 0.9242 200.81 0.6000 t7.79 0.007015 Table4. Low-temperature,experimental specific heats of diop- 365.40 0.9331 19.54 0.007979 3i1.10 0.9413 Series5 2t.46 0.009164 side.(Sample mass was 32.O83g (in vacuo).Data for diopside 376.97 0.9490 23.53 0.01070 consistof 92measurements between 8.6 and 382.0 K.) 382.08 0.9553 20s.94 0.6144 25.81 0.07275 385.99 0.9597 211.00 0.6285 28.32 0.01552 215.93 0.6416 31.9q a.ol922 Temp. Specifi c Temp. Specific Temp. SPecific Series3 220.90 0.6548 34.25 0.02444 heat heat 225.9t 0.6677 37.66 0.03084 heat 51.10 0.06693 230.87 0.6dol 41.25 0.03839 K K U(g.K) K U(s.K) 56.15 0.07931 235.87 0.5928 45.30 0.04783 U(s.K) 60.76 0.09406 240.90 0.7051 8 65.60 0.1102 245.89 0.7168 Series I Series5 Series 9 70.53 0.1278 250.83 0.7280 Series 0.06145 75.70 0.t472 255.81 0.7390 50.42 107.87 0.2728 237.52 0.6577 0.1679 54.86 0.07483 298.38 0.7692 81.00 302.64 0.7765 1t2.82 0.2919 ?43.69 0.6706 86.10 0.1883 Series 6 59.67 0.08989 308.20 0.7848 II7.67 0.3104 249.79 0.6829 91.05 0.2081 0.7946 123.61 0.3326 255.81 0.6944 0.7500 314.55 95.78 0.2270 260.84 0.8047 129.67 0.3548 26t.77 0.7062 0.2459 265.84 0.7610 32t.52 100.48 0.8141 134.88 0.3735 267.67 0.7174 0.2656 270.88 0.7117 328.24 105.42 334.91 0.8233 140.28 0.3923 273.54 0.7?83 110.36 0.2855 275.97 0.7820 341.53 0.8319 145.80 0.4110 279.39 0.7378 115.32 0.3053 28t.0? 0.1923 285.19 0.7475 0.3253 286.04 0.8025 t20.32 Series2 Series6 125.35 0.3450 291.10 0.8131 Series l0 0.82v 130.33 0.3643 296.22 0.8252 151.36 0.4294 0.3825 301.31 0.8310 336.38 135.15 343.10 0.8339 156.90 0.4472 8.62 0.001184 306.45 0.8403 162.36 0.4643 9.32 0.001311 311.65 0.8489 Series3 167.68 0.4806 9.97 0.001442 t72.90 0.4961 349.68 0.8426 178.01 0.5110 Series l1 356.23 0.8509 183.05 0.5251 362.13 0.8591 188.05 0.5391 11.35 0.001578 369.19 0.8669 193.04 0.5523 t2.26 0.001591 375.61 0.8747 198.04 0.5653 13.40 0.001818 381.99 0.8815 203.09 0.5781 t4.72 0.002072 impurities and for deviation from end-memberstoichiome- 208.?4 0.s908 16.19 0.002388 try by the sameprocedure used for anthophyllite.A sample Series 4 213.51 0.6033 1'1.78 0.002864 2t8.92 0.6161 t9.47 0.003602 of 222.321g was assumedto consistof 1 mole of diopside 54.74 0.07265 224.49 0.6288 ?t.37 0.004638 [CaM(SiO.)2,216.553g] and 3.617g SiO2(quartz),1.381 60.50 0.09142 23.56 0.006166 65.44 0.1084 Series7 25.93 0.008311 g FerO, (hematite),0.444 E AlrO, (corundum), 0.348 g 70.33 0.1261 28.53 0.01125 CaO, and 0.092g MnO (manganosite).The differencebe- 75.36 0.1451 229.78 0.6407 31.33 0.01520 80.41 0.1647 ?35.19 0.6539 34.34 0.02036 tween the uncorrectedand correctedCi valuesis 3.3Voat 85.52 0.1850 241.93 0.6669 37.69 0.02695 20 K, O.9o/oat 50 K, and approximately0.15% at all tem- 90.66 0.2053 248.27 0.6835 41.45 0.03527 95.81 0.2256 254.82 0.6937 45.64 0.04568 peraturesgreater than 100K. 100.94 0.2458 261.51 0.7076 50.24 0.05854 The experimentalCi data for wollastonitewere correct- 55.29 0.O74?L Series8 60.66 0.09176 ed for impurities and deviation from end-memberstoichi- ometry by assumingthat a 116.604g of sampleconsists of 268.15 0,7250 ?74.93 0,7312 1 mole of pure wollastonite(CaSiO3, ll6.lu g) and 0.185 281.63 0.74?2 g CaO,0.141 g MgO (periclase),0.061g Al3O3 (corundum), 288.22 0.7538 294.64 0.7640 and 0.056g Fe2O3(hematite). The diflerencebetween the 300.87 0.7737 uncorrectedand impurity-correctedCi valuesis O.25%oat KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES 253 Table 5. Low-temperature,experimental specffic heats of bron- mately 15 K were obtained from this extrapolation.This zite. (Sample mass was 25.162g (in vacuo). Data for bronzite procedure resulted in minor changes to the molar C$ consistof 96 measurementsbetween 5.5 and 3E7.4K.) valuesin this temperaturerange, and negligiblediflerences to the integratedthermodynamic properties (i.e., S? - SB). Temp. Specifi c Temp. Specific Temp. Specific Our procedure for correcting the diopside measurernents heat heat heat for the Schottky effectcaused by the Fe2+ impurity can be K J/(e.K) J/(s.K) K J/(s.K) readily justified by comparing the heat capacitiesfrom the linear extrapolation with: (1) the heat capacity measure- Series1 Series6 Seriesl0 ments of Leadbetteret al. (1977)between 1.5 and 25 K on 297.37 0.77?8 Lzt.7t 0.3137 288.41 0.7599 synthetic diopside, and (2) heat capacitiescalculated from 300.74 0.7809 I?6.62 0.3321 ?93.79 0.7701 the Debye model using a value for @o of 668 K obtained 306.43 0.7908 131.55 0.3503 299.23 0.7787 312.40 0.8004 136.61 0.3685 304.64 0.7873 from the elasticconstant data of Levien et al. (1979)using 318.43 0.8098 141.69 0.3864 the method of Robie and Edwards (1966).For magnesio- 324.60 0.8193 Seriesll 330.80 0.8282 Series 7 anthophyllite correctedto a pure Mg composition,Ci was 336.89 0.8374 5.50 0.002114 146.16 0.4038 6.01 0.002910 Senies2 151.80 0.4210 6.53 0.003392 156.80 0.4376 7.04 0.004116 333.09 0.8328 161.78 0.4358 7.64 0.00453i Table6. Low-temperature,experimental specific heats of synthet- 166.75 0.4696 8.29 0.005067 ic enstatite.(Sample mass was 23.287 g (in vacuo).Data for syn- Series3 Itt.73 0.4850 9.06 0.005869 thetic enstatite consist of 109 measurements b€tween 5.2 and 176.76 0.5002 9.90 0.006513 343.77 0.8466 10.93 0.007006 385.3K.) 347.09 0.8518 Series8 12.12 0.007385 353.07 0.8598 13.42 0.007600 359.02 0.8678 181.44 0.5140 14.88 0.007753 Temp. Specifi c Temp. Specific Temp. Specifi c 364.97 0.875? 186,65 0.5291 16.51 0.007790 heat heat heat 370.99 0.8833 192.03 0.544? 18.19 0.007949 316.97 0.8906 I97.33 0.5586 20.04 0,008300 K J/(g.K) K J/(e.K) K J/(s.K) 382.42 0.8965 202.54 0.5726 22.05 0,008850 387.39 0.9017 207.79 0.5859 24.18 0.009742 213.06 0.s995 26.59 0.01124 Series1 Series 5 Series 11 Series4 218.26 0.6125 29.33 0.01355 223,40 0.6248 32,29 0.01700 318.87 0.8521 t56.27 0.4506 12.75 0.000548 53.01 0.06168 2?8.58 0.6371 35.67 0.02202 3?4.41 0.8613 161.09 0.4674 14.09 0.000798 57.86 0.07613 233.80 0.6493 39.40 0.02861 330.33 0.8706 165.96 0.4839 15.30 0.001000 62.33 0.09006 238.96 0.6608 43.23 0.03657 336.3i 0.8801 170.83 0.5004 r6.69 0.001337 67.05 0.1058 244.06 0.6724 47.19 0.04714 342.44 0.8888 175.70 0.5163 78.27 0.001778 7i.88 0.12?8 52.98 0.06r50 180.59 0.5324 79.92 0.002447 76.90 0.l4l4 Series9 58.18 0.07701 Series2 185.49 0.5474 ?1.71 0.003332 190.41 0.5624 23.62 0.004365 Series5 ?40.02 0.6629 348.60 0.8982 195.36 0.5771 25.77 0.005815 245.30 0.6751 354.80 0.9067 200.32 0.5914 28.I1 0.007649 81.91 0.1604 250.56 0.6868 360.97 0.9156 205.31 0.6055 30.69 0.01036 86.89 0.1796 255.87 0.6976 367.09 0.9242 210.23 0.6193 33.58 0.01407 92,00 0.1993 261.33 0. 7084 373.18 0.9323 215.18 0.6324 36.19 0.01898 97.10 0.?19? ?66.84 0.7196 379.24 0.9401 39.89 0.02443 102.23 0.2390 272.29 0.7298 385.26 0.9463 Series6 43.34 0.03143 107.18 0.2585 277.70 0.7404 47.8? 0.04138 112.00 0.2769 283.07 0.7498 Series3 2r9.99 0.6454 5?.66 0.05462 r 16.91 0.2956 225.OO 0.6589 57.59 0,06933 52.79 0.05537 230.08 0.6714 57.69 0.07002 235.11 0.6839 Series12 62.06 0.08392 240.08 0.6965 66.69 0.09953 306.80 0.8323 71.46 0.1167 Series7 311.94 0.8408 Thermodynamic functions 76.35 0.1354 317.00 0.8493 - 81.40 0.1554 245.01 0.7081 3?2.02 0.8574 The thermodynamicproperties Ci' Si SB,@i- ffi)/f , 86.50 0.1760 249.98 0.7196 and -(Gi - m)lf are listed at integral temperatures 91.56 0.1968 254.99 0.7306 Series13 96.51 0.2r70 259.96 0.7413 from 0 to 380 K for magnesio-anthophyllite 101.29 0.2365 264.89 0.7519 5.?4 0.000001 [Mgu.rFeo.rSir022(OH)2and MgrSirOzz(OH)z],diopside, 106.32 0.?570 5.91 0.000024 11 1.57 0.?785 Series8 6.47 0.000079 bronzite(M go.rrFeo. r r SiO.), syntheticenstatite (MgSiOr), 116.70 0.2995 7.05 0.000079 and wollastonitein Tables8 through 13,respectively. 269.81 0.7614 7.89 0.000107 Series4 274.72 0.7721 8.85 0.900224 The methods describedby Westrum et al. (1968)were 279.]t 0.7826 9.72 0.000298 utilized to smooth the experimentaldata. The Ci data were Lzt.7I 0.3200 284.66 0.7923 10.56 0.000322 126.56 0.3391 289.66 0.8030 11.48 0.000469 extrapolatedfrom the lowestmeasured temperature to zero 131,37 0.3580 ?94.72 0.8115 t2.46 0.000582 Kelvin on a plot of Cfi,/T versus T2. For diopside 136.34 0,3773 299.74 0.8195 13,54 0.000719 and 141.49 0.3968 304.73 0.8293 14.74 0.000910 wollastonite, which exhibited small anomalies in CilT 146.61 0.4159 309.78 0.8375 16.08 0.001208 versusT2 becauseof trace quantities + 151.59 0.4341 314.88 0.8463 t7,62 0.001601 of Fe2 in their struc- 319.96 0.8553 t9.26 0.002240 ture, the data were extrapolatedgraphically to zero Kelvin 325.00 0.8627 2r.o7 0.003042 from a temperature 330.01 0.8705 23.O7 0.004063 above the anomaly.Smooth Cfi values 25.27 0.005493 for diopside and wollastonite between zero and approxi- 254 KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES Table 7. Low-temperature, experimental specific heats of wol- lastonite. (Sample mass was 29.231 g (in vacuo). Data for wol- lastonite consist of 94 measurements between 6.3 and 386.2 K.) 700 MgzSi802z(0Hlz Temp. Specific Temp. Specific Temp. Specific 600 Heat Heat Heat K U(g.K) K U(s.K) K J/(s.K) ? 500 Series3 Series7 Serteslr E r^^ 298.81 0.7423 130.73 0.3862 27r.47 0.7105 - 3Feo?Si8022(0H)2 303.86 0.7494 135.64 0.4018 ?76.50 0.7115 309.81 0.7572 140.56 0.4169 281.54 0.7t82 oo 1On 3t5.72 0.7648 145.56 0.4318 286.54 0.7259 o """ 321.68 0.77?0 150.54 0.4462 291.51 0.7338 327.69 0.7795 155.51 0.4602 296.54 0.7391 333,66 0.7866 160.48 0.4739 301.62 0.1473 200 165.45 0.4874 306.67 0.7537 Series4 170.51 0.5006 311.70 0.7600 339.66 0.7934 Series8 SeriesI2 100 345.79 0.8002 351.88 0.8070 175.r9 0.5123 6.27 0.000074 357.93 0.8140 180.15 0.5247 7.47 0.000240 363.95 0.8197 185.16 0.5367 8.33 0.000281 50 100 150 200 250 300 350 369.94 0.8255 190.20 0.5486 9.01 0.000503 TEMPERATURE( KELVINS) 375.90 0.8317 195.15 0.5598 9.64 0.000481 381.83 0.8370 200.14 0.5709 10.?1 0.000692 heat capacityofnatural anthophyl- 386.16 0.8413 205.16 0.5817 10.99 0.000675 Fig. 1. Experimentalmolar 210.11 0.5916 11.85 0.000851 lite [Mgu..Feo.?Si8O22(OH)2].The open squaresand solid trian- Series5 215.10 0.6018 12.81 0.001104 gles are experimentaldata for the Mg/Fe magnesio-anthophyllite 13.88 0.001432 52.83 0.094?2 Series9 I5.05 0.001895 determinedby adiabaticcalorimetry (this study)and DSC analysis 57.01 0,1102 16.54 0.002596 (Krupka et al., 1985),resPectively. The solid line is a least-squares 61.49 0.t274 222.57 0.617? 18.17 0.003712 dashedline is a least-squaresfit to the data 66.30 0.1462 226.55 0.6249 19.78 0.005178 fit to thc data. The 71.18 0.1656 231.68 0.6347 ?1.66 0.007197 correctedto the pure Mg composition MgrSi"Orr(OH)r. 76.06 0.1852 236.77 0.6445 ?3.77 0.01003 80.95 0.2056 241.74 0.6538 26.r5 0.01389 85.90 0.2254 ?46.67 0.6625 28.78 0.01897 90.82 0.2445 31.67 0.02560 95.64 0.?626 Senies10 34.95 0.03426 r00.51 0.2810 38.60 0.04486 105.51 0.2994 25r.58 0.6700 42;66 0.05768 ?56.62 0.6791 47.35 0.07352 Series6 26r.63 0.6886 52.38 0.09205 175 266.60 0.6973 57.40 0.1I 12 110.49 0.3r72 115.59 0.3353 120.93 0.3539 150 126.09 0.3709 ^ 125 :< = 100 extrapolatedto zero Kelvin according to the principle of correspondingstates (Lewis and Randall, 1961; Mc- 3 oo 7q Quarrie, 1973)with respectto tremolite. That is, the ratio per gram (Robie fff.b.r.Jl of the low-temperatureCfl of tremolite loDsc I and Stout, 1963)to the C; per gram of pure magnesio- 50 r (1932) I wosner | anthophyllite was usedfor a smooth extrapolation to zero (1s57) I r rins | Kelvin. 25 The molar Ci data weresmoothed graphically between 0 and approximately20 K, and analyticallyfrom 20 to 380 K by least-squaresfits to orthogonal polynomials (Justice 50 100 150 200 250 300 350 1969).Values of S?- s3,(I{i - Hillr, and -(Gi - Hillr TEMPERATURE(KELVINS) smoothed Cfi functions. were obtained by integrating the Fig. 2. Experimentalmolar heat capacityofdiopside. The open The smoothed Ci values and integlated thermodynamic squaresand solid diamonds are data determined by adiabatic properties for the Fe-bearing magnesio-anthophyllite calorimetry (this study) and DSC analysis(Krupka et al., 1985)' (Table 8) and for bronzite (Table 11)retain the heat capaci- respectively.The solid hexagonsand solid triangles are the low- ty contributions resulting from Fe2+ impurities. The en- temperatureCi data of Wagner (1932)and King (1957)'respec- tropy change Sise - S[,, in /(mol'K), is 538.9+2.7 tively. The solid line is a least-squaresfit to the experimentaldata for Mg/Fe-anthophyllite [Mgu..Feo.tSiBO22(OH)2]'from this study. KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES 255 Mognesio- Sronzile Anfhophyllife d OU 80 Y (9 - c 40 Y60 o =o - F oo() --20 oo 40 o- F Ad.bd,;l r200 l^osc I ta (xEt-vrHs2) Fig. 5. Plot of Ci/T versusT2 showingthe Schottky Ci anom- alies at low temperaturefor bronzite (Mgo,rFeo.rrSiOr), 50 100 150 200 250 300 350 magnesio-anthophyllite(Mg6.3Feo.rSirOrr(OH)r), and diopside. TEMPERATURE(KELVINS) Thelowest curve and data are for puresynthetic enstatite. Fig. 3. Experimental molar heat capacity of synthetic enstatite MgSiOr. The open squares and solid triangles are experimental data determined by adiabatic calorimetry (this study) and DSC 537.0+ 2.7for magnesio-anthophyllite[MgrSirOrr(OH)r], analysis (Krupka et al., 1985), respectively. The solid line is a 142.7+O.2 for diopside, 69.04+0.10 for bronzite least-squares fit to the experimental data. The dashed line repre- (Mgo.rrFeo.rrSiO3),66.27+0.10 for synthetic enstatite sents the Ci function of clinoenstatite given by Kelley (1943). (MgSiOr),and 81.69+0.12for wollastonite.The largerun- certaintiesfor the two valuesof magnesio-anthophyllitere- flect the impurity correctionsapplied to the experimental Cl data for anthophyllite. The entropy at 298.15K for the Fe-bearingmagnesio- anthophyllite does not include a term for the configura- tional entropy, Sir, that could arisefrom the random distri- bution of Fe and Mg on the M sites in the amphibole structure(e.g., Ulbrich and Waldbaum,1976).The configu- Y60 rational entropy was neglected for this anthophyllite o sample = becausethe cation distribution is not known for -) this particular sampleand becausecations may be partially orderedon the M sites(Finger, 1970). ocl(-) 4O Similarly, a value of Si, was not included in the tabu- Bronzile lated results for bronzite (Mgo.rrFee.rrSiOr) becausethe o Adiobotic Mg-Fe distribution is not known for this particular r osc sample.If the Mg and Fe were totally disorderedand the two sites were treated as equivalent, this Mg-Fe distri- lllollo slonife bution would result in a maximum value of S!, equal to 3.5 o Adiobotic O DSC J/(mol.K) [i.e., R (0.85ln 0.85+ 0.15 ln 0.15)(Ulbrich e Wogner(1932) and Walbaum,1976).1 50 100 150 200 250 300 350 Comparison with previous studies (KELVINS} TEMPERATURE Values given by King (1957)and Wagner (1932)for the Fig. 4. Experimental molar heat capacity of bronzite low-temperatureheat capacity of diopside are shown in (Mgo..rFeo.rrSiO.) and wollastonite. The open diamonds and Figure 2 for comparisonwith the smoothedCi valuesde- open squares are data determined by adiabatic calorimetry (this termined in this study. Data of the present study are in study) for bronzite and wollastonite, respectively. The solid good agreementwith the Ci values of King (1957) squares and solid hexagons are data determined by DSC analysis but (Krupka et al., 1985) for bronzite and wollastonite, respectively. differ significantlyfrom those of Wagner (1932).King's C! The solid triangles are the low-temperature data of Wagner (1932) data aregreater than the valuesfrom this study by 1.5%at for wollastonite. The solid curves are least-squares fits to the ex- 53.8 K to 0.10% at 72.9 K. At temperaturesbetween 77.5 perimental data of this study. and 296.OK, King's valuesare slightly lower than the new 256 KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES Table 8. Low-temperature molar thermodynamic properties of data are 1.5% greater than the C[ valuesfrom this study. magnesio-anthophyllite, Mgu..Feo.rSirOrr(OH)2. (Formula The good agreementbetween our value of Sies - S[ for weight : 802.900 g/mol) wollastoniteand that calculatedby Kelley and King (1961) from C! data of Wagner(1932) is strictly fortuitous. Temp. Heat Entropy EnthaI Py Gibbs energy capa cr ry functi on funct i on Magnetic contributions to the entropy of Mgo.rrFeo.t T ci 1si-sfit 1Hf-nlln -1ef-rivr rSiOt C$ of bronzite (Mgo.rrFeo.t5SiO.)at Kelvi n J/ (mol. K) The measured liquid-helium temperaturesis sigrrificantlygreater than that This anomalous behavior is es- 5 0.548 0.166 0.124 0.041 for synthetic enstatite. 10 3.t62 1.365 r.005 0. 350 pecially apparentwhen the data are plotted in the form of 15 4.641 2.974 2.009 0.965 (Fig. The larger values of CilT ate 20 6.132 4.485 ?.829 1.656 C[/T versus T2 5). 8.745 6.111 3.730 2.381 30 t2.90 8.044 4.886 3.158 35 18.94 10.46 6.440 4.023 40 ?6.36 13.46 8.453 5.009 propertiesof 45 35.30 t7.07 10.92 6.143 Table9. Low-temperaturemolar thermodynamic 50 45.54 21.31 I 3.86 7.443 anthophyllite corrected to pure Mg composition, MgrSirOrr(OH)r.(Formula weight : 780.874g/mol) 60 69.26 31.65 2t.06 10.58 70 96.42 44.32 29.85 t4.47 80 t?6.t 59.11 40.01 19.11 90 t57.2 75.75 51.29 24.46 Temp. Heat Ent ropy Enthalpy Gibbs energy 100 r88.9 93.95 63.47 30.49 capaci ty function function il0 ?20.6 I13.5 76.32 37.13 tro ,^o ^0, -to!-nilrr r20 25t.9 134.0 89.65 44.34 ( 5T-50., tr!-Hlvr ?82.5 155,4 103.3 52.06 130 (mol. 140 3r2.3 177.4 TIl .2 60.22 Kelvi n J/ K) 150 341.1 r99.9 131.2 68.78 0.0036 160 368.7 222.8 145.2 17.69 5 0.039 0.0132 0.0096 170 395.1 ?46.0 159.1 86.91 l0 0.299 0.101 0.075 0.026 180 420.4 269.3 r72.9 96.40 15 1.020 0.338 0.253 0.085 0.202 190 444.6 ?9?.7 186.6 106.1 20 2.480 0.810 0.608 200 467.7 316.I 200.1 116.0 25 4.998 1.610 1.213 0.397 2to 489.9 339.4 213.3 126.1 30 8.856 , a?o 2.t44 0.695 I. 12I 220 511.1 362.7 ?26.4 136.3 35 14.49 4.600 3.479 1.699 230 531.3 385,9 239.2 146.7 40 21.81 6.995 5.296 ?40 550.5 408.9 251.8 157.1 45 30.58 10.05 1.596 2.45r 3.392 ?50 568.9 431.8 ?64.r t67.7 50 40.87 13.79 10.40 5.882 260 586.5 454.4 276.2 178.3 60 65,00 23.3I I7,43 i88.9 70 92.88 35.38 26.l8 9.205 ?70 603.5 476.9 288.0 11 1( 280 619.8 499.i 299.5 199.6 80 123.5 49.16 36.40 210.3 90 155.6 66.14 47.85 t8.?9 ?90 635.3 521.1 310.9 t? 07 300 649,8 542.9 321.9 221.0 100 I88.5 84.24 60.?7 310 663.6 564.5 332.7 23r.7 110 ?21.3 103.7 73.42 30.32 320 676.8 585.7 343,3 242.5 120 253.6 t24.4 87.09 37.30 44.8? 330 689.7 606.8 353.6 ?53.2 130 285.3 i 45.9 101.1 340 702.3 627.5 363.6 ?63.9 140 3I5.0 168.2 115.4 52.83 350 714.3 648.I 373.5 274.6 150 345.8 19I.0 t29.8 61.29 360 7?5.9 668.4 383.I 285.2 160 374.3 214.3 r44.2 79.12 370 737.2 688.4 392.5 ?95.9 170 401.7 237.8 158.5 79.29 2.7 88.75 380 747.7 708.2 401.7 306.5 180 427.8 261.5 t7 190 452.8 285.3 186.8 98.47 200.7 108.4 3.15 608.7 483.9 291.6 r92.3 200 476.8 309.I 27 2r4.4 118,5 298.15 647.2 538.9 319.9 219.0 2r0 499.8 333.0 ?20 521.8 356.7 ??7.9 I28.8 230 542.8 380.4 24t.1 139.2 240 562.7 403.9 254.1 149.8 250 581.9 4?7.3 266.9 160.4 260 600.3 450.5 279.3 171.1 Ci data by 0.3%. At 298.15K, our entropy for diopsideis 270 618.0 473.4 291.5 181.9 0.3% lessthan King's value.On the other hand, Wagner's 280 635.0 496.2 303.5 192.7 290 651.1 518.8 315.2 203.6 Ci values (20.7- 39.3 K) are all approximately 100% 300 666.2 54I.I Jto. I 214.5 greaterthan the valuesobtained in this study. 310 680.5 563.? 337.9 225.3 320 694.2 585.0 348.8 236.2 The smooth low-temperatureCi valuesfor wollastonite, 330 707.6 606.6 359.4 241.I shown in Figure 4, are in significantdisagteement with the 340 720.6 6?7.9 369.9 258.0 350 733.1 649.0 380.I 268.9 wollastonite data of Wagner (1932).Wagner's C! data at the lowest temperatures(9.8 - 35.5K) are greaterthan our 360 745.I 669.8 390.I 279.7 370 756.9 690.4 399.8 290.6 valuesby 155% at 9.8 K and 26.4% at 19.5 K. Wagner's 380 167.7 7r0.7 409.4 301.4 data from 70.7to 120.1K are all lower than our C! values 273.r5 6?_3.4 480.6 ?95.3 r85.3 by an average 6%. At the higher temperatures 298.15 663.5 537.0 3?4.6 2t2.4 (L99.7- 373.2K), the agreementis better, and Wagner's KRUPKA ET AL.: I,OW.TEMPERATURE HEAT CAPACITIES 257 Table 10. Low-temperaturemolar thermodynamicproperties of arising from anomalousheat capacitiesbetween 5 and 30 diopside,CaMg(SiOr)r. (Formula weight : 216.553g,/mol) K is approximately 1 /(mol'K) or only 50 percentof the expectedmagnetic entropy. Temp. Heat Entropy Enthalpy cibbs energy Basedon their Mdssbauerstudies, Shenoy et d. (1969) capaci ty funct i on functi on concluded that, for bronzite (Fe,Mg, -,SiO.) where tro 1si-sf,) uf-xf,ln -(c?-H3) /r x < 0.39, there is no magnetic ordering down to 1.7 K. Therefore, wc may exclude coop€rative ordering of the Kel vi n ,l/ (mol. K) spinsas a sour@ofthe anomalousheat capacities, In order to test the possibility that the anomalousheat 5 0.009 0.0030 0.002? 0.0008 10 0.082 0.026 0.019 0.007 capacities are due to a Schottky effect, we have assumed l5 o.297 0.093 0.07I 0.022 that the lattice heat capacity of Mgo.rrFeo.r5SiO3below 20 u./15 0.234 0.178 0.056 25 1.544 0.482 0.368 0.114 approximately 20 K obeys the Debye model. The elastic 30 2.790 0.866 0.660 0.206 constantvalues of Frisillo and Barsch(1972) for a bronzite 35 4.576 t.4?4 1.086 0.338 40 6.799 2.176 1.657 0.518 45 9.424 3.124 2.371 0.753 50 4.269 3.223 1.046 Table 11. Low-ternp€raturemolar thermodynamicproperties of 60 19.29 7.r24 5.JIJ 1 et I : 70 27.02 10.67 7.854 2.816 bronzite,Mgo..rFco.rrSiO.. (Formula weight 105.120g/mol) 80 35.28 14.81 10.76 4.05I 90 43.80 19.46 13.96 5.501 100 52.40 24.52 7.146 Temp. Heat Entropy Enthalpy Gibbs energy 110 60.92 ?9.91 20.94 8.969 caPaci ty function function 120 69.21 35.57 24.6? 10.95 130 77.19 41.43 28.36 13.07 r' c9-P rs9-s9r'-I-o', - (Gi-H3)/T 140 84.82 47.43 32.12 I S ?1 1r!-rf,lrr 150 92.t\ 53.53 35.88 I/.OJ Kelvin ;/(mol.K) 160 99.09 59.70 39.52 20.09 170 105.7 65.9r 43.31 22.60 5 0. 146 0.035 0.021 0.008 180 u2.I 12.t4 46.96 25.18 10 0.694 0.329 0.241 0.088 190 118.0 /6. JD 50.54 27.81 15 0.817 0.643 0.4?0 0.223 200 t23.7 84.56 54.06 30.50 ?0 0.874 0.883 0.524 n ?qo 210 129.0 90.72 57.50 33.?2 z) 1.075 1.096 0.61I 0.485 220 134.I 96.84 60,87 35.97 JU r.503 t.327 0.72r 0.606 230 139.0 102.9 64.l6 38.75 2.2t3 1.608 0.879 0.729 240 143.8 108.9 67.38 4l .55 40 J. IJ/ 1.960 1.101 0.859 250 148.4 114.9 70.53 44.36 45 4.285 2.394 1.389 1.005 50 5.617 ?:er3 1.744 l. 169 ?60 r52.7 120.8 73.61 47.19 60 8.7?6 4.204 2.641 t. f,oJ t26.6 76.6? ?70 156.7 50.02 70 12.29 5.812 3.760 2.05? 280 160.4 L3?.4 79.54 52.86 80 16.16 7.702 5.065 ?.637 ?90 164.0 138.I 82.40 55.70 90 20.?! 9.838 6.52? J. JIO 300 167.4 143.7 85.I7 58.54 100 ?4.34 12.t8 8.097 4.084 3 310 t70.7 149. 87.88 61.38 110 28.44 14.69 9.760 4.933 320 174.0 154.7 90.52 64.21 t20 32.46 17.34 11.49 5.856 330 t77.l 160.1 93.l0 67.04 130 36.38 20.l0 13.25 6.845 340 179.9 165.5 95.61 69.86 140 40.17 22.93 15.04 7.892 t70.7 98.06 350 182.7 72.66 150 43.82 25.93 16.84 8.99I 360 I85.5 175.9 100.4 75.46 r60 47.32 28.77 18.63 10.14 370 188.2 I81.0 102.8 78.24 170 50.66 31.74 20.42 11.32 380 190.7 186.I 105.1 81.01 180 53.84 34.72 22.t9 t2.54 190 56.86 37.72 23.93 13.78 273.t5 157.9 128.5 77.55 50.92 200 59.74 40.71 25.65 15.05 298.t5 166.8 t42.7 84.66 58.02 210 62.48 43.69 27.34 16.35 220 65.l1 46.66 29.00 r/.oo 230 67.63 49.61 30.62 18.98 240 70.04 52.54 32.2? ?0.3? 250 7?.35 55.44 11 7a 21.67 260 74.54 58.32 35.30 ZJ.UZ presumably ?t0 76.63 OI.Id 36.80 24.38 causedby the substitution of Fe2* for Mg2+ 280 78.61 64.00 38.25 25.75 in the bronzite,thus permitting either a Schottky-typeheat ?90 80.50 66.79 39.68 ?7.11 300 82.32 69.55 41.07 28.48 capacity contribution and/or a cooperative (i.e., spin- 310 84.08 72.28 42.43 ?9.85 ordering) transition (Gopal, 1966).In either case,the total 320 85.78 74.98 43.76 3t.22 330 87.39 77.64 45.05 32.58 magneticentropy (Sfl"r)arising from the spins of the Fez+ 340 88.90 80.27 46.32 33.95 ions in the bronziteis: 350 90.34 82.87 41.56 35.31 360 91.75 85.43 48.77 JO.O/ Sfr.r:nRln(2s+1)' 370 93.14 87.97 4e.99 38.02 380 94.40 90.47 51.10 39.37 where s is the spin quantum number and equal to 2 for Fe2* (Gopal, 1966).Thus, Slr", for Mgo.rrFeo.l5sio3 273.15 77.26 62.0'l 37.26 24.81 298.t5 81.99 69.04 40.81 28.23 (wheren:0.15) is 2.01{(rnol .K). The observedentropy 25E KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES Table 12. Low-temperature molar thermodynamic properties of is likely, however,that the two levels are not totally de- synthetic enstatite, MgSiOr. (Formula weight : 100.389 g/mol) generate.In this case,an additional heat capacity maxi- mum would be expectedat a temperaturebelow 1.7 K, Temp. Heat Entropy Enthalpy Gi bbs energy arising from the splitting of the ground-statedoublet. Our capaci ty functi on functi on heat capacity extrapolation to zero Kelvin did not include this contribution to the entropy. This additional entropy rro'-P (s?-sB) (H?-H3)/T-( G?-H3)/T would be <0.86 J/(mol'K) (i.e.,0.15R (ln 2)). Kel v'i n J/(mol.K) Moreover,to obtain the entropy value for usein equilib- rium calculationsinvolving Mgo.rrFeo.15SiO3,one must 0.004 0.0012 0.0009 0.0003 also add the configurationalentropy (discussedpreviously) 10 0.029 0.0096 0.0072 0.0024 * +. 15 0.095 0.032 0.024 0.008 arisingfrom the substitutionof Fe2 for Mg2 20 0.252 0.078 0.059 0.019 25 0.526 0.16l 0.123 0.038 30 0.958 0.?92 0.223 0.069 35 1.617 0.487 0.373 0.114 40 2.41| 0.756 0.579 0.177 45 3.524 l. 106 0.846 0.260 50 4.764 I .540 I.I/) 0.366 Table 13. Low-temperaturemolar thermodynarnicproperties of wollastonite,CaSiOr. (Formula weight : 116.164glmol) 60 7.129 2.66? 2.012 0.650 70 tt.2l 4. 109 3.07? 1.037 80 15.04 9.O?J 4.325 L-aal 90 19.08 7.856 5.739 ?.t17 Temp. Heat Entropy Enthalpy Gibbsenergy 100 23.2r 10.08 7.280 2.800 caPaci tY function funct'ion I10 ?7.34 12.49 8.916 3.570 reo -1e!-uf,ln 120 31.41 15.04 10.62 4.419 1si-sf,l 1ni-riln 130 35.40 t7.71 12.38 5.338 Kelvi n J/(mo].K) 140 39.26 20.48 14.16 6.320 150 42.99 ,1 1t 15.96 7.359 5 0.006 0.0021 0.0016 0.0005 160 46.56 26.21 t7.76 8.446 10 0.057 0.018 0.014 0.004 170 49.97 29.13 19.55 9.577 15 0.2t7 0.066 0.050 0.016 180 aJ- aa 32.08 21.34 10.74 20 0.622 0.175 0.135 0.040 190 56.3? 35.04 23.l0 11.95 25 1.389 0.389 0.302 0.087 200 59.28 38.01 24.83 13.17 30 ?.522 0.731 0.573 0.164 210 62.11 40.97 26.54 I4.43 35 4.006 l. 233 0.954 0.280 220 64.8? 43.92 28.22 15.70 40 5.7l3 I.877 I.439 0.438 230 67.40 46.86 ?9.87 16.99 45 7.6?5 2.659 2.019 0.640 240 69,86 49.78 31.48 18.30 50 9.693 3.568 ?.682 0.886 250 72.21 52.68 33.06 19.61 60 14.14 5.723 4.2t6 I .507 260 74.44 55.55 5C.Or 20.94 70 18.78 8.249 5.963 2.?86 270 76.58 58.40 JD. IJ 22.28 80 23.43 11.06 7.857 3.205 280 78.62 6r.23 37.61 ?3.62 90 28.01 14,09 9.843 4.244 ?90 80.56 64.02 39.06 24.96 100 32.44 17.?7 11.88 5.386 40.47 26.31 300 82.39 66.78 110 37.60 20.56 r3.95 6.616 310 84.1? 69.51 41.85 ?7.66 120 40.76 23.93 16.01 7.918 43.20 29.01 320 85.77 130 44.60 27.35 18.07 9.281 330 87.36 74.87 44.51 30.36 48.2? 30.79 20.09 10.69 45.80 31.71 140 340 88.89 77.50 r50 51.65 34.23 22.08 12.15 350 90.35 80.10 47.05 33.05 37.67 24.03 13.64 34.40 160 54.90 360 91.78 82.67 48.27 57.99 41.09 ?5.94 15.l5 49.47 3s.73 170 370 93.17 85.20 180 60.91 44.49 27.80 16.69 380 94.46 87.70 50.63 37.07 190 oJ.o/ 47.86 ?9.6? 18.24 200 66.26 51.19 31.39 19.80 273.t5 77.24 59.30 36.60 22.70 68.7I 54.48 33.11 21.38 ?6.06 2r0 298.15 82.06 66.27 40.21 2?O 71.05 57.73 34.78 22.95 230 73.31 60.94 36,40 24.54 240 75.52 64.11 37.99 26.t2 250 77.66 67.23 39.53 27.70 260 79.70 70.32 41.04 29.28 ?70 81.60 73.36 42.51 30.86 of compositionMgo.rFeo rSiO3 were used to calculatea 280 I 3.34 76.36 43.93 32.43 290 84.95 79.32 45.32 34.00 Debye temperatureof 710 K with the methods described 300 86.47 82.22 46.67 35.56 by Robie and Edwards(1966). We usedthis Debye temper- 310 87.95 85.08 47.98 37.11 320 89.4? 87.90 49.25 38.65 ature to calculatethe lattice heat capacity,which was then 330 90.85 90.67 50.49 40.18 subtractedfrom the measuredheat capacity to obtain that 340 92.2t 93.40 51.69 41.71 350 93.49 96.10 52.87 43.23 part arising from the Schottky contribution. The simplest model that providesa reasonablefit (Fig. 6) to the residual 360 94.73 98.75 54.02 44.73 370 95.93 r0l .36 55.13 46.?3 heat capacitieswas obtainedwith a twoJevel model having 380 97.02 103.93 56.2? 47.71 a doubly degenerateground level and a triplet at 225 273.t5 8?.t7 74.3t 42.96 ?1 ?q cm-r. The agreementwith the Schottkymodel does not 298.15 86.19 81.69 46.42 1q r7 mean that theseare necessarilythe correct energylevels. It KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES 259 References Appleman,D. E. and Evans,T. H., Jr. (1963)Job 9214: Indexing 6.n and least-squaresrefinement of powder diffraction data.Nation- /oo al Technical Information Services, U.S. Dept. Commerce, o Springfield,Virginia, Document PB-216188. Bearth, P. (1970)Zur Eklogitbildung in den Westalpen.Fortsch- o ritte der Mineralogie, 47, 27-33. 4.0 L Bence,A. E. and Albee, A. L. (1968)Empirical correction factors r for the electron microprobe analysis of silicates and oxides. I Journafof Geology,7 6, 382-43. Bennington,K. O., Ferrante,M. J., and Stuve,J. M. (1978)Ther- Y modynamic data on the amphibole asbestosminerals amosite and crocidolite. U.S. Bureau Mines Report of Investigation E 30 = 8265. Borg, I. Y. and Smith, D. K. (1969) Calculated X-ray powder 3 I patterns for silicate minerals. Geological Society of America f 9cLo Memoir 122. _,i Buerger,M. J. and Prewitt, C. T. (1961)The crystal structuresof 2.0 wollastoniteand pectolite.Proceedings of the National Acade- my of Sciences,47, 188+1888. I Chernosky, J. 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Thermal of aluminum oxide from 0 to 1200"K.National Bureauof StandardsJournal of Research.57. equation4.25 in Gopal(1966) with EtlEo: 1.5and d : 22.5 qn-[. 67-82. Gopal, E. S. R. (1966) Specific Heats at Low Temperatures. Plenum Press,New York. Gronvold, F. and Westrum, E. F., Jr. (1959)a-Ferric oxide: Low Acknowledgments temperatureheat capacity and thermodynamicfunctions. Jour- nal ofthe AmericanChemical Society,8l, 1780-1783. This paper is partly basedon K. M. Krupka's Ph.D. researchat Gronvold, F., Westrum, E. F., Jr., and Chou, C. (1959)Heat ca- The PennsylvaniaState University. Profs. Bernard W. Evans and pacities and thermodynamicproperties of the pyrrhotites FeS Peter Misch at the University of Washingtonkindly provided the and Feo.rrrS from 5 to 350 K. Journal of ChemicalPhysics, 30, anthophyllite sample,and J. StephenHuebner of the U.S. Geo- 528-s31. logical Survey, Reston, Va., provided the bronzite sample.The Hellman, M. S. (1971)X-ray diffractometerdata reduction pro- authors are particularly gateful to Dr. David Veblen,who, while gram.U.S. GeologicalSurvey, Computer Contribution No. 9. at Arizona State University, inspecteda sectionof the anthophyl- Huebner, J. S., Duba, A., and Wiggings, L. B. (1979) Electrical lite sample for the presenceof hydrous pyribole structures.We conductivity of pyroxenewhich containstrivalent cations: Lab- also thank Howard T. Evans,Jr., of the U.S. GeologicalSurvey, J. oratory measurementsand the lunar temperatureprofile. Jour- StephenHuebner, Lowell B. Wiggins of IBM Corporation, and nal of Geophysical Research,84, 46524656. analystsof the U.S. GeologicalSurvey, Reston, Va., for their inval- Ito, J. (1975)High temperaturesolvent growrh of orthoenstatite, uable assistancein the characterization and chemical analysis of MgSiO., in air. GeophysicalResearch L€tters, 2, 533-535. our samples.We are also grateful to John L. Haas, Jr., Henry T. Justice,B. H. 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