Massimo Nespolo

Effects of the stacking faults on the calculated electron density of mica polytypes — The urovič effect

The occurrence of residues in the Fourier map of OD structures (polytypes in which pairs of building modules are geometrically equivalent) in the positions of the ‘virtual atoms9 of the corresponding family structure derives from the presence of stacking faults inside an otherwise ordered (periodic) matrix. These residues are commonly spurious peaks deriving from the refinement of the structure with a single scale factor for both the family and the non-family reflections, which may be instead on a different scale because of the different peak shape and background characterizing the two types of reflections, resulting in broadening and streaking of the non-family reflections. The ‘virtual atoms9 occur in the same positions of the atoms corresponding to the stacking faults, but the spurious peaks are in a quantitative relation with them only if the stacking faults diffract coherently. The case of mica polytypes is illustrated also with the aid of examples taken from the literature.

The oriented attachment mechanism in the formation of twins - a survey

The direct and indirect evidences for the oriented attachment of pre-formed crystals as a mechanism of twin formation are reviewed and discussed. Although rarer than the nucleation-stage formation, this mechanism, often overlooked, has been demonstrated in laboratory experiments, with the artificial production of twins. Moreover, the role of the oriented attachment in the formation of natural twins, although more likely to occur in environments where crystals are free of moving and interacting, is supported also by the occurrence of monoperiodic twins and of plesiotwins, whose origin cannot be explained by a nucleation-stage formation. The so far observed absence of diperiodic twins is discussed in terms of two-dimensional site-coincidence and twin obliquity.

Twinning by syngonic and metric merohedry. Analysis, classification and effects on the diffraction pattern

Twinning by merohedry involves crystals whose point group is a subgroup of the lattice symmetry. The case of crystals with a metric symmetry higher than the syngony, not considered in the previous classifications of twinning, is here analysed in terms of group-subgroup relations and pseudo-symmetry. Merohedry is classified into syngonic merohedry and metric merohedry, depending on whether the crystal lattice symmetry is equal to or higher than the syngony. It is shown that the metric merohedry corresponds to the degeneration of the pseudo-merohedry to zero obliquity, or to the degeneration of the reticular merohedry to twin index 1. A revised classification of merohedry into three classes, on the basis of the symmetry of the twin, is given. Class I includes twins in which the twin operation belongs to the Laue point group of the individual. Class IIA includes twins in which the twin operation belongs to the syngony of the individual but not to its Laue point group. Finally class IIB includes twins in which the twin operation does not belong to the syngony of the individual. The effect of the classes of twins onto the diffraction pattern is discussed.

Twin point groups and the polychromatic symmetry of twins

Abstract A new classification in terms of the number of independent twin elements is introduced and exploited to analyze the symmetry of multiple twins. The dichromatic point group description of twins is revised showing that, contrary to what stated in the previous literature, all the 58 dichromatic point groups represent the possible symmetry of some twins. This approach is extended in terms of polychromatic point groups and applied to some examples from the recent literature.

Applied geminography: symmetry analysis of twinned crystals and definition of twinning by reticular polyholohedry

The common classification of twinning into the four categories of twinning by merohedry (complete and exact overlap of the lattices of the twinned crystals), pseudomerohedry (complete but approximate overlap), reticular merohedry (partial but exact overlap) and reticular pseudomerohedry (partial and approximate overlap) is revised in terms of the complete (translational and point) lattice symmetry of the twin and of the individual. The new category of reticular polyholohedry is introduced for twins where the twin lattice has the same point symmetry but a different orientation of the individual lattice. It is shown that the degeneration to twin index 1 relates, in a parallel way, reticular merohedry to metric merohedry and reticular polyholohedry to syngonic merohedry. Some examples from the recent literature are analysed in terms of this revised classification.

First occurrence of a stacking sequence including (+ or -60 degrees , 180 degrees ) rotations in Mg-rich annite

Transmission electron microscopy (TEM) observation shows narrow regions in a Ti-containing Mg-rich annite of composition (K0.90Na0.02)(Mg0.72Fe2+1.78Mn0.03Ti0.27Al0.05)(Si2.77Al1.23)O10(OH,F)2 from a granitic rock, where the ±60° and 180° stacking angles occur extensively. These regions are a few hundreds of nanometers thick along the [001]* direction and are within 1M or 2M1 annite. The stacking sequence in one of these regions was determined by two atomic-resolution images recorded along [1̄10] and [010] of the same crystal. Stacking sequences with ± 120° or 180° rotations are dominant, although those with ±60° rotations occur also. Locally 2O and more complex sequences exist. Compositional analysis by TEM indicated no difference in the chemical compositions between these regions and the adjacent ones with regular 1M or 2M1 stacking sequence. The origin of these unusual stacking sequences in annite is discussed.

Geminography: the crystallography of twins

Abstract The geometric theory of twinning was developed almost a century ago. Despite its age, it still represents the fundamental approach to the analysis and interpretation of twinned crystals, in both the direct and the reciprocal space. In recent years, this theory has been extended not only in its formalism (group-subgroup analysis, chromatic symmetry) but also in its classification of special cases that were not recognized before. The geometrical theory of twinning is thus reviewed here with emphasis on lattice aspects and recent developments. The classification of various types of twins starts with Friedel’s well-known scheme, which distinguishes four cases according to whether the twin index n is equal to or larger than 1 and whether the obliquity ω is equal to or larger than 0: the computation of these quantities is discussed in detail. It is shown that the concept of obliquity is not sufficient to characterize the pseudo-symmetry of a lattice, and the consequent twinning, in the case of manifold twins. The application of the theory of coincidence-site lattices to twinning is presented. Finally, the effect of twinning on the diffraction pattern is illustrated with a number of examples.

Twins vs. modular crystal structures

Abstract The crystallographic nature of modular structures is analysed and discussed in terms of their symmetry and structure building operations. The modular crystal structures we discuss in this paper are homogeneous edifices, built by one or more types of modules related by a point-space operation, and the whole structure is described by an ordinary three-dimensional triperiodic space group. Because the term “twin” is often used, with or without modifiers, to describe symmetry operations that act as building mechanisms in modular structures, a comparison is made with twins, that are instead heterogeneous edifices, described not by a space group but by a (polychromatic) point group, where the individuals are related by operations in the vector space. A unifying scheme is proposed where the passage from heterogeneous to homogeneous structures, only apparently justified by a change of dimensions of the individuals, implies a change of space where the operations are defined.

A TEM study of long-period mica polytypes: determination of the stacking sequence of oxybiotite by means of atomic resolution images and Periodic Intensity Distribution (PID)

In this study it is shown that the stacking sequences in long-period mica polytypes (including a rare example of a mixed-rotation polytype, with a 36-layer long periodicity) can be unambiguously determined using atomic resolution images recorded down two zone axes separated by 30 degrees (e.g. [100] and [31;0]) at the same area. Uniformity of these stacking sequences in a large area is further confirmed by the correspondence between computed and observed Periodic Intensity Distributions (PIDs) in electron diffraction patterns. The appearance of long-period polytypes containing layers with different orientation parity may be explained by the coalescence of two small crystals during crystal growth.

First structure determination of an MDO-2 O mica polytype associated with a 1 M polytype

The structure refinement of associated phlogopite-2 O and phlogopite-1 M from the Khibiny massif (Kola Peninsula, Russia) is reported. Crystal data are: α = 5.2781(5), b = 9.141(1), c = 20.124(4) A, Ccmm (20); a = 5.305(2), b = 9.199(2), c = 10.232(4) A, β = 100.03(2)°, C 2/m (1 M ). Least-squares refinement of single-crystal X-ray diffraction data converged to R1 = 0.034 (2 O , 926 independent reflections) and 0.037 (1 M , 677 independent reflections). This is the first structure refinement of an MDO (standard) mica-2 O : two previous structure reports concerned anandite-2 O , which was not a true polytype, having an oP (primitive orthorhombic) lattice not compatible with the C -centred cell common to all mica polytypes. The two phlogopite polytypes show practically the same chemical composition (K 0 . 95Na 0.01 ) (Mg 2.16 Fe 0.34 Ti 0.04 Mn 0.04 Li 0.40 )[Si 3.40 Al 0.60 O 10 ][(OH) 1.35 F 0 .65] and no cation ordering. Both polytypes are affected by stacking disorder, which broadens the non-family reflections ( k ≠ 3n). As a consequence, the diffracted intensities of the two types are measured at different scales and large residues in the difference Fourier maps were observed at ± b /3 along [010], [310] and [310]. These residues ( uroviceffect ) disappear by carrying out the refinement with separate scale factors for the two types of reflections. On the basis of structural, morphology and zoning considerations the formation of the two associated polytypes is attributed to chemical oscillation in the crystallization mean.