Mica Polytypes: Systematic Description and Identification

Ross, Malcolm; Takeda, Hiroshi; Wones, David R.

doi:10.1126/science.151.3707.191

Cited by 126 publications

(106 citation statements)

References 6 publications

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“…Since the building layer(s) are in principle identical, at least two of the three parameters ± those in the plane of the layer ± are identical. As in the case of triperiodic epitaxy (Royer, 1928(Royer, , 1954, a threedimensional common sublattice exists (allotwin lattice), whose cell is based on the two common parameters in the plane of the layer, the third one being the shortest parameter, outside the plane of the layer, common to the cells of both individuals.…”

Section: Derivation Of Allotwin Diffraction Patternsmentioning

confidence: 99%

“…expressed the relative rotations between the ®rst and the ( j 1)th individual as a sequence of n j (mod 60 ) integers. Those symbols are not space-®xed and in some respects are midway between the Z symbols and the rotational RTW symbols (Ross et al, 1966). The correspondence with Z T symbols is simply Z T 1 3; Z T j 1 3 n j .…”

Section: M Polytypementioning

confidence: 99%

“…Micas, through their polytypes, give one of the most complex series of inorganic structures known to date (Smith & Yoder, 1956;Ross et al, 1966;Takeda, 1967;Rieder, 1970;Takeda & Ross, 1995;. Micas often form twins but the presence of twinning is not always evident through a morphological analysis.…”

Section: Introductionmentioning

confidence: 99%

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Twins and allotwins of basic mica polytypes: theoretical derivation and identification in the reciprocal space

Nespolo¹,

Ferraris²,

Takeda³

2000

Acta Cryst Sect A

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The geometry of the diffraction pattern from twins and allotwins of the four basic mica polytypes (1M, 2M 1 , 3T, 2M 2 ) is analysed in terms of the`minimal rhombus', a geometrical asymmetric unit in reciprocal space de®ned by nine translationally independent reciprocal-lattice rows. The minimal rhombus contains the necessary information to decompose the reciprocal lattice of twins or allotwins into the reciprocal lattices of the individuals. The nine translationally independent reciprocal-lattice rows are divided into three types (S, D and X): rows of different type are not overlapped by the n Â 60 rotations about c Ã , which correspond to the relative rotations between pairs of twinned or allotwinned individuals. A symbolic representation of the absolute orientation of the individuals, similar to that used for layers in polytypes, is introduced. The polytypes 1M and 2M 1 undergo twinning by reticular pseudo-merohedry with ®ve pairs of twin laws: they produce twelve independent twins, of which nine can be distinguished by the minimal rhombus analysis. The 2M 2 polytype has two pairs of twin laws by pseudo-merohedry, which give a single diffraction pattern geometrically indistinguishable from that of the single crystal, and three pairs of twin laws by reticular pseudo-merohedry, which give a single diffraction pattern different from that of the single crystal. The 3T polytype has three twin laws: one corresponds to complete merohedry and the other two to selective merohedry. Selective merohedry produces only partial restoration of the weighted reciprocal lattice built on the family rows and the presence of twinning can be recognized from the geometry of the diffraction pattern.

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Section: Derivation Of Allotwin Diffraction Patternsmentioning

confidence: 99%

Section: M Polytypementioning

confidence: 99%

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Twins and allotwins of basic mica polytypes: theoretical derivation and identification in the reciprocal space

Nespolo¹,

Ferraris²,

Takeda³

2000

Acta Cryst Sect A

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“…However, Ramsdell & Kohn (1951) discovered that the trigonal polytype 10H of SiC exhibits a diffraction pattern which is strictly hexagonal, and Ross, Takeda & Wones (1966) found that the symmetry of the X-ray diffraction pattern of the triclinic modification 10Tc 3 of mica is strictly monoclinic. Sadanaga & Takeda (1968) then theoretically dealt with the latter example, confirmed that under certain conditions the point group G D of the diffraction pattern D can be monoclinic when the point group G x of the structure X is triclinic, and proposed 0567-7394/79/010115-08501.00 the term 'diffraction enhancement of symmetry' for the cases in which the symmetry of the diffraction pattern of a crystal becomes higher than the point-group symmetry of the crystal, other than as a result of Friedel's law.…”

Section: Introductionmentioning

confidence: 99%

Basic theorems of vector symmetry in crystallography

Sadanaga¹,

Ohsumi²

1979

Acta Cryst Sect A

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An attempt has been made to deduce the condition necessary for diffraction enhancement of symmetry to occur in the diffraction pattern of a structure X, and because the symmetry of the diffraction pattern of X coincides with that of its vector set V, the symmetric feature of X derived from the symmetry of V was studied. The symmetry with the point group G z or Gv/G,,, according as X is inversion-symmetric or not, is defined as the vector symmetry of X, where G V is the point group of V and G, is the inversion group, and when the vector symmetry of X is C n, for example, X is specified as C,-vector-symmetric. When X is homometric with itself by a rotation of 2z#n, it is specified as n-fold self-homometric. X being n-fold self-homometric is the necessary and sufficient condition for X to be n-fold vector-symmetric. Also, X exhibits an enhanced vector (diffraction) symmetry if it is a spacegroupoid structure with the kernel whose point-group symmetry is, other than by addition of an inversion, higher than the point-group symmetry of X. Four examples of enhanced vector symmetry are examined.

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“…The periodicity in reciprocal space has been used to solve the structure of zinkenite (PbS Á Sb 2 S 3 ) Sadanaga & Takeda, 1964;Takeda & Horiuchi, 1971) and to identify minerals with a mixed-layer structure (D'yakonov, 1962, 1963). It has been successfully applied to identify the stacking sequences of polytypes of micas (Takeda & Donnay, 1965;Ross et al, 1966;Takeda, 1967), of SiC (Tokonami & Hosoya, 1965;Tokonami, 1966) and of SiC and ZnS (Farkas-Jahnke, 1966;Dornberger-Schiff & FarkasJahnke, 1970;. The Fourier transform of SiC and of the ZnS unit is much different from the atomic scattering factors, and the periodicity is recognized without dif®culty.…”

Section: Identi®cation Of the Stacking Sequencementioning

confidence: 99%

Periodic intensity distribution (PID) of mica polytypes: symbolism, structural model orientation and axial settings

et al. 1999

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Following a preliminary revisitation of the nomenclatures in use for mica polytypes, the properties of the periodic intensity distribution (PID) function, which represents the Fourier transform of the stacking sequence, are analysed. On the basis of the relative rotations of neighbouring layers, mica polytypes are classi®ed into three types; for each type, the PID exists in different subspaces of the reciprocal space. A revised procedure to compute the PID, in which further restrictions on the structural model orientation are introduced, is presented. A unifying terminology based upon the most common symbols used to describe mica polytypes (RTW, Z and TS) is derived; these symbols represent the geometrical basis for the computation of the PID. Results are presented for up to four layer polytypes and are compared with the re¯ection conditions derived by means of Zvyagin's functions. Both the PID values and the re¯ection conditions are expressed in suitable axial settings and compared with previous partial reports, revealing some errors in previous analyses. A computer program to compute PID from the stacking symbols is available.

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Mica Polytypes: Systematic Description and Identification

Cited by 126 publications

References 6 publications

Twins and allotwins of basic mica polytypes: theoretical derivation and identification in the reciprocal space

Twins and allotwins of basic mica polytypes: theoretical derivation and identification in the reciprocal space

Basic theorems of vector symmetry in crystallography

Periodic intensity distribution (PID) of mica polytypes: symbolism, structural model orientation and axial settings

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