Enantiomorphism of kaolinite: Manifestation at the levels of elementary layer and microcrystals

The right and left forms of the argillaceous mineral kaolinite (Al₂ Si₂O₅(OH)₄), which is wide-spread in nature, have been revealed for the first time by transmission electron microscopy and gold decoration in vacuum. The enantiomorphic forms of this mineral are established at the level of the elementary 7 ? layer, which determines the kaolinite structure, and at the level of nano- and microcrystals typical of this mineral. Both kaolinite forms are widespread in ancient and young weathering crusts. Enantiomorphic kaolinite microcrystals are formed in two ways: through the periodic formation of 2D nuclei and via helical growth, which is dominant for both kaolinite forms. The right- and left-handed kaolinite forms are observed in the samples under study with equal probability.     

Polytypism in MX2 Compounds: A Case of Mixed Equilibrium Phases

Classical polytypism in MX₂-type compounds has been investigated. It has been established that polytypism can be understood, not as the case of independent stacking of A, B, or C layers but in terms of basic structural units, the most stable and only equilibrium phases of the given compounds. Other polytypes are formed only as a result of various equivalent positions that these units can take a given cell height. A criterion to predict whether a given compound would exhibit polytypism is also suggested. Several problems in applying ANNNI and other spin models to polytypism have been pointed out and a modified Hamiltonian is suggested.     

STGR Model and Relation between Growth Rate and Polytypism

Effect of crystal growth rate on polytypism has been explained using STGR model. It has been suggested that during the process of growth, polytypes are formed from a suitable combination of basic units in accordance with the rate of growth. At a slower rate the most probable polytype is predicted to be different from the one at faster rate.     

Effect of purification on the polytypism in solution-grown cadmium iodide crystals

The effect of purification on the polytypism in cadmium iodide crystals has been studied by X-ray diffraction in three hundred and sixty polytypes. Formation of small period polytype 2H is governed by both temperature and impurities contained in the starting material. 4H is the most stable polytype and higher occurrence of unidentified polytypes in crystals of purified material has been attributed to free movement of edge dislocations during growth. The results have been examined against empirical conclusions of earlier investigations.     

A Statistical Thermodynamics and Growth Restrictions (STGR) Model of Polytypism with Special Reference to Zinc Sulfide

A model to explain polytypism based upon classical statistics and the idea of minimum sandwiches of basic phases has been developed. Presence of two or more phases under suitable thermodynamic conditions and restrictions imposed by statistical, structural, and growth factors have been elaborated. A new statistical approach is used and a criterion to find most probable polytypes of a compound has been evolved. Logical implications of the model are found in good agreement with the experimental data.     

Polymorphic–polytypic transition induced in crystals by interaction of spirals and 2D growth mechanisms

The relationship between crystal polymorphism and polytypism can be revealed by surface patterns through the interlacing of the growth spirals. Simple high-symmetry structures as SiC, ZnS, CdI2 and more complex low-symmetry layered structures as n-paraffins, n-alcohols and micas are concerned with polymorphic–polytypic transition. In this paper, we will show for the first time, through in situ AFM observations and X-ray diffractometry, that a protein polymorph (P2₁2₁2₁α-amylase) locally changes, during growth, to a monoclinic P2₁ polytype, thanks to the screw dislocation activity. The interplay between spiral steps and 2D nuclei of the polytypes coexisting in the same crystalline individual allows to foresee the consequences on the crystal quality. The discussion is extended to other mineral and biological molecules and a new general rule is proposed to explain the interactions between surface patterns and the bulk crystal structure.     

Effect of an External Electric Field on Polytypic Growth of CdI2 Crystals from Solutions

The effect of an external steady electric field on polytypic growth of CdI₂ crystals was investigated. Crystals were grown at four temperatures: 5, 25, 35, and 50°C with the use of four solvents: H₂O, C₂H₅OH, 3 H₂O + 1 C₂H₅OH and 1 H₂O + 1 C₂H₅OH. The electric field of the intensity 500 to 2500 V/cm was oriented in two directions: perpendicular or parallel to the c-axis of hexagonal plates of CdI₂ crystals. The analysis of the effect of the field on polytypism of CdI₂ was based on the analysis of the structure of about 800 crystals grown in the presence of electric field and of about 1000 crystals grown in neutral conditions. It was established that the weak electric field used for crystallization of CdI₂ does not influence noticeably the relative stability of basic polytypes (2H, 4H) and of complex polytypic structures (ordered and disordered). The electric field may influence the structure of CdI₂ crystals in two ways: (i) the polytypes formed in the presence of the field have on average two times larger cells than the polytypes formed in neutral conditions, (ii) the polytypes formed in neutral conditions have usually hexagonal cells; only 6 to 30% of polytypes are of rhombohedral type. When the electric field was used the percentage of rhombohedral polytypes increased to about 65%.     

On the occurrence of polytypism in single crystal CdTe thin films

Cadmium telluride thin films have been found to exhibit polytypism. The polytypes are formed when the as grown amorphous CdTe thin films undergo amorphous to crystalline transformation. The transformed single crystal regions correspond to different polytypes. Besides the well known zinc blende type 3 C cubic phase and less often found wurtzite type 2 H phase, four new polytypes (5 H, 6 H, 6 R and 15 R) the only ones known to-date have been found in the present investigation. In addition to the new polytypes, a new structural variant has also been found. This has the same ‘c’ parameter as that of the 2 H phase but has its ‘a’ lattice parameter as ‘a₀ \documentclass{article}\pagestyle{empty}\begin{document}$ a_{\rm o} \sqrt {3} $\end{document}’ (a₀ being the common lattice parameter of the polytypes). A feasible mechanism making the formation of polytypes intelligible has been suggested.     

Investigation of the properties of weakly reflective metamaterials with compensated chirality

The properties of an artificial anisotropic structure formed by microhelices have been numerically simulated by the example of a specially designed sample. The sample contains paired helices with right- and left-handed twisting directions, due to which the metamaterial chirality is compensated for. Helices are characterized by precalculated optimal parameters; as a result, the permittivity and permeability of metamaterial are approximately equal. Therefore, the wave impedance of the structure is close to the impedance of free space in the frequency range near 2 THz and the reflection of normally incident electromagnetic waves is weak. A boundary problem is solved and an analytical expression is obtained for the reflection and transmission coefficients of an electromagnetic wave passing through the structure. The simulated properties of the structure are compared with experimental results.     

Were J. Kepler and O. Krötenheerdt right?

It is established that one of the 12 Kepler nets (R, 3366 + 3636) belongs to Krötenheerdt nets. However, the number of Kepler nets remains 12, because one of them (L, 33336) is enantiomorphic. Along with 20 Krötenheerdt nets, there may be many other polytypes which enter infinite sequences of the O, OD, DO, D types.     

Electron diffraction study of the structural features of kaolinites

The structural variations of kaolinites have been investigated based on oblique-texture electron diffraction patterns. The features of manifestation of the 2D lattice of kaolinite layers in the geometry of the 20l and 13l reflections have been revealed. The manifestation of violations in the regular alternation of layers in kaolinites in the diffraction patterns has been analyzed using a numerical simulation of the diffraction profiles along the first (02l, 11l) and second (20l, 13l) ellipses of oblique-texture electron diffraction patterns. The simulation was performed for finite sequences of ten layers using the statistical Markov model in the quasihomogeneous approximation. It is shown that oblique-texture electron diffraction patterns can be used to reveal the coexistence of two phases with different structural perfections and particle morphologies in kaolinite samples.     

Structure determination of polytypes (II)

In this part different methods for structure determination of polytypes with diffraction methods are described. These methods are applied to periodic polytypes consisting of one or more sorts of layers and to disordered polytypes consisting of one sort of layers. Furthermore an example for the determination of the structural principle is given.     

Crystal structure of nacrite from the electron diffraction data

The crystal structure of the nacrite mineral of the kaolin group (space group Cc; R = 2.76%; 634 unique reflections) is refined from the digital oblique-texture electron diffraction patterns obtained with the use of imaging plates. The maxima characterizing the locations and potentials of the hydrogen atoms of the hydroxyl groups are revealed from the difference Fourier-potential syntheses. The O-H interatomic distances and the angles of inclination of the O-H bond with respect to the ab plane are equal to 0.97 Å and ?18.3° for the inner hydroxyl group and 0.92, 0.85, 0.93 Å and 60.8°, 67.8°, 58.4° for the outer hydroxyl groups, respectively. The O_donor-O_acceptor interatomic distances are 2.940, 2.949, and 3.121 Å. It is established that the electrostatic potential distributions of the hydrogen atoms of the inner hydroxyl group and one of the outer hydroxyl groups located in the vicinity of the symmetry pseudoplane m of the layer are characterized by anisotropy, which can indicate a statistical distribution of these hydrogen atoms.     

Growth mechanisms,polytypism, and real structure of kaolinite microcrystals

The mechanisms of growth of kaolinite microcrystals (0.1–5.0 μm in size) at deposits related to the cluvial weathering crust, as well as to the low-temperature and medium-temperature hydrothermal processes of transformations of minerals in different rocks in Russia, Kazakhstan, Ukraine, Czechia, Vietnam, India, Cuba, and Madagascar, are investigated using transmission electron microscopy and vacuum decoration with gold. It is established that kaolinite microcrystals grow according to two mechanisms: the mechanism of periodic formation of two-dimensional nuclei and the mechanism of spiral growth. The spiral growth of kaolinite microcrystals is dominant and occurs on steps of screw dislocations that differ in sign and magnitude of the Burgers vector along the c axis. The layered growth of kaolinite originates from a widespread source in the form of a step between polar (+ and ?) dislocations, i.e., a growth analogue of the Frank-Read dislocation source. The density of growth screw dislocations varies over a wide range and can be as high as ～10⁹ cm^?2. Layered stepped kaolinite growth pyramids for all mechanisms of growth on the (001) face of kaolinite exhibit the main features of the triclinic 1Tc and real structures of this mineral.     

Desymmetrization of OD Structures

It has been shown that the symmetry and structure of individual OD layers may depend on their actual stacking in a (polytypic) OD structure, leading to significant deviations from the ideal OD symmetry. This phenomenon has been called “desymmetrization of OD structures”; its significance for polytypism and for crystallochemistry is discussed.     

Entropy Contribution and Stacking Fault Energy of CdI2 Polytypes

The CdI₂ material when is grown by using the different techniques under a same growth conditions shows a rich character in crystallization with several phases (polytypes). The exhibition of these polytypes has been explained here by following the Gibb's phase rule. Therefore, an effort has also been made to calculate the stacking fault energy of these polytypes.     

New schemes for recording electron diffraction patterns of hexagonal and monoclinic crystals

Some new schemes for recording electron diffraction patterns of hexagonal crystals rotating around the axes lying in the (hk0) plane of the reciprocal lattice and monoclinic crystals rotating around the a and b axes of the direct lattice and the a* axis of the reciprocal lattice have been developed. Formulas for interpreting electron diffraction patterns are reported. The electron diffraction patterns obtained based on these schemes were used to solve the 2H and 3R polytypes of CdInGaS₄ crystals and the 3R polytype of Zn_1.5In₃Se₆ crystal with the parameters a = 4.046 and c = 59.292 Å, sp. gr. R3m.     

Structure of SiC‐Quantum Wells Studied by TEM and CBED

Multi‐quantum well structures of 3C/4H‐SiC polytypes grown either on stepped or on on‐axis hexagonal SiC by molecular beam epitaxy have been investigated by conventional and high resolution TEM. The 3C‐SiC layers were nearly free of defects and the interface between different polytypes was abrupt. For the 3C‐SiC layers the strain state and the lattice parameters have been investigated to a high accuracy by convergent beam electron diffraction (CBED).     

Powder study of propanthioamide dervative C8H6N2S2

The crystal structure of 2‐cyano‐3‐(2‐thienyl)prop‐2‐enethioamide (C₈H₆N₂S₂), a propanethioamide derivative was solved from high resolution laboratory X‐ray powder diffraction data collected at ambient conditions. Structure determination was performed by means of the global optimization method of simulated annealing at a resolution of 1.5 Å. Rietveld refinement yielded an R_WP value of 4.02% (P2₁/a, a = 15.8174(2) Å, b = 5.6502(1) Å, c = 11.0952(1) Å, β = 116.9923(7)°, V = 883.6(5) ų, Z = 4). The molecules are stacked in parallel layers and are stabilized by hydrogen bonds. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)