Section 9.2.2.3. Examples of some polytypic structures

The basic concepts were introduced by Pauling (1930a), Pauling (1930b) and confirmed later by the determination of concrete crystal structures. A crystallochemical analysis of these became the basis for generalizations and systemizations. The aim was the understanding of geometrical reasons for the polytypism of these substances as well as the development of identification routines through the derivation of basic polytypes (9.2.2.2.3). Smith & Yoder (1956) succeeded first in deriving the six basic polytypes in the mica family.

Since the 1950's, two main schools have developed: in the USA, represented mainly by Brindley, Bailey, and their co-workers (for details and references see Bailey, 1980, 1988a; Brindley, 1980), and in the former USSR, represented by Zvyagin and his co-workers (for details and references see Zvyagin, 1964, 1967; Zvyagin et al., 1979). Both these schools based their systemizations on idealized structural models corresponding to the ideas of Pauling, with hexagonal symmetry of tetrahedral sheets (see later). The US school uses indicative symbols (Guinier et al., 1984) for the designation of individual polytypes, and single-crystal as well as powder X-ray diffraction methods for their identification, whereas the USSR school uses unitary descriptive symbols for polytypes of all mineral groups and mainly electron diffraction on oblique textures for identification purposes. For the derivation of basic polytypes, both schools use crystallochemical considerations; symmetry principles are applied tacitly rather than explicitly.

In contrast to crystal structures based on close packings, where all relevant details of individual (even multilayer) polytypes can be recognized in the section, the structures of hydrous phyllosilicates are rather complex. For their representation, Figueiredo (1979) used the concept of condensed models.

Since 1970, the OD school has also made its contribution. In a series of articles, basic types of hydrous phyllosilicates have been interpreted as OD structures of N > 1 kinds of layers: the serpentine–kaolin group (Dornberger-Schiff & Ďurovič, 1975a, b), Mg-vermiculite (Weiss & Ďurovič, 1980), the mica group (Dornberger-Schiff, Backhaus & Ďurovič, 1982; Backhaus & Ďurovič, 1984; Ďurovič, Weiss & Backhaus, 1984; Weiss & Wiewióra, 1986), the talc–pyrophyllite group (Ďurovič & Weiss, 1983; Weiss & Ďurovič, 1985a), and the chlorite group (Ďurovič, Dornberger-Schiff & Weiss, 1983; Weiss & Ďurovič, 1983). The papers published before 1983 use the Pauling model; the later papers are based on the model of Radoslovich (1961) with trigonal symmetry of tetrahedral sheets. In all cases, MDO polytypes (9.2.2.2.3) have been derived systematically: their sets partially overlap with basic polytypes presented by the US or the USSR schools. The OD models allowed the use of unitary descriptive symbols for individual polytypes from which all the relevant symmetries can be determined (Ďurovič & Dornberger-Schiff, 1981) as well as of extended indicative Ramsdell symbols (Weiss & Ďurovič, 1985b). The results, including principles for identification of polytypes, have been summarized by Ďurovič (1981).

The main features of polytypes of basic types of hydrous phyllosilicates, of their diffraction patterns and principles for their identification, are given in the following.

9.2.2.3.1.1. General geometry

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Tetrahedral and octahedral sheets are the fundamental, two-dimensionally periodic structural units, common to all hydrous phyllosilicates. Any tetrahedral sheet consists of (Si,Al,Fe³⁺,Ti⁴⁺)O₄ tetrahedra joined by their three basal O atoms to form a network with symmetry P(3)1m (Fig. 9.2.2.6a ). The atomic coordinates can be related either to a hexagonal axial system with a primitive unit mesh and basis vectors , , or to an orthohexagonal system with a c-centred unit mesh and basis vectors a, b . Any octahedral sheet consists of M(O,OH)₆ octahedra with shared edges (Fig. 9.2.2.6b), and with cations M most frequently Mg²⁺, Al³⁺, Fe²⁺, Fe³⁺, but also Li⁺, Mn²⁺ 0.9 Å, etc. There are three octahedral sites per unit mesh . Crystallochemical classification distinguishes between two extreme cases: trioctahedral (all three octahedral sites are occupied) and dioctahedral (one site is – even statistically – empty). This classification is based on a bulk chemical composition. A classification from the symmetry point of view distinguishes between three cases: homo-octahedral [all three octahedral sites are occupied by the same kind of crystallochemical entity, i.e. either by the same kind of ion or by a statistical average of different kinds of ions including voids; symmetry of such a sheet is ;⁶meso-octahedral [two octahedral sites are occupied by the same kind of crystallo­chemical entity, the third by a different one, in an ordered way; symmetry ; and hetero-octahedral [each octahedral site is occupied by a different crystallochemical entity in an ordered way; symmetry P(3)12]. The prefixes homo-, meso-, hetero- can be combined with the prefixes tri-, di-, or used alone (Ďurovič, 1994).

Figure 9.2.2.6| top | pdf | (a) Tetrahedral sheet in a normal projection. Open circles: basal oxygen atoms, circles with black dots: apical oxygen atoms and tetrahedral cations. Hexagonal and orthohexagonal basis vectors and symbolic figures (ditrigons) for pictorial representation of these sheets are also shown. (b) Octahedral sheet. Open and shaded circles belong to the lower and the upper oxygen atomic planes, respectively; small triangles denote octahedral sites. Triangular stars on the right are the symbolic figures for pictorial representation of these sheets: the two triangles correspond to the lower and upper basis of any octahedron, respectively.

A tetrahedral sheet (Tet) can be combined with an octahedral sheet (Oc) either by a shared plane of apical O atoms (in all groups of hydrous phyllosilicates, Fig. 9.2.2.7a ), or by hydrogen bonds (in the serpentine–kaolin group and in the chlorite group, Fig. 9.2.2.7b). Two tetrahedral sheets can either form a pair anchored by interlayer cations (in the mica group, Fig. 9.2.2.8a ) or an unanchored pair (in the talc–pyrophyllite group, Fig. 9.2.2.8b).

Figure 9.2.2.7| top | pdf | Two possible combinations of one tetrahedral and one octahedral sheet (a) by shared apical O atoms, (b) by hydrogen bonds (side projection).

Figure 9.2.2.8| top | pdf | Combination of two adjacent tetrahedral sheets (a) in the mica group, (b) in the talc–pyrophyllite group (side projection).

The ambiguity in the stacking occurs at the centres between adjacent Tet and Oc and between adjacent Tet in the talc–pyrophyllite group. From the solved and refined crystal structures it follows that the displacement of (the origin of) one sheet relative to (the origin of) the adjacent one can only be one (or simultaneously three – for homo-octahedral sheets) of the nine vectors shown in Fig. 9.2.2.9.

Figure 9.2.2.9| top | pdf | The nine possible displacements in the structures of polytypes of phyllosilicates. The individual vectors are designated by their conventional numerical characters and the signs +, −. The zero displacement 〈*〉 is not indicated. The relations of these vectors to the basis vectors a1, a2 or a, b are evident.

The number of possible positions of one sheet relative to the adjacent one can be determined by the corresponding NFZ relations (9.2.2.2.1). As an example, the contact (Tet; Oc) by shared apical O atoms, and the contacts (Oc; Tet) by hydrogen bonds, for a homo-octahedral case, are illustrated in Figs. 9.2.2.10(a) and 9.2.2.10(b), (c), respectively. The two kinds of sheets are represented by the corresponding symbolic figures indicated in Fig. 9.2.2.6. For Fig. 9.2.2.10(a): the symmetry of Tet is P(3)1m, thus N = 6; the symmetry of Oc is and its position relative to Tet is such that the symmetry of the pair is P(3)1m, thus F = 6 and Z = 1: this stacking is unambiguous.⁷ But, if the sequence of these two sheets is reversed, Z = 3, because N_Oc = 18 (h centring of Oc). For Figs. 9.2.2.10(b) and (c), Z = 3. Similar relations can be derived for meso- and hetero-octahedral sheets as well as for the pair (Tet; Tet) in the talc–pyrophyllite group.

Figure 9.2.2.10| top | pdf | The NFZ relations (a) for the pair tetrahedral sheet–homo-octahedral sheet (with shared apical O atoms), (b), (c) for the pair homo-octahedral sheet–tetrahedral sheet (by hydrogen bonds). The sheets are represented by their symbolic figures; some relevant symmetry elements are also indicated. One of the possible positions (labelled 1) is drawn by full, the other two (2, 3) by broken lines.

A detailed geometrical analysis shows that the possible positions are always related by vectors ±b/3. This, together with the trigonal symmetry of the individual sheets, leads to the fact that any superposition structure (9.2.2.2.5) is trigonal (also rhombohedral) or hexagonal, and the set of diffractions with k_ort 0 mod3) has this symmetry too. This is important for the analysis of diffraction patterns.

Some characteristic features of basic types of hydrous phyllosilicates are as follows:

The serpentine–kaolin group : The general structural principle is shown in Fig. 9.2.2.11 . The structures belong to category II (9.2.2.2.7.2). In the homo-octahedral family, there are 12 non-equivalent (16 non-congruent) MDO polytypes (any two polytypes belonging to an enantiomorphous pair are equivalent but not congruent); in the meso-octahedral family, there are 36 non-equivalent (52 non-congruent) MDO polytypes. These sets are identical with the sets of standard or regular polytypes derived by Bailey (for references see Bailey, 1980) (trioctahedral) and by Zvyagin (1967) (dioctahedral and trioctahedral). The individual polytypes can be ranged into four groups (subfamilies, which are individual OD groupoid families), each with a characteristic superposition structure. Figure 9.2.2.11| top | pdf | Stereopair showing the sequence of sheets in the structures of the serpentine–kaolin group (kaolinite-1A, courtesy Zoltai & Stout, 1985), The mica group : The general structural principle is shown in Fig. 9.2.2.12 . The structures belong to category IV. There are 6 non-equivalent (8 non-congruent) homo-octahedral MDO polytypes, 14 (22) meso-octahedral, and 36 (60) hetero-octahedral MDO polytypes. The homo-octahedral MDO polytypes are identical with those derived by Smith & Yoder (1956); meso-octahedral MDO polytypes include also those with non-centrosymmetric 2:1 layers (Tet; Oc; Tet); some of these have also been derived by Zvyagin et al. (1979). The individual polytypes can be ranged into two groups (subfamilies). For complex polytypes and growth mechanisms, see Baronnet (1975, Baronnet, 1986). Figure 9.2.2.12| top | pdf | Stereopair showing the sequence of sheets in the structures of the mica group (muscovite-2M1, courtesy of Zoltai & Stout, 1985). The talc–pyrophyllite group : The general structural principle is shown in Fig. 9.2.2.13 . The structures belong to category I. There are 10 (12) MDO polytypes in the talc family (homo-octahedral) and 22 (30) MDO polytypes in the pyrophyllite family (meso-octahedral); some of these have been derived also by Zvyagin et al. (1979). The structures can be ranged into two groups (subfamilies). For more details, see also Evans & Guggenheim (1988). Figure 9.2.2.13| top | pdf | Stereopair showing the sequence of sheets in the structures of the talc–pyrophyllite group (pyrophyllite-2M, courtesy of Zoltai & Stout, 1985). The chlorite–vermiculite group : There are two kinds of octahedral sheets in these structures: the Oc sandwiched between two Tet and the interlayer (Fig. 9.2.2.14 ). The structures belong to category IV. Any Oc can be independently homo-, meso-, or hetero-octahedral, and thus, theoretically, there are nine families here. Although vermiculites have a crystal chemistry different from chlorites, they can be, from the symmetry point of view, treated together. There are 20 (24) homo-homo-octahedral, 44 (60) homo-meso-octahedral and 164 (256) meso-meso-octahedral MDO polytypes (the first prefix refers to the 2:1 layer, the second to the interlayer); the other families have not yet been treated. Some of these polytypes have also been derived by other authors (for references, see Bailey, 1980; Zvyagin et al., 1979). Figure 9.2.2.14| top | pdf | Stereopair showing the sequence of sheets in the structures of the chlorite–vermiculite group (chlorite-1M, courtesy of Zoltai & Stout, 1985).

In order to preserve a unitary system, some monoclinic polytypes necessitate a `third' setting, with the a axis unique. These should not be transformed into the standard second setting.

The crystal structure of this mineral has been determined by Szymański (1980). It turned out to be identical with that of the compound of the same composition synthesized earlier (Darriet, Bovin & Galy, 1976). The structure is monoclinic with space group C12/c1, lattice parameters a = 17.989 (6), b = 4.7924 (7), c = 5.500 (2) Å, β = 95.13 (3)°.

Structural units are formed of SbO₂–O–VO–O–SbO₂ extended along a, with adjacent units bonded along c through Sb—O—Sb and V—O—V bonds. Ribbons are thus formed with no bonding along b, and only the Sb—O interactions [2.561 (4) Å] along a (Fig. 9.2.2.17 ). This accounts for the excellent acicular cleavage.

Figure 9.2.2.17| top | pdf | The structure of stibivanite-2M. The unit cell is outlined and some relevant symmetry operations are indicated (after Merlino et al., 1989).

Merlino et al. (1989) recognized in this structure sheets of VO₅ square pyramids (Pyr) parallel to bc, with layer symmetry alternating with sheets containing chains of distorted SbO₃ tetrahedron-like pyramids (Tet) with layer symmetry (Fig. 9.2.2.18 ). Owing to the higher symmetry of Pyr, they concluded that there may also exist an alternative attachment of Tet to Pyr, such that the triples (Tet; Pyr; Tet) will exhibit the layer symmetry , and they will be arranged so that another polytype 2O with symmetry (Fig. 9.2.2.19 ) is formed [in the original 2M polytype, the triples (Tet; Pyr; Tet) have the layer symmetry ]. A mineral with such a structure, with lattice parameters a = 17.916 (3), b = 4.700 (1), c = 5.509 (1) Å, has actually been found.

Figure 9.2.2.18| top | pdf | The two kinds of OD layers in the stibivanite family (after Merlino et al., 1989).

Figure 9.2.2.19| top | pdf | The structure of stibivanite-2O (after Merlino et al., 1989).

The polytypism of stibivanite is reflected in its OD character: the two kinds of sheets Pyr and Tet correspond to two kinds of non-polar layers: their relative position is given by the family symbol: the NFZ relations being Both polytypes are slightly desymmetrized. Since the shift between the origins of Pyr and Tet is irrational, stibivanite has no superposition structure and thus the diffraction patterns of its polytypes have no common set of family diffractions. Another remarkable point is that the recognition of these structures as OD structures of layers has nothing to do with their system of chemical bonds (see above).

Among about 40 investigated crystals synthesized by Carlson (1967), not one was periodic. All diffraction patterns exhibited a common set of family diffractions, but the distribution of intensities along diffuse streaks varied from crystal to crystal (Ďurovič, 1968). The maxima on these streaks indicated in some cases a simultaneous presence of domains of three periodic polytypes – one system of diffuse maxima was always present and it was referred to a rectangular cell with a = 9.328 (5), b = 16.28 (1), c = 9.081 (6) Å with monoclinic symmetry. All crystals were more or less twinned, sometimes simulating orthorhombic symmetry in their diffraction patterns.

The superposition structure with A = a, B = b/2, C = 2c and space group Pbmm was solved first. Here, a comparison of the family diffractions with the diffraction pattern of the α modification (Frueh & Gray, 1968) proved decisive. It turned out that only one kind of Hg atom contributed with half weight to the superposition structure. This means that only these atoms repeat in the actual structure with periods b = 2B and c = 2C. All other atoms (in the first approximation) repeat with the periods of the superposition structure and thus do not contribute to the diffuse streaks.

The symmetry of the superposition structures is compatible with the OD groupoid family determined from systematic absences: where the subscripts 1/2 indicate translational components of b/4 (Dornberger-Schiff, 1964, pp. 41 ff.).

The solution of the structural principle thus necessitated only the correct location of the `disordered' Hg atom in one of two possible positions indicated by the superposition structure. An analysis of the Fourier transform relevant to the above OD groupoid family showed that the Patterson function calculated with coefficients shows interatomic vectors within any single OD layer, and it turned out that even a first generalized projection of the function yields the necessary `yes/no' answer.

The structural principle is shown in Fig. 9.2.2.20 .

Figure 9.2.2.20| top | pdf | The structural principle of γ-Hg3S2Cl2. The shared corners of the pyramids are occupied by the Hg atoms; unshared corners are occupied by the S atoms. A pair of layers, but only the Cl atoms at their common boundary, are drawn. The two geometrically equivalent arrangements (a) and (b) are shown.

There are two MDO polytypes in this family. Both are monoclinic (c axis unique) and consist of equivalent triples of OD layers. The first, MDO₁, is periodic after two layers and has symmetry A2/m. The second, MDO₂, is periodic after four layers, has symmetry F2/m and basis vectors 2a, b, c. Domains of MDO₁ were present in all crystals (the system of diffuse maxima, mentioned above), but some of them also contained small proportions of MDO₂.

Later, single crystals of pure periodic MDO₁ were also found in specimens prepared hydrothermally (Rabenau, private communication). The results of a structure analysis confirmed the previous results but indicated desymmetrization (Ďurovič, 1979). The atomic coordinates deviated significantly from the ideal OD model; the monoclinic angle became 90.5°. Even the family diffractions, which in the disordered crystals exhibited an orthorhombic symmetry, deviated significantly from it in their positions and intensities.

When encountering a polytypic substance showing disorder, many investigators try to find in their specimens a periodic single crystal suitable for a structure analysis by current methods. So far, no objections. But a common failing is that they often neglect to publish a detailed account of the disorder phenomena observed on their diffraction photographs: presence or absence of diffuse streaks, their position in reciprocal space, positions of diffuse maxima, suspicious twinning, non-space-group absences, higher symmetry of certain subsets of diffractions, etc. These data should always be published, even if the author does not interpret them: otherwise they will inevitably be lost. Similarly, preliminary diffraction photographs (even of poor quality) showing these phenomena and the crystals themselves should be preserved – they may be useful for someone in the future.