Phys Chem (1984) 10:217-229 PHYSICS CHEMISTRY [[MIHERALS © Springer-Verlag 1984

Polysynthetically-Twinned Structures of and

Yoshikazu Ohashi * Department of Geology, University of Pennsylvania, Philadelphia, PA 19104, USA

Abstract. structures of clinoenstatite, orthoenstatite, wollastonite polytypes established the structural relation- wollastonite-lT and wollastonite-2M (parawollastonite) ships between polytypes (Morimoto et al. 1960; Burnham were refined to an R factor 3-4 percent level. Molar vol- 1967; Morimoto and Koto 1969; Trojer 1968), and empha- umes at room temperature are 31.270(15), 31.315(8), sized the close relationship of the structure to the model 39.842(5) and 39.901(10) cm3/MSiO3, in the above-men- produced by applying mathematical operations to the basic tioned order, indicating that one-layer polytypes (clinoen- slab. Stacking sequences of new 3T, 4T, 5T, and 7T wollas- statite and wollastonite-lT) are stable at higher pressures tonite polytypes were determined (Henmi etal. 1978; than two-layer polytypes (orthoenstatite and wollastonite- Henmi et al. 1983), although refinements of atomic coordi- 2M). The polytypic relation of the enstatite polytypes can nates of these longer repeat polytypes were impossible. be described by four twinning operations - b glide [1 to Because of the similarities in chemistries and silicate (110), a glide I[ to (001), twofold screw axis [I to a (of linkages, and the existence of polytypes, enstatite and wol- orthoenstatite) and a twofold screw axis I[ to c. For the lastonite are often compared in parallel. Polytypes of ensta- wollastonite polytypes, twinning operations are twofold tite and wollastonite are, however, different in the way twin- screw axis II to b and a glide [I to (010). Structural adjust- ning is formed with respect to tetrahedral and octahedral ments after twinning are not necessarily the largest at the layers. A twinning plane of the wollastonite polytypes is twin boundary (true in enstatite but not so in wollastonite). not parallel to closest-packed layers. Thus the wol- In both cases octahedral sites that involve bridging lastonite polytypes cannot be regarded as unique stacking tend to show relatively large changes. Lattice strain ellip- of tetrahedral and octahedral layers, which is the case for soids associated with twinning are also different for ensta- enstatite. Enstatite transforms rapidly as temperature chan- tite and wollastonite, which implies that wollastonite may ges (Smyth 1974), whereas the direct transformation be- react differently from enstatite to non-hydrostatic pressure. tween wollastonite 1T and 2M has not been observed. De- terminations of phase relationships of polytypes are often complicated by small differences in free energy. Two major factors of the that may make two polytypes thermodynamically different are (1)difference in stacking Introduction and (2) distortion of the layer modules. A special case of polymorphs is polytypes that have a nearly The purpose of this study is to analyze (1) this local identical unit layer but are different in the stacking order structural relaxation, and (2) twinning relationships to of layers. Polytypes of metasilicates, MgSiO3 close-packed oxygen layers. The crystal structures of all enstatite, and metasilicates, CaSiO3 wollastonite, four polytypes have been determined previously but the have been described (e.g. Ito 1935, 1950) as unit cell scale precision of refined atomic coordinates varies from one re- twinning on the plane (100). For example, twolayer poly- finement to another. The first part of this study was acquisi- types (orthoenstatite and wollastonite-2M 1) may be derived tion of structural data with a comparable precision for poly- from an untwinned single layer polytype (clinoenstatite and type pairs of both enstatite and wollastonite. wollastonite-lT, respectively) by displacing a "slab" on the (100) plane. Early crystal structural work on and Experimental * Present address. ARCO Oil and Gas, Exploration and Produc- tion Research Center, Plano Texas 75075, USA Used in This Study In order to obtain single and untwinned crystals of identical 1 The form wollastonite-2M notation is used in this paper in place chemistries, crystals of ortho and clinoenstatite were synthe- of the Gard notation, wollastonite-M2abc (Bailey 1977), and the common name parawollastonite. Crystallographic descrip- sized by Dr. J. Ito using flux method (Ito 1975). Among tion of wollastonite is given for the conventional unit cell setting various clinoenstatites examined, these crystals were the with the tetrahedral chain parallel to b axis (not c axis) and only clinoenstatite that did not show apparent twinning the tetrahedral and octahedral layers parallel to (101) of wollas- on h01 precession photographs (Fig. 1). Apparently, un- tonite-1T and to (201) of wollastonite-2M twinned clinoenstatite can only be obtained from direct 218

Ca) CLEN1 Fig. l. Comparison of (h0:1) rows of clinoenstatite, twinned clinoenstatite, heated clinoenstatite, and orthoenstatite. Synthetic clinoenstatite, (c), often shows (b) CLEN2 twinning of equal amount of clinoenstatite in two orientations, (a) and (b). The apparent diffraction symmetry of this twinned clinoenstatite is Twinned CLEN (c) orthorhombic with a = 27 A. When untwinned clinoensatite is heated to over 500° C and quenched, the result, (d), (d) ~~ .... Heated CLEN shows a partial transformation to orthoenstatite, (e). An (h0:1) precession photograph of untwinned clinoenstatite is shown at the bottom. All photographs (e) OREN were taken with Mok~ radiation

of the orthoenstatite are 0.09 wt percent A1203, 0.08 wt per- cent TiO2, and 0.16 wt percent FeO (Sasaki et al. 1982). The two wollastonite crystals used in this study are from Willsboro, New York (wollastonite-lT) and Esashi mine, Iwata, Japan (wollastonite-2M) and are nearly identical in composition based on microprobe data (Table 1).

Unit Cell Constants and Molar Volume Extreme care was taken to minimize the experimental errors d so that a precise molar volume calculation could be made. Reflections were measured for 50 to 100 reflections using Buerger's ll4mm-diameter back-reflection Weissenberg camera in a high angle region, ranging from 120 to 170 de- grees of 20 for FeK radiation. The computer program, LCLSQ (Burnham 1962), was used to make corrections

Table 1. Electron microprobe analyses of wollastonite

Oxide weight %

SiOz FeO a MnO MgO CaO AIzO 3 total

WO:1T b 51.52 0.32 0.13 0.03 48.47 0.03 100.50 :1 C ~ WO2M 51.30 0.:10 0.06 0.07 47.99 0.21 99.73

crystallization from melt, but not through solid-solid phase Cations based on 3 oxygens transition from protoenstatite, as is the case of the system Si Fe Mn Mg Ca A1 total MgSiO 3 without flux (Dr. Jun Ito private comm. 1975). The orthoenstatite sample was reported to have impurities WO1T 0.994 0.005 0.002 0.000 1.002 0.000 2.003 of 0.27 wt percent V205 and 0.17 wt percent Li20 (Haw- WO2M 0.994 0.001 0.000 0.00:1 0.996 0.005 1.997 thorne and Ito 1977), which correspond to approximately one vanadium atom for 300 magnesium atoms and one lith- a All as FeO ium atom for 100 magnesium atoms. Additional impurities b Wollastonite 1T and 2M

Table 2. Refined unit cell parameters ~ of enstatite and wollastonite polytypes

a(A) b c c~ (deg.) ~ ? Cell V (A 3) Mole V (cm3) b

CLEN 9.606(1) 8.8131(7) 5.170(2) 90 108.35(1) 90 4:15.5(2) 31.270(15) OREN 18.225(2) 8.8128(6) 5.180(:1) 90 90 90 832.0(2) 31.315(8) WO1T 7.9258(4) 7.3202(4) 7.0653(4) 90.055(3) 95.217(3) 103.426(3) 396.96(5) 39.842(5) WO2M 15.424(1) 7.324(:1) 7.0692(7) 90 95.371 (4) 90 795.1 (2) 39.901 (:10)

a Back-reflection Weissenberg method with FeK radiation. Reflections with 20 ranging 120 to 170 degrees were used in a least-squares refinement. Wave lengths used are 1.93597, 1.93991, and 1.75653 A for FeK~2, c~1 and fl respectively (International Tables for X-ray Crystallography, vol. III) b Based on one formula unit of MSiO~ 219 due to camera eccentricity, film shrinkage, and crystal ab- Table 3. Crystal and refinement data for enstatite and wollastonite sorption. The refined parameters are given in Table 2. The difference in molar volume is 0.045 cm 3 with an Enstatite MgSiO 3 Wollastonite CaSiO 3 estimated standard deviation of 0.015 cm 3 for the enstatite CLEN a OREN a WO1T a WO2M a polytypes, and 0.059 with e.s.d. 0.010 cm 3 for the wollas- tonite polytypes. In both cases unit-repeat polytypes have Symmetry mono- ortho- triclinic mono- smaller molar volumes than the longer repeat polytypes, clinic rhombic clinic which is consistent with clinoenstatite (and wollastonite-1 T) being stable at higher pressures. P21/e Pbca P1 P21/a Source of synthetic natural crystal flux-grown Willsboro, Esashi Diffraction Data Collection and Refinements by J. Ito New York Mine, Iwate, X-ray diffraction intensity data were measured on an au- Japan tomated fourcircle diffractometer using an omega-two theta Size of crystal 0.11 0.14 0.13 0.09 variable scanning technique (Finger et al. 1973) with MoK~ (mm) x0.14 x0.21 x0.17 x0.11 radiation. Integrated intensities were corrected for Lorentz x 0.34 x 0.21 x 0.30 x 0.30 and polarization effects, and absorption corrections were Number of 1660 1525 2065 1824 computed by the numerical integration technique (Burnham reflections 1966). R factor (%)b Starting atomic coordinates used in the RFINE2 least- weighted 3.3 4.0 4.3 4.3 squares program (Finger and Prince 1975) were those of unweighted 3.1 3.3 3.3 6.8 (Burnham et al. 1971), lunar pigeonite (Ohashi and Finger 1974a), wollastonite-lT (Prewitt and Buerger " In all Tables in this paper these abbreviated symbols are used 1963), and wollastonite-2M (Trojer 1968). Crystal and re- for clinoenstatite, orthoenstatite, wollastonite-lT, and wollas- finement data are listed in Table 3. Atomic positional pa- tonite-2M. rameters (Table 4) and anisotropic temperature factors b Weighted R = [~, w(Fobs--Fcal)2/~ wF2obJ1/2 were refined without difficulty except for a few anisotropic Unweighted R = ~ [Fobs]- ]Fc,l]/~ IFobsl

Table 4. Atomic coordinates of enstatite and wollastonite polytypes

Atom x y z x y z

CLEN OREN M1 0.25111(7) 0.65330(7) 0.2177(1) 0.37584(4) 0.65383(8) 0.8660(1) M2 0.25581 (8) 0.01312(7) 0.2146(1) 0.37677(4) 0.48687(8) 0.3589(1) SiA 0.04331 (5) 0.34088(6) 0.29449(9) 0.27173(3) 0.34155(7) 0.0505(1) SiB 0.55339(5) 0.83718(6) 0.23007(9) 0.47353(3) 0.33739(6) 0.7980(1) O1A 0.8667(1) 0.3396(1) 0.1851(2) 0.18343(7) 0.3398(2) 0.0347(3) O2A 0.1228(I) 0.5009(i) 0.3218(3) 0.31106(8) 0.5023(2) 0.0433(3) O3A 0.1066(1) 0.2795(I) 0.6153(3) 0.30322(7) 0.2227(2) 0.8311(3) OIB 0.3762(1) 0.8399(1) 0.1247(3) 0.56243(7) 0.3402(2) 0.8001(3) O2B 0.6340(1) 0.9825(1) 0.3891(3) 0.43258(8) 0.4827(2) 0.6895(3) O3B 0.6053(1) 0.6942(1) 0.4540(3) 0.44742(8) 0.1952(2) 0.6039(3)

Cross WOIT WO2M Reference MI [1, 2] 0.19831(8) 0.42266(8) 0.76060(9) 0.40056(6) 0.6248(2) 0.7389(1) M2 [2, 3] 0.20241 (8) 0.92919(8) 0.76401(9) 0.39880(6) 0.1191 (2) 0.7362(1) M3 [3, 1] 0.50333(8) 0.75040(8) 0.52691(9) 0.24837(6) 0.3744(3) 0.9736(1) Sil [1, 2] 0.1851 (1) 0.3875(1) 0.2684(1) 0.4075(1) 0.6584(2) 0.2311 (2) Si2 [2, 1] 0.1849(1) 0.9542(1) 0.2691(1) 0.4077(1) 0.0927(2) 0.2311(2) Si3 [3, 3] 0.3973(1) 0.7236(1) 0.0561(1) 0.3014(1) 0.3761(2) 0.4438(2) OAt [3, 4] 0.3034(3) 0.4616(3) 0.4628(3) 0.3485(2) 0.6121 (7) 0.0366(4) OA2 [4, 3] 0.3014(3) 0.9385(3) 0.4641(3) 0.3493(2) 0.1329(8) 0.0369(4) OA3 [1, 1] 0.5705(3) 0.7688(3) 0.1988(3) 0.2147(2) 0.3712(8) 0.3011 (4) OB1 [5, 6] 0.9832(3) 0.3739(3) 0.2655(4) 0.5083(2) 0.6157(8) 0.2335(4) OB2 [6, 5] 0.9819(3) 0.8677(3) 0.2648(4) 0.5090(2) 0.1218(8) 0.2367(4) OB3 [2, 2] 0.4018(3) 0.7266(3) 0.8296(3) 0.2991(2) 0.3703(8) 0.6708(4) OC1 [9, 9] 0.2183(3) 0.1785(3) 0.2254(4) 0.3914(2) 0.8761 (6) 0.2753(4) OC2 [8, 7] 0.2713(3) 0.8704(3) 0.0938(3) 0.3639(2) 0.1970(5) 0.4053(5) OC3 [7, 8] 0.2735(3) 0.5126(3) 0.0931 (3) 0.3637(2) 0.5550(5) 0.4056(5) a Numbers in [ ] are atomic site numbers used by Prewitt and Buerger (/963) for WOIT and by Trojer (1968) for WO2M. For example, OA1 of this study corresponds to 03 of Prewitt and Buerger and 04 of Trojer 220

thermal parameters in wollastonite-2M, which will be dis- cussed below. (polyhedron) (mean misfit in A_) Discrepancies in atomic coordinates between this study twin boundary SiA 0.019 and previously reported atomic coordinates have been cal- M1 and M2 0.011 and 0.023 culated in terms of the estimated standard deviation (o-) SiB 0.005 of this study. Ito's orthoenstatite was refined at three labo- MI and M2 0.011 and 0.023 ratories and thus interlaboratory comparisons are possible. twin boundary SiA 0.019 The average discrepancy for orthoenstatite (Hawthorne and Ito t977) is about I ¢ with a maximum discrepancy of 4 a, and that for orthoenstatite (Sasaki et al. 1982) is 0.9 ~r with a maximum discrepancy of 2.7 o-. Average and maximum The mean misfit is relatively large near the twinning bound- discrepancies are, respectively, 30 and 150 a for clinoensta- ary and decreases toward the center of the twinned slab. tire (Morimoto et al. 1960), 2 and 12 o- for wollastonite-lT Particularly, the bridging oxygen O3A is shifted (note that (Prewitt and Buerger 1963), and 4 and 18 ~r for wollastonite- the O3A-O3A-O3A angle changes more than the O3B-O3B- 2M (Trojer 1968). O3B angle as shown in Table 8). Thus the M2 octahedron, Bond distances (Table 5) of wollastonite-2M of this which is coordinated to O3A, shows a relatively large dis- study are comparable with corresponding distances of wol- tortion, whereas the M1 octahedron, which is coordinated lastonite-lT (e.g., the Si-O ranges from 1.574 to 1.666A to only non-bridging oxygens O1 and 02, is relatively un- in wollastonite-2M). The variation of Si O distances is con- changed. The smallest distortion is seen in the SiB layer, sistent with other single-chain silicates, i.e., the shortest which is the furthest from the twinning boundaries. (~ 1.56 A) of non-bridging basal oxygens (02 of In contrast, for wollastonite the smallest misfit between and OB ofpyroxenoids) and the longest (~ 1.65 A) of bridg- octahedra (M3) is at the twin boundary as below. ing oxygens (03 of pyroxenes and OC of pyroxenoids). High-resolution transmission electron microscopic stu- dies (e.g., Jefferson et al. 1979; Veblen and Buseck 1979, 1980, 198t) clearly show that occurrences of mixed modes Table 5. Interatomic distances (~) in enstatite and wollastonite of polytypes in a single grain are quite common. Undoubt- polytypes edly, the specimens used in this study may also contain CLEN OREN CLEN OREN mixed polytypes. X-ray diffraction in effect averages out these local variations of the structure. The effect of such M1-O1A 2.141(1) 2.149(2) M2-O1A 2.092(1) 2.090(2) a disordered structure, however, should be detected as dif- -OIA 2.034(1) 2.028(2) -O2A 2.034(1) 2.031(2) fuse streaks, satellite reflections, and unusually large an- -O2A 2.008(1) 2.005(2) -O3A 2.279(1) 2.287(2) isotropic thermal parameters, if the volume of "foreign" -O1B 2.178(1) 2.169(2) -O1B 2.055(1) 2.056(2) phases is appreciable. In view of a possibility of such a -O1B 2.069(1) 2.064(2) -O2B 1.989(1) 1.992(2) disordered structure, anisotropic thermal parameters (Ta- -O2B 2.043(1) 2.044(2) -O3B 2.412(1) 2.444(2) ble 6) were checked carefully. Except for a few oxygens Mean 2.079 2.077 Mean 2.144 2.150 of wollastonite-2M none of thermal parameters are unusu- al. Even for these oxygens that exhibit non-positive definite SiA-O1A 1.611(1) 1.611(1) SiB-OIB 1.616(1) 1.620(1) -O2A 1.588(1) 1.588(2) -O2B 1.586(i) 1.585(2) quadratic surfaces for thermal vibrations, the smallest ei- -O3A 1.666(1) 1.663(2) -O3B 1.676(1) 1.676(2) genvalue is slightly negative but very close to zero (around -O3A 1.646(1) 1.648(2) -O3B 1.677(1) 1.679(2) --0.001 z~k2), and the intermediate and the largest axes are Mean 1.628 1.628 Mean 1.639 1.640 comparable with values for other chain silicates. None of the atoms shows abnormally large thermal vibrations that WO1T WO2M WO1T WO2M are often caused by atomic positional disorder rather than the real thermal vibrations. From the X-ray diffraction M1-OAI 2.326(2) 2.324(3) M2-OA2 2.321(2) 2.327(3) evidence, all four crystals refined in this study appear to -OA3 2.549(2) 2.531(5) -OA3 2.502(2) 2.519(5) be normal single phases. -OB1 2.295(2) 2.251(5) -OB1 2.357(2) 2.411(5) -OB2 2.266(2) 2.318(5) -OB2 2.311(2) 2.263(5) -OB3 2.445(2) 2.452(5) -OB3 2.423(2) 2.414(5) Polyhedral Differences -OC3 2.422(2) 2.425(4) -OC2 2.407(2) 2.419(4) To compare a finite set of atoms, polyhedral elements may Mean 2.384 2.384 Mean 2.387 2.392 be selected from two structures (for example, five atoms M3-OA1 2.345(2) 2.342(5) SiI-OA1 1.609(2) 1.612(4) for a tetrahedron, one and four oxygen atoms from -OAI 2.418(2) 2.430(5) -OB1 1.578(2) 1.584(3) orthoenstatite and clinoenstatite), and then translated and -OA2 2.356(2) 2.371(5) -OC1 1.644(2) 1.648(3) rotated in the three-dimensional space as a rigid body to -OA2 2.435(2) 2.417(5) -OC3 1.651(2) 1.646(4) superimpose on the corresponding tetrahedron of the sec- -OA3 2.422(2) 2.419(3) Mean 1.621 1.623 ond structure as closely as possible. An amount of misfit, -OB3 2.345(2) 2.348(3) measured in ~_, was calculated with equal weight for each Mean 2.386 2.387 atom from this fitting procedure (Table 7). For enstatite, Si2-OA2 1.606(2) 1.597(3) Si3-OA3 1.597(2) 1.598(3) the SiB tetrahedron shows the smallest discrepancy. This -OB2 1.583(2) 1.574(3) -OB3 1.604(2) 1.609(3) result, which is in agreement with the previous observation -OC2 1.652(2) 1.647(4) -OC3 1.661(2) 1.662(4) described above, can be interpreted quantitatively as the -Of1 1.636(2) 1.640(4) -OC2 1.664(2) 1.666(4) effect of local distortion caused by the different polytype Mean 1.619 1.615 Mean 1.632 1.634 modifications. 221

Table 6. Equivalent isotropic temperature factors (~2) and the principal root mean square amplitudes (A) of thermal ellipsoids in enstatite and wollastonite polytypes

Equivalent isotropic temperature factors (~x2) CLEN OREN CLEN OREN CLEN OREN

M1 0.41 (1) 0.37(1) M2 0.55(1) 0.57(1) SiA 0.29(1) 0.28(1) SiB 0.30(1) 0.27(1) O1A 0.37(2) 0.38(2) O2A 0.46(2) 0.47(2) O3A 0.47(2) 0.46(2) O1B 0.39(2) 0.39(2) O2B 0.49(2) 0.46(2) O3B 0.43(2) 0.41(2)

WO1T WO2M WO1T WO2M WO1T WO2M

M1 0.63(1) 0.61(1) M2 0.66(1) 0.56(2) M3 0.58(1) 0.60(1) Sil 0.49(1) 0.47(3) Si2 0.49(1) 0.54(3) Si3 0.49(1) 0.49(2) OA1 0.74(4) 0.63(6) OA2 0.77(4) 0.75(6) OA3 0.59(3) 0.55(5) OB1 0.91 (4) 0.70(6) OB2 0.96(4) 0.89(5) OB3 0.70(4) 0.70(5) OC1 0.98(4) 0.95(5) OC2 0.76(4) 0.86(6) OC3 0.75(4) 0.72(6)

Root mean square amplitudes (A) CLEN OREN CLEN OREN CLEN OREN

M1 0.068(2) 0.057(3) M2 0.071(2) 0.069(2) 0.072(2) 0.071(2) 0.082(2) 0.084(2) 0.077 (2) 0.076 (2) 0.095 (2) 0.099 (2) SiA 0.055(2) 0.052(2) SiB 0.058(2) 0.054(2) 0.062 (2) 0.060 (2) 0.062 (4) 0.059 (2) 0.064 (2) 0.067 (2) 0.063 (4) 0.063 (2) O1A 0.053(5) 0.062(5) O2A 0.062(4) 0.066(5) O3A 0.065(4) 0.060(6) 0.072(4) 0.064(5) 0.078(4) 0.071(5) 0.072(4) 0.072(4) 0.077(3) 0.080(4) 0.087(3) 0.091(4) 0.092(3) 0.094(4) OIB 0.063(4) 0.062(5) O2B 0.064(4) 0.067(5) O3B 0.059(4) 0.056(6) 0.067 (4) 0.068 (5) 0.073 (4) 0.070 (5) 0.072 (4) 0.073 (4) 0.078 (3) 0.080 (4) 0.095 (3) 0.091 (3) 0.088 (3) 0.085 (4)

WOIT WO2M WO1T WO2M WOIT WO2M

M1 0.067 (2) 0.063 (4) M2 0.065 (2) 0.053 (4) M3 0.064 (2) 0.053 (4) 0.094(2) 0.085(3) 0.094(2) 0.091(2) 0.091(2) 0.085(2) 0.103(1) 0.109(2) 0.108(1) 0.102(2) 0.097(1) 0.114(2) Sil 0.057(3) 0.064(7) Si2 0.055(3) 0.068(6) Si3 0.059(3) 0.053(5) 0.087 (2) 0.074 (4) 0.088 (2) 0.083 (4) 0.082 (2) 0.084 (3) 0.089(2) 0.091(3) 0.089(2) 0.095(3) 0.092(2) 0.093(3) OAI 0.085 (6) " OA2 0.091 (6) 0.068 (2) OA3 0.083 (6) " 0.100(5) 0.102(11) 0.099(6) 0.087(8) 0.094(6) 0.087(9) 0.106(5) 0.117(7) 0.105(5) 0.127(10) 0.104(5) 0.122(9) OB1 0.082(6) a OB2 0.085(6) 0.041 (2) OB3 0.076(6) 0.047(2) 0.099(6) 0.097(9) 0.097(6) 0.099(9) 0.087(6) 0.089(8) 0.135(5) 0.138(9) 0.140(5) 0.149(8) 0.095(6) 0.128(8) OC1 0.064(7) 0.076(10) OC2 0.060(8) 0.070(12) OC3 0.064(8) 0.053(16) 0.117(5) 0.107(8) 0.093(6) 0.113(9) 0.098(6) 0.100(9) 0.139(5) 0.137(6) 0.129(4) 0.122(8) 0.121(5) 0.121(8)

" Non-positive definite quadratic surface. The smallest eigen value is slightly negative close to zero

The M3 cation in wollastonite is coordinated with only (polyhedron) (mean misfit in ,~) non-bridging oxygens (OA's and OB's) as is the case for the M1 of enstatite. In both enstatite and wollastonite poly- M1 and M2 0.023 and 0.024 types, the octahedra that include bridging oxygens (O3's twin axis M3 0.010 in enstatite and OC's in wollastonite) show relatively large MI and M2 0.023 and 0.024 distortions between polytypes. M1 and M2 0.023 and 0.024 The silicate tetrahedra are subject to the same degree twin axis M3 0.010 of distortion when two wollastonite polytypes are compared MI and M2 0.023 and 0.024 (0.014, 0.017 and 0.015 A for the Sil, Si2 and Si3, respec- tively). 222

Table 7. Polyhedral comparison a

Enstatite Wollastonite misfit (A) misfit misfit misfit misfit(A) misfit misfit

SiA 0.004 SiB 0.004 MI 0.009 M2 0.019 Sil 0.012 Si2 0.020 Si3 0.019 O1A 0.023 O1B 0.007 O1A 0.010 O1A 0.023 OA1 0.011 OA2 0.012 OA3 0.009 O2A 0.022 O2B 0.005 O1A' 0.013 O2A 0.012 OBI 0.016 OB2 0.023 OB3 0.011 O3A 0.023 O3B 0.003 O2A 0.014 O3A 0.045 OC1 0.018 OC1 0.020 OC2 0.016 O3A' 0.022 O3B' 0.002 O1B 0.008 O1B 0.013 OC3 0.011 OC2 0.008 OC3 0.018 O1B' 0.010 O2B 0.033 O2B 0.011 O3B 0.019 mean 0.014 0.017 0.015 mean 0.019 0.005 0.011 0.023 M1 0.017 M2 0.016 M3 0.011 OAI 0.010 OA2 0.015 OAI 0.008 To compare two polyhedra, the second polyhedron was trans- OA3 0.028 OA3 0.029 OA1, 2 0.0148 lated and rotated as a rigid body superimposing the first polyhed- OB1 0.036 OB1 0.040 OA2 0.013 ron and the sum of squared discrepancies of corresponding OB2 0.037 OB2 0.036 OA2, 1 0.015 b atoms was minimized OB3 0.025 OB3 0.023 OA3 0.008 b Because of the symmetry difference in the M3 polyhedron, all OC3 0.010 OC2 0.010 OB3 0.001 coordinating oxygen numbers do not necessarily match between WO1T and WO2M. The OA1 and OA2 in WO1T correspond mean 0.023 0.024 0.010 to OA2 and OA1, respectively, in WO2M

Table 8. Bond angles (degrees) for silicate chains in enstatite and wollastonite polytypes

CLEN OREN WO1T WO2M

SiA-O3A-SiA' 133.3(1) 134.3(1) SiI-OC1-Si2 150.5(2) 150.6(2) SiB-O3B-SiB' 127.5 (1) 127.8 (1) Si2-OC2-Si3 139.8 (2) 140.5 (2) Si3-OC3-Sil 140.3 (2) 140.2(2) O3A-O3A'-O3A" 157.3(1) 159.0(1) OC1-OC2-OC3 155.3(1) 156.0(2) 03 B-O3B'-O3B" 138.4 (I) 139.1 (1) OC2-OC3-OC1 156.2 (1) 155.8 (2) OC3-OC1-OC2 131.6(1) 131.9 (2)

Table 9. Electrostatic site energies a (Kcal/mole) for enstatite and wollastonite

Site (1) (2) (1)-(2) Site (3) (4) (3)-(4) CLEN OREN Difference WO1T WO2M Difference

M1 - 1241.62 - 1243.91 2.29 M1 - 1020.1 - 1018.8 -- 1.3~ b M2 -- 1134.40 -- 1134.40 0.0 M2 -989.7 --988.3 -- 1.4J SiA -4400.52 -4407.01 6.49 M3 - 1013.5 - 1012.2 - 1.3

SiB - 4353.92 - 4348.93 - 4.99 Sil - 4434.0 - 4429.7 - 4.3 ~ b Si2 --4413.5 --4434.6 21.1J O1A - 1214.18 - 1210.66 - 3.52 Si3 -4404.9 -4392.4 - 11.6 O2A - 1214.03 - 1214.71 -0.68 O3A - 1424.08 - 1423.31 -0.77 OA1 - 1189.5 - 1188.1 - 1.5~ b OA2 - 1199.3 - 1203.9 4.7J OIB - 1216.90 -- 1216.27 --0.63 OA3 -- 1164.2 - 1164.8 0.6 O2B -- 1222.78 - 1223.80 1.02 O3B - 1410.29 - 1408.14 - 2.15 OBI - 1186.7 - 1181.9 --4.8~ b OB2 --1214.2 --1219.2 4.9J OB3 -1147.1 -1146.9 --0.1

OC1 - 1411.9 - 1400.9 11.0 OC2 - 1431.4 - 1430.5 - 0.9 ~b OC3 -- 1422.7 -- 1429.5 6.8 J a The electrostatic part of the energy required to remove a given ion from a crystal site to the infinity. Since the coulombic interaction is a long-range effect, the site energy reflects not only the nearest neighbor but also stacking difference in polytypes. Calculated with a Fourier method. Nominal charges are assumed (i.e. M 2+, Si 4+, and 0 2-) b In the wollastonite polytypes, the following pairs are related by the pseudo mirror plane: (M1-M2), (Sil-Si2), (OAI-OA2), (OB1-OB2) and (OC2-OC3). These would be energetically and symmetrically equivalent, if the mirror plane were true 223 % ;LEN cell

C

~|1 a ....

lite

Fig. 2. Unit-cell scale twinning relationship of (a) enstatite and (b) wotlastonite polytypes. Although the b glide parallel to (100) is usually attributed to enstatite polytypes, three WO2M - mono "~ b more symmetry elements will generate the cell same orthoenstatite structure. For wollastonite there are two ways to describe (b) Wollastonite the twinning relationship

Electrostatic Site Energy Table 10. Twinning relationships between monoclinic and ortho- rhombic space groups for the pyroxene structures The coulombic potential is a long-range interaction that decreases with the reciprocal of the interatomic distance. Monoclinic Orthorhombic space groups The influence of the second and higher neighbor atoms, space groups which cannot be analyzed by consideration of coordination Twinning operations a polyhedra, should be reflected in the electrostatic site ener- b glide a glide 21 II to a 21 II to c gies. The values (Table 9) calculated by Fourier methods (Bertaut 1953; Ohashi 1976) are good measures of differ- P21/c Pbca Pbca Pbca Pbca ences in the long-range atomic arrangements. However, it Pc Pbc21 P21ca P21ca Pbc21 must be emphasized that the model is an oversimplified P21 Pb21a Pb21a P212121 P212x21 one and does not yield thermodynamically meaningful site With local symmetry energies. In the enstatite polytypes, SiA shows larger site energy C2/c Pbca Pbca Pbca Pbca difference than does SiB. This is consistent with the poly- P21/n Pb21a Pb21a P212121 P212121 P2/c Pbc21 P21ca P21ca Pbe21 hedral misfit. O1A, the only oxygen in the SiA tetrahedron Cc Pbc21 P21ca P21ca Pbc21 that is on the other side of the twinning plane, also indi- C2 Pb21a Pb21a P212121 P212121 cates a relatively large difference in site energies. Except for SiA, SiB, and O1A, site energies for corresponding sites a In reference to the orthorhombic coordinate axes in enstatite polymorphs are similar between the two poly- types. The bond distances (Table 5) and shapes of the M1 and 16.2 kcal/mol, larger difference in wollastonite as compared M2 octahedra in the wollastonite polytypes are very similar. to enstatite are observed. In general, oxygens in the wollas- The site energies, however, clearly distinguish these two tonite polytypes show a larger discrepancy than those in sites (approximately 1,020 vs. 990 kcal/mol). Between the the enstatite polytypes. two polytypes all octahedral sites M1, M2, and M3 are similar in site energies. The apparent large discrepancy for Twinning Relationship of Polytypes Si2 of wollastonite polytypes is partly due to difference Enstatite. The unit cell of hypersthene (orthopyroxene with in the polarity of chain directions (compare Figs. 5 a and space group Pbca) was considered by Warren and Modell 5b). Considering the pseudosymmetry, Sil could be rela- 1930 to be a twinned cell (C2/c). Since Ito 1935 belled as Si2 in wollastonite-2M (then M1 and M2 must first pointed out, the twinning operation that would gener- also be changed to maintain consistent oxygen labeling). ate the Pbca cell from the P21/c cell has been almost always When these alternate pairs are compared, Sil (WO1T~Si2 referred to as the b-glide plane parallel to (100) in the SiA (WO2M)=0.6 kcal/mol, and Si2 (WOIT) Sil(WO2M)= layer (i.e., basal oxygens O2A and O3A are on the same 224

Octahedra

Tetrahedr;

Fig. 3. Projection of the wollastonite-2M structure along the tetrahedral chain direction. Note the tetrahedral and octahedral layers are parallel to (201) plane of the conventional unit cell of wollastonite-2M (the b axis is parallel to Wollastonite--2M the chains) 1 1

~, ff e~

,,/

:~, ~ 2 b './ 2 -. H % L 1 Wollastonite - 2 M <2 (3 C::~ Fig. 4. Projection of the wollastonite-2M structure onto the oxygen closepacked layer (201). The crystallographic b axis is in the vertical direction parallel to silicate chains. In this projection the a axis is from the top layer to the layer two levels below (see an arrow at the bottom) and the b axis spans two adjacent layers

side of the b glide whereas the apical oxygen O1A is on the a glide parallel to (001), the 21 axis parallel to c, and the other side). This description of the twinning operation, the 21 axis parallel to a are all equivalent. These four twin- however, is not unique. Other twinning operations can also ning operations, however, become distinct when the symme- be equally valid for the ortho- and clino-pyroxene relation- try of the clinopyroxene cell is reduced (Ohashi and Finger ship. As shown in Figure 2a, the b glide parallel to (100), 1974b). Table 10 lists all possible twinning relationships be- 225

Tetrahedral • chain direction down up

!gi':-. . .:.

;.'.'.-:.:,-...';,>~p

a) Wollastonite- 1T

Unit 2 (p21) ]

':3:.~.~ ~n'~. .i1:2. ::1:" -:l': ! .::[-. "...,-:.• :,1;; :.-i.. .:'- i.'.. , 5!I~i -..'- .....

i

I Unit l(pT) I b) Wollastonite-2M Fig. 5a and b. Comparison of tetrahedral chains in wollastonite polytypes. Crystallographic orientation is the same as in Figure 4. The oxygen close-packed layer is (201) in wollastonite-2M and (101) in wollastonite-lT

tween the 16 possible clinopyroxene space groups and 16 to the twinning plane are easier to visualize than those nor- orthopyroxene space groups as derived by Matsumoto and mal to the twinning plane. Banno 1970; Brown 1972; Ohashi 1973; Matsumoto 1974. A b glide parallel to (100) is commonly used in the literature Wollastonite. The space group of wollastonite-lT is P1 (Ito for enstatite, probably because twinning operations parallel 1950; Buerger 1956; Buerger and Prewitt 1961 ; Prewitt and 226

i/ Na 0

o

/ f Na 0

o

o

M1 : Ca-Mn, Fe M2 :Ca-Mn,Fe M I :Ca- Mn Fig. 6. Comparison of octahedral bands ALl Ca All Ca M3:Mn M2 :Ca-Mn of wollastonite, , and pectotite. M4:Ca Note that the distribution of symmetrically-equivalent sites (e.g., M1) Wollostonite -IT Wollastonite- 2 M Bustamite serandite is unique in each

Buerger 1963). In addition to an inversion center there is proximation wollastonite-lT may be regarded as the struc- a pseudomirror plane that is operative only within a layer ture with a + b/4 shift vector, whereas wollastonite-2M can (Ito et al. 1969). Although earlier described by Tolliday be approximated with alternating shifts of + b/4 and -b/4. 1958 as P21 with a non-lattice translation of (1/2, 1/4, 0), In the strict sense, however, these are not unit-cell-scale wollastonite-2M was refined by Trojer 1968 in the space twinned structures because the unit structures have different group P21/a. These two structures are actually very similar symmetry (p~ and p21). in spite of the apparent difference in symmetry (Vincent and Jeffery 1979). Two twin operations - 21 parallel to the b axis and Octahedral Exchangeability an a glide plane normal to the b axis may produce the The tetrahedral chain shifts (e.g., b/4 as in wollastonite) polytype 2M (Fig. 2b). The unit layer of both polytypes found in chain silicates with end member compositions al- has the same layer symmetry pl. The 2~ screw axis of wol- low for a polytypism to occur. Although the coordination lastonite-2M is a twin axis. of the octahedral bands adjacent to the shifted chain chan- The twinning relation of the wollastonite polytypes ges, the environment of the original M1 site, for example, (Fig. 3) is different from that of the enstatite polytypes becomes similar to that of M2. If M1 and M2 are chemically when the structures are considered. Neither of the tetrahed- identical, an "octahedral exchange mechanism" (see ral or octahedral layers is the same in two wollastonite Smyth, 1974; Coe and Kirby 1975) is possible. In other polytypes. Each layer has distinct arrangements. In wollas- words, M 1 may be relabelled M2 when the stacking changes tonite-2M the inversion relates, for example, unshaded and as in the case of clino- to ortho-stacking changes in ensta- shaded tetrahedral chains (see Fig. 3 or Fig. 5b), whereas rite. However, if the two sites are not chemical equivalents, a twofold screw axis relates two shaded (or unshaded) such an exchange is not possible and polytypism is unlikely. chains. In contrast, tetrahedral chains in wollastonite-lT Octahedral arrangements in three-tetrahedral-repeat pyr- are related by inversion operations. oxenoids are shown in Figure 6. The lack of exchangeability Ohashi and Finger 1978 attributed the structural differ- occurs in bustamite and intermediate serandite where octa- ences of wollastonite-lT, bustamite, and pectolite to the hedral occupancies are different, and polytypes have not unique stacking of tetrahedral and octahedral layers that been reported. In contrast, the exchangeability of Ca in are parallel to oxygen close-packed layers. The wollastonite- M1 and M2 of end-member pectolite does allow for poly- 2M structure projected on the (201) plane is shown in Fig- typism and such structures have been identified (Muller ure 4 (compare this with Fig. 3 of Ohashi and Finger 1978 1976). for wollastonite-lT, bustamite, and pectolite). The octahe- dral layer, for example, contains an alternating sequence of inversions and twofold screw axes with a translational Lattice Strain repeat normal to b of approximately 22 A. As has been discussed previously by Wenk 1969 ; Takeu- Because of distortions within the structure, multiple-unit chi and Haga 1971; Jefferson and Bown 1973; Wenk et al. polytypes do not have cell volumes that are exactly integer 1976; Hutchison and McLaren 1976, 1977, to a first ap- multiples of the unit-layer polytype. Lattice strain tensors 227

Table l I. Twinned unit cells and strain ellipsoids for enstatite and wollastonite polytypes

T-CLEN a OREN T-WOtT" WO2M

a (A) J8.235 (2) 18.225(2) 15.4184(8) 15.424(1) b 8.8131(7) 8.8128(6) 7.3202(4) 7.324(1) c 5.170(2) 5.180(1) 7.0653(4) 7.0692(7) fl (deg.) 95.364(8) 95.371(4) V(A 3) 831.0(4) 832.0(2) 793.9(1) 795.1(2) b Strain relative orien- Strain relative orien- axes strain b tation axes strain b tation

from T-CLEN to OREN from T-WOIT to WO2M axis 1 0.0019(4) [1 to c axis i 0.00058(11) 15(11) ° from + c to -a axis 2 -0.0000(1) II to b axis 2 0•00055(15) II to b axis 3 -0.0005(1) II to a axis 3 0•00036(7) 75(11) ° d from + c to +a (a) Enstatite volume 0.0014(5) volume 0.0015(2)

a Theoretically twinned cells were calculated as follows: a(T-CLEN) = 2a sinfl(CLEN) a (T-WO 1T) = 2a sin 7 (WO 1T) fl(T-WO1T) = acos(cos fl/siny) (WO1T) b (~ of WOIT (90.055 °) was assumed to be 90 ° Positive values mean an expansion associated with a change from theoretically twinned cell to observed cell ..... "'•'''•,-.•.. "'.- "'''''" ; "'"''''"

(see Ohashi and Burnham 1973; Ohashi and Finger 1973) have been computed for a change from the theoretically ...... 9 ...... -'''" ...... 8 ...... "'''•''".. twinned polytype to the observed two-layer polytype (Ta- .•• •.••" . • ...... ~ ...... "'.... -.. .''" ,,''" . ..--"'6''-... "'''- "'°-. ble 11 and Fig. 7). "'" "'" "'" • ..... 5'-., "''.. "'- "" .'• "" .''" •'"• ..... 4"-,. "''• "', "" %. Strain components are positive in the c-axis direction, • "" •'" ,'" -'" ..... 3 .... •'•• "'. "'- ", .." .•-" ..." ..•• ..•.'" ....2•.,.. "'.. "% '% %. •.• negative in a, and nearly zero in b for transitions from • ..- •.• ...• .-" ..,.'" .,..|,... "'..%• ". ". •. • theoretically-twinned clinoenstatite to orthoenstatite. After the twinning operation the extensional strain is applied in the tetrahedral chain or octahedral band direction and the compressive strain is normal to the tetrahedral or octahe- dral layers. The b length is constant. For wollastonite, all strain components are positive for a transition from theoretically-twinned wollastonite-lT to (b) Wollastonite observed wollastonite-2M. The strain ellipsoid is approxi- Fig. 7a and b. Stereographic projections of strain ellipsoids of en- mately uniaxially oblate (the first and the second strain statite and wollastonite. Strains are calculated for a change from components are nearly equal). The smallest principal axis a theoretically-twinned one-layer polytype to the observed two- layer polytype. The contour scale is arbitrary. The ellipsoid is elon- of the ellipsoid is 30 degrees beyond a toward c in the a-c gated along the c axis in enstatite and oblated along the minimum plane, a direction that does not correspond to any major axis in wollastonite crystal structural feature. Clinoenstatite can be obtained experimentally from Conclusions orthoenstatite even in the orthoenstatite stability field under non-hydrostatic conditions (Riecker and Rooney 1967; Enstatite and wollastonite both form polytypes that may Munoz 1968; Coe 1970; Coe and Muller 1970). Since little be described approximately as until-cell scale twins• The experimental data are available, the wollastonite transfor- relationship of the twinning operation to the structure, mation is also regarded analogously such that shear stress however, is different for each. The twinning plane is parallel can be important (see Wenk 1969, Coe 1970; Guggenheim to oxygen close-packed layers in the enstatite polytypes, 1978). A comparison of the lattice strain ellipsoids indicates, but is diagonal in the wollastonite polytypes. As a result however, that wollastonite is different from enstatite in both the enstatite polytypes may be regarded as a difference in magnitude and orientation of the strain components. The stacking of tetrahedral and octahedral layers that are com- way wollastonite responds to non-hydrostatic pressure can- mon to these polytypes. Between two polytypes of wollas- not be predicted at present, but it is certainly an important tonite the major difference is not only the stacking, but factor in explaining apparently random occurrences of wol- a changed topologic relationship between tetrahedral and lastonite polytypes. octahedral layers that produces symmetry differences• 228

Atomic readjustments after twinning are also different Hawthorne FC, Ito J (1977) Synthesis and crystal-structure refine- in the two metasilicate minerals. The polyhedral misfit is ment of transition-metal orthopyroxenes. I: Orthoenstatite and a maximum at the twin boundary and decreases toward (Mg,Mn,Co) orthopyroxene. Can Mineral 15:321-338 the center of the twinning slab in enstatite. In wollastonite Henmi C, Kawahara A, Henmi K, Kusachi I, Takeuchi Y (1983) the polyhedral misfit is a minimum at the twin boundary. The 3T, 4T and 5T polytypes of wollastonite from Kushiro, Hiroshima Prefecture, Japan. Am Mineral 68:15 163 Structural readjustments seem to be significant in the poly- Henmi C, Kusachi I, Kawahara A, Henmi K (1978) 7T wollaston- hedra that involve bridging oxygens in both enstatite and ite from Fuka, Okayama Prefecture. Mineral J (Japan) wollastonite. 9:169-181 Lattice strain associated with twinning is, to a first ap- Hutchison JL, McLaren AC (1976) Two-dimensional lattice images proximation, an elongated ellipsoid for enstatite and an of stacking disorder in wollastonite. Contrib Mineral Petrol oblate ellipsoid for wollastonite. Furthermore, three princi- 55: 303-309 pal strain components are all positive in wollastonite but Hutchison JL, McLaren AC (1977) Stacking disorder in wollaston- are positive, zero, and negative in enstatite, which may im- ire and its relationship to twinning and the structure of parawol- ply different behavior of the two minerals under non-hydro- lastonite. Contrib Mineral Petrol 61:11-13 International Tables for X-ray Crystallography, Vol. III (1968) static environments. Kynoch Press The twin operation between the two wollastonite poly- Ito J (1975) High temperature solvent growth of orthoenstatite, types of this study is not vectors with shifts of + b/4 and MgSiO3, in air. Geophys Res Lett 2:533-536 -b/4. The model based on these shift vectors is only an Ito T (1935) On the symmetry of the rhombic pyroxenes. Z Kristal- approximation and requires units slabs with different sym- logr 90 : 151-162 metry for each polytype. Ito T (1950) X-ray studies on polymorphism. Maruzen, Tokyo Ito T, Sadanaga R, Tak6uchi Y, Tokonami M (1969) The existence Acknowledgments. The author is grateful to Dr. Jun Ito, Prof. Mat- of partial mirrors in wollastonite. Proc Japan Acad 45:913-918 suo Nambu, Dr. Brian Mason, Dr. Hatten S. Yoder, Dr. George Jefferson DA, Bown MG (1973) Polytypism and stacking disorder Harlow, and Mr. M'hamed Bokreta for the specimens examined in wollastonite. Nature (London) Phys Sci 245 : 4344 for this study; to Dr. Larry W. 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