AmericanMineralogist, Volume 69, pages307-318, 1984
Heat capacity and thermodynamic functions for gehleniteand staurolite: with comments on the Schoitky anomaly in the heat capacity of staurolite
Bnucr S. HeutNcwAY AND Rlcneno A' RostB U.S. Geological Survey Reston, Virginia 22092
Abstract
The heat capacitiesof a synthetic gehleniteand a natural staurolite have been measured from 12and 5 K, respectively,to 370K by adiabaticcalorimetry, and the heatcapacities of staurolite 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 entropyof gehlenite,CazAlzSiOr, at 298.15K and l bar is 210-1t0.6J/(mol'K), which includes a configurational contribution of 11.506J/(mol ' K). The entropy of staurolite at 298.15K and I bar is reportedfor two compositionsas 1019.6112.0J/(mol ' K) for H2Al2 FeaAll5,SiaOasand ll0l.0-r12.0 J/(mol ' K) for (H3Alr.rsF4.to)C'e3.tzf4iaTi6.66Mn6.62 Alt.rs)(Mgo.aaAlrs.zdSieO+ewhere the configurationalentropy contributionsare 34.6 and 121.0J (mot . K), respectively.In addition, the entropy value reported for the second staurolite composition contains an additional l0 J representingthe estimated contribution of the magnetic entropy below about 5 K.
lntroduction lenite was annealedat 1525"Cfor 20 hours from a glassof gehlenite The annealedsample was crushed The heat capacities of gehlenite were measured be- composition. less than 150 mesh was removed' The tween 12 and 380 K in this study in order to reduce the and material masswas 28.0825g. The cell parameterswere a = uncertainty associatedwith the rather large extrapolation sample andc : 5.06747(lDland the calculatedcell necessaryto obtain the entropy contribution below 50 K 7.68658(23)A volumewas 9.01559(51)J/bar (Woodhead, 1977 , Table 3' from the older heat capacity data that were measured 3). Woodhead also reported that l0% of the glass re- between50 and 298 K by Weller and Kelley (1963).High- after the 20 hours of annealing. temperatureheat-content data for gehlenite were report- mained The chemical and physical properties of the staurQlite ed by Pankratz and Kelley (1964). were describedby Zen (1981,Table 4, page124, The heat capacitiesof staurolite were measuredin this sample The sample representeda separateof study between 5 and 368 K by low-temperatureadiabatic sample 355-1). staurolite from the Everett Formation collected calorimetry and between 340 and 900 K by differential natural near Lions Head, Conn. The crushed sample was dry scanningcalorimetry. We are not aware of previous heat- sieved to remove material smaller than 150 mesh. The capacity measurementsfor staurolite. The single set of mass was 31.9650g for the low-temperature heat-capacityresults has been corrected to two staurolite sample measurementsand 39.900mg for the differ- compositions, and estimatesof the Schottky heat capaci- calorimetric calorimetric measurements' ty have been made upon the basis of several simple ential scanning models for determining the lattice heat capacity for results staurolite. Similarly, simple models have been used to Experimental estimateconfigurational entropy terms for each staurolite The low-temperature adiabatic calorimeter and the formulation. methods and procedures followed in this study are de- scribedelsewhere (Robie and Hemingway,1972;Robie et Materials al.,1976and 1978).The heat capacitiesof staurolitewere The gehlenite sample was a portion of the sampleused measured from 340 to 900 K by using a differential by Woodhead (1977). A complete description of the scanning calorimeter and following the procedures out- sample preparation and of the physical and chemical lined by Krupka et al. (1979) and Hemingway et al. properties of the sample was given by Woodhead. The (1981).The onsetof decompositionofthis naturalstauro- sample was designated75001H by Woodhead. The geh- lite samplewas 910t10 K, at a heating rate of l0 trUmin. 0003-004)V84l030,{-0307$02.00 307 308 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE
The experimental specific heats for gehlenite and stau- Table 2. Experimental specificheats for staurolite. Series8 and 9 rolite are given in Tables I and 2, respectively, in the were results obtained by differential scanningcalorimetry chronological order of the measurements.The data have (Robie been corrected for curvature and Hemingway, r!rp. to;:lit" r.rp. to;:::t" r.rp. tt;:lit" 1972)but are uncorrected for chemical impurities. J/(r. r) I' J/(r. f,) K J/(s. x) Thermodynamic properties of gehlenite and staurolite 3Crl ar I S.r1.r 5 3.rla.9 The measured specific heat data were graphically ex- 29E.t2 0.7615 104.r3 0. 1902 {50.0 0.96t{ 304.E5 0.7152 r09.73 0. 2096 460.0 0.979r trapolated to 0 K from a plot of CIT vs. l. A more 3lt. t5 0.7E77 I I 5. 37 0.2297 {69.9 0. 9853 t19.09 0.8007 t2l. t3 0.2507 a79.9 0.995r completedescription of the treatment of the low-tempera- 325.35 0.El3t t26.92 0.27t5 {09.9 r.00tl ture data for staurolite is given in a subsequentsection. t32.67 0.2924 r99.9 r.0r37 8.81a.2 l3E.3E 0.lttl 169.9 0.96{3 Smoothed values of the thermodynamic functions of lra.0r 0.3335 at9.r 0.9901 heat capacity, 333.4t 0.E253 t49. t5 0. t537 489.t 0.9160 C!; entropy, Si, or entropy increment, Sfr 340.62 0.t366 155.t0 0. Itt5 {99.E r.0027 - S$; enthalpy function, (Ift - Iil)lT; and Gibbs energy 311.72 0.4473 161.03 0. t932 509.t 1.0076 - 354.75 0.E5t0 t66.66 0.4125 519.r t.0r2t function, (GI Iif;)lT; where r is the reference tempera- 361.tt 0. t679 529.0 r.0l18 ture, are given in Tables 3 through 7 for gehleniteand for 36t.66 0.t7t9 8.r1.r 6 tl9. E t.0262 tt9. E t.0321 two compositions of staurolite as (H3Al1.l5Feot.toxf'er'.t, 8.r1.. I 172.37 0. t3l7 t59.E 1.0393 r78.03 0.{509 569.E r.047r Fefi*roTio.orMn6.62Al11e)(Mg6.aaAl15.26)SiEO4s and as 4. t0 0.003254 Itt. 76 0.4695 579.E 1.0518 H2Al2FeaAll5SisOas.The reference temperature for the 5.t6 0.003375 It9.46 0.{E7E 5E9.7 t.0596 5.6t 0.003931 195.2l 0.5056 t99,1 t.06a9 low-temperatureheat capacity data is 0 K whereas298.15 6.5l 0.00456E200.95 0.5212 609.7 r.0713 K is 7.57 0.005343 206.tr 0.539t 619.7 1.079t used in the high-temperaturetabulation. 8.58 0.0061772r2.54 0. t5?5 629.1 r.0E75 9.47 0.005905 zr0. 42 0. 574r 639.7 t. O99t 10.3E o.00770E 224.17 0. 5909 649.7 l. Il25 I l. 35 0. 008444 2to.61 0. 6076 619.0 1.0920 Tablel Experimentalspecific heats for syntheticgehlenite t2.49 0.009165 237.09 0.6249 629.t r.0990 13.83 0.009927 243.56 0. 64l 7 639.7 l. lol3 15.31 0.0lo7l 649.7 l. t066 r6.97 0.0t 145 Setl€! 7 659.7 l. lt20 renp. to;::lt" Temp.to;::It. renp. toi::lt' I8.82 0.0t220 669.7 l. ll74 20.86 0.0r29E 249.t4 0.655r 579.7 t. l22l 23.06 0.01375 255.51 O.6709 6A9.7 r. t262 K J/(s.K) K ,r/(e.K) K ,r/(g.K) 25.46 0.01468 26r.88 0.6857 699.7 r. r27E 27.43 0.0r577 264.32 0.7001 709.1 l. r33E 30.19 0.01717 274.a8 0.7146 719.7 r. l39E Series 1 Series 3 Series 7 32.96 0.01922 28t.56 0. 7290 729.7 l.1425 36.41 0.02236 288.29 0.7433 739.7 l. 1477 12.16 0.00I 579 98.01 o.2823 247.63 0.6583 {o.50 0.02675 295.2t 0.7570 719.7 l. l5l0 13.41 0.002245 103.11 0.3009 247.tt 0.6706 44.97 0. 0325r 302.06 0,7699 759.7 l.1493 14.68 0.003088 108.10 0.3180 252.65 0.6803 50.07 0. 0405r ,89. I r. 1655 16.07 0.004?t7 113.26 0.3357 258.32 0.6903 55.82 0.05141 Serte! E 779.7 l.1640 17.68 0.005851 I 18.59 0.3541 264.09 0.7001 7A9.1 l.1705 19.63 0.008314 269.81 0.7092 S€rlea 4 3{0. lo 0. E397 799.1 t. lEO2 21.60 0.01121 Series 4 275.47 0.7186 350. l0 0. E550 849.{ l. l67E 23.64 0.01477 287.20 0.727 6 55.82 0. O5170 360.l0 0.8690 89E.9 r. l96r 26.10 0.01943 110.43 0.3244 256.91 0.7356 61.41 0.06333 370. l0 0. E794 29.03 0.02s69 I 15.64 0.3422 ?92.82 0.7452 56.8E 0.07595 3EO.l0 0.8921 3?.32 0.03408 120.65 0.3591 298.73 0.7538 73.02 0.09191 390. l0 0.9061 35.85 0.04418 I25.58 0.3749 79. ll 0. 1093 400.00 0.9154 39.74 0.05638 Serles 8 84.95 0. r2t0 4 lo. 00 0. 9289 44.16 0.07727 Series 5 90.75 0. 1455 420.00 0. 9394 49.05 0.08865 296.20 0.7503 96.35 0. r638 430. O0 0.9417 54.23 0.1088 135.90 0.4075 302.13 0.7587 101.90 0. IE26 4{0. o0 0.957t 141.13 0.4230 308.00 0.7 67 | Serles 2 146.32 0.4382 313.75 0.7741 151.43 0.4528 53.07 0.1044 156.46 0.4665 Serles 9 57.59 0.1222 161.49 0.4801 62.54 0.1418 166.67 0.4937 310.52 0.77t6 Following Ulbrich and Waldbaum (1976),a zero point 67.75 0.1625 t72.13 0.5078 3t7.32 0.7801 ' 72.73 0.1828 t77.72 0.5220 323.97 0.7893 entropy, S$,contribution of I 1.506J/(mol K) is included 77.25 0.2012 183.20 0.5352 330.57 0.7977 in the Gibbs energy function for gehlenitein Table 3. The 81.85 0.2197 337.13 0.8062 86.91 0.2396 Series 6 343.65 0.8136 entropy ofgehlenite at 298.15K and I bar, is, therefore, 92.30 0.2607 350.12 0.82r0 210.110.6J/(mol . K). The valuesfor the Gibbs energy 180.54 0.5312 356.57 0.8?82 185.99 0.5441 363.26 0.8356 function tabulated for the two staurolite compositions do 19t.27 0.5559 370.l8 0.8435 196 . 55 0.5681 377.07 0.8503 not include a zero point entropy contribution. This contri- 201.90 0. 5802 383.93 0.8556 bution is discussed,at length, below. 207.33 0.5921 2r2.84 0.6039 It should be noted that Woodhead (1977)has consid- 2t8.26 0.6154 223.61 0.6264 ered the question of how disorder in Si/Al on the Tz site 228.94 0.6357 would be reflected in the crystal structure of gehlenite. 234.20 0.6469 239.4t 0.5573 Woodhead concluded that gehlenite forming at low tem- peratures would obey the aluminum avoidance rule for HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 309
Table 3. Molar thermodynamic properties of gehlenite, - So and (Hr - Ho)lT should be 0.2% or less, which is Ca2Al2SiO7. within the experimental uncertainty of the data. The measuredheat capacitiesof natural staurolite were TEI.IP. HEAT ENTROPY ENTHALPY GIBBSENERGY corected to the two compositionslisted above by assum- CAPACITY FUI{CTIOI,I FUNCTION ing the principle of additivity and representingthe sample T c; (s;-s;) (H;-H;)/T -(ci-H;)/T as, fust, for Tables 4 and6, 1665.140 g of staurolite, 4.282 KELVI N J/(mol.K) g of corundum, 1.514g of lime, 4.394g of zincite,0.503 g of FeO, 0.403g of periclase,0.479 g of rutile, 0.426g of .0306 .0104 .0075 11.506 P2O5, 0.468 g of ice, and a deficiency of 0.142 e of 10 .239 .0785 .0583 11.526 15 .9I 4 .279 .2tL I 1.566 manganosite,and second, for Tables 5 and 7, 1703.737g 20 2.42t .725 .555 11.676 pyrophyllite, g 25 4.742 1.501 1.147 11 ,856 of staurolite, 356.263 g of 17.029 of 30 7.690 2.6t3 1.980 12. 136 brucite, 73.399e of magnesioferrite,5.430 g of hematite, 35 11.44 4.075 3.059 t2.522 40 15.69 5.875 4.367 13.014 328.725g of corundum,2.243 g of lime, 10.227e of rutile, 45 20.36 7.989 5.881 13.614 g g manganosite,and 6.510g of 50 25.37 10.39 7.577 14.320 0.710 of P2O5,1.9E6 of 60 36.04 15.95 Lt.42 16.03 zincite. The corrections representa changein the specific 70 47.15 22.34 15.73 18.11 80 58.25 29.36 20.35 20.51 90 69.01 36.85 25.17 23.t9 100 79.25 44.65 30.07 ?6.09 Table4. Low-temperaturemolar thermodynamic properties of ll0 88.91 52.66 34.98 29.19 staurolite,(Hdlr.rsFe6.i,o) Ge35zFe31+Tio.GMn6 g2All rs)(Mgo 44 120 98.04 60.80 39.86 32.44 Al1526)SisOas. The data af,e uncorrectedfor chemicalsite- 130 106.7 68.99 q4.67 35.82 140 1I5.0 77.20 49.40 39.31 configurationalcontributions to the entropy. 150 123.0 85.41 54.04 42.87 160 130.6 o1 RO 58.59 46.51 170 137.9 101.7 63.04 50,19 TEIIP. HEAT ENTROPY EilTHALPY GIBESEIIERGY lB0 144.9 109.8 67.40 53.92 CAPACI TY FUilCTI0ll FUI{CTI0N I On 151.6 117.8 71.65 57.68 200 157.9 r25.8 75.81 61.46 T ci (si-s;) 1xi-Hitrr -(c;-H;)/T 210 164.0 133.6 79.86 65.26 KELVI T{ .t/(mol.K) 2?O 169.7 141.4 83.82 69.06 230 t/f.r 149.0 87.67 72.87 240 180.3 156.6 9t.4? 76.69 a 5.37 2,99 2.09 0.91 250 185.2 164.1 95.08 80.49 l0 t2,32 8.87 5.41 3.40 260 190.0 l7t.4 98.64 84.29 l5 t7.55 14.95 8.7l 6,24 270 194.6 t78.7 102.1 88.08 20 2t.04 20.50 11.38 9.t2 280 199.0 185.8 105.5 91.85 2S 24.03 25.51 13.51 11.90 290 203.2 t92.9 r 08.8 95.61 30 28.19 30.23 15.56 14.57 300 207.2 199.8 tI2.0 99.36 35 34.54 35.04 17.89 I7.15 40 43.05 40.l8 20.47 19.70 310 211.1 206.7 115.1 103.1 45 53.98 45.85 23,57 22,29 320 ?14.9 213.5 118.2 106.8 50 67.15 52.2t 27.25 24.96 330 218.6 220.1 t?t.z 110.5 50 99.59 57.21 36.50 30.70 340 ?z?.0 226.7 124.1 It4.t 70 139.5 85.48 48.29 37.t8 350 tza.L 233.2 t26.9 117,8 80 195.8 107.I 62,53 44.54 360 2?8.1 239.6 t29.7 121.4 90 23t ,3 131.9 79.04 52.83 370 23t.2 245.9 132.4 L?5.0 100 292.6 159.7 97.60 52.11 3B0 233.8 252.1 135.0 128.5 ll0 350.5 190.3 118.0 72.35 273.t5 196.0 180.9 r03.2 89.27 t20 410.0 223.4 139.8 83.54 298.r5 206.s 198.6 111.4 98.66 130 470.2 258.5 162.9 95.64 140 530.3 295.6 187.0 108.6 150 590.0 334.2 211.9 t22.3 160 648.5 374.2 237.4 136.8 170 705.8 {15.2 263.2 152.0 the T2 sites. Following the interpretation given by Wood- 180 751.1 457.r 289.4 167.8 190 814.5 499.7 315.6 184.1 head, the configurational entropy for gehlenite would be 200 866.0 542.8 341.9 201.0 . 5.75J(mol K). Gehlenites synthesized at higher tem- 2t0 915.6 s86.3 368.0 218.3 peraturesappear to have greater disorder leading Wood- 220 963.4 630.0 394.0 236.0 230 1009.2 673.8 4t9.7 254.1 head to conclude that disorder of Si/Al on the T2 site 240 1053.0 7t7.7 445.2 ?72.5 250 1094.8 761.6 470.4 29r.2 would be temperature dependent. 260 I134.7 805.3 495.2 310.1 The heat capacitiesfor gehlenitewere not corrected for 270 tt7z.7 848.8 519.6 329.3 ?80 1208.9 892.I 543.5 348.6 the l0Voof uncrystallized glass (Woodhead, 1977).Robie 290 t243.3 935.2 567.1 368.I et al. (1978)have shown that the heat capacities of the 300 1276.0 9t7.9 590.2 387.7 feldsparsanalbite, high sanidine,and anorthite differ little 310 1306.9 t020.2 612.8 407-4 320 1336.5 t062.2 635.0 421.2 from the heat capacities of glassesof the same composi- 330 1365.0 I 103.7 656.6 447.l tion. These observed difierences yielded calculated dif- 340 t392.2 1144.9 677.9 467.0 350 t4t7 .7 I 185.6 698.7 487.0 ferencesof 0.8 to 2.3% in Sr - So. We can assume(as a 360 1442.0 t225.9 719.0 506.9 first approximation) that the difference in the gehlenite 365 1454.0 1245.9 729.0 516.9 system should be no larger than that in the feldspar 273.t5 1184.3 862.5 527.Z 335.3 298.l5 1270.l 970.0 585.9 384.0 system.Consequently, the uncertainty in the functions 51 310 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE
Table 5. Low-temperature molar thermodynamic properties of assuming that the impurities can be represented by staurolite, H2Al2FeaAll6SisOas.The data are uncorrected for phases for which specific heat data are available. Most chemical site-configurational contributions to the entropy. geochemistsbelieve that ideal additivity does not truly prevail, but where the required corrections are small (i.e., TEi'lP. IiTAT EIITiI(]PY II]TI]ALPY 0t;Lls E,,Eil0Y where the impurities representonly a small percentageof CAPACITY FIIIICTI()II FUI]CTIO]I the sample) the error associated with the correction is -1t;i-rrillr T ci 1sl-sit lrri-rrilrr often less than the uncertainty in the measured specific r(ELVIr,{ J/ (r,rol'r ) heat. The potential errors associatedwith this type of correc- 5 3.38 4.07 2.97 1.10 tion may by the impurity compo- l0 18.28 12.97 3.19 be minimized combining 25.38 21.3C 12-37 9.01 nents into phasesthat are structurally similar to the phase 20 29.03 29.75 16.51 ?5 31.47 19.z',d L7.23 under study (Robie et al., 1976and Klotz, 1950),or by 30 34.71 4?.49 21.54 20.95 usingacorresponding states argument (Robie etal.,1982, 35 40,08 43.23 23.7I 24.44 40 54.05 ?6,?8 27.77 or Stout and Catalano,1955). In either case,the colTec- 45 57.73 29.19 31.03 50 70.12 66.9? 32.65 tions may be applied directly to the measured specific 60 101.1 82.33 41.36 40.96 heats (Robie et al., 1976)in order to provide corrected 70 139.5 100.7 52.55 4S.15 BO 194.6 12?.? 66.10 56.03 thermodynamicparameters as a function of temperature, 90 ?35.4 146.8 82.11 64,72 properties 1C0 294.4 174.4 100.2 74.29 or the integrated may be corrected at a specific temperature (Westrum et a1., 1979). Both procedures 110 348.2 204.B 120.1 84.76 t20 407.5 237.6 141.5 96.11 should yield the same results at the same temperatureif 130 467.7 ?72.6 164.3 103.3 the same componentsare chosen. 140 528:0 309.5 198.1 1?1.4 150 qc7 0 340.0 212,n 135.? Two models are presentedin Table 8 in which the heat 160 647.0 347.B 239.1 149.7 170 704,6 428.8 263.8 164.9 capacities of staurolite as given in Tables 4 and 6 are lB0 760.5 470,6 2',d9.9 180.3 approximated by the summation approach. In model l, I90 sl4.4 513.2 316.1 I97.1 200 366,5 556.3 342.3 214.C the heat capacity of staurolite is approximated by the 210 916.9 599.9 363.5 231.3 summation of the heat capacities of equivalent oxide 220 965.4 643.6 39+.5 249.1 230 I012.n 6i17.6 420.4 267.2 ?41) I 056.6 731.6 4,i5,9 285.5 1099.0 775,6 471,? JUq. J 20c 1139.5 819.5 496,? 323.3 Table6. High-temperaturemolar thermodynamic properties for ?70 I178.1 En3.2 52t),7 342.5 280 rzt4.9 906.7 544.3 351.9 naturalstaurolite. The formulafor stauroliteis givenin Table4. 29t) r249.9 950.0 563.6 A chemicalsite-configurational entropy of 121.0J(mol ' K) and 300 1233.1 oo? a 401.1 an additional10.0 J/(mol ' K) of magneticentropy have been 310 1314.5 1035.5 614.6 addedto the entropyat298.15 K givenin Table4. Theequation 3?0 I 344.6 1077 .7 637.0 440.7 330 t?73.7 1119,5 659.9 460.7 fit the experimentaldata with an averagedeviation of 0,5Vo. 340 1401.6 1161.0 580.3 440,6 350 t427.7 t?02.0 701.3 500.7 360 rq52.3 L?42.5 5?0.7 TEMP. HEAT ENTRUPY ENTHALPY GIBBS BNERCT 365 t464.7 t262.1 731.9 530.7 CAPACIT! FU r,lcTloN I'UNC T ION
273.15 11Ct.9 876.9 52ti.4 34U.6 T' sr (nT-n296)/T -(cT-Ha9E)/T 298.15 r277,1 935.0 587.6 397.4 KELVIN J/(oor.K)
298.15 Il70.l tI0I.0 0.0 r I0l .0 heat (J/g . K, the quantity actually measured)of less than 325 | J49.2 12I4.0 l0E.3 1t05.7 350 14t3.0 1316,3 I99.2 rtl7.t O.lVo for the first case given above for heat-capacity 315 1469.4 14r5.8 282.r rr 33.7 valuesabove 125K and ofless than lVofor valuesfrom 8 400 1519,7 1512.3 357.9 1t54.4 425 r 564.9 1605, E 1t7E.2 to 125K, andfor the secondcomposition, of lessthan 1% 450 1505.8 I 696.4 491.9 I 204.5 475 t643.t L784.2 551.5 t232.7 above 300 K, less thar, 2Vofrom 150 to 300 K, and less 500 1677,4 1E69.4 607.0 t2b2 .4 than 3Vofrom 50 to 150 K. Below 50 K, the sum of the 525 I 708.9 1952.0 658.7 1293.3 550 r738.I 2032.2 707.1 t325.I specific heats of the impurity phasesbecomes negligible 575 1755.3 2IlU.l 152.6 I357.5 600 1790.6 2r85.7 795.3 I 390.4 compared to the measuredspecific heat of staurolite. 625 1814.3 2259.3 E35,5 t423.7 It is both instructive and important to examine the o50 1836.5 2330.9 873.7 L457.3 675 1857.5 2400.b 909.7 1490.9 assumptionsand procedures underlying the corrections 700 t877,2 2468.5 943,9 1524.6 applied to particularly 725 1895.9 2534.7 976.4 1558.3 the specific-heatdata, in light of 750 19t3,6 2599.3 1007.4 r 59r.9 the rather large mass correction necessaryto obtain the 775 1930.3 2662.3 1036.9 1625.5 800 1946,2 2723.9 I 065.0 I 65E.8 heat capacities of staurolite as listed in Tables 5 and 7. 825 1961.3 2784 .O 1092.0 L59Z.O Samples are initially chosen on the basis of chemical 850 i975.5 2A42.7 iIri.8 1725.O 875 1989.3 2900.2 r t 42.5 1757.8 purity and/or approximately correct stoichiometry. Cor- 900 2002.4 2956.4 rr66.2 1790.3 rections for small deviations from ideality are made HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 3ll
Table 7. High-temperaturemolax thermodynamic properties for Table E. Model I and 2 compositional approximations to natural ideal staurolite, H2Al2Fe4Alr6Si8O4s.A chemical site- staurolite. configurationalentropy of 34.6J/(mol . K) has beenadded to the entropy at 298.15 K given in Table 5. The equation fit the experimentaldata with an averagedeviation of 0.EVo. llodeI ilode I Phase t2 t2 TEIiP. HEAT ENTROPY ENTIIALPY CIEBS UN};RGY lilole s iloles CAPACITY FIJITCTION IUNCTION
T C^ sr (Hr-rt298)/T -(cT-d298)/T E Sl02 8.00 Tl 02 0.08 0.08 (Do1. KELVIN J/ K) Al203 8.80 7.47 itr0 0.02 0.02 ?.67 Hzo 1.50 29E.t5 r27l .l l0l9 . 6 0.0 I0I9.6 t25 1357.4 1133.2 108.9 r024.3 Fe203 0.268 0.268 Pyroplrylllte i ?? 350 L422.3 L236.2 200.5 r035.I 375 1479.6 I 336.4 283.9 1052.5 MgO 0.44 0.27 Fe5103 2.67 400 r 530, 7 1433.5 360.2 1073.J 430.5 1097.3 425 1576.8 t527.7 M9(0H) 2 0.17 450 1618.5 r5r9.o 495.3 r123.7 475 1556.6 L701 .6 555.4 ll52.I 500 1691.6 1793.5 511.4 lr82.l 525 L72l .9 r876.8 66J.6 I2I3 , 2 550 1753.9 t957.7 7t2.5 t245,2 +0.2Vo, 515 1761.9 2036.3 75E.4 1277 .9 56 of the model 2 data at 298.15K differs by only 500 1806.0 2rt2.7 80r.6 r3ll.l whereas that of model I is nearly 8Vogreatet. At 900 K, 625 1E32.6 2r87.0 a42.3 1344.6 650 1855.7 2259.3 880.9 r376.4 model 2 differs by -lVo whereasmodel I drfrersby +6%6. 675 LA71.6 2329.8 911.4 l4l2 . 4 - been corrected for the 700 1898.3 239A.4 952.0 t446.4 The values of 51 56 have 125 t9t 7.9 2465.4 985.0 r480.4 transitions in FeO, SiOz, and H2O. Consequently, the 750 I936.6 2530.7 I0t6.4 1514.3 775 1954.4 2594.5 I046.4 l54E.l best overall fit is obtained from model 2. 800 1971.4 2656.8 1075.0 I 581.8 The success of the model 2 components over those 825 1987.7 27r7 .t 1r02.5 1615.3 850 2003,2 2777.3 1128.7 I 648.6 chosen for model I lies in the similarity of the magnetic 875 2018.2 2835.6 rr53.9 1581.7 900 2032.5 2892.6 ll78.l r714.5
components.Two major changesare presentedin model 2. First, approximation of the contribution of OH to the specificheat of staurolite in model I is made by assuming that model I contains ice and water, whereasin model 2, the OH contribution is introduced through pyrophyllite and brucite. Second. the contribution of Fe2+ as FeO in model I was replaced through the introduction of the z40 differencein the specific heat of a mixed Mg-Fe enstatite o and the specific heat of pure Mg enstatite (Krupka et al., 1978,unpublished data), where this difference represent- 620 ed the composition FeSiO3. z u Differenceswere calculatedby subtractingthe summed (J e values U for each model from the smoothed heat capacities 40 given in Tables 4 and 6. These differences are shown in Figure l. At temperaturesgreater than 3fi) K, relatively little advantageis obtained by adopting one specific heat model over the other, with the exception of the effect of EXPTANATION - the a B transition in quartz. The specific heat of a o Model 2 transition in an oxide component is usually removed by a a Model I smoothing process. For the model I data presented in Figure 1, the effect of the c - B transition has been preserved as a visual reminder that when using the r00 200 300 400 500 600 700 800 900 integrated properties (e.g., entropy) approach, an addi- o tional correction may be required in order to maintain TEMPERATUREIN KELVINS smooth estimated values. Fig. l The percentage deviation ofthe model I and 2 (see text) Although local deviations of the model 2 specific heat summations from the measured heat capacity of staurolite. data from the measured heat capacity of staurolite are Positive deviations indicate values of the models which are relatively large at low temperatures,the entropy as 51 - smaller than the observed heat capacity of staurolite. 312 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE contribution of Fe2+ in enstatite and staurolite. The equal to the diference between two Einstein models that cooperative ordering efect in FeO is of a different form are related by two characteristic frequencies fs and 2fs than the apparent Schottky-type anomaly seen in the (see,for example, Gopal, 1966).Therefore, the contribu- dilute paramagnetic salts, staurolite and enstatite; see tion to the heat capacity and entropy of a material from Figure 2. In addition, pyrophyllite is a better approxima- the presence of excited energy states is related to the tion of the contribution of OH to the heat capacity of number of these energy levels and to their degeneracies. staurolite than the separateoxide components of corun- The free ferrous ion has 25-fold degeneracy in the dum, quartz, and ice. The heat capacity data for the ground state that can be reduced or removed, when the natural staurolite sample have been corrected to two ferrous ion is in a crystal, through the combined or arbitrarily chosen compositions as an example of the separateefects of the local crystal field and cooperative procedure. These corrections are only first approxima- spin-orbit coupling. The spatial distribution of the elec- tions becausewe do not have sufficient data to estimate tronic charge of the free ion is spherically symmetrical. mixing properties. These results may be adjusted in a However, when the ion is placed in a crystal the spacial similar manner to estimate values for other staurolite distribution of charges is altered by the distribution of compositions. chargesin the neighboringatoms. Chargedistributions (in the form of lobes and other shapes) that are directed Magnetic entropy of staurolite toward other atoms are elevated to higher energy levels Schottky (1922)postulated that the electronic systemof (splitting of levels) than those that are directed between some atoms in a crystal would undergo excitation be- neighboring atoms. Thus lower symmetry sites produce tween a ground state and higher energy states. Each greater splitting of energy levels. The efect ofthe typical energy state is also characterizedby a degree of degen- crystal field upon the ferrous ion is to elevate (remove) l0 eracy. For a simplified casein which there are two levels, levels beyond that which could be energetically accessi- each with equal degeneracy, it can be shown that the ble. The crystal field also exerts a torque upon the orbital contribution to the heat capacity of a crystal arising from momentum resulting in the orbital momentum not being the presence of electrons in an excited energy level is constant in direction and when resolved in Cartesian coordinates to average to zero. This process is called quenching of the magnetic moment of the angular mo- mentum. In some crystal structures the interaction between the A4 energy states of one atom are not independent of the oB atoms. In such sys- A energy states of similar neighboring tems, a mean energy is required to induce population of o the different energy states and the associated anomaly (typically a I peak) in the heat capacity is called a cooperative anomaly. Examples of cooperative anoma- lies of this type may be found in Robie et al. (1982, a,b) o V3 Ag for antiferromagnetic ordering in fayalite, tephroite and cobalt olivine. E Atr - A noncooperativesystem exists ifthe excitation ofthe 25 o z oo energy states of the atoms in the structure are indepen- F. o dent of the energy levels in the similar neighboringatoms. dt A Where no interdependence exists between the energy o ao levels of similar neighboring atoms, the total energy t5 A contributed is equal to the sum of the energies of the a$ independentlevels and theoretical treatment of the sys- AE EXP[ANATION tem is greatly simplified. o Stourolite The cooperative and noncooperativeanomalies will be o Model 2 ^ Model I called Schottky anomalies and the anomalies in the entropy or heat capacity will be called Schottky contribu- tions. The Schottky contribution is most easily defined where the energy separation of the different levels is 0 50 r00 r50 200 250 300 small. In these cases,the contribution is observedat very TEMPERATURE,IN KELVINS low temperatureswhere the lattice heat capacity becomes Fig. 2. A comparisonof the heat capacity of staurolite and the either a Debye-like contribution or an essentiallynegligi- values obtained from the model I and 2 summations(see text). ble contribution of the measured heat capacity. At low The data are presented as CJT to emphasize the Schottky temperaturesthe noncooperative Schottky heat capacity anomaly in staurolite. anomaly is typically expressedas a bell-shapedpeak that HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 313 is skewed toward higher temperatures.The temperature levels centered at 38 cm-r or less for the anomalies of the peak is related to the separationof the levels and observedin the 15 to 20 K region. Thus, the ferrous ions the amplitude of the peak is related to the ratio of the in staurolite may develop small separationsof the ground degeneraciesof the levels (e.g., Gopal, 1966).Examples state similar to those seen in the dilute ferrous salts. of this type of heat capacity anomaly may be found in the Raquet and Friedberg (1972)measured the heat capaci- results of Hill and Smith (1953).It is far more difrcult to ty of a ferrous salt (FeCl2 . 4H2O) of greater ferrous recognize Schottky contributions to the measured heat concentration than those studied by Lyon and Giaugue capacitieswhere the energy levels have a large energetic (1949)and Hill and Smith (1953). Raquet and Friedberg separationand the contribution occurrencesare at higher observed a sharp )r-type peak consistent with low-tem- temperatures.This subject has been excellently discussed perature antiferromagnetic ordering. However, the ex- by Westrum (1983) and therefore will not be discussed change energy associated with the antiferromagnetic further in this report. ordering was an order of magnitudesmaller than the zero- The magnetic contribution to the heat capacity of a field splitting of the ground state of Fe2+, that is, the )r system may be composed of both a cooperative and a peak for the cooperative processwas at a lower tempera- noncooperative contribution. Raquet and Friedberg ture than the noncooperative anomaly. (1972)concluded that the angular momentum of the 5D Our heat-capacity results do not extend to a low ground state of the Fe2+ ion in FeCl2 . 4H2O was enoughtemperature to rule out a cooperative interaction quenced and that the ground state of the five spin in staurolite nor do they rule out a small separationof a components was fully split by the combined effects of lower doublet of the Fe2* ion. Bearing in mind the spin ordering (cooperative) and crystal field splitting limitations of theory discussedabove and the ambiguity (noncooperative). associatedwith the chemistry of our staurolite sample, Mdssbauer spectra taken at 4.2Khave been interpret- we shall use several simple methods in an attempt to ed by Dickson and Smith (1976),Regnard (1976),and estimate that portion of the magnetic heat capacity and, Scorzelli et al. (1976) as indicating antiferromagnetic consequently,entropy not defined by our measurement. ordering in staurolite. Regnard found an ordering tem- In the preceding section, an empirical case was pre- peratureof 6tl K, and Dickson and Smith obtained7tl sentedin which the entropy of staurolite was shown to be K for the ordering temperature. However, the heat- adequatelyapproximated by the summation of entropies capacity values obtained in the temperaturerange of 5 to ofthe model 2 componentsbut not as favorably predicted 8 in this study do not indicate the strong cooperative by the summation of entropies of the model I compo- exchange that is characteristic of antiferromagnetic or- nents. In this section, we shall examine the theoretical dering. aspects of the magnetic entropy of staurolite, using a Dickson and Smith (1976) have observed ordering modified version of model 2 to approximate the staurolite attributable to antiferromagnetic ordering in FeAl2Oain lattice contribution to the entropy. Mdssbauer spectra obtained at temperaturesbelow 8 K. Staurolite is a paramagneticsalt. The low symmetry of Because of the temperature dependence of magnetic the several sites in which the Fe2* ion may be found susceptibility data, Roth (1964)suggested that antiferro- (Smith, 1968, and Tak€uchi et al., 1972) and the low magneticordering developed in FeAl2Oabelow 8 K, but concentration of Fe within several of those sites (Tak6u- he failed to detect an antiferromagnetic state in FeAl2Oa chi et al.) allow us to initially assume an ideal state for using neutron diffraction. Roth assumed that FeAl2Oa each Fe2+ ion in which the ion interacts only with its failed to show antiferromagneticorder in neutron diffrac- immediate crystal field and not with other Fe ions. The tion because of a strong interaction between Fe2* in same assumptioncan be made for Fe3+ and Mn2*. tetrahedrally and octahedrally coordinated sites that de- The iron transition group paramagnetic salts yield stroyed long range order on the tetrahedral sites. Similar- experimental magneton values consistent with calcula- ly, long range order in staurolite may not develop. tions assuming a quenched angular momentum. Conse- Lyon and Giauque (1949) and Hill and Smith (1953) quently, the contribution of the electronic system of the measuredthe heat capacities of the dilute paramagnetic iron transition group ions to the entropy is Rln(2S + 1), ferrous salts ferrous sulfate heptahydrate and ferrous where S is the spin quantum number for which S : 2 for ammonium sulfate hexahydrate, respectively. Neither Fe2* and S : 512for Mn2* and Fe3+ (e.g., see Kittel, ferrous compound showedan anomaly in the heat capaci- r976t. ty that would be consistent with an interpretation of Severalempirical approacheshave been used to extract antiferromagneticordering at low temperatures,although the magnetic contributions to the entropy and/or heat two maxima were observed in the low-temperature heat capacity (e.g., Lyon and Giauque, 1949;Osborne and capacitiesof each phase. These maxima were interpreted Westrum, 1953;Stout and Catalano, 1955;and Friedberg to be associatedwith a splitting of the ground state of the et al., 1962). Osborne and Westrum assumed that the ferrous ion into two levels of equal degeneracywith a lattice heat capacity could be approximated by the heat separationof 3 to 6.5 cm-r that gave rise to the specific- capacity of an isomorphousdiamagnetic phase containing heat anomalies at 2 to 4 K and a second group of three a similar cation. Lyon and Giauque, and Stout and 3t4 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE
Catalano using a similar approach, corrected the heat Rln(2S * 1), and, because at room temperature we are capacity of the isomorphous diamagnetic phase using a presumably at a temperature sumciently greater than the corresponding-statesargument. Friedberg et al. assumed maximum in the Schottky anomaly to assumethat there is that the lattice heat capacity behavedlike that ofa Debye an equal distribution among the spin states and hence a solid having Cp n T3 and that the magnetic contribution constant magneticcontribution to the entropy, why do we above the Schottky anomaly should go to zero as ?-2. worry about the specifics of the lattice and magnetic Friedberg et al. plotted CpTz as a function of T5 and fit entropies at low temperatures?". The answer lies in the the data with a straight line. The slope of this line energetics of the system. Should a cooperative interac- represented the best estimate of the constant for the tion exist, then the zero-splitting should be large com- Debye lattice approximation. pared to the exchange energy, and the specific heat of The use of an isomorphous diamagnetic phase as a staurolite should exhibit a cooperative anomaly at a N€el model for the lattice heat capacity of a paramagnetic point at some temperature less than the maximum in the phasecan be theoretically justified only if we assumethat Schottky anomaly, as was shown in the work of Fried- the Einstein and Debye temperaturesof the model differ berg et al. (1962)for FeCl2 . 4HzO (also see Kittel, 1976, little from those of the true lattice and we recall the Chapt. 14 and 15). Alternatively, should the magnetic additive properties of the Schottky anomaly given in the contribution of the Fe2* ion to the entropy of staurolite first paragraph of this section. arise from a splitting of the magnetic sublevels into an None of these procedures is directly applicable to an upper triplet and lower doublet as is commonly seen in interpretation of the Schottky anomaly in staurolite. No Fe2+paramagnetic salts (Friedberg et al., 1962and Lyon heat-capacitydata exist for a diamagneticphase isomor- and Giauque, 1949),then a substantialcontribution to the phous with staurolite. Furthermore, the approachused by entropy could arise below 4 K from a splitting of the Friedberg et al. (1962)assumes that all the paramagnetic lower doublet. Without a reasonably valid model for the ions experiencethe same zero-field splitting, that is, that magneticheat capacity distribution, we cannot determine all the paramagnetic ions reside in similar lattice sites what portion of the magnetic heat capacity has been having essentially identical crystal fields. Smith (1968) measureddirectly with the calorimeter. and Tak€uchi etal. (1972)analyzed gamma-ray resonance We may calculate the magnetic entropy for the iron spectra for staurolite and showed that the Fe site is only transition group ions to be 44.1 J/mol . K or 43.2 77Vo occupied by Fe2+. They have further shown that J/mol . K if we assumeall the iron as the Fe2+ion based only 80Voof the Fe2* ions are located in the Fe sites. upon the corrected chemical analysisfor the sample.The Similar results are given by Bancroft et al. (1967). The lattice entropy may be estimated in two ways, neither of structure analysis of staurolite by Smith (1968) locates which is very rigorous. Fe2* in the Fe site (tetrahedra)and in the A(3A), A(3B), A first approximation to the lattice heat capacity may U(l), and U(2) octahedra(using Smith's notation). The be obtained from a plot of CrT2 vs. T5 following, for U(1) and U(2) octahedra are larger than the Al(3A) and example, Friedberg et al. (1962).Using the roughly linear A(3B) octrahedra. Manganeseis located in the U(1) and trend for the experimental data in the 20 to 30 K region, U(2) octahedra. Smith noted that the Fe3+ reported in we obtain equation(l) chemical analysesof staurolites may represent oxidation during the analysis procedure because the Mcissbauer cp = 5890r-2+ 8l.25xlo-5?3 (l) pattern does not contain ferric iron peaks. Assuming that the electric fields produced by the from which we estimate the lattice heat capacity as CL = neighboring atoms at the A1(3A) and Al(3B) sites are 81.25xl0-5T3. The heat capacityderived from this equa- essentiallyidentical, and making similar assumptionsfor tion exceeds the measured heat capacity of staurolite U(1) and U(2) and for the tetrahedral Fe sites, we above 35 K, and the calculated magnetic entropy (mea- conclude that the Fe2* ions interact with a minimum of 3 sured entropy less the estimated lattice entropy of 26.5 different crystal fields which may yield a different distri- J/mol . K) is about half of that predicted from theory. The bution of split sublevels.This effect would not be seenin magneticheat capacity approximation derived from equa- the results of Krupka, Hemingway, and Robie (1978, tion (l) and designatedas model 3 is shown graphically in unpublisheddata) for enstatite becausethe crystal fields Figure 3. of the M1 and M2 sites would be nearly equivalent We are not surprised that the approach followed by (Morimoto, 1959).Consequently, we would expect the Friedberg et al. (1962)fails for staurolite. The Schottky maximum in the Schottky anomaly found by Krupka et anomaly reported by Friedberg et al. was located at about al. (1978,unpublished data) and shown schematicallyin 3 K where materials behave more like Debye solids than the model 2 data set to be more clearly defined and to they do at the 20 to 30 K temperature range of the represent a smaller energy spectrum than that seen in staurolite anomaly. Where multiple Schottky anomalies staurolite, as may be seen in Figure 2. can be expectedto be superimposedupon each other, as Somemay ask, "If we know the approximate contribu- in the case of staurolite, a component of the lower tion of the iron group transition ions to the entropy, temperature Schottky anomalies may contribute to the HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 3t5
at 170 K is 42.4 J/mol . K. This value represents about 96% of the theoretical magnetic entropy. We present two additional estimates of the magnetic heat capacity of staurolite in Figure 3. In the first case, : 14 o the lattice heat capacity estimatesfrom equation (2) were E subtractedfrom the observed heat capacity of staurolite. t In the second case, following the procedures outlined by (1962), (q Friedberg et al. we may estimate the averaged ii separationof an assumedupper triplet of the ground state of the Fe2+ion as 38.8 cm-l from the coefficientof T-2 \ term in equation (l) and, following the equationsgiven by Lewis and Randall (1961, p. 423), we calculate the \ magnetic entropy and heat capacity by assumingall iron o 20 ''o ''{o 160 '€o as Fe2+. For convenience,this shall be designatedmodel ::"*Jr*.,:'-,,;i: 4. Also following Friedberg et al., one may calculate an averageseparation of 30.7 cm-r from the temperatureof Fig. 3. Estimatesof the magneticheat capacity of staurolite. the maximum in the Schottky anomaly. Thediamonds represent the values obtained assuming the lattice Becauseof the complexity of the staurolite structure, heatcapacity (model 3) obtainedfrom equation(l). The open we cannot expect to be able to extract physically mean- squareswere obtained assuming the lattice heat capacity (model ingful data regarding the splitting of the ground state of 2) obtainedfrom equation(2). The trianglesand circleswere calculatedfrom the equationsof Lewis and Randall(1961), the iron group transition ions in a particular site in assumingan uppertriplet anda lowerdoublet with a separation staurolite from the measuredheat capacity data, because of 38.Ecm-t and30.7-t respectively, as model 4. the heat capacity is an average of all such effects. It is unlikely that either of the postulated energy levels is completely degenerateas we have assumed. However, slope derived from the data fit as Ce'F vs.?6, causing an Friedberg et al. (1962)have shown that, even though the error in the estimate of the lattice component. number oflevels and their distributions cannot be unique- An alternate approximation to the lattice heat capacity ly determined, one can eliminate some arrangementsby may be made using the model 2 summation discussed examining the variation of the maximum of the Schottky above combined with the version of the corresponding- anomaly, C.u*, with the various arrangementsof levels statesargument presented by Lyon and Giauque (1949). and distributions. Gopal (1966)presented a similar argu- Lyon and Giauque (1949) found the ratio of the heat ment. For staurolite, we find that C-.* from each approx- . capacity of FeSOa 7H2Oto the heat capacity of diamag- imation is close to the predicted C."* : 0.62R for the . netic ZnSOa 7HzO, both taken at the sametemperature, model of energy levels used above. to vary linearly between 65 and 200 K. If we substitute Adequate measurements of paramagnetic resonance the heat capacity of the synthetic MgSiO3(Krupka et al., and susceptibility for staurolite have not been found in 1978,unpublished data) for the calculated heat capacity the literature. Runciman et al. (1973) have calculated a of FeSiO3used in the model 2 approximation, then the scaled model 2 c,an be used as an estimate of the heat capacity of a diamagnetic phase for staurolite in the | 006 procedure described by Lyon and Giauque. N In Figure 4, we present a plot of the ratio of the heat ,t' r oos capacity of staurolite, Cp.. to the heat capacity of the 4_ u t oo,o scaledmodel 2 summation,Cp,2. Between 170 and 350K, F the ratio varies linearly. We can approximate the lattice d loo3 heat capacity of staurolite from equation (2) if we assume U that the model 2 summation is a reasonableapproxima- * rooz tion to the lattice heat capacity at room temperatureand if U ? roor we assumethat the ratio maintains the same relationship - at lower temperatures. t0L t50 cp.Jcp.z= 1.000+ 3 x l0-5(T- 160.6) (2) IEMPERATURE,IN KETVINS The construction of this model requires the that total Fig. 4. Ratio of the measuredheat capacity of staurolite to the thermal contribution to the excess heat capacity arising heat capacity calculated at the same temperature from the from the electronic system be fully developed below the modified version of the model 2 approximation discussedin text. temperature at which the ratio of Cp,JCp,z becomes The linear equation derived from this ratio is usedto estimatethe linear. The magnetic entropy calculated from this model lattice heat capacity of staurolite below 100 K. 316 HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE separation of 1.5 cm-l for a lower doublet for Fe2* in suggestthat the measuredheat capacity of staurolite and octahedral coordination in enstatite. They reported un- the extrapolation of these data to 0 K underestimatethe published paramagneticspectrum data in support of their magneticcontribution to the entropy of staurolite. On the interpretation. Similarly, Runciman et al. (1973)calculat- basis of the evidence and observationspresented above, ed a splitting of 0.27 cm-r for Fe2* in octahedral coordi- limits can be placed upon the error in the entropy of nation in olivine. Friedberg et al. (1962)suggest a splitting staurolite attributable to unresolved magnetic entropy of less than 0.8 cm-l for the lower doublet for Fe2* in below 5 K as 10t10 J/mol . K. octahedral coordination in FeCl2 . 4H2O. Consequently, it is reasonableto assumethat the crystal field of stauro- Chemical site-configurational contributions to the lite would causea small separationof the lower doublet of entropy of staurolite the ground state of Fe2+. Because our specific heat Ulbrich and Waldbaum 0976\ have calculated the measurementsfor staurolite show a continuous decrease chemical site-configurationaland the magnetic contribu- (within the limits of experimental accuracy) both in the tions to the entropy of staurolite. These calculations are absolutevalue and in the estimatedmagnetic contribution based upon a simplification of the occupanicesreported below 15 K, we can safely assume that if a split lower by Smith (1968).For a chemical composition for stauro- doubletexists, the separationmust be lessthan 0.8 cm-r. lite as HaFeaAllsSi6Oas,Ulbrich and Waldbaumgave 53.5 If model 4 were a fair representationof the behavior of J/(mol ' K) for the magnetic entropy (therefore assuming Fe2* in staurolite, then an entropy contribution of Rln 2 all iron as Fe2*) and 23.0Ji(mol . K) for the chemical site- per mole of Fe2+ would be developedbelow I K. This configurational entropy. entropy contribution would be added to the values calcu- Smith (1968)and Tak6uchi etal. (1972\have shown that lated from the model 2 and 3 approaches,yielding 60.9 the formula for staurolite adopted by Ulbrich and Wald- and 45.0 Jimol . K, respectively, for the magnetic entro- baum(1976) is too idealized,as it requiresnearly halfthe py. The model 4 heat capacities are not a good represen- iron to be in the ferric state for electroneutrality, which is tation of either the model 2 or 3 estimatedheat capacities. at variance with experimental results showing iron to be Although the peak temperatures and maxima values as predominantly in the ferrous state. N6ray-Szab6 and derived from the model 2 and 3 approximations are Sasv6ri (1958) have given the formula HzFe+AheSisO+a generallyconsistent with these values derived from mod- for staurolite which requires all iron to be in the ferrous el 4, the agreementin estimated heat-capacity values is state for electrostatic balance. Smith noted that this particularly poor at temperaturesbelow the maximum in formula conflicts with the water contents reported by the Schottky anomaly where the lattice heat capacity Juurinen (1956).Tak€uchi et al. reported a substantially contributions becomenegligible. Even when a separation lower water content for the staurolite they studied than of 30.7cm-r lsee discussionof model 3 above)is consid- that found by Juurinen, but they still require three hydro- ered, the slope of the Schottky anomaly at temperatures gensper 48 oxygens. below the maximum is not consistent with the theoretical On the basis of an analysis of the location of hydrogen values calculated from model 4 (see Fig. 3). in staurolite and eight chemical analyses for staurolite, Although several explanations for the difierence be- Takduchi et al. (l972'l have shown that the ideal staurolite tween the theoretical and experimental estimated curves should have between 2 and 4 hydrogens per 48 oxygens. could be presented, we think that the mismatch reflects Substantial substitutions of divalent Mg for Al and of Al the antiferromagnetic ordering observed by Scorzelli et for Si can lead to higher water contents in staurolite. al. (1976),Dickson and Smith (1976),and Regnard(1976). Thus, we may take the two formulations of Takduchi et The lack of a pronouncedanomaly in the low temperature al. cited above to represent the two limiting cases for heat capacity of staurolite is not inconsistent with this ideal staurolite. interpretation when one considers the concentration of Smith (1968) has shown that Al and Fe are found in chemical impurities and the non-ideal distribution of Fe2+ slightly higher concentrations in the A1(3A) sites as in natural staurolite, where both effects would contribute compared to Al(3B). The Al(3) octahedra cannot accom- to a broadeningofthe peak associatedwith spin ordering. modate concurrent occupancy of an octahedral cation Regnardand Scorzelliet al. have noted that at4.2Kthe and hydrogen (Takduchi et al., 1972). This limitation quadrupole interaction is of the same order of magnitude would imply a correspondingly higher occupancy of hy- as that produced by magnetic interactions. drogen in the A(3B) octahedra(the P(lB) sites of Takdu- A calculation of the magnetic entropy of staurolite chi et al.). Tak6uchi et al. found nearly identical occupan- based upon the model 2lattice approximation discussed cy of hydrogenin the P(lB) and P(lA) sites(where P(lA) above yields a value of about 42 Jlmol . K at tempera- is located in the Al(3A) octahedra). Consequently, we tures sufficiently larger than the temperatureof the maxi- may treat the Al(3) octahedra as being identical, without mum in the Schottky anomaly to allow us to assumethat causinga significanterror in our estimatesof the chemical the magneticcontribution is constant. Although no claims site-configurationalcontribution to the entropy of stauro- are made herein for the absolute accuracy of our lattice lite. model. we think that the model is sufficientlv accurate to Following the procedures and assumptionsoutlined by HEMINGWAY AND ROBIE: GEHLENITE AND STAUROLITE 317
Ulbrich and Waldbaum (1976)and using the site occupan- Dickinson, B. L. and Smith, G. (1976)Low-temperature optical cy data of Smith (1968)as a guide, we may estimate 34.6 absorption and Mossbauer spectra of staurolite and spinel. and 121.0J/(mol . K) for the chemical site-configurational CanadianMineralogist, 14, 206-215. entropy contribution for staurolite having the composi- Friedberg, S. A., Cohen, A. F. and SchellengJ. H. (1962)The specific heat of FeCl2 ' 4H2O between 1.15 and 20 K. Journal tions H2Al2FeaAll6Si6Oasand (H3Al1.1rFe.6.io)tn"3.t, of the Physical Society of Japan, 17, 515-517. FeSj4Tio.gEMno.ozAlr.rs)(Mg6.aaAl15.26)Si6Oas, respective- Ganguly, J. (196E)Analysis of the stabilities of chloritoid and ly. staurolite and someequilibria in the system FeO-AlzOr-SiOr H2M2. American Journal of Science, 26f,277-29E. Entropy of staurolite Ganguly, J. (1972)Staurolite stability and related parageneses: The entropy of staurolite may be calculated through a Theory, experiments, and application. Journal of Petrology, summation of the calorimetrically determined entropy, 13.335-365. the chemical site-configurationalentropy, and additional Copal, E. S. R. (1966) Specific Heats at Low Temperatures. magnetic entropy not extracted through the measured Plenum,New York. R. A. (l9El) Heat heat capacities, or obtained through an analysis of re- Hemingway,B. S., Krupka, K. M. andRobie, capacities of the alkali feldspars between 350 and 1000K from versed phase equilibrium data. Ultimately, equilibrium differential scanning calorimetry, the thermodynamic func- data must be used to evaluate the accuracy of our tions of the alkali feldspars from 298.15 to 1400K, and the estimates of the additional magnetic and chemical site- reaction quartz + jadeite = analbite. American Mineralogist, configurationalentropies. 66,1202-1215. Our best estimate of the entropy of staurolite as Hill, R. W. and Smith, P. L. (1953)The anomalousspecific heat (H3Ah.rsFeo2.to)(Fez2.izFe3.1+Tro.oaMno.ozAlr.rs) (Mgo.s offerrous ammonium sulphate. Physical Society of London, Alr5.26)Si8O4Eat 298.15 K and I bar is ll0l.0-+12 ProceedingsA, 66, 22E-232. J/(mol ' K); for H2Al2FeaAl16SfuOa6our best estimate is Hoschek, G. (1967)Untersuchungen zum stabilitdtsbereichvon 1019.6+l2 J/(mol . K). An additional10 J hasbeen added chloritoid und staurolith. Contributions to Mineralogy and to the entropy of the natural staurolite composition on the Petrology, 14, 123-162. Hoschek, G. (1969)The stability of staurolite and chloritoid and basis of our analysis of the magnetic entropy. We think their significancein metamorphismof pelitic rocks. Contribu- that the assumptionsthat have been made in calculating tions to Mineralogy and Petrology, 22,2OE-232. the entropy of the latter composition will yield a value Juurinen, A. (1956) Composition and properties of staurolite. that may be consideredto representthe minimum entropy Annals of the Academy of Science Fennical, Series A. III for this ideal staurolite. Geol.,47,l-53. Relatively few experimental phase equilibrium data Kittel, C. (1976)Introduction to Solid State Physics.John Wiley involving staurolite exist in the literature (Richardson, & Sons,Inc., New York. 1966, 1968; Hoschek, 1967, 1969;and Ganguly, 1968, Klotz, I. M. (1950) Chemical Thermodynamics. Prentice-Hall, 1972;Rao and Johannes, 1979;Y ardley, l98l; Pigageand Inc. Englewood Clifis, New Jersey. (1979) Greenwood, 19E2).Of those data, many reactionsinvolve Krupka, K. M., Robie, R. A., and Hemingway, B. S. High-temperatureheat capacitiesof corundum, periclase, an- phaseslike almandine, chloritoid, and Fe-cordierite for orthite, CaAlzSi2OEglass, muscovite, pyrophyllite, KAlSirOs which we good have no estimates of the entropy. The glass,grossular, and NaAlSi3Osglass. American Mineralogist, equilibriurn data are not reversed for reactions involving 64. E6-101. staurolite and iron phases,like magnetite,for which good Lewis, G. N., and Randall,M. (1961)Thermodynamics. Revised estimates of the entropy exist. Consequently, we are by Pitzer, K. S. and Brewer, L., McGraw-Hill Book Co., New unable to further examine the accuracy of our estimates York. of the entropy of staurolite at this time. Lyon, D. N. and Giauque, W. F. (1949)Magnetism and the third law of thermodynamics.Magnetic properties of ferrous sulfate Acknowledgments heptahydratefrom I to 20 K. Heat capacity from I to 310 K. Journal ofthe American Chemical Society, 71,1647-1656. JamesA. Woodheadprovided the gehlenitesample from Morimoto, N. (1959)The structural relations among three poly- materialhe synthesizedand characterized for his PhDdisserta- morphs of MgSiO3-enstatite,protoenstatite, and clinoensta- tion. E-an Zen providedthe staurolitesample and supervised tite. CarnegieInstitution of Washington Year Book, 58, 197. Jane H. Hammarstromwho preparedand characterizedthe N6ray-Szab6, I. and Sasv6ri, K. (195E) On the structure of sample.A FORTRANprogram used to calculatethe Schottky staurolite, HFezAlqSLOz+.Acta Crystallographica, ll, E62- thermalfunctions was kindly providedby RobertChirico. We 865. thankour U.S. GeologicalSurvey colleagues, H. TrenHaselton Osborne, D. W. and Westrum, E. F., Jr. (1953) The heat andSusan W. Kiefer for their helpfulcomments. capacity of thorium dioxide from l0 to 305 K. The heat capacityanomalies in uranium dioxide and neptuniumdioxide. References Journal of Chemical Physics, 21, 1884. Bancroft,G. M., Maddock,A. G. and Burns,R. G. (1967) Pankratz, L. B. and Kelley, K. K. (1964)High-temperature heat Applicationsof the Mrissbauereffect to silicatemineralogy-I. contents and entropies of akermanite, cordierite, gehlenite, Iron silicatesof known crystal structures.Geochimica et and merwinite. U.S. Bureau of Mines Report of Investiga- CosmochimicaActa. 31. 2219-2246. tions. 6555. 318
Pigage,L. C. and Greenwood,H. J. (1982)Internally consistent Mcissbauerspectra and electron exchangein tourmaline and estimates of pressure and temperature: The staurolite prob- staurolite. Journal de Physique, Colloque C6, 37, 801-805. lem. American Journal of Science. 282.943-969. Smith, J. V. (1968)The crystal structure of staurolite. American Rao, B. B. and Johannes,W. (1979)Further data on the stability Mineralogist,53, I 139-1155. of staurolite + quartz and related assemblages.Neues Jahr- Stout, J. W. and Catalano, E. (1955) Heat capacity of zinc buch fiir Mineralogie Monatshefte, 437-M7. fluoride from 1l to 300 K. Thermodynamic functions of zinc Raquet, C. A. and Friedberg, S. A. (1972) Heat capacity of fluoride. Entropy and heat capacity associatedwith the anti- FeCl2'4H2O between0.4 and 5.3 K. PhysicalReview B, 6, ferromagnetic ordering of manganousfluoride, ferrous fluo- 4301-4309. ride. cobaltous flouride. and nickelous fluoride. Journal of Regnard, J. R. (1976) M