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Heat capacities of synthetic hedenbergite, ferrobustamite and CaFeSi2O6 glass
0016.7037/87/53.00 * .oo
GmchimranC~hrmr~AnuVd.JI,pp2211-2217 0 Pegsmom Jownds Ltd. 1987. Prinud In USA
Heat capacities of synthetic hedenbergite, ferrobustamite, and CaFeSi206 glass H. T. HASELTON, JR., R. A. ROBIE and B. S. HEMINGWAY U.S. Geological Survey, 959 Nat&ml Center, Reston, VA 22092, U.S.A. (Received January 12, 1987; accepted in revisedform May 26, 1987) Abstract-Heat capacities have been measured for synthetic hedenbergite (9-647 K), ferrobustamite (5 746 K), and CaFeSisc)s.glass (6-380 K) by low-t~~mtu~ adiabatic and differemial scanning calorimetry. The heat capacity of each of these structural forms of CaFeSirOs exhibits anomalous behavior at low temperatures The X-peak in the hedenbergite heat-capacity curve at 34.5 K is due to antiferromagnetic ordering of the I@’ ions. Ferrobustamite has a bump in its heat-capacity curve at temperatures less than 20 K, which could be due to weak cooperative magnetic ordering or to a Schottky anomaly. Surprisingly, a broad peak with a maximum at 68 K is present in the heat-capacity curve of the glass. If this maximum, which occurs at a higher temperature than in hedenbergite is caused by magnetic ordering, it could indicate that the range of distortions of the iron sites in the glass is quite small and that coupling between iron atoms is stronger in the glass than in the edge-shared octahedral chains of hedenbergite. The standard entropy change, S&.irr - S,“, is 174.2 + 0.3, 180.5 rf:0.3, and 185.7 rt 0.4 J/molaK for hedenbergite, ferrobustamite and CaFeSi,O, glass, respectively. Ferrobustamite is partially disordered in CaFe distribution at high temperatures, but the dependence of the configurational entropy on temperature cannot be evaluated due to a lack of info~ation. At high temperatures (298- 1600 IQ, the heat capacity of hedenbergite may be represented by the equation C,“(J/molsK) = 310.46 +0.012573-2039.93T-*R-
1.84604 x 106Tw2
and the heat capacity of ferrobustamite may be represented by Cs (J/m01 - K) = 403.83 - O.O4444T+ t .597 X 10s5T2- 3757.3Teif2. INTRODUCTION
in the c direction. RWDPORT and BURNHAM(1973) determined the crystal structure of a synthetic, end-member ferrobustamite and a natural Fe-poor fe~b~te. In this structure, Fe resides on four, ~phicaIly distinct -sitesM(l)M(4). Iron is concentrated on the smaller, and more regular M( 1) and M(3) sites in ordered ftrrobustamite, but in their synthetic sample, sign&ant amounts of Fe were also present on M(2) and M(4). The larger, irregular M(2) and M(4) sites coordinate loosely with additional oxygens yielding 7- and g-fold coordination, respectively. Despite the problems posed by using a heavily twinned sample, which lowered the quality of their refinement RMWORT and BURNHAM (1973) concluded that Fe tended to order onto the M(3) site in Fe-poor ferrobustamite. In a structural study of a higher quality, natural Fe-poor ferrobustamite crystal, YAMANAKAet al. (1977) showed that Fe segregates almost exchrsively onto the M(3) site, but the Fe can be disordered significantly by a relatively short heating period at 14 13 K. Therefore, the Fe distribution must be considered in phase equilibrium calculations. Heat capacities were also measured for C’aFeSilOa glass because the data could be useful in mcxlelling the thermodynamic properties of compositionally complex zig-zag chains
THE PHASERELATIONSof hedenbergite and ferrobustamite are geologically important as potential sources of information about the conditions of Q-Fe skarn formation. Reactions can be written for the oxidation and sulfidation of these minerals, and reactions involving hedenbergite have been studied experimentally by GUSTAFWN (1934), BURTON et al. (1982), and GAMBLE(1982). We are not aware of a natural occurrence of iron-rich ferrobustamite, pmsumably, because cooling rates may be too low to prevent inversion to hedenbergite. For example, WAGER and DEER (1939) found hedenbergitic pyroxenes in tkyalite ferrogabbros in the Skacrgaard intrusion which they interpreted to be formed by inversion (see also discussion by LINDSLEY, 1967). Fe-poor fmbustamite, on the other hand, has been reported to occur in shams, principally in Japan (see ABRECHT, 1980, Table 1). The melting relations and boundary for the transition of hedenbergite to ferrobustamite at high pressure inthesystemCaG-FeG-SiO~weredeterminedbyLINDSLEY(1967). The transition temperature at atmospheric pressure is 1233 K (BOWEN e%al., 1933) which agrees well with a projection of Lindsley’s results at high pressures. Iron-poor fmbustamite, which results from solid solution of fsrrobustamite toward wollastonite, is stable at lower temperatures than the end-member composition (RU’~XTEIN,197 1). The crystal structure of the C2/c pyroxene hedenbergite has been refined at six temperatures from 297 to 1273 K by CAMERONet al. (1973). All Fe resides on the M( 1) octahedral sites which form edge-shared,
melts. PREVIOUS WORK BENNINGTONet al. (1984) measu& heat capacities (12.31 I47 K) and an enthalpy of formation by HF solution calorimetry for a natural hedenbergite sample of composition
(Ca.g~,6M)41805%3F~~~Fe~.wMn.,MbXSi206) frem the L=y Mine, South Mountain, I&ho. They obtained values of
2211
2212
H. T. Haselton, Jr., R. A. Robie and B. !I. Hemingway
S&s-S;=
172.~~0.42J/moi.K~d~~(l~,298.15 f 3.58 lcJ/mol; they also observed a peak in the low-tempemture heat capacities at 26.5 K. O’NEILL and NAVROTSKY(1980) deduced a heat of transition from ferrobustamite. to hedenbergite of 8.25 + 1.49 kJ/mol from heats of solution in molten 2PbG. &OS at 970 K. By means of magnetic susceptibihty measurements and M&sbauer spectroscopy, COEYand GHCSE (1985) determined that synthetic hedenbergite orders antiferromagnetically at 38 K. K) = -2849.14
~~e~~~~. The CaFeSii-pb glass was prepamd from SiC&glass and reagent grade FerOs and C&O,. The mix was first decarbonated at 1073 K in air and then reduced at 1223 K with a gas mixture of Co2/Hz = 2.33. A AgT#dm crucible, which had been used to reduce hematite over a period of several days at the same temperature and gas mixing ratio, was used for this reduction. The reduced oxide mix was fused twice at 1573 K in a platinum crucible for ahout 1.5 hr per fusion in the same C!@-Ha gas mixture. The glass was ground coarsely between fusions, and the melt was quenched by withdrawing the crucii from the &mace and immersing it in liquid nitrogen. The color of the resulting glass was dark gray. In order to limit the absorption of iron by the crucible during the fusions, we in&By treated the cnrcible by melting a CaGFeG-Si(& mix containing about 40 wt.% Fe0 at 1623 K for a total of 20 houts, again, with the same gas ratio. We weighed the crucible before and after the fusions in order to have an of the absorption of iron Born indicatiou somewhat m the starting materiaI. During the two fusions, the crucible gained approximateIy 0.03 g which would cormspond to about 0.6% of the total iron in the glass. If this iron metal loas were the only change in composition from ideal stoichiometry, the resulting formula would be Cat,xuFee&ix~O~.~. ~~~~~ple~~~rn~~~ a phoney apparatus at 9 kbar and 1273 IC for 6-24 hr in graphite cae The yield was about 2.3 g per run. Differences in run duration did not result in noticeable changes in crysmlhnity. Reauhs in THOMPSONand KUSHIRO(1972) and WOERMANNet al. (1977) indicate that the CGH system should but&r iron in the fenous state at the chosen P-T condition. The w hedenbergite was in the form of green discs composed of l-10 firn crystah. Adhering graphite was removed by repeated treatments in a low-temperature asher (International Plasma Corp.*) in which the ambient temperature was leas than 373 K. The only apparent change during this process was a general lightening of color, it did not result in a yellowish tint which would suggest surface oxidation. The hedenbergite was converted to ferrobustamite by heating at 1323 K for 20 hr in the same C&Hz &as mixture. During the conversion, the color of the material chan8ed from green to light gray. A small amount (< 1%) of birefringent material was seen in the glass sample. It occurredin patches and the X-my peaks indicated that it was ferrobusmmite. There was no evidence of fayalite which has a heat+mpacity anomaly in the same temperature range as the anomaly found in the glass. The w heat capacities were not corrected for the presence of the ferrobustamite. No second phases were detected in either the hedenbergite or the ferrobustamite when examined with a polarixing light micmscope, with powder x-ray diIIiaction, or in the scanning electron micromope using b&scattered electron imaging Averaged analyses for random chips of CaFe&O6 glass, hedenbergite, and ferrobustamite, which were obtained with an ARL-SEMQ electron microprobe ( I5 kV, 100 namp, 2 gm spot-size), are listed in Table 1. Synthetic fayalite was the standard for iron and natural diopside was
l The use of trade names is for descriptive purposes only and does not imply endorsement by the U.S. Geological Survey.
cd&
Glmbb
(0.19) 28.24 (0.26) 48.59 (0.47) 99.38 (0.60) 22.55
0
FeQ Ekl
ltbdmberlitc
FblTohrtabite
I&al
22.31 (0.52) 23.04 (0.48) 22.60 28.72 toa) 28.60 (O.SSl 26.96 99.95 48.91 10.61) (0.34) 106.67 49.13 lO.51) (0.43) lwJ.00 46.44
03
l.Goo
0.984
Fe Si
0.978 2.011
0,989 2.014
1.009 0.974 2.008
I.600 1.000 2.060
fayalite was the standard for iron and natural diopside was used for calcium and silicon. The analyses are consistent with a CaFeSirOb stoichiometry within the analytical uncertainty, but the analyses are also consistent with some iron loss during fusions as discus& above. standard deviations for CaO and Fe0 (Table 1) am larger for the hedenbergite and ferrobu& ~~a~~~~~r~~~~Ani~on of the individual anaIyses of hedenbergite and f~bustamite shows that low Fe0 vahtes conespond to high CaO values. This indicates that the crystals are not as homogeneous as the glass Unit-cell perameters were refined from x-ray data collected with Cu K, radiation, a Ys”/min scan rate, silicon metal (uc, = 0.543088 nm; Htrlmruu> ef al., 1975) as an internal standard, and the refinement program written by APpLEMAN and EVANS ( 1973). The resultingunit-cell parametersare a = 0.984911) nm, b = O.QO28f1) nm, c = 0.525 I( 1) nm, and @ = 104.91(l)* for hedenbergite and a = 0.76QO(2) nm, b = 0.7112(l) nm, c = 1.3764(2) nm, Q = i~~2~~ . = 95.20(1)0, and y = 103.58(H” fork volumes are 67.956 1) cm3 and 73.0&2) cm3 for hedenbergite and ferrobustamite, mepectively. The numbers in parentheses are 1 standard deviation in the least aign&ant 6gum. These parameters agree well with previous results for synthetic hadenbergite (LINDSLEY, 1967; VELILUVand BURNWAM,196% CAMERONet al., 1973) and synthetic ferrobustamite (Rnwc PORTand BURNHAM,1973). Bjorn Mysen (Geophysical Laboratory) collected M&sbauer spectra for the glass and he& enbergite samples at 77 and 298 K and gave the foIlowing interpretations (B. MYSEN, written communication, 1984). The Fe absorption peaks in the spectra of the glass were fit with two doublets. Ahhough the fits to the spectra might be interpreted to indicate that two iron sites with differing degrees of distortion exist in this glass, a mnge of local geometries could result in similar spectra. The concentration of Fes’ was less than the detection level of 2-3% of the total iron. The M&batter technique is more sensitive to Fe’+ in crystaIline materials than in 8lw, and the spectra of the hedenbetSite indicate that 3-4% of the total iron is Fe3+. The oxidation could have resulted from the synthesis at high pressures or from the ashing procedure. The hyperfine pammeters for both Fe’+ and Fe3+ are consistent with network modifying Fe2” and Fes+ (VIRGOand MYSEN, 1985). Calotimetry. The low-tempemtme heat-capaciry data were collected using an automated adiabatic calorimeter which has been described by ROBIEand H-WAY (1972) and HgHINGWAYd al. ( 1984). Sample weighta amected for buoyancy, were 17.6483 g of hedenbergite, 17.5626 g of fen&us&it&, and 23.0703 a of CaFeSi~O~ glass Anproximately 4 X lo’-’ mol of heliumwas ptesemidthe caIor&ter to p&n~~tc thermal equilibration. The estimated accuracy of the C,, measurements is approximately 5% at 5 K and 0.2% at temperatures greater than 50 K. The results are listed in the chronological order of moasumm ent in Tables 2-4 and am shown in Fig 1 for temperatures less than 80 K. The results were
1mp.
x series 8.72 9.39 10.46 ii.32 12.86 14.27 13.84 17.60 19.32 21.66 24.04 :s 32:90 36.87 46.22 51.23 57.01 63.17 69.44 73.15 81.93 88.06 94.11 100.11 106.04 111.92 117.73 :::-:: 133:oo 140.68 146.34 131.98 137.60 163.19 168.73 174.30 179.83 183.36 190.67 196.36 201 .a4 207.31 212.78 218.25 223.72 229.21 234.72 240.23 243.74 231.23
::::::
267.77
ntrt
capacrty J/(nol
*K)
0.7420 0.9679 1.207 1.443 1.826 2.311 2.904 3.666 4.705 6.091 8.057 10.67 13.02 21.73 18.36 20.10 23.00 27.14 32.60 37.92 43.98 49.93 33.31 60.65 63.61 70.35 74.90 79.61 64.12 88.66 93.09 97.26 101.3 103.1 108.8
:::+; 13716 140.2 143.0 145.8 148.1 135.6 133.0 133.3 137.4 159.3 161.6 164.0
caplclty
K
J/(ml !%rtts
1
:::-: 119:2 122.4 123.6 128.6
HCLt
Temp.
273.28 278.77 284.25 289.71 295.13 300.58 303.97 311.34 316.67
*K)
:x :;:g 44:07 45.16 46.21 47.38 48.49 49.60 60.10 32.60 35.25 37.91 60.63 scr4cs 306.10 311.43
capacity
K
J/(nol
series
1 166.3 168.3 170.6 172.6 174.9 176.0 177.5 178.9 181.6 2
24.28 25.53 26.36 27.29 28.42 29.44 30.23 30.84 31.43 31.99 32.56 33.12 33.69 34.25 34.81 35.39 35.96 36.54 37.10 37.66 38.22 39.34 39.92
nsrt
TCRP .
8.27 9.53 :x 13:16 14.71 16.03 17.28 18.30 19.66 20.82 21.96 23.02 23.59 23.53 22.28 20.21 18.39 18.04 17.95 18.01 16.47 18.65 18.83 19.07 18.97 19.38 19.71 19.75
2%
21.34 21.89 22.38
::+ 27:83 30.02 3 177.9 179.4
316.41 321.39 326.51 331.62 336.71 341.11 346.83 331.89 336.92 361.94 366.93 311.90 376.65
‘K) 3 181.0 182.4 184.7 185.8 186.9 188.5 189.4 190.7 192.6 194.0 195.3 196.5 l97.6
scr1cs
4 187.6 190.1 192.8 195.3 198.0 200.7 202.8 204.4 206.4 209.0 210.3 211.8 214.0 215.7 217.7 219.6 220.9
339.3 349.3 339.2 369.2 379.2 389.1 399.1 409.1 419.0 429.0 439.0 448.9 438.9 468.8 470.8 486.8 497.8 series 468.6 476.6 486.5 498.5 308.3 318.4 328.4 338.3 348.3 358.3 368.2 570.2 3a8.2 398.1 608.1 618.1 628.0 638.0 647.0
215.7 217.5 217.9 218.3 220.1 220.3 221.2 222.4 222.9 224.0 224.5 225.3 226.2 227.2 228.8 229.7 231.7 235.7 234.8
s&kg
Cal-
the pnnxdurmdcs&bed by ~EMINOWAY
(1981). The asmpks wee containai in unxded gold pans.WewrcunabktocompMesati&ktoryscansathigbcr tempaatuRstbnthemcawedmqcsbccawcofsigualinst&ilhy, passii due to oxidation of the samph. The expri~trlnluaue~inTPbksZand3.Athi%ternzsfNtiK), the heat capachy of hedenber8ite ef ul.
C,“(J/moi.K)-310.46+0.012573 - 2039.93T-‘/2 - 1.84604x 106T2 and the heat capwity of fermbustamite may be
represented
by
Cj’ Wmol *K) * 403.83 - 0.04444T + 1.597X IO-‘T2 - 3757.37+. ~~~~~~Y~~~~~~~~~. TheP0wmliiwemc0mtmi&t0j0hlthelow-temprrature
RESULTS
The entropy change, S&.rs - S,”, is 174.2 +. 0.3, 180.5 + 0.3, and 185.7 f 0.4 J/mol - K for hedenbergite, ferrobustamite, and caFeSizOd glass, respectively. The value of 172.46 rt 0.62 J/m01 - K at 298.15 K measured by BENNINGTONet al. (1984) for a natural sample of hedenbergite, wbicb d&red considerably from end-member composition, and the estimated entropy of hedenber&e given by HELGESON et al. ( 1978) are close to the messwed value for our synthetic sample. In hedenbergite, iron remains on the M(1) site at higb temperatures (CAMERONet al., 1973); therefore,
Table 3.
5
to zem kdvin by usin a CJT vs.T2plot. Smoothed values of the heat mpacity and derived thermodynamic functions arelistedinTabkE_7. ) orimeterfting
attemperatureshi@ertbantheme&u&mn8e.ThGap proximation assumes that the heat capecities of oxides are additiveathi&temperatumandthattbefbattcapacityof d&side is a s&able 8&e. Note that there am no matsurements at temperatures greater than 647 K for hedenber8ite and 747 K for femibustamie. The avem8e deviation of the p0iynomids t0 the mepsund data is 0.5%. The ~l~0~~ wem not comtmincd by dummy pointp at temperaturesmtcr than16OOK.
Temp. 1:
scricr 3.36 5.83 6.43 6.97 7.73 8.61 9.59 10.68 ii.89 13.21 14.66 16.23
la.00
19.92 22.02 24.35 26.95 29.83 33.09 36.72 45.38 30.f4 36.29 62.47 68.80 73.12 81.37 87.34 93.63 99.66 103.63 111.33 117.41 123.23 129.01 134.76 140.47 146.16 151.83 137.47 163.09 168.70 :::-8’: 183:40 190.93 196.43 201.96
Expcrimtrl hut capxCltl*S for Synthetic fmokrstaite. 3erics 1 wui 2 ware ls6wed by lat6Qmture adiabatic c4lwimetry an6 se186 b-5 ere amred by diffweiRfr1 rcmlnp crlorimetry.
neat
capacity J/(nol
-II
1 3.090 3.380 3.414 3.718 4.067 4.338 4.589 4.834 3.066 3.260 3.343 5.162 6.044 6.4bB 6.931 7.623 0.373 9.904 11.72 14.01 19.27 22.82 27.36 33.13 39.19 43.99 31.91 37.67 63.02 67.94 72.63 77.27 81.83 86.34 SO.67 94.92 98.98 102.9 106.7 .._ _
Heit Temp. capacity K
sor1ts
.I)
Jllrol
1
207.46 212.96 228.44 223.91 229.39
137.7 140.3
234.74 240.15 243.23 250.29 253.39 260.88 266.17 271.46 276.73 281.99 287.25 292.48 297.64 302.80
130.1 132.3 133.3 137.4 158.3 160.6 162.5 164.3 166.3 168.5 170.4 172.6 174.3 176.4
323.35 3na.43 333.49 338.53 343.58 348.61 353.63 338.65 363.64 368.61 373.56 378.30
:x 1eo:5 181.9 ia3.7 184.6 185.9 186.8 188.6 189.9 190.8 192.3 193.3 194.0 196.0
113.7 116.9 120.1 123.3 126.4
339.1 349.0 339.0 369.0 378.9
187.3 198.8 192.8 194.6 197.1
:::*:
398.9 388.9 408.8
196.0 200.4 202.5
:::*: 147:7 2
3
,I”..9
133:o
lItat Tamp. capacity 1:
J/(mol
series u8.a 426.7 43a,7 448.7 438.6 468.6 478.6 480.5 497.5 series
3 205.4 203.8 207.5 210.3 212.0 213.2 214.7 217.3 219.2 4
468.6 478.6 4aa.5 498.5 308.5 516.4 328.4 336.3 348.3 35ai3
::x 218hl 220.6 222.1 223.2 224.2 225.2 227.0
:::-; 3ae:2 398.1 608.i 618.1 628.0 638.0 647.0
229.1 227.6 229.5 230.1 231.0 231.3 232.2 232.4 233.2
series 618.1 62a;O 638.0 648.0 637.9 667.9 677.8 687 -8 697.8 707.7 717.7 727.7 737.6 746.6
*KI
214.2
3 231.7 231.9 232.8 232.6 233.0 232.8 233.5 234.5 235.4 236.7 238.4 240.0 242.2 243.8
H. T. Haselton, Jr., R. A. Robie and B. S. Hemingway
2214 Table 4.
Low-taperature experimental heat capacltler for weSi*06 glass.
tionof4Rln2 = 23.05 J/mol - K which would be added to the measured value of 180.5 J/mol K. It is quite possible that disorder in end-member ferrobustamite, and in Fe-poor ferrobustamite, will be variable in the temperature range of interest for phase equilib rium calculations. At present, we have information from several sources (discussed below) concerning Msite disorder in ferrobustamite, but no studies directly address the dependence of disorder on temperature. A zero-point contigurational entropy should be added to the measured values for the CaFeSi,O, glass, but, again, the amount of this contribution is umzrtain. Much additional new information would be required for an accurate calculation. Information on disorder in synthetic ferrobustamite can be derived from a comparison of the entropy calculated from heat-capacity measurements with values calculated from phase equilibrium experiments (LIND SLEY, 1967) and with high-temperature heats of solution (O'NEILLand NAVROTSKY, 1980). LINDSLEY (1967) determined the location of the hedenbergiteferrobustamite transition to 1543 K and 13 kbar where the transition intersects the liquidus. The boundary is well constrained by experiments, is linear within experimental uncertainty, and can be represented by the equation P (bar) = 42T (K) - 5 1800. From the slope of the boundary, we calculate an entropy of transition of 19.0 +- 0.3 J/mol - K. The entropy of transition at high pressures calculated from the heat-capacity data, assuming no disorder in ferrobustamite, is 5.7 J/ mol. K, and the value is nearly constant over the temperature range of the boundary. The difference of 13.3 J/mol *K is attributed to disorder in ferrobustamite. If the disorder is distributed equally over the four M sites, the 13.3 J/mol*K corresponds to a 14% interchange l
Temp.
neat cap4city
Temp.
K
J/(mol-K)
K
Series 5.14 6.10 7.38 8.27 9.35 10.37 11.48 12.76 14.14 15.67 17.36 19.24 21.32 23.63 26.19 29.03 32.23 35.82 44.25 49.25 54.78 60.75 66.96 73.28 79.50 85.51 91.44 97.36 103.19 108.94 114.62 120.25 125.82 131.34 136.82 142.25 147.64
1 2.060 2.419 2.729 2.786 3.130 3.535 3.967 4.505 5.044 5.719 6.514 7.450 8.499 9.757 11.27 13.44 15.35 17.88 24.11 27.62 33.30 40.20 45.70 48.49 54.20 59.51 64.54 69.26 73.62 77.07 82.11 86.17 90.21 94.14 97.91 101.5 104.9
Series 152.99 158.32 163.61 168.87 174.12 179.34 184.54 189.71 194.86 200.01 205.13 210.23 215.32 Series 220.36 225.39 230.36 235.35 240.39 245.42 250.44 255.45 260.46 265.49 270.55 275.59 280.62 285.63 290.63 295.62 300.60 305.56 310.51 315.44 320.36 325.28 330.19
neat capacity J/(mol*K) 1 108.3 111.5 114.6 117.7 120.6 123.5 126.2 128.8 131.5 134.1 136.6 138.9 141.2 2 143.6 i45.7 147.8 149.8 151.7 153.7 155.8 157.8 160.0 161.8 163.5 165.3 167.4 169.0 171.0 172.5 174.0 175.5 177.0 180.2 180.4 181.9 183.2
Temp.
Heat capacity
K
J/(mol*K)
Series 335.05 340.42 345.70 351.01 356.35 361.68 367.00 372.31 377.62 382.91 Series 52.90 54.02 54.95 55.91 57.01 59.18 60.28 61.38 62.46 63.54 64.63 65.71 66.79 67.86 68.94 70.03 71.11 72.19 13.25 74.33 75.40 76.46 77.53 78.61 79.69
3 184.3 185.5 187.1 188.3 189.1 190.7 191.3 193.3 195.1 196.0 4 31.11 32.38 33.47 34.38 35.89 38.57 39.19 40.28 41.49 42.74 43.60 44.46 45.37 46.48 46.72 46.04 46.42 47.28 48.28 49.22 50.39 51.51 52.55 53.40 54.44
no additional entropy arises from cation disorder on the M(I) and M(2) crystaUographic sites. The disordering of iron on the M( 1)-M(4) sites in ferrobustamite could result in a maximum con6gurational contribu-
0
b
FIG.1. Measured heat capacities at temperatures less than 80 K forCaFeSi206 glass, hedenbergite, and ferrobustamite. An anomaly is present in the heat capacities of each stmctural state of CaFBi~06. Circle = hedenbergite; triangle = ferrobustamite; and diamond = glass.
Hedenhergiteheatcapxity Table 5.
Temp.
Smoothed thermdynric properties for hedenberglte. Fomwla weight = 248.095 g/ml.
neat
Entropy
capacity T
t;
0 0 'T-'0
Kelvin
5 10 15 20 25 :: :: 50 60 70 GO 90 100
Enthalpy function (Ii;-H;)/T
Gibbs energy function -(G;-H;)/T
J/(mol -K) 0.197 1.097 2.604 5.050 9.041 15.74 22.65 18.71 20.10 22.16 29.58 38.53 48.02 57.13 65.53
0.089 0.446 1.152 2.204 3.722 5.904 9.039 11.56 13.86 16.05 20.71 25.93 31.69 37.88 44.34
0.060 0.312 0.804 1.532 2.600 4.178 6.503 8.064 9.316 10.47 13.00 16.00 19.41 23.10 26.93
0.029 0.134 0.348 0.672 1.122 1.726 2.536 3.516 4.540 5.585 1.711 9.933 12.29 14.70 17.42
110 120 130 140 150 160 170 180 190 200
73.52 81.41 89.21 96.73 103.8 110.4 116.6 122.6 128.3 133.8
50.96 57.70 64.52 71.41 78.33 85.24 92.12 98.96 105.7 112.5
30.80 34.69 38.58 42.47 46.33 50.12 53.85 57.51 61.08 64.58
20.16 23.01 25.94 28.94 32.00 35.12 38.27 41.45 44.65 47.88
210 220 230 240 250 260 270 280 290 300
138.9 143.9 148.5 152.8 157.0 161.0 165.0 168.9 172.6 175.9
119.1 125.7 132.2 138.6 144.9 151.2 157.3 163.4 169.4 175.3
68.00 71.34 74.59 77.76 80.85 83.85 86.78 89.65 92.44 95.17
51.11 54.35 57.59 60.84 64.07 67.30 70.52 73.73 76.93 80.11
310 320 330 340 350 360 370 273.15 298.15
179.1 182.2 185.2 187.9 190.6 193.3 196.0 166.2 175.3
181.1 186.8 192.5 198.1 203.5 208.9 214.3 169.2 174.2
97.83 100.4 102.9 105.4 107.8 110.1 112.4 87.69 94.67
03.27 86.42 89.55 92.66 95.75 98.82 101.9 71.54 79.52
of Fe and Ca atoms. However, the structural refinements of iron-poor ferrobustamite (RAPOPORT and BURNHAM,1973; YAMANAKAez al., 1977) indicated that Fe orders preferentially onto M(3) and preferential ordering could be expected for end-member ferrobustamite as well. In these simple calculations, we have included a thermal expansivity of 3.0 X IO-‘/K for hedenbergite (CAMERONet al., 1973) and approximated the expansivity of ferrobustamite by a value of 2.4 X IO-‘/K for wollastonite (H. T. EVANS,JR, unpublished data, cited in KRUPKAet al., 1979). We conclude that synthetic ferrobustamite is slightly, but significantly, disordered in experiments at high pressures in the temperature range 1223-1543 K. This conclusion is in agreement with the observation that a natural Fe-poor ferrobustamite can be partially disordered by a relatively short heating period at 14 13 K (YAMANAKA ef al., 1977).
O’NEILL and NAVROTSKY(1980) determined an enthalpy of transition for the hedenbergite-ferrobustamite reaction by measuring heats of solution of hedenbergite and ferrobustamite in molten 2FbO - B203 at 970 K. They noted that their measured heat of transition, 8.25 f 1.49 kJ/mol, was much less than they
2215
had expected based on the slope of the hedenbergite-
ferrobustamite transition boundary. Unlike our heatcapacity measurements, the heats of solution reflect the amount of cation disorder in the sample. Their measured enthalpy of transition corresponds to an entropy of transition of 6.7 f 1.2 J/mol * K, which indicates that their ferrobustamite sample was essentially ordered. If their ferrobustamite sample was partially disordered initially, as the phase equilibrium study by LINDSLEY(1967) would suggest, their measurements indicate that synthetic ferrobustamite may order in a few hours at 970 K, the time and temperature in the calorimeter experiments. If fmbustamite does order during the calorimeter equilibration period, the rate of Ca-Fe interchange is fast. The high-temperature relations of hedenbergite and ferrobustamite have been compared with those of the isostructural chemical analogues, johannsenite and bustamite.. The similar slopes and volumes of transition (ANGEL, 1984) indicate that bustamite also may be partially disordered at high temperatures. The best-characterized reaction for the calculation of the free energy and enthalpy of formation for hedenbergite involves the oxidation of hedenbetgite to
Table 6.
Temp. T
Sloothed thermodynaic properties for ferrobustamite. Formula weight . 248.095 g/ml.
neat
capacity c;
Entropy s;-s;
Kelvin
Enthalpy function (II;-H;)/T
Gibbs energy function -(G;-H;)IT
J/(ROl*K)
2.925 4.669 5.591 6.529 7.906 10.00 12.87 15.91 19.03 22.49 30.84 40.55 50.56 59.81 68.23
2.464 5.113 7.190 8.917 10.51 12.12 13.87 15.79 17.84 20.02 24.83 30.31 36.38 42.08 49.62
1.419 2.672 3.500 4.131 4.739 5.420 6.281 7.295 0.424 9.654 12.46 15.77 19.50 23.47 27.53
1.045 2.441 3.690 4.786 5.772 6.695 7.594 a.497 9.418 10.37 12.37 14.53 16.88 19.40 22.09
110 120 130 140 150 160 170 180 190 200
76.14 83.87 91.41 98.63 105.4 111.8 117.7 123.4 128.8 134.0
56.50 63.45 70.47 77.51 84.55 91.56 98.51 105.4 112.2 119.0
31.60 35.63 39.63 43.59 47.49 51.31 55.05 58.68 62.23 65.70
24.90 27.02 30.83 33.92 37.06 40.24 43.47 46.72 49.99 53.27
210 220 230 240 250 260 270 280 290 300
138.9 143.6 148.0 152.2 156.3 160.2 164.0 167.8 171.5 175.0
125.6 132.2 138.7 145.1 151.4 157.6 163.7 169.7 175.7 181.5
69.07 72.35 75.55 78.65 81.68 84.62 87.49 90.29 93.03 95.70
56.55 59.04 63.13 66.41 69.68 72.94 76.19 79.42 02.64 05.84
310 320 330 340 350 360 370 273.15 298.15
178.1 181.0 183.7 186.3 188.8 191.2 193.6 165.2 174.4
187.3 193.0 198.6 204.2 209.6 215.0 220.2 165.6 180.5
98.31 100.9 103.3 105.7 108.1 110.3 112.6 88.38 95.21
89.02 92.18 95.32 98.44 101.5 104.6 107.7 77.21 86.25
H. T. Haselton, Jr., R. A. Robie and B. S. Hemin@vay
2216 Table
Temp. T
7.
Smothed thendynamic properties for CaFeSipOs glass. Fomla weight = 248.095 g/mol.
Heat capacity c;
Entropy
Enthalpy function
q-5;
(H;-H;)/T
:; :“5 40 45 50 60 70 80 90 100
-(G;-H;)/T
J/(mol *K)
Kelvin
1: I5
Gibbs energy function
1.375 3.419 5.418 7.848 10.53 14.04 17.27 21.01 24.59 26.29 39.17 46.50 54.75 63.36 71.25
0.557 2.295 4.044 5.926 7.956 10.18 ::*::: 17:a1 20.59 26.68 33.39 40.07 47.02 54.11
0.363 1.486 2.451 3.488 4.620 5.895 7.280 8.761 10.33 11.93 15.54 19.55 23.37 27.34 31.35
0.194 0.809 1.593 2.438 3.336 4.288 5.300 6.368 7.490 8.660 11.14 13.84 16.70 19.68 22.77
110 120 130 140 150 160 170 180 190 200
78.67 86.01 93.20 100.0 106.4 112.5 118.3 123.8 129.0 134.1
61.25 68.41 75.58 82.74 89.86 96.92 103.9 110.8 117.7 124.4
35.31 39.23 43.11 46.93 50.69 54.36 57.95 61.46 64.88 68.21
25.94 29.18 32.47 35.81 39.18 42.56 45.97 49.38 52.80 56.21
210 220 230 240 250 260 270 280 290 300
138.8 143.4 147.6 151.6 155.6 159.7 163.4 167.0 170.6 173.8
131.1 137.6 144.1 150.5
71.46 74.63 77.71 80.71
156.7 162.9 169.0 175.0 181.0 186.8
tt:.:: as:25 91.96 94.61 97.20
59.62 63.01 66.40 69.77 73.12 76.46 79.70 83.07 86.34 89.59
310 320 330 340 350 360 370 380 273.15 298.15
177*3 180.7 183.1 185.5 188.0 190.0 192.5 195.5 164.5 173.2
192.5 198.2 203.8 209.3 214.7 220.1 225.3 230.3 170.9 185.7
99.73 102.2 104.6 107.0 109.2 111.5 113.6 115.7 90.11 96.73
92.82 96.03 99.21 102.4 105.5 108.6 111.7 114.8 80.82 89.00
with a maximum at about 68 K occms in the heatcapacity curve of the glass. The peak probably corresponds to a magnetic transition. The presence of a magnetic trzmsition in the glass at a higher temperature
than in hedenbergite might indicate that the iron sites in the glass have a narrow range of distortion and that the coupling among iron atoms is stronger than in the edge-shared octahedral chains of hedenbergite. If the iron site in CaFeSi&,j @ is well defined, a wide range of site distortion is not the explanation for the broadening of Fe absorption peaks in the MWbauer spectra relative to Fe absorption peaks for hedenbergite. The broadening of the Fe absorption peaks for glasses relative to peaks for crysWine material has been observed for many silicate compositions (VIRGOand MYSEN, 1985). Acknowfedgements-We especially thank Bjorn Mysen for running and interpreting the M&sbauer scans of the hedenbergite and CaFeSi20~ glass. We also thank I-Ming Chou, Donald H. Lindsley, Charles A. Lawson. Pascal Richet, and Alexandra Navrotsky for critical reviews of the manuscript.
Editorial handling:B. J. Wood REFERENCJB ABRECHTJ. (1980) Stability relations in the system Casio,-
&MnSizD6~eSi206. Contrib. Mineral. Petrol.74,253261. ANGEL R. J. (1984) The experimental deviation of the johann~nite-b~ite eqdlibrium inversion boundary.
Contrib. Mineral. Petrol. f&,272-218. APPLEMAN D. E. and EVANSH. T. JR. (1973) Job 9214: in-
dexing and least-squares refinement of powder diffraction data. U.S. Department of Commerce National Technical Info~ation Senice, PBZ- 16188. BENNINGTON K. O., BEYERR. P. and BROWNR. R. (1984) Thermodynamicpropertiesof hedenbergite, a complex sil-
icate of Ca, Fe, Mn, and Mg. U.S. Bur. Mines Rent. Inv.
andradite, magnetite, and quartz. This calculation was done by ROBE ef al. (1987) utilizing the present heatcapacity data for hedenbergite and their new heat-capacitydataforandradite. TheircaicuIatedvalue&based on the phase equilibrium study by BURTON et al. (19821, are W29a = -2674.3 + 5.8 and AHz298 = -2837.6 It 5.8 J/mol. The CaFeSi20~ composition presents an ~~mrnon opportunity to observe the effact of structural state on magnetic behavior. An anomaly is present in each of the three low-temperature heat capacity curves (Fig. 1). The peak in the hedenbergite heat capacity curve, which occurs at 34.5 K, is the result of antiferromagnetic ordering (COEY and GHOSE, 1985). The corresponding anomaly observed in a natural hedenbergite sample by BENNINGTON etal.(1984) lies at a lower temperature, 263 K, due to the lower concentration of iron. An i&defined bump is present in the ferrobustamite heat capacity at temperatures below 20 K. The cause of the bump could be weak cooperative magnetic o&ring or a Schottky anomaly (GOPAL, 1966). A cooperative magnetic transition is expected to be hindered by the disordering of iron on four crystallographicaliy distinct sites. Surprisingly, a broad peak
8873, 19~. ~OWEN N. L., SCXAIRERJ. F. and FQSNJAK E. (1933) The svstem CaO-FeO-Sia. Amer. .i. Sci: X193-284. BURTONJ. C., TAYLOR L. A. and CHou’I. M. (1982) The
f&T and f&T stabiity relations of hedenbqite and of hedenbergite-johannseenitesolid solutions. Econ. Geol. 77,
764-783. CAMERONM., SUENOS., &win C. T. and PAP~KE J. J. (1973) ~~-~rn~t~ crystalchemistry of acmite, diop
side, hedenbergite, jade&e, spodumene, and ureyite. Amer. Mineral. 58, 594-6 18. COEY J. M. D. and GHOSES. (1985) Magnetic order in hedenbergite, CaFeSi~06. Solid State Commun. 53,143-145. GAMBLER. P. f 1982) An experimental study of sulfidation reactions involving andradite and hedenbergite.&on. Geol. 77.784-797. GOPALE. S. R. (1966) SpecificHeats at Low
Temperatures.
Plenum Press, 24Op. GUSTAFSONW. I. (1974) The stabilityof andmdite, heden-
berg&e,and related minerals in the system Ca-Fe&OH.
J. Petrol. 15,455-4%. HELGE~~NH. C., DELANY J. M., NESBITT H. W. and BIRD D. K. ( 1978) Summary and critique of the thermodynamic
properties of rock-forming minerals. Amer. J. Sci. 2784
I-229. HEMINGWAYB. S., KRUPKAK. M. and RO~IER. A. (198 1) Heat capacitiesof the aIkaiifeMsparsbetween350 and IO00 K from ditkentiaf scanningcatorimetry,the &emmdynamic functions of the alkali feldspars from 298.15 to 1400
Hedenbe@e heat capacity I& and the reaction quartx + jade&e = analbite. Amer. Mineral. 66,1202-1215. HEMINGWAY B. S., ROBE R. A., KI?-IXICKJ. A., GREW E. S., NELENJ. A. and LONDOND. (1984) The heat capacities of osumilite fkom 298.15 to 1000 K the thermodynamic properties of two natural &lo&es to 500 K and the thermodynamic properties of p&elite to 1800K. Amer. Mineral. 69,701-710. HUBBARD C. R., SWANSON H. E. and MAUERF. A. (1975) A silicon powder d&action standard reference matetisl. J. A&. Crystall. 8,45-48. KRUPKAK. M., ROBIER. A. and HEMINOWAYB. S. ( 1979) Hi&-temperature heat capacities of corundum, per&se, anorthite, CaAlsSi~O~ glass, muscovite, pyrophyllite, KAh&ct, glass, grossular, and NaAl!Ii& glass. Amer. Mineral. 64 86: 101. LINDSLEY D. H. ( 1967) The join hedenhergite-fermsihte at high pressures and temperatures. Carnegie fnst. Wash. Yea&. 65,230-234. G’NEILLH. ST. C. and NAVROTSKY A. (1980) The thetmo dynamics of the clinopyroxene to pymxenoid phase transition in the systemsCaO-“FeO”-SiG and CaO-MnO-SiQ . Eos 61, 1147. RAFOPORT P. A. and m C. W. (1973)Ferrobustamite: The crystal structures of two Cs, Fe baits pytoxenoids. Z. Krist~lw. U&419-437. ROBIER. A., ZHAO B., HEMINGWAY B. S. and BARTON M. D. ( 1987)Heat capacity and thermodynamic propetties
2217
of andradite garnet, CasFe2Si,0i2, between 10 and 1000 K. Geochim. Cosmochim. Acta 51,2219-2224. ROBIER. A. and HE~&NGWAY B. S. (1972) Calorimeters for heat of solution and low-tempemtum heat capacity measurements. U.S. Geol. Survey Prqj Paper 75.5. RUTSTEINM. S. ( 1971) Re-emmmation of the wollastonitehedenkrgite (CaSiO&kFeSi@~) equihbrk Amer. Mineral. 56.2040-2052. THOMPSON R. N. and Kus~mo 1.(1972)The oxygen t@city within graphite capsules in piston-cylinder apparatus. Curnegie Inst. Wash. Yea& 71,6 15-6 16. VEBLEN D. R. and BURNHAM C. W. (1969) The crystal structures of hedenbe&e. end farosalite. Can. Miner&. 10,147. VIRGOD. and MYSEN B. 0. (1985) The structural state of iron in oxidixed vs. reduced glassesat 1 atm: A “Fe M&sbauer study. Phys. Chem. Minerals 12,65-76. WAGERL. R. and DEERW. A. (1939) Geokgical investigations in East Greenland, III. Petrology of the Skaergaard intrusion, Kange~Bu@uaq, East Greenland. Medd. Grnnland 105. l-355. WOERMANN E., KNJXHTB., ROSENHAUER M. and ULMER G. C. (1977) The stability of graphite in the system C-O. Ext. Abstr., 2nd In& Kimberlite Conf., Santa Fe, New Mexico. YAMANAKA T., SADANAGA R. and TAIOEUCS~I Y. (1977) Structural variation in the fmobustamite solid solution. Amer. Mineral. 62,1216-1224.
GmchimranC~hrmr~AnuVd.JI,pp2211-2217 0 Pegsmom Jownds Ltd. 1987. Prinud In USA
Heat capacities of synthetic hedenbergite, ferrobustamite, and CaFeSi206 glass H. T. HASELTON, JR., R. A. ROBIE and B. S. HEMINGWAY U.S. Geological Survey, 959 Nat&ml Center, Reston, VA 22092, U.S.A. (Received January 12, 1987; accepted in revisedform May 26, 1987) Abstract-Heat capacities have been measured for synthetic hedenbergite (9-647 K), ferrobustamite (5 746 K), and CaFeSisc)s.glass (6-380 K) by low-t~~mtu~ adiabatic and differemial scanning calorimetry. The heat capacity of each of these structural forms of CaFeSirOs exhibits anomalous behavior at low temperatures The X-peak in the hedenbergite heat-capacity curve at 34.5 K is due to antiferromagnetic ordering of the I@’ ions. Ferrobustamite has a bump in its heat-capacity curve at temperatures less than 20 K, which could be due to weak cooperative magnetic ordering or to a Schottky anomaly. Surprisingly, a broad peak with a maximum at 68 K is present in the heat-capacity curve of the glass. If this maximum, which occurs at a higher temperature than in hedenbergite is caused by magnetic ordering, it could indicate that the range of distortions of the iron sites in the glass is quite small and that coupling between iron atoms is stronger in the glass than in the edge-shared octahedral chains of hedenbergite. The standard entropy change, S&.irr - S,“, is 174.2 + 0.3, 180.5 rf:0.3, and 185.7 rt 0.4 J/molaK for hedenbergite, ferrobustamite and CaFeSi,O, glass, respectively. Ferrobustamite is partially disordered in CaFe distribution at high temperatures, but the dependence of the configurational entropy on temperature cannot be evaluated due to a lack of info~ation. At high temperatures (298- 1600 IQ, the heat capacity of hedenbergite may be represented by the equation C,“(J/molsK) = 310.46 +0.012573-2039.93T-*R-
1.84604 x 106Tw2
and the heat capacity of ferrobustamite may be represented by Cs (J/m01 - K) = 403.83 - O.O4444T+ t .597 X 10s5T2- 3757.3Teif2. INTRODUCTION
in the c direction. RWDPORT and BURNHAM(1973) determined the crystal structure of a synthetic, end-member ferrobustamite and a natural Fe-poor fe~b~te. In this structure, Fe resides on four, ~phicaIly distinct -sitesM(l)M(4). Iron is concentrated on the smaller, and more regular M( 1) and M(3) sites in ordered ftrrobustamite, but in their synthetic sample, sign&ant amounts of Fe were also present on M(2) and M(4). The larger, irregular M(2) and M(4) sites coordinate loosely with additional oxygens yielding 7- and g-fold coordination, respectively. Despite the problems posed by using a heavily twinned sample, which lowered the quality of their refinement RMWORT and BURNHAM (1973) concluded that Fe tended to order onto the M(3) site in Fe-poor ferrobustamite. In a structural study of a higher quality, natural Fe-poor ferrobustamite crystal, YAMANAKAet al. (1977) showed that Fe segregates almost exchrsively onto the M(3) site, but the Fe can be disordered significantly by a relatively short heating period at 14 13 K. Therefore, the Fe distribution must be considered in phase equilibrium calculations. Heat capacities were also measured for C’aFeSilOa glass because the data could be useful in mcxlelling the thermodynamic properties of compositionally complex zig-zag chains
THE PHASERELATIONSof hedenbergite and ferrobustamite are geologically important as potential sources of information about the conditions of Q-Fe skarn formation. Reactions can be written for the oxidation and sulfidation of these minerals, and reactions involving hedenbergite have been studied experimentally by GUSTAFWN (1934), BURTON et al. (1982), and GAMBLE(1982). We are not aware of a natural occurrence of iron-rich ferrobustamite, pmsumably, because cooling rates may be too low to prevent inversion to hedenbergite. For example, WAGER and DEER (1939) found hedenbergitic pyroxenes in tkyalite ferrogabbros in the Skacrgaard intrusion which they interpreted to be formed by inversion (see also discussion by LINDSLEY, 1967). Fe-poor fmbustamite, on the other hand, has been reported to occur in shams, principally in Japan (see ABRECHT, 1980, Table 1). The melting relations and boundary for the transition of hedenbergite to ferrobustamite at high pressure inthesystemCaG-FeG-SiO~weredeterminedbyLINDSLEY(1967). The transition temperature at atmospheric pressure is 1233 K (BOWEN e%al., 1933) which agrees well with a projection of Lindsley’s results at high pressures. Iron-poor fmbustamite, which results from solid solution of fsrrobustamite toward wollastonite, is stable at lower temperatures than the end-member composition (RU’~XTEIN,197 1). The crystal structure of the C2/c pyroxene hedenbergite has been refined at six temperatures from 297 to 1273 K by CAMERONet al. (1973). All Fe resides on the M( 1) octahedral sites which form edge-shared,
melts. PREVIOUS WORK BENNINGTONet al. (1984) measu& heat capacities (12.31 I47 K) and an enthalpy of formation by HF solution calorimetry for a natural hedenbergite sample of composition
(Ca.g~,6M)41805%3F~~~Fe~.wMn.,MbXSi206) frem the L=y Mine, South Mountain, I&ho. They obtained values of
2211
2212
H. T. Haselton, Jr., R. A. Robie and B. !I. Hemingway
S&s-S;=
172.~~0.42J/moi.K~d~~(l~,298.15 f 3.58 lcJ/mol; they also observed a peak in the low-tempemture heat capacities at 26.5 K. O’NEILL and NAVROTSKY(1980) deduced a heat of transition from ferrobustamite. to hedenbergite of 8.25 + 1.49 kJ/mol from heats of solution in molten 2PbG. &OS at 970 K. By means of magnetic susceptibihty measurements and M&sbauer spectroscopy, COEYand GHCSE (1985) determined that synthetic hedenbergite orders antiferromagnetically at 38 K. K) = -2849.14
~~e~~~~. The CaFeSii-pb glass was prepamd from SiC&glass and reagent grade FerOs and C&O,. The mix was first decarbonated at 1073 K in air and then reduced at 1223 K with a gas mixture of Co2/Hz = 2.33. A AgT#dm crucible, which had been used to reduce hematite over a period of several days at the same temperature and gas mixing ratio, was used for this reduction. The reduced oxide mix was fused twice at 1573 K in a platinum crucible for ahout 1.5 hr per fusion in the same C!@-Ha gas mixture. The glass was ground coarsely between fusions, and the melt was quenched by withdrawing the crucii from the &mace and immersing it in liquid nitrogen. The color of the resulting glass was dark gray. In order to limit the absorption of iron by the crucible during the fusions, we in&By treated the cnrcible by melting a CaGFeG-Si(& mix containing about 40 wt.% Fe0 at 1623 K for a total of 20 houts, again, with the same gas ratio. We weighed the crucible before and after the fusions in order to have an of the absorption of iron Born indicatiou somewhat m the starting materiaI. During the two fusions, the crucible gained approximateIy 0.03 g which would cormspond to about 0.6% of the total iron in the glass. If this iron metal loas were the only change in composition from ideal stoichiometry, the resulting formula would be Cat,xuFee&ix~O~.~. ~~~~~ple~~~rn~~~ a phoney apparatus at 9 kbar and 1273 IC for 6-24 hr in graphite cae The yield was about 2.3 g per run. Differences in run duration did not result in noticeable changes in crysmlhnity. Reauhs in THOMPSONand KUSHIRO(1972) and WOERMANNet al. (1977) indicate that the CGH system should but&r iron in the fenous state at the chosen P-T condition. The w hedenbergite was in the form of green discs composed of l-10 firn crystah. Adhering graphite was removed by repeated treatments in a low-temperature asher (International Plasma Corp.*) in which the ambient temperature was leas than 373 K. The only apparent change during this process was a general lightening of color, it did not result in a yellowish tint which would suggest surface oxidation. The hedenbergite was converted to ferrobustamite by heating at 1323 K for 20 hr in the same C&Hz &as mixture. During the conversion, the color of the material chan8ed from green to light gray. A small amount (< 1%) of birefringent material was seen in the glass sample. It occurredin patches and the X-my peaks indicated that it was ferrobusmmite. There was no evidence of fayalite which has a heat+mpacity anomaly in the same temperature range as the anomaly found in the glass. The w heat capacities were not corrected for the presence of the ferrobustamite. No second phases were detected in either the hedenbergite or the ferrobustamite when examined with a polarixing light micmscope, with powder x-ray diIIiaction, or in the scanning electron micromope using b&scattered electron imaging Averaged analyses for random chips of CaFe&O6 glass, hedenbergite, and ferrobustamite, which were obtained with an ARL-SEMQ electron microprobe ( I5 kV, 100 namp, 2 gm spot-size), are listed in Table 1. Synthetic fayalite was the standard for iron and natural diopside was
l The use of trade names is for descriptive purposes only and does not imply endorsement by the U.S. Geological Survey.
cd&
Glmbb
(0.19) 28.24 (0.26) 48.59 (0.47) 99.38 (0.60) 22.55
0
FeQ Ekl
ltbdmberlitc
FblTohrtabite
I&al
22.31 (0.52) 23.04 (0.48) 22.60 28.72 toa) 28.60 (O.SSl 26.96 99.95 48.91 10.61) (0.34) 106.67 49.13 lO.51) (0.43) lwJ.00 46.44
03
l.Goo
0.984
Fe Si
0.978 2.011
0,989 2.014
1.009 0.974 2.008
I.600 1.000 2.060
fayalite was the standard for iron and natural diopside was used for calcium and silicon. The analyses are consistent with a CaFeSirOb stoichiometry within the analytical uncertainty, but the analyses are also consistent with some iron loss during fusions as discus& above. standard deviations for CaO and Fe0 (Table 1) am larger for the hedenbergite and ferrobu& ~~a~~~~~r~~~~Ani~on of the individual anaIyses of hedenbergite and f~bustamite shows that low Fe0 vahtes conespond to high CaO values. This indicates that the crystals are not as homogeneous as the glass Unit-cell perameters were refined from x-ray data collected with Cu K, radiation, a Ys”/min scan rate, silicon metal (uc, = 0.543088 nm; Htrlmruu> ef al., 1975) as an internal standard, and the refinement program written by APpLEMAN and EVANS ( 1973). The resultingunit-cell parametersare a = 0.984911) nm, b = O.QO28f1) nm, c = 0.525 I( 1) nm, and @ = 104.91(l)* for hedenbergite and a = 0.76QO(2) nm, b = 0.7112(l) nm, c = 1.3764(2) nm, Q = i~~2~~ . = 95.20(1)0, and y = 103.58(H” fork volumes are 67.956 1) cm3 and 73.0&2) cm3 for hedenbergite and ferrobustamite, mepectively. The numbers in parentheses are 1 standard deviation in the least aign&ant 6gum. These parameters agree well with previous results for synthetic hadenbergite (LINDSLEY, 1967; VELILUVand BURNWAM,196% CAMERONet al., 1973) and synthetic ferrobustamite (Rnwc PORTand BURNHAM,1973). Bjorn Mysen (Geophysical Laboratory) collected M&sbauer spectra for the glass and he& enbergite samples at 77 and 298 K and gave the foIlowing interpretations (B. MYSEN, written communication, 1984). The Fe absorption peaks in the spectra of the glass were fit with two doublets. Ahhough the fits to the spectra might be interpreted to indicate that two iron sites with differing degrees of distortion exist in this glass, a mnge of local geometries could result in similar spectra. The concentration of Fes’ was less than the detection level of 2-3% of the total iron. The M&batter technique is more sensitive to Fe’+ in crystaIline materials than in 8lw, and the spectra of the hedenbetSite indicate that 3-4% of the total iron is Fe3+. The oxidation could have resulted from the synthesis at high pressures or from the ashing procedure. The hyperfine pammeters for both Fe’+ and Fe3+ are consistent with network modifying Fe2” and Fes+ (VIRGOand MYSEN, 1985). Calotimetry. The low-tempemtme heat-capaciry data were collected using an automated adiabatic calorimeter which has been described by ROBIEand H-WAY (1972) and HgHINGWAYd al. ( 1984). Sample weighta amected for buoyancy, were 17.6483 g of hedenbergite, 17.5626 g of fen&us&it&, and 23.0703 a of CaFeSi~O~ glass Anproximately 4 X lo’-’ mol of heliumwas ptesemidthe caIor&ter to p&n~~tc thermal equilibration. The estimated accuracy of the C,, measurements is approximately 5% at 5 K and 0.2% at temperatures greater than 50 K. The results are listed in the chronological order of moasumm ent in Tables 2-4 and am shown in Fig 1 for temperatures less than 80 K. The results were
1mp.
x series 8.72 9.39 10.46 ii.32 12.86 14.27 13.84 17.60 19.32 21.66 24.04 :s 32:90 36.87 46.22 51.23 57.01 63.17 69.44 73.15 81.93 88.06 94.11 100.11 106.04 111.92 117.73 :::-:: 133:oo 140.68 146.34 131.98 137.60 163.19 168.73 174.30 179.83 183.36 190.67 196.36 201 .a4 207.31 212.78 218.25 223.72 229.21 234.72 240.23 243.74 231.23
::::::
267.77
ntrt
capacrty J/(nol
*K)
0.7420 0.9679 1.207 1.443 1.826 2.311 2.904 3.666 4.705 6.091 8.057 10.67 13.02 21.73 18.36 20.10 23.00 27.14 32.60 37.92 43.98 49.93 33.31 60.65 63.61 70.35 74.90 79.61 64.12 88.66 93.09 97.26 101.3 103.1 108.8
:::+; 13716 140.2 143.0 145.8 148.1 135.6 133.0 133.3 137.4 159.3 161.6 164.0
caplclty
K
J/(ml !%rtts
1
:::-: 119:2 122.4 123.6 128.6
HCLt
Temp.
273.28 278.77 284.25 289.71 295.13 300.58 303.97 311.34 316.67
*K)
:x :;:g 44:07 45.16 46.21 47.38 48.49 49.60 60.10 32.60 35.25 37.91 60.63 scr4cs 306.10 311.43
capacity
K
J/(nol
series
1 166.3 168.3 170.6 172.6 174.9 176.0 177.5 178.9 181.6 2
24.28 25.53 26.36 27.29 28.42 29.44 30.23 30.84 31.43 31.99 32.56 33.12 33.69 34.25 34.81 35.39 35.96 36.54 37.10 37.66 38.22 39.34 39.92
nsrt
TCRP .
8.27 9.53 :x 13:16 14.71 16.03 17.28 18.30 19.66 20.82 21.96 23.02 23.59 23.53 22.28 20.21 18.39 18.04 17.95 18.01 16.47 18.65 18.83 19.07 18.97 19.38 19.71 19.75
2%
21.34 21.89 22.38
::+ 27:83 30.02 3 177.9 179.4
316.41 321.39 326.51 331.62 336.71 341.11 346.83 331.89 336.92 361.94 366.93 311.90 376.65
‘K) 3 181.0 182.4 184.7 185.8 186.9 188.5 189.4 190.7 192.6 194.0 195.3 196.5 l97.6
scr1cs
4 187.6 190.1 192.8 195.3 198.0 200.7 202.8 204.4 206.4 209.0 210.3 211.8 214.0 215.7 217.7 219.6 220.9
339.3 349.3 339.2 369.2 379.2 389.1 399.1 409.1 419.0 429.0 439.0 448.9 438.9 468.8 470.8 486.8 497.8 series 468.6 476.6 486.5 498.5 308.3 318.4 328.4 338.3 348.3 358.3 368.2 570.2 3a8.2 398.1 608.1 618.1 628.0 638.0 647.0
215.7 217.5 217.9 218.3 220.1 220.3 221.2 222.4 222.9 224.0 224.5 225.3 226.2 227.2 228.8 229.7 231.7 235.7 234.8
s&kg
Cal-
the pnnxdurmdcs&bed by ~EMINOWAY
(1981). The asmpks wee containai in unxded gold pans.WewrcunabktocompMesati&ktoryscansathigbcr tempaatuRstbnthemcawedmqcsbccawcofsigualinst&ilhy, passii due to oxidation of the samph. The expri~trlnluaue~inTPbksZand3.Athi%ternzsfNtiK), the heat capachy of hedenber8ite ef ul.
C,“(J/moi.K)-310.46+0.012573 - 2039.93T-‘/2 - 1.84604x 106T2 and the heat capwity of fermbustamite may be
represented
by
Cj’ Wmol *K) * 403.83 - 0.04444T + 1.597X IO-‘T2 - 3757.37+. ~~~~~~Y~~~~~~~~~. TheP0wmliiwemc0mtmi&t0j0hlthelow-temprrature
RESULTS
The entropy change, S&.rs - S,”, is 174.2 +. 0.3, 180.5 + 0.3, and 185.7 f 0.4 J/mol - K for hedenbergite, ferrobustamite, and caFeSizOd glass, respectively. The value of 172.46 rt 0.62 J/m01 - K at 298.15 K measured by BENNINGTONet al. (1984) for a natural sample of hedenbergite, wbicb d&red considerably from end-member composition, and the estimated entropy of hedenber&e given by HELGESON et al. ( 1978) are close to the messwed value for our synthetic sample. In hedenbergite, iron remains on the M(1) site at higb temperatures (CAMERONet al., 1973); therefore,
Table 3.
5
to zem kdvin by usin a CJT vs.T2plot. Smoothed values of the heat mpacity and derived thermodynamic functions arelistedinTabkE_7. ) orimeterfting
attemperatureshi@ertbantheme&u&mn8e.ThGap proximation assumes that the heat capecities of oxides are additiveathi&temperatumandthattbefbattcapacityof d&side is a s&able 8&e. Note that there am no matsurements at temperatures greater than 647 K for hedenber8ite and 747 K for femibustamie. The avem8e deviation of the p0iynomids t0 the mepsund data is 0.5%. The ~l~0~~ wem not comtmincd by dummy pointp at temperaturesmtcr than16OOK.
Temp. 1:
scricr 3.36 5.83 6.43 6.97 7.73 8.61 9.59 10.68 ii.89 13.21 14.66 16.23
la.00
19.92 22.02 24.35 26.95 29.83 33.09 36.72 45.38 30.f4 36.29 62.47 68.80 73.12 81.37 87.34 93.63 99.66 103.63 111.33 117.41 123.23 129.01 134.76 140.47 146.16 151.83 137.47 163.09 168.70 :::-8’: 183:40 190.93 196.43 201.96
Expcrimtrl hut capxCltl*S for Synthetic fmokrstaite. 3erics 1 wui 2 ware ls6wed by lat6Qmture adiabatic c4lwimetry an6 se186 b-5 ere amred by diffweiRfr1 rcmlnp crlorimetry.
neat
capacity J/(nol
-II
1 3.090 3.380 3.414 3.718 4.067 4.338 4.589 4.834 3.066 3.260 3.343 5.162 6.044 6.4bB 6.931 7.623 0.373 9.904 11.72 14.01 19.27 22.82 27.36 33.13 39.19 43.99 31.91 37.67 63.02 67.94 72.63 77.27 81.83 86.34 SO.67 94.92 98.98 102.9 106.7 .._ _
Heit Temp. capacity K
sor1ts
.I)
Jllrol
1
207.46 212.96 228.44 223.91 229.39
137.7 140.3
234.74 240.15 243.23 250.29 253.39 260.88 266.17 271.46 276.73 281.99 287.25 292.48 297.64 302.80
130.1 132.3 133.3 137.4 158.3 160.6 162.5 164.3 166.3 168.5 170.4 172.6 174.3 176.4
323.35 3na.43 333.49 338.53 343.58 348.61 353.63 338.65 363.64 368.61 373.56 378.30
:x 1eo:5 181.9 ia3.7 184.6 185.9 186.8 188.6 189.9 190.8 192.3 193.3 194.0 196.0
113.7 116.9 120.1 123.3 126.4
339.1 349.0 339.0 369.0 378.9
187.3 198.8 192.8 194.6 197.1
:::*:
398.9 388.9 408.8
196.0 200.4 202.5
:::*: 147:7 2
3
,I”..9
133:o
lItat Tamp. capacity 1:
J/(mol
series u8.a 426.7 43a,7 448.7 438.6 468.6 478.6 480.5 497.5 series
3 205.4 203.8 207.5 210.3 212.0 213.2 214.7 217.3 219.2 4
468.6 478.6 4aa.5 498.5 308.5 516.4 328.4 336.3 348.3 35ai3
::x 218hl 220.6 222.1 223.2 224.2 225.2 227.0
:::-; 3ae:2 398.1 608.i 618.1 628.0 638.0 647.0
229.1 227.6 229.5 230.1 231.0 231.3 232.2 232.4 233.2
series 618.1 62a;O 638.0 648.0 637.9 667.9 677.8 687 -8 697.8 707.7 717.7 727.7 737.6 746.6
*KI
214.2
3 231.7 231.9 232.8 232.6 233.0 232.8 233.5 234.5 235.4 236.7 238.4 240.0 242.2 243.8
H. T. Haselton, Jr., R. A. Robie and B. S. Hemingway
2214 Table 4.
Low-taperature experimental heat capacltler for weSi*06 glass.
tionof4Rln2 = 23.05 J/mol - K which would be added to the measured value of 180.5 J/mol K. It is quite possible that disorder in end-member ferrobustamite, and in Fe-poor ferrobustamite, will be variable in the temperature range of interest for phase equilib rium calculations. At present, we have information from several sources (discussed below) concerning Msite disorder in ferrobustamite, but no studies directly address the dependence of disorder on temperature. A zero-point contigurational entropy should be added to the measured values for the CaFeSi,O, glass, but, again, the amount of this contribution is umzrtain. Much additional new information would be required for an accurate calculation. Information on disorder in synthetic ferrobustamite can be derived from a comparison of the entropy calculated from heat-capacity measurements with values calculated from phase equilibrium experiments (LIND SLEY, 1967) and with high-temperature heats of solution (O'NEILLand NAVROTSKY, 1980). LINDSLEY (1967) determined the location of the hedenbergiteferrobustamite transition to 1543 K and 13 kbar where the transition intersects the liquidus. The boundary is well constrained by experiments, is linear within experimental uncertainty, and can be represented by the equation P (bar) = 42T (K) - 5 1800. From the slope of the boundary, we calculate an entropy of transition of 19.0 +- 0.3 J/mol - K. The entropy of transition at high pressures calculated from the heat-capacity data, assuming no disorder in ferrobustamite, is 5.7 J/ mol. K, and the value is nearly constant over the temperature range of the boundary. The difference of 13.3 J/mol *K is attributed to disorder in ferrobustamite. If the disorder is distributed equally over the four M sites, the 13.3 J/mol*K corresponds to a 14% interchange l
Temp.
neat cap4city
Temp.
K
J/(mol-K)
K
Series 5.14 6.10 7.38 8.27 9.35 10.37 11.48 12.76 14.14 15.67 17.36 19.24 21.32 23.63 26.19 29.03 32.23 35.82 44.25 49.25 54.78 60.75 66.96 73.28 79.50 85.51 91.44 97.36 103.19 108.94 114.62 120.25 125.82 131.34 136.82 142.25 147.64
1 2.060 2.419 2.729 2.786 3.130 3.535 3.967 4.505 5.044 5.719 6.514 7.450 8.499 9.757 11.27 13.44 15.35 17.88 24.11 27.62 33.30 40.20 45.70 48.49 54.20 59.51 64.54 69.26 73.62 77.07 82.11 86.17 90.21 94.14 97.91 101.5 104.9
Series 152.99 158.32 163.61 168.87 174.12 179.34 184.54 189.71 194.86 200.01 205.13 210.23 215.32 Series 220.36 225.39 230.36 235.35 240.39 245.42 250.44 255.45 260.46 265.49 270.55 275.59 280.62 285.63 290.63 295.62 300.60 305.56 310.51 315.44 320.36 325.28 330.19
neat capacity J/(mol*K) 1 108.3 111.5 114.6 117.7 120.6 123.5 126.2 128.8 131.5 134.1 136.6 138.9 141.2 2 143.6 i45.7 147.8 149.8 151.7 153.7 155.8 157.8 160.0 161.8 163.5 165.3 167.4 169.0 171.0 172.5 174.0 175.5 177.0 180.2 180.4 181.9 183.2
Temp.
Heat capacity
K
J/(mol*K)
Series 335.05 340.42 345.70 351.01 356.35 361.68 367.00 372.31 377.62 382.91 Series 52.90 54.02 54.95 55.91 57.01 59.18 60.28 61.38 62.46 63.54 64.63 65.71 66.79 67.86 68.94 70.03 71.11 72.19 13.25 74.33 75.40 76.46 77.53 78.61 79.69
3 184.3 185.5 187.1 188.3 189.1 190.7 191.3 193.3 195.1 196.0 4 31.11 32.38 33.47 34.38 35.89 38.57 39.19 40.28 41.49 42.74 43.60 44.46 45.37 46.48 46.72 46.04 46.42 47.28 48.28 49.22 50.39 51.51 52.55 53.40 54.44
no additional entropy arises from cation disorder on the M(I) and M(2) crystaUographic sites. The disordering of iron on the M( 1)-M(4) sites in ferrobustamite could result in a maximum con6gurational contribu-
0
b
FIG.1. Measured heat capacities at temperatures less than 80 K forCaFeSi206 glass, hedenbergite, and ferrobustamite. An anomaly is present in the heat capacities of each stmctural state of CaFBi~06. Circle = hedenbergite; triangle = ferrobustamite; and diamond = glass.
Hedenhergiteheatcapxity Table 5.
Temp.
Smoothed thermdynric properties for hedenberglte. Fomwla weight = 248.095 g/ml.
neat
Entropy
capacity T
t;
0 0 'T-'0
Kelvin
5 10 15 20 25 :: :: 50 60 70 GO 90 100
Enthalpy function (Ii;-H;)/T
Gibbs energy function -(G;-H;)/T
J/(mol -K) 0.197 1.097 2.604 5.050 9.041 15.74 22.65 18.71 20.10 22.16 29.58 38.53 48.02 57.13 65.53
0.089 0.446 1.152 2.204 3.722 5.904 9.039 11.56 13.86 16.05 20.71 25.93 31.69 37.88 44.34
0.060 0.312 0.804 1.532 2.600 4.178 6.503 8.064 9.316 10.47 13.00 16.00 19.41 23.10 26.93
0.029 0.134 0.348 0.672 1.122 1.726 2.536 3.516 4.540 5.585 1.711 9.933 12.29 14.70 17.42
110 120 130 140 150 160 170 180 190 200
73.52 81.41 89.21 96.73 103.8 110.4 116.6 122.6 128.3 133.8
50.96 57.70 64.52 71.41 78.33 85.24 92.12 98.96 105.7 112.5
30.80 34.69 38.58 42.47 46.33 50.12 53.85 57.51 61.08 64.58
20.16 23.01 25.94 28.94 32.00 35.12 38.27 41.45 44.65 47.88
210 220 230 240 250 260 270 280 290 300
138.9 143.9 148.5 152.8 157.0 161.0 165.0 168.9 172.6 175.9
119.1 125.7 132.2 138.6 144.9 151.2 157.3 163.4 169.4 175.3
68.00 71.34 74.59 77.76 80.85 83.85 86.78 89.65 92.44 95.17
51.11 54.35 57.59 60.84 64.07 67.30 70.52 73.73 76.93 80.11
310 320 330 340 350 360 370 273.15 298.15
179.1 182.2 185.2 187.9 190.6 193.3 196.0 166.2 175.3
181.1 186.8 192.5 198.1 203.5 208.9 214.3 169.2 174.2
97.83 100.4 102.9 105.4 107.8 110.1 112.4 87.69 94.67
03.27 86.42 89.55 92.66 95.75 98.82 101.9 71.54 79.52
of Fe and Ca atoms. However, the structural refinements of iron-poor ferrobustamite (RAPOPORT and BURNHAM,1973; YAMANAKAez al., 1977) indicated that Fe orders preferentially onto M(3) and preferential ordering could be expected for end-member ferrobustamite as well. In these simple calculations, we have included a thermal expansivity of 3.0 X IO-‘/K for hedenbergite (CAMERONet al., 1973) and approximated the expansivity of ferrobustamite by a value of 2.4 X IO-‘/K for wollastonite (H. T. EVANS,JR, unpublished data, cited in KRUPKAet al., 1979). We conclude that synthetic ferrobustamite is slightly, but significantly, disordered in experiments at high pressures in the temperature range 1223-1543 K. This conclusion is in agreement with the observation that a natural Fe-poor ferrobustamite can be partially disordered by a relatively short heating period at 14 13 K (YAMANAKA ef al., 1977).
O’NEILL and NAVROTSKY(1980) determined an enthalpy of transition for the hedenbergite-ferrobustamite reaction by measuring heats of solution of hedenbergite and ferrobustamite in molten 2FbO - B203 at 970 K. They noted that their measured heat of transition, 8.25 f 1.49 kJ/mol, was much less than they
2215
had expected based on the slope of the hedenbergite-
ferrobustamite transition boundary. Unlike our heatcapacity measurements, the heats of solution reflect the amount of cation disorder in the sample. Their measured enthalpy of transition corresponds to an entropy of transition of 6.7 f 1.2 J/mol * K, which indicates that their ferrobustamite sample was essentially ordered. If their ferrobustamite sample was partially disordered initially, as the phase equilibrium study by LINDSLEY(1967) would suggest, their measurements indicate that synthetic ferrobustamite may order in a few hours at 970 K, the time and temperature in the calorimeter experiments. If fmbustamite does order during the calorimeter equilibration period, the rate of Ca-Fe interchange is fast. The high-temperature relations of hedenbergite and ferrobustamite have been compared with those of the isostructural chemical analogues, johannsenite and bustamite.. The similar slopes and volumes of transition (ANGEL, 1984) indicate that bustamite also may be partially disordered at high temperatures. The best-characterized reaction for the calculation of the free energy and enthalpy of formation for hedenbergite involves the oxidation of hedenbetgite to
Table 6.
Temp. T
Sloothed thermodynaic properties for ferrobustamite. Formula weight . 248.095 g/ml.
neat
capacity c;
Entropy s;-s;
Kelvin
Enthalpy function (II;-H;)/T
Gibbs energy function -(G;-H;)IT
J/(ROl*K)
2.925 4.669 5.591 6.529 7.906 10.00 12.87 15.91 19.03 22.49 30.84 40.55 50.56 59.81 68.23
2.464 5.113 7.190 8.917 10.51 12.12 13.87 15.79 17.84 20.02 24.83 30.31 36.38 42.08 49.62
1.419 2.672 3.500 4.131 4.739 5.420 6.281 7.295 0.424 9.654 12.46 15.77 19.50 23.47 27.53
1.045 2.441 3.690 4.786 5.772 6.695 7.594 a.497 9.418 10.37 12.37 14.53 16.88 19.40 22.09
110 120 130 140 150 160 170 180 190 200
76.14 83.87 91.41 98.63 105.4 111.8 117.7 123.4 128.8 134.0
56.50 63.45 70.47 77.51 84.55 91.56 98.51 105.4 112.2 119.0
31.60 35.63 39.63 43.59 47.49 51.31 55.05 58.68 62.23 65.70
24.90 27.02 30.83 33.92 37.06 40.24 43.47 46.72 49.99 53.27
210 220 230 240 250 260 270 280 290 300
138.9 143.6 148.0 152.2 156.3 160.2 164.0 167.8 171.5 175.0
125.6 132.2 138.7 145.1 151.4 157.6 163.7 169.7 175.7 181.5
69.07 72.35 75.55 78.65 81.68 84.62 87.49 90.29 93.03 95.70
56.55 59.04 63.13 66.41 69.68 72.94 76.19 79.42 02.64 05.84
310 320 330 340 350 360 370 273.15 298.15
178.1 181.0 183.7 186.3 188.8 191.2 193.6 165.2 174.4
187.3 193.0 198.6 204.2 209.6 215.0 220.2 165.6 180.5
98.31 100.9 103.3 105.7 108.1 110.3 112.6 88.38 95.21
89.02 92.18 95.32 98.44 101.5 104.6 107.7 77.21 86.25
H. T. Haselton, Jr., R. A. Robie and B. S. Hemin@vay
2216 Table
Temp. T
7.
Smothed thendynamic properties for CaFeSipOs glass. Fomla weight = 248.095 g/mol.
Heat capacity c;
Entropy
Enthalpy function
q-5;
(H;-H;)/T
:; :“5 40 45 50 60 70 80 90 100
-(G;-H;)/T
J/(mol *K)
Kelvin
1: I5
Gibbs energy function
1.375 3.419 5.418 7.848 10.53 14.04 17.27 21.01 24.59 26.29 39.17 46.50 54.75 63.36 71.25
0.557 2.295 4.044 5.926 7.956 10.18 ::*::: 17:a1 20.59 26.68 33.39 40.07 47.02 54.11
0.363 1.486 2.451 3.488 4.620 5.895 7.280 8.761 10.33 11.93 15.54 19.55 23.37 27.34 31.35
0.194 0.809 1.593 2.438 3.336 4.288 5.300 6.368 7.490 8.660 11.14 13.84 16.70 19.68 22.77
110 120 130 140 150 160 170 180 190 200
78.67 86.01 93.20 100.0 106.4 112.5 118.3 123.8 129.0 134.1
61.25 68.41 75.58 82.74 89.86 96.92 103.9 110.8 117.7 124.4
35.31 39.23 43.11 46.93 50.69 54.36 57.95 61.46 64.88 68.21
25.94 29.18 32.47 35.81 39.18 42.56 45.97 49.38 52.80 56.21
210 220 230 240 250 260 270 280 290 300
138.8 143.4 147.6 151.6 155.6 159.7 163.4 167.0 170.6 173.8
131.1 137.6 144.1 150.5
71.46 74.63 77.71 80.71
156.7 162.9 169.0 175.0 181.0 186.8
tt:.:: as:25 91.96 94.61 97.20
59.62 63.01 66.40 69.77 73.12 76.46 79.70 83.07 86.34 89.59
310 320 330 340 350 360 370 380 273.15 298.15
177*3 180.7 183.1 185.5 188.0 190.0 192.5 195.5 164.5 173.2
192.5 198.2 203.8 209.3 214.7 220.1 225.3 230.3 170.9 185.7
99.73 102.2 104.6 107.0 109.2 111.5 113.6 115.7 90.11 96.73
92.82 96.03 99.21 102.4 105.5 108.6 111.7 114.8 80.82 89.00
with a maximum at about 68 K occms in the heatcapacity curve of the glass. The peak probably corresponds to a magnetic transition. The presence of a magnetic trzmsition in the glass at a higher temperature
than in hedenbergite might indicate that the iron sites in the glass have a narrow range of distortion and that the coupling among iron atoms is stronger than in the edge-shared octahedral chains of hedenbergite. If the iron site in CaFeSi&,j @ is well defined, a wide range of site distortion is not the explanation for the broadening of Fe absorption peaks in the MWbauer spectra relative to Fe absorption peaks for hedenbergite. The broadening of the Fe absorption peaks for glasses relative to peaks for crysWine material has been observed for many silicate compositions (VIRGOand MYSEN, 1985). Acknowfedgements-We especially thank Bjorn Mysen for running and interpreting the M&sbauer scans of the hedenbergite and CaFeSi20~ glass. We also thank I-Ming Chou, Donald H. Lindsley, Charles A. Lawson. Pascal Richet, and Alexandra Navrotsky for critical reviews of the manuscript.
Editorial handling:B. J. Wood REFERENCJB ABRECHTJ. (1980) Stability relations in the system Casio,-
&MnSizD6~eSi206. Contrib. Mineral. Petrol.74,253261. ANGEL R. J. (1984) The experimental deviation of the johann~nite-b~ite eqdlibrium inversion boundary.
Contrib. Mineral. Petrol. f&,272-218. APPLEMAN D. E. and EVANSH. T. JR. (1973) Job 9214: in-
dexing and least-squares refinement of powder diffraction data. U.S. Department of Commerce National Technical Info~ation Senice, PBZ- 16188. BENNINGTON K. O., BEYERR. P. and BROWNR. R. (1984) Thermodynamicpropertiesof hedenbergite, a complex sil-
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andradite, magnetite, and quartz. This calculation was done by ROBE ef al. (1987) utilizing the present heatcapacity data for hedenbergite and their new heat-capacitydataforandradite. TheircaicuIatedvalue&based on the phase equilibrium study by BURTON et al. (19821, are W29a = -2674.3 + 5.8 and AHz298 = -2837.6 It 5.8 J/mol. The CaFeSi20~ composition presents an ~~mrnon opportunity to observe the effact of structural state on magnetic behavior. An anomaly is present in each of the three low-temperature heat capacity curves (Fig. 1). The peak in the hedenbergite heat capacity curve, which occurs at 34.5 K, is the result of antiferromagnetic ordering (COEY and GHOSE, 1985). The corresponding anomaly observed in a natural hedenbergite sample by BENNINGTON etal.(1984) lies at a lower temperature, 263 K, due to the lower concentration of iron. An i&defined bump is present in the ferrobustamite heat capacity at temperatures below 20 K. The cause of the bump could be weak cooperative magnetic o&ring or a Schottky anomaly (GOPAL, 1966). A cooperative magnetic transition is expected to be hindered by the disordering of iron on four crystallographicaliy distinct sites. Surprisingly, a broad peak
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2217
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