TEM Investigation of Lewiston, Idaho, Fibrolite: Microstructure and Grain

American Mineralogist, Volume 84, pages 152±159, 1999

TEM investigation of Lewiston, Idaho, ®brolite: Microstructure and grain boundary energetics

R. LEE PENN,1,* JILLIAN F. BANFIELD,2 AND DERRILL M. KERRICK3

1Materials Science Program, University of Wisconsin-Madison, Madison, Wisconsin 53706, U.S.A. 2Department of Geology and Geophysics, University of Wisconsin-Madison, Madison, Wisconsin 53706, U.S.A. 3Department of Geosciences, Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A.

ABSTRACT High-resolution transmission electron microscopy (HRTEM) revealed that a sample of ®ne-grained Lewiston, Idaho, ®brolite is predominantly ®brolite with trace amounts of poorly crystalline layer silicates. The ®brolite consists of aggregates of acicular grains where the c axis of each grain is parallel to the elongation direction. Widths of 195 grains were measured: The average is 0.41 ␮m, the mode is 0.29 ␮m, and the range is 0.05±1.57 ␮m. No stacking faults or other extended defects were observed in any of the grains. Grain boundary energies were calculated using the symmetrical dislocation tilt wall theory (SDTW) and measurements of misorientation between the c axes of neighboring ®brolite crystals. The angles of misorientation range from 1Њ to 11Њ, yielding grain boundary energies ranging from 310 to 967 ergs/cm2, respectively, with an average energy of 610 ergs/ cm2. Modeling the ®brolite grains as in®nitely long cylinders and using the experimentally measured average grain diameter, an average molar grain boundary energy of 320 J/mol was calculated. This excess grain boundary energy could correspond to a shift of as much as ϩ140 ЊC in the andalusite-sillimanite boundary and ϩ30 ЊC in the kyanite-sillimanite boundary. Typical ®brolite grain boundaries adopt relatively high-energy con®gurations. We attribute this to ®brolite nucleation at pre-existing low-angle grain boundaries in layer silicates, preserving misorientations, and conferring a ®ne-grained texture.

INTRODUCTION stood and are used to obtain pressure and temperature Phase relations in most coarse-grained rocks are well information for metapelitic rocks. Because micro-scale understood. However, when crystal size is small, a sig- features such as disorder, small grain size, defects, and ni®cant portion of the volume of material is comprised compositional variation can be indicators of higher en- of grain boundaries or surfaces. Atoms with unsatis®ed ergy (or non-equilibrium) conditions, microstructural and distorted coordination environments are a source of characterization of phases is essential for the determina- excess energy and thus can signi®cantly perturb mineral tion of thermobarometric histories. stability ®elds and phase transformation kinetics (Gold- Univariant reactions in the kyanite-andalusite-silliman- stein et al. 1992). The particle size dependence of stability ite system involve reconstructive phase transformations ®elds is most important where the structure energies of that change the coordination number of aluminum and the polymorphs are similar. In some systems (e.g., Fe-oxides, connectivity of the silicate tetrahedra. These reactions are Langmuir and Whittemore 1971; CdS, Goldstein et al. sluggish because they require rupture of strong Al-O and 1992; Ti-oxides, Gribb and Ban®eld 1997; Al-oxides, Si-O bonds and the driving forces are small. Consequent- McHale et al. 1997) ``metastable'' compounds can be- ly, small errors in experimental determinations of the uni- come stable as particle size is reduced, leading to particle- variant equilibria result in substantial uncertainty in the size dependent stability ®elds (Zhang and Ban®eld, un- phase boundaries and thus, the location of the triple point. published manuscript). Furthermore, ®ne grain size, small amounts of impurities,

The aluminosilicate (Al2SiO5) polymorphs (kyanite, an- or compositional variation, in addition to any structural dalusite, and sillimanite) are common metamorphic min- and microstructural factors that modify the total energy erals. Fibrolite is the ®ne-grained acicular habit of silli- of the aluminosilicate phases, can signi®cantly modify the manite that is common in medium- to high-grade positions of the stability ®elds for kyanite, andalusite, and metapelitic rocks. Aluminosilicates are extremely impor- sillimanite. tant in petrologic studies because the aluminosilicate Over the past two decades, considerable effort has been phase relations are generally believed to be well under- expended to identify factors that affect the energetics of the aluminosilicate phases. Dislocation density, cation * E-mail: [email protected] substitution, aluminum-silicon disorder, non-stoichiome- 0003±004X/99/0102±0152$05.00 152 PENN ET AL.: TEM OF FIBROLITE 153 try, grain boundary area, and crystallographic mismatch mismatch between adjacent grains, no studies have con- between adjacent grains have been suggested as factors ducted the grain boundary characterization necessary to that modify phase stability (Helgeson 1978; Kerrick model the energy of ®brolite compared to coarse silli- 1986; Holdaway and Mukhopadhyay 1993). Comparisons manite. Kerrick (1990) described a preliminary study by of thermodynamic studies designed to determine the en- Wenk and Medrano where samples consisting of ®brolite ergetic differences between ®brolite and coarse-grained aggregates were examined using electron diffraction to sillimanite yield con¯icting results. Experimental hydro- determine that the angular mismatch between neighboring thermal studies of Richardson et al. (1968), which ex- grains of ®brolite was Ͻ15Њ. Based on that preliminary amined the extent of reaction between phases at various study, Kerrick (1990) used the symmetrical dislocation temperatures and pressures, used a sillimanite/®brolite tilt wall (SDTW) theory to estimate the grain boundary sample (Brandywine Springs, Delaware) that was about contribution to the total free energy of ®brolite. 30 vol% ®brolite, whereas those of Newton (1966, 1969) In this study, we measure the angular mismatch be- used ®brolite-free sillimanite (Licht®eld, Connecticut). tween adjacent ®brolite crystals and grain diameters, and Their results were in relatively good agreement, suggest- use this information to estimate the grain boundary con- ing that the presence of ®brolite does not shift the Al2SiO5 tribution to the total free energy using the SDTW theory equilibrium boundaries (Kerrick 1990). However, in an for a ®brolite sample from Lewiston, Idaho. We also eval- investigation of the andalusite-sillimanite phase bound- uate the importance of dislocation density and planar de- ary, Holdaway (1971) performed hydrothermal experi- fects to the thermodynamic analysis, the layer silicate ments using andalusite (Minas Gerais, Brazil) and silli- mineralogy, and the origin of the ®brolite grain boundary manite (Benson Mines, New York or Montville structure. Quadrangle, Connecticut) in one vessel and andalusite, sillimanite, and ®brolite (a mixture from Williamston, EXPERIMENTAL METHODS Australia or Jefferson City, Colorado) in another. He ob- Fibrolite from Lewiston, Idaho, has been extensively served early reaction of ®brolite to andalusite, suggesting characterized, e.g., for calorimetry (Hemingway et al., that ®brolite was less thermodynamically stable under the unpublished manuscript; Topor et al. 1989), non-stoichi- pressure and temperature conditions. ometry (Kerrick 1990; Hemingway et al. 1991), Al/Si Anderson and Kleppa (1969) found measurable differ- disorder (Hemingway et al. 1991), and thermal expansion ences in the heats-of-solution of ®brolite (Custer, South (Hemingway et al. 1991). Powders of ®brolite and coarse- Dakota) and sillimanite (Benson Mines, New York) using grained sillimanite from Benson Mines, New York were molten oxide calorimetry. Similarly, Salje (1986) found examined using a Scintag PadV X-ray Powder signi®cant differences in the heat capacities of sillimanite Diffractometer. (from Waldeck, Germany; TraÈskbole, Finland; and Sri Four 3 mm ϫ 3 mm pieces of ®brolite were cut from Lanka) and ®brolite (Garcujuela, Spain), although those two standard 30 ␮m thin sections, mechanically thinned, results are considered questionable due to insuf®cient argon ion-milled to electron transparency, and examined sample size for the procedure used (Hemingway et al. using a Phillips CM20 ultra-twin 200 kV high-resolution 1991). In contrast, Hemingway et al. (1991) reported heat transmission electron microscope (HRTEM) equipped capacities for sillimanite (Sri Lanka) and ®brolite (Lew- with a GE twin window energy dispersive X-ray (EDX) iston, Idaho) that were virtually identical at 298 K and and a NORAN voyager analyzer. differed by Ͻ1% at 1000 K. Topor's et al. (1989) mean The degree of misorientation between adjacent crystals measurements of the heat-of-solution of sillimanite (Sri of ®brolite was determined using selected-area electron Lanka) and ®brolite (Lewiston, Idaho) suggest that ®- diffraction (SAED). Using the TEM sample holder tilting brolite has a slightly less negative heat-of-formation than mechanisms, the sample was tilted until one grain was sillimanite. However, the precision of the measurements oriented with respect to the electron beam, and the tilts preclude a de®nitive conclusion regarding the differences of the sample holder and the electron diffraction pattern in the enthalpies of formation. Thus, although some ex- recorded. The same procedure was repeated for the ad- perimental evidence suggests an energy difference be- jacent grain. The degree of misorientation between the tween coarse-grained sillimanite and ®brolite, which three principle crystallographic directions was determined would require different stability ®elds, the difference from the SAED patterns and sample tilt information using would probably be small and likely be masked by inher- computer-based stereographic methods. ent uncertainty in experimental measurements. In an alternative approach, Holdaway (1971) computed RESULTS a molar surface energy for ®brolite of 351 Ϯ 71 J/mol, assuming a square cross-section and grain diameters of Lattice parameter comparison about 0.3 ␮m, and using typical surface energies for sil- XRD examination of powders of ®brolite from Lew- icates. This value corresponds to a temperature shift of iston, Idaho, and coarse-grained sillimanite from Benson about 120 ЊC from the sillimanite/andalusite equilibrium. Mines, New York, revealed no signi®cant differences in Although it is known how to calculate the free energy lattice parameters. A 50/50 mixture of the two materials contribution to total energy due to grain size and angular showed no splitting of peaks. The full width at half max- 154 PENN ET AL.: TEM OF FIBROLITE

FIGURE 2. TEM micrograph of low-angle tilt boundary between a grain of ®brolite (F) and a grain of layer silicate (LS). FIGURE 1. TEM micrograph showing a typical area of ®- brolite from Lewiston, Idaho.

a two-layer period and ␣ ഠ 85Њ. The ®nal 10% of layer imum peak height and 2 position of each peak were ␪ silicates observed in this sample are characterized by or- identical, within the standard error of the technique. dered stacking characterized with one (␣ ± 90Њ) or four- Mineralogy layer (␣ϭ90Њ ) periods in 02l. All layers silicates with 90 and the four-layer structure are non-standard Samples consisted of aggregates of acicular ®brolite ␣ ± Њ polytypes. grains, with their c axes parallel to the ®ber axes, and approximately 1% layer silicates, present at grain bound- Two predominant layer silicate morphologies were ob- aries. Figure 1 shows microstructure typical of Lewiston, served. In the ®rst, the layer silicates are elongated per- Idaho, ®brolite. No quartz or corundum was observed in pendicular to [001] with the basal planes parallel to the this sample. elongation direction of the ®brolite. In this case, ®brolite The layer silicate mineralogy is complex. SAED pat- crystals appear to have been partially or completely re- terns indicate that the basal spacing is ϳ1.0 nm. All [010] placed by the layer silicate crystallizing along ®brolite SAED patterns show a one-layer period in 20l, indicating grain boundaries (Fig. 2). The crystallographic relation- that all are group A polytypes (Bailey 1988). The ␤ angle ship most commonly observed between this type of layer varied considerably. Most commonly, ␤ measured be- silicate crystal and ®brolite was 120*®brolite approximately tween and 95Њ and 100Њ. Streaking of 02l re¯ections in- parallel to c*layer silicate with the very small angular mismatch dicates stacking is poorly ordered or disordered in rough- (0Њ±2Њ). In addition, c*®brolite approximately parallel to ly 10% of these crystals. Approximately 30% of crystals c*layer silicate (0Њ to 15Њ mismatch) and b*®brolite approximately have ordered stacking with ␣ϭ90Њ. This layer silicate is parallel to c*layer silicate (0Њ to 15Њ mismatch) relationships probably structurally related to 2M1 muscovite. EDX an- were observed. In the second case, the layer silicates are alyses indicate an Al-rich composition with interlayer Na, tiny crystals bridging gaps between the corners or tips of Ca, and some K (no Mg or Fe was detected). These dioc- adjacent ®brolite grains. Sheet silicates ranged in width tahedral layer silicates, which damage rapidly in the elec- from less than 0.1 ␮m to about 0.5 ␮m. The two-layer tron beam, are probably smectite. In about 50% of crys- silicate morphologies have indistinguishable chemical tals, [100] SAED patterns indicate ordered stacking with compositions. PENN ET AL.: TEM OF FIBROLITE 155

TABLE 1. Measured angles (in degrees) between principal directions in adjacent grains of Lewiston, Idaho ®brolite

Boundaries ⌬a ⌬b ⌬c P215-P217 1 1 1 P219-P221 2 2 2 P174-P179 2 3 2 P210-P212 3 2 2 P151-P154 1 3 3 P212-P215 2 4 2 P165-P170 2 5 3 P179-P181 5 4 4 P210-P203 4 6 1 P203-P204 6 5 1 P174-P175 5 5 5 P217-P219 7 5 3 P174-P181 3 6 7 P186-P187 7 7 3 P175-P181 8 3 8 P151-P159 8 8 3 P182-P185 9 9 2 P208-P209 12 6 11 P179-P182 15 15 2 P175-P178 20 20 2 P209-P210 18 17 8 P178-P186 48 48 4 P170-P171 49 18 43 P221-P222 53 53 11 P195-P198 45 52 31

Grain boundary and microstructure characterization Table 1 lists the angular mismatch calculated for 25 grains. In 84% of the boundaries analyzed, the angular FIGURE 3. TEM micrograph of a low-angle grain boundary between two ®brolite crystallites where the degree of angular mismatch between the three principle crystallographic di- mismatch between the c axes is 1Њ. The zone axis SAED patterns rections is Ͻ20Њ, with a mismatch between the c axes are shown for each grain. In this image, the left-hand grain is Ͻ12Њ. In 92% of the boundaries, the angular mismatch oriented with respect to the electron beam. between neighboring c axes is Ͻ12Њ, and most are Ͻ6Њ. Figure 3 is an HRTEM image of a boundary where the angular mismatch between the c axes of neighboring grains is 1Њ. The absence of thickness or moireÂ fringes indicates that the boundary is nearly parallel to the electron beam direction. Based on the indexing of the electron diffraction patterns for each grain, the boundary plane is approximately parallel to (110). Samples were examined with a petrographic microscope in order to estimate apparent average grain diameters. Crystals appeared to be at least a few micrometers in diameter. However, analysis of 20 TEM negatives re- veal the actual average grain diameter to be 0.41 ␮m, the mode to be 0.29 ␮m, and the range to be 0.05±1.57 ␮m, as seen in Figure 4. In the samples examined, dislocation densities are extremely low; in fact, in almost all cases, ®brolite crystals are essentially dislocation free (K108/cm2). No other extended defects were observed. Furthermore, SAED patterns show no evidence of streaking parallel to any direction, thereby suggesting little or no Al/Si disorder. Modeling grain boundary energy using symmetrical dislocation tilt wall theory Because the degree of angular mismatch between the c axes is typically Ͻ15Њ, the ``symmetrical dislocation tilt FIGURE 4. Grain widths of 195 ®brolite grains measured wall'' (SDTW) theory can be used to model the grain from 20 TEM micrographs. 156 PENN ET AL.: TEM OF FIBROLITE

FIGURE 6. Dislocation tilt wall grain boundary energy as a function of angular mismatch, calculated using Equation 1.

angular mismatch calculated from Equation 1 is shown in Figure 6. When ␪ is small, the ␪ln␪ term dominates,

but when ␪ is large, the ␪ln(b/ro) term dominates. Con- sequently, Equation 1 predicts a maximum computed grain boundary energy for an angular mismatch of about 10Њ (Kerrick 1990). FIGURE 5. TEM micrograph of a low-angle tilt boundary be- Because the SDTW approach models grain boundaries tween two grains of ®brolite where the angle of mismatch be- as a series of pure edge dislocations with the adjacent tween the c axes of each grain is 5Њ. Edge dislocations can clearly crystals symmetrically disposed about the boundary, it be seen if the image is viewed from a low angle. cannot accommodate asymmetry in the boundary. The c axis is parallel to the elongation direction, thus, usually boundary energy (Kerrick 1990). The advantage of lies in or is slightly inclined to the boundary between SDTW is that no surface energy measurement is required adjacent ®brolite grains. Consequently, in applying the because the energies of the grain boundaries are calcu- SDTW model to estimate the grain boundary contribution lated from measured parameters (␮ϭshear modulus; ␪ to the total energy of Lewiston, Idaho, ®brolite, we chose ϭ degree of angular mismatch). Symmetrical tilt walls to use the misorientation between the c axes of adjacent are modeled as a series of parallel edge dislocations with grains. This model does not account for the angular mis- the lattice structures of the grains symmetrically disposed match between the a and b crystallographic axes. How- about the boundary. These dislocations are clearly visible ever, using the angular mismatch between the other two in Figure 5, where the angle of tilt at this boundary be- axes does not result in a signi®cantly different ETW. tween the c axes of these two ®brolite crystals is about ETW was calculated for each boundary. Results ranged 5Њ. The plane containing the edge dislocations is the from 310 to 970 ergs/cm2. The average energy of the boundary between two symmetrically disposed crystals, dislocation tilt wall boundaries characterized in this sam- and ␪ is the angle of misorientation between the two ple is 610 ergs/cm2. The molar grain boundary area (A) grains. The tilt wall energy (ETW) as a function of angular was calculated using the experimentally obtained average misorientation is computed from: diameters of ®brolite crystals reported in Figure 2. Fi- brolite crystals were modeled as a single cylinder whose E ϭ [␮b/4␲(1 Ϫ␯)]␪[ln (b/r ) Ϫ ln ␪] (1) TW o length was determined using the experimentally deter- where ␯ is Poisson's ratio. Values for ␯ and ␮ were both mined average radius (0.2 ␮m) and the molar volume 3 taken for sillimanite from Birch (1966) and Vaughan and (200.68 cm /mol). Using the average ETW and A, the ex- Weidner (1978), respectively. In addition, assuming that cess energy due to grain boundaries was calculated to be ro ϭ 2b (Kerrick, 1986) where b is the magnitude of the 320 J/mol (or 300 J/mol if b ϭ d(110). Burgers vector. By far the most common grain boundary Figure 7 shows the potential shift in the andalusite- orientation is approximately parallel to (110), with a Bur- sillimanite and the kyanite-sillimanite curves for the cal- gers vector of d(110) ϭ 0.53 nm. Tilt wall energy vs. culated excess molar energy from the excess grain bound- PENN ET AL.: TEM OF FIBROLITE 157

for nucleation of coarse-grained sillimanite or to recrys- tallize ®brolite to sillimanite. The higher energy of ®- brolite supports the experimental results of Anderson and Kleppa (1969), Holdaway (1971), Salje (1986), and Topor et al. (1989) but contradicts the results of heat capacity comparisons performed by Hemingway et al. (1991) and several experimental studies involving the sillimanite and kyanite phase boundary by Richardson et al. (1968) and Newton (1966, 1969). When andalusite and ®brolite coexist, the ®brolite fre- quently appears to be the result of a reaction between other matrix minerals rather than replacement of andalusite (Kerrick 1990). Fibrolite crystallization as long thin crystals related by low-angle tilt boundaries also suggests that ®brolite is not crystallizing from coarse-grained andalusite or kyanite. The tendency for ®brolite crystals to grow such that their c axes are rotated by comparatively unfavorable amounts needs to be rationalized. Because FIGURE 7. Shift of the andalusite-sillimanite and the kyanite- ®brolite is ubiquitously associated with micas, the expla- sillimanite phase boundaries due to the excess molar grain nation for both of these phenomena may be found in the boundary energy of 320 J/mol as calculated for Lewiston, Idaho, ®brolite using the SDTW model (dashed lines). The solid lines nucleation process. Previous TEM studies (e.g., Peacor 1992; Kogure and represent the equilibrium phase diagram for Al2SiO5 calculated using data from Helgeson et al. (1978). Murakami 1998; Ban®eld et al., unpublished data) have revealed that layer silicates are characterized by a sub- micrometers to a few micrometers wide crystals separated ary area found in ®brolite. The excess molar grain bound- by low-angle grain boundaries. Misorientation between ary energy of 320 J/mol could result in as much as a 140 adjacent layer silicates is often ϳ10Њ. If ®brolite crystals ЊC shift of the andalusite-sillimanite equilibrium bound- replace micas during prograde metamorphism, nucleation ary and 30 ЊC shift of the kyanite-sillimanite equilibrium may occur at mica grain boundaries due to the lower en- boundary. ergy barrier compared to nucleation of an isolated crystal in the matrix. If micas were topotactically replaced by DISCUSSION AND CONCLUSIONS ®brolite crystals nucleated at these sites, the resulting ®- Determination of the grain boundary contribution to brolitic mass would preserve the misorientation of the the total energy of ®brolite using electron diffraction and preexisting layer silicate. This may explain the relatively the SDTW theory results in a calculation of the alumi- high-energy grain boundary structure. Some supporting nosilicate phase diagram where the andalusite/sillimanite evidence for topotactic relationships between layer sili- boundary is potentially shifted by 140 ЊC and the kyanite/ cates and ®brolite is found in retrograde textures reported sillimanite boundary is shifted by 30 ЊC (Fig. 7). This here. However, further work is needed to determine if analysis represents a minimum estimate of the excess ®brolite crystals do in fact form by topotactic nucleation grain boundary energy in ®brolite because SDTW theory at layer silicate grain boundaries. Subsequent annealing does not account for dislocation core energies. In metals, of the resulting ®brous mass to large crystals of silliman- the core energy represents 10±15% of the total (Kerrick ite would involve recrystallization, presumably requiring 1990). Furthermore, the covalent nature of bonding in considerable overstepping of the phase boundary, as not- minerals like sillimanite likely means that the core energy ed above. of dislocations may represent Ͼ15% of the total energy Layer silicates are ubiquitous but volumetrically minor (Kerrick 1990). Additional assumptions include the mag- constituents of the Lewiston, Idaho, ®brolite sample nitude of the grain boundary energy contribution as in- (Ͻ1%). The structural and chemical characteristics sug- dependent of pressure and temperature and the angular gest they are dioctahedral smectites formed by topotactic mismatch as ``frozen in'' from a particular metamorphic replacement during a low-temperature aqueous alteration event. event. It is interesting to note that the layer silicates, most It is indisputable that grain boundaries contribute ex- of which are characterized by stacking order, are poly- cess energy, but the implications for the texture devel- typically diverse and include polytypes not normally en- opment in speci®c metamorphic rocks are complex to countered in 2:1 layer silicates. From the point of view predict. The result shown in Figure 7 contradicts ®eld of the thermodynamic characterization of ®brolite, the ex- observations indicating ®brolite in metapelites at lower istence of layer silicates is extremely important. The layer grades than coarse sillimanite (e.g., see Pattison 1992 and silicate crystals are too ®ne to allow physical separation Kerrick 1990). This may be simply a kinetic effect that from ®brolite, thus represent a possible source of error in re¯ects larger overstepping of the phase boundary needed calorimetric and stoichiometry studies. 158 PENN ET AL.: TEM OF FIBROLITE

Grain boundary energy may not be solely responsible No signi®cant differences in the non-stoichiometry of for the excess energy of ®brolite in comparison to coarse- sillimanite and ®brolite have been found. However, most grained sillimanite. The presence of dislocations, stacking chemical analyses were obtained using the electron probe, faults, Al/Si disorder, and non-stoichiometry could sig- which could mask 1±2 wt% variations in Al/Si ratios. ni®cantly contribute to the total energy of ®brolite. Based Few wet chemical analyses exist, and these may be com- on dislocation density determinations and calculated promised by intergrown quartz and layer silicates. As- strain energies, Kerrick (1986, 1990) argued that signi®- suming no signi®cant nonstoichiometry, we conclude that cant perturbations of the andalusite-sillimanite equilibri- the primary source of excess energy in ®brolite compared um boundary would require dislocation densities greater to sillimanite is grain boundary energy. than 5 ϫ 109/cm2. In one ®brolite sample, analyzed by Wenk (1983), showed dislocation densities in excess of ACKNOWLEDGMENTS 10 2 this number (10 /cm ). Five other samples analyzed by The authors thank B.L. Dutrow, L.P. Baumgartner, J.W. Valley, M. Mill- Gordan Nord (U.S. Geological Survey) showed average ing, S.E. Babcock, and D. Sykes for helpful comments, with special thanks densities well below 108/cm2 (Kerrick 1986). Similarly, to G. Nord and B.S. Hemingway for thoughtful reviews, and acknowledge Doukhan et al. (1985) examined ®brolite using TEM and ®nancial support from NSF grant no. EAR-950817 and a fellowship from the National Physical Science Consortium to R.L. Penn. reported that grains were essentially dislocation free. For comparison, Doukhan et al. (1985) also examined rela- REFERENCES CITED tively coarse-grained sillimanite crystals, with cross sections ranging from 10±100 ␮m, and found dislocation Anderson, P.A.M. and Kleppa, O.J. (1969) The thermochemistry of the 8 2 kyanite-sillimanite equilibrium. American Journal of Science, 267, 285± densities of 1 to 5 ϫ 10 /cm . In this study of Lewiston, 290. 8 2 Idaho, ®brolite, very low dislocation densities (K10 /cm ) Bailey, S.W. (1988) X-ray diffraction identi®cation of the polytypes of were observed. Furthermore, there was no evidence of mica, serpentine, and chlorite. Clays and Clay Minerals, 36, 193±213. stacking faults in our samples. Beger, R.M. (1979) Aluminum-silicon ordering in sillimanite and mullite, Zen (1969), Holdaway (1971), Greenwood (1972), and 312 p. 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