Clays and Clay Minerals, VoL 48, No. 2, 282-289, 2000. M I X E D L A Y E R I N G OF ILLITE-SMECTITE: RESULTS F R O M HIGH-RESOLUTION TRANSMISSION ELECTRON MICROSCOPY AND LATTICE-ENERGY CALCULATIONS JUAN OLIVES, MARC AMOURIC, AND RI~GIS PERBOST CRMC2-CNRS, Campus de Luminy, Case 913, 13288 Marseille cedex 09, France A b s t r a c t - - M i x e d layering of illite-smectite was studied both experimentally, by using high-resolution transmission electron microscopy (HRTEM) and analytical electron microscopy (AEM), and theoretically, by using lattice-energy calculations. Samples from a hydrothermal origin show the transformation of smectite to illite with different ordering types in the illite-smectite layer sequences. Ordering ranges from complete disordered (Reichweite, R = 0 type) in the less transformed samples to increased local order, with IS and IIS sequences (R = 1 and R = 2, respectively; I = illite, S = smectite) in more illitized samples. Lattice-energy calculations are used to determine the structure of the illite-smectite sequence, which corresponds to the minimum energy. The unit layers are: O0.sTI'TO0.s (O, T, and I', respectively, denote the octahedral and tetrahedral sheets, and the interlayer. The 0.5 signifies half of the octahedral cations.) For example, the arrangements of the perfectly ordered . . . I S I S . . . and . . . I I S I I S . . . sequences are respectively... OM(TI'T)~OM(TI'T)s... a n d . . . Ou~(TI'T)IOI(TI'T)IOM(TI'T)s . . . (the subscripts I, S, and M, respectively, refer to compositions of illite, smectite, and midway between at 0.5). Such arrangements produce a polar model for TOT layers, which display a T1OMTs structure in the case of IS adjacent layers. Furthermore, the lattice energies of . . . I S I S . . . and . . . I I S I I S . . . are found to be nearly equal to the corresponding sums of the lattice energies of illite and smectite. This result indicates that interstratified illite-smectite and the two-phase assemblage of illite + smectite have similar stabilities. On the basis of the above model, the solid-state transformation of one smectite layer to one illite layer, which produces mixed-layer sequences, involves the transformation of an O0.sTI'TO0 ~ unit of smectite into the same corresponding unit of illite. Key Words--HRTEM-AEM, lllite-Smectite, Lattice-Energy Calculations, Mixed Layering, Polar 2:1 Layers. INTRODUCTION T h e t r a n s f o r m a t i o n of s m e c t i t e to illite is a r e a c t i o n w h i c h occurs d u r i n g d i a g e n e s i s or at h y d r o t h e r m a l conditions. M i x e d l a y e r i n g o f illite-smectite, w h i c h results f r o m this process, h a s b e e n i n t e n s i v e l y studied b y X - r a y d i f f r a c t i o n ( X R D ; e.g., Srodofi, 1984; I n o u e et al., 1987; R e y n o l d s , 1992) a n d directly o b s e r v e d b y high-resolution transmission electron microscopy ( H R T E M ) . A c c o r d i n g to c o m p u t e r - i m a g e s i m u l a t i o n s o f G u t h r i e a n d V e b l e n (1989, 1990), illite a n d s m e c t i t e layers c a n b e c o m m o n l y d i f f e r e n t i a t e d b y u s i n g m i c r o s c o p e o v e r f o c u s conditions. O n s u c h a basis, seq u e n c e s o f illite-smectite interstratification o f e i t h e r d i s o r d e r e d or o r d e r e d t y p e s , w e r e o b s e r v e d b y H R T E M (e.g., A h n a n d Peacor, 1989; V e b l e n et aL, 1990; J i a n g et al., 1990; A m o u r i c a n d 0 l i v e s , 1991; M u r a k a r n i et al., 1993; 0 l i v e s and A m o u r i c , 1994a, 1994b; H u g g e t t , 1995). I n f o r m a t i o n a b o u t illitization mechanisms (solid-state, dissolution-crystallization) w a s also o b t a i n e d f r o m H R T E M observations ( A m o u r i c a n d Olives, 1991; B u a t i e r e t al., 1992; M u r a k a m i et al., 1993). A m o u r i c a n d O l i v e s (1991) p r e s e n t e d H R T E M obs e r v a t i o n s o n illite, smectite, a n d illite-smectite (inv o l v i n g h y d r a t e d s m e c t i t e w i t h d ( 0 0 1 ) = 1.25 n m ) in a s m e c t i t e - r i c h s a m p l e f r o m h y d r o t h e r m a l origin a n d Copyright 9 2000, The Clay Minerals Society s h o w i n g a smectite-to-illite t r a n s f o r m a t i o n . T h e present p a p e r c o m p l e t e s this study w i t h t w o a d d i t i o n a l illitic samples. T h e s e three s a m p l e s are r e p r e s e n t a t i v e o f this h y d r o t h e r m a l t r a n s f o r m a t i o n a n d s h o w various ( d i s o r d e r e d a n d ordered) illite-smectite interstratification s e q u e n c e s as o b s e r v e d b y H R T E M . In addition, the c h e m i c a l v a r i a t i o n s o f the m i x e d - l a y e r m i n e r a l s are characterized by analytical electron microscopy (AEM). A t h e o r e t i c a l a p p r o a c h o n the b a s i s o f l a t t i c e - e n e r g y c a l c u l a t i o n s is u s e d to d e t e r m i n e the structure o f m i x e d - l a y e r illite-smectite b y e n e r g y m i n i m i z a t i o n m e t h o d s . T h e a p p r o a c h c o n s i d e r s various types of polar a n d n o n - p o l a r 2:1 layers (see O l i v e s a n d A m o u r i c , 1994a, 1994b). E n e r g y c a l c u l a t i o n s also lead to a better u n d e r s t a n d i n g o f the relative stability o f t h e s e m i n erals a n d yield a d e s c r i p t i o n at the unit-cell scale o f the solid-state illitization m e c h a n i s m . MATERIALS AND METHODS T h e studied m a t e r i a l s b e l o n g to a h y d r o t h e r m a l series f r o m the S h i n z a n area, A k i t a P r e f e c t u r e , Japan. In this area, the h y d r o t h e r m a l alteration o f silicic volcanic glass ( M i o c e n e E p o c h ) p r o d u c e d a series b e t w e e n s m e c t i t e a n d illite. T h e m i n e r a l a s s e m b l a g e c o n s i s t s o f interstratified illite-smectite, illite, smectite, quartz, 282 Vol. 48, No. 2, 2000 Mixed layering of illite-smectite 283 beam intensity with a low-light camera to reduce possible damage caused by the electron beam. The microscope is equipped with a Tracor (TN 5502) energydispersive X-ray spectrometer using a Si(Li) detector for AEM. Chemical microanalyses were obtained using a beam diameter of 5-20 n m at a constant beam current. Data were processed by a program based on the method of Cliff and Lorimer (1975). Note that possible volatility of elements is accounted for by this method, because the elemental constituents are obtained by comparison to appropriate layer-silicate standards. EXPERIMENTAL RESULTS Figure 1. Lattice-fringe images of various randomly disordered mixed-layer illite-smectite sequences, from the smectite-rich sample studied here (see text). [Image (a) from Amouric and 0lives, 1991, and (b) from Olives and Amouric, 1994a.] In the smectite-rich sample, three minerals coexist: smectite, illite, and interstratified illite-smectite. In the other samples, only illite and interstratified illite-smectite were present. Owing to the experimental techniques used (ultramicrotome cutting, low electronbeam intensity), the smectite crystallites showed d(001) values of 1.25 nm, indicating that H20 was present in the interlayer (Amouric and Olives, 1991). This observation was used to identify 1-nm repeat distances as illite (and 1.25-nm repeats as smectite). In images of interlayered minerals, the positions of the lattice fringes are sensitive to experimental conditions (e.g., focus, crystal orientation, crystal thickness). The simulations of Guthrie and Veblen (1990) showed that, under special conditions (overfocus), bright lattice fringes may overlay the octahedral sites of the 2:1 layer, thus leading to a close correspondence between the spacings of the bright lattice fringes and layer thickness. Images of mixed-layer illite-smectite (Figures 1 and 2) were obtained with such conditions. Representative examples of these images are presented in Figure 2a and 2c which shows two sets of fringes: (1) dark fringes of 1.25-nm thickness and (2) gray fringes of 1-nm thickness, which correspond to smectite and illite layers, respectively. Mixed-layer illite-smectite and chlorite (Inoue and Utada, 1983). The three specimens selected contain interstratified illite-smectite with, respectively, 68, 40, and 20% smectite, as determined by XRD (Inoue et al., 1987). The samples, reduced to a powder and embedded in Araldite resin, were cut with a diamond knife of an LKB Ultramicrotome. The < 5 0 - n m thick sections were deposited on carbon-coated copper grids. This technique better preserves smectite from dehydration than ion milling. Bright-field images were taken with a JEOL 2000 FX electron microscope (200-kV accelerating voltage, 1,8-mm spherical aberration coefficient) with a 50-1xm objective aperture. Focus values were in the range +50 to +100 nm for one-dimensional images and of about - 1 0 0 n m for two-dimensional images. Specimens were observed at very low In the smectite-rich sample, the observed sequences of illite-smectite interstratification are disordered (Amouric and Olives, 1991). For example, Figure 1 shows the respective interlayering sequences SIISS, SISIIISS, and SSSISISS (S = smectite, I = illite). We consider the sequences as alternations of packets of smectite units and packets of illite units, with the respective numbers of units of Ns and NI, where Ns and NI are integers. In general, the sequences of this sample may be described as randomly disordered interstratifications (Reichweite, R = 0) in which Ns and NI are equal to 1-5 and 1-3, respectively. Because no significant differences were found in the interlayering sequences between the more illitic sampies, they are referred to as illite-rich samples. In these samples, consecutive smectite layers were not ob- 284 Olives, Amouric, and Perbost Clays and Clay Minerals Figure 2. Lattice-fringe images of various locally ordered mixed-layer illite-smectite sequences, from the illite-rich samples studied here (see text). Note perfect R = 1 order in (c), and R = 2 in (d). [Images (a), (c), and (d) from Olives and Amouric, 1994a.] served, which clearly indicates an ordered interstratification, i.e., R --> 1. Such interstratifications are illustrated in Figure 2a and 2b by SIIISIISIII and IIISIISIIISIS. Thus, such sequences are described with Ns = 1 and N~ varying from 1 to 3. Locally, perfectly ordered R -- 1 sequences ( I S I S . . . ) or R = 2 sequences ( I I S I I S . . . ) were observed also, i n v o l v i n g a few repeat units: e.g., four consecutive IS units in Figure 2c, and three IIS units in Figure 2d. Such a trend, f r o m disordered interstratification sequences to locally ordered sequences, as the percentage of smectite decreases, is similar to the case of interstratified kaolinite-smectite ( A m o u r i c and Olives, 1998). Illite N o significant change was o b s e r v e d in the morphology and the polytypism of illite crystals a m o n g the three samples. The previous descriptions ( A m o u r i c and Olives, 1991) remain valid for all the samples. Illite crystals contain 7 - 2 0 parallel layers and have a lateral extension o f 5 0 - 2 0 0 nrn. In t w o - d i m e n s i o n a l structure images, each interlayer region appears as a line of white dots with 0.45-nm spacing, and the shift b e t w e e n two consecutive such lines represents the proj e c t e d stagger b e t w e e n the two tetrahedral sheets T o f the (2:1) T O T layer, where O represents the octahedral sheet of the same 2:1 layer ( A m o u r i c et al., 1978, 1981; Iijima and Buseck, 1978). T h e s e images show for all the samples that the polytype is 1M with wellordered stacking (Figure 3). A c c o r d i n g to A m o u r i c and Olives (1991), I M illite crystals are p r o d u c e d by a dissolution-crystallization mechanism. Chemistry Structural formulae of illite-smectite w e r e normalized on the basis of O10(OH)2. The related standard Vol. 48, No. 2, 2000 Mixed layering of illite-smectite 285 Figure 3. Structure images of illite crystals, from (a) the smectite-rich sample and (b) an illite-rich sample. The illite crystals are of a regular 1M polytype. [Image (a) from Amouric and Olives, 1991.] deviations are 0.06 for Si and A1, 0.04 for Mg and Fe, and 0.02 for Ca and K. On the basis of A E M microanalyses, smectite, illite, and interstratified illite-smectite are dioctahedral. By grouping Fe (considered as Fe 3§ with octahedral A1, and Ca with K (Na being neglected), the analyses are illustrated in the pyrophyllite Si4A12010(OH)2-muscovite K(Si3A1)A12Ox0(OH)2-celadonite KSia(A1Mg)O~0(OH) 2 diagram of Figure 4. Mixedlayer illite-smectite shows a chemical trend from montmorillonite to illite. The chemical reaction involves the fixation of K and (tetrahedral and octahedral) AI in montmorillonite, to produce illite and the emission of H20, Si, Mg, and Fe. On the basis of four tetrahedral cations, the number of Fe atoms decreases from 0.08 in the smectite-rich sample to 0.04 in the illite-rich samples and the number of Ca atoms is nearly constant at 0.04. This indicates a chemical modification of the interlayer, tetrahedral, and octahedral cations. Celadonite ELECTROSTATIC-ENERGY CALCULATIONS For a better understanding of the structure and the stability of interstratified illite-srnectite, electrostaticenergy calculations were performed to compare the energies of various possible mixed-layer structures with illite and smectite as end-members. For this case, the energy thermodynamic function is adequate because the energy of mixing of the layers is nearly equal to the enthalpy of mixing (where the cell volumes are assumed constant) and to the Gibbs free energy of mixing (because the configurational entropy of mixing vanishes for the perfectly ordered sequences studied). Vibrational aspects were not taken into account. A first approximation to the lattice energy is given by the electrostatic Ewald energy (or Madelung energy). Justification is presented below. The Ewald energies are calculated from the "overlap method" (Olives, 1986a, section 2.4.2), which is presented in the following section. The convergence of this method is rapid, compared to the classical methods of Ewald (1921) or Bertaut (1952). The overlap method Pyrophyllite M uscovite Figure 4. AEM microanalyses of mixed-layer illite-smectite, from the smectite-rich sample (black circles) and the illite-rich samples (open circles) studied. Note the chemical trend from montmorillonite (Mon) to illite (I). The electrostatic energy of an ionic crystal in which the ions are considered as point charges was calculated by Madelung (1918) for the special case of cubic crystals, and then by Ewald (1921), who gave a general formula valid for any crystal. Owing to the long-range nature of electrostatic interactions, the electrostatic energy per volume unit (more precisely, the limit of this energy when the crystal becomes infinitely large) depends on the atomic configuration of the surface of the crystal. The Ewald energy represents the minimum of this electrostatic energy per volume unit with respect to all possible atomic configurations of the surface of the crystal (Olives, 1986b, 1987). 286 Olives, Amouric, and Perbost Clays and Clay Minerals Table 1. Interstratified structures corresponding to I'TOT units, TI'TO units, etc., for the ordered layer sequences...ISIS... a n d . . . I I S I I S . . . (I = illite, S = smectite; I', T, and O, respectively, denote the interlayer, tetrahedral, and octahedral regions). The subscripts I, S, and M, respectively, refer to compositions of illite, smectite, and midway between at 0.5. U n i t s i n v o l v e d in t h e interstratification I'TOT units TI'TO units I'0.sTOTI'0 ~ units T0.5I'TOT0.5 units O0.sTI'TO0.5 units 9 . .(I'TOT)I(I'TOT)s... 9 9 . 9 9 . .I'ra(TOT)II'M(TOT)s... . . 9 . 9 9 . .O~(TI'T)IOM(TI'T)s... In the overlap method, the Ewald energy, E, is calculated as E = E1 - E2 + E3, in which E 1 is the reciprocal-lattice sum, E1 = (1/2~rV) "~ IF(h)~(h)12/h 2, with h~0 F(h) = ~ I n t e r s t r a t i f i e d s t r u c t u r e s for . . . I I S I I S . . . I n t e r s t r a t i f i e d structures for . . . I S I S . . . quexp(2~rih.u), u tp(h) = 3(sin ot - a cos c 0 / a 3, E2 = (3/5R) ~ et = 2~rRllhll; qu2; u and E 3 is the direct lattice sum, E3 = (1/2R) ~ ~ Iln + u - ~ quqv 9 . .(TI'TO)I(TI'TO)I(TI'TO)s... .I'M(TOT)II'I(TOT)II'M(TOT)s... .TM(I'TO)ITI(I'TO)~TM(I'TO)s... .OM(TI'T)IOI(TI'T)IOM(TI'T)s... the two compositions o f (dehydrated) smectite, S 1 = (Na, K)o.asSi4(All.65Mgo.35)Olo(OH)2 (montmorillonite) and $2 = (Na, K)o.35(Sia.65Alo.35)A12OIo(OH)2 (beidellite). F o r m a l charges, qK = qNa = 1, qsi = 4, qA1 = 3, qMg = 2 , q n = 1 , q o = - 2 , w e r e used with m e a n charges for the interlayer, tetrahedral, and octahedral cations, e.g., 0.75, [(3.6 • 4) + (0.4 x 3)]/4, and [(1.65 • 3) + (0.35 • 2)]/2, respectively, for the above I~ composition. The E w a l d energies o f illite I1, illite I2, smectite $1, and smectite $2 w e r e calculated at - 8 0 . 5 8 4 2 , - 8 0 . 1 6 3 5 , - 8 1 . 9 9 6 8 , and - 8 1 . 5 2 6 1 M J mol 1, respectively (12 o x y g e n atoms per molecule; 1 M J = 106 J). The uncertainty of these values and the following ones are < 0 . 5 • 10 -4 M J mo1-1. vii < 2R Mixed-layer illite-smectite • ( l / x - 6/5 + x2/2 - 3x3/16 + x5/160), with Illite and smectite h a v e the same general structure I ' T O T I ' T O T . . . ( T O T layers separated by interlayer regions I'), but the I', T, and O regions are occupied by different cations. A fundamental p r o b l e m concerning the nature of m i x e d - l a y e r illite-smectite is the structure of the individual illite and smectite layers. Possibilities include: I ' T O T units, T I ' T O units, etc. Table 1 shows the interstratified structures corresponding to unit layers, for t w o o r d e r e d l a y e r s e q u e n c e s ...ISIS... and . . . I I S I I S . . . . In this table, the subscript M indicates a c o m p o s i t i o n m i d w a y b e t w e e n illite and smectite at 0.5 and refers to a r a n d o m mixture of the corresponding cations. Thus, for OM, with the above I2 and $1 compositions, the m e a n charge, [3 + (1.65 • 3 + 0.35 x 2)/2]/2, is used for the octahedral cations. N o t e that, either for t h e . . . I S I S . . . or for the . ..IISIIS... case, the derived structures h a v e the same first-neighbor interactions (oxygen-cation and o x y g e n - o x y g e n ) , although the arrangements differ. Thus, the short-range energies (van der Waals attraction, overlap repulsion) are identical for these structures, and the differences b e t w e e n the lattice energies are only related to the long-range electrostatic energy. The calculated E w a l d energies of the preceding m i x e d - l a y e r structures are g i v e n in Table 2 for ...ISIS... and in Table 3 for . . . I I S I I S . . . . for the various compositions used. F o r all cases, the results indicate that the m o r e stable interstratification structure ( m i n i m u m energy) is based on O0.sTI'TO0. 5 units. ... x = IIn + u - vii/R. In these expressions, n denotes the lattice vectors, u or v denotes the positions of the ions o f the origin cell n = 0, qu is the charge of the ion at position u, h denotes the reciprocal-lattice vectors, V is the v o l u m e of the cell, R is a length parameter of any positive value (E does not depend on R), i = N/Z-], h. u denotes the inner product, and Ilyll denotes the length of any vector y. As R increases, the n u m b e r of terms in the finite sum E3 increases but, at the same time, the series E1 converges more rapidly. In our case, a v e r y rapid conv e r g e n c e was obtained with a value of R close to the cell dimension, e.g., at R = 1 nm. S m e c t i t e a n d illite Because the smectite and illite structures are not k n o w n accurately, we have used the coordinates f r o m Jenkins and Hartman (1979) as derived f r o m Sidore n k o et al. (1975) for an Al-rich 1M m i c a for the structure of illite, (dehydrated) smectite, and interstratified illite-smectite. The 1M polytype was assumed for the three minerals. The structure relaxation was neglected. Various compositions were used, n a m e l y the two c o m positions of illite, I x = Ko.75(Si3.6Alo.4)(All.65Mgo.35 )O10(OH)2 and 12 = Ko.75(Si3.25Alo.75)A12Oxo(OH)2, and Vol. 48, No. 2, 2000 Mixed layering of illite-smectite 287 Table 2. Calculated Ewald energies of the mixed-layer structures corresponding to I'TOT units, TI'TO units, etc. (see Table 1), for the ordered layer sequence ...ISIS .... The last column gives the Ewald energy of the two-phases illite + smectite assemblage with the same composition (i.e., energy of illite + energy of smectite). Various compositions of illite (I t, I2) and smectite (S~, Sz) were used (see text). Values are in MJ mol 1 = 106 I mol -t and refer to 24 oxygen atoms per molecule. The more stable interstratification structure (minimum energy) is based on O05TI'TO05 units. The energy of the mixed-layer . . . I S I S . , . (with O05TI'TO0. 5 units) is close to the corresponding energy of the two-phases illite + smectite assemblage. I'TOT units TI'TO units lnterstratified sequence . . . I S I S . . . I'05TOTI'0~ units T0~I'TOT05 units O05TI'TOo 5 units Two-phase illite + smectite assemblage I182 -162.5088 -162.0361 1281 --162.0903 I2S2 -161.6175 -162.5809 -162.0533 -162.1031 -161.6896 -162.5381 -162.0654 -162.1196 -161.6468 -162.5558 -162.0449 -162.1350 -161.6645 -162.5809 -162.0867 -162.1365 -161.6896 -162.5809 -162.1103 -162.1602 -161.6896 Compositions 1181 M o r e o v e r , this m o d e l c o r r e s p o n d s to the m i n i m u m energy in c o m p a r i s o n to the o t h e r m o d e l s b a s e d o n OxTI'TO1 x, I'xTOTI'l-x, or T~I'TOT~ x units (0 -----x <-1). T h i s result indicates that the layers i n v o l v e d i n t h e interstratification are p r o b a b l y O0.sTI'TO05 (Olives a n d A m o u r i c , 1994a, 1994b). W h e n the o c t a h e d r a l c o m p o s i t i o n s o f illite a n d s m e c t i t e are identical, i.e., f o r IiS l a n d I282, note that the interstratification structure b a s e d o n O05TI'TO0.5 u n i t s c o i n c i d e s w i t h that b a s e d o n T I ' T O units. T h e interstratification m a y t h e n b e described as the s u p e r p o s i t i o n o f illitic or smectitic T I ' T units, separated b y o c t a h e d r a l sheets o f M, I, or S c o m p o s i t i o n (for the r e s p e c t i v e cases o f IS, II, or SS a d j a c e n t layers). F i g u r e 5 illustrates a n e x a m p l e o f the ...ISIS... interstratification. T h e l a t t i c e - e n e r g y calc u l a t i o n s lead to a p o l a r m o d e l for T O T layers (with t w o tetrahedral sheets o f different c o m p o s i t i o n s ; see S 0 - M 0 " ,', ls M 0 M T 7 - e.g., Gtiven, 1991). I n d e e d , the p r e c i s e a r r a n g e m e n t is T~OMTs for the c a s e o f IS a d j a c e n t layers. S u c h a p o l a r m o d e l (first p r o p o s e d b y S u d o et al., 1962) is in agreem e n t w i t h e x p a n d a b i l i t y m e a s u r e m e n t s , X R D analysis, a n d H R T E M i m a g i n g (e.g., R e y n o l d s , 1980; J i a n g et al., 1990; V e b l e n et al., 1990), a n d is s u p p o r t e d b y N M R s p e c t r o s c o p y ( B a r t o n et al., 1985; A l t a n e r et al., 1988; J a k o b s e n et al., 1995). O n the b a s i s o f t h e s e results, A l t a n e r a n d Y l a g a n ( 1 9 9 7 ) also f a v o r e d t h e p o l a r m o d e l a n d a s s u m e d this m o d e l to c o m p a r e the m e c h a n i s m s for s m e c t i t e illitization. F u r t h e r m o r e , the e n e r g i e s o b t a i n e d for the m i x e d layers . . . I S I S . . . a n d . . . I I S I I S . . . ( w i t h O0.sTI'TO0s units) are close to the c o r r e s p o n d i n g e n e r g i e s o f the t w o - p h a s e a s s e m b l a g e o f illite + s m e c t i t e (Tables 2 a n d 3). T h u s , the e n e r g y o f m i x i n g o f the t w o t y p e s o f layers is n e a r l y e q u a l to zero. W h e n the o c t a h e d r a l c o m p o s i t i o n s o f illite a n d s m e c t i t e are identical, i.e., for I1St a n d I282, note that the e n e r g y o f t h e m i x e d l a y e r is e q u a l to that o f the t w o - p h a s e a s s e m b l a g e o f illite + smectite. A s i m i l a r r e s u l t w a s o b t a i n e d for interstratified b i o t i t e - c h l o r i t e ( 0 l i v e s , 1985, 1986a). T h e stability o f i n t e r l a y e r e d illite-smectite is t h e n s i m i l a r to the stability o f an a s s e m b l a g e c o n t a i n i n g d i s c r e t e illite a n d smectite. T h i s r e s u l t m a y e x p l a i n the c o e x i s t e n c e o f illite, smectite, a n d interstratified i l l i t e - s m e c tite, w h i c h w a s o b s e r v e d in our s m e c t i t e - r i c h s a m p l e ( A m o u r i c a n d 0 l i v e s , 1991; also e.g., D o n g et aL, 1997). Summary of assumptions I Figure 5. Structure of the ordered mixed-layer illite-smect i t e . . . I S I S . . . as determined by the minimization of the lattice energy. The corresponding arrangement is . . . OM(TI'T)~OM(TI'T)s... (I', T, O = interlayer, tetrahedral, and octahedral regions, respectively; I, S, M = compositions of illite, smectite, and midway between at 0.5, respectively). T h e electrostatic E w a l d e n e r g y was c o n s i d e r e d as a first a p p r o x i m a t i o n to the lattice energy. E w a l d energies w e r e c a l c u l a t e d f r o m the o v e r l a p m e t h o d (Olives, 1986a, s e c t i o n 2.4.2) w h i c h p r o v i d e s r a p i d c o n v e r gence. F o r m a l c h a r g e s w e r e used. R a n d o m d i s t r i b u t i o n o f c a t i o n s i n e a c h o c t a h e d r a l , tetrahedral, or i n t e r l a y e r region was assumed. Identical coordinates were used for t h e structure o f illite, ( d e h y d r a t e d ) smectite, a n d interstratified i l l i t e - s m e c t i t e ( 1 M p o l y t y p e w a s ass u m e d for t h e t h r e e m i n e r a l s ) . S t r u c t u r e r e l a x a t i o n w a s neglected. T w o c o m p o s i t i o n s o f illite (I1, I2) a n d t w o c o m p o s i t i o n s o f s m e c t i t e (S1, $2) w e r e used. 288 Olives, Amouric, and Perbost Clays and Clay Minerals Table 3. Calculated Ewald energies of the mixed-layer structures corresponding to I'TOT units, TI'TO units, etc. (see Table 1), for the ordered layer sequence . . . I I S I I S . . . The last column gives the Ewald energy of the two-phase assemblage of illite + smectite with the same composition (i.e., 2 • energy of illite + energy of smectite). Various compositions of illite 01, I2) and smectite ($1, $2) were used (see text). Values are in MJ mo1-1 = 106 J tool ~ and refer to 36 oxygen atoms per molecule. The more stable interstratification structure (minimum energy) is based on O0.sTI'TO05 units. The energy of the mixed-layer 9 O0.sTI'TO0.5 units) is close to the corresponding energy of the two-phases illite + smectite assemblage. Compositions III1SI IlI1S2 I212S1 IzIzSz I'TOT units TI'TO units -243.0682 -242.5954 -242.2289 -241.7561 -243.1651 -242.6184 -242.2476 -241.8531 Interstratifiedsequence. . .IISIIS... I'0~TOTI'o.5units TosI'TOTo5 units -243.1223 -242.6495 -242.2830 -241.8103 Consequences f o r the smectite-to-illite solid-state mechanism In A m o u r i c and 0 l i v e s (1991), t w o illitization m e c h a n i s m s w e r e d e t e c t e d on the basis o f H R T E M observations: (1) d i s s o l u t i o n o f s m e c t i t e and crystallization o f illite, w h i c h p r o d u c e s 1M illite crystals, and (2) solid-state t r a n s f o r m a t i o n o f one s m e c t i t e layer to one illite layer, w h i c h leads to m i x e d - l a y e r illite-smecrite. This latter m e c h a n i s m was also s u p p o r t e d b y the H R T E M study o f M u r a k a m i et aL (1993). The t e r m " s o l i d - s t a t e " is u s e d h e r e in a b r o a d sense, b e c a u s e m a s s transport is o b v i o u s l y i n v o l v e d in such a transition. Thus, the t r a n s f o r m a t i o n occurs w i t h i n a solid, at the unit-cell scale, at the b o u n d a r y o f the n e w l y dev e l o p i n g layer and the r e a c t i o n is p r o b a b l y facilitated by the p r e s e n c e o f water. The m a j o r part o f the preexisting solid is p r e s e r v e d (e.g., V e b l e n and Buseck, 1980; Olives et al., 1983; E g g l e t o n and Banfield, 1985; A m o u r i c and 0 l i v e s , 1998). T h e interstratification d e t e r m i n e d b y the a b o v e calculations has important c o n s e q u e n c e s for this transformation: the m e c h a n i s m p r o b a b l y consists o f a lateral t r a n s f o r m a t i o n o f an O0.sTI'TO0.5 unit o f s m e c t i t e into the s a m e unit o f illite. The r e a c t i o n m o s t p r o b a b l y b e g i n s at the interlayer, I', b e c a u s e o f its h i g h ion and w a t e r - e x c h a n g e capacity, and p r o p a g a t e s to the t w o adjacent TO0.5 units. The reaction t h e n laterally runs along the layer so that an O0.sTI'TO0.5 unit o f smectite is p r o g r e s s i v e l y t r a n s f o r m e d into the s a m e c o r r e s p o n d i n g unit o f illite. ACKNOWLEDGMENTS We thank A. Inoue for providing the samples studied. We also acknowledge the helpful comments of S. Guggenheim, R Heaney, R. Cygan, and H. Dong. REFERENCES Ahn, J.H. and Peacor, D.R. 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