Heat Capacities and Thermodynamic Functions for Beryl, Beralrsiuotr

American Mineralogist, Volume 7I, pages 557-568, 1986

Heat capacitiesand thermodynamicfunctions for beryl, BerAlrSiuOtr, phenakite, BerSiOn,euclase, BeAlSiOo(OH)' bertranditeo BeoSirOt(OH)r,and chrysoberyl' BeAl2Oa

B. S. HnluNcw.q,Y U.S. GeologicalSurvey, Reston, Y irgrnia22092 M. D. B.nnroN Departmentof Earthand SpaceSciences, University of California,Los Angeles,Los Angeles,California 90024 R. A. Ronrn, H. T. HLsnr.roN, Jn. U.S. GeologicalSurvey, Reston, Y irginia22092

Ansrru,cr The heat capacities of beryl, phenakite, euclase,and bertrandite have been measured betweenabout 5 and 800 K by combined quasi-adiabaticcryogenic calorimetry and differential scanningcalorimetry. The heat capacitiesof chrysoberylhave beenmeasured from 340 to 800 K. The resulting data have been combined with solution and phase-equilibrium experimentaldata and simultaneouslyfit using the program pHAS2oto provide an internally consistent set of thermodynamic properties for several important beryllium phases.The experimentalheat capacitiesand tablesof derived thermodynamic propertiesare presented in this report. The derived thermodynamic properties at I bar and 298.15 K for the stoichiometric beryllium phasesberyl, phenakite, euclase,and bertrandite are entropies of 346.7 + 4.7, 63.37+0.27,89.09+0.40, andl72.l+0.77 J/(mol'K),respectively,andGibbsfree energiesof formation(elements) of -8500.36 + 6.39, -2028.39 + 3.78, -2370.17 + 3.04, and -4300.62 + 5.45 kJlmol, respectively,and, -2176.16 + 3.18kJ/mol for chrysoberyl. The coefficientscr to c, of the heat-capacityfunctions are as follows:

valid phase ct c2 c, x 105 c4 c, x 10-6 range beryl 1625.842 -0.425206 12.0318 -20 180.94 6.82544 200-1800K phenakite 428.492 -0.099 582 1.9886 -5 670.47 2.0826 200-1800K euclase 532.920 -0.150729 4.1223 -6726.30 2.1976 200-1800K bertrandite 825.336 -0.099 651 -10 570.31 3.662r7200-1400 K chrysoberyl 362.701 -0.083 527 2.2482 -4033.69 -6.7976 200-1800K

whereC!: cr * ctT + crT2* coT-os* crT-2and Zisinkelvins.

phase-equilibriumexperimental data, and a discussionof fNrnonucrroN the petrology of selectedberyllium phases. Recent advancesin technology (Webster and London, All economicberyllium depositsare postmaglnaticand 1979) have improved the mechanical properties of be- related to acidic igneousrocks, generallybiotite granites, granites (Beus, 1966). ryllium products at both room temperature and at ele- but rarely high-silica and alkalic vated temperaturesand have led to a renewedexpansion The deposits are geneticallyrelated to late stagesofpeg- in the use of beryllium in, and perhaps beyond, the tra- matitic processesor to various stagesof hydrothermal ditional ur.as of weapons, space, optical, nuclear, and processes(Jahns, 1955). Historically, beryllium produc- guidance systems; alloy-propirty modification; and, in tion was limited to handpicking large beryl crystalsfrom military aircraft, disc brakes. The renewedinterest in be- beryl-bearing ganitic pegmatites. More recently, beryl- de- ryllium applications has rekindled an interest in the geo- lium has been produced from hydrothermally altered chemistry and thermodynamic properties of beryllium- posits suchas Iron Mountain, New Mexico (Jahns, 1944)' bearing phases.We report here the heat capacities and and Spor Mountain, Thomas Range,Utah (Staatz,1963). derived thermodynamic functions for beryl, phenakite, The pegmatitic process and related hydrothermal pro- euclase,bertrandite, and chrysoberyl.A companion paper cesseshave been reviewed by Jahns (1955) and by Jahns (Barton, 1986) presents an evaluation of solution and and Burnham (1969). 0003404x/86/0304-0557$02.00 557 558 HEMINGWAY ET AL.: THERMODYNAMICDATA FOR SELECTEDBe MINERALS

Table l. Experimental low-temperature heat capacitiesof Table 2. Experimental low-temperature heat capacities of beryl, BerAlrSi6Ors.0.36HrO phenakite, Be,SiOo

Heat Heat Ca,i Tedp. --_: - Heat _ Ileat _ Heat - TenD.' Teup.- feoD.' . reEp' feEp. capaclty capaclty capaclty capacity cApaclty capaclty

K J/(ooL'K) K J/(do1.K) K J/ (uo1'K) K J/(nol-'K) K J/(nol'K) K J/(noI'K)

Serles I SerLe6 2 Serlea 3 Serles I Serleg 1 Serl.es 4

299.16 442.2 169.80 262.6 4.95 0.9516 8.07 0.0130 193.17 57,42 3L5.49 100.7 303.41 447.5 t75.47 272.3 5.33 0.8519 9.15 0.0179 198.80 59.12 318.94 101.7 308.37 452.6 181.1r 281,9 5.77 0.7386 10.18 0.0t90 204.42 62.Or 324.05 103.2 313.36 457.7 186.75 29r,6 6.2L O.7534 r1.38 0.0215 210.03 64,23 328.96 104,6 318.54 462.9 L92.37 300,8 6.72 0.8776 L2,74 0.0327 2r5.63 66.48 333.86 106.0 197.98 309.8 7 .40 0.9821 14.r9 0,O497 22L.22 68.64 338,88 107.4 Ser1e6 2 203.58 318.4 8 .20 L,026 15.79 0.0685 226.81 70.80 343.90 108.6 209.L7 326,6 9.10 L.2L4 L7.55 0.088s 348.92 109.8 54.89 42.60 2!4.7 3 334.8 10.11 1.410 19.50 O,L2L7 Serles 2 353.93 110.9 59.92 5r.45 220.29 343.0 11.23 L,544 2L,66 0.1635 358.91 Lr2.O 64.67 59,99 22s.84 351.2 t2 ,48 r .746 24.O5 0.2273 23r.06 72.44 363.88 113.1 69.96 69.95 231.39 359.0 13.85 L.992 26.12 0.3244 236.45 74.49 368,83 r14.s 76.O5 81.98 236.95 367.L 15 .36 2.29r 29.7L 0.4805 24r.57 76.34 373.78 115.6 82.O7 94.07 242.50 374.3 17 .01 2.699 33.04 0.7246 246.14 78,23 378.7L r16.5 88.13 LO6.2 248.O4 381.7 18.82 1.242 36.77 r.062 252.r1 80.15 94.19 118.4 253.58 388,8 20,84 3.983 45.61 r.910 257.58 82.07 Serles 5 100.21 130.4 2s9.10 395.8 23,O9 4.935 50.85 2.66L 262.99 84.00 106.19 r42.4 264.63 402.8 25.59 6 .259 56.67 3.835 273.76 87.83 297. L3 95.3I LL2.L2 154.2 270.L6 409.4 28.38 8,087 62.9L 5,4L7 279.r7 89.55 302.42 97.26 118.00 166.0 275.68 415.5 31.50 10.56 69.28 7.334 284.53 91.30 r23.85 L77 .6 281.19 422.4 34.99 13.8I 15.65 9.515 289.84 93.07 Serles 6 r29,6't r88.9 286.69 428,8 38.89 18.10 81 .95 rL.7 9 295,L5 94.75 L35.46 200.2 292.16 435.1 43.28 23.87 88.15 r4.08 300.43 96.29 28.15 0.4006 L4L.24 2LL.2 291.62 440,8 48.19 30.89 94.30 16.38 305.68 97.83 29.34 0.4595 146.99 222.0 303.07 446,3 53.69 40.0r r00.39 18.67 310.89 99.47 30.1 9 0.5099 r52.7 2 232.4 308,49 451 .9 LO6.42 21.00 316.08 10r.0 31.11 0.5805 158.43 242.6 Serle€ 4 It2.41 23.38 32.24 0.66s3 r64.13 252.8 f18.34 25.80 Serles 3 33.34 0.1 557 317,36 460.5 L24.24 28.28 14.46 0.8515 322.54 466,3 130. r r 30.7 9 265.51 84.80 35.59 0.9558 327.52 472.8 r35,94 33.25 266.54 85. r4 36.72 1.066 332.52 477.5 L41.75 35.73 267.47 85.76 37.84 r. t7 7 337.7 0 480.7 r47.54 38,22 268.40 86,02 40.08 L.407 342.86 486.0 153.31 40.65 269.37 86.51 41.2L 1.545 159.05 43.07 270.35 87.00 42.32 L.679 L64.7 8 45.50 27L.32 87.00 43.43 L.787 r70 .49 41.94 272,29 86.99 45.65 r.907 generalized 176.18 50.30 273.26 87,2L 46.7 7 2.049 The geochemistryof the beryllium phases 181.86 52.67 274.23 87.61 47.88 2.r9- studiedin this report may be summarizedas follows. Beryl r87 .52 55.05 48.99 2.356 50.10 2.528 is the most abundant beryllium mineral and is most com- 5L.20 2.7L2 monly found in granite pegmatitesand granites. 52.3t 2.963 Beryl is 53.40 3.109 also commonly found in greisensand quartz veins and 54,5r 3.372 occasionally in skarns and other metamorphic rocks. Chrysoberylis the secondmost abundant beryllium mineral; however, the formation of chrysoberyl appears to in Barton (1986).Beus (1966) and Mulligan (1968) dis- require either a local enrichment of aluminum or a re- cussedvarious beryllium deposits. duced silica activity. Chrysoberyl is most abundant in Kelley ( I 939) measuredthe heat capacitiesofbromellite fluoritized skarns and is only occasionallyfound in peg- and phenakite betweenabout 54 and 294 K. Chaseet al. matites. Bertrandite is one of the few beryllium minerals (1974) reported that Kelley's data for bromellite deviate that has a relatively wide occurrenceand is found in most by +500/oat 56 K, *80/oat 100 K, and +10/oat 200 K deposits of beryllium minerals. Bertrandite is present in from more recent measurementsbased upon improved commercial quantities in hydrothermally altered tuffs in technology.Similar systematicerrors can be expectedfor the westernpart ofthe Thomas Range,Utah (Staatz,1963). the heat-capacitydata for phenakite reported by Kelley. In pegmatites,bertrandite forms in the late stages,com- This study was motivated by the need to provide a monly forming as a hydrothermal alteration product of consistentset of thermodynamic functions for important beryl or other beryllium phasesoften with euclase,mus- beryllium minerals to aid in the development of geo- covite, or bavenite coprecipitating as the sink for alumi- chemical models for beryllium ore genesisand to help in num releasedin the alteration process.Euclase is relatively the development of extraction proceduresfor beryllium rare and is generallyfound in lower-temperaturelate-stage obtained from new source materials. To this end, low- hydrothermal vein deposits. Phenakite forms in a wider temperatureheat-capacity measurements of beryl, phen- range of deposits than euclase,but phenakite formation akite, euclase,and bertrandite were combined with high- appearsto be restrictedto depositionalenvironments with temperatureheat capacitiesfor theseand other beryllium- moderate to low aluminum activity. A more complete bearingphases and with phase-equilibriumdata and were discussionofthe petrologyofthese minerals may be found simultaneouslyevaluated. HEMINGWAY ET AL,: THERMODYNAMIC DATA FOR SELECTED BC MINERALS 559

Table 3. Experimental low-temperatureheat capacitiesof Table 4. Experimental low-temperatureheat capacitiesof euclase,BeAlSiO.(OH) bertrandite, BenSirOt(OH),

qarr _ Ilea t lleat -'-. - lleat renp. IIea t reDD.' . fen9. TenD. f enD.' reop. capaclty capaclEy capaci ty L4P4Lr Lt capacl Ey ""fili., K J/(DoI'K) K J/(nor'K) K J/(no1'K) ( J/ (oo 1'K) K J/ (noI'K) K J/ (no 1'K)

Serles I Serles 2 Serles 3 serl.es I se!leg 2 Serles 3

297.9r L26.4 L89.62 18.26 356.97 r45.7 305.3r 228.7 79.70 38.98 259.85 L99.7 301.98 128.1 194.82 81.02 36r.94 r47.3 309.81 23L.9 85.82 44.51 260.79 200.7 307.47 129.a 200.00 83.69 366.89 148.8 3r4.68 234.7 91.86 50.05 26r.7 2 20t.6 313.00 131.8 205.t6 86.32 371.84 L49.7 319 .59 237.8 97.85 262,66 203.4 210,30 88.85 376.76 150.9 324.60 240.4 103.78 61.01 263.60 203.8 Serles 2 2r5.43 91.45 381.68 152.2 329.60 243,r 109.63 66.82 264. s3 205.5 220.55 93 .9 3 334.60 246.2 Lr5 .42 71.88 265,47 207.2 53.05 5.525 225.66 96.37 serles 4 339.59 249,3 T2L.L7 77.46 266.41 208.0 59.97 8.026 230.80 98.8r 344.60 252.3 r26,88 82.89 267.34 zlr.4 66.65 10.37 235.95 101.3 6.03 0.0103 349.62 254.7 r32,55 88.28 268.27 2L3.5 73.85 13.61 24t.09 103.7 6.54 0.0218 354.63 257.9 138.19 93.50 269.20 2L2.9 79 .56 16.42 246,22 106.0 7.72 0 .0295 3s9.63 260,7 143.80 98.71 270,t5 212.0 82.28 L7.77 25L,34 108.2 7.77 0.0187 364.62 262.9 r49.39 104.0 27L.O8 211.3 86.O7 19.68 256.45 110,4 8.60 0.0128 369.60 265.4 154.95 109.0 272,OL 2r2.3 91.13 22,38 26L.54 LLz.5 9.45 0.0162 374.56 269.4 L60,49 tt4 .2 272.95 2LL.L 96.34 25.t2 266,66 I 14.6 10.40 0,0262 379.52 270.4 166.00 119.3 273.88 209.7 102.10 28.28 271,80 116.7 11.5 1 0.0292 l1 7 .49 t24.3 274.81 2r0.1 r07.87 31,55 276,92 118.7 12.75 0.0354 Serles 2 r76.97 r29,3 275.74 211.0 113.60 34.86 282.02 120.'l L4.r2 0.0538 LA2.4 4 r34.3 276,67 209.6 119.31 38.21 287.I2 122.7 15.61 0.0782 5.99 0.0616 187.89 139.1 277.60 2r0.2 r24.96 4r.54 292.19 124,6 r7 .29 0.1I 52 6 .49 0.0666 193.32 143.8 278,53 211.8 130.55 t4.79 297.25 t26.4 19.16 0.1122 6.93 0.r054 r98.74 148.5 279 .46 212.4 136.10 48.08 302.30 128.3 2r.22 0.2398 o.t362 204.L5 t53.2 280.39 2L2.2 14r.61 5L.29 307,33 130.1 23.52 0.3209 8.07 o.L255 209.54 L57.6 28r,32 212.7 L47.O7 54.43 3r2.36 r31.8 26,O9 0.4483 o,L398 2L4.92 L62.r 282,24 2r3.2 15 2.50 57.54 317.38 133.5 28.96 0.6666 9.30 o,1584 220.29 166.5 283.17 2L5.0 157.89 60.62 32.t7 r.004 10.02 o.1984 225.66 170.9 284.09 2t5.6 L63.26 63.66 Serles 3 35.79 L,477 10.87 0.2553 23L.02 L75.2 285.02 216.7 r68.58 66.73 39,84 2.255 11.87 o,27ro 236.38 179.8 287.80 2r7 ,9 173.88 69.73 327.32 136.5 44,37 3.171 13.00 o.3429 24L.75 r84.3 292.4r 220.8 L79.r4 72.7r 332,26 138.0 49.47 4.340 r4.28 o.4390 247.rO 188.7 297,OO 223.9 184.39 75.55 337.r4 r39.7 55.11 6.300 r5.70 0.5818 252.45 193.3 301,59 227.O 342.O2 14r.6 6L.23 4.421 r7.33 o.7720 257.79 197.3 306.1 8 229,8 341.OO r42.9 67,60 10.73 19.14 r .039 263.Lr 203,7 310.76 232.8 351.99 L44.O 2r.L6 L . 436 268.42 2r3.9 3 1s.34 236.O 23.43 r.943 273.79 2to.7 319.91 238.6 25.99 2.546 279 .23 2L2.O 28.85 3.434 284.58 Serleg 4 32.04 4.659 289.84 2L9.2 S*rpr,ns AND APPARATUS 35,60 6.103 295,11 222.6 51.99 16,75 39.60 L287 300.38 225,9 53.69 18.34 Beryl (synthetic emerald) was provided by Richard M. 44,08 10.81 305,64 229.5 54.64 19.29 Vacuum Ventures, Inc. The low-tem- 49.11 L4.29 57,62 22.69 Mandle, President, 54,67 19.60 Serles 62.68 26.92 peratureheat-capacity sample that weighed 25.1618 g, 60.71 67.79 30.28 ,L6 194.6 73.28 33,71 61.O6 29.68 255 'r8.84 correctedfor buoyancy,was made up oflarge, dark-green, 73.43 34.03 256.!3 t96.2 38,16 tabular crystal fragments.The scanning-calorimetersam- 257.O5 t96.1 84.31 43.r1 257.97 L97,O 89.76 48.10 ple was 22.826 mg in a single crystal fragment. The cell 258.9L 198.5 95.17 53.06 parametersare q :0.9286(9) nm and c : 0.9193(4)nm, and the molar volume is 203.27(7) cm3. Sixteen microprobe analyseswere made using analyzedberyl, pollucite, pacity sampleweighed 30.4317g, correctedfor buoyancy. and severalglasses as standards.The averagevalues (weight The scanning-calorimetricsample was 22.837 mg. Mi- percent)were BeO 14.16(assumed), AlrO, 18.12,CrrO, croprobe analysesof similar material (Barton, 1986) re- 0.37, SiO, 65.99,and H2O 1.2 (by weight loss).The ap- vealed only silicon at the level of detection (0.05 wto/ofor proximate formula calculated for the synthetic emerald elements heavier than F). The cell parameters are a: was Ber(AlorruCroo,o)rSiuOr8'0.36HrO.The sample was 1.2472(l) nm and c :0.8253(2) nm, and the molar vol- analyzed for Na, Mg, Fe, K, and Ca, all of which were ume is 37.19cm3. lessthan the level of detection (0.05 wto/o).Heat-capacity Euclase [BeAlSiO.(OH)] was provided by Richard measurementswere also made at elevated temperatures Gaines from material collected in Minas Gerais, Brazll. on chips that had been dried at about 1673K for I h. Microprobe analysis of the sample detected only alumi- X-ray difraction analysis of similarly dehydrated beryl num and silicon. The samplewas analyzedfor F, Na, Mg, showedno changein cell parametersnor the presenceof Fe, K Ca, Cr, and Cs, all of which were below the level secondaryphases. of detection(0.5 wto/ofor F and 0.05 wto/ofor the remaining A phenakite (BerSiOo)sample was obtained from the elements). The cell constants for the sample are a: Wilson Collection (USNM 158142).The sourcewas listed 0.47703(29)nm, b:1.43235(54) nm, c: 0.46317(39) as Brazil. The sample was composed ofclear, glassychunks nm, and p: 100.416(62)',and the molar volume is of about 3 mm diameter. The low-temperature heat-ca- 46.86(6) cm3.The low-temperature heat-capacitysample 560 HEMINGWAY ET AL.: THERMODYNAMICDATA FOR SELECTEDBe MINERALS

Table 5. Molar thermodynamic properties of beryl, Table 6. Molar thermodynamic properties of phenakite, BerAlrSiuO,r.0.36HrO,to 340 K BerSiOo,to370 K

Tedp. Ileat Entropy Enthalpy clbbs energy Temp. IIea t Entropy Enthalpy Glbbs energy capaciEy functlon functlon capaci ty funct 1on funct lon

-/co -Ho r c; r;-r; (H;-H;)/r -(c;-H;)/r r c; r;-r; \rT/Ho -Houo//) /T \ /T

J/ (no1'K) Ke lvin J/ (no1'K)

5 0.140 0.046 0.034 0.012 5 0.002 0,001 0.00r 0.000 l0 0.873 o .327 o.240 0.087 10 0.0r7 0.006 0.004 0.002 t5 2.09r 0.899 o.644 0.255 t) 0.058 0.019 0 .014 0.005 20 3.660 t.704 1.191 0.513 20 0.137 0.046 0 .034 0.012 2) 5,92r 2.745 1.894 0.851 25 0.258 0.087 0.065 0.023 30 9.318 4.I07 2.832 r.27 5 30 0.500 0.154 0,115 0.038 35 13.82 5.858 4.068 r.801 0.900 0.259 o.r91 0.062 40 19.48 8.069 5.627 2 .442 40 1.409 0.412 0.316 0.096 45 26.22 10.75 3.212 45 1 .880 0.606 0.455 0.r41 50 33.84 13.89 9.774 4.tt9 50 2.5L3 0 .834 0.635 0.199 60 5l .57 2L.51 r5.24 6.365 6g 4.643 L.467 1.113 0.354 70 70.08 30.93 2r.7 4 9 .192 10 7.577 2.394 1.818 o.575 80 89.87 4I .57 29.01 t2.56 80 1r.05 3.628 2.75L 0 ,8'l 7 90 110.0 53.32 36.89 16.43 90 14,74 5 .L42 3.877 L,264 r00 130.0 65.94 45.20 20.74 100 18.53 6.890 r .738

t lo 150.0 79,27 53,82 110 22.4s 8.839 6.546 2.293 120 t59,9 93.18 62.66 30.51 r20 26.52 10.97 8.039 2.926 130 189.6 LO7.6 7r.68 35.88 130 30.71 13.25 9.62r 3.631 140 208.8 L22.3 80.79 41.53 140 34.96 r.s.68 r1,28 4 .405 r50 227,4 t37.4 89.95 47.4r 150 39.23 18.24 13.00 160 245.4 t52 .6 99.1.r 53.5r 150 43.48 20,91 r4.77 6.!37 170 263.0 168.0 r08.2 59.79 t70 47.7 2 23.67 16.59 7,O81 180 280.1 183.5 117.3 66.24 180 5r .92 26. 52 18.43 8.087 190 296.9 199.1 L26.3 72.82 190 56.09 29,44 20.31 9.r33 200 312.8 214.8 135.3 19.53 200 60.19 32.42 22.20 1o.22

2ro 328.0 230.4 L44.1 86.34 2LO 64,22 35.45 24.rO 11.35 220 342,7 246.O 93.25 220 68.16 38.53 26.02 L2.52 230 357,L 261.6 100.2 230 72.O2 4r,65 27.93 t3.72 240 371.0 277.r 169.8 107.3 240 75.77 44.79 29.85 r4.95 250 384.2 292.5 178.1 tL4.4 250 79.43 47.96 3r.76 L6.20 260 396.9 307.8 186.3 I21.5 260 82.99 51.15 33.66 l7 .49 270 409.1 323.O 194.3 t28.7 270 86.46 54.34 r8.79 280 42t.O 338.1 202.2 135.9 280 89.82 57.55 37.43 20.L2 290 432.4 353.1 209.9 r43.1 290 93.07 60.76 39,29 2L.46 300 443.4 367,9 2I7 .5 150.4 300 96.20 63.97 4t.L4 22.83

310 453.9 382.6 225.O r57 .6 310 99.20 42.96 24.21 320 464.2 397.2 232.3 764.9 320 102. r 70.37 25.60 330 474.2 4tr.b 239.5 r7 2.2 330 104.8 73.55 4D.)) 27.OO 340 483,6 425.9 246.5 L79.4 340 107.5 76.72 48.30 28.42 273.L5 472.9 327.8 196.8 131.0 350 110.0 79,87 50.03 29.84 298,t5 44r .4 365.2 216.1 r49.0 360 LL2.4 83.00 5t.72 31.28 370 114.8 86.12 53.40 32.72 273.L5 87.53 55.35 Jb'I) L9.2L 298.L5 95.63 63.37 40.80 22.57 weighed33.4966 g, correctedfor buoyancy.The scanning- calorimetricsample was 26.178mg. sampleare q:0.54801(3) rrr, b: 0.94119(7)nm, and Bertrandite [BeoSirOr(OH)r]was obtained from the Field c:0.44288(3) nm, and the molar volume is 34.32 cm3. Museum of Natural History GMNH 6969). The source Low-temperature heat capacitieswere measuredusing location listed was Albany, Maine. Microprobe analyses the intermittent heating method under quasi-adiabatic of the sample detectedonly silicon. A few of the crystals conditions. The cryostathas beendescribed by Robie and were cloudy in appearance.Inspection of some of these Hemingway (1972),the provisional low-temperaturescale crystalsrevealed the presenceof a claylike phase.The cell by Robie et al. (1978), and the electrical measurement constantsfor the sample are a:0.87135(4) rm, !: system by Hemingway et al. (1984). The samples were 1.52677(14)nm, and c:0.4583(3) nm, and the molar sealedin the calorimeter under a small pressureof pure volumeis 91.50(l) cm3.WeightJoss studies indicatedthat helium gas (about 5 kPa). the sample contained 7.4(6) wto/oHrO. The low-temper- High-temperature heat capacitieswere determined by ature heat-capacitysample weighed 22.4678 g, corrected differential scanning calorimetry (DSC) following the pro- for buoyancy. The scanning-calorimetric sample was ceduresoutlined by Heming;wayet al. ( I 98 I ). The samples 25.006mg. were enclosedin unsealedgold pans. The chrysoberyl(BeAlrOo) sample was a tabular crystal The formula weightswere basedupon the 1975 values fragment.The pale-greengrain was opaqueand contained for the atomic weights(Commission on Atomic Weights, 3.1 wto/oFerO. (Fe by microprobe). The scanning-calori- 1976). The formulaweights are 5 44.74, 53 7. 505, I 10. 107, metric sample was 20.429 mg. The cell constantsfor the 145.084,238.230, and,126.973 g, respectively,for beryl HEMINGWAY ET AL.: THERMODYNAMIC DATA FOR SELECTED BE MINERALS 561

Table 7. Molar thermodynamic properties of euclase, Table 8. Molar thermodynamic properties of bertrandite, BeAlSiO"(OH), to 380 K BeoSi,O,(OH)r,to 370 K

Teup. lleat Entropy Enthalpy Glbbs energy Tedp. lleat Entropy Enthalpy Glbbs energY capacl ty f unctlon functlon capacity futrcElon fudctlon -(c;-H;)/r r c; r;-16 (Hi-n;)/r -(c;-H;)ir r -P r;-r; (E;-H;)/r

J/ (oo 1 'K) Kelvln J/(no1'K)

5 0.002 0.001 0 .000 0.000 5 0,021 0.007 0 .005 0.002 10 0.017 0.005 0.004 0.001 10 0.r64 0.055 0.041 0.014 15 0.069 0.020 0.015 0,005 15 0.517 0.r79 0.133 0.046 20 0,L97 0.0s5 0.043 0,012 20 1.198 0.409 0.303 0.105 25 0.387 0.119 0,092 o.o27 25 2 .300 0.79r 0.590 o.202 30 o.767 0.219 0.169 0.050 30 3.860 0.994 0.343 35 r.361 0.379 o,294 0.085 35 5.845 2,O79 1.543 0.536 40 2 .282 0 ,6 r8 0.482 0.135 40 8.488 3.025 2,240 0.785 45 3.296 0.945 0.738 0.206 45 4.I88 3.091 1,097 50 4,525 1.35r 1.051 0.300 50 15.02 5 .561 4.O94 t.473 60 8.00r 2.478 1.915 0.563 60 24.62 9.15r 6.7L2 2 .438 70 11.80 3.984 3.043 0.940 70 5L.bt 13.50 9.800 3.703 80 16.6r 5.861 4 .433 1.434 80 39.22 18.20 L2.98 5.2r8 90 2t.15 8.118 6.069 2.O49 90 48.31 23.34 16.40 6.942 100 27.L3 10.69 7 .905 2.7A2 100 28.91 20.05 8.857

110 32,78 13.54 9.901 3 .628 110 66.98 34.83 23.89 10.95 120 38.60 16.64 72.06 4.58r t20 76.34 41.06 27.87 13.r9 130 44.48 19.96 r4.32 5.635 r30 85,82 47.55 31.96 15.59 r40 50.33 23.47 L6.69 6.782 140 95.20 54.25 18.11 r50 56.L2 27.r4 L9.t2 8.016 104.5 6r.14 40.39 20.74 160 61.85 JO.94 2t .6L 9.330 150 113.7 68.17 44.69 23.49 r70 67.54 34.86 24,15 to.72 170 L22.9 75.34 49.O2 26.33 180 73.11 38.88 t2.t7 180 r32.O 82.63 53.38 190 78.49 42.98 29.30 13,68 r90 140.9 90.01 57.15 32.26 200 83.69 47.r4 31.89 200 r49.6 97.46 62.r3 35.33

210 88.75 51.3s 34.48 16.87 210 158.0 105.0 66.49 38,47 220 93.68 55.59 37.06 18.53 220 166.3 I 12.5 70,84 4t .66 230 98.48 59.86 39.62 20.24 230 r7 4 .4 120.1 75.r7 44.90 240 103.1 64.15 42.t7 21.98 240 L82.5 L27,7 79,47 48.19 250 to7,6 68.45 44.70 23.75 250 190.9 135.3 83,76 51.53 260 r l l .9 72.7 6 47.20 25.55 260 200,1 r43.0 88.06 54.89 270 116.0 77.06 49.64 27.38 270 209.8 150,7 92.42 58.30 280 119.9 8r.35 52.12 29.23 280 2t3.3 158,4 96.68 61.14 290 r23.7 85.62 54.52 31.r0 290 21A.9 166,0 100.8 65.20 300 127.4 89.88 56.89 300 225.6 173.5 104,8 68.69

310 130.9 94.11 59.22 34.89 3 10 232.1 181.0 108.8 72.r9 320 134.3 98.32 61.51 36.81 320 238.2 188.5 112.8 75.7 | 330 L37.5 102.5 63.17 38.74 330 243.8 195.9 116,7 79.24 340 140.7 106.7 65.98 40.67 340 249.5 203.3 L20.5 a2.78 350 143.7 110,8 68,16 42.62 350 255.L 2r0.6 r24 .3 86.33 360 L46.6 114.9 70.30 44.51 360 260.7 2t7.9 128.0 89.88 370 L49,3 118.9 72.40 46.52 370 266.0 225.L 93.44 380 151.9 ],22.9 74.45 48.48 213.t5 211.1 r53,2 93.78 59.38 273.t5 tt7 .2 78.41 50,45 27.96 298,!5 224.4 L72.1 104.1 68.04 298.15 t26.7 89.09 )b.4) 32.64

K), respectively,for beryl (Be3Al2Si6O'8' 0.36 HrO), phen- . of the compositionBerAlrSi6O,8 0.36HrO, stoichiometric akite, euclase,and bertrandite. Our value for the entropy beryl, phenakite, euclase,bertrandite, and chrysoberyl. of phenakite is about l.5ololower than the value reported phenakite are Low-rnvrpnRATURE HEAT cApAcrrIES AND by Kelley (1939). Our heat capacities for reported by Kelley (1939) at THERMODYNAMIC FUNCTIONS roughly equivalent to those the higher temperatures, but at lower temperatures the for phenakite, Heat-capacity measurements beryl, eu- values show significant deviations. Kelley's (1939) heat clase,and bertrandite are listed in the chronologicalorder capacitiesare l3o/olarger near 55 K. Similar discrepancies (series)in Tables l-4. The results of measurement are were noted by Chaseet al. (1974) for BeO (Kelley, 1939) for (e.g.,Robie and Hemingway 1972). corrected curvature , and were expectedin this study. The data were smoothed using cubic spline routines and were graphically extrapolatedto zero kelvin using the ex- HtcH-rnupERATURE HEAT CApACITIESAND perimental and smoothed values for temperatures less THERMODYNAMIC FUNCTIONS than 30 K plotted in the form of Co/T vs. T2. Smoothed High-temperatureheat-capacity measurements for ber- values of the heat capacitiesand derived thermodynamic yl (BerAlrSi.Ort'0.36HrO),anhydrous beryl powder, functions are listed in Tables 5-8. phenakite, euclase,bertrandite, and chrysoberyl were made The entropychanges, ^Si - ,S3,a|298.15 K are 365.2 + between 340 and about 800 K. The experimental values 0.7.63.37t 0.13.89.09+ 0.l8,and172.1 ! 0.34Jl(mol' are listed in Tables 9-14. Each scan representsone con- 562 HEMINGWAY ET AL.: THERMODYNAMIC DATA FOR SELECTED Be MINERALS

Table 9. Experimental high-temperature heat capacities of Table 10. Experimental high-temperatureheat capacitiesof beryl, BerAlrSi6O,8.0.36HrO beryl, BerAlrSi.O,,

- Heat Heat _ HeaE - Heat l{eat _ Heat reEP' feEP' . lenD. femD.- , f€nP. IEND.- capacity capacl Ey capaci ty capacrEy capacL ty capacl Ey

K J/(nol.K) K J/(Eol'K) K J/(oo1'K) K J/(no1.K) K J/(no1'K) K J/(uo1'K)

Scan 1 Scan 5 Scan 9 scan 1 Scan 8 Scan 15

343.5 483.3 522.4 597.0 690.9 648.0 343.5 470.2 572,0 60I .6 340,9 46r.7 363.3 500.1 542,2 603.1 710.8 654.4 363.3 487.7 591 .8 603.6 350.9 47L.2 383.1 517.3 562.0 610.6 730.6 659.8 383.1 503.2 611.7 610.3 360.9 478.6 403.0 531.8 581.9 620.0 749 .5 667.5 403.0 5r1.5 631.5 618.4 370.8 486.6 422.8 545.s 600.7 626.5 422.8 531.0 650.4 631.9 380.8 495,3 tt42.6 558.1 62r.6 632.8 Scan I0 442.6 541.4 390,8 502.6 462.4 570.7 64L.4 638.3 462,4 555.5 Scan 9 400.8 509.4 482.3 582.3 661.3 647.6 690.9 654.4 482.3 567,s 410.8 517.8 501.1 592,9 681.1 649,2 7r0.8 657.9 501.1 576 ,3 572.O 606.4 420,8 524.O 700.0 657.L 730,6 662.L 591.8 6t3.7 430.7 530.6 Scan 2 749.s 668,0 Scan 2 67t.7 619.8 440.7 538.0 Scan 6 63r.5 627.8 450.7 545.4 343.5 482.6 SCan lr 343.5 469,6 650.4 636.0 460,7 550.8 363.3 499.4 522.4 595.2 363.3 484.7 470,7 558.6 383.1 5L6.6 542.2 605.2 740,5 650,1 383.1 500.3 scan 10 403.0 531.3 562.O 613.7 760.4 664.6 403.0 5r4.2 Scan Lj 422.8 544.7 58r.9 622.4 780.2 669,2 422.8 526,8 62!.6 619 .8 442.6 557.l 600.7 628.6 799 .r 671.L 442.6 540.1 64t ,4 624.2 470,7 559.5 462.4 568.5 62L.6 635,5 462.4 552.8 66r.3 627.3 480.7 563.8 482.3 580.9 64r .4 64r ,5 Scan l2 482.3 566.s 68r.1 636.r 490.7 57L.6 501.1 59t.4 66L.3 647.6 501.1 577.6 700.0 642.7 s00,6 578.6 68r.1 654.6 740.5 665.8 510.6 581.0 Scan 3 700,0 660.2 760 .4 666,3 Scan 3 Scan 1I 520.6 585.0 180.2 677.8 530.6 590.9 472,8 571.9 Scan 7 799.7 680.2 472.8 559.2 62t.6 619.5 540,6 s92.8 492,6 587.1 492.5 569.2 64t.4 626.L 550 ,6 595.2 5L2,4 595.2 571.8 618.2 Scan 13 5L2.4 516 .8 66r.1 629,5 560.5 598.9 532.3 601.5 591.6 626.O 532.3 586.9 681.r 634,4 570.5 602.O 551.1 615.3 6LL,4 633.2 858.8 709,2 551.r 593.4 700.0 637,2 580.5 604.8 63r.3 638.2 868.6 7rr.2 590.5 6LO.2 Scan 4 650.1 646.4 878.4 114.7 scan 4 SCan LZ 600.5 611.0 887.2 7r1.2 472.8 578.2 Scan 8 s22.4 578.r 690.9 630.0 scad 18 492.6 586.7 542.2 587.6 7r0.8 637,O 5L2.4 595.9 571 .8 625.1 562.O 595.0 730.6 642.4 590.5 609.4 532.3 606.0 s9r.6 632.3 581.9 610.7 749.5 648.0 600.5 615.0 551.1 6r3.8 611,4 638.9 600.7 610.7 610.4 619.1 63r.3 643.9 Scan 13 620.4 623,5 650.1 648.0 Scan 5 630.4 626.4 690.9 636.3 640.4 628.6 480.7 562.6 710.8 642.O 650.4 630.2 490.7 570 ,4 730 .6 645.6 660.4 631.5 500.6 576 .2 749 ,5 645.6 670.3 632.4 680.3 632.5 tinuous set of measurementsunder one experimental set- Scan 6 SCan L4 690.3 634.4 up. The data were collected at infrequent intervals over 770.2 645.4 740.5 643,2 Scan 19 a 2-yr period with two measurementchambers, the initial 780.2 654.9 760.4 648,7 790.2 658.1 180.2 653.6 600,5 612.6 chamber having failed electrically. 800.2 660.0 799.r 657,7 The high-temperatureresults were combined w'ith the Scan 7 scan 15 low-temperatureheat capacitiesfrom this study, or in the 710.2 6s0.8 740.5 648.9 case of chrysoberyl with the data of Furukawa and Saba 780,2 655.7 760.4 65r.0 (1965),and simultaneouslyfit with the solution and phase- 790.2 663.1 7AO.2 655.3 800.2 66L.7 799.L 660.9 equilibrium data described by Barton (1986) using the program pHASzo(Haas and Fisher, 1976).pHAS2o attempts to fit all data types within the respectiveprecision ofthe data type and, therefore, does not degradethe precision trandite and euclase.Equations for the smoothed heat ofrelatively precisedata like that for heat capacities.The capacitiesare given in Table 15. heat capacities for the hydrous beryl sample were cor- We have adopted the Gibbs free energiesand uncer- rected for the small amount of CrrO, using the data of tainties calculated by Barton (1986) from the simulta- Robie et al. (1979) and for HrO using an estimated heat neousregression analysis ofthe data set discussedabove. capacity of 67 J/(mol.K) for cagedHrO. The heat capac- These results have been combined with the entropies at ities for chrysoberyl (listed in Table 14) were corrected 298.15 K reported in this study for phenakite, euclase, for 3.1 wto/oFerO, using the data of Robie et al. (1979). and bertrandite; the entropy at 298.15 K for chrysoberyl Heat capacitieswere estimated for temperaturesgreater reported by Furukawa and Saba (1965); the entropy at than 800 K. It should be noted that heat capacitieswere 298.15 K for beryl obtained by Barton (1986) through estimatedonly to 1000 and 1500 K, respectively,for ber- multiple regression;the equationslisted in Table 15; and HEMINGWAY ET AL.: THERMODYNAMIC DATA FOR SELECTEDBC MINERALS 563

Table I l. Experimental high-temperature heat capacities of Table 12. Experimental high-temperature heat capacities of phenakite, BerSiOo euclase,BeAlSiO.(OH)

- Heat IIeat - Heat 'f- Hea t IIeat Va.r reED. . feop. fenD' . eED.' teoD. f eoD.' _ capacl Ey capaclty capacl Ey capaclEy capacLty capacl Ey

K J/(nol'K) K J/(no1'K) K J/(not'K) K J/(nol'K) K J/(oo1'K) K J/(oo1'K)

Scan 1 Scan 2 Scan 4 scan I Scao 5 Scan 1O

340.0 tol .2 410.8 r25 .O 580,5 149.1 343.s r40.9 522.4 t77.4 690.9 196.8 350.0 109.4 420.8 L27,2 590.5 150.r 363.3 L46.6 542.2 180.5 710.8 L98.2 360,0 111.5 430.7 128.8 600.5 150,8 383.r 151.9 562.O 183.4 730.6 199.8 370,0 113.6 440.7 r30 .2 610.5 151.8 403.0 156.8 58r.9 186.3 749 ,5 201.8 380.0 115.5 450.7 131.1 620.4 L52.5 422.A 16r.3 600.7 188.5 390.0 rr7.6 460.7 L31.2 630,4 752.9 442.6 L65,4 62r.6 190.8 Scan 11 400.0 119.5 470.7 r35.5 640.4 153,2 462,4 t69.4 641.4 L92.! 410.0 rzL,7 480.7 r37 .5 650,4 L54.4 482,1 173.1 661.3 193.5 690.9 r96.8 420.O L23.8 490.1 r 38,5 660.4 155.1 501.1 I76.r 681.1 L95.7 710.8 198.3 430.0 r25.9 500.6 139.6 670.4 rs6,0 700.0 r97.8 730.6 L99.9 440.0 t27 ,9 680.4 rs4 .9 scan 2 749.5 202.2 450.0 L29.8 Scan 3 690.3 159.3 scan 6 460.0 r31.3 700.3 159.3 470,7 167.1 Scan 12 470.0 t32.8 460.7 L33.2 480.7 171.0 62L.6 191.6 480.0 135.r 4'to.7 L34.9 Scao 5 490.7 L73.2 64r.4 L92,4 740.5 200.9 490.0 t37 .5 480,7 136.8 500.6 t75.3 661.3 193,9 760.4 202.A 500.0 139.0 490.7 138.I 690.3 r57.1 510.5 L76.5 68r.1 196.3 780.2 203.8 500.6 139.9 700.3 r58,r 520,6 178.1 700.0 198.5 799.r 205.O Scatr 2 510.6 r39.9 710.3 r59 .1 530.6 t79.1 520.6 r42.L 120.3 159.5 540.6 r80.3 scan 7 Scan 13 330.9 rO4.4 530.6 L43.2 730.3 L60.7 s50.6 181.7 340.9 106.4 540.6 r44.5 740.3 161.4 560.5 183.0 590.5 187.0 740 .5 201.5 350.9 109.3 550.6 L45.4 750.2 161.9 570.5 184.0 600.5 188.5 760.4 202.7 360.9 111.8 560.5 146.1 760 .2 162.3 580.5 185.0 610.4 189.7 780,2 204.4 370.8 r14.6 570.5 146.8 770.2 L62.4 s90.5 L86.7 620.4 190.8 799,r 206.r 380.8 117.5 580,5 r47.7 780.2 163.8 600.5 r87 .2 630.4 191.8 390.8 720,4 590.5 L48.7 790.2 L64.3 640.4 r92.9 Scan l4 400.8 r22.6 600.5 149.5 800.2 L64.9 scan 3 650.4 194.0 660.4 194.2 770 .2 205.O 472.A L72.4 610,3 195.0 780.2 204.2 492.6 t75.5 690.3 196.3 790.2 203.5 5L2.4 178.3 532.3 181.7 Scan 8 Scan 15 ancillary data from Robie et al. (1979) to provide the 551.1 r84,3 values 571.8 185,0 770.2 203.3 smoothed ofthe heat capacitiesand derived ther- Scan 4 s9r.6 187.3 180.2 204,O modynamic functions listed in Tables 16-20 for the tem- 6rr.4 189.5 790.2 20r.9 472,8 17r.9 63r.3 191.3 800.2 203.6 perature interval 298.15 to 1800 K (1200 K for bertran- 492,6 r74.9 650.1 193.5 dite). 5L2.4 177,9 Scan t6 532.3 181.1 scan 9 551.1 183./ 8 58.8 207.3 DrscussroN 571.8 185,8 868.6 21O.4 591.6 187.5 The entropy correction for the HrO in beryl may be 6rI.4 r90.3 631.3 191.9 estimatedby assumingthat the HrO in beryl is similar in 650.1 r93.3 bonding characteristicsto that in analcime or clinoptilolite. Under this assumptionwe calculatethe entropy contribution of I mol of H,O to be 55 J/(mol.K) at 298.15 K from the data of Johnson et al. (1982) for analcime and estimate a heat capacity for beryl that is only about 190/o dehydratedanalcime or 57 J/(mol'K) calculatedfrom the of the measuredheat capacity at 16 K. The heat capacity data of Hemingway and Robie (1984) for clinoptilolite. of 0.36 mol of ice is similarly about 200/oof the measured The calculated value for the entropy of anhydrous beryl heat capacity at 16 K. Finally, a Schottky contribution to at 298.| 5 K is 345.0 + 5 J/(mol. K) basedupon this model the heat capacity,arising from Cr3+ions in solid solution, and is in excellent agreementwith the value of 346.7 + may be expectedat very low temperatures.However, it 4.7 J/(mol'K) predictedfrom the multiple regressionanal- is unlikely that the contribution would be 600/oof the heat ysis (Barton, 1986). capacity observed at 16 K. We have no explanation for The heat capacity of beryl is unexpectedly high at low the deviation of our measuredheat capacitiesfrom our temperatures(ess than 30 K) for a cornpound with such theoretical estimates. a low mean atomic weight. We can calculate the Debye Small numbers of fluid inclusions in the phenakite and temperatures for two beryls, goshenite as 795.6 K and bertrandite samplesproduced small anomaliesin the heat aquamarine as 799.1 K, from the elastic constant mea- capacities near 269 K. The bertrandite sample produced surementsof Yoon and Newnham (1973). The heat ca- a largeranomalous heat capacityand, therefore,contained pacity of material with a Debye temperature of approxi- a greater quantity of fluid, generally associated with a mately 800 K can be representedreasonably well to about claylike phase. The smoothed values of the thermody- 16 K by a Debye function. From sucha function we would namic properties ofthese phaseshave been correctedfor 564 HEMINGWAY ET AL.: THERMODYNAMIC DATA FOR SELECTED Be MINERALS

Table 13. Experimental high-temperatureheat capacitiesof Table 14. Experimental high-temperatureheat capacitiesof bertrandite, BeoSirOr(OH), chrysoberyl,BeAlrOo

Heat Ca.r---: _ Ileat Heat - Heat renp. renp, Tef,p. f euD.' f eoD. fCDD. ..f::i." capacl ty LdPaLr L' caPaclEy capaclty LdPdLTLJ

K J/(nol.K) K J/(no1'K) K J/(no1'K) K J/(Eo1'K) K J / ( moI'K) K J/(oo1.K)

Scan 1 Scatr 3 Scan 5 scan I Scan 2 Scan 4

343.5 250.7 340.8 251.9 472 .8 309.3 340.0 LL5.7 420.8 133.0 580.5 155.1 363.3 26r.6 350.8 258.0 492.6 315.3 350.0 1r7.8 430.7 L34.7 590.5 155.8 383.r 27t.9 360.8 263.r 5r2.4 320.8 360.0 119.9 440.7 136.3 600.5 155.6 403.0 280.3 370.8 26A.3 532.3 327.2 370.0 t22.O 450.7 138.1 610.5 L57.2 422.A 288.3 380.8 272.9 551.1 331.6 380.0 t23.7 460.1 I 39.4 620.4 L57.2 442.6 295.7 390.8 276,r 390.0 125.8 410.7 r4r.3 630,4 159.0 462.4 303.3 400.7 280.6 Scan 6 400.0 t21.4 480.7 L42.O 640.4 158.9 482.3 310.4 4r0.7 2a4,9 410.0 t29.4 490.1 r44.4 650.4 160.0 501.1 316,s 420,1 289.0 470.6 306.6 420.O 131 ,3 500,6 145.5 660.4 r60,6 430.7 293.2 480.6 310.0 430.0 133.0 Scan 2 440,7 296.3 490.6 3t 2 ,9 440.0 134 ,8 Scan 3 Scan 5 500,6 315.5 450.0 136.8 450.7 300,2 Scan 4 520.6 32L.7 450.0 138.2 460.7 140.3 670.4 161.3 460.7 303,4 530.6 323.2 470.O 139.9 470.7 141.3 680.4 161.9 470.6 307.3 472.8 310.0 540.5 325.5 480.0 141,9 480.7 690.3 163.5 480.6 3I0.4 492.6 315.5 550.5 327.9 490.0 143.8 490.7 t43.9 700.3 164.4 490.6 314.0 512.4 321.2 560.5 330.2 500.0 145.4 500.5 145.0 500.6 3t7.6 532,3 328.1 570.5 333.2 510.6 Scan 6 55r.1 333.5 s80.5 335,1 Scan 2 520.6 r47 .4 590.5 339.0 530,6 t48.5 690.3 16r.2 600.5 342.4 340.9 116.9 540,6 L49.9 700.3 161,8 350.9 tl9 .2 550.6 I51.1 710.3 163.3 360.9 tzr,2 s60.5 720.3 r63.3 370.8 123.5 570.s 730.3 164.8 380.8 L24.9 580.s L54.2 740.3 165.8 the small contribution to the heat capacitiesof the H2O 390.8 r27.5 590.5 155.4 750.2 166.8 in the inclusions. 400.8 r29.3 500.5 156.5 760.2 t67 .l 4 10.8 L31,2 770.2 t67,2 The high-temperatureheat capacitieswere obtained de- 780.2 167.0 spite significant problems. 790.2 t6A.2 experimental At temperatures 800.2 t58.2 greater than about 470 K, small quantities of volatiles were emitted from some of the samples during the differential-scanning-calorimetricmeasurements. The ex- cess heat required for difusion of the volatiles to the the propertiesofequations usedto fit experimentalresults, sample surfaceand for vaporization from the surfacere- the function of the Haas-Fisher equation, are different sulted in a large scatterin calculatedheat capacitiesand, from the propertiesofequations developedto extrapolate in somecases, the calculation oferroneous heat capacities or estimate values beyond the known universe of exper- from the DSC scans(Hemingway and Kirby, unpub. data, imental results. Such diferences and the consequencesof 1985). Experimental results obtained for temperatures ignoring such differencesare discussedin mathematics greater than 800 K were of poor quality and were not coursesand are beyond the scope of this paper. Well- reported. Therefore, it is estimated that the uncertainties behavedequations, that is, equationsthat do not quickly in the high-temperatureheat capacitiesm ay averase+2o/o. changeslope beyond the end points ofa data set (e.g.,the Use of the Haas-Fisherequation for high-temperature Meyer-Kelley equation) do not guaranteereliable extrap- C" extrapolations recently has been criticized, in partic- olations of experimental data. It is sufficient to note that ular with respectto equation form. It should be noted that the problems discussedby severalauthors lie in the mis-

Table 15. Heat capacity equations for selectedberyllium minerals

t3 "1 "2 "4 "5

Beryl t525.842 -O.425206 1.20318x10'4 -20180.94 6.82544xro6

Phenaklte 428.492 -0.099582 1.9886 x1o-5 -s67o.47 2.0826 x1o6

Euclase 532 ,920 -O . r507 29 4.1223 x10-5 -6726,30 2.r976 x106

BertrandiEe 825.336 -0.099651 -10570.3I 1.66217x).O6

Chrysoberyl 362.7O1 -0.083527 2.2482 xlo-5 -4033.69 -6,7916 xto4

The foro of the equatlod 1s

ci = .r + c2"r+ + + "rt2 "oT-o'5 "rt-2 HEMINGWAY ET AL.: THERMODYNAMIC DATA FOR SELECTED BE MINERALS 565

Table 16. Molar thermodynamic properties of beryl, BerAlrSiuO'*,to 1800 K

Temp . Heat EntroPY Enthalpy Gibbs energy Formatlon fron the eleoents capacity functloil functlof, Gtoos Enthalpy free enerqy los K- .; s;-s6 (H;-H;e8)/r -(G;-H;e8)/r " kelvln J/(ool'K) kJ / ool

298.15 4r7.8 145.7 0 .000 346.7 -9006.56 -8500.36 1489.23 Uncertalnty 7.10 6 .39 300 419,8 349.3 2.583 346.7 -9006.36 -8497.O7 t479.47 400 508.6 483.t r18.75 364.3 -9014.86 -8331.73 1088.01 500 568,1 603.4 203.05 400.4 -9008.66 -8r56.06 852.O57

600 609.1 710.8 261 , 51, 443.1 700 638.1 807.0 318.51 488.5 800 659,8 893.7 359.90 533.9 900 576.3 972.5 394.18 578.3 1000 689.6 ro44 423.08 62t .3

1r00 700.9 I1I1 447.83 662.9 1200 711,0 rL7 2 469.35 702.8 1300 720.7 | 229 488.31 747.1 1400 730.5 1283 505.26 777.9 1500 740.7 1334 520.61 813.3

.4 -a997.7 3 -6307.7 6 205 '927 1600 751,.7 1382 534.7| 847 " - -. - r700 763.6 1428 547, aL 880.2 : r;, o:i 6" -ei;; ; o"' i;;-. 5a; I 800 176.7 r47 2 560.16 91r.8 -9271.44 -5952.f2 172.732

Tradsltiong 1n the reference state eleoents

Alumlnun. . . .. neltlng poi.nt 933.25 K Berylllum.... alpha - beta 1527 K neltlng point 1560 K sl1icon..,... nelting poidt 1585 K

Table 17. Molar thermodynamic properties of phenakite, BerSiOo,to 1800 K

Tenp . Heat En tropy Enthalpy Gibbs energy Forna tion frod the elements capacity function funcElon Gibbs Enthalpy free etrersy Ios-r K- r c; r; -r;

kelvin kJ /no1

298.15 95.60 63,37 0.000 63.37 -2t43.r2 -2028.39 355.365 Uncertalnty O.27 3.78 3.74 300 96.16 63.96 0.591 63.31 -2143.08 -2027,62 353.040 400 121.3 95,31 27.835 67.41 -2143.91 -r989.03 259.7 40 500 138,4 L24.3 48.351 75.99 -21,43,47 -1950.33 203.749

600 150.2 150,7 64.402 46.28 -2142.59 -1912.15 166.467 700 158.5 t14.5 77 .282 97.21 -2140,59 -1873.5s 139,806 800 L64.3 196.1 87.816 108.2 -2t38.65 -1835.55 119.849 900 168.5 2t5 ,1 96.563 119.1 -2136.58 -r797.76 104.339 1000 17r.6 233.6 r03.92 r29.7 -2134.4A -t7 60.20 9r.943

1100 173.8 250,0 110.17 139.9 -2132.44 -r722.82 81.810 1200 175.4 265.2 115.54 r49.7 -2130.49 -L685.67 73.375 1300 L76.6 279.3 t20.20 159.1 -2t2a.66 -1648.70 66.246 1400 L77.6 292.5 t24.26 168.2 -2127.02 -1611.96 60.143 1500 r7a,4 304.7 r21 .84 176.e -_-_?l?5-:22-- ---127-'-:\L-_--_2!:8-29 1600 r19.r 316.3 13r.02 185.2 --:;;o;'.;;"'-2153.6t -1531.69 50.200 1700 r79,9 327.r r33.88 re3.3 -ii;6'.ee""-ie'.oZ; 1800 180,7 337.5 136.45 201.0 -2200,14 -1457.5L 42.295

Tranaltlons 1n the reference 6tate elenents

Beryllluo. . . . alpha - beta 1527 K Beltlng point 1560 K sillcon. . .,. . neltlng polnt 1685 K 566 HEMINGWAY ET AL.: THERMODYNAMIC DATA FOR SELECTED Be MINERALS

Table 18. Molar thermodynamic properties of euclase,BeAlSiOo(OH), to 1800 K

Temp. lleat Entropy Enthalpy Glbbs energy Foroatlon froo lhe elenents capactty function functlon Clbbs Enthalpy free eoerqv Ios-r K- T C: "T-oo kelvln kJ/Eo1

298.t5 t26 .8 89.09 0 .000 89.09 -2532.9L -2310.17 415.243 Uncertalnty 0.40 3.05 3.04 300 r27,5 89.88 0,784 89.09 -2532.86 -2369.rO 4r2,497 400 t55.6 130,8 94.48 -2533,97 -23t4.34 302.221 500 r75.8 r68.0 62.469 I05.5 -2533.40 -2259.50 236,048

600 188.8 201.3 82.5L4 118.8 -253r.89 -2204.84 191.948 700 t97 .9 231.1 98.384 r32 .7 -2529.87 -2150,49 160,47r 800 204.3 258.0 111,25 L46.7 -2s27.59 -2096.45 r36.884 900 209,2 282.3 Lzl.A7 150.5 '- -2525.26 ' -2042.64 '- 118.552 I 000 2t2.9 304.6 130.79 173.8 :t;;; .6;" -i;;A'.i;" i6;'.;ee

IIOO 216.0 325,O 138,40 r86.6 -2531.08 -1934.01 9r.838 1200 218.8 343.9 144.99 198.9 -2529.22 -1880.55 81.858 1300 361.5 150.16 210.8 -2525,85 -1825,86 73.364 1400 224.0 378.1 155.90 222.1 -2523.r7 -L772.26 66.124 I 500 226.9 393.6 L50 . 54 - -:25-?o-:!2 - - - -!7-L8-'-6-!- - - - -22:8-!9 -2532.27 -7664.77 1600 230.0 408.3 L64.7 I 243.6 --:;;;;-.iZ-'- " -54.349 r700 233.4 422.4 168.71 253.7 :ieio.;;'- i;'.;Ao I 800 237,3 435.8 t72.42 263.4 -2575.55 -L553.32 45.076

Transltlon6 ln the reference gtate eleEents

Aluolnum..... EeltLng polnt 933.25 K Beryll.ium.... alpha - beta 1527 K oelting polnt 1560 K Slllcon...... neltlng polnt 1685 K

application of the Haas-Fisher equation and not in the minerals may be found in a companion paper by Barton form of the equation, and that responsibility for devel- (1986). oping and justifying alogrithms to extrapolatevalues beyond the experimentally determined data set always re- AcrNowlnocMENTs sides with those who need to make the estimate. An Wethank our U.S.Geological Survey colleague Harvey Belkin expandeddiscussion ofthe petrology and a discussionof for examiningour sampleof bertrandite and bringing to our solution and phase-equilibrium data for the beryllium attentionthe presenceof the claylikeimpurity. This work was

Table 19. Molar thermodynamic properties of bertrandite, BeoSiOt(OH)r, to 1800 K

Tenp. Ileat Entropy Enthalpy Glbbs ene!gy capacity functlon function G1bb6 Enthalpy free enersy log-t K- oT-to

kelvln kJ/dol

298.15 224.7 t72.1 0.000 172.1 -4580.50 -4300.62 753,45r Uncertalnty 0.8 5,47 5.46 300 225.9 1.389 L72.L -4580.38 -4300.50 748.783 400 279.8 246.3 64.67L 181.7 -4580.80 -4204.85 549.097 500 3r7 .4 JIJ.I 111.68 20t .4 -457a.19 -4111.16 429.490

600 344.2 148,33 225.1 -4573.67 -40r8.13 349.809 700 363.s 428.O L77.76 250.3 -4567,89 -3925.96 292.958 800 377.6 477.6 201.91 275.6 -456r.30 -3834.74 250.383 900 387.8 522.7 222.03 300.6 -4554.26 -3744.3L 2L7,3t4 1000 395.1 563.9 239.OO 324.9 -4547.02 -3654.65 190.899

1100 400.0 601.8 253.43 348.4 -4539.82 -3565.77 t69.324 1200 403.2 636.8 265.79 37r.0 -4532.82 -3477 .58 151.3 7 s HEMINGWAY ET AL.: THERMODYNAMICDATA FOR SELECTEDBC MINERALS 567

Table20. Molar thermodynamicproperties of chrysoberyl,BeAlrOo, to 1800K

Tenp. Ileat Entropy Enthalpy Glbbe energy Poroatlon from Ehe elenents capaclty functlon functlon Gtbbe Enth&IpY free energY log K. I r .; t;-t; (H;-H;eB)/r -(ci-H;e8)/r

kelvln J/(Do1'K) kJ/ool

298.15 105.4 66.25 0,000 66.25 -2298 .49 -2t76.16 38L.254 1 1a Uncertalnty 0.30 J.IO 106.0 56.90 o .652 66.25 -2298.45 -2r75.35 378.762 300 '10.75 400 130.8 101.1 30.366 -2299.35 -2L13,28 278.578 500 145.9 132.0 79.97 -2298.92 -2092.91 2L8,645

600 155.8 159.6 68.590 90.99 700 t62 .1 184.1 8r.568 102.6 800 167.5 206.2 92 . 025 tt4.2 900 226.2 100.63 r25.5 t 000 L74.O 107.83 136.5

I100 r76,1 26r .0 r r3.96 L47.L r 200 178.4 276,5 r19.24 L57.2 1300 180.2 290.8 L23,86 L67.O 1400 182.0 304.2 L27.95 L76.3 1500 183.8 316.9 l3r.6r tdf.J

1600 185.7 328.8 r34.93 -2320. L9 -1633,50 53.328 1700 187.8 340,I 137.98 202.r -2318.2r -1590.63 48,874 1800 190.1 350.9 140.82 2ro.r -23L6.O4 -t547 .85 44.9r7

Traneltlons 1o the reference state elenents

Aluoinun.. ... oeltl.ng polnt 933.25 K Berylllun.... alpha - beta f527 K oelttng polnt 1560 K

partially supported by a grant from the National Science Foun- Hemingway,B.S., Robie, R.A., Kittrick, J.A., Grew, E.S.,Nelen, dation to M. D. Barton (EAR84-08388). J.A., and London, David. (1984) The heat capacitiesofos- umilite from 298. 15 to 1000K the thermodynamic properties of two natural chlorites to 500 K, and the thermodynamic RcrnnrNcns properties of petalite to 1800 K. American Mineralogist, 69, Barton, M.D. (1986) Phaseequilibria and thermodynamic prop- 70r-7r0. erties of minerals in the system BeO-AltOr-SiO2-H2O, w'ith Jahns,R.H. (1944) Beryllium and tungsten depositsof the Iron petrologic applications. American Mineralogist, 7 | , 277 -300 . Mountain district, Sierra and Socorro Counties,New Mexico. Beus,A.A. (1966) Geochemistry of beryllium. Page,L.R. (Ed.), In Strategic mineral investigations, U.S. Geological Survey Lachman, F. (translation),W. H. Freemanand Company, San Bulletin 945.45-79. Francisco. - (1955) The study of pegmatites.Economic Geology, Fif- Chase, M.W., Cumutt, J.L., Hu, A.T., Prophet, H., Syverud, tieth Anniversary Volume, 1025-1 130. A.N., and Walker, L.C. (1974) rANAFthermochemical tables, Jahns, R.H., and Burnham, C.W. (1969) Experimental studies 1974supplement. Journal ofPhysical and Chemical Reference of pegmatite genesis:I. A model for the derivation and crys- Data, 3, 381. tallization of granite pegmatites.Economic Geology, 64,843- Commission on Atomic Weights. (1976) Atomic weights of the 864. elements.Pure and Applied Chemistry,47,75-95. Johnson, G.K., Flotow, H.E., O'Hare, P.A.G., and Wise, W.S. Furukawa, G.T., and Saba,W.G. (1965) Heat capacityand ther- (1982) Thermodynamic studiesof zeolites:Analcime and de- modynamic properties of beryllium aluminate (chrysoberyl), hydrated analcime. American Mineralogist, 67, 736-7 48. BeO.AlrOr, from 16 to 380"K. Journal of Research of the Kelley, K.K. (1939) The specific heats at low temperaturesof National Bureau ofStandards, ,4,69,13-18. beryllium oxide and beryllium orthosilicate(phenakite). Amer- Haas,J.L., Jr., and Fisher, J.R. (1976) Simultaneousevaluation ican Chemical SocietyJournal,6l, 1217-1218. and correlation of thermodynamic data. American Journal of Mulligan, Robert. (1968) Geology of Canadian beryllium de- Science,276,525-545. posits. Geological Survey of Canada, Economic Geology Re' Hemingway, B.S., and Robie, R.A. (1984) The thermodynamic port Number 23. properties of zeolites: Low-temperature heat capacities and Robie, R.A., and Hemingway, B.S. (1972) Calorimetersfor heat thermodynamic functions for phillipsite and clinoptilolite. Es- of solution and low-temperature heat capacity measurements. timates of the thermochemical properties of water at low tem- U.S. GeologicalSurvey ProfessionalPaper 755. peratures. American Mineralogist, 69, 692-7 00. Robie, R.A., Hemingway, B.S., and Wilson, W.H. (1978) Low- Hemingway, B.S., Krupka, K.M., and Robie, R.A. (1981) Heat temperature heat capacities and entropies of feldspar glasses capacitiesofthe alkali feldsparsbetween 350 and 1000 K from and of anorthite. American Mineralogist, 63, 109-123. differential scanning calorimetry, the thermodynamic func- Robie, R.A., Hemingway, B.S., and Fisher, J.R. (1979) Ther- tions ofthe alkali feldsparsfrom 298.15 to 1400 K, and the modynamic properties of minerals and related substances at reaction quartz + jadeite : analbite. American Mineralogist, 298.15 K and I bar (105pascals) pressure and at higher tem- 66.r202-r2rs. peratures.U.S. Geological Survey Bulletin 1452. 568 HEMINGWAYET AL,: THERMODYNAMIC DATA FOR SELECTED Be MINERALS

Staatz, M.H. (1963) Geology of the bcryltium deposits in the yoon, H.S., and Newnham, R.E. (1973) The elastic properties Jh9m3s Range, Juab County, Utah. U.S. Geological Survey of beryl. Acta Crystallographica,A29, 507-509. Bulletin ll42-M. Webster, Donald, and London, G.J. (1979) Beryllium science MeNuscnrpr REcETvEDFrsnueny 28, 1985 and technology.Plenum Press,New York. MeNuscnrpr AccEprEDOcronsn 10. 1985