StauLaRite

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Heat capacity and thermodynamic unctionsfor gehleniteand staurolite: with commentson the Schoitky anomaly n the heat capacityof staurolite

AmericanMineralogist,Volume69,pages307-318,1984

Bnucr S. HeutNcwAY AND Rlcneno A' RostBU.S. Geological SurveyReston, Virginia 22092

AbstractThe heat capacitiesof a syntheticgehleniteand a natural staurolitehave beenmeasuredfrom 12and 5 K, respectively, o 370K by adiabatic alorimetry,and he heatcapacities fstaurolite have been measured o 900 K by differential scanningcalorimetry. Stauroliteexhibits a Schottky thermal anomaly having a maximum near 21 K.Smoothed values of the thermodynamic properties of heat capacity, entropy, and

enthalpy function and Gibbs energy function are given for integral temperatures.Theentropyof gehlenite, azAlzSiOr,t 298.15 and bar is 210-1t0.6J/(mol'K), whichincludes a configurationalcontribution of 11.506 /(mol ' K). The entropy of staurolite at298.15K and I bar is reported or two compositions s 1019.6112.0/(mol K) for H2Al2FeaAll5,SiaOasnd ll0l.0-r12.0 J/(mol ' K) for (H3Alr.rsF4.to)C'e3.tzf4iaTi6.66Mn6.62Alt.rs)(Mgo.aaAlrs.zdSieO+ehere the configurational ntropy contributionsare 34.6and121.0J (mot . K), respectively. n addition, the entropy value reported or the secondstaurolitecompositioncontains an additional l0 J representing he estimatedcontributionof the magnetic entropy below about 5 K.

lntroductionThe heat capacities of gehlenite were measuredbe-tween 12 and 380 K in this study in order to reduce theuncertaintyassociatedwith the rather largeextrapolationnecessary o obtain the entropy contribution below 50 Kfrom the older heat capacity data that were measuredbetween50 and 298 K by Weller and Kelley (1963).High-temperatureheat-contentdata for gehlenitewere report-ed by Pankratz and Kelley (1964).The heat capacitiesof staurolitewere measured n thisstudy between 5 and 368K by low-temperatureadiabaticcalorimetry and between 340 and 900 K by differentialscanningcalorimetry. We are not aware of previousheat-

capacity measurementsor staurolite. The single set ofheat-capacity esultshas been correctedto two staurolitecompositions, and estimatesof the Schottky heat capaci-ty have been made upon the basis of several simplemodels for determining the lattice heat capacity forstaurolite. Similarly, simple models have been used toestimateconfigurationalentropy terms for eachstauroliteformulation.Materials

The gehlenitesamplewas a portion of the sampleusedby Woodhead (1977). A complete description of thesample preparation and of the physical and chemicalproperties of the sample was given by Woodhead. Thesamplewas designated75001Hby Woodhead.The geh-0003-004)V84l030,{-0307$02.00 307

lenite was annealedat 1525"Cor 20hours from a glassofgehlenitecomposition.The annealedsamplewas crushedand material less than 150 mesh was removed' Thesamplemasswas 28.0825 . Thecellparameters erea =7.68658(23)Andc : 5.06747(lDland thecalculated el lvolumewas 9.01559(51)/bar Woodhead,1977Table 3'3). Woodhead also reported that l0% of the glass re-mainedafter the 20 hours of annealing.The chemical and physical properties of the staurQlitesamplewere describedby Zen (1981,Table4, page124,sample 355-1).The sample representeda separateofnatural staurolite from the Everett Formation collectednear Lions Head, Conn. The crushedsamplewas drysieved to remove material smaller than 150 mesh. Thesample mass was 31.9650g for the low-temperaturecalorimetric measurementsand 39.900mg for the differ-ential scanningcalorimetric measurements'

Experimental resultsThe low-temperature adiabatic calorimeter and themethods and procedures followed in this study are de-scribedelsewhereRobieandHemingway,1972;Robieetal.,1976and 1978). he heatcapacities f stauroliteweremeasured from 340 to 900 K by using a differentialscanningcalorimeter and following the proceduresout-

lined by Krupka et al. (1979) and Hemingway et al.(1981). he onsetof decomposition fthis naturalstauro-lite samplewas 910t10 K, at a heatingrate of l0 trUmin.


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308 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITEThe experimentalspecificheats or gehleniteand stau-rolite are given in Tables I and 2, respectively, in thechronologicalorder of the measurements.The data havebeen corrected for curvature (Robie and Hemingway,1972)but are uncorrected or chemical mpurities.

Thermodynamic properties of gehlenite andstauroliteThe measuredspecific heat data were graphically ex-trapolated to 0 K from a plot of CIT vs. l. A morecompletedescriptionof the treatmentof the low-tempera-ture data for staurolite is given in a subsequentsection.Smoothed values of the thermodynamic functions ofheat capacity, C!; entropy, Si, or entropy increment,Sfr- S$; enthalpy function, (Ift - Iil)lT; and Gibbs energyfunction, (GI - Iif;)lT; where r is the reference empera-ture, are given in Tables 3 through 7 for gehleniteand for

two compositions of staurolite as (H3Al1.5Feot.toxf'er'.t,Fefi*roTio.orMn6.62Al1e)(Mg6.aaAl15.26)SiEO4snd asH2Al2FeaAll5SisOas.he reference temperature for thelow-temperatureheat capacitydata s 0 K whereas298.15K is used n the high-temperature abulation.

Table Experimentalpecific eats or synthetic ehleniter enp . t o ; : : l t " Temp . o ; : : I t . renp . to i : : l t '

K , r / ( g . K ) J / ( s . K ) K , r / ( e . K )

Table 2. Experimentalspecificheats or staurolite. Series8 and9were results obtained by differential scanningcalorimetryr ! rp . to ; : l i t " r . rp . to ; : : : t "

J / ( r . r ) I ' J / ( r . f , )r.rp. tt;: l i t"

K J / ( s . x )

S e r ie s 11 2 . 1 6 0 . 0 0 5 71 3 .4 1 0 .0 0 2 2 4 51 4 . 6 8 0 . 0 0 3 0 8 81 6 . 0 7 0 . 0 0 4 ? t 71 7 . 6 8 0 . 0 0 5 8 5 11 9 . 6 3 0 . 0 0 8 3 1 42 1 . 6 0 0 . 0 1 1 2 12 3 . 6 4 0 . 0 1 4 7 72 6 . 1 0 0 . 0 1 4 32 9 . 0 3 0 . 0 2 s 6 93 ? . 3 2 0 . 0 3 4 0 83 5 . 8 5 0 . 0 4 4 1 83 9 . 7 4 0 . 0 5 6 3 84 4 . 1 6 0 . 0 7 7 2 74 9 . 0 5 0 . 0 8 8 6 55 4 . 2 3 0 . 1 0 8 8S e r le s 25 3 . 0 7 0 . 1 0 4 45 7 . 5 9 0 . 1 2 2 26 2 . 5 4 0 . 1 4 1 86 7 7 5 0 . 1 6 2 57 2 . 7 3 0 . 1 8 2 87 7 . 2 5 0 . 2 0 1 28 1 . 8 5 0 . 2 1 9 78 6 . 9 1 0 . 2 3 9 69 2 . 3 0 0 . 2 6 0 7

3C l a r I2 9 E . 2 0 . 7 6 1 53 0 4 . 5 0 . 7 1 5 23 l t . t 5 0 . 7 E 7 7t 1 9 . 0 9 0 . 8 0 0 73 2 5 . 3 5 0 .E l 3 t

8 . 8 1 a . 23 3 3 . 4 t 0 . E 2 5 33 4 0 . 6 2 0 . 3 6 63 1 1 . 7 2 0 . 4 4 7 33 5 4 . 7 5 0 .E 5 t 03 6 1 . t 0 . 6 7 93 6 t . 6 6 0 . 7 t 98 . r1 . . I4 . 0 0 .0 0 3 2 5 45 . 6 0 . 0 0 3 3 7 55 .6 t 0 . 0 0 3 9 3 16 . 5 l 0 . 0 0 4 5 6 E7 . 5 7 0 . 0 0 5 3 4 38 . 5 8 0 . 0 0 6 1 7 79 . 4 7 0 . 0 0 5 9 0 51 0 . 3 E o . 0 0 7 7 0 EI l . 3 5 0 . 0 0 8 4 4 4t 2 . 4 9 0 . 0 0 9 1 6 51 3 . 8 3 0 . 0 0 9 9 2 71 5 . 3 1 0 . 0 l o 7 lr 6 . 9 7 0 . 0 t 1 4 5I 8 . 8 2 0 . 0 t 2 2 02 0 . 8 6 0 . 0 r 2 9 E2 3 . 0 6 0 . 0 1 3 7 52 5 . 4 6 0 . 0 1 4 6 82 7 . 4 3 0 . 0 r 5 7 73 0 . 1 9 0 . 0 1 7 1 73 2 . 9 6 0 . 0 1 9 2 23 6 . 4 1 0 . 0 2 2 3 6{ o . 5 0 0 . 0 2 6 7 54 4 .9 7 0 . 0 3 2 5 r5 0 .0 7 0 . 0 4 0 5 r5 5 . 8 2 0 . 0 5 1 4 1

S r l e a 45 5 . 8 2 0 . O 5 1 7 06 1 . 4 1 0 . 0 6 3 3 35 6 . 8 E 0 . 0 7 5 9 57 3 . 0 2 0 . 0 9 1 9 17 9 . l 0 . 1 0 9 38 4 . 9 5 0 . r 2 t 09 0 . 7 5 0 . 1 4 5 59 6 . 3 5 0 . r 6 3 81 0 1 . 9 0 0 . I E 2 6

S.r1.r 51 0 4 . 3 0 . 1 9 0 2r 0 9 . 7 3 0 . 2 0 9 6I I 5 . 3 7 0 .2 2 9 7t 2 l . t 3 0 . 2 5 0 7t 2 6 . 9 2 0 . 2 7 5t 3 2 . 6 7 0 . 2 9 2 4l 3 E . 3 E 0 . t t ll r a . 0 r 0 . 3 3 3 5t4 9 . 5 0 . 5 3 71 5 5 . 0 0 . t t 51 6 1 . 0 3 0 . 9 3 2t 6 6 . 6 6 0 . 4 1 2 58 . r1 . r 6

1 7 2 .3 7 0 . 3 l 7r 7 8 . 0 3 0 . 5 0 9I t t . 7 6 0 .4 6 9 5I t 9 . 4 6 0 . E 7 E1 9 5 . l 0 . 5 0 5 62 0 0 . 5 0 .5 2 1 22 0 6 . t r 0 . 5 3 9 t2 r2 .5 4 0 . 5 ?5z r0 . 4 2 0 . 5 7 4224.17 0. 59092 to .6 1 0 . 60762 3 7 .0 9 0 .6 2 4 9243.56 0. 64 7S e t l ! 7

2 4 9 . 4 0 . 6 5 5 r2 5 5 . 5 1 O . 6 7 0 92 6 r . 8 8 0 . 6 8 5 72 6 4 . 3 2 0 . 7 0 0 12 7 4 . a 8 0 . 7 1 4 62 8 t . 5 6 0 . 7 2 9 02 8 8 . 2 9 0 . 7 4 3 32 9 5 . 2 t 0 . 7 5 7 03 0 2 . 0 6 0 , 7 6 9 9S e r t e ! E

3 { 0 . l o 0 . E 3 9 73 5 0 . l 0 0 . E 5 5 03 6 0 . 0 0 . 8 6 9 03 7 0 . 0 0 . E 7 9 43 E O . 0 0 . 8 9 2 13 9 0 . 0 0 . 9 0 6 14 0 0 . 0 0 0 . 9 1 5 44 o . 0 0 0 . 9 2 8 94 2 0 . 0 0 0 . 9 3 9 44 3 0 . O 0 0 . 9 4 1 74 { 0 . o 0 0 . 9 5 7 t

3 . r l a . 9{ 5 0 . 0 0 . 9 6 t {4 6 0 . 0 0 . 9 7 9 r{ 6 9 . 9 0 . 9 8 5 3a 7 9 . 9 0 . 9 9 5 r{ 0 9 . 9 r . 0 0 t lr 9 9 . 9 r . 0 r 3 71 6 9 . 9 0 . 9 6 { 3a t 9 . 0 . 9 9 0 14 8 9 . 0 .9 1 6 0{ 9 9 .E r . 0 0 2 75 0 9 . 1 .0 0 7 65 1 9 . t . 0 r 2 t5 2 9 . 0 r . 0 l 1 8t l 9 . E t . 0 2 6 2t t 9 . E t . 0 3 2 1t 5 9 .E 1 . 0 3 9 35 6 9 . r . 0 4 7 r5 7 9 . 1 . 0 5 1 85 E 9 . 7 t . 0 5 9 6t9 9 ,1 t .0 6 a 96 0 9 . 7 r . 0 7 1 36 1 9 . 7 1 . 0 7 9 t6 2 9 .1 r . 0 E7 56 3 9 .7 t . O 9 9 t6 4 9 . 7 l . I l 2 56 1 9 . 0 1 . 0 9 2 06 2 9 . t r . 0 9 9 06 3 9 .7 l . l o l 36 4 9 .7 l . t 0 6 66 5 9 . 7 l . l t 2 06 6 9 . 7 l . l l 7 45 7 9 . 7 t . l 2 2 l6A9.7 r. t2626 9 9 .7 r . r2 7 E7 0 9 .1 l . r3 3 E7 1 9 . 7 r . l 3 9 E7 2 9 . 7 l . 1 4 2 57 3 9 . 7 l . 1 4 7 77 1 9 . 7 l . l 5 l 07 5 9 . 7 l . 1 4 9 3,8 9 . r . 1 6 5 57 7 9 . 7 l . 1 6 4 07 A 9 . 1 l . 1 7 0 57 9 9 .1 t . lEO 28 4 9 . l . l 6 7 E8 9 E . 9 r . l 9 6 r

S e r i s 39 8 . 0 1 o . 2 8 2 31 0 3 . 1 1 0 . 3 0 0 91 0 8 . 1 0 0 . 3 1 8 01 1 3 . 2 6 0 . 3 3 5 7I 1 8 . 5 9 0 . 3 5 4 1S e r ie s 4

1 1 0 . 4 3 0 . 3 2 4 4I 1 5 . 6 4 0 . 3 4 2 21 2 0 . 6 5 0 . 3 5 9 1I 2 5 . 5 8 0 . 3 7 4 9S e r i e s 5

1 3 5 . 9 0 0 . 4 0 7 51 4 1 . 1 3 0 . 4 2 3 01 4 6 . 3 2 0 . 4 3 8 21 5 1 . 4 3 0 . 4 5 2 81 5 6 . 4 6 0 . 4 6 6 51 6 1 . 4 9 0 . 4 8 0 11 6 6 . 6 7 0 . 4 9 3 7t 72 . 1 3 0 . 5 0 7 8t 7 7 . 7 2 0 . 5 2 2 01 8 3 . 2 0 0 . 5 3 5 2S e r ie s 6

1 8 0 . 5 4 0 . 5 3 1 21 8 5 . 9 9 0 . 5 4 4 11 9 t . 2 7 0 . 5 5 5 919 6 5 5 0 . 5 6 8 12 0 1 9 0 0 . 5 8 0 22 0 7 3 3 0 . 5 9 2 12 r 2 . 8 4 0 . 6 0 3 92 t 8 . 2 6 0 . 6 1 5 42 2 3 .6 1 0 .6 2 6 42 2 8 .9 4 0 .6 3 5 72 3 4 . 2 0 0 . 6 4 6 92 3 9 . 4 t 0 . 5 5 7 3

S e r ie s 72 4 7 . 6 3 0 . 6 5 8 32 4 7 . t t 0 . 6 7 0 62 5 2 .6 5 0 .6 8 0 32 5 8 .3 2 0 .6 9 0 32 6 4 . 0 9 0 . 7 0 0 12 6 9 . 8 1 0 . 7 0 9 22 7 5 . 4 7 0 . 7 1 8 62 8 7 . 2 0 0 . 72 72 5 6 . 9 1 0 . 7 3 5 6? 9 2 .8 2 0 .7 4 5 22 9 8 . 7 3 0 . 7 5 3 8S e r l s 8

2 9 6 . 2 0 0 . 75 0 33 0 2 . 1 3 0 . 7 5 8 73 0 8 . 0 0 0 76 73 1 3 . 7 5 0 . 7 7 4 1

S e r l e s 93 1 0 . 5 2 0 . 7 7 t 63 t 7 . 3 2 0 . 7 8 0 13 2 3 .9 7 0 .7 8 9 33 3 0 . 5 7 0 . 7 9 7 73 3 7 . 1 3 0 . 8 0 6 23 4 3 . 6 5 0 . 8 1 3 63 5 0 . 1 2 0 . 8 2 r 03 5 6 . 5 7 0 . 8 ? 8 23 6 3 . 2 6 0 . 8 3 5 63 7 0 . 8 0 . 8 4 3 53 7 7 . 0 7 0 . 8 5 0 33 8 3 . 9 3 0 . 8 5 5 6

Following Ulbrich and Waldbaum (1976),a zero pointentropy, S$,contribution of I 1.506 /(mol ' K) is includedin the Gibbs energy unction for gehlenite n Table 3. Theentropy ofgehlenite at 298.15K and I bar, is, therefore,210.110.6J/(mol . K). The values or the Gibbs energyfunction tabulated or the two staurolite compositions donot includea zeropoint entropy contribution. This contri-bution is discussed,at length, below.It should be noted that Woodhead (1977)has consid-ered the questionof how disorder in Si/Al on the Tz sitewould be reflected in the crystal structure of gehlenite.Woodheadconcluded that gehlenite orming at low tem-peratureswould obey the aluminum avoidance rule for


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Table 3. Molar thermodynamic properties of gehlenite,Ca2Al2SiO7.

309- Soand (Hr - Ho)lT should be 0.2% or less, which iswithin the experimentaluncertainty of the data.The measuredheat capacitiesof naturalstaurolitewerecorected to the two compositions isted above by assum-ing the principle of additivity and representing he sampleas, fust, for Tables 4 and6, 1665. 40g of staurolite,4.282g of corundum 1.514 of lime, 4.394g of zincite,0.503gof FeO, 0.403g of periclase,0.479g of rutile, 0.426g ofP2O5, 0.468 g of ice, and a deficiency of 0.142 e ofmanganosite,and second, or Tables 5 and 7, 1703.737of staurolite, 356.263 g of pyrophyllite, 17.029 g ofbrucite, 73.399e of magnesioferrite,5.430g of hematite,328.725 of corundum,2.243g of lime, 10.227 of rutile,0.710g of P2O5,1.9E6 of manganosite, nd 6.510g ofzincite. The correctionsrepresenta change n the specificTable4. Low-temperature olar hermodynamicroperties fstaurolite,Hdlr.rsFe6.i,o)e35zFe31+Tio.GMn62All s)(Mgo4Al15 6)SisOas.he data af,e uncorrectedor chemicalsite-configurationalontributionso the entropy.

HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE

T EI . IP . HEAT ENT RO PYC A P A C I T YT c ; (s ; - s ; )KELV N

E N T H A L P Y G I B B S N E R G YF UI { CT IO I , I F UNCT IO N( H ; - H ; ) / T - ( c i - H ; ) / T

J / ( m o l . K )

1 01 52 02 53 03 54 04 55 06 07 08 09 01 0 0l l 01201 3 01 4 01 5 01 6 01 7 0l B 0I O n2 0 0

8 8 . 19 8 . 0 41 0 6 . 71 I 5 . 01 2 3 01 3 0 . 61 3 7 91 4 4 . 91 5 1 . 61 5 7 . 91 6 4 . 01 6 9 . 7t / f . r1 8 0 . 31 8 5 . 21 9 0 . 01 9 4 . 61 9 9 . 02 0 3 .22 0 7 22 1 1 . 1? 1 4 . 92 1 8 . 6? z ? . 0t z a . L2 ? 8 . 12 3 t .22 3 3 . 8

5 2 .6 66 0 .8 06 8 . 9 97 7 2 08 5 . 4 1o 1 R O1 0 1 . 71 0 9 . 81 1 7 . 8r 2 5 . 81 3 3 . 61 4 1 . 41 4 9 . 01 5 6 . 61 6 4 . 1l 7 t . 4t 78 . 71 8 5 . 8t9 2 .91 9 9 . 82 0 6 .72 1 3 . 52 2 0 .12 2 6 .7233.22 3 9 .62 4 5 .92 5 2 .11 8 0 . 91 9 8 . 6

T E I I P .

TKELV T{

. 0 3 0 6 . 0 1 0 4. 2 3 9 . 0 7 8 5. 9 4 . 2 7 92 . 4 2 t . 7 2 54 . 7 2 1 . 5 0 17 . 6 9 0 2 . 6 t 31 1 . 4 4 4 . 0 7 51 5 . 6 9 5 . 8 7 52 0 . 3 6 7 . 9 8 92 5 . 3 7 1 0 . 3 93 6 . 0 4 1 5 . 9 54 7 . 1 5 2 2 . 3 45 8 . 2 5 2 9 . 3 66 9 . 0 1 3 6 . 8 57 9 . 2 5 4 4 . 6 5

. 0 0 7 5. 0 5 8 3.2 tL. 5 5 51 . 1 4 71 . 9 8 03 . 0 5 94 . 3 6 75 . 8 8 17 . 5 7 7L t . 4 21 5 . 7 32 0 . 3 52 5 . 1 73 0 . 0 73 4 . 9 83 9 . 8 6q 4 . 6 74 9 4 054 0 45 8 . 5 96 3 . 0 46 7 . 4 07 1 . 6 57 5 . 8 17 9 . 8 68 3 8 28 7 . 6 79 t . 4 ?9 5 0 89 8 . 6 41 0 2 . 11 0 5 . 5

r 0 8 . 8t I 2 . 01 1 5 . 11 1 8 . 2t ? t . z1 2 4 1t2 6 .9t 2 9 . 71 3 2 . 41 3 5 . 0

1 1 . 5 0 61 1 . 5 2 6I 1 . 5 6 61 1 . 6 7 611 8 5 61 2 1 3 6t 2 . 5 2 21 3 0 1 41 3 . 6 1 41 4 . 3 2 01 6 . 0 31 8 . 1 12 0 . 5 12 3 . t 9? 6 . 0 92 9 . 1 93 2 .4 43 5 . 8 23 9 . 3 14 2 .8 74 6 . 5 15 0 , 1 95 3 . 9 25 7 . 6 86 1 . 4 66 5 . 2 66 9 0 67 2 . 8 77 6 . 6 98 0 . 4 98 4 . 2 98 8 . 0 89 1 . 8 59 5 . 6 19 9 .3 6

1 0 3 . 11 0 6 . 81 1 0 . 5I t 4 . t1 1 7 , 81 2 1 . 4L ? 5 . 01 2 8 . 58 9 . 2 79 8 .6 6

5 . 3 7t 2 , 3 2t 7 . 5 52 t .0 42 4 .0 32 8 . 1 93 4 .5 44 3 . 0 55 3 . 9 86 7 . 1 59 9 . 5 91 3 9 . 51 9 . 823t 3292.6

3 5 0 . 54 1 0 . 04 7 0 . 25 3 0 .5 9 0 .6 4 8 . 57 0 5 . 87 5 1 . 18 1 4 . 58 6 6 . 09 1 5 . 69 6 3 41 0 0 9 . 21 0 5 3 . 01 0 9 4 . 8I 1 3 4 .t t 7 z .71 2 0 8 . 9t243.31 2 7 6 . 0

1 3 0 6 . 91 3 3 6 . 51 3 6 5 . 0t392.2t4 t7 . 71 4 4 2 . 01 4 5 4 . 0

2 , 9 98 . 81 4 . 9 52 0 .5 02 5 . 5 13 0 . 2 33 5 . 0 44 0 . 84 5 . 8 55 2 .2 t5 7 2 18 5 . 4 81 0 7 .1 3 1 . 91 5 9 . 7

1 9 0 . 32 2 3 42 5 8 .52 9 5 . 63 3 4 . 23 7 4 . 2{ 1 5 . 24 5 7 .4 9 9 .7542.8s8 6 .36 3 0 . 06 7 3 . 87 t 7 . 77 6 1 68 0 5 . 38 4 8 . 88 9 2 .9 3 5 . 29 t 7 . 9

t020.2t062.2I 1 0 3 .1 1 4 4 . 9I 1 8 5 . 6t225.91 2 4 . 98 6 2 .9 7 0 . 0

2 . 0 95 . 4 18 . 7 l1 1 . 3 81 3 . 5 11 5 . 5 61 7 . 8 92 0 4 72 3 ,5 72 7 2 53 6 . 5 04 8 .2 96 2 ,5 37 9 0 49 7 6 0

1 1 8 . 01 3 9 . 8162.91 8 7 . 02 1 1 9237 4263.2289 43 1 5 . 63 4 1 . 93 6 8 03 9 4 04 t9 .74 4 5 .24 7 0 44 9 5 .25 1 9 . 65 4 3 . 55 6 7 . 15 9 0 .26 1 2 . 86 3 5 . 06 5 6 66 7 7 . 96 9 8 . 77 1 9 . 07 2 9 .0

0 . 9 13 4 06 , 2 49 . t 21 1 . 9 01 4 . 5 7I 7 . 1 51 9 . 7 02 2 , 2 92 4 . 9 63 0 . 7 03 7 . 84 4 .5 45 2 8 35 2 . 1 17 2 . 3 58 3 . 5 49 5 . 6 41 0 8 . 6t 2 2 . 31 3 6 81 5 2 . 01 6 7 . 81 8 4 . 1

2 0 1 . 02 1 8 . 32 3 6 . 02 5 4 .1? 7 . 52 9 r .23 1 0 . 13 2 9 . 33 4 8 . 63 6 8 .3 8 7 . 74 0 7 44 21 24 4 7 l4 6 7 . 04 8 7 05 0 6 . 95 1 6 . 9

HEAT ENT RO PYCAPACT Y E i lT HAL PY G IBESEI IERG YF Ui lCT I0 l l F U I { CT I0 Nc i (s i -s ; ) 1x i -Hi t r r - (c ; -H; ) /T. t / ( m o l K )102 ?O2 3 02402502602 70280

2903 0 03 1 03203 3 03 403 5 03 603 7 03 B0

al 0l 5202 S3 03 5404 5505 07 080901 0 0

l l 0t201 3 014 01 5 01 6 01 7 018 01 9 02002t022023 02402502 6 027 0?8 029030 03 1 032 03 3 03 4 03 5 036 03 6 5

2 7 . t 5 1 9 6 02 9 8 . r 5 2 0 6 . s r 0 3 . 21 1 1 . 4

the T2 sites. Following the interpretationgivenby Wood-head, the configurational entropy for gehlenitewould be5.75J(mol K). Gehlenites synthesized at higher tem-peraturesappear o have greaterdisorder leading Wood-head to conclude that disorder of Si/Al on the T2 sitewould be temperaturedependent.The heatcapacities or gehlenitewere not corrected orthe l0Voof uncrystallizedglass(Woodhead,1977).Robieet al. (1978)have shown that the heat capacities of thefeldsparsanalbite, high sanidine,and anorthitediffer littlefrom the heat capacities of glassesof the same composi-tion. These observed difierences yielded calculated dif-ferencesof 0.8 to 2.3% in Sr - So.We can assume as afirst approximation) that the difference in the gehlenitesystem should be no larger than that in the feldsparsystem.Consequently, he uncertainty n the functions 51

2 7 3 . t 5 1 1 8 4 . 32 9 8 . 5 1 2 7 0 . 3 3 5 . 33 8 4 . 05 2 7 Z5 8 5 . 9


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310 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE

T E i ' lP .T

r (EL V I r , {

Table 5. Low-temperature molar thermodynamic properties ofstaurolite, H2Al2FeaAll6SisOas. he data are uncorrected forchemical site-confi urational contributions to the entropy.assuming that the impurities can be represented byphases or which specific heat data are available. Mostgeochemistsbelieve that ideal additivity does not trulyprevail, but where the required corrections aresmall(i.e.,wherethe impurities representonly a smallpercentageofthe sample) the error associatedwith the correction isoften less than the uncertainty in the measured specificheat.The potentialerrors associatedwith this type of correc-tion maybe minimizedby combining he impurity compo-nents nto phases hat are structurally similar to the phaseunder study (Robie et al., 1976and Klotz, 1950),or byusingacorresponding tates rgument Robieetal.,1982,or Stout and Catalano,1955). n either case, he colTec-tions may be applied directly to the measuredspecificheats (Robie et al., 1976) n order to provide correctedthermodynamicparametersas a function of temperature,or the integratedpropertiesmay be corrected at a specifictemperature (Westrum et a1., 1979). Both proceduresshould yield the sameresults at the same emperature fthe same componentsare chosen.Two modelsare presented n Table 8 in which the heatcapacities of staurolite as given in Tables 4 and 6 areapproximated by the summation approach. In model l,the heat capacity of staurolite is approximated by thesummation of the heat capacities of equivalent oxide

Table6. High-temperatureolar hermodynamicropertiesornatural taurolite. he ormula or staurolitesgivenn Table4.A chemical ite-configurationalntropyof 121.0 (mol ' K) andan additional10.0J/(mol K) of magnetic ntropyhave beenadded o theentropyat298.15 given n Table4. Theequationfit theexperimentalatawith an average eviation f 0,5Vo.

E N T R U P Y E N T H A L P YFU , lcT loNs r ( n T - n 2 9 6 ) / TJ / ( o o r . K )

I i T A T E I I T i I ( ] P Y I I ] T I ] A L P YC A P A C I T Y F I I I I C T I ( ) I Ic i 1s l - s i t l r r i - r r i l r rJ ( r , r o lr )

0 t ; L l s E , , E i l 0 YF U I ] C T I O ] I- 1 t ; i - r r i l l r

5l 02 0? 53 03 54 04 55 06 07 0B O9 01 C 0

1 1 0t2 01 3 01 4 01 5 01 6 01 7 0l B 0I 9 02002 1 0220230?41)2 0 c? 7 02 8 02 9 t )3 0 0

2 0 4 .2 3 7 6? 7 2 . 63 0 9 . 53 4 0 . 03 4 7 .4 2 8 . 84 7 0 , 65 1 3 . 25 5 6 . 35 9 9 . 96 4 3 . 66 i 1 7 . 67 3 1 . 67 7 5 , 68 1 9 . 5E n 3 . 29 0 6 . 79 5 0 . 0o o ? a

2 . 9 73 . 1 91 2 3 71 6 . 5 119.z ' ,d2 1 . 5 42 3 . 7? 6 , ? 82 9 . 1 93 2 . 6 54 1 . 3 65 2 5 56 6 . 1 08 2 . 1 11 0 0 . 21 2 0 . 11 4 1 . 51 6 4 . 31 9 8 . 12 1 2 ,n2 3 9 . 12 6 3 . 82 ' , d 9 . 93 1 6 . 13 4 2 . 33 6 3 . 53 9 + . 54 2 0 44 , i 5 , 94 7 , ?4 9 6 , ?5 2 t )75 4 4 . 35 6 3 . 66 1 4 . 66 3 7 . 06 5 9 . 95 8 0 . 37 0 1 . 37 3 1 . 95 2 t i . 45 8 7 . 6

1 . 1 09 . 0 1

L 7 2 32 0 . 9 52 4 4 42 7 . 7 73 1 . 0 34 0 . 9 64 S . 1 55 6 . 0 36 4 , 7 27 4 . 2 98 4 . 7 69 6 . 1 11 0 3 . 31 ? 1 . 41 3 5 . ?1 4 9 . 71 6 4 . 91 8 0 . 3I 9 7 . 12 1 4 . C

2 3 1 . 32 4 9 . 12 6 7 . 22 8 5 . 5J U q . J3 2 3 . 33 4 2 . 53 5 1 . 94 0 1 . 14 4 0 . 74 6 0 . 74 4 0 , 65 0 0 . 75 ? 0 . 75 3 0 . 73 4 U . 639 7 4

3 . 3 81 8 . 2 82 5 . 3 82 9 . 0 33 1 . 4 73 4 . 7 14 0 , 0 85 7 . 7 37 0 . 1 21 0 1 . 11 3 9 51 9 4 . 6? 3 5 4294 4

3 4 8 . 24 0 7 . 54 6 7 75 2 8 : 0q c 7 06 4 7 07 0 4 , 67 6 0 . 5s l 4 . 43 6 6 , 59 1 6 . 99 6 5 . 4I 0 1 2 . nI 0 5 6 . 61 0 9 9 . 01 1 3 9 . 5I 1 7 8 . 1r z t 4 . 9r 2 4 9 . 91 2 3 3 . 1

4 . 0 71 2 9 72 1 . 3 C2 9 . 74 ? 4 94 3 . 2 35 4 . 0 56 6 . 9 ?8 2 . 3 31 0 0 . 71 2 ? . ?1 4 6 . 81 7 4 . 4

3 1 0 1 3 1 4 . 53 ? 0 I 3 4 4 . 63 3 0 t ? 7 3 . 73 4 0 1 4 0 1 . 63 5 0 t 4 2 7 . 73 6 0 r q 5 2 . 33 6 5 t 4 6 4 . 72 7 3 . 1 5 1 1 C t . 92 9 8 . 1 5 r 2 7 7 , 1

1 0 3 5 . 51 0 7 71 1 1 9 , 51 1 6 1 . 0t ? 0 2 . 0L ? 4 2 . 5t2 6 2 18 7 6 . 99 3 5 . 0

T E M P . H E A TCAPACI !T '

K E L V IN

G I B B S B N E R C TI 'UNC ON- ( c T - H a 9 E ) / T

heat(J/g . K, the quantity actually measured)of less hanO.lVo for the first case given above for heat-capacityvaluesabove125K and ofless than lVofor values rom 8to 125K, and or the second omposition, f less han 1%above 300 K, less thar, 2Vo rom 150 o 300 K, and lessthan 3Vo rom 50 to 150 K. Below 50 K, the sum of thespecificheatsof the impurity phasesbecomesnegligiblecompared o the measuredspecific heat of staurolite.It is both instructive and important to examine theassumptionsand proceduresunderlying the correctionsapplied to the specific-heatdata, particularly in light ofthe rather large masscorrection necessary o obtain theheat capacitiesof staurolite as listed in Tables 5 and 7.Samples are initially chosen on the basis of chemicalpurity and/or approximately correct stoichiometry. Cor-rections for small deviations from ideality are made

2 9 8 . 1 5 I l 7 0 . l3 2 5 | J 4 9 23 5 0 1 4 t 3 . 03 1 5 1 4 6 9 . 44 0 0 1 5 1 9 , 74 2 5 r 5 6 4 . 94 5 0 1 5 0 5 . 84 7 5 t 6 4 3 . t5 0 0 1 6 7 7 , 45 2 5 I 7 0 8 . 95 5 0 r 7 3 8 . I5 7 5 1 7 5 5 . 36 0 0 1 7 9 0 . 66 2 5 1 8 1 4 . 3o 5 0 1 8 3 6 . 56 7 5 1 8 5 7 . 57 0 0 t 8 7 7 , 27 2 5 1 8 9 5 . 97 5 0 1 9 t 3 , 67 7 5 1 9 3 0 . 38 0 0 1 9 4 6 , 28 2 5 1 9 6 1 . 38 5 0 i 9 7 5 . 58 7 5 1 9 8 9 . 39 0 0 2 0 0 2 . 4

t I 0 I . 01 2 I 4 . 01 3 1 6 , 31 4 r 5 . 81 5 1 2 . 316 0 5 ,EI 6 9 6 . 4L 7 8 4 . 21 E 6 9 . 41 9 5 2 . 02 0 3 2 22 I l U . l2 r 8 5 . 72 2 5 9 . 32 3 3 0 . 92 4 0 0 .b2 4 6 8 . 52 5 3 4 72 5 9 9 32 6 6 2 32 72 3 . 92 7 4 O2 A 4 2 . 72 9 0 0 22 9 5 6 . 4

0 . 0l 0 E . 3I 9 9 . 22 8 2 .3 5 7 . 94 9 1 . 95 5 1 56 0 7 . 06 5 8 . 77 0 7 . 11 5 2 . 679 5 . 3E 3 5 , 58 7 3 . 79 0 9 . 79 4 3 , 99 7 6 . 41 0 0 7 . 41 0 3 6 . 9I 0 6 5 . 01 0 9 2 . 0i I r i . 8r 4 2 . 5r r 6 6 . 2

r 0 l . 01 t 0 5 . 7r t l 7 . tr 3 3 . 71 t 5 4 . 41 t 7 E . 2I 2 0 4 . 5t 2 3 2 . 7t 2 b 2 41 2 9 3 . 3t 3 2 5 .I 3 5 7 . 5I 3 9 0 .4t 4 2 3 . 7L 4 5 7 . 31 4 9 0 . 91 5 2 4 . 61 5 5 8 . 3r 5 9 r 91 6 2 5 5I 6 5 E . 8L 5 9 Z . O1 7 2 5 . O1 7 5 7 . 81 7 9 0 . 3


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HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 3 l lTable 7. High-temperaturemolax hermodynamicproperties forideal staurolite, H2Al2Fe4Alr6Si8O4s. chemical site-configurationalentropy of 34.6J/(mol . K) hasbeenadded o theentropy at 298.15 K given in Table 5. The equation fit theexperimentaldata with an averagedeviation of 0.EVo.

Table E. Model I and 2 compositional approximations to naturalstaurolite.

Phasellode

t 2liloles

ilode It 2ilolesEI iP . HEATCAPACI Y

T CEKELVIN

EN T R O PY EN T I I AL PY C I EBS U N } ; R G YF I J I T C T I O N I U N C T I O N

s r ( H r - r t 2 9 8 ) / T - ( c T - d 2 9 8 ) / TJ / ( D o 1 . K )

Sl02 8.00Al203 8.80

Tl 02itr0Hzo

0.080.021 .5 0

0.080.02

i ? ?

2 .6 7

? .6 77 .4 7

0 . 01 0 8 . 92 0 0 . 52 8 3 . 93 6 0 24 3 0 . 54 9 5 . 35 5 5 . 45 1 1 . 46 6 J . 67 t 2 . 57 5 E . 48 0 r . 6a 4 2 . 38 8 0 . 99 1 1 . 49 5 2 . 09 8 5 . 0I 0 t 6 . 4I 0 4 6 . 41 0 7 5 . 01 r 0 2 . 51 1 2 8 . 7r r 5 3 . 9l l 7 8 . l

I 0 I 9 . 6r 0 2 4 . 3r 0 3 5 . I1 0 5 2 . 51 0 7 3 .1 0 9 7 . 3r 1 2 3 . 7l l 5 2 . Il r 8 2 . lI 2 I 3 2t 2 4 5 , 21 2 7 9r 3 l l . l1 3 4 4 . 6r 3 7 6 . 4l 4 l 2 . 4t 4 4 6 4r 4 8 0 . 41 5 1 4 . 3l 5 4 E . lI 5 8 1 81 6 1 5 . 3I 6 4 8 . 61 5 8 1 . 7r 7 1 4 . 5

components.Two major changesare presented n model2. First, approximation of the contribution of OH to thespecificheatof staurolite n model I is madeby assumingthat model I contains ce and water, whereas n model 2,the OH contribution is introduced through pyrophylliteand brucite. Second. he contribution of Fe2+ as FeO inmodel I was replaced through the introduction of thedifference n the specific heatof a mixed Mg-Fe enstatiteand the specific heat of pure Mg enstatite(Krupka et al.,1978,unpublisheddata), where this difference represent-ed the composition FeSiO3.Differenceswere calculatedby subtracting he summedvalues or each model from the smoothedheat capacitiesgiven in Tables 4 and 6. These differences are shown inFigure l. At temperaturesgreater than 3fi) K, relativelylittle advantages obtained by adopting one specific heatmodel over the other, with the exception of the effect ofthe a - B transition in quartz. The specific heat of atransition in an oxide component s usually removedby asmoothing process. For the model I data presented nFigure 1, the effect of the c - B transition has beenpreserved as a visual reminder that when using theintegratedproperties (e.g., entropy) approach, an addi-tional correction may be required in order to maintainsmoothestimated values.

Although local deviations of the model 2 specific heatdata from the measured heat capacity of staurolite arerelatively largeat low temperatures, he entropy as51 -

Fe203 0.268 0.268 PyroplrylllteFe513gO 0.44 0.27

M90H )2 0.17

56 of the model 2 data at 298.15K differs by only +0.2Vo,whereas hat of model I is nearly 8Vogreatet.At 900 K,model 2 differs by -lVo whereasmodel I drfrersby +6%6.The values of 51 - 56 have been corrected for thetransitions in FeO, SiOz, and H2O. Consequently, thebest overall fit is obtained from model 2.The success of the model 2 components over thosechosen or model I lies in the similarity of the magnetic

EXPTANATIONo Model 2a Model I

o r00 200 300 400 500 600 700 800 900TEMPERATUREN KELVINS

Fig. l The percentage deviation ofthe model I and 2 (see text)summations from the measured heat capacity of staurolite.Positive deviations indicate values of the models which aresmaller than the observed heat capacity of staurolite.

2 9 E . 5 r 2 7 l lt 2 5 1 3 5 7 . 43 5 0 L 4 2 2 . 33 7 5 1 4 7 9 . 64 0 0 r 5 3 0 , 74 2 5 1 5 7 6 . 84 5 0 1 6 1 8 . 54 7 5 1 5 5 6 . 65 0 0 1 6 9 1 . 65 2 5 L 7 l . 95 5 0 1 7 5 3 . 95 1 5 1 7 6 1 . 95 0 0 1 8 0 6 . 06 2 5 1 E 3 2 . 66 5 0 1 8 5 5 . 76 7 5 L A 7 1 . 67 0 0 1 8 9 8 . 31 2 5 t 9 t 7 . 975 0 I 9 3 6 . 67 7 5 1 9 5 4 . 48 0 0 1 9 7 1 . 48 2 5 1 9 8 7 . 78 5 0 2 0 0 3 , 28 75 2 0 1 . 29 0 0 2 0 3 2 .

l 0 l 9 . 61 1 3 3 . 2L 2 3 6 2I 3 3 6 .41 4 3 3 . 5t 5 2 7 . 7r 5 r 9 . oL 7 1 61 7 9 3 . 5r 8 7 6 . 8t 9 5 7 . 72 0 3 6 . 32 r t 2 . 72 r 8 7 . 02 2 5 9 32 3 2 9 . 82 3 9 A . 42 4 6 5 . 42 5 3 0 . 72 5 9 4 . 52 6 5 6 . 82 7 7 t2 7 7 7 . 32 8 3 5 . 62 8 9 2 6

z 4 0o6 2 0zu(JeU4 0


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312 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITEcontribution of Fe2+ in enstatite and staurolite. Thecooperative ordering efect in FeO is of a different formthan the apparent Schottky-type anomaly seen in thedilute paramagneticsalts, staurolite and enstatite; seeFigure 2. In addition, pyrophyllite is a better approxima-tion of the contribution of OH to the heat capacity ofstaurolite than the separateoxide components of corun-dum, quartz, and ice. The heat capacity data for thenatural staurolite sample have been corrected to twoarbitrarily chosen compositions as an example of theprocedure. These corrections are only first approxima-tions becausewe do not have sufficient data to estimatemixing properties. These results may be adjusted in asimilar manner to estimate values for other staurolitecompositions.

Magnetic entropy of stauroliteSchottky (1922)postulated hat the electronic systemofsome atoms in a crystal would undergo excitation be-tween a ground state and higher energy states. Eachenergy state is also characterizedby a degree of degen-eracy. For a simplified case n which there are two levels,each with equal degeneracy, t can be shown that thecontribution to the heat capacity of a crystal arising romthe presenceof electrons in an excited energy level is

0 50 r00 r50 200 250 300TEMPERATURE,N KELVINS

Fig. 2. A comparisonof the heat capacity of s taurolite andthevaluesobtained from the model I and 2 summations see ext).The data are presented as CJT to emphasize the Schottkyanomaly n staurolite.

equal to the diference between wo Einstein models hatare related by two characteristic frequencies s and 2fs(see, or example, Gopal, 1966).Therefore, the contribu-tion to the heat capacity and entropy of a material fromthe presenceof excited energy states is related to thenumberof these energy evels and to their degeneracies.The free ferrous ion has 25-fold degeneracy n theground state that can be reduced or removed, when theferrous ion is in a crystal, through the combined orseparateefects of the local crystal field and cooperativespin-orbit coupling. The spatial distribution of the elec-tronic charge of the free ion is spherically symmetrical.However, when the ion is placed in a crystal the spacialdistribution of charges s altered by the distribution ofchargesn the neighboringatoms.Chargedistributions(inthe form of lobes and other shapes) that are directedtoward other atoms are elevatedto higher energy evels(splitting of levels) than those that are directed betweenneighboringatoms. Thus lower symmetry sites producegreatersplitting of energy evels. The efect ofthe typicalcrystal field upon the ferrous ion is to elevate remove) 0levels beyond that which could be energeticallyaccessi-ble. The crystal field also exerts a torque upon the orbitalmomentumresulting in the orbital momentum not beingconstant in direction and when resolved in Cartesiancoordinates to average to zero. This process is calledquenchingof the magnetic moment of the angular mo-mentum.In some crystal structures the interaction between theenergy states of one atom are not independent of theenergy states of similar neighboringatoms. In such sys-tems, a mean energy s required to induce population ofthe different energy states and the associated anomaly(typically a I peak) in the heat capacity is called acooperative anomaly. Examples of cooperative anoma-lies of this type may be found in Robie et al. (1982,a,b)for antiferromagnetic ordering in fayalite, tephroite andcobalt olivine.A noncooperativesystem exists ifthe excitation oftheenergy states of the atoms in the structure are indepen-dentof the energy evels n the similar neighboringatoms.Where no interdependence exists between the energylevels of similar neighboring atoms, the total energycontributed is equal to the sum of the energies of theindependent evels and theoretical treatment of the sys-tem is greatly simplified.The cooperative and noncooperativeanomalieswill becalled Schottky anomalies and the anomalies in theentropyor heat capacitywill be calledSchottky contribu-tions. The Schottky contribution is most easily definedwhere the energy separation of the different levels issmall. In these cases, he contribution is observedat verylow temperatureswherethe lattice heat capacity becomeseither a Debye-like contribution or an essentiallynegligi-ble contribution of the measuredheat capacity. At lowtemperatures he noncooperative Schottky heat capacityanomaly s typically expressedas a bell-shapedpeak that

V 3E- 2 5z

F.d t

t 5

A 4o BAo

EXP[ANATIONo Stouroliteo Model 2^ Model I

oA gA t r

oo o

oA oa o

Aa $A E


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HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 313is skewed toward higher temperatures.The temperatureof the peak is related to the separationof the levels andthe amplitude of the peak is related to the ratio of thedegeneracies f the levels (e.g., Gopal, 1966).Examplesof this type of heat capacity anomaly may be found in theresultsof Hill and Smith (1953). t is far more difrcult torecognize Schottky contributions to the measured heatcapacitieswhere the energy evels have a largeenergeticseparationand the contribution occurrencesare at highertemperatures.This subjecthas been excellently discussedby Westrum (1983)and therefore will not be discussedfurther in this report.The magnetic contribution to the heat capacity of asystem may be composed of both a cooperative and anoncooperative contribution. Raquet and Friedberg(1972)concluded that the angular momentum of the 5Dground state of the Fe2+ ion in FeCl2 . 4H2O wasquenced and that the ground state of the five spincomponentswas fully split by the combined effects ofspin ordering (cooperative) and crystal field splitting(noncooperative).

Mdssbauerspectra aken at 4.2Khave been nterpret-ed by Dickson and Smith (1976),Regnard 1976),andScorzelli et al. (1976) as indicating antiferromagneticordering in staurolite. Regnard found an ordering tem-peratureof 6tl K, and Dickson and Smithobtained7t lK for the ordering temperature. However, the heat-capacity valuesobtained n the temperature angeof 5 to8 in this study do not indicate the strong cooperativeexchange hat is characteristic of antiferromagnetic or-dering.Dickson and Smith (1976) have observed orderingattributable to antiferromagneticordering in FeAl2Oa nMdssbauerspectraobtained at temperaturesbelow 8 K.Because of the temperature dependence of magneticsusceptibility data, Roth (1964)suggested hat antiferro-magneticordering developed n FeAl2Oabelow 8 K, buthe failed to detect an antiferromagnetic state n FeAl2Oausing neutron diffraction. Roth assumed that FeAl2Oafailed to show antiferromagneticorder in neutron diffrac-tion because of a strong interaction between Fe2* intetrahedrally and octahedrally coordinated sites that de-stroyed ong rangeorder on the tetrahedral sites. Similar-ly, long range order in staurolite may not develop.Lyon and Giauque (1949)and Hill and Smith (1953)measured he heat capacities of the dilute paramagneticferrous salts ferrous sulfate heptahydrate and ferrousammonium sulfate hexahydrate, respectively. Neitherferrouscompoundshowedan anomaly n the heat capaci-ty that would be consistent with an interpretation ofantiferromagneticordering at low temperatures,althoughtwo maxima were observed n the low-temperature heatcapacitiesof eachphase.These maxima were interpretedto be associatedwith a splitting of the ground state of theferrous ion into two levels of equal degeneracywith aseparationof 3 to 6.5 cm-r that gave rise to the specific-heat anomaliesat 2 to 4 K and a secondgroup of three

levels centered at 38 cm-r or less for the anomaliesobserved n the 15 o 20 K region. Thus, the ferrous ionsin staurolite may develop small separationsof the groundstate similar to those seen n the dilute ferrous salts.Raquetand Friedberg(1972)measured he heatcapaci-ty of a ferrous salt (FeCl2. 4H2O) of greater ferrousconcentration than those studied by Lyon and Giaugue(1949)and Hill and Smith (1953).Raquet and Friedbergobserved a sharp )r-type peak consistent with low-tem-perature antiferromagnetic ordering. However, the ex-change energy associated with the antiferromagneticorderingwas an order of magnitudesmaller han the zero-field splitting of the ground state of Fe2+, that is, the )rpeakfor the cooperativeprocesswas at a lower tempera-ture than the noncooperative anomaly.Our heat-capacity results do not extend to a lowenough emperature o rule out a cooperative nteractionin staurolite nor do they rule out a small separationof alower doublet of the Fe2* ion. Bearing in mind thelimitations of theory discussedabove and the ambiguityassociatedwith the chemistry of our staurolite sample,we shall use several simple methods in an attempt toestimate hat portion of the magnetic heat capacity and,consequently,entropy not defined by our measurement.In the preceding section, an empirical case was pre-sented n which the entropy of staurolitewas shown to beadequatelyapproximated by the summationof entropiesofthe model 2 componentsbut not as avorably predictedby the summation of entropies of the model I compo-nents. In this section, we shall examine the theoreticalaspectsof the magnetic entropy of staurolite, using amodified version of model 2 to approximate he staurolitelattice contribution to the entropy.Staurolite s a paramagneticsalt. The low symmetry ofthe several sites in which the Fe2* ion may be found(Smith, 1968, and Takuchi et al., 1972) and the lowconcentration of Fe within several of those sites (Tak6u-chi et al.) allow us to initially assume an ideal state foreach Fe2+ ion in which the ion interacts only with itsimmediate crystal field and not with other Fe ions. Thesameassumptioncan be made or Fe3+ and Mn2*.The iron transition group paramagnetic salts yieldexperimental magneton values consistent with calcula-tions assuminga quenchedangular momentum. Conse-quently, the contribution of the electronic system of theiron transition group ions to the entropy is Rln(2S + 1),where S is the spin quantumnumber for which S : 2 forFe2* and S : 512 or Mn2* and Fe3+(e.g., see Kittel,r976t.Severalempirical approaches ave been used o extractthe magnetic contributions to the entropy and/or heatcapacity (e.g., Lyon and Giauque, 1949;Osborne andWestrum, 1953;Stout and Catalano, 1955;and Friedberget al., 1962).Osborne and Westrum assumed that thelattice heat capacity could be approximated by the heatcapacity of an somorphousdiamagneticphasecontaininga similar cation. Lyon and Giauque, and Stout and


8/12

3t4 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITECatalano using a similar approach, corrected the heatcapacity of the isomorphousdiamagneticphase using acorresponding-states rgument.Friedberg et al. assumedthat the lattice heatcapacity behaved ike that ofa Debyesolid having Cp n T3 and that the magneticcontributionabove the Schottky anomaly should go to zero as ?-2.Friedberg et al. plotted CpTz as a function of T5 and fitthe data with a straight line. The slope of this linerepresentedthe best estimate of the constant for theDebye lattice approximation.The use of an isomorphous diamagnetic phase as amodel for the lattice heat capacity of a paramagneticphasecan be theoretically ustified only if we assume hatthe Einstein and Debye temperaturesof the model differlittle from those of the true lattice and we recall theadditive propertiesof the Schottky anomalygiven in thefirst paragraphof this section.

None of these procedures s directly applicable to aninterpretation of the Schottky anomaly in staurolite. Noheat-capacitydata exist for a diamagneticphase somor-phouswith staurolite.Furthermore, the approachusedbyFriedberget al. (1962)assumes hat all the paramagneticions experience he samezero-fieldsplitting, that is, thatall the paramagnetic ons reside in similar lattice siteshaving essentially identical crystal fields. Smith (1968)and Takuchi etal. (1972)analyzedgamma-ray esonancespectra or stauroliteand showed that the Fe site is only77Vooccupiedby Fe2+. They have further shown thatonly 80Voof the Fe2* ions are located in the Fe sites.Similar results are given by Bancroft et al. (1967).Thestructure analysis of staurolite by Smith (1968) ocatesFe2* in the Fe site (tetrahedra)and n the A(3A), A(3B),U(l), and U(2) octahedra usingSmith's notation).TheU(1) and U(2) octahedraare larger than the Al(3A) andA(3B) octrahedra.Manganeses located in the U(1) andU(2) octahedra. Smith noted that the Fe3+ reported inchemicalanalysesof staurolitesmay representoxidationduring the analysis procedure because the Mcissbauerpattern does not contain ferric iron peaks.Assuming that the electric fields produced by theneighboring atoms at the A1(3A) and Al(3B) sites areessentially dentical, and making similar assumptions orU(1) and U(2) and for the tetrahedral Fe sites, weconclude hat the Fe2* ions interact with a minimum of 3different crystal fields which may yield a different distri-bution of split sublevels.This effect would not be seen nthe results of Krupka, Hemingway, and Robie (1978,unpublisheddata) for enstatite because he crystal fieldsof the M1 and M2 sites would be nearly equivalent(Morimoto, 1959).Consequently,we would expect themaximum in the Schottky anomaly found by Krupka etal . (1978,unpublished ata)and shown schematicallynthe model 2 data set to be more clearly defined and torepresent a smaller energy spectrum than that seen instaurolite, as may be seen n Figure 2.Somemay ask, "If we know the approximatecontribu-tion of the iron group transition ions to the entropy,

Rln(2S * 1), and, because at room temperature we arepresumablyat a temperature sumciently greater han themaximum n the Schottky anomaly o assume hat there san equal distribution among the spin states and hence aconstantmagneticcontribution to the entropy, why do weworry about the specifics of the lattice and magneticentropies at low temperatures?". The answer ies in theenergeticsof the system. Should a cooperative interac-tion exist, then the zero-splitting should be large com-pared to the exchange energy, and the specific heat ofstauroliteshould exhibit a cooperative anomaly at a Nelpoint at some emperature ess than the maximum in theSchottky anomaly, as was shown in the work of Fried-berget al. (1962) or FeCl2 . 4HzO also see Kittel, 1976,Chapt. 14 and 15). Alternatively, should the magneticcontribution of the Fe2* ion to the entropy of staurolitearise from a splitting of the magnetic sublevels nto anupper triplet and lower doublet as is commonly seen nFe2+paramagneticsalts(Friedberget al., 1962and Lyonand Giauque, 1949), hen a substantialcontribution to theentropy could arise below 4 K from a splitting of thelower doublet. Without a reasonably valid model for themagneticheatcapacity distribution, we cannot determinewhat portion of the magnetic heat capacity has beenmeasureddirectly with the calorimeter.We may calculate the magnetic entropy for the irontransition group ions to be 44.1 J/mol . K or 43.2J/mol . K if we assumeall the iron as the Fe2+ on basedupon the corrected chemical analysis or the sample.Thelattice entropy may be estimated n two ways, neither ofwhich is very rigorous.A first approximation to the lattice heat capacity maybe obtained from a plot of CrT2 vs. T5 following, forexample, Friedberget al. (1962).Using the roughly lineartrend for the experimentaldata in the 20 to 30 K region,we obtain equation l)

cp = 5890r-2+ 8l .25xlo-5?3 ( l)from which we estimate he lattice heat capacity as CL =81.25x 0-5T3.The heat capacityderived rom this equa-tion exceeds the measuredheat capacity of stauroliteabove 35 K, and the calculated magnetic entropy (mea-sured entropy less the estimated attice entropy of 26.5J/mol . K) is about half of that predicted rom theory. Themagneticheatcapacity approximation derived rom equa-tion (l) and designatedas model 3 is showngraphically nFigure 3.We are not surprised that the approach followed byFriedberg et al. (1962) ails for staurolite. The Schottkyanomaly eportedby Friedberg et al. was ocated at about3 K where materialsbehave more like Debye solids thanthey do at the 20 to 30 K temperature range of thestaurolite anomaly. Where multiple Schottky anomaliescan be expected o be superimposedupon eachother, asin the case of staurolite, a component of the lowertemperature Schottky anomalies may contribute to the


9/12

HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 3 t5

: 1 4oEt( q

o 20 ''o::"*Jr*.,:'-,,;i:

''{o 160 'oFig. 3. Estimates f the magneticeatcapacity f staurolite.Thediamondsepresenthevalues btained ssuminghe atticeheatcapacity model3) obtained rom equation l). The opensquares ereobtained ssuminghe atticeheatcapacitymodel2) obtained rom equation 2). The triangles nd circleswerecalculatedrom the equations f Lewis and Randall 1961),assumingn upper riplet anda lowerdoubletwitha separationof 38.E m-t and30.7-t espectively,smodel .

slopederived from the data fit as Ce'F vs.?6,causinganerror in the estimate of the lattice component.An alternate approximation to the lattice heat capacitymay be made using the model 2 summation discussedabove combined with the version of the corresponding-statesargumentpresentedby Lyon and Giauque(1949).Lyon and Giauque (1949) found the ratio of the heatcapacityof FeSOa 7H2O o the heat capacityof diamag-netic ZnSOa 7HzO, both taken at the same emperature,to vary linearly between 65 and 200 K. If we substitutethe heat capacityof the syntheticMgSiO3 Krupka et al.,1978,unpublisheddata) for the calculatedheat capacityof FeSiO3used in the model 2 approximation, then thescaled model 2 c,anbe used as an estimate of the heatcapacity of a diamagnetic phase for staurolite in theproceduredescribed by Lyon and Giauque.In Figure 4, we presenta plot of the ratio of the heatcapacity of staurolite, Cp.. to the heat capacity of thescaledmodel2 summation,Cp,2.Between170and 350K,the ratio varies linearly. We can approximatethe latticeheatcapacityof staurolite from equation(2) f we assumethat the model 2 summation s a reasonableapproxima-tion to the latticeheat capacity at room temperatureand fwe assume hat the ratio maintains the same elationshipat lower temperatures.

cp.Jcp.z 1.000+3 x l0-5(T- 160.6) (2)The construction of this model requires that the totalthermal contribution to the excess heat capacity arisingfrom the electronic system be fully developed below thetemperature at which the ratio of Cp,JCp,z becomeslinear. The magnetic entropy calculated rom this model

at 170 K is 42.4 J/mol . K. This value representsabout96% of the theoretical magnetic entropy.We present two additional estimates of the magneticheat capacity of staurolite in Figure 3. In the first case,the lattice heat capacity estimates rom equation(2) weresubtracted rom the observed heat capacity of staurolite.In the secondcase, ollowing the proceduresoutlined byFriedberg et al. (1962),we may estimate the averagedseparationof an assumedupper triplet of the groundstateof the Fe2+ on as 38.8 cm-l from the coefficientof T-2term in equation l) and, following the equationsgivenbyLewis and Randall (1961, p. 423), we calculate themagnetic entropy and heat capacity by assumingall ironas Fe2+. For convenience, his shall be designatedmodel4. Also following Friedberg et al., one may calculateanaverageseparationof 30.7cm-r from the temperatureofthe maximum in the Schottky anomaly.

Becauseof the complexity of the staurolite structure,we cannot expect to be able to extract physically mean-ingful data regarding the splitting of the ground state ofthe iron group transition ions in a particular site instaurolite rom the measuredheat capacity data, becausethe heat capacity is an average of all such effects. It isunlikely that either of the postulated energy levels iscompletely degenerateas we have assumed. However,Friedberg et al. (1962)have shown that, even though thenumber oflevels and their distributions cannot be unique-ly determined, one can eliminate some arrangementsbyexamining he variation of the maximum of the Schottkyanomaly, C.u*, with the various arrangementsof levelsand distributions. Gopal (1966)presenteda similar argu-ment. For staurolite,we find that C-.* from each approx-imation is close to the predicted C."* : 0.62R for themodel of energy evels used above.Adequate measurements of paramagnetic resonanceand susceptibility for staurolite have not been found inthe literature. Runciman et al. (1973)have calculateda| 006

N,t' r oos4_u t oo,o

Fd l o o 3U* r o o zU? r oo r-

t 0 Lt 50IEMPERATURE,N KETVINS

Fig. 4. Ratio of the measuredheat capacity of staurolite o theheat capacity calculated at the same temperature from themodified versionof the model 2 approximation discussedn text.The linear equationderived rom this ratio is used o estimate helattice heat capacity of staurolite below 100 K.

i i\\


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316 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITEseparationof 1.5 cm-l for a lower doublet for Fe2* inoctahedral coordination in enstatite. They reported un-published paramagneticspectrum data n support of theirinterpretation. Similarly, Runciman et al. (1973)calculat-ed a splitting of 0.27cm-r for Fe2* in octahedral coordi-nation n olivine. Friedberg et al. (1962)suggesta splittingof less han 0.8 cm-l for the lower doublet for Fe2* inoctahedralcoordination in FeCl2 . 4H2O. Consequently,it is reasonable o assume hat the crystal field of stauro-lite would causea small separationof the lower doublet ofthe ground state of Fe2+. Because our specific heatmeasurementsor staurolite show a continuous decrease(within the limits of experimental accuracy) both in theabsolutevalueand n the estimatedmagneticcontributionbelow 15 K, we can safely assume hat if a split lowerdoubletexists, he separationmustbe ess han0.8 cm-r.If model 4 were a fair representationof the behavior ofFe2* in staurolite, then an entropy contribution of Rln 2per mole of Fe2+ would be developedbelow I K. Thisentropy contribution would be added o the valuescalcu-lated from the model 2 and 3 approaches,yielding 60.9and 45.0Jimol . K, respectively, for the magnetic entro-py. The model 4 heat capacitiesare not a good represen-tation of either the model 2 or 3 estimatedheat capacities.Although the peak temperaturesand maxima values asderived from the model 2 and 3 approximations aregenerallyconsistent with these valuesderivedfrom mod-el 4, the agreement n estimated heat-capacity values isparticularly poor at temperaturesbelow the maximum inthe Schottky anomaly where the lattice heat capacitycontributionsbecomenegligible. Even when a separationof 30.7cm-r lseediscussion f model 3 above) s consid-ered, the slope of the Schottky anomaly at temperaturesbelow the maximum is not consistentwith the theoreticalvaluescalculated rom model 4 (seeFig. 3).Although several explanations for the difierence be-tween the theoretical and experimental estimated curvescould be presented,we think that the mismatch reflectsthe antiferromagneticordering observed by Scorzelli etal. (1976),Dickson and Smith (1976),and Regnard 1976).The lack of a pronouncedanomaly n the low temperatureheat capacity of staurolite is not inconsistent with thisinterpretation when one considers the concentration ofchemical mpurities and the non-ideal distribution of Fe2+in natural staurolite, where both effectswould contributeto a broadeningofthe peakassociatedwith spin ordering.Regnardand Scorzelliet al. have noted hat at4.2Kthequadrupole nteraction is of the same order of magnitudeas that producedby magnetic nteractions.A calculation of the magnetic entropy of staurolitebased upon the model 2lattice approximation discussedabove yields a value of about 42 Jlmol . K at tempera-tures sufficiently arger than the temperatureof the maxi-mum in the Schottky anomaly to allow us to assume hatthe magneticcontribution is constant. Although no claimsare madeherein for the absolute accuracy of our latticemodel. we think that the model is sufficientlv accurate o

suggest hat the measuredheat capacity of stauroliteandthe extrapolation of these data to 0 K underestimate hemagneticcontribution to the entropy of staurolite. On thebasis of the evidence and observationspresentedabove,limits can be placed upon the error in the entropy ofstaurolite attributable to unresolved magnetic entropybelow 5 K as 10t10 J/mol . K.

Chemical site-configurational contributions to theentropy of stauroliteUlbrich and Waldbaum 0976\ have calculated thechemical site-configurationaland the magnetic contribu-tions to the entropy of staurolite. Thesecalculationsarebased upon a simplification of the occupanices eportedby Smith (1968).For a chemical compositionfor stauro-lite as HaFeaAllsSi6Oas,lbrich and Waldbaum ave53.5J/(mol ' K) for the magnetic entropy (thereforeassuming

all iron as Fe2*) and 23.0Ji(mol . K) for the chemical site-configurationalentropy.Smith(1968)and Tak6uchi etal. (1972\have shown hatthe formula for staurolite adopted by Ulbrich and Wald-baum 1976)s too idealized,as t requiresnearlyhalftheiron to be n the ferric state or electroneutrality,which isat variance with experimentalresults showing ron to bepredominantly in the ferrous state. N6ray-Szab6 andSasv6ri (1958)have given the formula HzFe+AheSisO+afor staurolite which requires all iron to be in the ferrousstate for electrostatic balance. Smith noted that thisformula conflicts with the water contents reported byJuurinen (1956).Takuchi et al. reported a substantiallylower water content for the staurolite they studied thanthat found by Juurinen,but they still require threehydro-gensper 48 oxygens.On the basis of an analysis of the location of hydrogenin staurolite and eight chemical analyses or staurolite,Takduchiet al. (l972'lhave shownthat the ideal stauroliteshould have between 2 and4 hydrogensper 48 oxygens.Substantial substitutions of divalent Mg for Al and of Alfor Si can lead to higher water contents in staurolite.Thus, we may take the two formulations of Takduchi etal. cited above to represent the two limiting cases forideal staurolite.

Smith (1968)has shown that Al and Fe are found inslightly higher concentrations in the A1(3A) sites ascompared o Al(3B). The Al(3) octahedra cannot accom-modate concurrent occupancy of an octahedral cationand hydrogen (Takduchi et al., 1972). This limitationwould imply a correspondinglyhigher occupancy of hy-drogen n the A(3B) octahedra the P(lB) sitesof Takdu-chi et al.). Tak6uchi et al. found nearly identical occupan-cy of hydrogen n the P(lB) and P(lA) sites whereP(lA)is located in the Al(3A) octahedra). Consequently, wemay treat the Al(3) octahedra as being identical, withoutcausinga significanterror in our estimatesof the chemicalsite-configurational ontribution to the entropy of stauro-lite.Following the proceduresand assumptionsoutlined by


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HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 317Ulbrich and Waldbaum(1976)and using he site occupan-cy dataof Smith (1968)as a guide, we may estimate 34.6and 121.0 /(mol . K) for the chemical site-configurationalentropy contribution for staurolite having the composi-tions H2Al2FeaAll6Si6Oasnd (H3Al1.1rFe.6.io)tn"3.t,FeSj4Tio.gEMno.ozAlr.rs)Mg6.aaAl15.26)Si6Oas,espective-ly.

Entropy of stauroliteThe entropy of staurolite may be calculatedthrough asummation of the calorimetrically determined entropy,the chemical site-configurationalentropy, and additionalmagnetic entropy not extracted through the measuredheat capacities, or obtained through an analysis of re-versed phase equilibrium data. Ultimately, equilibriumdata must be used to evaluate the accuracy of ourestimatesof the additional magnetic and chemical site-configurationalentropies.Our best estimate of the entropy of staurolite as(H3Ah.rsFeo2.to) Fez2.izFe3.1+Tro.oaMno.ozAlr.rs)Mgo.sAlr5.26)Si8O4Et 298.15 K and I bar is l l0l.0-+12J/(mol ' K); for H2Al2FeaAl16SfuOa6ur best estimate is1019.6+2 J/(mol . K). An additional10J hasbeenaddedto the entropy of the natural staurolite compositionon thebasisof our analysis of the magneticentropy. We thinkthat the assumptions hat have been made n calculatingthe entropy of the latter composition will yield a valuethat may be considered o represent he minimumentropyfor this ideal staurolite.Relatively few experimental phase equilibrium data

involving staurolite exist in the literature (Richardson,1966, 1968;Hoschek, 1967, 1969;and Ganguly, 1968,1972;Rao andJohannes 1979;Yardley, l98l; PigageandGreenwood,19E2).Of those data,many reactions nvolvephases ike almandine, chloritoid, and Fe-cordierite forwhich we have no good estimatesof the entropy. Theequilibriurndata are not reversed or reactions nvolvingstauroliteand ron phases, ike magnetite, or which goodestimates of the entropy exist. Consequently, we areunable to further examine the accuracyof our estimatesof the entropy of staurolite at this time.AcknowledgmentsJamesA. Woodhead rovided he gehlenite ample rommaterial e synthesizedndcharacterizedor his PhDdisserta-tion. E-an Zen provided he staurolite ample nd supervisedJane H. Hammarstrom ho prepared nd characterizedhesample. FORTRANprogram sed o calculatehe Schottkythermal unctionswas kindly providedby RobertChirico.Wethankour U.S.Geological urvey olleagues,. TrenHaseltonandSusanW. Kiefer for theirhelpfulcomments.

ReferencesBancroft,G. M., Maddock,A. G. and Burns,R. G. (1967)Applications f the Mrissbauerffect o silicatemineralogy-I.

Iron silicatesof known crystal structures.Geochimica tCosmochimicacta.31 2219-2246.

Dickinson, B. L. and Smith, G. (1976)Low-temperature opticalabsorption and Mossbauer spectra of staurolite and spinel.CanadianMineralogist, 14, 206-215.Friedberg, S. A., Cohen, A. F. and SchellengJ. H. (1962)Thespecific heat of FeCl2 4H2O between 1.15 and 20 K. Journalof the Physical Society of Japan, 17, 515-517.Ganguly, J. (196E)Analysis of the stabilities of chloritoid andstaurolite and someequilibria n the system FeO-AlzOr-SiOrH2M2. American Journal of Science, 26f,277-29E.Ganguly, J. (1972)Staurolite stability and related parageneses:Theory, experiments,and application. Journal of Petrology,13.335-365.Copal, E. S. R. (1966) Specific Heats at Low Temperatures.Plenum,New York.Hemingway,B. S., Krupka, K. M. andRobie,R. A. (l9El) Heatcapacities of the alkali feldspars between 350 and 1000K fromdifferential scanning calorimetry, the thermodynamic func-tions of the alkali feldspars from 298.15 o 1400K, and thereaction quartz + jadeite = analbite. American Mineralogist,

66,1202-1215.Hill, R. W. and Smith, P. L. (1953)The anomalousspecific heatofferrous ammonium sulphate. Physical Society of London,ProceedingsA, 66, 22E-232.Hoschek, G. (1967)Untersuchungenzum stabilitdtsbereich onchloritoid und staurolith. Contributions to Mineralogy andPetrology, 14, 123-162.Hoschek, G. (1969)The stability of stauroliteand chloritoid andtheir significance n metamorphismof pelitic rocks. Contribu-tions to Mineralogy and Petrology, 22,2OE-232.Juurinen, A. (1956)Composition and properties of staurolite.Annals of the Academy of Science Fennical, Series A. IIIGeol.,47, -53.Kittel, C. (1976) ntroduction to Solid State Physics.John Wiley& Sons, nc., New York.Klotz, I. M. (1950)Chemical Thermodynamics. Prentice-Hall,Inc. EnglewoodClifis, New Jersey.Krupka, K. M., Robie, R. A., and Hemingway, B. S. (1979)High-temperatureheat capacitiesof corundum, periclase,an-orthite, CaAlzSi2OElass,muscovite, pyrophyllite, KAlSirOsglass,grossular,and NaAlSi3Osglass.American Mineralogist,64. E6-101.Lewis, G. N., and Randall,M. (1961) hermodynamics. evisedby Pitzer, K. S. and Brewer, L., McGraw-Hill Book Co., NewYork.Lyon, D. N. and Giauque,W. F. (1949)Magnetismand the thirdlaw of thermodynamics.Magneticpropertiesof ferrous sulfateheptahydrate rom I to 20 K. Heat capacity from I to 310K.Journal ofthe American Chemical Society, 71,1647-1656.Morimoto, N. (1959)The structural relations among hree poly-morphs of MgSiO3-enstatite,protoenstatite, and clinoensta-tite. Carnegie nstitution of WashingtonYear Book, 58, 197.N6ray-Szab6, I. and Sasv6ri , K. (195E)On the structure ofstaurolite, HFezAlqSLOz+.Acta Crystallographica, ll, E62-865.Osborne, D. W. and Westrum, E. F., Jr. (1953)The heatcapacity of thorium dioxide from l0 to 305 K. The heatcapacityanomalies n uranium dioxide andneptuniumdioxide.Journal of Chemical Physics,21, 1884.Pankratz, L. B. and Kelley, K. K. (1964)High-temperatureheatcontents and entropies of akermanite, cordierite, gehlenite,and merwinite. U.S. Bureau of Mines Report of Investiga-tions. 6555.


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318Pigage, . C. andGreenwood,H. J. (1982)nternallyconsistentestimates of pressure and temperature:The staurolite prob-lem. American Journal of Science. 282.943-969.Rao, B. B. and Johannes,W. (1979)Further data on the stabil ityof staurolite + quartz and related assemblages.Neues Jahr-buch fiir Mineralogie Monatshefte, 437-M7.Raquet, C. A. and Friedberg, S. A. (1972) Heat capacity ofFeCl2'4H2O between0.4 and 5.3 K. PhysicalReview B, 6,4301-4309.Regnard, J. R. (1976)M

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