Heat capacity and thermodynamic functions for gehlenite and staurolite: with commentson the Schoitky anomaly in the heat capacity of staurolite

American Mineralogist, Volume 69, pages 307-318, 1984

Bnucr S. HeutNcwAY AND Rlcneno A' RostB

U.S. Geological SurveyReston, Virginia 22092

Abstract

The heat capacities of a synthetic gehlenite and a natural staurolite have been measuredfrom 12 and 5 K, respectively, to 370 K by adiabatic calorimetry, and the heat capacities ofstaurolite have been measured to 900 K by differential scanning calorimetry. Staurolite

exhibits 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. The

entropy of gehlenite, CazAlzSiOr, at 298.15 K and l bar is 210-1t0.6 J/(mol'K), whichincludes a configurational contribution of 11.506 J/(mol ' K). The entropy of staurolite at

298.15 K and I bar is reported for two compositions as 1019.6112.0 J/(mol ' K) for H2Al2FeaAll5,SiaOas and ll0l.0-r12.0 J/(mol ' K) for (H3Alr.rsF4.to) C'e3.tzf4iaTi6.66Mn6.62Alt.rs)(Mgo.aaAlrs.zdSieO+e where the configurational entropy contributions are 34.6 and121.0 J (mot . K), respectively. In addition, the entropy value reported for the second

staurolite composition contains an additional l0 J representing the estimated contributionof the magnetic entropy below about 5 K.

lntroduction

The heat capacities of gehlenite were measured be-tween 12 and 380 K in this study in order to reduce theuncertainty associated with the rather large extrapolationnecessary to obtain the entropy contribution below 50 Kfrom the older heat capacity data that were measuredbetween 50 and 298 K by Weller and Kelley (1963). High-temperature heat-content data for gehlenite were report-ed by Pankratz and Kelley (1964).

The heat capacities of staurolite were measured in thisstudy between 5 and 368 K by low-temperature adiabaticcalorimetry and between 340 and 900 K by differentialscanning calorimetry. We are not aware of previous heat-capacity measurements for staurolite. The single set ofheat-capacity results has been corrected to two staurolitecompositions, and estimates of 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 toestimate configurational entropy terms for each stauroliteformulation.

Materials

The gehlenite sample was a portion of the sample usedby Woodhead (1977). A complete description of thesample preparation and of the physical and chemicalproperties of the sample was given by Woodhead. Thesample was designated 75001H by Woodhead. The geh-

0003-004)V84l030,{-0307$02.00 307

lenite was annealed at 1525"C for 20 hours from a glass ofgehlenite composition. The annealed sample was crushedand material less than 150 mesh was removed' Thesample mass was 28.0825 g. The cell parameters were a =

7.68658(23)A and c : 5.06747(lDland the calculated cellvolume was 9.01559(51) J/bar (Woodhead, 1977 , Table 3'3). Woodhead also reported that l0% of the glass re-mained after the 20 hours of annealing.

The chemical and physical properties of the staurQlitesample were described by Zen (1981, Table 4, page 124,sample 355-1). The sample represented a separate ofnatural staurolite from the Everett Formation collectednear Lions Head, Conn. The crushed sample was drysieved to remove material smaller than 150 mesh. Thesample mass was 31.9650 g for the low-temperaturecalorimetric measurements and 39.900 mg for the differ-ential scanning calorimetric measurements'

Experimental results

The low-temperature adiabatic calorimeter and themethods and procedures followed in this study are de-scribed elsewhere (Robie and Hemingway,1972; Robie etal.,1976 and 1978). The heat capacities of staurolite weremeasured from 340 to 900 K by using a differentialscanning calorimeter and following the procedures out-lined by Krupka et al. (1979) and Hemingway et al.(1981). The onset of decomposition ofthis natural stauro-lite sample was 910t10 K, at a heating rate of l0 trUmin.

308 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE

The experimental specific heats for gehlenite and stau-rolite are given in Tables I and 2, respectively, in thechronological order of the measurements. The data havebeen corrected for curvature (Robie and Hemingway,1972)but are uncorrected for chemical impurities.

Thermodynamic properties of gehlenite andstaurolite

The measured specific heat data were graphically ex-trapolated to 0 K from a plot of CIT vs. l. A morecomplete description of the treatment of the low-tempera-ture data for staurolite is given in a subsequent section.

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 tempera-ture, are given in Tables 3 through 7 for gehlenite and fortwo compositions of staurolite as (H3Al1. l5Feot.toxf'er'.t,Fefi*roTio.orMn6.62Al1 1e)(Mg6.aaAl15.26)SiEO4s and asH2Al2FeaAll5SisOas. The reference temperature for thelow-temperature heat capacity data is 0 K whereas 298.15K is used in the high-temperature tabulation.

Table l Experimental specific heats for synthetic gehlenite

r e n p . t o ; : : l t " T e m p . t o ; : : I t . renp . t o i : : l t '

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

Table 2. Experimental specific heats for staurolite. Series 8 and 9were results obtained by differential scanning calorimetry

r ! 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 i e s 1

1 2 . 1 6 0 . 0 0 I 5 7 913 .41 0 .0022451 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 9 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 8

S e r l e s 2

5 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 r l a r I

2 9 E . t 2 0 . 7 6 1 53 0 4 . E 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 . 2

3 3 3 . 4 t 0 . E 2 5 33 4 0 . 6 2 0 . t 3 6 63 1 1 . 7 2 0 . 4 4 7 33 5 4 . 7 5 0 . E 5 t 0361 . t t 0 . t 6793 6 t . 6 6 0 . t 7 t 9

8 . r1 . . I

4 . t 0 0 .0032545 . t 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 5

1 0 . 3 E o . 0 0 7 7 0 EI l . 35 0 . 008444t 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 7 544 .97 0 . 0325 r50 .07 0 . 0405 r5 5 . 8 2 0 . 0 5 1 4 1

S € r l e a 4

5 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 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 8

1 0 1 . 9 0 0 . I E 2 6

S.r1.r 5

104 . r 3 0 . 1902r 0 9 . 7 3 0 . 2 0 9 6I I 5 . 37 0 .2297t 2 l . t 3 0 . 2 5 0 7t 2 6 . 9 2 0 . 2 7 t 5t 3 2 . 6 7 0 . 2 9 2 4l 3 E . 3 E 0 . l t t ll r a . 0 r 0 . 3 3 3 5t49 . t 5 0 . t 537155 . t 0 0 . I t t 51 6 1 . 0 3 0 . t 9 3 2t 6 6 . 6 6 0 . 4 1 2 5

8 . r1 . r 6

172 .37 0 . t 3 l 7r 7 8 . 0 3 0 . { 5 0 9I t t . 76 0 .4695I t 9 . 4 6 0 . { E 7 E1 9 5 . 2 l 0 . 5 0 5 6200 . 95 0 .52122 0 6 . t r 0 . 5 3 9 t2 r2 .54 0 . t 5?5z r0 . 42 0 . 574 r224.17 0. 59092 to .61 0 . 6076237 .09 0 .6249243. 56 0. 64 l 7

S e t l € ! 7

2 4 9 . t 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 9

S 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 . l 0 0 . 8 6 9 03 7 0 . l 0 0 . E 7 9 43 E O . l 0 0 . 8 9 2 13 9 0 . l 0 0 . 9 0 6 14 0 0 . 0 0 0 . 9 1 5 44 l 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 . r 0 . 9 9 0 1489 . t 0 . 9160{ 9 9 . E r . 0 0 2 7509 . t 1 . 00765 1 9 . r t . 0 r 2 t5 2 9 . 0 r . 0 l 1 8t l 9 . E t . 0262t t 9 . E t . 0 3 2 1t 5 9 . E 1 . 0 3 9 35 6 9 . E r . 0 4 7 r5 7 9 . E 1 . 0 5 1 85 E 9 . 7 t . 0 5 9 6t99 ,1 t . 06a96 0 9 . 7 r . 0 7 1 36 1 9 . 7 1 . 0 7 9 t629 .1 r . 0E75639 .7 t . O99 t6 4 9 . 7 l . I l 2 56 1 9 . 0 1 . 0 9 2 0629 . t r . 0990639 .7 l . l o l 3649 .7 l . t 0666 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 . t262699 .7 r . r 27E709 .1 l . r 33E7 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 3,89 . I r . 16557 7 9 . 7 l . 1 6 4 07 A 9 . 1 l . 1 7 0 5799 .1 t . lEO2849 . { l . l 67E8 9 E . 9 r . l 9 6 r

S e r i e s 3

9 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 1

S e r i e 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 9

S 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 7 2 . 1 3 0 . 5 0 7 8t 7 7 . 7 2 0 . 5 2 2 01 8 3 . 2 0 0 . 5 3 5 2

S e r i e 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 91 9 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 4223 .61 0 .6264228 .94 0 .63572 3 4 . 2 0 0 . 6 4 6 92 3 9 . 4 t 0 . 5 5 7 3

S e r i e s 7

2 4 7 . 6 3 0 . 6 5 8 32 4 7 . t t 0 . 6 7 0 6252 .65 0 .6803258 .32 0 .69032 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 . 7 2 7 62 5 6 . 9 1 0 . 7 3 5 6?92 .82 0 .74522 9 8 . 7 3 0 . 7 5 3 8

S e r l e s 8

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

S e r l e s 9

3 1 0 . 5 2 0 . 7 7 t 63 t 7 . 3 2 0 . 7 8 0 1323 .97 0 .78933 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 . l 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 J/(mol ' K) is includedin the Gibbs energy function for gehlenite in Table 3. Theentropy ofgehlenite at 298.15 K and I bar, is, therefore,210.110.6 J/(mol . K). The values for the Gibbs energyfunction tabulated for the two staurolite compositions donot include a zero point entropy contribution. This contri-bution is discussed, at length, below.

It should be noted that Woodhead (1977) has consid-ered the question of how disorder in Si/Al on the Tz sitewould be reflected in the crystal structure of gehlenite.Woodhead concluded that gehlenite forming at low tem-peratures would obey the aluminum avoidance rule for

Table 3. Molar thermodynamic properties of gehlenite,Ca2Al2SiO7.

309

- So and (Hr - Ho)lT should be 0.2% or less, which iswithin the experimental uncertainty of the data.

The measured heat capacities of natural staurolite werecorected to the two compositions listed above by assum-ing the principle of additivity and representing the sampleas, fust, for Tables 4 and 6, 1665. 140 g of staurolite, 4.282g of corundum , 1.514 g of lime, 4.394 g of zincite, 0.503 gof FeO, 0.403 g of periclase, 0.479 g of rutile, 0.426 g ofP2O5, 0.468 g of ice, and a deficiency of 0.142 e ofmanganosite, and second, for Tables 5 and 7, 1703.737 gof staurolite, 356.263 g of pyrophyllite, 17.029 g ofbrucite, 73.399 e of magnesioferrite, 5.430 g of hematite,328.725 g of corundum,2.243 g of lime, 10.227 e of rutile,0.710 g of P2O5, 1.9E6 g of manganosite, and 6.510 g ofzincite. The corrections represent a change in the specific

Table 4. Low-temperature molar thermodynamic properties ofstaurolite, (Hdlr.rsFe6.i,o) Ge35zFe31+Tio.GMn6 g2All rs)(Mgo 44Al15 26)SisOas. The data af,e uncorrected for chemical site-

configurational contributions to the entropy.

HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE

TEI . IP . HEAT ENTROPYC A P A C I T Y

T c ; ( s ; - s ; )

KELV I N

E N T H A L P Y G I B B S E N E R G YFUI {CT IO I , I FUNCTION

( H ; - H ; ) / T - ( c i - H ; ) / T

J / ( m o l . K )

1 01 5

2 02 53 03 54 04 55 06 07 08090

1 0 0

l l 01201 3 01 4 01 5 01 6 01 7 0l B 0I O n

2 0 0

8 8 . 9 19 8 . 0 4

1 0 6 . 71 I 5 . 01 2 3 . 01 3 0 . 61 3 7 . 91 4 4 . 91 5 1 . 61 5 7 . 9

1 6 4 . 01 6 9 . 7t / f . r1 8 0 . 31 8 5 . 21 9 0 . 01 9 4 . 61 9 9 . 0203 .2207 . 2

2 1 1 . 1? 1 4 . 92 1 8 . 6? z ? . 0t z a . L2 ? 8 . 123 t . 22 3 3 . 8

52 .666 0 . 8 06 8 . 9 97 7 . 2 08 5 . 4 1o 1 R O

1 0 1 . 71 0 9 . 81 1 7 . 8r 2 5 . 8

1 3 3 . 61 4 1 . 41 4 9 . 01 5 6 . 61 6 4 . 1l 7 t . 4t 7 8 . 71 8 5 . 8t92 .91 9 9 . 8

206 .72 1 3 . 5220 .1226 .7233.2239 .6245 .9252 .1

1 8 0 . 91 9 8 . 6

T E I I P .

T

KELV I T{

. 0 3 0 6 . 0 1 0 4

. 2 3 9 . 0 7 8 5

. 9 I 4 . 2 7 92 . 4 2 t . 7 2 54 . 7 4 2 1 . 5 0 17 . 6 9 0 2 . 6 t 3

1 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 7

L t . 4 21 5 . 7 32 0 . 3 52 5 . 1 73 0 . 0 7

3 4 . 9 83 9 . 8 6q 4 . 6 74 9 . 4 054 . 045 8 . 5 96 3 . 0 46 7 . 4 07 1 . 6 57 5 . 8 1

7 9 . 8 68 3 . 8 28 7 . 6 79 t . 4 ?9 5 . 0 89 8 . 6 4

1 0 2 . 11 0 5 . 5r 0 8 . 8t I 2 . 0

1 1 5 . 11 1 8 . 2t ? t . z1 2 4 . 1t26 .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 61 1 , 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 9

2 9 . 1 932 .443 5 . 8 23 9 . 3 142 .874 6 . 5 15 0 , 1 95 3 . 9 25 7 . 6 86 1 . 4 6

6 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 . 5

8 9 . 2 79 8 . 6 6

5 . 3 7t 2 , 3 2t 7 . 5 52 t . 0424 .032 8 . 1 93 4 . 5 44 3 . 0 55 3 . 9 86 7 . 1 59 9 . 5 9

1 3 9 . 51 9 5 . 823t ,3292.6

3 5 0 . 54 1 0 . 04 7 0 . 25 3 0 . 35 9 0 . 06 4 8 . 57 0 5 . 87 5 1 . 18 1 4 . 58 6 6 . 0

9 1 5 . 69 6 3 . 4

1 0 0 9 . 21 0 5 3 . 01 0 9 4 . 8I 1 3 4 . 7t t 7z .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 . 8 7

1 4 . 9 52 0 . 5 02 5 . 5 13 0 . 2 33 5 . 0 44 0 . l 84 5 . 8 552 .2 t5 7 . 2 18 5 . 4 8

1 0 7 . I1 3 1 . 91 5 9 . 7

1 9 0 . 3223 . 4258 .52 9 5 . 63 3 4 . 23 7 4 . 2{ 1 5 . 24 5 7 . r499 .7542.8

s86 . 36 3 0 . 06 7 3 . 87 t 7 . 77 6 1 . 68 0 5 . 38 4 8 . 88 9 2 . I9 3 5 . 29 t 7 . 9

t020.2t062.2I 1 0 3 . 71 1 4 4 . 9I 1 8 5 . 6t225.91 2 4 5 . 9

8 6 2 . 59 7 0 . 0

2 . 0 95 . 4 18 . 7 l

1 1 . 3 81 3 . 5 11 5 . 5 61 7 . 8 92 0 . 4 723 ,572 7 . 2 53 6 . 5 048 .2962 ,537 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 . 9

368 . 03 9 4 . 04 t9 .7445 .24 7 0 . 4495 .25 1 9 . 65 4 3 . 55 6 7 . 1590 .2

6 1 2 . 86 3 5 . 06 5 6 . 66 7 7 . 96 9 8 . 77 1 9 . 0729 .0

0 . 9 13 . 4 06 , 2 49 . t 2

1 1 . 9 01 4 . 5 7I 7 . 1 51 9 . 7 02 2 , 2 92 4 . 9 63 0 . 7 03 7 . t 844 .545 2 . 8 35 2 . 1 1

7 2 . 3 58 3 . 5 49 5 . 6 4

1 0 8 . 6t 2 2 . 31 3 6 . 81 5 2 . 01 6 7 . 81 8 4 . 12 0 1 . 0

2 1 8 . 32 3 6 . 0254 .1? 7 2 . 529 r . 23 1 0 . 13 2 9 . 33 4 8 . 63 6 8 . I3 8 7 . 7

407 -4421 . 2447 . l4 6 7 . 0487 . 05 0 6 . 95 1 6 . 9

HEAT ENTROPYCAPAC I TY

E i lTHALPY G IBES E I IERGYFU i lCT I0 l l FU I {CT I0N

c i (s i -s ; ) 1x i -Hi t r r - (c ; -H;) /T. t / ( m o l . K )210

2?O2 3 02402502602702802903 0 0

3 1 03203 3 03403 5 03603 7 03B0

al 0l 5202 S3 03 5404 5505 07 08090

1 0 0

l l 0t201 3 01401 5 01 6 01 7 01801 9 0200

2t02202302402502 6 0270?80290300

3 1 03203 3 03 4 03 5 03603 6 5

2 7 3 . 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 interpretation given by Wood-head, the configurational entropy for gehlenite would be5.75J(mol . K). Gehlenites synthesized at higher tem-peratures appear to have greater disorder leading Wood-head to conclude that disorder of Si/Al on the T2 sitewould be temperature dependent.

The heat capacities for gehlenite were not corrected forthe l0Vo of uncrystallized glass (Woodhead, 1977). Robieet al. (1978) have shown that the heat capacities of thefeldspars analbite, high sanidine, and anorthite differ littlefrom the heat capacities of glasses of the same composi-tion. These observed difierences yielded calculated dif-ferences of 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, the uncertainty in the functions 51

2 7 3 . t 5 1 1 8 4 . 32 9 8 . l 5 1 2 7 0 . l

3 3 5 . 33 8 4 . 0

527 .Z5 8 5 . 9

310 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE

TE i ' lP .

T

r (ELV I r , {

Table 5. Low-temperature molar thermodynamic properties ofstaurolite, H2Al2FeaAll6SisOas. The data are uncorrected for

chemical site-confi gurational contributions to the entropy.

assuming that the impurities can be represented byphases for which specific heat data are available. Mostgeochemists believe that ideal additivity does not trulyprevail, but where the required corrections are small (i.e.,where the impurities represent only a small percentage ofthe sample) the error associated with the correction isoften less than the uncertainty in the measured specificheat.

The potential errors associated with this type of correc-tion may be minimized by combining the impurity compo-nents into phases that are structurally similar to the phaseunder study (Robie et al., 1976 and Klotz, 1950), or byusing acorresponding states argument (Robie etal.,1982,or Stout and Catalano, 1955). In either case, the colTec-tions may be applied directly to the measured specificheats (Robie et al., 1976) in order to provide correctedthermodynamic parameters as a function of temperature,or the integrated properties may be corrected at a specifictemperature (Westrum et a1., 1979). Both proceduresshould yield the same results at the same temperature ifthe same components are chosen.

Two models are presented in 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

Table 6. High-temperature molar thermodynamic properties fornatural staurolite. The formula for staurolite is given in Table 4.A chemical site-configurational entropy of 121.0 J(mol ' K) andan additional 10.0 J/(mol ' K) of magnetic entropy have beenadded to the entropy at298.15 K given in Table 4. The equation

fit the experimental data with an average deviation of 0,5Vo.

E N T R U P Y E N T H A L P YF U r , l cT loN

s r ( n T - n 2 9 6 ) / T

J / ( 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 I

c i 1s l - s i t l r r i - r r i l r rJ / ( r , r o l ' r )

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 0

2 0? 53 03 54 04 55 06 07 0B O9 0

1 C 0

1 1 0t201 3 01 4 01 5 01 6 01 7 0l B 0I 9 0200

2 1 0220230?41)

2 0 c? 7 02 8 029 t )3 0 0

2 0 4 . B2 3 7 . 6? 7 2 . 63 0 9 . 53 4 0 . 03 4 7 . B4 2 8 . 84 7 0 , 65 1 3 . 25 5 6 . 3

5 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 9

12 -371 6 . 5 119.z ' ,d2 1 . 5 42 3 . 7 I? 6 , ? 82 9 . 1 93 2 . 6 54 1 . 3 65 2 . 5 56 6 . 1 08 2 . 1 1

1 0 0 . 2

1 2 0 . 11 4 1 . 51 6 4 . 31 9 8 . 1212 ,n2 3 9 . 12 6 3 . 82 ' , d 9 . 93 1 6 . 13 4 2 . 3

3 6 3 . 53 9 + . 54 2 0 . 44 , i 5 , 94 7 1 , ?4 9 6 , ?52 t ) , 75 4 4 . 35 6 3 . 6

6 1 4 . 66 3 7 . 06 5 9 . 95 8 0 . 37 0 1 . 3

7 3 1 . 9

5 2 t i . 45 8 7 . 6

1 . 1 0

9 . 0 1

L 7 . 2 32 0 . 9 52 4 . 4 42 7 . 7 73 1 . 0 3

4 0 . 9 64 S . 1 55 6 . 0 36 4 , 7 27 4 . 2 9

8 4 . 7 69 6 . 1 1

1 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 . J

3 2 3 . 33 4 2 . 53 5 1 . 9

4 0 1 . 1

4 4 0 . 74 6 0 . 74 4 0 , 65 0 0 . 75 ? 0 . 75 3 0 . 7

3 4 U . 6397 . 4

3 . 3 81 8 . 2 82 5 . 3 82 9 . 0 33 1 . 4 73 4 . 7 14 0 , 0 8

5 7 . 7 37 0 . 1 2

1 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 , 5

9 1 6 . 99 6 5 . 4

I 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 . 7 5

4 ? . 4 94 3 . 2 35 4 . 0 5

6 6 . 9 ?8 2 . 3 3

1 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 . 7

2 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 7 . 71 1 1 9 , 51 1 6 1 . 0t ? 0 2 . 0L ? 4 2 . 5t262 . 1

8 7 6 . 99 3 5 . 0

T E M P . H E A TCAPACI T !

T '

K E L V I N

G I B B S B N E R C TI 'U NC T ION

- ( c T - H a 9 E ) / T

heat (J/g . K, the quantity actually measured) of less thanO.lVo for the first case given above for heat-capacityvalues above 125 K and ofless than lVofor values from 8to 125 K, and for the second composition, of less than 1%above 300 K, less thar, 2Vo from 150 to 300 K, and lessthan 3Vo from 50 to 150 K. Below 50 K, the sum of thespecific heats of the impurity phases becomes negligiblecompared to the measured specific heat of staurolite.

It is both instructive and important to examine theassumptions and procedures underlying the correctionsapplied to the specific-heat data, particularly in light ofthe rather large mass correction necessary to obtain theheat capacities of 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 . 31 6 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 7 2 3 . 92 7 8 4 . O2 A 4 2 . 72 9 0 0 . 22 9 5 6 . 4

0 . 0l 0 E . 3I 9 9 . 22 8 2 . r3 5 7 . 9

4 9 1 . 95 5 1 . 56 0 7 . 06 5 8 . 77 0 7 . 11 5 2 . 67 9 5 . 3E 3 5 , 58 7 3 . 79 0 9 . 79 4 3 , 99 7 6 . 4

1 0 0 7 . 41 0 3 6 . 9I 0 6 5 . 01 0 9 2 . 0i I r i . 8r t 4 2 . 5r r 6 6 . 2

r I 0 l . 01 t 0 5 . 7r t l 7 . tr r 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 . II 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

HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 3 l l

Table 7. High-temperature molax thermodynamic properties forideal staurol i te, H2Al2Fe4Alr6Si8O4s. A chemical si te-configurational entropy of 34.6 J/(mol . K) has been added to theentropy at 298.15 K given in Table 5. The equation fit the

experimental data with an average deviation of 0.EVo.

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

Phase

llode I

t 2

lilol e s

ilode I

t 2

ilol esTEI iP . HEATCAPACI TY

T CE

KELVI N

E N T R O P Y E N T I I A L P Y C I E B S 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 ) / T

J / ( D o 1 . K )

Sl02 8.00

Al 203 8.80

Tl 02

itr0

Hzo

0.08

0.02

1 .50

0.08

0.02

i ? ?

2 .67

? .67

7 .47

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 . 0

I 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 . J1 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 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 changes are presented in model2. First, approximation of the contribution of OH to thespecific heat of staurolite in model I is made by assumingthat model I contains ice and water, whereas in model 2,the OH contribution is introduced through pyrophylliteand brucite. Second. the contribution of Fe2+ as FeO inmodel I was replaced through the introduction of thedifference in the specific heat of a mixed Mg-Fe enstatiteand the specific heat of pure Mg enstatite (Krupka et al.,1978, unpublished data), where this difference represent-ed the composition FeSiO3.

Differences were calculated by subtracting the summedvalues for each model from the smoothed heat capacitiesgiven in Tables 4 and 6. These differences are shown inFigure l. At temperatures greater than 3fi) K, relativelylittle advantage is 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 is usually removed by asmoothing process. For the model I data presented inFigure 1, the effect of the c - B transition has beenpreserved as a visual reminder that when using theintegrated properties (e.g., entropy) approach, an addi-tional correction may be required in order to maintainsmooth estimated values.

Although local deviations of the model 2 specific heatdata from the measured heat capacity of staurolite arerelatively large at low temperatures, the entropy as 51 -

Fe203 0.268 0.268 Pyroplrylllte

Fe51 03MgO 0.44 0.27

M9 (0H) 2 0.17

56 of the model 2 data at 298.15 K differs by only +0.2Vo,whereas that of model I is nearly 8Vo greatet. At 900 K,model 2 differs by -lVo whereas model 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 for model I lies in the similarity of the magnetic

EXPTANATION

o Model 2

a Model I

o r00 200 300 400 500 600 700 800 900

TEMPERATURE IN 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 are

smaller than the observed heat capacity of staurolite.

2 9 E . t 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 2 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 . 97 5 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 7 5 2 0 1 8 . 29 0 0 2 0 3 2 . 5

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 0 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 r 7 . t2 7 7 7 . 32 8 3 5 . 62 8 9 2 . 6

z 4 0o

6 2 0

zu(JeU4 0

312 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE

contribution of Fe2+ in enstatite and staurolite. Thecooperative ordering efect in FeO is of a different formthan the apparent Schottky-type anomaly seen in thedilute paramagnetic salts, 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 separate oxide 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 because we 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 staurolite

Schottky (1922) postulated that the electronic system ofsome atoms in a crystal would undergo excitation be-tween a ground state and higher energy states. Eachenergy state is also characterized by a degree of degen-eracy. For a simplified case in which there are two levels,each with equal degeneracy, it can be shown that thecontribution to the heat capacity of a crystal arising fromthe presence of electrons in an excited energy level is

0 50 r 00 r 50 200 250 300

TEMPERATURE, IN KELVINS

Fig. 2. A comparison of the heat capacity of staurolite and thevalues obtained from the model I and 2 summations (see text).The data are presented as CJT to emphasize the Schottkyanomaly in staurolite.

equal to the diference between two Einstein models thatare related by two characteristic frequencies fs and 2fs(see, for example, Gopal, 1966). Therefore, the contribu-tion to the heat capacity and entropy of a material fromthe presence of excited energy states is related to thenumber of these energy levels and to their degeneracies.

The free ferrous ion has 25-fold degeneracy in theground state that can be reduced or removed, when theferrous ion is in a crystal, through the combined orseparate efects 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 is altered by the distribution ofcharges in the neighboring atoms. Charge distributions (inthe form of lobes and other shapes) that are directedtoward other atoms are elevated to higher energy levels(splitting of levels) than those that are directed betweenneighboring atoms. Thus lower symmetry sites producegreater splitting of energy levels. The efect ofthe typicalcrystal field upon the ferrous ion is to elevate (remove) l0levels beyond that which could be energetically accessi-ble. The crystal field also exerts a torque upon the orbitalmomentum resulting in the orbital momentum not beingconstant in direction and when resolved in Cartesiancoordinates to average to zero. This process is calledquenching of 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 neighboring atoms. In such sys-tems, a mean energy is 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 noncooperative system exists ifthe excitation oftheenergy states of the atoms in the structure are indepen-dent of the energy levels in the similar neighboring atoms.Where no interdependence exists between the energylevels of similar neighboring atoms, the total energycontributed is equal to the sum of the energies of theindependent levels and theoretical treatment of the sys-tem is greatly simplified.

The cooperative and noncooperative anomalies will becalled Schottky anomalies and the anomalies in theentropy or heat capacity will be called Schottky contribu-tions. The Schottky contribution is most easily definedwhere the energy separation of the different levels issmall. In these cases, the contribution is observed at verylow temperatures where the lattice heat capacity becomeseither a Debye-like contribution or an essentially negligi-ble contribution of the measured heat capacity. At lowtemperatures the noncooperative Schottky heat capacityanomaly is typically expressed as a bell-shaped peak that

V 3

E- 2 5z

F.

d t

t 5

A 4

o BA

o

EXP[ANATION

o Stouroliteo Model 2

^ Model I

oA g

A t r

oo o

o

Ao

a oA

a $A E

HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 313

is skewed toward higher temperatures. The temperatureof the peak is related to the separation of the levels andthe amplitude of the peak is related to the ratio of thedegeneracies of the levels (e.g., Gopal, 1966). Examplesof this type of heat capacity anomaly may be found in theresults of Hill and Smith (1953). It is far more difrcult torecognize Schottky contributions to the measured heatcapacities where the energy levels have a large energeticseparation and the contribution occurrences are at highertemperatures. This subject has 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 5D

ground state of the Fe2+ ion in FeCl2 . 4H2O wasquenced and that the ground state of the five spincomponents was fully split by the combined effects ofspin ordering (cooperative) and crystal field splitting(noncooperative).

Mdssbauer spectra taken at 4.2Khave been interpret-ed by Dickson and Smith (1976), Regnard (1976), andScorzelli et al. (1976) as indicating antiferromagneticordering in staurolite. Regnard found an ordering tem-perature of 6tl K, and Dickson and Smith obtained 7tlK for the ordering temperature. However, the heat-capacity values obtained in the temperature range of 5 to8 in this study do not indicate the strong cooperativeexchange that is characteristic of antiferromagnetic or-dering.

Dickson and Smith (1976) have observed orderingattributable to antiferromagnetic ordering in FeAl2Oa inMdssbauer spectra obtained at temperatures below 8 K.Because of the temperature dependence of magneticsusceptibility data, Roth (1964) suggested that antiferro-magnetic ordering developed in FeAl2Oa below 8 K, buthe failed to detect an antiferromagnetic state in FeAl2Oausing neutron diffraction. Roth assumed that FeAl2Oafailed to show antiferromagnetic order in neutron diffrac-tion because of a strong interaction between Fe2* intetrahedrally and octahedrally coordinated sites that de-stroyed long range order on the tetrahedral sites. Similar-ly, long range order in staurolite may not develop.

Lyon and Giauque (1949) and Hill and Smith (1953)measured the heat capacities of the dilute paramagneticferrous salts ferrous sulfate heptahydrate and ferrousammonium sulfate hexahydrate, respectively. Neitherferrous compound showed an anomaly in the heat capaci-ty that would be consistent with an interpretation ofantiferromagnetic ordering at low temperatures, althoughtwo maxima were observed in the low-temperature heatcapacities of each phase. These maxima were interpretedto be associated with a splitting of the ground state of theferrous ion into two levels of equal degeneracy with aseparation of 3 to 6.5 cm-r that gave rise to the specific-heat anomalies at 2 to 4 K and a second group of three

levels centered at 38 cm-r or less for the anomaliesobserved in the 15 to 20 K region. Thus, the ferrous ionsin staurolite may develop small separations of the groundstate similar to those seen in the dilute ferrous salts.

Raquet and Friedberg (1972) measured the heat capaci-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 antiferromagneticordering was an order of magnitude smaller than the zero-field splitting of the ground state of Fe2+, that is, the )rpeak for the cooperative process was at a lower tempera-ture than the noncooperative anomaly.

Our heat-capacity results do not extend to a lowenough temperature to rule out a cooperative interactionin staurolite nor do they rule out a small separation of alower doublet of the Fe2* ion. Bearing in mind thelimitations of theory discussed above and the ambiguityassociated with the chemistry of our staurolite sample,we shall use several simple methods in an attempt toestimate that portion of the magnetic heat capacity and,consequently, entropy not defined by our measurement.

In the preceding section, an empirical case was pre-sented in which the entropy of staurolite was shown to beadequately approximated by the summation of entropiesofthe model 2 components but not as favorably predictedby the summation of entropies of the model I compo-nents. In this section, we shall examine the theoreticalaspects of the magnetic entropy of staurolite, using amodified version of model 2 to approximate the staurolitelattice contribution to the entropy.

Staurolite is a paramagnetic salt. The low symmetry ofthe several sites in which the Fe2* ion may be found(Smith, 1968, and Tak€uchi 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. Thesame assumption can be made for Fe3+ and Mn2*.

The iron transition group paramagnetic salts yieldexperimental magneton values consistent with calcula-tions assuming a quenched angular 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 quantum number for which S : 2 forFe2* and S : 512 for Mn2* and Fe3+ (e.g., see Kittel,r976t.

Several empirical approaches have been used to 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 isomorphous diamagnetic phase containinga similar cation. Lyon and Giauque, and Stout and

3t4 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE

Catalano using a similar approach, corrected the heatcapacity of the isomorphous diamagnetic phase using acorresponding-states argument. Friedberg et al. assumedthat the lattice heat capacity behaved like that ofa Debyesolid having Cp n T3 and that the magnetic contributionabove 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 linerepresented the 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 paramagneticphase can be theoretically justified only if we assume thatthe Einstein and Debye temperatures of the model differlittle from those of the true lattice and we recall theadditive properties of the Schottky anomaly given in thefirst paragraph of this section.

None of these procedures is directly applicable to aninterpretation of the Schottky anomaly in staurolite. Noheat-capacity data exist for a diamagnetic phase isomor-phous with staurolite. Furthermore, the approach used byFriedberg et al. (1962) assumes that all the paramagneticions experience the same zero-field splitting, that is, thatall the paramagnetic ions reside in similar lattice siteshaving essentially identical crystal fields. Smith (1968)and Tak€uchi etal. (1972) analyzed gamma-ray resonancespectra for staurolite and showed that the Fe site is only77Vo occupied by Fe2+. They have further shown thatonly 80Vo of 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) locatesFe2* in the Fe site (tetrahedra) and in the A(3A), A(3B),U(l), and U(2) octahedra (using Smith's notation). TheU(1) and U(2) octahedra are larger than the Al(3A) andA(3B) octrahedra. Manganese is located in the U(1) andU(2) octahedra. Smith noted that the Fe3+ reported inchemical analyses of staurolites may represent oxidationduring 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 identical, and making similar assumptions forU(1) and U(2) and for the tetrahedral Fe sites, weconclude that 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 inthe results of Krupka, Hemingway, and Robie (1978,unpublished data) for enstatite because the 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 data) and shown schematically inthe model 2 data set to be more clearly defined and torepresent a smaller energy spectrum than that seen instaurolite, as may be seen in Figure 2.

Some may ask, "If we know the approximate contribu-tion of the iron group transition ions to the entropy,

Rln(2S * 1), and, because at room temperature we arepresumably at a temperature sumciently greater than themaximum in the Schottky anomaly to assume that there isan equal distribution among the spin states and hence aconstant magnetic contribution to the entropy, why do weworry about the specifics of the lattice and magneticentropies at low temperatures?". The answer lies in theenergetics of 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 ofstaurolite should exhibit a cooperative anomaly at a N€elpoint at some temperature less than the maximum in theSchottky anomaly, as was shown in the work of Fried-berg et al. (1962) for 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 into anupper triplet and lower doublet as is commonly seen inFe2+ paramagnetic salts (Friedberg et al., 1962 and Lyonand Giauque, 1949), then a substantial contribution to theentropy could arise below 4 K from a splitting of thelower doublet. Without a reasonably valid model for themagnetic heat capacity distribution, we cannot determinewhat portion of the magnetic heat capacity has beenmeasured directly 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 assume all the iron as the Fe2+ ion basedupon the corrected chemical analysis for the sample. Thelattice entropy may be estimated in 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, Friedberg et al. (1962). Using the roughly lineartrend for the experimental data in the 20 to 30 K region,we obtain equation (l)

cp = 5890r-2 + 8 l .25xlo-5?3 ( l )

from which we estimate the lattice heat capacity as CL =81.25x l0-5T3. The heat capacity derived from this equa-tion exceeds the measured heat capacity of stauroliteabove 35 K, and the calculated magnetic entropy (mea-sured entropy less the estimated lattice entropy of 26.5J/mol . K) is about half of that predicted from theory. Themagnetic heat capacity approximation derived from equa-tion (l) and designated as model 3 is shown graphically inFigure 3.

We are not surprised that the approach followed byFriedberg et al. (1962) fails for staurolite. The Schottkyanomaly reported by Friedberg et al. was located at about3 K where materials behave more like Debye solids thanthey do at the 20 to 30 K temperature range of thestaurolite anomaly. Where multiple Schottky anomaliescan be expected to be superimposed upon each other, asin the case of staurolite, a component of the lowertemperature Schottky anomalies may contribute to the

HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 3 t5

: 1 4oE

t

( q

o 20 ''o

::"*Jr*.,:'-,,;i: ''{o 160 '€o

Fig. 3. Estimates of the magnetic heat capacity of staurolite.The diamonds represent the values obtained assuming the latticeheat capacity (model 3) obtained from equation (l). The opensquares were obtained assuming the lattice heat capacity (model2) obtained from equation (2). The triangles and circles werecalculated from the equations of Lewis and Randall (1961),assuming an upper triplet and a lower doublet with a separationof 38.E cm-t and 30.7-t respectively, as model 4.

slope derived from the data fit as Ce'F vs.?6, causing anerror 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-states argument presented by Lyon and Giauque (1949).Lyon and Giauque (1949) found the ratio of the heatcapacity of FeSOa . 7H2O to the heat capacity of diamag-netic ZnSOa . 7HzO, both taken at the same temperature,to vary linearly between 65 and 200 K. If we substitutethe heat capacity of the synthetic MgSiO3 (Krupka et al.,1978, unpublished data) for the calculated heat capacityof FeSiO3 used in the model 2 approximation, then thescaled model 2 c,an be used as an estimate of the heatcapacity of a diamagnetic phase for staurolite in theprocedure described by Lyon and Giauque.

In Figure 4, we present a plot of the ratio of the heatcapacity of staurolite, Cp.. to the heat capacity of thescaled model 2 summation, Cp,2. Between 170 and 350 K,the ratio varies linearly. We can approximate the latticeheat capacity of staurolite from equation (2) if we assumethat the model 2 summation is a reasonable approxima-tion to the lattice heat capacity at room temperature and ifwe assume that the ratio maintains the same relationshipat 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 from this model

at 170 K is 42.4 J/mol . K. This value represents about96% 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 from equation (2) weresubtracted from the observed heat capacity of staurolite.In the second case, following the procedures outlined byFriedberg et al. (1962), we may estimate the averagedseparation of an assumed upper triplet of the ground stateof the Fe2+ ion as 38.8 cm-l from the coefficient of T-2term in equation (l) and, following the equations given byLewis and Randall (1961, p. 423), we calculate themagnetic entropy and heat capacity by assuming all ironas Fe2+. For convenience, this shall be designated model4. Also following Friedberg et al., one may calculate anaverage separation of 30.7 cm-r from the temperature ofthe maximum in the Schottky anomaly.

Because of 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 from the measured heat capacity data, becausethe heat capacity is an average of all such effects. It isunlikely that either of the postulated energy levels iscompletely degenerate as 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 arrangements byexamining the variation of the maximum of the Schottkyanomaly, C.u*, with the various arrangements of levelsand distributions. Gopal (1966) presented a 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 levels used above.

Adequate measurements of paramagnetic resonanceand susceptibility for staurolite have not been found inthe literature. Runciman et al. (1973) have calculated a

| 006

N

,t' r oos

4_u t oo,o

F

d l o o 3

U* r o o z

U

? r o o r-

t 0 Lt 5 0

IEMPERATURE, IN KETVINS

Fig. 4. Ratio of the measured heat capacity of staurolite to theheat capacity calculated at the same temperature from themodified version of the model 2 approximation discussed in text.The linear equation derived from this ratio is used to estimate thelattice heat capacity of staurolite below 100 K.

i i\

\

316 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE

separation of 1.5 cm-l for a lower doublet for Fe2* inoctahedral coordination in enstatite. They reported un-published paramagnetic spectrum data in support of theirinterpretation. Similarly, Runciman et al. (1973) calculat-ed a splitting of 0.27 cm-r for Fe2* in octahedral coordi-nation in olivine. Friedberg et al. (1962) suggest a splittingof less than 0.8 cm-l for the lower doublet for Fe2* inoctahedral coordination in FeCl2 . 4H2O. Consequently,it is reasonable to assume that the crystal field of stauro-lite would cause a small separation of the lower doublet ofthe ground state of Fe2+. Because our specific heatmeasurements for staurolite show a continuous decrease(within the limits of experimental accuracy) both in theabsolute value and in the estimated magnetic contributionbelow 15 K, we can safely assume that if a split lowerdoublet exists, the separation must be less than 0.8 cm-r.

If model 4 were a fair representation of the behavior ofFe2* in staurolite, then an entropy contribution of Rln 2per mole of Fe2+ would be developed below I K. Thisentropy contribution would be added to the values calcu-lated from the model 2 and 3 approaches, yielding 60.9and 45.0 Jimol . K, respectively, for the magnetic entro-py. The model 4 heat capacities are not a good represen-tation of either the model 2 or 3 estimated heat capacities.Although the peak temperatures and maxima values asderived from the model 2 and 3 approximations aregenerally consistent with these values derived from mod-el 4, the agreement in estimated heat-capacity values isparticularly poor at temperatures below the maximum inthe Schottky anomaly where the lattice heat capacitycontributions become negligible. Even when a separationof 30.7 cm-r lsee discussion of model 3 above) is consid-ered, the slope of the Schottky anomaly at temperaturesbelow the maximum is not consistent with the theoreticalvalues calculated from model 4 (see Fig. 3).

Although several explanations for the difierence be-tween the theoretical and experimental estimated curvescould be presented, we think that the mismatch reflectsthe antiferromagnetic ordering observed by Scorzelli etal. (1976), Dickson and Smith (1976), and Regnard (1976).The lack of a pronounced anomaly in the low temperatureheat capacity of staurolite is not inconsistent with thisinterpretation when one considers the concentration ofchemical impurities and the non-ideal distribution of Fe2+in natural staurolite, where both effects would contributeto a broadening ofthe peak associated with spin ordering.Regnard and Scorzelli et al. have noted that at4.2Kthequadrupole interaction is of the same order of magnitudeas that produced by magnetic interactions.

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 larger than the temperature of the maxi-mum in the Schottky anomaly to allow us to assume thatthe magnetic contribution is constant. Although no claimsare made herein for the absolute accuracy of our latticemodel. we think that the model is sufficientlv accurate to

suggest that the measured heat capacity of staurolite andthe extrapolation of these data to 0 K underestimate themagnetic contribution to the entropy of staurolite. On thebasis of the evidence and observations presented above,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 staurolite

Ulbrich and Waldbaum 0976\ have calculated thechemical site-configurational and the magnetic contribu-tions to the entropy of staurolite. These calculations arebased upon a simplification of the occupanices reportedby Smith (1968). For a chemical composition for stauro-lite as HaFeaAllsSi6Oas, Ulbrich and Waldbaum gave 53.5J/(mol ' K) for the magnetic entropy (therefore assumingall iron as Fe2*) and 23.0 Ji(mol . K) for the chemical site-confi gurational entropy.

Smith (1968) and Tak6uchi etal. (1972\ have shown thatthe formula for staurolite adopted by Ulbrich and Wald-baum (1976) is too idealized, as it requires nearly halftheiron to be in the ferric state for electroneutrality, which isat variance with experimental results showing iron 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). Tak€uchi et al. reported a substantiallylower water content for the staurolite they studied thanthat found by Juurinen, but they still require three hydro-gens per 48 oxygens.

On the basis of an analysis of the location of hydrogenin staurolite and eight chemical analyses for staurolite,Takduchi et al. (l972'l have shown that the ideal stauroliteshould have between 2 and 4 hydrogens per 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 to Al(3B). The Al(3) octahedra cannot accom-modate concurrent occupancy of an octahedral cationand hydrogen (Takduchi et al., 1972). This limitationwould imply a correspondingly higher occupancy of hy-drogen in the A(3B) octahedra (the P(lB) sites of Takdu-chi et al.). Tak6uchi et al. found nearly identical occupan-cy of hydrogen in the P(lB) and P(lA) sites (where P(lA)is located in the Al(3A) octahedra). Consequently, wemay treat the Al(3) octahedra as being identical, withoutcausing a significant error in our estimates of the chemicalsite-configurational contribution to the entropy of stauro-lite.

Following the procedures and assumptions outlined by

HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 317

Ulbrich and Waldbaum (1976) and using the site occupan-cy data of Smith (1968) as a guide, we may estimate 34.6and 121.0 J/(mol . K) for the chemical site-configurationalentropy contribution for staurolite having the composi-tions H2Al2FeaAll6Si6Oas and (H3Al1.1rFe.6.io) tn"3.t,FeSj4Tio.gEMno.ozAlr.rs) (Mg6.aaAl15.26)Si6Oas, respective-ly.

Entropy of staurolite

The entropy of staurolite may be calculated through asummation of the calorimetrically determined entropy,the chemical site-configurational entropy, 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 ourestimates of the additional magnetic and chemical site-configurational entropies.

Our best estimate of the entropy of staurolite as(H3Ah.rsFeo2.to) (Fez2.izFe3.1+Tro.oaMno.ozAlr.rs) (Mgo.sAlr5.26)Si8O4E at 298.15 K and I bar is l l0l.0-+12J/(mol ' K); for H2Al2FeaAl16SfuOa6 our best estimate is1019.6+ l2 J/(mol . K). An additional 10 J has been addedto the entropy of the natural staurolite composition on thebasis of our analysis of the magnetic entropy. We thinkthat the assumptions that have been made in calculatingthe entropy of the latter composition will yield a valuethat may be considered to represent the minimum entropyfor this ideal staurolite.

Relatively few experimental phase equilibrium datainvolving staurolite exist in the literature (Richardson,1966, 1968; Hoschek, 1967, 1969; and Ganguly, 1968,1972; Rao and Johannes , 1979;Y ardley, l98l; Pigage andGreenwood, 19E2). Of those data, many reactions involvephases like almandine, chloritoid, and Fe-cordierite forwhich we have no good estimates of the entropy. Theequilibriurn data are not reversed for reactions involvingstaurolite and iron phases, like magnetite, for which goodestimates of the entropy exist. Consequently, we areunable to further examine the accuracy of our estimatesof the entropy of staurolite at this time.

Acknowledgments

James A. Woodhead provided the gehlenite sample frommaterial he synthesized and characterized for his PhD disserta-tion. E-an Zen provided the staurolite sample and supervisedJane H. Hammarstrom who prepared and characterized thesample. A FORTRAN program used to calculate the Schottkythermal functions was kindly provided by Robert Chirico. Wethank our U.S. Geological Survey colleagues, H. Tren Haseltonand Susan W. Kiefer for their helpful comments.

References

Bancroft, G. M., Maddock, A. G. and Burns, R. G. (1967)Applications of the Mrissbauer effect to silicate mineralogy-I.Iron silicates of known crystal structures. Geochimica etCosmochimica Acta. 31 . 2219-2246.

Dickinson, B. L. and Smith, G. (1976) Low-temperature opticalabsorption and Mossbauer spectra of staurolite and spinel.Canadian Mineralogist, 14, 206-215.

Friedberg, S. A., Cohen, A. F. and Schelleng J. 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 some equilibria in 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. and Robie, R. A. (l9El) Heatcapacities of the alkali feldspars between 350 and 1000 K fromdifferential scanning calorimetry, the thermodynamic func-tions of the alkali feldspars from 298.15 to 1400 K, and thereaction quartz + jadeite = analbite. American Mineralogist,66,1202-1215.

Hill, R. W. and Smith, P. L. (1953) The anomalous specific heatofferrous ammonium sulphate. Physical Society of London,Proceedings A, 66, 22E-232.

Hoschek, G. (1967) Untersuchungen zum stabilitdtsbereich vonchloritoid und staurolith. Contributions to Mineralogy andPetrology, 14, 123-162.

Hoschek, G. (1969) The stability of staurolite and chloritoid andtheir significance in metamorphism of 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, l-53.

Kittel, C. (1976) Introduction to Solid State Physics. John Wiley& Sons, Inc., New York.

Klotz, I. M. (1950) Chemical Thermodynamics. Prentice-Hall,Inc. Englewood Clifis, New Jersey.

Krupka, K. M., Robie, R. A., and Hemingway, B. S. (1979)High-temperature heat capacities of corundum, periclase, an-orthite, CaAlzSi2OE glass, muscovite, pyrophyllite, KAlSirOsglass, grossular, and NaAlSi3Os glass. American Mineralogist,64. E6-101.

Lewis, G. N., and Randall, M. (1961) Thermodynamics. Revisedby Pitzer, K. S. and Brewer, L., McGraw-Hill Book Co., NewYork.

Lyon, D. N. and Giauque, W. F. (1949) Magnetism and the thirdlaw of thermodynamics. Magnetic properties of ferrous sulfateheptahydrate from I to 20 K. Heat capacity from I to 310 K.Journal ofthe American Chemical Society, 71,1647-1656.

Morimoto, N. (1959) The structural relations among three poly-morphs of MgSiO3-enstatite, protoenstatite, and clinoensta-tite. Carnegie Institution of Washington Year 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 heatcapacity anomalies in uranium dioxide and neptunium dioxide.Journal of Chemical Physics, 21, 1884.

Pankratz, L. B. and Kelley, K. K. (1964) High-temperature heatcontents and entropies of akermanite, cordierite, gehlenite,and merwinite. U.S. Bureau of Mines Report of Investiga-tions. 6555.

3 1 8

Pigage, L. C. and Greenwood, H. J. (1982) Internally consistentestimates 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 stabilityof 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 between 0.4 and 5.3 K. Physical Review B, 6,4301-4309.

Regnard, J. R. (1976) M<issbauer study of natural crystals ofstaurolite. Journal de Physique, Colloque C6, 3'7,797-800.

Richardson, S. W. (1966) Staurolite, Carnegie Institute of Wash-ington Year Book, 65, 24E-252.

Richardson, S. W. (1968) Staurolite stability in a part of thesystem Fe-Al-Si-O-H. Journal of Petrology, 9, 467-488.

Robie, R. A. and Hemingway, B. S. (1972) Calorimeters for heatof solution and low-temperature heat capacity measurements.U.S. Geological Survey Professional Paper 755.

Robie, R. A., Hemingway, B. S. and Takei, H. (1982) Heatcapacities and entropies of Mg2SiOa, Mn2SiOa, and Co2SiOabetween 5 and 380 K. American Mineralogist, 67, 470482.

Robie, R. A. and Hemingway, B. S., and Wilson, W. H. (1976)The heat capacities of Calorimetry Conference copperand of muscovite KAlr(AlSi3)Oro(OH)2, pyrophyl l i reAl2Si4Oro(OH)r, and illite K:(AlzMg) (Si1aAl2)Oa6(OH)s be-tween 15 and 375 K and their standard entropies at 298.15 K.U.S. Geological Survey Journal of Research, 4,631-644.

Robie, R. A., Hemingway, B. S. and Wilson, W. H. (1978) Low-temperature heat capacities and entropies of feldspar glassesand of anorthite. American Mineralogist, 63, 109-123.

Roth, W. L. (1964) Magnetic properties of normal spinels withonly A-A interactions. Journal de Physique, 25,507-515.

Runciman, W. A., Sengupta, D. and Marshall, M. (1973) Thepolarized spectra of iron in silicates. L Enstatite. AmericanMineralogist, 58, 444450.

Runciman, W. A., Sengupta, D., and Gourley, J. T. (1973) Thepolarized spectra of iron in silicates. II. Olivine. AmericanMineralogist, 58, 451456.

Schottky, W. (1922) The rotation of atomic axes in solids (withmagnetic, thermal and chemical applications). PhysikalischeZeitschrift. 23. 448-455.

Scorzelli, R. B., Baggio-Saitorvitch, E. and Danon, J. (1976)

Mcissbauer spectra and electron exchange in tourmaline andstaurolite. Journal de Physique, Colloque C6, 37, 801-805.

Smith, J. V. (1968) The crystal structure of staurolite. AmericanMineralogist, 53, I 139-1 155.

Stout, J. W. and Catalano, E. (1955) Heat capacity of zincfluoride from 1l to 300 K. Thermodynamic functions of zincfluoride. Entropy and heat capacity associated with the anti-ferromagnetic ordering of manganous fluoride, ferrous fluo-ride. cobaltous flouride. and nickelous fluoride. Journal ofChemical Physics, 23, 2013-2022.

Takduchi, Y., Aikawa, N., and Yamamoto, T. (1972) Thehydrogen locations and chemical compositions of staurolite.Zeitschrift fiir Kristallographie, 136, l-22.

Ulbrich, H. H. and Waldbaum, D. R. (1976) Structural and othercontributions to the thirdlaw entropies of sificates. Geochi-mica et Cosmochimica Acta. 40. l-24.

Weller, W. W. and Kelley, K. K. (1963) Low-temperature heatcapacities and entropies at298.15 K ofakermanite, cordierite,gehlenite, and merwinite. U.S. Bureau of Mines Report ofInvestigations 6343.

Westrum, E. F., Jr. (1983) Lattice and Schottky contributions tothe morphology of lanthanide heat capacities. Journal ofChemical Thermodynamics, 15, 305-325.

Westrum, E. F., Jr., Essene, E. J. and Perkins, D., III (1979)Thermophysical propert ies of the garnet grossular:Ca3Al2Si3O12. Journal of Chemical Tbermodynamics, 11, 57-66.

Woodhead, J. A. (1977) The crystallographic and calorimetriceffects of Al-Si distribution of the tetrahedral sites of melilite.Ph.D. dissertation, Princeton, University Microfrlms, AnnArbor, Michigan.

Yardley, B. W. D. (1981) A note of the composition and stabilityof Fe-staurolite. Neues Jahrbuch fiir Mineralogie Monats-chefte. H3. 127-132.

Zen, E-an (1981) Metamorphic mineral assemblages of slightlycalcic pelitic rocks in and around the Taconic allochthon,southwest Massachusetts and adjacent Connecticut and NewYork. U.S. Geological Survey Professional Paper ll13.

Manuscript received, March 3, 1983;accepted for publication, October 3, /983.