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The inhomogeneous (complex) polytype 3M 2 of finely dispersed muscovite with the structure formed by layers with different parity of azimuthal orientations (561) or relative rotations $$[11\bar 2]$$ was identified for the first time using the oblique-texture electron diffraction patterns. The specimen had no rigorous order in layer alternation, which is reflected in the distortion of the reflection positions and intensities. It is shown that the most probable defects reduce to the replacement of the layer orientations characteristic of the 3M 2 polytype by layer orientation characteristic of the 2M 2 polytype. This fact indicates that, under certain conditions, the prismatic coordination of interlayer cations in micas is preferable.

Being an independent method of structure analysis, electron diffraction provides original data which are essential contributions to all the fields where this method is used. An important place of electron diffraction among other structural methods is illustrated by the results of the studies once started on clay minerals and continued on the objects extremely important for structural mineralogy, which stimulated the development of a new field—modular crystallography.

The nomenclature of phyllosilicates is discussed in relation to structural variations of layers and interlayers. Some discrepancies in the nomenclature which arose due to historical reasons and different viewpoints may be reconciled if the choice of the construction units (layers or their parts) is related to definite sets of structures for which these units are common. Features of idealized models approximating real structures should be considered for classification and derivation of nomenclature sets, whereas priority is given to structural variations before lattice and symmetry characteristics. Layer polymorphs, pseudopolytypes, polytypes (both simple and complex), and OD structures are distinguished. Particular results obtained for micas as a model example of phyllosilicates in relation to modular structures in general are considered in an Appendix.

Layer stackings in the ideal and real kaolinite structures are considered in terms of layer orientations i = 1, 2 .... 6, intra- and interlayer displacements of adjacent 0- and T-sheets, si and t k, distortions of these displacements ~1 and ~2, deviations of unit cell parameters "q~ = bEi/a2 i - 3, E i = ~/i - �9 r/2, and normal projections c~ of the axis vector c on the ab plane. The ideal monoclinic angle of dickite (Cnx = -1A) and the deviation ct - ~r/2 ~ 0 for kaolinite are explained by combinations of the ~1 and ~2 values in the sequence of symbols si and t k defining the corresponding structures. Twenty stacking variants in the 3 successive layers of the kaolinite structure are derived, incorporating layer orientations of the same parity, displacements t+, = (0, -+ ~5) and reflection operations in planes normal to the axis b 3. Two deformation mechanisms are proposed for the accom- modation of successive layer unit cells adjusting either angular or linear parameters at the agreement of either linear or angular parameters corresponding.

Oxyborate structures are considered as being built of two types of order-disorder (OD) layers which serve as building modules, which explain the formation of different structural modifications, both homogeneous maximum degree of order (MDO) and inhomogeneous (periodic and aperiodic), lattice and diffraction features. Stacking faults are a direct consequence of the OD nature of the building modules

Polytypism is considered in relation to other notions of crystal substances composed of definite building modules according to the proposed systematics of modular structures. For a given choice of building modules there is a hierarchic sequence of notions: modular structures—polysomes, monosomes—hybrids—polytypes—OD structures.

The modular approach (MA) is applied to the system composed of Ca2SiO4-, Ca(OH)2- and Ca4Si3O10-building units (BU) shortly designed by letters S, P and T (corresponding to the names of substances having the same compositions: shannonite, portlandite and triorthosilicate). Symbols n, u, [unk], ū, b, d, p, q, (n[unk]), (ūu), S, Z are used for notation of the BU's and their sequences, formulation of the stacking rules and derivation of structures satisfying the homogeneity condition. The latter form a basis for the analysis of inhomogeneous structures as series members between the homogeneous structures for which functional variations of properties and formation conditions may be constructed.

The first section of this chapter concerns scattering factors for the diffraction of electrons by crystalline solids. An explanation of the theory of scattering by a perfect crystal is followed by a discussion of the kinematical, two-beam and phase-grating approximations. Relativistic and absorption effects are considered. Extensive tables of atomic scattering amplitudes for electrons for neutral and ionized atoms are presented. The second section of the chapter briefly discusses the parameterization of electron atomic scattering factors. Tables of useful parameters as a function of accelerating voltage and elastic atomic scattering factors for neutral atoms are given. Complex scattering factors for the diffraction of electrons by gases are discussed in the third section of the chapter. This section includes tables of scattering factors of interest for gas-phase electron diffraction from atoms and molecules in the keV energy region. In addition to the tables and a description of their uses, a discussion of the theoretical uncertainties related to the material in the tables is also provided. The tables give scattering factors for elastic and inelastic scattering from free atoms. The theory of molecular scattering based on these atomic quantities is also discussed. Electron energy-loss spectroscopy on solids is discussed in the fourth section of the chapter. Topics covered include: the use of electron beams; single and multiple scattering; the classification of the different excitations in a spectrum; instrumentation; and the excitation spectra of valence and core electrons. The fifth section of the chapter describes oriented texture patterns. Lamellar and fibre texture patterns are discussed and applications to metals and organic materials are mentioned. The computation of dynamic wave amplitudes in then described in the sixth section of the chapter. This section deals first with the multislice method. The numerical procedure is outlined and factors that influence the choice of thickness of the slice are discussed. Two checks that can be performed during a multislice calculation are noted. The Bloch-wave method is then described. The use of Bloch waves to describe electron diffraction and electron imaging in thin crystals is outlined together with the concept of the dispersion surface. These emerge as natural solutions of the Schrodinger equation with a periodic optical potential to generate the elastic scattering and also the loss of intensity from the coherent wave field due to thermal diffuse and inelastic scattering. The Bloch-wave approach is a useful complement to the multislice method and provides a clear picture of wave propagation in perfect and imperfect crystals. In the seventh section of the chapter, the measurement of structure factors and the determination of crystal thickness by electron diffraction are described. The use of convergent-beam electron diffraction to obtain integrated intensities is discussed and the relationship between intensity features and the dispersion surface is explained. The last section of the chapter concerns crystal-structure determination by high-resolution microscopy. This technique allows the arrangement of atomic columns in thin crystals to be observed directly. The resolution of the best instruments is now slightly below 0.1 nm. The images usually show a projection through a slice of crystal about 20 nm thick, however tomographic (three-dimensional) reconstruction is now possible at nanometre resolution. The images show the host of microphases, grain boundaries, twins, line and planar defects which broad-beam methods, such as X-ray diffraction, provide the average scattering from. These defects often control the properties of crystals, engineering materials and electronic devices. Individual nanostructures, such as carbon nanotubes and catalyst particles, may be imaged at atomic resolution. Fine twinning, polytypes, intergrowth of oxide phases etc. can be identified, and increasingly the detailed atomic structure of defects (such as oxide, superconductor and semiconductor interfaces) is being determined. Substitutional dopant atoms have recently been imaged for the first time. In biology the method is limited by radiation damage; however by summing many images of identical randomly oriented macromolecules, tomographic density maps can be reconstructed at subnanometre resolution from hydrated proteins which cannot be crystallized (e.g. membrane proteins). This section reviews the theoretical principles of high-resolution electron microscopy, including few-beam and structure image formation, effects of electron-optical lens aberrations, partial coherence, resolution-limiting factors, image-simulation methods, dynamical effects, and a summary of super-resolution schemes. Keywords: absorption; atomic scattering amplitudes; atomic scattering factors; Bethe theory; Bloch-wave method; core-electron spectroscopy; core-loss spectroscopy; crystal thickness; crystalline solids; dielectric description; dynamical diffraction; dynamical wave amplitudes; EELS; elastic scattering; electron diffraction; electron energy-loss spectroscopy; electron microscopy; electrons; free-electron gas; high-resolution electron microscopy; HREM; hyper-resolution; inelastic scattering; lamellar textures; lattice-fringe images; molecular scattering factors; multiple scattering; multislice method; oriented texture patterns; plasmons; real solids; relativistic effects; STEM; scanning transmission electron microscopes; scattering factors; solid-state effects; spectrometers; structure factors; surface plasmons; texture; wave amplitudes; X-ray diffraction

Conditions for observation of GS bands for the 137 space groups exhibiting these extinctions

The various modular approaches to the structure type of sapphirine are presented and discussed. Like biopyriboles sapphirine is built up by TOT rod modules (where T stands for tetrahedral chains and O for octahedral ribbons) which are connected as the corresponding modules in biopyriboles. Two distinct orientations (S, Z) of the modules are possible; their structures and stacking ways are constrained by the condition of cubic close packing of oxygen atoms. The various possible stacking ways are presented and the homogeneous sequences are indicated. The order-disorder (OD) character of sapphirine is discussed in terms of one kind of OD layers, with presentation of the OD groupoid family and indication of the structures with maximum degree of order (MDO structures), as well as in terms of two kinds of layers, namely as a regular alternation of slices 〈P〉 and 〈S〉 cut from the structures of pyroxene and spinel, respectively. Finally, the diffraction features of sapphirine are discussed in relation to the different modular approaches.

A crystal with its strictly periodic atomic structure represents a natural, very symmetrical three-dimensional diffraction grating for wavelengths of the order of the interatomic distances. Crystal structure analysis is thus based on the theories of symmetry (space groups) on the one hand and of interaction of radiation with solids (diffraction) on the other. The diffraction techniques, with the help of extensive computer calculations, lead to the atomic arrangements of crystalline materials. Depending on the problem. X-rays, electrons, or neutrons are used, which provide the electron-density, electrostatic potential density and nuclear density (also magnetic spin density) distribution, respectively, in a crystal.

The crystalline state of matter is realized by a perfectly periodic atom distribution in space and, as a rule, is thermodynamically stable. Natural and artificial crystals, however, contain defects. Modulated structures can be regarded as a variety of defect structures. The term modulated structure is used to describe any periodic or partly periodic perturbation of a crystal structure with a repetition distance greater than basic cell dimensions. The number and variety of the known structural modulations is large. They can be commensurate or incommensurate depending on a multiple or nonmultiple relation between basic and perturbated unit cell dimensions. A modulation can be longitudinal or trans-versal, of a displacement or substitution, sinusoidal or triangular, or presented by their combination (Fig. 14a, b). One can see in the reciprocal space (in X-ray or electron diffraction patterns) strong spots from the starting structures satellites (Fig. 14b, bottom). Distances between main (strong) reflections and satellites are multiple for a commensurate case and irrational for an incommensurate one.

Experience with polytype families of layered structures and the theory of OD structures consisting of layers made it possible to elaborate generally applicable principles for a full description of polytypes by symbols. According to these principles, the exact stacking sequence of building layers (BLs) in any given polytype may be described by a symbol which, in general, has the form Erfahrungen mit Polytypenfamilien von Schichtstrukturen und die Theorie der OD-Strukturen aus Schichten gestatteten die Herausarbeitung von allgemein anwendbaren Prinzipien zur vollstandigen Beschreibung von Polytypen mit Hilfe von Symbolen. Dabei wird die exakte Stapelfolge der Schichten eines Polytyps durch ein Symbol beschrieben, dessen allgemeine Form

An earlier report [Acta Cryst. (1977), A33, 681-684] by a joint IUCr-IMA committee on the nomenclature of polytypism has been revised and extended. Two kinds of symbolism are recommended for use with either simple or complicated polytypic structures. The first consists of 'indicative symbols' in a modified Gard notation, the second of 'descriptive symbols' based on earlier proposals by Dornberger-Schiff, I)urovi~ and Zvyagin. The polytypism of ZnS and SrGeO3 provides examples for the use of descriptive symbolism.

was analyzed by M6ssbauer spectroscopy, magnetization and magnetic susceptibility measurements. The iron is entirely ferric, and the main feature of the M6ssbauer spectrum at room temperature is a single absorption line with isomer shift 6 = 0.36(1) mm/sec due to iron in M2 sites. The line is broadened by a slight quadrupole splitting A = 0.18(1) mm/sec, the smallest yet reported for a sheet silicate. Weaker features corresponding to quadrupole doublets with relative intensities of 7% and 8% having 6 = 0.43(1) mm/sec; A = 1.22(2) mm/sec and 6 = 0.14(1) m m/sec; A = 0.59(2) mm/sec are assigned to ferric iron in nonequivalent octa- hedral and tetrahedral sites, respectively, giving the following formula, based on published chemical analysis: Cao.o5(Fe 3+

Graphite is the end member for a series of states of carbonaceous materials differing in structural ordering, which are determined by the distortion in the individual layers, and the regularity of orientation and positions. Consequently, the structural features of graphite and graphitized carbon have attracted much attention in research on the conversion of natural organic substances during coalification and metamorphism. The authors have combined X-ray and electron diffraction methods, in which the advantages of the one compensate for the weakness of the other, so one can evaluate the structural data correctly. They examined graphites from various deposits and rocks in the USSR, which enabled them both to evaluate the variations in polytype composition and to identify diffraction features expressing the specific differences of graphite polytypes from the polytypes of other substances. 26 references.

Ferrihydrite (2.5 Fe2O2-4.5 H2O) is an unstable colloidal mineral. It dissolves in highly alkaline solutions and is precipitated from them in the form of goethite. Jarosite is stable at very low pH but is decomposed at higher values of pH with separation of iron oxides. Experiments show that in rapid decomposition of jarosite a protohematite substance, ferrihydrite, is formed. This transformation occurs at moderate pH values when solutions percolate through the aggregates of jarosite. Ferrihydrite, an unstable colloidal hydrated oxide of ferric iron, changes spontaneously to stable hematite with time. Very slow decomposition of jarosite results in its replacement by iron hydroxide, goethite. Under laboratory conditions in alkaline solutions lepidocrocite may be obtained from jarosite. The synthesis of this iron hydroxide passes through a stage of intermediate products: ferrihydrite and hydrated ferric oxide - ferriprotolepidocrocite, formed by solution of ferrihydrite in strongly alkaline solutions. The t...

(1985). EFFECT OF TEMPERATURE AND TIME ON THE PHASE CHARACTERISTICS AND STRUCTURE OF SULFIDES IN THE MoS2-ReS2 SERIES. International Geology Review: Vol. 27, No. 5, pp. 615-624.

Two modifications of the delta-hydroxide of iron have been synthesized under laboratory conditions. Both are formed topotactically by the rapid course of the abiogenic reaction of the oxidation of Fe+2 at the expense of Fe(OH)2. Natural δ'-FeOOH, for which the authors propose the name "feroxyhyte," was found as yellowish-brown deposits in iron-manganese nodules from the bottom of the Pacific Ocean, Baltic, White, and Kara seas, and in gley soils. Feroxyhyte is an unstable hydrous oxide of iron, apparently transformed spontaneously into goethite, the stable modification of FeOOH. Its theoretical composition is Fe2O3 - 89.86, H2O - 10. 147%.

In iron-manganese nodules from the floor of Pacific ocean, Baltic, White Sea and Kara Sea, iron bydroxide δ'-FeOOH was analysed in the laboratory. In buried ooze, reduction processes generate Fe(HCO3)2 which migrates into the upper part of the bottom ooze and into near bottom sea water where Fe(OH)2 is formed. The oxidation process of Fe2+ to Fe3+, without participation of iron bacteria, leads to the topotactic transformation of Fe(OH)2 to δ'-FeOOH. Marine water does not contain Fe2+ and cannot be a direct source of iron deposited in the nodules. Discovery of δ'-FeOOH in marine nodules permits the consideration that both iron and manganese were derived from the buried bottom mud, which during diagenetic processes led to the transfer of these metals in solutions and their upward migration.

(1970). Polytypes of molybdenite and their occurrence in ores. International Geology Review: Vol. 12, No. 1, pp. 74-86.

The formation of textures in specimens is a natural consequence of the tendency of crystals highly anisotropic in shape to deposit on the substrate surface in a preferred orientation. The corresponding diffraction patterns have special advantages in the solution of problems of phase and structural analysis. Lamellar textures composed of crystals with the most developed face parallel to the substrate plane but randomly rotated about its normal are especially important. Such specimens satisfy the experimental requirements of transmission electron diffraction (TED) and patterns obtained under oblique position of the textures to the incident beam (oblique texture patterns — OTP’s — Fig. 1) are valuable property of the electron diffraction method. They contain regular hkl-reflection sets distributed in two dimensions permitting to perform structural studies for a great variety of objects sometimes with location of hydrogen positions 1–4. In this respect, they are the most effective means in application to fine-grained materials and imperfect structures. In view of the great efficiency of the texture patterns (TP’s) they were recently introduced also in the X-ray diffraction practice 5–7.

The ferric analogue of pyrophyllite (ideal formula Fe 2 Si 4 O 10 (OH) 2 ) and related phases that form evenly expanded or mixed-layer structures with water have been found and identified by means of electron and X-ray diffraction.