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Sillimanite—disordering enthalpy by calorimetry
Geochlmk~et Cesm~htmioa Acta, 1973, Vol. 37. pp. 3497 to 36CI3. Pergamon Press. Printed in Northern Ireland
sillhhte-disordering
enthalpy by calorimetry
A. NAVROTSKY,* R. C. NEWTONS- and 0. J_ KLEFPA !l%eJames Fr8nck Institute, The University of Chicago, Chicago, Illinois 60637, U.S.A.
Ab&&-Heat
of solution measurements in an oxide-melt were performed on s8mples of heat-treated in the range 12OO-1700°C 8t pressures of 16-23 kbsr. A distinot entl-&py of solution decrement relative to the unhested ~~~ of about I.3 kc/mole is shown by s8mples run 8t 14OO-1650% Pressure vsrietions in the range 16-23 kbar u8use little change in the heat of solution in this temperature range. This pressure-independent ‘platesu’ in heat of solution is interpreted to be due to Al-Si disordering on tetrehedrsl sites in the sillim8mte structure. A simple ~rn~r8t~-de~ndent disordering model developed by KAVROTSKY 8nd IELEPPA (1967) for spine&sfeeda to 8n Al--@ interchange enthafpy, mint, of 10 f 1 kcsl/mole, in good agreement with the value derived by HOLDAWAY (1971) on entirely different grounds. Above 1560°C, larger heat of solution decrements were observed. Microprobe analyses of quenched maples indicate that the sillimsnite hss not deviated signifio8ntly from the ideel formul8. Some unknown profound disordering process 1118~account for the heat e&&s in the very high temper8ture range. Unit oell volumes of quenched semples 81~0 describe 8 ‘pleteau region in the tempemture range 1400-155O’C. This plateau consists of 8n increacle of the 5 crystallographic axis beginning at 1350% without much change in the other 8xes in the range 135O-1650°C. A sudden expansion of the a-8x& occurs between 1550 and 1630’%. We oonclude that Al-Si disorder of the type postulsted by BE~ER et al. (1970), and HOLDAWAY (1971) has been confirmed c8lorimetric8lly for samples heated under pressure in the temperature r8nge 1400-165O’C. nat,ural sillim&te
fiE THERMODYNA~\~ICSof the aluminum silicates has been the subject of intense experimental study and considerable controversy in recent years. Numerous experimental studies of equilibrium relations among the A&&O, polymorphs sillimanite, kyauite and andalusite have yielded different results. A number of explanations have been proposed to account for the discrepancies. These include error in pressure calibration of e~eriment&l apparatus (RICHARDSON et al., 1967); the effect of strain energy of materials in high pressure runs (FYFE, 1969; NEWTON, 1969); the effect of surface energy of the very severely ground starting material used by some investigators (NEWTON, 1969), the possibility that sillimanite cannot be considered to be simply stoichiometric Al&GO,, either because of s, si~i~cant iron content (ALTI&AUS, 1969) or because of the existence of an alumina-rich solid solution series at high temperatures and pressures extending toward the mull&e (3Al,O, .2SiO,) composition (RAMYA et al., IQ69), and, finally, the possibility of Al-Si disorder on ~tr&he~~l sites in the siIIima~te struct~e (ZEN, 1967; ~DE~O~ snd KLEPPA, 1969; BE~ER et ai., 1970; HOLDAWAY, 1971; CHATTERJEE and SCHREYER,
1972;
* Department t Department
GREENWOOD, 1972.
See Discussion
section
below).
of Chemistry, A.&on8 State U~versity, Tempe, A&on8 85281, U.S.A. of Geophysical Sciences, University of Chicago, Chicago, Illinois 60637, U.S.A.
2497
2498
A. NAVROTSKY, R. C. NEWTON and 0. J. KLEPPA
The idea of temperature-dependent Al-Si tetrahedral disorder in sillimanite was developed by HOLDAWAY(1971) into a quantitative theory which sought to bring the more unambiguous of the experimental observations into line with published thermodynamic data in order to achieve a self-consistent Al,SiO, stability diagram. Using a simple oation-exchange reaction modeled after the disordering theory of NAVROTSKYand KLEPPA (1967) for spinels, Holdaway calculated the energy of Al and Si interchange on tetrahedral sites. His principal numerical input was his experimentally measured dP/dT slope of the sillimanite-andalusite phase boundary. The value of the interchange enthalpy, AHint,which bestfitted the experimental data, was 14.75 kcal/mole. With this interchange energy, Holdaway’s theory gives about 10 per cent equilibrium Al-Si disorder at 1000°C and about 20 per cent at 14OO’C. Disordering of this magnitude would be expected to have significant effects on the slopes and positions of the high-temperature portions of the stability boundaries in the Al,SiO, diagram. It is equally likely that any appreciable departure of sillimanite from the Al,SiO, composition, most plausibly in the direction of mullite, would also have a marked influence on the phase relations. Changes in the unit cell parameters of sillimanite heat treated under pressure have been observed (BEOER et al., 1970; HARIYA et al., 1969; CHATTERJEE and SCHREYER,1972). When natural sillimanite is heated above about 1400°C for some hours in a pressure range between about 7 and 25 kbar, which avoids the fields of stability of mullite and kaynite, changes of lattice parameters occur, the magnitudes of which apparently depend on temperature, pressure and time. The most notable changes are expansions of the b and a crystallographic axes. This observation has been interpreted in two ways. HARIYA et al. (1969) made a number of heating experiments on sillimanite under pressure and concluded from an analysis of powder X-ray diffraction data on this material that sillimanite migrates toward mullite in composition at high temperatures. They were unable to show that quartz was exsolved from the sillimanite because their starting sillimanites contained quartz. BEQERet al. (1970), on the other hand suggested, on the basis of lattice constant changes and changes in the intensities of X-ray diffraction maxima in single-crystal photographs of heat-treated material, that sillimanite undergoes Al-Si tetrahedral disordering at constant composition. They cited preliminary electron microprobe analyses to support their interpretation. CHATTERJEE and SCHREYER(1972) found temperature-dependent changes in the unit cell constants of natural sillimanite used in their experimental study of the reaction of enstatite and sillimanite to sapphirine and quartz at high temperatures and pressures. They concluded that on-composition disordering was responsible. Finally, certain sillimanite samples from inclusions in volcanic rocks have somewhat anomalous unit cell constants, as, for example, the sillimanite inclusions from the lava of Asama Volcano (ARAMAKIand ROY, 1962). KWAK (1971) analyzed a number of such sillimanites and concluded that there was no signifioant deviation from the ideal formula. previous experience in this laboratory in the application of high temperature solution calorimetry to the thermochemistry of the kyanite-sillimanite equilibrium (ANDERSONand KLEPPA, 1969), and to disordering in albite (HOLY and KLEPPA, 1967), and in natural MgAl,O, spine1 (NA~ROTSKYand KLEPPA,1967) suggested to
Sillimanite-disordering
enthalpy by calorimetry
2499
us that cation disordering in sillimanite could be detected and studied by this method. The aim of the present study was to measure the heat of solution of natural sillimanite exposed in the laboratory to various pressure and temperature conditions, and to attempt to decide whether, using the adjuncts of X-ray diffraction and electron probe microanalysis, any heat effects so determined could be the result of cation disordering or of heterogeneous reaction. It may be stated at the outset that both an enthalpy effect and lattice parameter changes indeed have been detected and that the present results favor on-composition atomic rearrangements, rather than a compositional shift toward mullite, -as their cause, at least in the temperature range below 16OO’C. EXPERIMENTAL METHODS Starting material. All of the present calorimetric runs were made on natural sillimanite from Brandywine Springs, Delaware, kindly provided by P. M. Bell. This sillimanite was beautifully crystalline and suitable for hand-picking. A few small red grains of a foreign phase were easily removed. The X-ray powder pattern of the sillimanite showed very small amounts of quartz probably less than 3 per cent by volume. Polished thin-section grain mounts revealed that this quartz was present as 6ne lamellar intergrowths in about 30 per cent of the sillimanite grains. The quartz appeared to be quite inert during the heat-treating process. A semiquantitative spectrographic analysis revealed 0.05 per cent V; 0.01 per cent B, Cr, Fe; 0.005 per cent Mg, Ti, Mn; and O-001 per cent Ca, Ni, Cu, Ag, as the most abundant impurities. High pressure PUTLQ.A piston-cylinder apparatus with a 1 in. diameter carbide chamber and piston was used. The solid pressure medium was Pyrex glass and talc (NEWTON,1972). Samples were contained in either graphite crucibles or welded platinum jackets within holders of AlSiMag 222 (American Lava Co.) surrounded by cylindrical graphite heaters. Most of the runs were made at a corrected pressure of 16-18 kbar (a nominal pressure of 20 kbar). Temperature was controlled automatically and measured by W-25 per cent Re vs W-3 per cent Re thermocouples in contact with the graphite or platinum containers but protected from contamination by a film of alundum cement. When the heating power necessary to maintain a given apparent temperature began to drift downward by an amount equivalent to E-25%, which always happened sooner or later, depending on the temperature, the run was terminated and quenched to below 1OO’C in a few seconds. The observed power drift effectively limited run times to about 2 hr at 17OO’C and about 10 hr at 1400%. Calwimetry. After a high pressure run, the hard pellet of sillimanite was removed from its graphite or platinum container, crushed in a hard steel mortar, and ground to a fine powder under acetone in an agate mortar. Powdered samples from runs in graphite containers were generally gray in color because of graphite contamination. The graphite was burned off at 850% in air for at least 5 hr, which yielded a white powder showing no residual graphite. About 70-75 mg of material was recovered from one high pressure run in graphite container. This was generally enough for two calorimeter runs and a preliminary X-ray scan. High pressure runs in platinum jackets yielded only 40-50 mg of sample. The calorimetric equipment and technique have been described previously (ANDERSON and KLEPPA, 1969; KLEPPA, 1960). All solution experiments were performed at 690 f 1% using molten 2PbO . BsOs as solvent. Sample size was 20-40 mg per run. X-Ray lattice parameter determinationa. All samples treated above 1500°C were scanned for any new phases using a Norelco diffractometer with CuK, radiation at a speed of 1’ (26)/min. No new phases were found. Quartzwas still present in approximately the same amount as in the untreated material, even in the 1700’ runs. A portion of all of the samples used in the calorimetric runs was scanned at l/2’ (20) with a corundum internal standard to approximately characterize the lattice parameter changes. A special series of nine runs on platinum-jacketed samples was made at 18 kbar in the range 1200-1700% in order to characterize as carefully as possible the unit-cell parameter changes. The powdered quenched charges of the runs were scanned at l/S” (26)/min with an internal standard of National Bureau of Standards MgAlsO,
A. NAVROTSKY, R. C. NEWTON and 0. J.
2600
KLEPPA
spinel. Twelve to Gfteen sillimanite lines were measured and subjected to a computer leastsquares unit-cell refinement (BTJR~EAM, 1962). Microscopy ar& electroonprobe miwoanalysis. Some additional runs on Brandywine Springs sillimanite were made for optical and microanalytic study. Pellets from runs at 1600% and 1700% were ground and polished. Reflected light study of these revealed fine lamellae of lower reflectivity than the sillimanite in some grains. These had exactly the same appearance as the lamellae in the untreated material, suggesting that the quartz is inert under these run conditions. These mounts were analyzed with an ARL electron microprobe using a sub-micron beam diameter. Traverses were made across grains containing low-reflectance lamellae, and individual lame&e as well as lamella-free grains were analyzed for Si and Al. Grains of untreated Brandywine Springs sillimanite served as a convenient standard. RESULTS
OF EXPERIMENTS
The heats of solution of sillimanite treated under various pressure and temperature conditions are presented in Table 1. Figure 1 shows graphically the difference in Table 1. Results of calorimetric studies on sillimanite samples heated at various temperatures and pressures
(WZ’)
(kbP)
(hrt)
Interchange enthalpy Initifd cslculstion Fourth iteretion$
Calorimetry
Sample trestment Container
mg/semple 38.87 62.55 61.93 41.13 45.29 44.45 31.47 43.74 32.27 49.07 23.91 38.14 32.96 27.38 38.46 33.51 35.27 34.29 40.45 33.87 37.36 28.38 35.78 37.16 30.16 37*56 31.83 34.96 29.06 23.00 30.45 20.27 39.71 31.96
Untreated
1200
16-18
6.0
C
1326 1400
16-18 16-18
10.0 7.5
C C
1460
16-18
6.0
C
1476
16-18
12.0
C
1600 1600
18-18 23
4.0 4.0
C C
1600 1600 1630
16-18 16-18 16-18
6.6 6.0 6.0
Pt Pt C
1600
16-18
3.0
C
1660 1700
16-18 IS.18
3.0 2.0
Pt C
1700
23
1.5
C
AH::,1 (kcal/mole) Av. 7.057 6.926 7.343 7.028 7.443 6.863 7.327 6.948 7.693 6.860 6.741 7.244 7.171 7.066 6.867 6.944 6.967 6.028 6.949 6.611 6.691 6.841 6.691 6.483 6.516 6.627 6.930 4.661 6.029 3.86 3.359 3.114 4.195 4.385
AH%,
4.6RT
zt
AHintS
-
AHr.p.
AHint
7.11 ho.29
7.21 7.07 6.91
0.0784
0.0839
14.29
0.0909
16.29
6.00
0.0698
0.0786
14.15
0.0863
15.06
6.78
0.0845
0.0874
15.22
0.0930
16.34
5.69 6.77
0.0876 0.0827
0*0891 0.0864
14.94 16.61
0.0960 0.0926
16.95 16.62
6.00
0.0686
0.0776
14.31
0.0849
16.31
6.73
0.0837
0.0870
16.86
0.0930
16.88
4.86
0.132
3.86 3.24
0.184 0.216
4.29
0.166 =
* AHOaB= &%mtrested t 5 = mole fraction Al $ AHint = interchange
=
14.98
on Si sites, from equation (3). enthalpy for reaction Al& + Sisi = Alsi + Sia, from ARObs = zHint. 0 Celoulation corm&ad for equilibrium disorder in etarting material (aw text).
AV. =
16.06
Sillimanite-disordering
5
s=
‘,
SE
I’ 4
43-
E c8
;:‘;:
$
;;$
$;‘f;
g&item’
’
I
’
A RUNS AT 23 Kb, in graphite ---EXPERIMENTAL CURVE AT 16Kb -EOUILIBRIUM CURVE i
AHint=16kCsl 25 = a I/MY II 2 o_+_____-_---_____+-__j I” a I I! I I 600
1090
BOO
2501
enthalpy by calorimetry
’ i:/+
-
,i+
II
I
1200
Temperature,
11
1400
1
1600
IBOO
"C
Fig. 1. Heat of solution data on quenched samples of Brandywine Springs (Del.) sillimanite heat-treated at high pressure. Solid line is calculated from simple Al-Si tetrahedral disorder with AH,,t = 16 kcal/mol (see text). Table 2. Unit cell constants of Brandywine Springs sillimanite samples heat-treated capsules at 16-18 kbar in the temperature range 1200-1700% Run duration (hr)
Temperature (“C) Untreated 1300 1350 1400 1450 1500 1550 1630 1700
J* 7.485 7.484 7.484 7.487 7.488 7.486 7.489 7.497 7.500
10 7: 72 6& 5f
34
3 2
* Uncertainty
(f$* J* 7,673 7.675 7.677 7.680 7.682 7.684 7.684 7.689 7.690
5.769
5.771 5.772 6.770 5.771 6.770 5.768 5.768 6.767
331.262 331.478 331.674 331.791 331.939 331.920 331.873 332.484 332574
f + f i f * & f f
0.075 0.054 0.070 0.117 0.086 0.084 0.087 0.139 0.119
*O.OOl-0.002 d.
= G .5
I.2 oa
tt
33’.o,200
t
1300
I
I I I I 1400 1500 Temperature ‘C
It
1600
Ii
1700
Fig. 2. Unit cell volumes of quenched samples of sillimanite heat-treated under pressures of 16-18 kbar. Data taken from Table 2. The value at 1200°C refers to untreated material. 10
in Pt
2602
A.
NAVROTSKY,
R. C. NEWTONmd 0. J. KIBPPA
heat of solution between the untreated and treated samples, A&_,,, - AIf-,,p = AfL*, as a function of temperature. The plotted points are the average of the two calorimeter runs on each quenched charge, except for the runs in platinum jackets, for each of which only enough material was available to make one oalorimeter run. The unit cell constants of runs in the range 1300-1700°C at 18 kbar are presented in Table 2, and the unit cell volumes are shown as a function of temperature in Fig. 2. The curve in Fig. 1 can be divided into three portions: (a) a low temperature region, T < 1350°C, in which essentially no change in heat of solution is observed; (b) a region of 1400’ < T < 1550°C in which AH,,, increases only slightly with temperat~e and not sig~ficantly with pressnre in the range 16-23 kbar; (c) a region, for T > 155O”C,where AH,,, increases markedly with T and is substantia~y smaller in magnitude at 23 kbar than at 16 b-bar for a given temperature. The intermediate region appears as a shoulder or plateau in the curve. A long run was made in the range 1450-15OO’C to check for the possibility that the plateau region in the heat of solution curve might be an incidental product of the duration of runs which had been determined by the observed rate of power drift (possibly due to the thermooouple contamination). A run at 16-18 kbar was started at 1600°C. After 12 hr, the heater power had dropped by an amount equivalent to a 50°C decrease in temperature. This run in the ‘plateau region’ was three times as long as the 1500°C rrms and twice as long as the 14OO’Crun yet showed essentially the same heat of solution as the shorter runs in the plateau region. The runs in platinum jackets showed heat of solution results entirely consistent with the runs from graphite containers, and demonstrate that the observed changes in solution enthalpy are not due to reaction with the container material. The change of unit cell volume with run temperature appears to be regularly related to the change in heat of solution. Figure 2 shows a ‘plateau region’ in unit cell volume corresponding to the plateau in the heat of solution curve. The trend of the b crystallographic axis shows the strongest early change with heat-treatment. The plateau region in the unit-cell volume is a result of b-axis increase with little change in the other axes. Samples heated above 1600°C show an abrupt large change in the a-axis, with a volume increase approaching & per cent. Reversibility of the change in unit cell parameters was investigated in a run made at 165O’C and 18 kbar for 3 hr. Unit cell measurements of the quenehed material was made and then this material was run again at 1500°C and 18 kbar for 4 hr. The large changes of unit cell parameters resulting from the 165O’C run were not reversed by the 15OO*Crun. Microanalysis of a 17OO’Crun clearly showed silica-rich lamellae in some grains. No analyzable area was large enough to avoid overlapping Al counts from neighboring sillimanite. The X-ray diffractograms showed that the siliceous lamellae were quartz and not a silica-rich glass. Quartz lamellae larger than a fraction of a micron across could be detected by lower reflectivity and avoided. Analyses at several positions on a large, apparently quartz-free, grain gave compositions in mole fractions as follows.
Sillimanit~sordering
enthalpy by calorimetry
2603
The Si to Al ratio seems to be slightly greater than unity, but the deviation from the ideal formula may not be significant in view of experimental errors. There is certainly no indication of approach to the mullite composition. The possibility remains that extremely fine quartz lamellae were present in very uniform dispersion. The absolute amount of quartz present, as indicated by the diffractogram, would be much too small to produce the observed heat effects. DISCUSSION We propose the following interpretation, which is consistent with all our data and with previous observations on sillimanites of different thermal history. Unequilibrated region. In Region (a), the low-temperature interval of Fig. 1, disordering of the sillimanite occurs too slowly for any change in heat of solution to be observed in samples annealed only a few hours. The fact that the sample treated at 12OO’C and 16 kbar for 5 hr showed essentially the same heat of solution as the untreated samples shows that the enthalpy effect associated with any strain energy introduced into the samples by the high pressure conditions is immeasurably small, since the strain introduced at 1200°C would be expected to be equal to or possibly greater than that introduced at higher temperatures. The heats of solution presented in Table 1 are not corrected for the small amount of quartz present. The measurements on untreated sillimanite agree within experimental error with the heat of solution values on other sillimanite samples reported by ANDERSON and KLEPPA (1969). Plateau region. The shoulder region [Region (b)] can be understood in terms of near-equilibrium Al-Si disordering on tetrahedral sites. If one uses the simple model proposed by NAVROTSKYand KLEPPA (1967) and applied to sillimanite by HOLDAWAY(1971), then, for the disordering reaction ALi + Sisi = R
=
[a+/(1 -
MS,
+
SLl
(1)
2)2] = exp (-AH,IW,
(2)
where x is the mole fraction of Al on Si sites in the partially disordered crystal, AH, is the enthalpy of interchange when one mole of Al atoms is transferred from Al to Si sites. In this model, the entropy of disordering is assumed to be configurational only, and the molar enthalpy of interchange is presumed independent of the degree of disorder. AH,,, is now equated to the enthalpy change corresponding to the creation of degree of disorder x, and can be set equal to xAHlnt. Substituted into relation (2) this gives, after rearranging, x log,, [( 1 - x)/z] = AH,,,/4*6
RT.
(3)
Since AHobs and T are known, one can calculate x and AH,,,. The region for which AH,,, so calculated is constant corresponds to the region in which the simple model adequately represents the enthalpy data. Since x in equation (3) can vary from zero (complete order) to O-5 (complete randomness) the function x log [( 1 - x)/z] starts at zero, goes through a maximum of O-123 at x = 0.23 and drops to zero at x = 0.5. That is, for the simple disorder model, the ratio AH,,,/4*6 RT cannot exceed 0.123 regardless of the actual value of the molar interchange energy, although
2504
A. NA~ROTBKY, R. G. NEWTON and 0. J. KLEFTA
the temperature at which a given degree of disorder is attained obviously depends on the magnitude of the interchange enthalpy. In applying this theory to the present heat of solution me~ements in the plateau region to deduce a value of the interchange enthalpy, AHint, it is necessary to take into account initial disorder present in the sillimanite starting material. Inasmuch as the Brandywine Springs sillimanite was formed in a high grade metamorphic en~ronment, it is reasonable to suppose that some disorder characteristic of the temperature of formation is preserved in the sillimanite. A temperature of 65O'C f 50% would be consistent with the various estimates of the limits of atability of sillimanite under a pressure of a few kilobars in a temperature range below that where melting would probably have been widespread (RICHARDSON et d., 1967; HOLDAWAY,1971). In the present analysis, it was assumed that the Brandywine Springs sillimanite has an equilibrium Al-Si disorder corresponding to a temperature of 650°C. An initial average interchange enthalpy of 14.90 k~al/mole was calculated neglecting this disorder and a value of the x-parameter at 650% was calculated from equation (2). Enthalpy increments corresponding to the equilibrium 6BO’C disordering were then added to the quantities AHmt,,,tea - AHr P which result from the plateau region runs to give modified values of AH,,,. &ew values of AHint were calculated from equation (3)and the relation xAHint = AH,,,. These values of AH,,, were averaged and a new x for 650°C was calculated, etc. Four iterations of this process converged on a self-consistent AH,,, of 16.05rf O-81 koal/mole. The cal~ula~d AH,,, as a function of temperature based on a AH,, of I6 kcal~mole is plotted in Fig. 1. A good fit to the actual data defining the plateau region can be seen. This fact and the good agreement of the interchange enthalpy so deduced with the value of 14.75 kcal/mole calculated by HOLDAWAY(1971) and from the e~~mentai A.l,SiO, stability diagram lend considerable weight to the interpretation that the plateau region represents equilibrium or near-equilibrium disordering. The observed rapid onset of equilibrium in Al-Si disordering in a temperature range of less than 100°C is consistent with a process such as diffusion whose rate depends exponentially on a large activation energy. The volume change of disordering would be expected to be small, by analogy with spinels (FISCHER,1967)and feldspars (ROBIE and WALDBAUM,1968). Accordingly, the degree of disorder and observed enthalpy effects in the plateau region should be insensitive to pressure, as is observed. Note that our observed volume changes resulting from disordering anneal are significantly smaller than the values calculated by HOLDAWAY(1971) from the simple disordering model and the measured Al,SiOs eq~ibrium diagram. High temperature region. For temperatures above 155O*C,the values of AH,++/ 4-6RT markedly exceed the maximum values of O-123possible in the simple disorder model, making calculation of any value of AH, impossible for disordering of only two atoms over two sites per ‘molecule’. A more sop~sticated mo~~eation of this model which would allow for the variation of interchange enthalpy with degree of disorder and for nonconfigurational entropy contributions might be expected to change the calculated values of AH intby perhaps 20 per cent, but it could not easily account for the much larger values of AH,,, at the higher ~mperat~es or for the sharp increase in AH,,,, between 1600 and 1700°C. This evidence, together with
Sillimanite--disordering enthalpyby calorimetry
2606
the substantially larger lattice parameter shifts for runs above 1600% and the significant effect of pressure on the heat of solution in this temperature range point to a more profound change of state occurring in the high temperature region. Partial melting is rendered implausible by the persistence of the quartz lamellae at 1700°C: the sillimanite would react with quartz to produce a melt at a lower temperature than it would melt separately. Any siliceous melt produced would certainly be too viscous to crystallize quartz in the quench. The low-reflectance lamellae seen in the polished mount of the 17OO’Crun were of an aspect identical to those of the 15OO’C run, and were the same as in the untreated material except for kinking and warping. Boundaries of lamellae were sharp, with no indication of reaction zones. DEVRIES (1964) showed that kyanite and sillimanite melt to corundum plus siliceous liquid in the general pressure range of the present experiments. His sillimanite melting boundary, based on a preliminary experimental investigation, lies well above 1700°C at 16 kbar. No trace of corundum could be found in either the di&actogram or in the polished mount of the 1700% run. The microanalysis results do not support the notion that the sillimanite changes composition toward mullite in the high temperature region. The sillimanite in the 1700°C run could have been, if anything, slightly more siliceous than the untreated material, but the differences in the analyses are not of certain significance in terms of the precision of the measurements. A simple explanation of behavior in the high temperature region which is compatible with all of the present data is that disordering in sillimanite takes place in two or more stages with increasing temperature. At temperatures in the range 1400-165O’C near-equilibrium Al-Si disordering of the type postulated by HOLDAWAY (1971) with a AH intof about 16 kcal/mole, is produced in runs of a few hours’ duration. Above 155O’C a more profound (disordering?) process involving a larger ohange in enthalpy is produced in runs of short duration. The contribution that such a process would make to the equilibrium disorder in the metamorphic temperature range would be utterly negligible. A two-stage disordering process related to the one postulated here was proposed by HOLM and KLEPPA (1967) to interpret their heat of solution measurements on heat-treated natural albite of initial low structural state. An anneal of low albite at 1045’C for 3-15 days produced a AH,,, relative to the untreated material of 2.4 kcal/mole. Further annealing produced an additional 1.0 kcal effect. No additional heat increment was observed in material annealed for periods up to three weeks. The authors inferred that the initial faster disordering step produces an albite of intermediate Si-Al disordering and that the process of randomization is essentially complete after longer heat-treatment. Some implications for the equilibrium Al,SiO, diagram and for the experimental attempts to define it stem from the present results. It seems likely, as HOLDAWAY (1971) claims, that Al-Si equilibrium disorder must be taken into account in order to reconcile experimentally-determined P-T stability boundaries of the Al,SiC, polymorphs with measured entropy data. At lower temperatures, in the range of metamorphic processes (SOO-800°C) the amount of disorder deduced by HOLDAWAY (1971) and corroborated by the present study is small. Even so, the entropy
2506
A. NAVROTSKY, R. C. NEWTON
and 0.
J. KLEPPA
difference of the transfo~ation andalusi~~~ima~te is so small that the entropy of disorder could have a very significant effect in increasing the magnitude of the dP/dT slope. The entropy difference of the kyanite-sillimanite boundary is larger, so that sillimanite disorder in the temperature range of greatest geological interest (below 800°C) should not affect the dP/dT slope much. On the other hand, this consideration will enter strongly in the temperature range where experimental reversals of the equilibrium may be achieved, that is above 13OO’C. Values of the parameter z found for this temperature range of amount 0.10 (corresponding to 20 per cent disordering) would give configurational entropy increments of about 2 caljdeg mole. This would result in a much steeper dP/dT slope for the kyanite~lirna~~ boundary than would be calculated from the Third-Law entropies. This consideration would be particularly important in e~~rnent~ deter~atio~ where synthetic sillimanite is used, which might be expected to maintain significant nonequilibrium disorder, even at 1300-14OO’C where reversals of the equilibrium can be achieved. The kyanite-sillimanite boundary is probably interrupted by melting to corundum plus liquid at about 1600°C (DE VRIES, 1964). Therefore, the large high temperature thermal event found in the present study, which is possibly due to profound disordering of so far unknown character, would not influence the kyanite-sillimanite boundary over much of its length. As a referee of the present paper, Greenwood brought to our attention his very recent memoir on Al-% disorder in sillima~~ (GREENWOOD, 1972). In this paper the disorder problem is treated by a method related to that used in classical orderdisorder theory, and is discussed in terms of the Bragg-~~liarns order parameter s. This parameter ranges from 1 for complete order to 0 for complete disorder. The relation between s and our own disorder parameter, x, is simply x = ( 1 - 9)/2. In terms of Z, Greenwood’s expression for the enthalpy of disorder [equation (19)) becomes AH”Greenwood= AF’(l
- s2) = 4AH%(l
- 2).
As single crystal X-ray refinements are unable to detect Al-Si disorder below about 5 per cent, and as Al-Si disorder in natural sillimanites, if present, presumably is frozen in at temperatures of amout 500-700% Greenwood concludes that the value of ~~~w~d should be of the order of 25-55 kcal; his preferred value is 4 kcal. Mow mr,t, as defined by us, is equal to the limiting value of dAHemnwoodfdzat 2 = 0, i.e. AHint = 4AH&eenwood.The numerical agreement between our experimentally determined value of AHint and Greenwood’s estimate is rather better than could be expected. It should be recognized here that the disordering theory of Greenwood, using his preferred value of AH” = 4 koal/mole, predicts substantially higher degrees of disorder in the temperature range 1400-1550°C than our own data or the theoretical treatment of Holdaway infer. Above 1550°C, however, the observed enthalpy values rise sharply with increasing temperature to a value at 17OO’C near the maximum enthalpy of disorder predicted by Greenwood. It is possible that this lack of quantitative agreement in the range 1400-1550’~ must be attributed to the approxima~ character of the Greenwood (and Bragg-Williams) theory.
Sillimani%-dieorderingenthalpyby calorimetry
2607
investigations of disordering in binary alloys [see, e.g. C~PMAN and have led to a reeo~tion of the very highly co-operative character of these tr~~fo~&tio~, i.e. they have demonstrated that most of the disordering occurs in a quite narrow temperature range near the temperature of complete disorder, 21,(O-9 c T/T,< 1-O). The enthalpy of disorder similarly rises more sharply as T,isapproached than predicted by the Bragg-Williams theory. Re-examining our results in the light of these observations, it has occurred to us that the complete rsnge of 0nthalpy d&a shown in Fig. 1 possibly may be explained by a single, co-operative disordering process with &critical temperature of the order of 1700°C. In the temper&me range 1400-L550°C, disorder is relatively slight and is adequately approximated by the Holdaway treatment. However, above 1550°C, the co-operative character of the disordering process dominates and the enthalpy of disorder rises sharply, as is observed. X-Ray
WEEP
(19.50) 3
Ac~now~e~~rne~t~We are indebted to P. M. BELL of the Geophysical Laboratory, Carnegie Institute of Washington, for providing the samples of sillimanitefrom Brandywine Springs, Del., and to Miss M. C. BACHELDERwho carried out the spectrographic analysis. The authors acknowledge helpful discussionwith C. W. BURN~AMand J. F. HAYS of Harvard University. Finally, we are grateful to H. J. GREENWOOD and M. J. HOLDAWAYfor constructivecomments as referees of the paper. Financial support for the present investigation was received from National Science Foundation grant 22904 (R. C. N), and from the Petroleum Research Fund administered by the Ameriaan Chemical Society (0. J. K). The general support of materials research at the University of Chicago provided by the NSF-MRL Program also is aolmowledged. REFERENCES ALTEAUSE, (1969) Experimental evidence that the reaction of lryaniteto form sillimaniteis at least bivariant. Amer. J. Sci. 337, 272-277. ANDERSONP. A. M. and KLEPPA0. J. (1969) The the~o~he~st~ of the Hyatt-sillim~~ equilibrium. Amer. J. Sci. 367, 285-290. A~AMAEI S. and ROY R. (1962) Revised phase diagram for the system Al,O,-SiO,. J. Amer. Ceram. Sot. 4!j,229-242. BEGERR. M., BORNEAMC. W. and HAYS J. F. (1970) Structural ohangesin sillimanite at high temperature. Program Geol. Sot. Amer. Meeting in Milwaukee, Nov. 11-13, pp. 490-491. BURNHAEZ C. W. (1962) Lattice constant refinement. C%wwgGsIs&. Wad. Yew&. 61,132-135. CHATTERJZZN. D. and SC~REYER W. (1972) The reaction enstatite,,. _t sillimanite = sapphirine,,, + quartz in the system MgO-Al,Os--SiO,. Con&rib.Mineral. P&d. 36, 49-62. CHIPMAND. and WARREN B. E. (1950) X-Ray measurement of long range order in /l-brass. J. Appl. Phys. 21, 696-697. DEVRIES R. C. (1964) The system AlsSiO, at high temperatures and pressures. J. Amer. Ceram. Sot. 47, 230-237. FISCHERP. (1967) Neutron diffra&ion study of the effect of thermal history on the structures of magnesium aluminate and zinc aluminate spinels. 2. K&&o&~. 124, 275-302. FYFE W. S, (1969) Some second thoughts on A&O,-SiO,. AmeT. J. Sci. 287,291~296. GREENWOOD H. J. (1972) Alw-Sirv disorderin sillimaniteand its effect on phase relations of the aluminium silicate minerals. &ol. Sot. Amer. Mem. 132, 553-571. HARIYA Y., DOLLASEW. A. and KENNEDYG. C. (1969) An experimental investigation of the relationship of mulfite to sillimanite. Amer. M&es-at. 54, 1419-1441. HOLDAWAYM. J. (1971) Stability of andalusi~ and the aluminum silicate phase diagram. Amev. J. SC&271, 97-131. HOLM J. L. and KLEPPA 0. 5. (1966) Thermodynamics of the disordering process in albite (NaAlSisOs). Amer. Mineral. 63, 123-132. KLEPPA0. J. (1960) A new twin high temperature reaction calorimeter. The heats of mixing in liquid sodium-potassium nitrates. J. Phys. C&em.64, 1937-1940.
2508
A. NA~~OTSKY, R. C. NEWTON
end 0. J. KLEPPA
KWH T. A. P. (1971) Compositions of natural sillimsnites from volcanic inclusions end metemorphic rocks. Amev. Mirmd. 56, 1750-1759. NAVROTSKYA. end KLEPPA 0. J. (1967) The thermodynamics of c&ion distributions in simple apinels. J. Inorg. Nucl. Ckmn. 29, 2201-2214. NEWTON R. C. (1969) Some high-pressure hydrothermal experiments on severely ground kyanite and sillimanite. Amer. J. Sci. 267, 278-284. NEWTON R. C. (1972) An experimental determination of the high-pressure stability limits of msgnesien cordierite under wet and dry conditions. J. Geol. 80, 398-420. RICHARDSONS. W., BELL P. M. and GILBERT M. C. (1967) Kyenite-sillimanite equilibrium between 700’ end 1500°. Amer. J. Sci. 266, 513-541. ROBIE R. A. and WALDBA~ D. R. (1968) Thermodynamic properties of minersls and related substances at 298.15’K (25.0%) end one atmosphere (l-013 brtrs) pressure and st higher temperatures. Bull. Gwl. Sot. Amer. 1259,l-256. ZEN E. A. (1967) Possible compositional effects on the kyanite-sillimanite equilibrium. Program Geol. Sot. Amer. Ann. Meeting in New Orleans, Nov. 20-22, 246-247.
sillhhte-disordering
enthalpy by calorimetry
A. NAVROTSKY,* R. C. NEWTONS- and 0. J_ KLEFPA !l%eJames Fr8nck Institute, The University of Chicago, Chicago, Illinois 60637, U.S.A.
Ab&&-Heat
of solution measurements in an oxide-melt were performed on s8mples of heat-treated in the range 12OO-1700°C 8t pressures of 16-23 kbsr. A distinot entl-&py of solution decrement relative to the unhested ~~~ of about I.3 kc/mole is shown by s8mples run 8t 14OO-1650% Pressure vsrietions in the range 16-23 kbar u8use little change in the heat of solution in this temperature range. This pressure-independent ‘platesu’ in heat of solution is interpreted to be due to Al-Si disordering on tetrehedrsl sites in the sillim8mte structure. A simple ~rn~r8t~-de~ndent disordering model developed by KAVROTSKY 8nd IELEPPA (1967) for spine&sfeeda to 8n Al--@ interchange enthafpy, mint, of 10 f 1 kcsl/mole, in good agreement with the value derived by HOLDAWAY (1971) on entirely different grounds. Above 1560°C, larger heat of solution decrements were observed. Microprobe analyses of quenched maples indicate that the sillimsnite hss not deviated signifio8ntly from the ideel formul8. Some unknown profound disordering process 1118~account for the heat e&&s in the very high temper8ture range. Unit oell volumes of quenched semples 81~0 describe 8 ‘pleteau region in the tempemture range 1400-155O’C. This plateau consists of 8n increacle of the 5 crystallographic axis beginning at 1350% without much change in the other 8xes in the range 135O-1650°C. A sudden expansion of the a-8x& occurs between 1550 and 1630’%. We oonclude that Al-Si disorder of the type postulsted by BE~ER et al. (1970), and HOLDAWAY (1971) has been confirmed c8lorimetric8lly for samples heated under pressure in the temperature r8nge 1400-165O’C. nat,ural sillim&te
fiE THERMODYNA~\~ICSof the aluminum silicates has been the subject of intense experimental study and considerable controversy in recent years. Numerous experimental studies of equilibrium relations among the A&&O, polymorphs sillimanite, kyauite and andalusite have yielded different results. A number of explanations have been proposed to account for the discrepancies. These include error in pressure calibration of e~eriment&l apparatus (RICHARDSON et al., 1967); the effect of strain energy of materials in high pressure runs (FYFE, 1969; NEWTON, 1969); the effect of surface energy of the very severely ground starting material used by some investigators (NEWTON, 1969), the possibility that sillimanite cannot be considered to be simply stoichiometric Al&GO,, either because of s, si~i~cant iron content (ALTI&AUS, 1969) or because of the existence of an alumina-rich solid solution series at high temperatures and pressures extending toward the mull&e (3Al,O, .2SiO,) composition (RAMYA et al., IQ69), and, finally, the possibility of Al-Si disorder on ~tr&he~~l sites in the siIIima~te struct~e (ZEN, 1967; ~DE~O~ snd KLEPPA, 1969; BE~ER et ai., 1970; HOLDAWAY, 1971; CHATTERJEE and SCHREYER,
1972;
* Department t Department
GREENWOOD, 1972.
See Discussion
section
below).
of Chemistry, A.&on8 State U~versity, Tempe, A&on8 85281, U.S.A. of Geophysical Sciences, University of Chicago, Chicago, Illinois 60637, U.S.A.
2497
2498
A. NAVROTSKY, R. C. NEWTON and 0. J. KLEPPA
The idea of temperature-dependent Al-Si tetrahedral disorder in sillimanite was developed by HOLDAWAY(1971) into a quantitative theory which sought to bring the more unambiguous of the experimental observations into line with published thermodynamic data in order to achieve a self-consistent Al,SiO, stability diagram. Using a simple oation-exchange reaction modeled after the disordering theory of NAVROTSKYand KLEPPA (1967) for spinels, Holdaway calculated the energy of Al and Si interchange on tetrahedral sites. His principal numerical input was his experimentally measured dP/dT slope of the sillimanite-andalusite phase boundary. The value of the interchange enthalpy, AHint,which bestfitted the experimental data, was 14.75 kcal/mole. With this interchange energy, Holdaway’s theory gives about 10 per cent equilibrium Al-Si disorder at 1000°C and about 20 per cent at 14OO’C. Disordering of this magnitude would be expected to have significant effects on the slopes and positions of the high-temperature portions of the stability boundaries in the Al,SiO, diagram. It is equally likely that any appreciable departure of sillimanite from the Al,SiO, composition, most plausibly in the direction of mullite, would also have a marked influence on the phase relations. Changes in the unit cell parameters of sillimanite heat treated under pressure have been observed (BEOER et al., 1970; HARIYA et al., 1969; CHATTERJEE and SCHREYER,1972). When natural sillimanite is heated above about 1400°C for some hours in a pressure range between about 7 and 25 kbar, which avoids the fields of stability of mullite and kaynite, changes of lattice parameters occur, the magnitudes of which apparently depend on temperature, pressure and time. The most notable changes are expansions of the b and a crystallographic axes. This observation has been interpreted in two ways. HARIYA et al. (1969) made a number of heating experiments on sillimanite under pressure and concluded from an analysis of powder X-ray diffraction data on this material that sillimanite migrates toward mullite in composition at high temperatures. They were unable to show that quartz was exsolved from the sillimanite because their starting sillimanites contained quartz. BEQERet al. (1970), on the other hand suggested, on the basis of lattice constant changes and changes in the intensities of X-ray diffraction maxima in single-crystal photographs of heat-treated material, that sillimanite undergoes Al-Si tetrahedral disordering at constant composition. They cited preliminary electron microprobe analyses to support their interpretation. CHATTERJEE and SCHREYER(1972) found temperature-dependent changes in the unit cell constants of natural sillimanite used in their experimental study of the reaction of enstatite and sillimanite to sapphirine and quartz at high temperatures and pressures. They concluded that on-composition disordering was responsible. Finally, certain sillimanite samples from inclusions in volcanic rocks have somewhat anomalous unit cell constants, as, for example, the sillimanite inclusions from the lava of Asama Volcano (ARAMAKIand ROY, 1962). KWAK (1971) analyzed a number of such sillimanites and concluded that there was no signifioant deviation from the ideal formula. previous experience in this laboratory in the application of high temperature solution calorimetry to the thermochemistry of the kyanite-sillimanite equilibrium (ANDERSONand KLEPPA, 1969), and to disordering in albite (HOLY and KLEPPA, 1967), and in natural MgAl,O, spine1 (NA~ROTSKYand KLEPPA,1967) suggested to
Sillimanite-disordering
enthalpy by calorimetry
2499
us that cation disordering in sillimanite could be detected and studied by this method. The aim of the present study was to measure the heat of solution of natural sillimanite exposed in the laboratory to various pressure and temperature conditions, and to attempt to decide whether, using the adjuncts of X-ray diffraction and electron probe microanalysis, any heat effects so determined could be the result of cation disordering or of heterogeneous reaction. It may be stated at the outset that both an enthalpy effect and lattice parameter changes indeed have been detected and that the present results favor on-composition atomic rearrangements, rather than a compositional shift toward mullite, -as their cause, at least in the temperature range below 16OO’C. EXPERIMENTAL METHODS Starting material. All of the present calorimetric runs were made on natural sillimanite from Brandywine Springs, Delaware, kindly provided by P. M. Bell. This sillimanite was beautifully crystalline and suitable for hand-picking. A few small red grains of a foreign phase were easily removed. The X-ray powder pattern of the sillimanite showed very small amounts of quartz probably less than 3 per cent by volume. Polished thin-section grain mounts revealed that this quartz was present as 6ne lamellar intergrowths in about 30 per cent of the sillimanite grains. The quartz appeared to be quite inert during the heat-treating process. A semiquantitative spectrographic analysis revealed 0.05 per cent V; 0.01 per cent B, Cr, Fe; 0.005 per cent Mg, Ti, Mn; and O-001 per cent Ca, Ni, Cu, Ag, as the most abundant impurities. High pressure PUTLQ.A piston-cylinder apparatus with a 1 in. diameter carbide chamber and piston was used. The solid pressure medium was Pyrex glass and talc (NEWTON,1972). Samples were contained in either graphite crucibles or welded platinum jackets within holders of AlSiMag 222 (American Lava Co.) surrounded by cylindrical graphite heaters. Most of the runs were made at a corrected pressure of 16-18 kbar (a nominal pressure of 20 kbar). Temperature was controlled automatically and measured by W-25 per cent Re vs W-3 per cent Re thermocouples in contact with the graphite or platinum containers but protected from contamination by a film of alundum cement. When the heating power necessary to maintain a given apparent temperature began to drift downward by an amount equivalent to E-25%, which always happened sooner or later, depending on the temperature, the run was terminated and quenched to below 1OO’C in a few seconds. The observed power drift effectively limited run times to about 2 hr at 17OO’C and about 10 hr at 1400%. Calwimetry. After a high pressure run, the hard pellet of sillimanite was removed from its graphite or platinum container, crushed in a hard steel mortar, and ground to a fine powder under acetone in an agate mortar. Powdered samples from runs in graphite containers were generally gray in color because of graphite contamination. The graphite was burned off at 850% in air for at least 5 hr, which yielded a white powder showing no residual graphite. About 70-75 mg of material was recovered from one high pressure run in graphite container. This was generally enough for two calorimeter runs and a preliminary X-ray scan. High pressure runs in platinum jackets yielded only 40-50 mg of sample. The calorimetric equipment and technique have been described previously (ANDERSON and KLEPPA, 1969; KLEPPA, 1960). All solution experiments were performed at 690 f 1% using molten 2PbO . BsOs as solvent. Sample size was 20-40 mg per run. X-Ray lattice parameter determinationa. All samples treated above 1500°C were scanned for any new phases using a Norelco diffractometer with CuK, radiation at a speed of 1’ (26)/min. No new phases were found. Quartzwas still present in approximately the same amount as in the untreated material, even in the 1700’ runs. A portion of all of the samples used in the calorimetric runs was scanned at l/2’ (20) with a corundum internal standard to approximately characterize the lattice parameter changes. A special series of nine runs on platinum-jacketed samples was made at 18 kbar in the range 1200-1700% in order to characterize as carefully as possible the unit-cell parameter changes. The powdered quenched charges of the runs were scanned at l/S” (26)/min with an internal standard of National Bureau of Standards MgAlsO,
A. NAVROTSKY, R. C. NEWTON and 0. J.
2600
KLEPPA
spinel. Twelve to Gfteen sillimanite lines were measured and subjected to a computer leastsquares unit-cell refinement (BTJR~EAM, 1962). Microscopy ar& electroonprobe miwoanalysis. Some additional runs on Brandywine Springs sillimanite were made for optical and microanalytic study. Pellets from runs at 1600% and 1700% were ground and polished. Reflected light study of these revealed fine lamellae of lower reflectivity than the sillimanite in some grains. These had exactly the same appearance as the lamellae in the untreated material, suggesting that the quartz is inert under these run conditions. These mounts were analyzed with an ARL electron microprobe using a sub-micron beam diameter. Traverses were made across grains containing low-reflectance lamellae, and individual lame&e as well as lamella-free grains were analyzed for Si and Al. Grains of untreated Brandywine Springs sillimanite served as a convenient standard. RESULTS
OF EXPERIMENTS
The heats of solution of sillimanite treated under various pressure and temperature conditions are presented in Table 1. Figure 1 shows graphically the difference in Table 1. Results of calorimetric studies on sillimanite samples heated at various temperatures and pressures
(WZ’)
(kbP)
(hrt)
Interchange enthalpy Initifd cslculstion Fourth iteretion$
Calorimetry
Sample trestment Container
mg/semple 38.87 62.55 61.93 41.13 45.29 44.45 31.47 43.74 32.27 49.07 23.91 38.14 32.96 27.38 38.46 33.51 35.27 34.29 40.45 33.87 37.36 28.38 35.78 37.16 30.16 37*56 31.83 34.96 29.06 23.00 30.45 20.27 39.71 31.96
Untreated
1200
16-18
6.0
C
1326 1400
16-18 16-18
10.0 7.5
C C
1460
16-18
6.0
C
1476
16-18
12.0
C
1600 1600
18-18 23
4.0 4.0
C C
1600 1600 1630
16-18 16-18 16-18
6.6 6.0 6.0
Pt Pt C
1600
16-18
3.0
C
1660 1700
16-18 IS.18
3.0 2.0
Pt C
1700
23
1.5
C
AH::,1 (kcal/mole) Av. 7.057 6.926 7.343 7.028 7.443 6.863 7.327 6.948 7.693 6.860 6.741 7.244 7.171 7.066 6.867 6.944 6.967 6.028 6.949 6.611 6.691 6.841 6.691 6.483 6.516 6.627 6.930 4.661 6.029 3.86 3.359 3.114 4.195 4.385
AH%,
4.6RT
zt
AHintS
-
AHr.p.
AHint
7.11 ho.29
7.21 7.07 6.91
0.0784
0.0839
14.29
0.0909
16.29
6.00
0.0698
0.0786
14.15
0.0863
15.06
6.78
0.0845
0.0874
15.22
0.0930
16.34
5.69 6.77
0.0876 0.0827
0*0891 0.0864
14.94 16.61
0.0960 0.0926
16.95 16.62
6.00
0.0686
0.0776
14.31
0.0849
16.31
6.73
0.0837
0.0870
16.86
0.0930
16.88
4.86
0.132
3.86 3.24
0.184 0.216
4.29
0.166 =
* AHOaB= &%mtrested t 5 = mole fraction Al $ AHint = interchange
=
14.98
on Si sites, from equation (3). enthalpy for reaction Al& + Sisi = Alsi + Sia, from ARObs = zHint. 0 Celoulation corm&ad for equilibrium disorder in etarting material (aw text).
AV. =
16.06
Sillimanite-disordering
5
s=
‘,
SE
I’ 4
43-
E c8
;:‘;:
$
;;$
$;‘f;
g&item’
’
I
’
A RUNS AT 23 Kb, in graphite ---EXPERIMENTAL CURVE AT 16Kb -EOUILIBRIUM CURVE i
AHint=16kCsl 25 = a I/MY II 2 o_+_____-_---_____+-__j I” a I I! I I 600
1090
BOO
2501
enthalpy by calorimetry
’ i:/+
-
,i+
II
I
1200
Temperature,
11
1400
1
1600
IBOO
"C
Fig. 1. Heat of solution data on quenched samples of Brandywine Springs (Del.) sillimanite heat-treated at high pressure. Solid line is calculated from simple Al-Si tetrahedral disorder with AH,,t = 16 kcal/mol (see text). Table 2. Unit cell constants of Brandywine Springs sillimanite samples heat-treated capsules at 16-18 kbar in the temperature range 1200-1700% Run duration (hr)
Temperature (“C) Untreated 1300 1350 1400 1450 1500 1550 1630 1700
J* 7.485 7.484 7.484 7.487 7.488 7.486 7.489 7.497 7.500
10 7: 72 6& 5f
34
3 2
* Uncertainty
(f$* J* 7,673 7.675 7.677 7.680 7.682 7.684 7.684 7.689 7.690
5.769
5.771 5.772 6.770 5.771 6.770 5.768 5.768 6.767
331.262 331.478 331.674 331.791 331.939 331.920 331.873 332.484 332574
f + f i f * & f f
0.075 0.054 0.070 0.117 0.086 0.084 0.087 0.139 0.119
*O.OOl-0.002 d.
= G .5
I.2 oa
tt
33’.o,200
t
1300
I
I I I I 1400 1500 Temperature ‘C
It
1600
Ii
1700
Fig. 2. Unit cell volumes of quenched samples of sillimanite heat-treated under pressures of 16-18 kbar. Data taken from Table 2. The value at 1200°C refers to untreated material. 10
in Pt
2602
A.
NAVROTSKY,
R. C. NEWTONmd 0. J. KIBPPA
heat of solution between the untreated and treated samples, A&_,,, - AIf-,,p = AfL*, as a function of temperature. The plotted points are the average of the two calorimeter runs on each quenched charge, except for the runs in platinum jackets, for each of which only enough material was available to make one oalorimeter run. The unit cell constants of runs in the range 1300-1700°C at 18 kbar are presented in Table 2, and the unit cell volumes are shown as a function of temperature in Fig. 2. The curve in Fig. 1 can be divided into three portions: (a) a low temperature region, T < 1350°C, in which essentially no change in heat of solution is observed; (b) a region of 1400’ < T < 1550°C in which AH,,, increases only slightly with temperat~e and not sig~ficantly with pressnre in the range 16-23 kbar; (c) a region, for T > 155O”C,where AH,,, increases markedly with T and is substantia~y smaller in magnitude at 23 kbar than at 16 b-bar for a given temperature. The intermediate region appears as a shoulder or plateau in the curve. A long run was made in the range 1450-15OO’C to check for the possibility that the plateau region in the heat of solution curve might be an incidental product of the duration of runs which had been determined by the observed rate of power drift (possibly due to the thermooouple contamination). A run at 16-18 kbar was started at 1600°C. After 12 hr, the heater power had dropped by an amount equivalent to a 50°C decrease in temperature. This run in the ‘plateau region’ was three times as long as the 1500°C rrms and twice as long as the 14OO’Crun yet showed essentially the same heat of solution as the shorter runs in the plateau region. The runs in platinum jackets showed heat of solution results entirely consistent with the runs from graphite containers, and demonstrate that the observed changes in solution enthalpy are not due to reaction with the container material. The change of unit cell volume with run temperature appears to be regularly related to the change in heat of solution. Figure 2 shows a ‘plateau region’ in unit cell volume corresponding to the plateau in the heat of solution curve. The trend of the b crystallographic axis shows the strongest early change with heat-treatment. The plateau region in the unit-cell volume is a result of b-axis increase with little change in the other axes. Samples heated above 1600°C show an abrupt large change in the a-axis, with a volume increase approaching & per cent. Reversibility of the change in unit cell parameters was investigated in a run made at 165O’C and 18 kbar for 3 hr. Unit cell measurements of the quenehed material was made and then this material was run again at 1500°C and 18 kbar for 4 hr. The large changes of unit cell parameters resulting from the 165O’C run were not reversed by the 15OO*Crun. Microanalysis of a 17OO’Crun clearly showed silica-rich lamellae in some grains. No analyzable area was large enough to avoid overlapping Al counts from neighboring sillimanite. The X-ray diffractograms showed that the siliceous lamellae were quartz and not a silica-rich glass. Quartz lamellae larger than a fraction of a micron across could be detected by lower reflectivity and avoided. Analyses at several positions on a large, apparently quartz-free, grain gave compositions in mole fractions as follows.
Sillimanit~sordering
enthalpy by calorimetry
2603
The Si to Al ratio seems to be slightly greater than unity, but the deviation from the ideal formula may not be significant in view of experimental errors. There is certainly no indication of approach to the mullite composition. The possibility remains that extremely fine quartz lamellae were present in very uniform dispersion. The absolute amount of quartz present, as indicated by the diffractogram, would be much too small to produce the observed heat effects. DISCUSSION We propose the following interpretation, which is consistent with all our data and with previous observations on sillimanites of different thermal history. Unequilibrated region. In Region (a), the low-temperature interval of Fig. 1, disordering of the sillimanite occurs too slowly for any change in heat of solution to be observed in samples annealed only a few hours. The fact that the sample treated at 12OO’C and 16 kbar for 5 hr showed essentially the same heat of solution as the untreated samples shows that the enthalpy effect associated with any strain energy introduced into the samples by the high pressure conditions is immeasurably small, since the strain introduced at 1200°C would be expected to be equal to or possibly greater than that introduced at higher temperatures. The heats of solution presented in Table 1 are not corrected for the small amount of quartz present. The measurements on untreated sillimanite agree within experimental error with the heat of solution values on other sillimanite samples reported by ANDERSON and KLEPPA (1969). Plateau region. The shoulder region [Region (b)] can be understood in terms of near-equilibrium Al-Si disordering on tetrahedral sites. If one uses the simple model proposed by NAVROTSKYand KLEPPA (1967) and applied to sillimanite by HOLDAWAY(1971), then, for the disordering reaction ALi + Sisi = R
=
[a+/(1 -
MS,
+
SLl
(1)
2)2] = exp (-AH,IW,
(2)
where x is the mole fraction of Al on Si sites in the partially disordered crystal, AH, is the enthalpy of interchange when one mole of Al atoms is transferred from Al to Si sites. In this model, the entropy of disordering is assumed to be configurational only, and the molar enthalpy of interchange is presumed independent of the degree of disorder. AH,,, is now equated to the enthalpy change corresponding to the creation of degree of disorder x, and can be set equal to xAHlnt. Substituted into relation (2) this gives, after rearranging, x log,, [( 1 - x)/z] = AH,,,/4*6
RT.
(3)
Since AHobs and T are known, one can calculate x and AH,,,. The region for which AH,,, so calculated is constant corresponds to the region in which the simple model adequately represents the enthalpy data. Since x in equation (3) can vary from zero (complete order) to O-5 (complete randomness) the function x log [( 1 - x)/z] starts at zero, goes through a maximum of O-123 at x = 0.23 and drops to zero at x = 0.5. That is, for the simple disorder model, the ratio AH,,,/4*6 RT cannot exceed 0.123 regardless of the actual value of the molar interchange energy, although
2504
A. NA~ROTBKY, R. G. NEWTON and 0. J. KLEFTA
the temperature at which a given degree of disorder is attained obviously depends on the magnitude of the interchange enthalpy. In applying this theory to the present heat of solution me~ements in the plateau region to deduce a value of the interchange enthalpy, AHint, it is necessary to take into account initial disorder present in the sillimanite starting material. Inasmuch as the Brandywine Springs sillimanite was formed in a high grade metamorphic en~ronment, it is reasonable to suppose that some disorder characteristic of the temperature of formation is preserved in the sillimanite. A temperature of 65O'C f 50% would be consistent with the various estimates of the limits of atability of sillimanite under a pressure of a few kilobars in a temperature range below that where melting would probably have been widespread (RICHARDSON et d., 1967; HOLDAWAY,1971). In the present analysis, it was assumed that the Brandywine Springs sillimanite has an equilibrium Al-Si disorder corresponding to a temperature of 650°C. An initial average interchange enthalpy of 14.90 k~al/mole was calculated neglecting this disorder and a value of the x-parameter at 650% was calculated from equation (2). Enthalpy increments corresponding to the equilibrium 6BO’C disordering were then added to the quantities AHmt,,,tea - AHr P which result from the plateau region runs to give modified values of AH,,,. &ew values of AHint were calculated from equation (3)and the relation xAHint = AH,,,. These values of AH,,, were averaged and a new x for 650°C was calculated, etc. Four iterations of this process converged on a self-consistent AH,,, of 16.05rf O-81 koal/mole. The cal~ula~d AH,,, as a function of temperature based on a AH,, of I6 kcal~mole is plotted in Fig. 1. A good fit to the actual data defining the plateau region can be seen. This fact and the good agreement of the interchange enthalpy so deduced with the value of 14.75 kcal/mole calculated by HOLDAWAY(1971) and from the e~~mentai A.l,SiO, stability diagram lend considerable weight to the interpretation that the plateau region represents equilibrium or near-equilibrium disordering. The observed rapid onset of equilibrium in Al-Si disordering in a temperature range of less than 100°C is consistent with a process such as diffusion whose rate depends exponentially on a large activation energy. The volume change of disordering would be expected to be small, by analogy with spinels (FISCHER,1967)and feldspars (ROBIE and WALDBAUM,1968). Accordingly, the degree of disorder and observed enthalpy effects in the plateau region should be insensitive to pressure, as is observed. Note that our observed volume changes resulting from disordering anneal are significantly smaller than the values calculated by HOLDAWAY(1971) from the simple disordering model and the measured Al,SiOs eq~ibrium diagram. High temperature region. For temperatures above 155O*C,the values of AH,++/ 4-6RT markedly exceed the maximum values of O-123possible in the simple disorder model, making calculation of any value of AH, impossible for disordering of only two atoms over two sites per ‘molecule’. A more sop~sticated mo~~eation of this model which would allow for the variation of interchange enthalpy with degree of disorder and for nonconfigurational entropy contributions might be expected to change the calculated values of AH intby perhaps 20 per cent, but it could not easily account for the much larger values of AH,,, at the higher ~mperat~es or for the sharp increase in AH,,,, between 1600 and 1700°C. This evidence, together with
Sillimanite--disordering enthalpyby calorimetry
2606
the substantially larger lattice parameter shifts for runs above 1600% and the significant effect of pressure on the heat of solution in this temperature range point to a more profound change of state occurring in the high temperature region. Partial melting is rendered implausible by the persistence of the quartz lamellae at 1700°C: the sillimanite would react with quartz to produce a melt at a lower temperature than it would melt separately. Any siliceous melt produced would certainly be too viscous to crystallize quartz in the quench. The low-reflectance lamellae seen in the polished mount of the 17OO’Crun were of an aspect identical to those of the 15OO’C run, and were the same as in the untreated material except for kinking and warping. Boundaries of lamellae were sharp, with no indication of reaction zones. DEVRIES (1964) showed that kyanite and sillimanite melt to corundum plus siliceous liquid in the general pressure range of the present experiments. His sillimanite melting boundary, based on a preliminary experimental investigation, lies well above 1700°C at 16 kbar. No trace of corundum could be found in either the di&actogram or in the polished mount of the 1700% run. The microanalysis results do not support the notion that the sillimanite changes composition toward mullite in the high temperature region. The sillimanite in the 1700°C run could have been, if anything, slightly more siliceous than the untreated material, but the differences in the analyses are not of certain significance in terms of the precision of the measurements. A simple explanation of behavior in the high temperature region which is compatible with all of the present data is that disordering in sillimanite takes place in two or more stages with increasing temperature. At temperatures in the range 1400-165O’C near-equilibrium Al-Si disordering of the type postulated by HOLDAWAY (1971) with a AH intof about 16 kcal/mole, is produced in runs of a few hours’ duration. Above 155O’C a more profound (disordering?) process involving a larger ohange in enthalpy is produced in runs of short duration. The contribution that such a process would make to the equilibrium disorder in the metamorphic temperature range would be utterly negligible. A two-stage disordering process related to the one postulated here was proposed by HOLM and KLEPPA (1967) to interpret their heat of solution measurements on heat-treated natural albite of initial low structural state. An anneal of low albite at 1045’C for 3-15 days produced a AH,,, relative to the untreated material of 2.4 kcal/mole. Further annealing produced an additional 1.0 kcal effect. No additional heat increment was observed in material annealed for periods up to three weeks. The authors inferred that the initial faster disordering step produces an albite of intermediate Si-Al disordering and that the process of randomization is essentially complete after longer heat-treatment. Some implications for the equilibrium Al,SiO, diagram and for the experimental attempts to define it stem from the present results. It seems likely, as HOLDAWAY (1971) claims, that Al-Si equilibrium disorder must be taken into account in order to reconcile experimentally-determined P-T stability boundaries of the Al,SiC, polymorphs with measured entropy data. At lower temperatures, in the range of metamorphic processes (SOO-800°C) the amount of disorder deduced by HOLDAWAY (1971) and corroborated by the present study is small. Even so, the entropy
2506
A. NAVROTSKY, R. C. NEWTON
and 0.
J. KLEPPA
difference of the transfo~ation andalusi~~~ima~te is so small that the entropy of disorder could have a very significant effect in increasing the magnitude of the dP/dT slope. The entropy difference of the kyanite-sillimanite boundary is larger, so that sillimanite disorder in the temperature range of greatest geological interest (below 800°C) should not affect the dP/dT slope much. On the other hand, this consideration will enter strongly in the temperature range where experimental reversals of the equilibrium may be achieved, that is above 13OO’C. Values of the parameter z found for this temperature range of amount 0.10 (corresponding to 20 per cent disordering) would give configurational entropy increments of about 2 caljdeg mole. This would result in a much steeper dP/dT slope for the kyanite~lirna~~ boundary than would be calculated from the Third-Law entropies. This consideration would be particularly important in e~~rnent~ deter~atio~ where synthetic sillimanite is used, which might be expected to maintain significant nonequilibrium disorder, even at 1300-14OO’C where reversals of the equilibrium can be achieved. The kyanite-sillimanite boundary is probably interrupted by melting to corundum plus liquid at about 1600°C (DE VRIES, 1964). Therefore, the large high temperature thermal event found in the present study, which is possibly due to profound disordering of so far unknown character, would not influence the kyanite-sillimanite boundary over much of its length. As a referee of the present paper, Greenwood brought to our attention his very recent memoir on Al-% disorder in sillima~~ (GREENWOOD, 1972). In this paper the disorder problem is treated by a method related to that used in classical orderdisorder theory, and is discussed in terms of the Bragg-~~liarns order parameter s. This parameter ranges from 1 for complete order to 0 for complete disorder. The relation between s and our own disorder parameter, x, is simply x = ( 1 - 9)/2. In terms of Z, Greenwood’s expression for the enthalpy of disorder [equation (19)) becomes AH”Greenwood= AF’(l
- s2) = 4AH%(l
- 2).
As single crystal X-ray refinements are unable to detect Al-Si disorder below about 5 per cent, and as Al-Si disorder in natural sillimanites, if present, presumably is frozen in at temperatures of amout 500-700% Greenwood concludes that the value of ~~~w~d should be of the order of 25-55 kcal; his preferred value is 4 kcal. Mow mr,t, as defined by us, is equal to the limiting value of dAHemnwoodfdzat 2 = 0, i.e. AHint = 4AH&eenwood.The numerical agreement between our experimentally determined value of AHint and Greenwood’s estimate is rather better than could be expected. It should be recognized here that the disordering theory of Greenwood, using his preferred value of AH” = 4 koal/mole, predicts substantially higher degrees of disorder in the temperature range 1400-1550°C than our own data or the theoretical treatment of Holdaway infer. Above 1550°C, however, the observed enthalpy values rise sharply with increasing temperature to a value at 17OO’C near the maximum enthalpy of disorder predicted by Greenwood. It is possible that this lack of quantitative agreement in the range 1400-1550’~ must be attributed to the approxima~ character of the Greenwood (and Bragg-Williams) theory.
Sillimani%-dieorderingenthalpyby calorimetry
2607
investigations of disordering in binary alloys [see, e.g. C~PMAN and have led to a reeo~tion of the very highly co-operative character of these tr~~fo~&tio~, i.e. they have demonstrated that most of the disordering occurs in a quite narrow temperature range near the temperature of complete disorder, 21,(O-9 c T/T,< 1-O). The enthalpy of disorder similarly rises more sharply as T,isapproached than predicted by the Bragg-Williams theory. Re-examining our results in the light of these observations, it has occurred to us that the complete rsnge of 0nthalpy d&a shown in Fig. 1 possibly may be explained by a single, co-operative disordering process with &critical temperature of the order of 1700°C. In the temper&me range 1400-L550°C, disorder is relatively slight and is adequately approximated by the Holdaway treatment. However, above 1550°C, the co-operative character of the disordering process dominates and the enthalpy of disorder rises sharply, as is observed. X-Ray
WEEP
(19.50) 3
Ac~now~e~~rne~t~We are indebted to P. M. BELL of the Geophysical Laboratory, Carnegie Institute of Washington, for providing the samples of sillimanitefrom Brandywine Springs, Del., and to Miss M. C. BACHELDERwho carried out the spectrographic analysis. The authors acknowledge helpful discussionwith C. W. BURN~AMand J. F. HAYS of Harvard University. Finally, we are grateful to H. J. GREENWOOD and M. J. HOLDAWAYfor constructivecomments as referees of the paper. Financial support for the present investigation was received from National Science Foundation grant 22904 (R. C. N), and from the Petroleum Research Fund administered by the Ameriaan Chemical Society (0. J. K). The general support of materials research at the University of Chicago provided by the NSF-MRL Program also is aolmowledged. REFERENCES ALTEAUSE, (1969) Experimental evidence that the reaction of lryaniteto form sillimaniteis at least bivariant. Amer. J. Sci. 337, 272-277. ANDERSONP. A. M. and KLEPPA0. J. (1969) The the~o~he~st~ of the Hyatt-sillim~~ equilibrium. Amer. J. Sci. 367, 285-290. A~AMAEI S. and ROY R. (1962) Revised phase diagram for the system Al,O,-SiO,. J. Amer. Ceram. Sot. 4!j,229-242. BEGERR. M., BORNEAMC. W. and HAYS J. F. (1970) Structural ohangesin sillimanite at high temperature. Program Geol. Sot. Amer. Meeting in Milwaukee, Nov. 11-13, pp. 490-491. BURNHAEZ C. W. (1962) Lattice constant refinement. C%wwgGsIs&. Wad. Yew&. 61,132-135. CHATTERJZZN. D. and SC~REYER W. (1972) The reaction enstatite,,. _t sillimanite = sapphirine,,, + quartz in the system MgO-Al,Os--SiO,. Con&rib.Mineral. P&d. 36, 49-62. CHIPMAND. and WARREN B. E. (1950) X-Ray measurement of long range order in /l-brass. J. Appl. Phys. 21, 696-697. DEVRIES R. C. (1964) The system AlsSiO, at high temperatures and pressures. J. Amer. Ceram. Sot. 47, 230-237. FISCHERP. (1967) Neutron diffra&ion study of the effect of thermal history on the structures of magnesium aluminate and zinc aluminate spinels. 2. K&&o&~. 124, 275-302. FYFE W. S, (1969) Some second thoughts on A&O,-SiO,. AmeT. J. Sci. 287,291~296. GREENWOOD H. J. (1972) Alw-Sirv disorderin sillimaniteand its effect on phase relations of the aluminium silicate minerals. &ol. Sot. Amer. Mem. 132, 553-571. HARIYA Y., DOLLASEW. A. and KENNEDYG. C. (1969) An experimental investigation of the relationship of mulfite to sillimanite. Amer. M&es-at. 54, 1419-1441. HOLDAWAYM. J. (1971) Stability of andalusi~ and the aluminum silicate phase diagram. Amev. J. SC&271, 97-131. HOLM J. L. and KLEPPA 0. 5. (1966) Thermodynamics of the disordering process in albite (NaAlSisOs). Amer. Mineral. 63, 123-132. KLEPPA0. J. (1960) A new twin high temperature reaction calorimeter. The heats of mixing in liquid sodium-potassium nitrates. J. Phys. C&em.64, 1937-1940.
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A. NA~~OTSKY, R. C. NEWTON
end 0. J. KLEPPA
KWH T. A. P. (1971) Compositions of natural sillimsnites from volcanic inclusions end metemorphic rocks. Amev. Mirmd. 56, 1750-1759. NAVROTSKYA. end KLEPPA 0. J. (1967) The thermodynamics of c&ion distributions in simple apinels. J. Inorg. Nucl. Ckmn. 29, 2201-2214. NEWTON R. C. (1969) Some high-pressure hydrothermal experiments on severely ground kyanite and sillimanite. Amer. J. Sci. 267, 278-284. NEWTON R. C. (1972) An experimental determination of the high-pressure stability limits of msgnesien cordierite under wet and dry conditions. J. Geol. 80, 398-420. RICHARDSONS. W., BELL P. M. and GILBERT M. C. (1967) Kyenite-sillimanite equilibrium between 700’ end 1500°. Amer. J. Sci. 266, 513-541. ROBIE R. A. and WALDBA~ D. R. (1968) Thermodynamic properties of minersls and related substances at 298.15’K (25.0%) end one atmosphere (l-013 brtrs) pressure and st higher temperatures. Bull. Gwl. Sot. Amer. 1259,l-256. ZEN E. A. (1967) Possible compositional effects on the kyanite-sillimanite equilibrium. Program Geol. Sot. Amer. Ann. Meeting in New Orleans, Nov. 20-22, 246-247.