Anerican Mineralogist, Volume 70, pages 249-260, I9B5

Low-temperature_heat-capacities and derived thermodynamic properties ofanthophyllite, diofside, enstatite, bronzite, and wollast'onitt

Kn.nrern M. Knupr,ll

D e p artment of G e o scienc e sThe Pennsylaania State Unioersity

U niuersity P ark, Pennsyluania I 6802

RIcnc,RD A. Ronn, Bnucn S. HnMrNcw,qy

U.S. Geological SurueyReston, Virginia 22092

Dnnnrr,r, M. Knnnrcr

D e p ar tment of G e o scienc esThe Pennsyloania State Uniuersity

U niuersity P ark, P ennsyluania I 6802

,c.ND JUN Iro2

The James Franck InstituteThe Uniuersity of Chicago

Chicago, Illinois 606 3 7

Abstract

The heat capacities for magnesio-anthophyllite, diopside, synthetic enstatite, bronzite, andwollastonite were measured between 5 and 385 K by use of an adiabatic calorimeter. Theentropy change si* - s3, in f(mol' K), is 538.9 +2-7 for magnesio-anthophyllite[Mgu..Feo.rsiEo22(oH)2], 142.7 +o.2 for diopside, 66.27 +o.ro for synthetic ensiatite(MgSior), 69.04+0.10 for bronzite (Mgo.rrFeo.rrSior), and 8r.69+0.r2 for wollastonite. Theheat capacity, ci, for magnesio-anthophyllite, corrected to a composition of pure Mg-anthophyllite [Mgrsiroz(oH)r], results in a sles - sfi value of 537.o*2.7 /(mol.K). Theseresults represent only the entropy calculated from the measured heat capacities. No configu-rational entropy was added.

Although our Ci values for diopside and wollastonite differ significantly from those ofprevious studies, especially at cryogenic temperatures, our entropies at 298.15 K are in closeagreement with the commonly accepted values. Schottky heat capacity anomalies were ob-served below 25 K for magnesio-anthophyllite, diopside, and bronzite. The contribution ofthe magnetic entropy arising from the interaction of Fe2+ with the ligand ficld of the crystalsis discussed.

IntroductionThe previously accepted entropies for diopside and wol-

lastonite at 298.15 K were based on a limited number oflow-temperature Cfl measurements. King (1957) andWagner (1932) reported Ci values for diopside between 50and 300 K and between 20 and 40 K, respectively. Wagner

r Present address: Geosciences Research and Engineering De-partrnent, Battelle, Pacific Northwest Laboratories, Richland,Washington 99352.

2 Deceased.

0003-{04xl85/03O44249$02.W 249

(1932) also measured the Cfi of wollastonite over several,often narrow, temp€rature intervals between 9 and 3(X K.Prior to this study, low-temperature Ci data for magnesio-anthophyllite and enstatite were nonexistent, and heat ca-pacity measurements by Kelley (1943) between 52 and 296K for a poorly characterized sample of clinoenstatite wereused to estimate the thermodynamic properties of enstatite.Reliable values for the entropies of these phases are criti-cally important to calculating the high-temperature stabili-ty of these minerals and the metamorphic and igneousequilibria involving them.

250

Table 1. Chemical analyses of samples used in low-temperature

heat capacity measurements

KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES

Minerals

M agne sio - antho ph yllit e, M g 6.sF e 6. 1 Si BO 2 z ( O H ) 2The anthophyllite sample, designated'1.3.71.10, was collected by

Prof. Peter Misch in the North Cascades at mile-marker 132.5

along the North Cascades Highway (Washington Route 20) north

of the eastern part of Lake Diablo. A small vein of light-green'

coarse-bladed anthophyllite was cut from the specimen, crushed,

and sieved to the range of -35 to +100 mesh. Impurities were

removed from the sample by using a Franz3 magnetic separator

and heavyJiquid techniques. X-ray powder-diffraction methods

showed that the separated anthophyllite contained talc (<5%) as

the only impurity.The chemical analysis given in Table I is in close agreement

with unpublished electron probe analyses provided by Prof. Misch

and with other probe analyses completed during this study. Or-

thorhombic symmetry for the sample was confirmed by use of a

petrographic microscope. The unit-cell dimensions for the calori-

metric sample, given in T,able 2, are in good agreement with the

values for synthetic, pure-Mg anthophyllite (Chernosky and

Autio, 1979) and for natural anthophyllite (Finger, 1970).

The anthophyllite sample was also tnalyznd for the presence of

3 The use of trade names is for descriptive purposes only anddoes not imply endorsement by Battelle, Pacific Northwest Labo-ratories, U.S. Geologic Survey, or The Pennsylvania State Univer'srty.

hydrous pyribole structures (Veblen et al., 19'17 ; Veblen and Burn-

ham, l978a,b). The magnesio-anthophyllite sample is composed of

at least 95 percent (by volume) double chain material and approxi-

mately 5 percent wider chains (Veblen, wdtten communication,

1978). The distribution of disordered, wider chain material is not

homogeneous in the sample. A description of the intergrowth

structures in this anthophyllite sample was given by Veblen and

Buseck (1979).

Diopside, CaMg(SiO) 2

The white diopside sample was collected by one of us (DMK)

from an area near Zermztt, Switzerland studied by Bearth (1970),

and was used in the experimental study of Slaughter et al' (1975)'

Examinations by means of X-ray diffraction and a petrogaphic

microscope did not reveal any impurities in the powdered diop-

side. The chemical composition given in Table I is in close agree'

ment with the analyses presented by Slaughter et al. (1975)' The

cell dimensions given in Table 2 are in excellent agreernent with

the values for diopside presentd by Borg and Smith (1969) and in

the Joint Committee of Powder Diffraction Standards (rcros) file

lI-654.

Bronzite, M g s.s 5F e s., 5SiO g

The bronzite sample was described by Huebner et al. (1979)'

The calorimetric sample consisted of 3l pale-brown, single-crystal

chips, that ranged in mass from 0.19 to 1.65 g. Optical examina-

tion of each chip did not reveal any impurities. The composition

of each chip was determined by electron-rnicroprobe analysis

using the method of Bence and Albee (1968). Multiple spot analy-

ses of each chip revealed no chemical inhomogeneities within any

single chip. A weighted-average chemical composition for this

sample is given in Table 1. Unit-cell dimensions were measured for

the most Mg- and Fe-rich bronzite chips, designated K30 and

K3l, respectively. The refined cell constants (Table 2) are in good

agreement with those for bronzite as given in JCPDS patterns

19-605 and 26-876.

S ynthetic enstotite, M gSiO 3

Enstatite crystals were prepared by growth from a lithium-

vanadomolybdate flux using the method of Ito {1975). Residual

flux was removed by solution with H2O in a sonic cleaner aftergentle crushing of the crystals. Further details are given by

Kiupka (1984). Semi-quantitative emission spectroscopy analysis

detected (maximal values): Li: 1100 ppm, Mo : 1200 ppm'

Ni : 100 ppm, P : 910 ppm, V : 1500 Ppm, and Zr : l2O ppm'

Microprobe results (Table 1) show that the synthetic enstatite is

essentially pure, stoichiometric MgSiO3. Unit-cell dimensions

were measured for two samples of synthetic MgSiOr and are given

in Table 2. Cell dimensions of the calorimetric sample are in excel-

lent agreement with those given by Ito (1975) for a similarly syn-

thesized enstatite.

Wollastonite, CaSiOg

The wollastonite sample from Willsboro, Essex County, New

York, was purchased from Wards Natural Science Establishment'

The specimen was crushed, sieved to the range of -35 to +100

mesh, and separated by heavyJiquid techniques. X-ray diffraction

and optical measurements on the final sample did not reveal any

impurities. Chemical analyses of the separated wollastonite are

given in Table 1. The refined cell constants (Table 2) are in close

agreement with the values for wollastonite given by Buerger and

Prewitt (1961).

f l a g n e s i o - - D i o p s i d e d - E n s t a t i t e . *a n t h o p h y l l i t e d ( s y n t h e t l c ) "

B r o n z i t e H o t l a s t o n i t e d( n a t u r a l ) c

Si 02

Ti 02

Al 203

C r Z 0 3

Fe203

F e 0

fi90

Mn0

N i 0

C a 0

N a 2 0

Kzo

Pzos

coz

H2o*

Hzo-

Tota 1 :

5 9 . 4

0 . I

0 . 9 5

0 .1 r

0 .57

5 . 7

3 0 . 2

0 . 1 2

0 . 1 2

0.20

0 . 0 7

0.03

0 , 0 1

2 . t

0 . 2 2

0 . 0 0

0 . 2 0

0.09

0,48

1 8 . 0

59.2n

0.00

o . l 2 e

40.80

1 0 . 1 1 e

3 I . 6 1

0 , l 9

5 1 . 8

0 .00

<0.05

0.05"

0 . t 2

5 5 . 8 6

0 . 1 0

0 . 2 9

0.04

25,2 0 .00

0 . 0 1

0 . 0 2

0,03

0 . 0 1

0 . 6 4

0.08

0 . 0 0

4 8 . 5

0 . 0 1

0 . 0 I

0 .00

0.00

(0 .01

100.52 100. I 0 100.20 9 8 . 8 2 1 0 0 , 4 9

aAnalyses completed by conbinat ion of atomic absorpt ion sPect 'oscopy and

s t a n l a r d w e t - c h e m i c a l t e c h n i q u e s . S e e S h a p i . o ( 1 9 7 5 ) f o r a d e s c r i p t i o n

o f t h e s e a n a l Y t i c a l t e c h n i q u e s .DAveraqe of 84 spot probe analyses.g i , i i i q h i i a - i " i - 9 i ' o t ' a t o t a t o i 5 5 s p o t p r o b e a n a l v s e s f o . 3 1 b r o n z i t e c h i p s 'd T o t a l i r o n a s F e 2 0 ? .e T o t a l i r o n a s F e o , -

KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES

Table 2. Cell constants for samples used in heat capacity measurements

251

Magnes i o -an thophy l I i te

D i o p s i d e - - - - - - -B ronz i t e - - - - - - - - - - - -Ens ta t i t e - - - - - - t lo l I as ton i te( na tu ra l )

K30 K31(synthet ic)

I t o - l l t o -7

a ( n m )

b ( n m )

c ( n n )

B

v ( n m 3 )

N

1 . 8 5 3 6 ( 3 )

1 T A A O r 2 \

o . 5 2 7 7 ( r )

90.

90 '

90'

1 . 7 6 0 6 ( 4 )

38

0 . e 7 4 9 ( 1 )

0 .8925 ( I )

0 . 5 2 5 1 1 ( 9 )

90'

r O s o 4 8 . 2 , ( e )

90"

0 .43966 ( 8 )

32

1 .8250 (3 ) 7 .824e (2 )

0 . 8 8 3 7 ( 1 ) 0 . 8 8 4 3 ( 1 )

0 . 5 1 9 0 ( 1 ) 0 . 5 1 e 3 ( l )

90" 90"

90' 90"

90' 90"

0 .8370 (2 ) 0 .8380 (2 )

29 30

r .8228(? l r .82re(2)

0 .8816 (1 ) 0 .8814 ( l )

0 . 5 1 8 0 ( 1 ) 0 . s 1 7 8 ( 1 )

90" 90.

90' 90.

90' 90"

0 .8325 (2 ) 0 .8316 (2 )

28 34

0 . 7 e 2 s ( 1 )

0.7322(2)

0 .7069 ( r )

e o " 4 ' ( 2 )

9 s ' 1 3 . 8 ' ( e )

1 0 3 " l e ' ( l )

0 . 3e74 ( 1 )

23

N o t e : C e l l d i m e n s i o n s g i v e n i n n a n o m e t e r s ( 1 n m = l 0 A ) .d i m e n s i o n s w e r e m e a s u r e d u s i n g C u K c r a d i a t i o n . a N . i( a = 0 . 6 1 9 7 1 t 0 . 0 0 0 1 n m ) a s a n i n t e r n a l s t a n d a r d .

N = Number o f re f lec t ions used in ' leas t -squares re f inement

N u m b e r i n p a r e n t h e s e s i s u n c e r t a i n t y i n l a s t d i g i t . C e l lf i l t e r , a s c a n n i n g r a t e o f 0 . 2 5 o 2 0 l m i n , a n d B a F z

program wr i t ten by App leman and Evans (1973) .

Apparatus and proceduresLow-temperature Ci measurements were made using the

apparatus and techniques described by Robie and Heming-way (1972) and Robie et al. (1976). The observed heat ca-pacities were corrected for curvature (Robie and Heming-way, 1972) and for small quantities of He gas, generallybetween 9.6 x 10-s and 8.4 x 10-4 moles of gas, whichwere introduced into the calorimeter during the loading inorder to promote thermal equilibration at cryogenic tem-peratures (Robie et al., 1976). The 1975 atomic weights(Commission on Atomic Weights, 1976), were used to cal-culate the gram-formula weights of the measured com-pounds.

Experimental resultsThe experimental specific heats of magnesio-

anthophyllite, diopside, bronzite, synthetic enstatite, andwollastonite are listed in their chronological order ofmeasurement in Tables 3 through 7, respectively. Thesample masses (in vacuo) and number of calorimetricmeasurements made with each sample are given in theheadings of Table 3 through 7. These experimental valueshave been corrected for curvature but not for deviationfrorn their ideal end-member formulas. The estimated un-certainty of the experimental data is +5.0% at 5 K,+l.O% at 15 K, and +0.15% between 25 and 380 K(Robie et al., 1978). The experimental Cfl data, corrected forimpurities, are shown in Figures 1 through 4.

The experimental Ci data for magnesio-anthophyllitewere corrected for chemical impurities (secondary phases)and for deviation from end-member stoichiometry by theprocedure described by Krupka (1984) and Robie et al.(1976, p. 640). Corrections were first applied to the Cfidata to obtain a solid-solution magnesio-anthophyllite

[Mgu..Feo.rSi8O22(OH)2] by assuming that 848.382 g ofimpure anthophyllite consist of I mole of magnesio-anthophyllite (802.900 g) and 14.239 g NaAlSi.O, glass,10.838 g CaSiO. (wollastonite),5.711 g FerO, (hematite),4.629 g AlrO. (corundum), 4.350 g SiO, (quartz), 3.535 gKAlSi3Oe glass, 2.552 g Feo.rS (pyrrhotite), and 1.O22 gMnO (manganosite). The low-temperature Ci data forNaAlSi.O' and KAlSi.O, glasses were from Robie et al.(1978), CaSiO, from this study, FerO. from Gronvold andWestrum (1959), AlrO3 from Furukawa et al. (1956), SiO2from unpublished data by Prof. E. F. Westrum, Jr. (Univer-sity of Michigan), Feo.rS from Gronvold et al. (1959),amosite from Bennington et al. (1978), and the remainderof the Ci data were taken from Kelley and King (1961).The selection of these phases for impurity corrections wasbased on the availability of accurate C[ data for the con-stituents. The difference between the uncorrected Cfi valuesand those calculated for Mgu.. Feo.rSirOrr(OH), is 3.8%at 50 K, and <O.5o/o at all temperatures greater than100 K.

The experimental C! data for magnesio-anthophyllitewere similarly corrected to a pure Mg-anthophyllite byassuming that 936.445 g of the impure sample contains Imole of Mg-anthophyllite [MgrSi.O rr(OH)r, 780.874 g],and 103.982 g FerSi6Orr(OH), (amosite-fibrous ferro-anthophyllite), 15.734 g NaAlSi.O, glass, 11.977 g CaSiO,(wollastonite), 6.306 g FerO. (hematite), 5.108 g AlrO,(corundum), 4.77L g SiO, (quartz),3.924 g KAlSi.O, glass,2.815 g FeOo.rS (pyrrhotite), and 1.128 g MnO (mangano-site). The difference between the uncorrected and correctedCfi values is l4c'/o at 50 K, decreases to 0.3% at 1(X) K, andincreases to approximately 3Yo at temperatures greaterthan 275 K.

The C! data for diopside were corrected for chemical

252

Table 3. Low-ternperature, experimental specific heats ofmagresio-anthophyllite. (Sample mass was 22.lll g (in vacuo).Data for magnesio-anthophyllite consist of 94 measurements be-

twcen 5.4 and 386.0 K.)

Temp. Spec l f i cheat

K U ( g . K )

Temp.

KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES

Ser i es I

305 .29 0 .8379311 .12 0 .8476317 .34 0 .8584323.41 0.8685329 .43 0 .8782335.40 0.8882

Se r i es 2

341 .71 0 .8981347.70 0.9069353 .66 0 .9159359.57 0.9242365 .40 0 .93313 i1 .10 0 .9413376.97 0.9490382.08 0.9553385.99 0.9597

Se r i es 3

51 .10 0 .0669356 .15 0 .0793160.76 0.0940665 .60 0 .110270 .53 0 .127875 .70 0 . t 47281 .00 0 .167986 .10 0 .188391.05 0.208195 .78 0 .2270

100.48 0.2459105 .42 0 .2656110 .36 0 .2855115 .32 0 .3053t20.32 0.3253125 .35 0 .3450130 .33 0 .3643135 .15 0 .3825

Se r i es 4

140 .17 0 .4013145 .11 0 .4195150 .13 0 .4376155 .18 0 .4552160.?2 0.4727165.26 0.4897170 .30 0 .5064175 .35 0 .5228180 .41 0 .5392185.48 0.5547190.57 0.5702195 .68 0 .5852200.81 0.6000

Se r i es 5

20s .94 0 .6144211 .00 0 .6285215 .93 0 .6416220.90 0.6548225 .9 t 0 .6677230.87 0.6dol235.87 0.5928240.90 0.7051245 .89 0 .7168250 .83 0 .7280255 .81 0 .7390

Ser ies 6

260.84 0.7500265.84 0.7610270 .88 0 .7117275.97 0.782028t.0? 0.1923286.04 0.8025291 .10 0 .8131296.22 0.82v301 .31 0 .8310306.45 0.8403311 .65 0 .8489

Ser ies 7

5 .43 0 .0011486.00 0.0015236 .61 0 .0019077 .35 0 .0023998.2t 9.0029229 .07 0 .0034109 .95 0 .003911

10.97 0.00446212 .13 0 .00499813.38 0.00543014.72 0.00588016 .19 0 .006361t7 .79 0 .00701519 .54 0 .0079792t.46 0.00916423 .53 0 .0107025.81 0.0727528.32 0.0155231 .9q a .o l 92234.25 0.0244437.66 0.0308441 .25 0 .0383945 .30 0 .04783

Ser ies 8

50.42 0.0614554.86 0.0748359.67 0.08989

Temp. Spec i f i cheat

K U ( s . K )

S p e c i f i c T e m p . S p e c i f i cheat heat

K J / ( g . K ) K J / ( g . K )

20 K, 0.08% at 100 K, and less than 0.03% at all temper-atures greater than 150 K.

Below 25 K, the specific heats for magn€sio-anthophyllito, diopside, and bronzite are significantlylarger than those for wollastonite and synthetic enstatite.This difference is presumably due to a Schottky-type con-tribution (Gopal, 1966) to the heat capacity at very lowtemperatures arising from the small amount of Fe2+ insolid solution. Because the Schottky contributions are sig-nificant for the magnesio-anthophyllite and bronzite sam-ples, their heat capacities exhibit anomalous "plateaus"near 15 K. The C! anomalies are especially apparent whenthe data are plotted in the form of CS|T versus f2, wherothe anomalies are seen to have a maximum value near 100K2 (Fig. 5). The evaluation of the entropy contributionfrom the Schottky effects for bronzite will be discussed in alater section.

Table 4. Low-temperature, experimental specific heats of diop-side. (Sample mass was 32.O83 g (in vacuo). Data for diopside

consist of 92 measurements between 8.6 and 382.0 K.)

T e m p . S p e c i f i c T e m p . S P e c i f i cheat heat

K U ( g . K ) K U ( s . K )

impurities and for deviation from end-member stoichiome-try by the same procedure used for anthophyllite. A sampleof 222.321 g was assumed to consist of 1 mole of diopside[CaM(SiO.)2,216.553 g] and 3.617 g SiO2 (quartz),1.381g FerO, (hematite), 0.444 E AlrO, (corundum), 0.348 gCaO, and 0.092 g MnO (manganosite). The difference be-tween the uncorrected and corrected Ci values is 3.3Vo at20 K, O.9o/o at 50 K, and approximately 0.15% at all tem-peratures greater than 100 K.

The experimental Ci data for wollastonite were correct-ed for impurities and deviation from end-member stoichi-ometry by assuming that a 116.604 g of sample consists of1 mole of pure wollastonite (CaSiO3, ll6.lu g) and 0.185g CaO, 0.141 g MgO (periclase),0.061 g Al3O3 (corundum),and 0.056 g Fe2O3 (hematite). The diflerence between theuncorrected and impurity-corrected Ci values is O.25%o at

Ser i es I

298.38 0.7692302 .64 0 .7765308.20 0.7848314 .55 0 .794632t.52 0.8047328.24 0.8141334.91 0.8233341 .53 0 .8319

Se r i es 2

336.38 0.8252343 .10 0 .8339

Se r i es 3

349.68 0.8426356.23 0.8509362.13 0.8591369 .19 0 .8669375 .61 0 .8747381.99 0.8815

Ser ies 4

54.74 0.0726560 .50 0 .0914265.44 0.108470 .33 0 .126175 .36 0 .145180 .41 0 .164785 .52 0 .185090.66 0.205395 .81 0 .2256

100 .94 0 .2458

Se r i es 5

107 .87 0 .27281t2.82 0.2919II7.67 0.3104123 .61 0 .3326129.67 0.3548134 .88 0 .3735140 .28 0 .3923145 .80 0 .4110

Se r i es 6

151 .36 0 .4294156.90 0.4472162.36 0.4643167.68 0.4806t72 .90 0 .4961178 .01 0 .5110183 .05 0 .5251188 .05 0 .5391193 .04 0 .5523198 .04 0 .5653203 .09 0 .5781208.?4 0.s908213 .51 0 .60332t8.92 0.6161224 .49 0 .6288

Se r i es 7

229.78 0.6407?35.19 0.6539241.93 0.6669248.27 0.6835254.82 0.6937261 .51 0 .7076

Se r i es 8

268 .15 0 ,7250?74.93 0,7312281 .63 0 .74?2288.22 0.7538294.64 0.7640300 .87 0 .7737

Ser ies 9

237.52 0.6577?43.69 0.6706249.79 0.6829255 .81 0 .694426t.77 0.7062267 .67 0 .7174273.54 0.7?83279.39 0.7378285 .19 0 .7475

Ser ies l0

8 .62 0 .0011849 .32 0 .0013119 .97 0 .001442

Ser i es l1

11 .35 0 .001578t2 .26 0 .00159113 .40 0 .001818t4.72 0.00207216 .19 0 .0023881'1.78 0.002864t9.47 0.003602? t . 37 0 .00463823.56 0.00616625.93 0.00831128 .53 0 .0112531 .33 0 .0152034.34 0.0203637 .69 0 .0269541 .45 0 .0352745 .64 0 .0456850.24 0.0585455 .29 0 .O7 4?L60 .66 0 .09176

KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES 253

Temp. Spec i f i cheat

K J / ( e . K )

Spec i f i c Temp. Spec i f i cheat heat

J / ( s . K ) K J / ( s . K )

Table 5. Low-temperature, experimental specffic heats of bron-zite. (Sample mass was 25.162 g (in vacuo). Data for bronzite

consist of 96 measurements between 5.5 and 3E7.4 K.)

mately 15 K were obtained from this extrapolation. Thisprocedure resulted in minor changes to the molar C$values in this temperature range, and negligible diflerencesto the integrated thermodynamic properties (i.e., S? - SB).Our procedure for correcting the diopside measurernentsfor the Schottky effect caused by the Fe2+ impurity can bereadily justified by comparing the heat capacities from thelinear extrapolation with: (1) the heat capacity measure-ments of Leadbetter et al. (1977) between 1.5 and 25 K onsynthetic diopside, and (2) heat capacities calculated fromthe Debye model using a value for @o of 668 K obtainedfrom the elastic constant data of Levien et al. (1979) usingthe method of Robie and Edwards (1966). For magnesio-anthophyllite corrected to a pure Mg composition, Ci was

Table 6. Low-temperature, experimental specific heats of synthet-ic enstatite. (Sample mass was 23.287 g (in vacuo). Data for syn-thetic enstatite consist of 109 measurements b€tween 5.2 and

385.3 K.)

Temp.

Ser i es 1

297 .37 0 .77?8300 .74 0 .7809306 .43 0 .7908312 .40 0 .8004318.43 0.8098324.60 0.8193330.80 0.8282336.89 0.8374

Sen ies 2

333 .09 0 .8328

Se r i es 3

343.77 0.8466347 .09 0 .8518353 .07 0 .8598359 .02 0 .8678364.97 0.875?370 .99 0 .8833316.97 0.8906382.42 0.8965387 .39 0 .9017

Se r i es 4

53 .01 0 .0616857 .86 0 .0761362.33 0.0900667 .05 0 .10587i .88 0.12?876 .90 0 . l 4 l 4

Se r i es 5

81 . 91 0 . 160486 .89 0 .179692 ,00 0 .199397 .10 0 .?19?

102.23 0.2390107 .18 0 .25851 12.00 0.2769r 16 .91 0 .2956

Se r i es 6

Lz t . 7 t 0 . 3137I?6 .62 0 .3321131 .55 0 .3503136 .61 0 .3685141 .69 0 .3864

Ser i es 7

146.16 0.4038151 .80 0 .4210156 .80 0 .4376161 .78 0 .4358166 .75 0 .4696I t t . 73 0 .4850176 .76 0 .5002

Se r i es 8

181 .44 0 .5140186 ,65 0 .5291192.03 0.544?I97 .33 0 .5586202.54 0.5726207.79 0.5859213 .06 0 . s995218.26 0.6125223,40 0.62482?8 .58 0 .6371233 .80 0 .6493238.96 0.6608244.06 0.6724

Se r i es 9

?40.02 0.6629245.30 0.6751250 .56 0 .6868255.87 0.6976261 .33 0. 7084?66 .84 0 .7196272.29 0.7298277 .70 0 .7404283 .07 0 .7498

Se r i es l 0

288.41 0.7599?93 .79 0 .7701299.23 0.7787304 .64 0 .7873

Se r i es l l

5 . 50 0 .0021146 .01 0 .0029106 .53 0 .0033927 .04 0 .0041167 .64 0 .00453 i8 .29 0 .0050679.06 0.0058699 .90 0 .006513

10 .93 0 .00700612.12 0.00738513.42 0.00760014 .88 0 .00775316 .51 0 .00779018 .19 0 .00794920.04 0,00830022.05 0,00885024.18 0.00974226 .59 0 .0112429 .33 0 .0135532,29 0.0170035.67 0.0220239 .40 0 .0286143.23 0.0365747 .19 0 .0471452 .98 0 .06 r5058 .18 0 .07701

Temp. Spec i f i cheat

K J / ( g . K )

Temp. Spec i f i c Temp.heat

K J / ( e . K ) K

S p e c i f i cheat

J / ( s . K )

Thermodynamic functionsThe thermodynamic properties Ci' Si - SB, @i- ffi)/f ,

and -(Gi - m)lf are listed at integral temperaturesfrom 0 to 380 K for magnesio-anthophyllite[Mgu.rFeo.rSir022(OH)2 and MgrSirOzz(OH)z], diopside,bronzite (M go.r rFeo. r r SiO.), synthetic enstatite (MgSiOr),and wollastonite in Tables 8 through 13, respectively.

The methods described by Westrum et al. (1968) wereutilized to smooth the experimental data. The Ci data wereextrapolated from the lowest measured temperature to zeroKelvin on a plot of Cfi,/T versus T2. For diopside andwollastonite, which exhibited small anomalies in CilTversus T2 because of trace quantities of Fe2 + in their struc-ture, the data were extrapolated graphically to zero Kelvinfrom a temperature above the anomaly. Smooth Cfi valuesfor diopside and wollastonite between zero and approxi-

Ser i es 1

318 .87 0 .85213?4 .41 0 .8613330 .33 0 .8706336 .3 i 0 . 8801342.44 0.8888

Se r i es 2

348.60 0.8982354 .80 0 .9067360 .97 0 .9156367.09 0.9242373 .18 0 .9323379.24 0.9401385 .26 0 .9463

Se r i es 3

52.79 0.0553757 .69 0 .0700262.06 0.0839266 .69 0 .0995371 .46 0 .116776 .35 0 .135481 .40 0 .155486 .50 0 .176091 .56 0 .196896 .51 0 .2 r70

101 .29 0 .2365106 .32 0 .?5701 1 1 .57 0 .?785116 .70 0 .2995

Se r i es 4

Lzt .7I 0.3200126.56 0.3391131 ,37 0 .3580136 .34 0 ,3773141 .49 0 .3968146 .61 0 .4159151 .59 0 .4341

Ser ies 5

t56.27 0.4506161 .09 0 .4674165 .96 0 .4839170 .83 0 .5004175 .70 0 .5163180.59 0.5324185 .49 0 .5474190.41 0.5624195 .36 0 .5771200.32 0.5914205 .31 0 .6055210.23 0.6193215.18 0.6324

Se r i es 6

2 r9 .99 0 .6454225 .OO 0 .6589230 .08 0 .6714235 .11 0 .6839240.08 0.6965

Se r i es 7

245.01 0.7081249.98 0.7196254.99 0.7306259.96 0.7413264 .89 0 .7519

Se r i es 8

269 .81 0 .7614274 .72 0 .7721279.] t 0.7826284.66 0.7923289.66 0.8030?94 .72 0 .8115299.74 0.8195304 .73 0 .8293309 .78 0 .8375314 .88 0 .8463319 .96 0 .8553325.00 0.8627330.01 0.8705

Ser ies 11

12.75 0.00054814.09 0.00079815 .30 0 .001000r6 .69 0 .00133778.27 0.00177879.92 0.002447?1 .71 0 .00333223.62 0.00436525.77 0.00581528 . I 1 0 .00764930 .69 0 .0103633 .58 0 .0140736.19 0.0189839.89 0.0244343 .34 0 .0314347.8? 0.041385? .66 0 .0546257 .59 0 ,06933

Ser i es 12

306.80 0.832331 1.94 0.8408317 .00 0 .84933?2 .02 0 .8574

Se r i es 13

5 .?4 0 .0000015 .91 0 .0000246 .47 0 .0000797 .05 0 .0000797 .89 0 .0001078.85 0.9002249 .72 0 .000298

10.56 0.00032211.48 0.000469t2.46 0.00058213 ,54 0 .00071914.74 0.00091016.08 0.001208t7 ,62 0 .001601t9.26 0.0022402 r .o7 0 .00304223 .O7 0 .00406325.27 0.005493

254

Table 7. Low-temperature, experimental specific heats of wol-

lastonite. (Sample mass was 29.231 g (in vacuo). Data for wol-

lastonite consist of 94 measurements between 6.3 and 386.2 K.)

KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES

T e m p . S p e c i f i c T e m p . S p e c i f i cHeat Heat

MgzSi802z(0H lz

3Feo ?Si8022(0H)2

50 100 150 200 250 300 350TEMPERATURE ( KELVINS)

Fig. 1. Experimental molar heat capacity ofnatural anthophyl-lite [Mgu..Feo.?Si8O22(OH)2]. The open squares and solid trian-gles are experimental data for the Mg/Fe magnesio-anthophyllitedetermined by adiabatic calorimetry (this study) and DSC analysis(Krupka et al., 1985), resPectively. The solid line is a least-squaresfit to thc data. The dashed line is a least-squares fit to the datacorrected to the pure Mg composition MgrSi"Orr(OH)r.

50 100 150 200 250 300 350T E M P E R A T U R E ( K E L V I N S )

Fig. 2. Experimental molar heat capacity ofdiopside. The open

squares and solid diamonds are data determined by adiabatic

calorimetry (this study) and DSC analysis (Krupka et al., 1985)'

respectively. The solid hexagons and solid triangles are the low-

temperature Ci data of Wagner (1932) and King (1957)' respec-

tively. The solid line is a least-squares fit to the experimental data

from this study.

700

T e m p . S p e c i f i cHeat

K U ( g . K ) K U ( s . K ) K J / ( s . K )

600

? 500

Ser i es 3

298 .81 0 .7423303 .86 0 .7494309 .81 0 .75723t5.72 0.7648321 .68 0 .77?0327 .69 0 .7795333 ,66 0 .7866

Se r i es 4

339 .66 0 .7934345.79 0.8002351 .88 0 .8070357 .93 0 .8140363 .95 0 .8197369 .94 0 .8255375 .90 0 .8317381 .83 0 .8370386 .16 0 .8413

Se r i es 5

52.83 0.094?257 .01 0 ,1 10261 .49 0. t27466.30 0.14627 1 . 1 8 0 . 1 6 5 676 .06 0 .185280 .95 0 .205685.90 0.225490.82 0.244595 .64 0 .?626

r00 .51 0 .2810105 .51 0 .2994

Se r i es 6

110 .49 0 .3 r72115 .59 0 .3353120 .93 0 .3539126 .09 0 .3709

Se r i es 7

130 .73 0 .3862135 .64 0 .4018140 .56 0 .4169145 .56 0 .4318150.54 0.4462155 .51 0 .4602160 .48 0 .4739165 .45 0 .4874170 .51 0 .5006

Se r i es 8

1 7 5 . r 9 0 . 5 1 2 3180.15 0.5247185 .16 0 .5367190 .20 0 .5486195 .15 0 .5598200 .14 0 .5709205 .16 0 .5817210 .11 0 .5916215 .10 0 .6018

Se r i es 9

222 .57 0 .617?226.55 0.6249231 .68 0 .6347236.77 0.6445241.74 0.6538?46.67 0.6625

Sen ies 10

25 r .58 0 .6700?56.62 0.679126 r .63 0 .6886266 .60 0 .6973

Se r tes l r

2 7 r . 4 7 0 . 7 1 0 5?76 .50 0 .7115281 .54 0 .7 t82286.54 0.7259291 .51 0 .7338296.54 0.7391301 .62 0 .1473306 .67 0 .7537311 .70 0 .7600

Se r i es I 2

6 .27 0 .0000747.47 0.0002408 .33 0 .0002819.01 0.0005039 .64 0 .000481

10.?1 0.00069210.99 0.00067511 .85 0 .00085112 .81 0 .00110413 .88 0 .001432I5 .05 0 .00189516.54 0.00259618 .17 0 .00371219 .78 0 .005178?1 .66 0 .007197?3 .77 0 .0100326 . r5 0 .0138928.78 0.0189731.67 0.0256034 .95 0 .0342638.60 0.0448642;66 0.0576847 .35 0 .0735252 .38 0 .092055 7 . 4 0 0 . 1 I 1 2

E r^^

-

o o 1 O no " " "

200

100

175

150

^ 125:<

= 100

3o o 7 q

50

25

extrapolated to zero Kelvin according to the principle ofcorresponding states (Lewis and Randall, 1961; Mc-

Quarrie, 1973) with respect to tremolite. That is, the ratioof the low-temperature Cfl per gram of tremolite (Robieand Stout, 1963) to the C; per gram of pure magnesio-anthophyllite was used for a smooth extrapolation to zeroKelvin.

The molar Ci data were smoothed graphically between 0and approximately 20 K, and analytically from 20 to 380 Kby least-squares fits to orthogonal polynomials (Justice1969). Values of S? - s3, (I{i - Hillr, and -(Gi - Hillrwere obtained by integrating the smoothed Cfi functions.The smoothed Ci values and integlated thermodynamicproperties for the Fe-bearing magnesio-anthophyllite(Table 8) and for bronzite (Table 11) retain the heat capaci-ty contributions resulting from Fe2+ impurities. The en-tropy change Sise - S[,, in /(mol'K), is 538.9 +2.7for Mg/Fe-anthophyllite [Mgu..Feo.tSiBO22(OH)2]'

fff.b.r.Jll oDsc II r wosner (1932)

|I r r ins (1s57) |

KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES 255

d O UY

(9

-c 4 0o

F

o o 2 0( ) - -

80

Y 6 0o=-

o o 4 0o -

F Ad.bd,;ll ^osc I

50 100 150 200 250 300 350TEMPERATURE (KELVINS)

Fig. 3. Experimental molar heat capacity of synthetic enstatiteMgSiOr. The open squares and solid triangles are experimentaldata determined by adiabatic calorimetry (this study) and DSCanalysis (Krupka et al., 1985), respectively. The solid line is aleast-squares fit to the experimental data. The dashed line repre-sents the Ci function of clinoenstatite given by Kelley (1943).

50 100 150 200 250 300 350TEMPERATURE (KELVINS}

Fig. 4. Experimental molar heat capacity of bronzite(Mgo..rFeo.rrSiO.) and wollastonite. The open diamonds andopen squares are data determined by adiabatic calorimetry (thisstudy) for bronzite and wollastonite, respectively. The solidsquares and solid hexagons are data determined by DSC analysis(Krupka et al., 1985) for bronzite and wollastonite, respectively.The solid triangles are the low-temperature data of Wagner (1932)for wollastonite. The solid curves are least-squares fits to the ex-perimental data of this study.

r200

ta ( xEt-vrHs2)Fig. 5. Plot of Ci/T versus T2 showing the Schottky Ci anom-

alies at low temperature for bronzite (Mgo,rFeo.rrSiOr),magnesio-anthophyllite (Mg6.3Feo.rSirOrr(OH)r), and diopside.The lowest curve and data are for pure synthetic enstatite.

537.0 + 2.7 for magnesio-anthophyllite [MgrSirOrr(OH)r],142.7 +O.2 for diopside, 69.04+0.10 for bronzite(Mgo.rrFeo.rrSiO3), 66.27+0.10 for synthetic enstatite(MgSiOr), and 81.69+0.12 for wollastonite. The larger un-certainties for the two values of magnesio-anthophyllite re-flect the impurity corrections applied to the experimentalCl data for anthophyllite.

The entropy at 298.15 K for the Fe-bearing magnesio-anthophyllite does not include a term for the configura-tional entropy, Sir, that could arise from the random distri-bution of Fe and Mg on the M sites in the amphibolestructure (e.g., Ulbrich and Waldbaum,1976). The configu-rational entropy was neglected for this anthophyllitesample because the cation distribution is not known forthis particular sample and because cations may be partiallyordered on the M sites (Finger, 1970).

Similarly, a value of Si, was not included in the tabu-lated results for bronzite (Mgo.rrFee.rrSiOr) because theMg-Fe distribution is not known for this particularsample. If the Mg and Fe were totally disordered and thetwo sites were treated as equivalent, this Mg-Fe distri-bution would result in a maximum value of S!, equal to 3.5J/(mol.K) [i.e., R (0.85 ln 0.85 + 0.15 ln 0.15) (Ulbrichand Walbaum,1976).1

Comparison with previous studies

Values given by King (1957) and Wagner (1932) for thelow-temperature heat capacity of diopside are shown inFigure 2 for comparison with the smoothed Ci values de-termined in this study. Data of the present study are ingood agreement with the Ci values of King (1957) butdiffer significantly from those of Wagner (1932). King's C!data are greater than the values from this study by 1.5% at53.8 K to 0.10% at 72.9 K. At temperatures between 77.5and 296.O K, King's values are slightly lower than the new

Y 6 0

o=-)

oc l 4O(-)

Mognesio-Sronzi le Anfhophyl l i fe

Bronzi le

o Ad iobot icr osc

lllol lo slonifeo Ad iobot icO DSCe Wogner (1932)

256

Table 8. Low-temperature molar thermodynamic properties ofmagnesio-anthophyllite, Mgu..Feo.rSirOrr(OH)2. (Formula

weight : 802.900 g/mol)

KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES

Temp. Heatca pa c r ry

Ent ropy Entha I Pyfunct i on

Gibbs energyfunc t i on

-1ef-r ivr

data are 1.5% greater than the C[ values from this study.The good agreement between our value of Sies - S[ forwollastonite and that calculated by Kelley and King (1961)from C! data of Wagner (1932) is strictly fortuitous.

Magnetic contributions to the entropy ofMgo.rrFeo.t rSiOt

The measured C$ of bronzite (Mgo.rrFeo.t5SiO.) atliquid-helium temperatures is sigrrificantly greater than thatfor synthetic enstatite. This anomalous behavior is es-pecially apparent when the data are plotted in the form ofC[/T versus T2 (Fig. 5). The larger values of CilT ate

Table 9. Low-temperature molar thermodynamic properties ofanthophyllite corrected to pure Mg composition,

MgrSirOrr(OH)r. (Formula weight : 780.874 g/mol)

T

Kel v i n

ci 1si-sfit 1Hf-nllnJ / (mo l . K)

5101 520

3035404550

0 .5483.t624.6416 . 1 3 28 .745

t2 .9018 .94?6 .3635 .3045 .54

69.2696.42

t ? 6 . tt57.2r88 .9?20.625t.9?82.53 r 2 . 33 4 1 . 1

368 .73 9 5 . 1420.4444.6467 .7489 .95 1 1 . 1531 . 3550 .5568 .9

586 .5603 .5619 .8635 .3649,8663.6676 .8689 .77 0 2 . 37 14.3

7 ? 5 . 97 3 7 . 2747 .7

608 .7647 .2

0 .1661 . 3652 . 9 7 44 .4856 . 1 1 18 .044

10 .461 3 . 4 6t 7 . 0 72 1 . 3 1

3 1 . 6 544.325 9 . 1 17 5 . 7 59 3 . 9 5

I 1 3 . 5134 .01 5 5 , 4177 .4r 9 9 . 9

222 .8?46.0269.3?9? .73 1 6 . I339 .4362.7385 ,9408.94 3 1 . 8

454 .447 6 .9499. i5 2 1 . 1542.9564 .5585 .7606 .8627 . 5648. I

668 .4688 .4708.2

483 .9538 .9

0 .124r . 0052 .009?.8293 .7 304.8866 .4408 . 4 5 3

10 .92I 3.86

2t.0629.854 0 . 0 15 1 . 2 963.477 6 . 3 289 .65

103 .3TI l .21 3 1 . 2

145.21 5 9 . 1r 7 2 . 9186 .6200 .12 1 3 . 3?26 .4239.2251 .8?64.r

276.2288 .0299.53 1 0 . 9321 . 9332.7343 ,335 3 .6363 .637 3 .5

383. I392 .5401 . 7

291 .6319 .9

0 . 0 4 10. 3500 .9651 .6562 .3813 .1584 .0235 .0096 . 1 4 37 . 4 4 3

10 .58t4.471 9 . 1 124.4630 .493 7 . 1 344 . 3452 .0660.2268 .78

17 .698 6 . 9 196 .40

106 . 11 1 6 . 0126.11 3 6 . 3146.71 5 7 . 1t67 .7

1 7 8 . 3i 88 .9199 .62 1 0 . 3221.023r.7242.5?53.2?63.92 7 4 . 6

285.2?95.9306 .5

r92.3219 .0

Ent ropy

, ^ o ^ 0 ,( 5T-50. ,

60708090

100i l 0r20130140150

1601701801902002to220230?40?50

260?70280?90300310320330340350

360370380

Temp. Heatcapa c i t y

t r o

K e l v i n

Entha lpy Gibbs energyfunc t ion func t ion

tr!-Hlvr -to!-ni lrrJ / ( m o l . K )

2 7 3 . 1 5298.15

5l01 520253035404550

2 7 3 . r 5298.15

0 .0390.2991 . 0202.4804 .9988 .856

14 .492 1 . 8 130 .5840.87

65 ,0092 .88

123.5155 .6I88 .5?21.3253.6285 .33 I5 .0345 .8

374 .3401 .7427 .845 2 .847 6 .8499 .8521 . 8542.8562.75 8 1 . 9

600 .36 18 .0635 .06 5 1 . 1666.2680 .5694.2707 .67 20.67 3 3 . 1

745 . I756 .9167 .7

6?_3.46 6 3 . 5

0 .01 320 . 1 0 10 .3380 .81 01 . 6 1 0, a ? o

4 .6006 .995

10 .0513.79

2 3 . 3 I35 .3849.1 666 . 1484.24

103 .7t24 .4i 4 5 . 9168.21 9 I . 0

214.3237.82 6 1 . 5285 .3309. I333 .0356 .7380 .4403 .94?7 . 3

4 5 0 . 547 3 .4496.2518 .85 4 I . I563.?585 .0606 .66 ? 7 . 9649 .0

669 . 8690.47 r0.7

480 .65 3 7 . 0

0 .00960 .0750 . 2 5 30 .6081 . 2 1 32 . t 443 .4795.2961 .596

1 0 . 4 0

I 7 , 4 326 . l 836 .4047 .8560.?77 3 . 4 287 .09

101 . 11 1 5 . 4t29.8

r44.21 5 8 . 5t 7 2 . 7186 .8200.72 r 4 . 4??7 .924t.1254.1266.9

279.3291.5303 .53 1 5 . 2J t o . I337.9348.8359 .4369 .9380. I

390. I399 .8409 .4

?95.33?4 .6

0.00360 .0260 .0850 .2020 .3970 .695I . 1 2 I1 .6992 .45 r3 .392

5 .8829.205

1 1 1 (

t8.?9t ? 0 7

30 .3237 .3044.8?52 .8 361.29

79 .1279 .2988 .7598.47

108 .41 1 8 , 5I28 .8139.2149 .8160 .4

1 7 1 . 1181 . 9192.7203.6214.52 2 5 . 3236.2241 . I258 .0268.9

279.7290.6301 . 4

r85 .32 t 2 . 4

607 08090

100110120130140150

1601701801902002r0?20230240250

260270280290300310320330340350

360370380

Ci data by 0.3%. At 298.15 K, our entropy for diopside is0.3% less than King's value. On the other hand, Wagner'sCi values (20.7 - 39.3 K) are all approximately 100%greater than the values obtained in this study.

The smooth low-temperature Ci values for wollastonite,shown in Figure 4, are in significant disagteement with thewollastonite data of Wagner (1932). Wagner's C! data atthe lowest temperatures (9.8 - 35.5 K) are greater than ourvalues by 155% at 9.8 K and 26.4% at 19.5 K. Wagner'sdata from 70.7 to 120.1 K are all lower than our C! valuesby an average 6%. At the higher temperatures(L99.7 - 373.2 K), the agreement is better, and Wagner's

Table 10. Low-temperature molar thermodynamic properties ofdiopside, CaMg(SiOr)r. (Formula weight : 216.553 g,/mol)

257

arising from anomalous heat capacities between 5 and 30K is approximately 1 /(mol'K) or only 50 percent of theexpected magnetic entropy.

Based on their Mdssbauer studies, Shenoy et d. (1969)concluded that, for bronzite (Fe,Mg, -,SiO.) wherex < 0.39, there is no magnetic ordering down to 1.7 K.Therefore, wc may exclude coop€rative ordering of thespins as a sour@ ofthe anomalous heat capacities,

In order to test the possibility that the anomalous heatcapacities are due to a Schottky effect, we have assumedthat the lattice heat capacity of Mgo.rrFeo.r5SiO3 belowapproximately 20 K obeys the Debye model. The elasticconstant values of Frisillo and Barsch (1972) for a bronzite

Table 11. Low-ternp€rature molar thermodynamic properties ofbronzite, Mgo..rFco.rrSiO.. (Formula weight : 105.120 g/mol)

KRUPKA ET AL.: I,OW.TEMPERATURE HEAT CAPACITIES

Temp. Heatcapac i t y

t r o

Kel vi n

Ent ropy Enthal pyfunct i on

1si-sf,) uf-xf,ln, l / (mol . K)

cibbs energyfunct i on

- (c?-H3) /r

510l520253035404550

0.0090.082o.297u . / 1 51 .5442.7904 .5766.7999.424

19.2927 .0235 .2843.8052.4060.9269.217 7 . 1 984.8292.t \

99.09105 .7u 2 . I1 1 8 . 0t23.7129 .0134. I139 .0143 .8148 .4

r52.7156 .7160.4164.0167 .4t70.7174 .0t77 . l179 .9182.7

I85 .5188 .2190 .7

157 .9166.8

0.00300 .0260.0930.2340.4820.866t . 4?42 .1763.1244.269

7 . r2410 .6714 .8119 .4624.52?9 .9135 .574 1 . 4 347.4353 .53

59 .7065 .9 r12 . t 4/ 6 . J D

84 .5690.7296 .84

102 .9108 .9114 .9

1 20 .8t26.6L3? .4138. I143 .7149. 3154 .7160 .1165 .5t70.7

175 .9I81 .0186. I

128 .5t42.7

0.002?0 .0 190 .07 I0 .1780 .3680.6601 .0861 .6572 .3713 .223

5 . J I J

7 .85410 .7613 .96

20.9424.6?28 .3632.1235.88

39 .524 3 . 3 146.9650 .5454 .0657 .5060,8764 . l 66 7 . 3 87 0 . 5 3

7 3 .6176.6?79.5482.4085. I787 .8890.5293 . l 09 5 . 6 198.06

100.4102 .8105 .1

77 .5584.66

0.00080.0070.0220.0560 . 1 1 40 .2060 .3380 .5 180 .7531 .046

1 e t I

2.8164 .05 I5 .5017 . 1 4 68 .969

10 .9513 .07I S ? 1

I / . O J

20.0922 .6025 .1827 .8130 .5033.?235 .9738 .7 54 l . 5544 .36

47 .1950.0252 .8655 .7058 .5461 .3864.2167 .0469.8672.66

75.4678.248 1 . 0 1

50 .9258.02

Ke l v i n

60708090

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360370380

Temp. Heat EntropycaPac i ty

r c9 rs9-s9r' - P ' - I - o ' ,

Entha lpy Gibbs energyfunc t ion func t ion

1r!-rf,lrr - (Gi-H3)/T

; / ( m o l . K )

51015?0z)J U

404550

0. 1460 .6940 .8170 .8741 .075r . 5032.2t3J . I J /

4.2855 . 6 1 7

8 .7?612.2916 . 1620.?!?4 .3428.4432.4636.3840.1743.82

47.3250.6653.8456.8659.7 462.486 5 . l 167.6370.047 ? . 3 5

7 4 .5476 .6 378 .6180.5082.3284.0885 .7887 .3988.9090 .34

9 1 . 7 593. 1494.40

77 .2681 .99

0 .0350 .3290 .6430.8831 .096t . 3271.6081 .9602.394?:er34.2045 .8127 .7029.838

12 . t 814 .6917.3420. l022 .9325 .93

28.773 1 . 7 434.7 237 .724 0 . 7 143.6946 .6649 .6152.5455 .44

58 .32O I . I d

64 .0066.7969 .5572.287 4 .9877 . 6480.2782.87

85 .4387.9790 .47

62.0'l69.04

0.0210 .2410 .4?00 .5240 .61 I0.72r0.8791 . 1 0 11.3891 .7 44

2.6413 .7605.0656 .52?8.0979 .760

11 .4913.2515.0416 .84

18 .6320.422 2 . t 923 .9325.6527 .3429.0030 .6232.2?1 1 7 a

35 .3036.8038 .2539.6841 .0742.4343.7645 .0546.3241 .56

48.774e.995 1 . 1 0

37.2640 .81

0.0080.0880.223n ? q o

0 .4850.6060 .7290 .8591 .005l . 169

t . f , o J

2.05??.637J . J I O

4 .0844 .9335 .8566 .8457.8928 .99 I

10 .1411.32t2.5413 .7815 .0516 .35r / . o o18.98?0 .3?21.67

Z J . U Z24.3825.75? 7 . 1 128.48?9.853t.2232 .5833 .9535 .31

J O . O /

38.0239 .37

24.8128.23

273.t5298. t5

60708090

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r60170180190200210220230240250

260?t0280?90300310320330340350

360370380

presumably caused by the substitution of Fe2* for Mg2+in the bronzite, thus permitting either a Schottky-type heatcapacity contribution and/or a cooperative (i.e., spin-ordering) transition (Gopal, 1966). In either case, the totalmagnetic entropy (Sfl"r) arising from the spins of the Fez+ions in the bronzite is:

S f r . r : n R l n ( 2 s + 1 ) '

where s is the spin quantum number and equal to 2 forFe2* (Gopal, 1966). Thus, Slr", for Mgo.rrFeo.l5sio3(where n:0.15) is 2.01 {(rnol .K). The observed entropy

273 .15298. t5

25E KRUPKA ET AL.: LOW-TEMPERATURE HEAT CAPACITIES

Temp. Heatca pac i t y

r r o' - P

Kel v' i n

Entropy Enthalpyfunct i on

(s?-sB) (H?-H3)/TJ / ( m o l . K )

Gi bbs energyfunc t i on

- ( G?-H3)/T

Table 12. Low-temperature molar thermodynamic properties ofsynthetic enstatite, MgSiOr. (Formula weight : 100.389 g/mol)

is likely, however, that the two levels are not totally de-generate. In this case, an additional heat capacity maxi-mum would be expected at a temperature below 1.7 K,arising from the splitting of the ground-state doublet. Ourheat capacity extrapolation to zero Kelvin did not includethis contribution to the entropy. This additional entropywould be <0.86 J/(mol'K) (i.e.,0.15 R (ln 2)).

Moreover, to obtain the entropy value for use in equilib-rium calculations involving Mgo.rrFeo.15SiO3, one mustalso add the configurational entropy (discussed previously)arising from the substitution of Fe2 * for Mg2 +.

Table 13. Low-temperature molar thermodynarnic properties ofwollastonite, CaSiOr. (Formula weight : 116.164 glmol)

101520253035404550

0.0040.0290 .0950 .2520 .5260.9581 . 6 1 72 .41 |3.5244 .764

7 .129tt .2 l15 .0419 .0823.2r

?7 .343 1 . 4 135 .4039.2642.99

46 .5649.97a J - a a

56.3?59 .286 2 . 1 164.8?67 .4069 ,8672 .21

7 4 .4476 . 5878.6280 .568 2 . 3 984.1?85.7787 .3688.8990 .35

9 1 . 7 89 3 . 1 794 .46

77 .2482 .06

0.001 20 .00960 .0320 .0780 . 16 l0 .?920 .4870 .756l . 106I . 540

2 .66?4. 1099 . O ? J

7 .85610.08

12 .491 5 . 0 4t7 .7120.48, 1 1 t

26.212 9 . 1 332 .0835 .0438 .0140 .9743.9246.8649.7852 .68

5 5 . 5 558.406r.2364.0266 .7869 .51

7 4 .8777 .508 0 . 1 0

82.6785 .2087 .70

59 .3066.27

0.00090.00720 .0240 .0590 . 1 2 30 .2230 . 3 7 30 .5790 .846I . I / )

2.0123 .07?4.3255 .7 397.280

8 .91610 .6 212 .381 4 . 1 615 .96

t7 .761 9 . 5 521.3423 . l 024.8326 .5428.22?9 .8731 .4833 .06

5 C . O rJ D . I J37 .6139.0640.4741 .8543 .2044 .5145.8047 .05

48.2749.4750 .63

36 .6040 .21

0.00030.00240.0080 .0190.0 380.0690 . 1 1 40 . 1 7 70 .2600 .366

0 .6501 .037L - a a l

?.t172 .800

3 .5704 .4195 .3386 .3207 .359

8 .4469 .577

10 .741 1 . 9 51 3 . 1 7I4 .4315 .7016 .9918 .3019 .61

20.9422 .28?3 .6224.962 6 . 3 1?7 .6629 .0130 .363 1 . 7 133 .05

34.403 s . 7 337 . 07

2 2 . 7 0?6 .06

0.0060 .0570.2t70 . 6 2 21 .389? .5224.0065 . 7 l 37 .6?59 .693

1 4 . 1 418 .7823.4328 .0132.4437 .6040.7 644 .6048.2?5 1 . 6 5

54 .9057 . 9960 .91o J . o /

66.2668 .7 I7 1 . 0 57 3 . 3 175.5277 .66

79.708 1 . 6 0I 3 .3484 .9586.4787 .9589.4?90 .8592.2t93 .49

94.7395 .9397.02

8 ? . t 786. 19

0 .00210 .0 180 .0660 . 1 7 50.3890 .7 31l . 233I .8772.6593 .568

5 .7238.249

1 1 .0614 ,0917 .?720.5623 .932 7 . 3 530 .7934.23

37 . 674 1 . 0 944 .4947.865 1 . 1 954.4857 .7360 .946 4 . 1 16 7 . 2 3

70 .327 3 .3676 .3679 .3282.2285 .0887 .9090 .6793 .409 6 . 1 0

98 .75r0 l . 36103 .93

7 4 . 3 t81 .69

0 .00160 .0140 .0500 . 1 3 50. 3020 . 5 7 30 .954I . 4392 .019?.682

4.2t65 . 9 6 37 . 8579 .843

11 .88r 3 .9516 .0118 .0720.0922 .08

24.03?5 .9427.80?9 .6?3 1 . 3 93 3 . 1 134 .7836 ,4037 .9939. 53

41 .0442.5143 .9345.3246.6747 .9849.2550 .4951 .6952.87

54.025 5 . 1 356.2?

42.9646.42

0.00050.0040 .0160.0400.0870 .1640 .2800 .4380 .6400.886

I . 5072.?863. 2054.2445. 3866 .6167 . 9 1 89.281

10 .691 2 . 1 5

1 3 .641 5 . l 516 .6918.2419 .8021 .3822 .9524.5426.t227 .70

29.2830 .863 2 .4334 .0035 .563 7 . 1 138 .6540. 184 1 . 7 143.23

44 .7346.?347 .71

? 1 ? q

1 q r 7

607 08090

100

I10120130140150

160170180190200210220230240250

260270280?90300310320330340350

360370380

27 3 . t 5298 .15

Temp. HeatcaPac i tY

r e o

Ke l v i n

Entropy Enthalpy Gibbs energyfunct ion funct ' ion

1si-sf,l 1ni-rilnJ / ( m o ] . K )

-1e!-uf,ln

5101520253035404550

of composition Mgo.rFeo rSiO3 were used to calculate aDebye temperature of 710 K with the methods describedby Robie and Edwards (1966). We used this Debye temper-ature to calculate the lattice heat capacity, which was thensubtracted from the measured heat capacity to obtain thatpart arising from the Schottky contribution. The simplestmodel that provides a reasonable fit (Fig. 6) to the residualheat capacities was obtained with a twoJevel model havinga doubly degenerate ground level and a triplet at 225cm-r. The agreement with the Schottky model does notmean that these are necessarily the correct energy levels. It

607 08090

1001 1 0120130140r50

1601701801902002r02?O230240250

260?70280290300310320330340350

360370380

2 7 3 . t 5298 .15

/ o oo

Lo

rI

I

f

_,i

II

/5 1 0 1 5 2 0 2 5

TEMPERATURE (KELVINS)

Fig. 6. Schottky heat capacities for bronzite(Mgo.rrFeo.rrSiOr). The open squares are data determined in thisstudy by adiabatic calorimetry. The solid line is calculated fromequation 4.25 in Gopal (1966) with EtlEo : 1.5 and d : 22.5 qn-[.

AcknowledgmentsThis paper is partly based on K. M. Krupka's Ph.D. research at

The Pennsylvania State University. Profs. Bernard W. Evans andPeter Misch at the University of Washington kindly provided theanthophyllite sample, and J. Stephen Huebner of the U.S. Geo-logical Survey, Reston, Va., provided the bronzite sample. Theauthors are particularly gateful to Dr. David Veblen, who, whileat Arizona State University, inspected a section of the anthophyl-lite sample for the presence of hydrous pyribole structures. Wealso thank Howard T. Evans, Jr., of the U.S. Geological Survey, J.Stephen Huebner, Lowell B. Wiggins of IBM Corporation, andanalysts of the U.S. Geological Survey, Reston, Va., for their inval-uable assistance in the characterization and chemical analysis ofour samples. We are also grateful to John L. Haas, Jr., Henry T.Hazelton, Jr., Susan W. Kiefer, and Donald E. Voigbt, all of theU.S. Geological Survey, and Bruce D. Velde at Ecole NormaleSup6rior, Paris, France, for critically reviewing the manuscriptand for their helpful comments. This work was supported by theU.S. Geological Survey and by grants EAR 76-84199 and EAR79-08244 from the Earth Sciences Division of the National ScienceFoundation to D. M. Kerrick. We also thank the Battelle. PacificNorthwest Laboratory for providing funds for the preparation ofthis manuscript.

259

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6 . n

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Y

E 3 0=

39 c Lo

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Manuscript receiued, December 7, 1983:accepteilfor publication, Nouember 19, 1984.