A New polytype notation for CdI2 type structures. The thr symbols

The thr notation is introduced to describe any stacking variant as a mixture of fractions of the three simplest or regular polytypes: 2H (trigonal), 4H (hexagonal), and 6R (rhombohedral). The new notation is compared with existing ones and applied to pairs of homometric structures and to the characterization of stacking faults.     

A Comparative Study of Existing Polytype Notations with Reference to the CdI2 Polytypes

Existing polytype notations have been critically examined to select a single notation which can describe the CdI₂ structures completely and most conveniently. A comparative study shows that the Zhdanov notation fulfils both the conditions. However, the ambiguities in the similar looking symbols is removed by employing some simple criteria proposed by Jain and Trigunayat for deciding the equivalent structures. Further, being numerical in nature this is the easiest notation to handle.     

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.     

Complex (nonstandard) six-layer polytypes of lizardite revealed from oblique-texture electron diffraction patterns

Association of simple (1T and 3R) and two complex (nonstandard) orthogonal polytypes of the serpentine mineral lizardite from the Catoca kimberlite pipe (West Africa) association is revealed from oblique-texture electron diffraction patterns. A six-layer polytype with an ordered superposition of equally oriented layers (notation 3₂3₂3₄3₄3₆3₆ or ++??00) belonging to the structural group A and a three-layer (336 or I,I,II) or a six-layer (336366 or I,I,II,I,II,II) polytype with alternating oppositely oriented layers and semi-disordered structure are identified using polytype analysis.     

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.     

Homometric polytypes

A new theorem on homometric polytypes is presented. Examples of homometric close-packed structures and MX₂-polytypes are given. The method derived may be used to construct homometric n-tuplets by means of decomposition procedures.     

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%.     

Zn1−xCdx polytype single crystals with various degree of order

The results of X-ray investigations of the polytype structures formed in solid solutions of Zn_1–xCd_xSe are presented. For compositions of 0.22 < x < 0.35 polytypes 8H, 6H, 4H, and DS (disordered structure) are present. The Zn_1–xCd_xS single crystals of 0 ≦ x ≦ 0 were obtained by Bridgman's method under high protective argon pressure from the melt. The structures are characterised by FARKASZ -JAHNKE statistical parameters π(m,p), and by parameters P_LH of the polytype unit cell formation probability.     

Polytypes of the system Fe1−xS

The structures of Fe_1−xS (0 < x < 0.135) are members of a family of derivative structures in the sense of Megaw. The NiAs structure as aristotype is the simplest and most symmetrical member of this family. The other polytypes of Fe_1−xS may be derived as hettotypes by lowering the symmetry. The loss of symmetry in changing from the aristotype to the hettotype may be of various kinds: small displacements of Fe and S atoms from the NiAs positions and/or Fe vacancies in some atomic planes occur. The structures of the system Fe_1−xS are interpreted as OD structures consisting of OD layers. The symmetry relations of the structures of FeS and Fe₇S₈ are described by OD groupoid families. Polymorphism, twinning and stacking faults are explained on this basis.     

Preparation and properties of ferroelastic/ferroelectric polytypes of antimony(III) oxide iodine,Sb5O7I

Antimony oxide iodide, Sb₅O₇I (?7Sb₂O₃.SbI₃), is monoclinic and exists in at least 8 polytypic modifications. Crystals of these (transparent, pseudohexagonal prisms up to 15 × 10 × 5 mm³) were grown by vacuum sublimation and identified by optical and X-ray methods. Depending on the stacking sequence of characteristic slabs of antimony and oxygen in the (monoclinic) b-direction, centric and acentric polytypes result. The former show pure ferroelastic, the latter combined ferroelastic + ferroelectric behaviour. All polytypes transform reversibly into hexagonal, nonferroic phases at characteristic Curie temperatures between 165 and 208°C. The crystals can assume one of the three stable orientation states which may be mutually switched into each other by successive application of comprehensive stress (of the order of 10⁶ N/m²) on the three pairs of prism faces. In the ferroelectric polytypes the spontaneous polarization (about 5 × 10^-3 C/m²) is not reversible but only reorientable by ± 120° by coercive fields in the order of 2–5 kV/cm. Ferroelectricity and ferroelasticity are fully coupled.     

On the Structural and Electronic Characteristics of Titanium Sulphide (Tis1.7) Crystals

TiS_1.7 crystals have been grown by vapour transport technique employing a two-zone furnace with the temperatures of reaction and growth zone maintained at 1073 K and 973 K, respectively. We have measured the variation of electrical conductivity (s̀) with temperature (T) of TiS_1.7 single crystals. It has been found that the conductivity increases at temperatures T > 433 K, which provides convincing evidence that the TiS_1.7 crystal is a semiconductor. Another electronic characteristic of TiS_1.7 crystals observed in the present investigation is the occurrence of voltage controlled negative resistance (VCNR) at a field of 32.1 V cm^-1 to 35.7 V cm^-1. All the polytypes of TiS_1.7 were found to exhibit VCNR nearly at the same field which indicates that the VCNR is polytype independent property. The occurrence of VCNR has been explained on the intervally transfer of electrons in the conduction band.     

3D-graphite structure

The structure of clusters of some new carbon 3D-graphite phases have been calculated using the molecular-mechanics methods. It is established that 3D-graphite polytypes α_{1, 1}, α_{1, 3}, α_{1, 5}, α_{2, 1}, α_{2, 3}, α_{3, 1}, β_{1, 2}, β_{1, 4}, β_{1, 6}, β_{2, 1}, and β_{3, 2} consist of sp ²-hybridized atoms, have hexagonal unit cells, and differ in regards to the structure of layers and order of their alternation. A possible way to experimentally synthesize new carbon phases is proposed: the polymerization and carbonization of hydrocarbon molecules.     

Solvent effect on the polytype structure of CdI2 crystals

Single crystal platelets of cadmium iodide have been grown from alcohols: n-propyl, isobutyl and isoamyl and from their aqueous solutions. The structures of 880 crystals has been identified and the effect of solvent on the polytype structure of CdI₂ has been discussed regarding: the stability of the basic structures 2H and 4H, the structure of complex polytypes, the effect of the solvent on the structure of faults, the period of polytypes. Some relations indicating the role of the solvent in the formation of polytype structure of CdI₂ have been found.     

Studies on syntactically coalesced Silicon Carbide polytype structures

The structure of two new silicon carbide polytypes, found in syntactic coalescence with a basic structure 6 H, have been worked out. The structure of polytype 21 H is [(33)₂63] and that of polytype 93R is [(33)₄34]₃. The polytype 93R belongs to the structure series [(33)_n34]₃. One of the (00.1) growth face reveals the growth spiral. The splitting of diffraction spots indicates the existence of a high period polytype in the crystal. This high period polytype have been identified as 558H or 1674R. The growth mechanism have been discussed in the light of above observations.     

Local lattice strains in the system of cubic Zn0.999Fe0.001S x Se1 − x (0 ≤ x ≤ 1) crystals

The structure of cubic Zn_0.999Fe_0.001S _x Se_{1 ? x} (0 ≤ x ≤ 1) crystals obtained by vapor-phase chemical transport has been investigated by thermal-neutron diffraction. The diffraction patterns of these crystals are found to exhibit previously unknown diffuse-scattering effects related to local static atomic displacements in the metastable fcc lattice. It is substantiated that the tendency to form polytypes, which is characteristic to a greater extent of zinc sulfide, can be a key factor of instability in the lattice of compounds belonging to the series of anion-substituted solid solutions under study.     

Lorentz and polarization factor correction in the structure determination of cadmium iodied polytypes

An error in the application of Lorentz and polarization factor correction to the structure determination of cadmium iodide polytypes, so far overlooked by earlier workers, has been pointed out. Attention has been drawn to the fact that the intensities for 10 · l spots should be calculated for the range l = 2n to 4n, instead of the range l = 0 to 2n, employed until now.     

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.     

A narrow process window for the preparation of polytypes of microcrystalline silicon carbide thin films by hot-wire CVD method

Effects of deposition conditions on the structure of microcrystalline silicon carbide (μc-SiC) films prepared by hot-wire chemical vapor deposition (hot-wire CVD) method have been investigated. It is found from X-ray diffraction patterns of the film that a diffraction peak from crystallites from hexagonal polytypes of SiC is observed in addition to those of 3 C-SiC crystallites. This result is obtained in the film under a narrow deposition conditions of SiH₃CH₃ gas pressure of 8 Pa, the H₂ gas pressure of 80–300 Pa and the total gas pressure of 40–300 Pa under fixed substrate and filament temperatures employed in this study. Furthermore, the grain size of hexagonal crystallites (about 20 nm) on c-Si substrates becomes larger than that of 3 C-SiC crystallites (about 10 nm) for the films deposited under the total gas pressure of 36–88 Pa. The fact that microcrystalline hexagonal SiC can be deposited under limited deposition conditions could be interpreted in the context of a result for c-SiC polytypes prepared by thermal CVD method.     

Prediction of the structures in the family of La(IO<Subscript>3</Subscript>)<Subscript>3</Subscript> iodates based on topology and symmetry analysis within the OD theory

Topology and symmetry analysis of the structures of the La (IO₃)₃ family is performed within the Dornberger-Schiff OD theory. Two-dimensional periodic blocks (“layers”) of two types are found in the monoclinic La (IO₃)₃ iodate; the local symmetry of one of these blocks is higher than the symmetry of the structure as a whole. This feature defines the possibility of varying the relative position of the pairs of “layers” and the existence of structures other than the structure studied. Three hypothetical polytypes with the maximum degree of ordering that belong to different crystal systems (triclinic, monoclinic, and trigonal) and disordered structures are predicted by the OD theory. This example demonstrates the possibilities of the OD theory for predicting structures.