Previous studies of the defect structure of kaolinite have examined samples having a restricted level of defects. This study examined nine kaolinite samples having a large diversity of defect contents, as indicated by Hinckley indexes ranging from 1.44 to 0.18. The samples were chosen so as to cover this range in as regular a manner as possible. The types and abundances of the defects were determined by examining the X-ray powder diffraction profiles for the 02,11 and 20,13 bands. The diffraction intensities were measured by counting for a fixed time in steps of 0.01°2θ. Analysis of these diffraction profiles indicated that (1) the major defect is the existence of a translation between adjacent layers, which is not the usual (approximately a/3), but is related to that translation by the pseudo-mirror plane coincident with the long diagonal of the unit cell; (2) the existence of a few C layers among the B layer stacking is a minor defect; (3) many of the samples could be accurately modeled only by assuming the existence of two kaolinite phases; (4) the existence of only a few C layers in some samples does not support the idea of a continuous series from kaolinite to dickite through disordered intermediates; and (5) the Hinckley indexes of several samples depend on the relative proportions of the two types of kaolinite in the mixture.

The nine kaolinite samples fall into three groups: those having a low to moderate abundance of defects (Hinckley index > 0.43) are mixtures of two types of kaolinite (one almost free of defects, the other richer in defects); those having low Hinckley indexes (0.43 to 0.18) are single phases with different proportions of defects; and those which contain a single type of kaolinite, unlike the others in the nature of the interlayer translations and the greater abundance of C layers. The agreement between calculated and observed X-ray diffraction profiles is excellent for all specimens, except one sample (from Charentes) for which the fit is acceptable but not perfect.

A comparison of the structural characteristics of the kaolin-group minerals, mainly kaolinite and dickite, shows that they differ in both the two-dimensional periodicity in the 1:1 layers and the rotation angles of the polyhedra. Distortions in a real 1:1 layer, compared with an idealized layer, do not allow such stacking faults as ± 120° layer rotations and vacancy displacements, because the second layer is incommensurable with the first. The 1:1 layer structure and the fact that the unit cell is symmetrical with respect to the plane passing through the long diagonal of the unit cell suggest the possibility of defects resulting from the two stacking sequences for the same layers. For a regular alternation of translations, a halloysite-like structure should be the end-member of such a series of defect kaolinite types.

The formation of layers having vacant octahedral C-sites is another possible type of fault. Because of the minor dilference between γ and 90°, dickite-like layers should exist. A regular alternation of B and C layers yields dickite as the end-member structure. In materials containing few defects, stacking faults of both types lead to similar X-ray powder diffraction patterns. Thus, the nature of the stacking faults is difficult to determine experimentally. In materials containing many defects, however, the two models lead to different calculated diffraction patterns. Therefore, only a study of defect-rich types of kaolinite can determine which types of defects exist in natural kaolinite samples.

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 tk, distortions of these displacements δ1 and δ2, deviations of unit cell parameters ηi = b2i/a2i − 3, εi = γi − π/2, and normal projections cn of the axis vector c on the ab plane.

The ideal monoclinic angle of dickite (cnx = −1/3) and the deviation α - π/2 ≠ 0 for kaolinite are explained by combinations of the δ1 and δ2 values in the sequence of symbols si and tk 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, ± 1/3] and reflection operations in planes normal to the axis b3. Two deformation mechanisms are proposed for the accommodation of successive layer unit cells adjusting either angular or linear parameters at the agreement of either linear or angular parameters corresponding.

Stacking disorder in celadonite, a dioctahedral mica with Fe and Mg as major octahedral cations and which generally adopts the 1M stacking sequence, was investigated mainly by using transmission electron microscopy (TEM). The selected-area electron diffraction patterns with 0kl reflections along the [100] beam direction correspond to the 1M stacking but those along the [110], $\left[1\overline{1}0\right]$\$\end{document}, [010], [310], and $\left[3\overline{1}0\right]$\$\end{document} directions are frequently streaked along the [001]* direction or contain extra spots from twinned domains. Three-dimensional stacking analyses using sets of two high-resolution TEM images along different directions of the same area of one crystal indicate that all stacking faults involve only 180° layer rotations. These stacking faults produce greater peaks of 0kl reflections than expected in powder X-ray diffraction (XRD) patterns. Simulation of the XRD patterns indicated that 180° layer rotations occur at >10% of total interlayer regions in one celadonite specimen. The interlayer region of celadonite is characterized by a near-zero ditrigonal rotation angle, a small surface corrugation of the basal oxygen plane, and a small amount of Al substitution in the tetrahedral sheets. These features suggest that there is no preference for any of the six stacking angles around the interlayer region. The abundance of 180° layer rotation rather than ±60° and ±120° in the present specimens may be related to their ribbon-like morphologies elongated along the a axis.

Carbonate-intercalated layered double hydroxides of Co(II) and Ni(II) with Fe(III) and Al(III) were precipitated under different conditions (pH = 8–12; T= 25–80°C). All the samples are replete with stacking faults which are not eliminated by post-precipitation hydrothermal treatment (80–180°C, 18 h). DIFFaX simulations show that the layer stacking sequence of the disordered samples can be generated by a mixture of motifs corresponding to the 3R1 and 2H1 polytypes. These specific sequences are selected in preference to others because of the need for hydrogen bonding between the intercalated carbonates and hydroxide sheets. Thermodynamic considerations show that faulted crystals have greater stability than ordered crystals. Stacking faults arising from a mixture of 3R1 and 2H1 motifs, while having the same enthalpy as that of the ordered crystal, nevertheless contribute to thermodynamic stability by enhancing disorder.

From leaching experiments with metallic uranium-aluminum research reactor fuel elements in repository-relevant MgCl2-rich salt brines, a Mg-Al layered double hydroxide (LDH) with chloride as the interlayer anion was identified as a crystalline secondary phase component. The incorporation behavior of europium into the structure of the Mg-Al-Cl LDH was investigated. Synthesis via co-precipitation was performed. The Mg-Al-Eu-Cl LDH obtained was treated with a concentrated ammonium carbonate solution. No release of Eu was detected; hence the molar stoichiometry of the LDH remained stable with respect to Mg, Al and Eu. This chemical behavior might be the first indication of the incorporation of Eu.

The material was further examined by powder X-ray diffraction. Structural parameters were obtained from comparisons of simulated and experimental diffraction patterns of a ${\text{CO}}_3^{2-}$${\rm{CO}}_3^{2 - }$-exchanged Mg-Al-Eu LDH and a Mg-Al LDH. The two materials showed different behaviors according to stacking order and lattice parameters. This is an indirect indication of the incorporation of Eu.

A comparative crystallochemical study was performed on natural and synthetic hydrotalcite-like compounds with similar compositions. The nature of the brucite-like sheet stacking was addressed by means of powder X-ray diffraction. From the resulting electron diffraction patterns it was possible to establish the order-disorder of the cations in the brucite-like sheet. The results show that a natural sample from Snarum is an intergrowth of hydrotalcite (3R1 polytype) and manasseite (2H1 polytype) at a ratio of 77:23 (wt.%). An aluminian serpentine is associated with the hydrotalcite and manasseite minerals. The structure of a synthetic sample, Mg:Al = 2:1, was determined as space group $R\overline{3}m$. For a few crystals in this sample, the octahedral cation distribution is compatible with the observed supercell (a = a′ √3). A second synthetic sample showed the presence of stacking faults and was described as a random layer sequence of two polytypes (3R and 2H).

X-ray diffraction patterns of oriented mounts of clay minerals are often used in clay mineralogy for qualitative and quantitative purposes. Fequently occurring stacking defects, in particular, can be characterized by this technique. Modeling of these diffraction profiles has become an important tool in obtaining structural information about the nature of stacking order. Manual matching of calculated and observed patterns is time consuming and user dependent. Automatic refinement procedures are, therefore, desirable. An improved approach for the treatment of disordered layer structures within a Rietveld refinement is presented here. The recursive calculation of structure factors, similar to that of the simulation program DIFFaX, was introduced in the Rietveld code BGMN. Complete implementation is formulated within the interpreter language of the Rietveld code and is transparent as well as flexible. Such a method has opened the application of Rietveld refinement to patterns of oriented mounts where only basal reflections of stacking disordered structures were recorded. The DIFFaX code was used to simulate basal reflections of illite-smectite mixed layers (I-S) with different ratios of illitic and smectitic layers and with different degrees of long-range ordering (Reichweite). Rietveld refinements with these simulated patterns were used to evaluate the application of this new approach. Several I-S with different degrees of ordering were also chosen as tests for the refinement of basal reflections. The samples were prepared as standard airdried and ethylene glycol-solvated, oriented specimens. Realistic structural parameters were obtained for the composition and ordering of the I-S.

Layered metal hydroxides exhibit non-uniform broadening of lines in their X-ray powder diffraction (XRPD) patterns, which cannot always be explained on the basis of crystallite size effects. In the case of hexagonal solids such as nickel hydroxide, DIFFaX simulations of the XRPD patterns show that: (1) stacking faults and turbostratic disorder at low (<30%) incidence selectively broaden the h0l reflections; (2) turbostratic disorder at high (>40%) incidence causes asymmetric broadening of the hk0 reflections and a complete extinction of the hkl reflections while leaving 00l unchanged; (3) interstratification selectively broadens the non-hk0 reflections; and (4) cation vacancies reduce the relative intensity of the 100 reflection. In contrast, a reduction in the thickness of the crystallites along the stacking direction of the layers selectively broadens the 00l reflections while a reduction in the disc diameter causes the progressive broadening and extinction of the hk0 reflections. Comparison with experimental data shows that several kinds of disorders have to be invoked to account for the observed broadening. DIFFaX simulations enable the quantification of the different kinds of disorder.

X-ray diffraction (XRD) of powdered materials is one of the most common methods used for structural characterization as well as for the quantification of mineral contents in mixtures. The application of the Rietveld method for that purpose requires structure models for each phase. The recursive calculation of structure factors was applied here to the Rietveld refinement of XRD powder patterns of illite-smectite (I-S) minerals. This approach allowed implementation of stacking disorder in structural models. Models for disordered stacking of cis-vacant and trans-vacant dioctahedral 2:1 layers as well as rotational disorder were combined with models for mixed layering of illitic and smectitic layers.

The DIFFaX code was used to simulate non-basal (hk) reflections of illites with different degrees of disorder. Rietveld refinements of these simulated patterns were used to evaluate the application of this new approach. A model describing rotational disorder (n·120° and n·60° rotations) and mixed layering of cis-vacant and trans-vacant dioctahedral layers was tested. Different starting parameters led to identical results within the ranges of standard deviations and confirmed the stability of the automatic refinement procedure. The influence on the refinement result of an incorrect choice of fixed parameters was demonstrated.

The hk model was combined with models describing the basal reflections of disordered I-S and tested on measured data. A glauconitic mineral (Urkut, Hungary), an ordered I-S (ISCz-1, a special clay in the Source Clays Repository of The Clay Minerals Society), and a dioctahedral I-S (F4, Füzérradvány, Hungary) were used as test substances. Parameters describing the mixed layering of illitic and smectitic layers were compared with the results from refinements of oriented mounts and showed good agreement. A pattern of a physical mixture of an I-S mineral and a turbostratically disordered smectite was analyzed in order to test the new approach for application in quantitative phase analysis. The quantitative Rietveld phase analysis results were found to be satisfactory.

The characteristics of electron channeling contrast (ECC) of stacking faults in a [101] single-crystal 316L fcc (face-centered cubic) stainless steel have been evaluated. Channeling contrast was analyzed from a series of ECC images taken as a function of sample tilt at ~0.1° increments across the (111) Kikuchi band. The most relevant imaging parameters of the fault contrast, namely the number of fringes, fringe intensity, and fringe spacing, were analyzed under different channeling conditions. The present work shows that the channeling contrast of stacking faults exhibits strong dependence on the sign and magnitude of the deviation parameter, w (w = s ξg, where s is the excitation vector and ξg is the extinction distance). This effect has strong influence on channeling conditions for fault imaging and g.R analysis for determining the nature of a stacking fault. g.R analysis was evaluated by the method developed by Gevers et al. (1963) on g-reversion experiments of ECC images of a stacking fault configuration. The interplay between the stacking fault nature and ε-martensite is analyzed.

Iron-cross twins of pyrite are well known among mineralogists, however it is quite surprising that the conditions of their formation remain unexplored. To address this question we studied pyrite twins from the Upper Permian silts of Mt. Katarina near Ljubljana (Slovenia), which represent one of the most typical geological environments for twinned pyrite. Mineralization of pyrite starts with a reduction of the primary red-coloured hematite-rich sediment by sulfide-rich fluids that penetrated the strata. A short period of magnetite crystallization is observed prior to pyrite crystallization, which indicates a gradual reduction process. Sulfur isotope analysis of pyrite shows an enrichment in δ34S, suggesting its origin from the neighbouring red-bed deposit. Other sulfides, such as chalcopyrite and galena, formed at the end of pyrite crystallization. Remnants of mineralizing fluids trapped at the interfaces between the inclusions and host pyrite show trace amounts of Pb and Cu, indicating their presence in the solutions throughout the period of pyrite crystallization. An electron microscopy and spectroscopy study of twin boundaries showed that interpenetration twinning is accomplished through a complex 3D intergrowth of primary {110} Cu-rich twin boundaries, and secondary {100} boundaries that are pure. We show that approximately one monolayer of Cu atoms is necessary to stabilize the {110} twin structure. When the source of Cu is interrupted, the two crystal domains continue to form {100} interfaces, that are more favourable for pure pyrite.

The program FAULTS has been used to simulate the X-ray powder diffraction (XRD), neutron powder diffraction (NPD), and electron diffraction (ED) patterns of several structural models for LiNi1/3Mn1/3Co1/3O2, including different types of ordering of the transition metal (TM) cations in the TM slabs, different amounts of Li+/NiII+ cation mixing and different amounts of stacking faults. The results demonstrate the relevance of the structural information provided by NPD and ED data as compared with XRD to characterize the microstructure of NMC (LiNi1−y-zMnyCozO2) compounds.

The microstructural evolution during spark plasma sintering of ultrafine WC–1 wt% Si (n-WC–Si) is presented. At 1323 K (T < TmSi), extensive stacking faults on the $\left\{ {10\bar 10} \right\}$ prismatic planes are observed. The defect microstructure can be described as a combined shear of $1/6\left\langle {\bar 12\bar 13} \right\rangle$ on the prism planes and simultaneous out-diffusion of carbon through the faults to the interparticle boundaries. At temperatures near TmSi (1673 K), a large fraction of abnormally grown platelets is observed. These platelets contain a single planar defect on their basal planes, described by a ${1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}\left\langle {10\bar 10} \right\rangle$ translation of the carbon atoms across a Σ1 grain boundary (GB). Three factors contribute to the abnormally high density of platelets: (i) the low-temperature prismatic dislocations interact to form facet-roughening steps/kinks that act as nucleation sites, (ii) a liquid phase triggers an increased growth rate in the vicinity of the Si inclusions, and (c) the basal twin produces a re-entrant edge for 2D nucleation.

Hexagonal boron nitride (hBN) is a promising material for a range of applications including deep-ultraviolet light emission. Despite extensive experimental studies, some fundamental aspects of hBN remain unknown, such as the type of stacking faults likely to be present and their influence on electronic properties. In this paper, different stacking configurations of hBN are investigated using CASTEP, a pseudopotential density functional theory code. AB-b stacking faults, in which B atoms are positioned directly on top of one another while N atoms are located above the center of BN hexagons, are shown to be likely in conventional AB stacked hBN. Bandstructure calculations predict a single direct bandgap structure that may be responsible for the discrepancies in bandgap type observed experimentally. Calculations of the near edge structure showed that different stackings of hBN are distinguishable using measurements of core-loss edges in X-ray absorption and electron energy loss spectroscopy. AB stacking was found to best reproduce features in the experimental B and N K-edges. The calculations also show that splitting of the 1s to π* peak in the B K-edge, recently observed experimentally, may be accounted for by the presence of AB-b stacking faults.

A synthetic catalyst precursor formed by sulfiding ferrihydrite (Fe3+O(OH)) in the presence of a hydrogen donor produces X-ray diffraction patterns resembling a mixture of both naturally occurring FeS2 polymorphs marcasite and pyrite. The diffraction peaks display a differential broadening, however, wherein only those peaks coincident to both marcasite and pyrite are strong and sharp, a feature that cannot be accounted for by a simple physical mixture. The broadening is analogous to that found in hexagonal cobalt, where occasional stacking faults produce interstratification of the hexagonal and cubic close-packed forms, resulting in strongly coherent diffraction only along the stacking direction. The crystal structures of marcasite and pyrite are virtually identical if viewed perpendicular to the (101) and (001) planes, respectively. Calculation of diffraction patterns based upon models of interstratifying marcasite and pyrite layers along these planes demonstrates that a sequence with marcasite-to-pyrite and pyrite-to-marcasite stacking fault probabilities of 0.22 provides a good fit to the experimental pattern. This interstratified material is a precursor to a species that shows catalytic activity for cleaving C-C bonds between aromatic rings and benzylic carbon atoms at low (<350 °C) temperatures.

Two different approaches for studying sample’s contributions to diffraction-line broadening are analyzed by applying them to several nickel hydroxide samples. Both are based in the refinement of powder diffraction data but differ in the microstructural model used. The first one consists in the refinement of the powder diffraction pattern using the FAULTS program, a modification of DIFFaX, which assigns peak broadening mainly to the presence of stacking faults and treats finite size effects by convolution with a Voigt function. The second method makes use of the program FULLPROF, which allows the use of linear combinations of spherical harmonics to model peak broadening coming from anisotropic size effects. The complementary use of transmission electron microscopy has allowed us to evaluate the best approach for the Ni(OH)2 case. In addition, peak shifts, corresponding to reflections 10l (l≠0) were observed in defective nickel hydroxide samples that can be directly correlated with the degree of faulting.

A review of transmission electron microscopy studies of planar defects in 18R and 2H martensites in Cu-Zn-Al alloys is presented. The non-basal plane faults observed in the 2H structure, the F1 faults, show two kinds of dislocations at their ends. In contrast, two types of non-basal plane faults are observed in the 18R structure, Fo and Fx faults. The non-basal plane faults can be composed of segments of Fo and Fx faults. Six types of imperfect dislocations appear, depending on the type of basal plane fault ending at the non-basal plane fault. The Burgers vectors of all these dislocations have been determined from the contrast analysis of the images and HREM observations.

We have performed systematic first-principles pseudopotential local density functional calculations of stacking faults in GaN and AlN. Their band offsets and the charge accumulation at stacking fault interfaces has been investigated, taking fully into account the effects of lattice relaxation and electric polarization. We find the stacking fault junctions to be of type I in both materials. However, the intrinsic valence band offsets are close to zero, so that the conduction band offsets result mostly from the differences in the energy gaps between the cubic and wurtzite phases. The charge accumulated at the interface between the cubic and wurtzite phase is found to be 0.009 and 0.003 C/m2 for the AlN and GaN stacking fault, respectively.