Wedge-shaped Crystals Research Articles

The structure of the eggshell and eggshell membranes of Crocodylus niloticus.

The macro- and microstructure, elemental composition, and crystallographic characteristics of the eggshell and eggshell membranes of the Crocodylus niloticus egg was investigated using optical and electron microscopy, energy-dispersive X-ray spectroscopy (EDS), electron backscatter diffraction (EBSD) and computerised tomography. The translucent ellipsoid egg is composed of two basic layers, the outer calcified layer referred to as the shell and an inner organic fibre layer, referred to as the shell membrane. The outer inorganic calcite shell is further divided into an external, palisade and mammillary layers with pore channels traversing the shell. The external layer is a thin layer of amorphous calcium and phosphorus, the underlying palisade layer consist of irregular wedge-shaped crystals composed calcite with traces of magnesium, sodium, sulphur and phosphorus. The crystals are mostly elongated, orientated perpendicular to the shell surface ending in cone-shaped knobs, which forms the inner mammillary layer. The elemental composition of the mammillae is like that of the palisade layer, but the crystal structure is much smaller and orientated randomly. The highest number of mammillae and shell pores are found at the equator of the egg, becoming fewer towards the egg poles. The shell thickness follows the same pattern, with the thickest area located at the equator. The eggshell membrane located right beneath and embedded in the mammillary layer of the shell; it is made up of unorganised fibre sheets roughly orientated at right angles to one another. Individual fibres consist of numerous smaller fibrils forming open channels that run longitudinally through the fibre.

New Minerals from the Redmond Mine, North Carolina, USA: I. Redmondite, Hydroredmondite, and Sulfatoredmondite, Three Minerals Containing the Novel [Pb8O2Zn(OH)6]8+ Structural Unit

AbstractThe new minerals redmondite (IMA2021–072), [Pb8O2Zn(OH)6](S2O3)4, hydroredmondite (IMA2021–073), [Pb8O2Zn(OH)6](S2O3)4·2H2O, and sulfatoredmondite (IMA2021–089), [Pb8O2Zn(OH)6](SO4)4·6H2O, were found in the Redmond mine, Haywood County, North Carolina, USA, where they occur together in a highly unusual secondary assemblage that comprises a variety of rare Pb-Zn-Cu sulfates, thiosulfates, and carbonates. The properties of redmondite are as follows: colorless to shades of brown, transparent equant rhombs to about 1 mm; white streak; adamantine luster; brittle; Mohs hardness 2; conchoidal fracture; no cleavage; 5.757 g/cm3 calculated density; biaxial with α = 1.96–1.97, β = 1.97–1.98, γ = 1.97–1.98; extreme dispersion. The properties of hydroredmondite are as follows: colorless, transparent prisms, blades, and tablets up to about 1 mm; white streak; adamantine luster; brittle; Mohs hardness 2; curved and stepped fracture; good cleavages on {101} and ; 5.124 g/cm3 calculated density; biaxial (+) with α = 1.830(5), β = 1.880(calc), γ = 1.950(calc), 2Vmeas = 83(1)°. The properties of sulfatoredmondite are as follows: colorless, transparent wedge-shaped crystals to about 2 mm; white streak; adamantine luster; brittle; Mohs hardness 2; curved, irregular fracture; no cleavage; 5.173 g/cm3 calculated density; biaxial (+), α = 1.780(5), β = 1.850(calc), γ = 1.860(calc), 2Vmeas = 40(3)°; moderate r > v dispersion. Electron probe microanalyses provided the empirical formulae: Pb8.16Zn1.00S6+3.97S2−3.97O20H5.79, Pb8.00Zn1.00S6+4.00S2−4.00O22H9.98, and Pb8.00Zn0.99S6+4.00S2−0.89O29.11H17.98 for redmondite, hydroredmondite, and sulfatoredmondite, respectively. Redmondite is monoclinic, P21/c, a = 9.1672(4), b = 10.6576(4), c = 14.0620(10) Å, β = 101.173(7)°, V = 1347.83(12) Å3, and Z = 2. Hydroredmondite is monoclinic, P21/n, a = 12.5991(9), b = 9.2819(4), c = 12.9774(9) Å, β = 90.443(6)°, V = 1517.57(16) Å3, and Z = 2. Sulfatoredmondite is monoclinic, C2/m, a = 17.294(2), b = 7.3668(9), c = 12.7271(18) Å, β = 110.622(9)°, V = 1517.5(4) Å3, and Z = 2. The crystal structures of redmondite (R1 = 0.0346 for 2061 I > 2σI), hydroredmondite (R1 = 0.0346 for 3022 I > 2σI), and sulfatoredmondite (R1 = 0.0344 for 1661 I > 2σI) are all based on the same [Pb8O2Zn(OH)6]8+ structural unit.

X-ray two-wave dynamical diffraction analogue of Talbot effect

Imaging of periodic objects in free space brings us to the Talbot effect in optics, for x-rays and for matter waves. X-ray dynamical diffraction imaging of periodic objects inside a crystal has scientific and applied interest. Thus, we arrive at the concept of the dynamical diffraction Talbot effect in a crystal. This work is the first attempt to investigate the Talbot effect inside a medium. Using the Green function formalism, an exact formula for the diffracted wave amplitude is found. By means of ‘paraxial’ approximation, which is an analogue of the paraxial approximation in optics, it is shown that the dynamical diffraction Talbot effect takes place. Expressions for polarization sensitive Talbot and corrected Talbot distances are obtained. We analyse the influences of absorption, Bragg filtration of harmonics and polarization on the dynamical diffraction Talbot effect. For the first time, simulated Talbot carpets inside the crystal are obtained, which show that the predictions, obtained by ‘paraxial’ approximation, are true. We present the dynamical diffraction Talbot carpets observation method by means of a wedge-shaped crystal. The dynamical diffraction Talbot effect can be used for investigation of objects and crystal defects and deformations. Dynamical diffraction Talbot effect investigations in optics, for electrons and neutrons, are possible.

Correlative micro-diffraction and differential phase contrast study of mean inner potential and subtle beam-specimen interaction

We present a correlative micro-diffraction and differential phase contrast (DPC) study within scanning transmission electron microscopy (STEM) on the determination of mean inner potential (MIP) and explain the origin of subtle beam-specimen interactions at the edge of wedge-shaped crystals using both experiment and simulation. Our measurement of MIP of Si and GaAs resulted in 12.48 ± 0.22 V and 14.15 ± 0.22 V, respectively, from directly evaluating beam refraction in micro-diffraction mode. DPC-STEM measurements gave very similar values. Fresnel fringes within the diffraction disk resulting from interaction of the highly coherent electron beam with the aperture are observed and a numerical simulation scheme is implemented to reproduce the effect of the specimen on the fringe pattern. Perfect agreement between experiment and simulation has been achieved in terms of subtle displacements of the fringes upon approaching the sample edge with the electron probe. The existence of the fringes has minor effect on the DPC-STEM signal, which is well below the noise level of our setup at practically reasonable acquisition times. We suggest the possibility to perform pseudo-contactless probing of weak potential differences in beam sensitive samples by evaluating the subtle displacements of Fresnel fringes quantitatively.

Publisher’s note

We present a correlative micro-diffraction and differential phase contrast (DPC) study within scanning transmission electron microscopy (STEM) on the determination of mean inner potential (MIP) and explain the origin of subtle beam-specimen interactions at the edge of wedge-shaped crystals using both experiment and simulation. Our measurement of MIP of Si and GaAs resulted in 12.48 ± 0.22V and 14.15 ± 0.22V, respectively, from directly evaluating beam refraction in micro-diffraction mode. DPC-STEM measurements gave very similar values. Fresnel fringes within the diffraction disk resulting from interaction of the highly coherent electron beam with the aperture are observed and a numerical simulation scheme is implemented to reproduce the effect of the specimen on the fringe pattern. Perfect agreement between experiment and simulation has been achieved in terms of subtle displacements of the fringes upon approaching the sample edge with the electron probe. The existence of the fringes has minor effect on the DPC-STEM signal, which is well below the noise level of our setup at practically reasonable acquisition times. We suggest the possibility to perform pseudo-contactless probing of weak potential differences in beam sensitive samples by evaluating the subtle displacements of Fresnel fringes quantitatively.

Dependence of X-ray diffraction patterns on the parameters of primary incident beam

X-ray diffraction patterns obtained from a plane-parallel crystalline plate with a spherical cavity and from a wedge-shaped crystal have been investigated depending on the collimation of the primary incident beam. It is shown that in the case of ribbon-like incident beam the sectional topograms, obtained from the wedge-shaped crystal, have the form of V-shaped or straight fringes depending on the orientation of reflecting planes relative to the surface of the X-ray ribbon-like beam. In the case of a wide parallel beam or an asymmetrically reflected wide monochromatic beam the parallel fringes are obtained from the wedge-shaped crystals, and the circular fringes are obtained from the plane-parallel crystalline plates with a spherical cavity. For the primary ribbon-like beam the V-shaped patterns acquire the form of circular fringes as a result of scanning the crystal with a spherical cavity and the X-ray film.

The growth of anatase bipyramidal crystals during hydrothermal synthesis

The morphology, size and growth of anatase TiO2 crystals have been studied using a transmission electron microscope (TEM) and X-ray powder diffraction (XRD). The material was prepared by hydrothermal synthesis from aqueous suspension of amorphous TiO2 at temperatures from 40 to 200°C and times up to 200h. The size of the crystals increased with the synthesis temperature and time from around 6 to 20nm. From high-resolution TEM images shape of crystals was reconstructed. It was found that in the initial stages of growth anatase crystals adopt uncommon morphologies, which were combination of basic crystallographic forms typical for anatase, however these forms were not developed symmetrically as determined by the surface energy values for these particular planes. The asymmetry and abnormal growth into rod-like and wedge-shaped crystals was most probably a consequence of inhomogeneous supply of building material due to high competition among numerous (relatively) rapidly growing randomly oriented nanocrystals. This leads to highly non-equilibrium conditions in the initial growth stages. Close to equilibrium at higher temperatures and times all crystals tend to adopt simple bipyramidal morphology.

Effective object planes for aberration-corrected transmission electron microscopy

In aberration-corrected transmission electron microscopy, the image contrast depends sensitively on the focus value. With the point resolution extended to an information limit of below 0.1nm, even a focus change of as small as one nanometer could give a significant change in image contrast. Therefore, it is necessary to consider in detail the optimum focus condition in order to take full advantage of aberration-correction. In this study, the thickness dependence of the minimum contrast focus has been investigated by dynamical image simulations for amorphous model structures of carbon, germanium, and tungsten, which were constructed by molecular dynamics simulations. The calculation results show that the minimum contrast focus varies with the object thickness, supporting the use of an effective object plane close to the midplane instead of the exit plane of a sample, as suggested by Bonhomme and Beorchia [J. Phys. D: Appl. Phys. 16, 705 (1983)] and Lentzen [Microscopy and Microanalysis 12, 191 (2006)]. Thus supported particles and wedge-shaped crystals with symmetrical top and bottom surfaces could be imaged at a focus condition independent of the uneven bottom face. Image simulations of crystalline samples as a function of focus and thickness show: for an object thickness of less than 10nm, the optimum focus condition is matched better if the midplane of the object, instead of the exit plane, is chosen as reference plane.

Investigations of a wedge-shaped nematic liquid crystal cell using Mach–Zehnder interferometer

We report optical interferometric studies of a wedge-shaped nematic liquid crystal cell. Interference fringes were observed when a nematic liquid crystal cell was placed in one of the arms of Mach–Zehnder interferometer. In the case of homogenous gap cell, the fringe contrast remained unaffected on applying voltage. However, in the case of wedge-shaped cell, the fringe contrast was found to degrade under an applied electric (DC) field and it became poorer at higher voltages. At higher voltages the fringe contrast improved where complete switching occurred. The degradation in fringe contrast due to wedge-shaped cell structure might find applications for speckle reduction in future laser-based rear projection displays.

Geochemical and geological controls on the genesis of gem-quality "Paraiba Tourmaline" in granitic pegmatites from northeastern Brazil

The electric blue Paraiba Tourmaline (PT) occurs in northeastern Brazil only in four deposits of zoned and highly fractionated granitic pegmatites of the Borborema Pegmatitic Province (BPP). These PT-bearing pegmatites are rich in spodumene or lepidolite, and are emplaced in iron-poor quartzites or metaconglomerates of the Neoproterozoic Equador Formation. Black comb-textured dravitic tourmaline in the border zone indicates crystallization from a boron-bearing granitic magma. The PT occurs at the transition between the albite-rich inner intermediate zone (IIZ) and the quartz core of the pegmatites, in primary wedge-shaped crystals of near-end-member color-zoned elbaite, arranged in fan-like, radial or comb-textured groups of crystals. The PT most commonly forms the intermediate growth-zone of color-zoned elbaite crystals having a pink to red core and a green to dark green rind. The PT-bearing pegmatites are distinguished by intensive late replacement of primary K-feldspar, spodumene, elbaite and Li-phosphates by lepidolite. The lepidolite replacement of zoned elbaite is highly selective; it begins in the core, then affects the light blue intermediate zones, and preferentially leaves intact the green rim. PT crystals or crystal zones preserved from lepidolite replacement are rare, and occur enveloped in quartz of the pegmatite core or in vug fillings. According to electron-microprobe data on color-zoned elbaite crystals, PT crystal-zones are distinguished not only by high Cu contents, but also by higher values of Li and F (mostly fluor-elbaite), Fe concentrations near zero, and lower concentrations of Mn than the contiguous zones with other colors. Increasing Fe + Mg concentrations are responsible for the green color in the rims enveloping PT, even if Cu values remain elevated. Values of Al, X □ and Mn are slightly elevated in the pink zones in comparison with PT in the same crystal. Textural relations indicate that PT formed by direct crystallization from a pegmatite-forming melt rich in B, Li and F, at the early stage of formation of the quartz core, and prior to the appearance of secondary lepidolite and other late hydrothermal minerals. The difference between PT-bearing and other elbaite-rich pegmatites may not necessarily be the failure to produce primary PT, but also the failure to preserve it from late conversion to lepidolite. The formation of PT is linked with low content of mafic minerals in the wallrock and in the pegmatite-forming melt itself.

Seawater spray injury to Quercus acutissima leaves: Crystal deposition, stomatal clogging, and chloroplast degeneration

Effects of seawater spray on leaf structure were investigated in Quercus acutissima by electron microscopy and X-ray microanalysis. Two-year-old seedlings of Q. acutissima were sprayed with seawater and kept in a greenhouse maintained at 25°C. The most recognizable symptoms of seawater-sprayed seedlings included leaf necrosis, crystal deposition, stomatal clogging, and chloroplast degeneration. Field emission scanning electron microscopy revealed that the leaf surface was covered with additional layers of remnants of seawater spray. Composed of sodium and chloride, cube-shaped crystals (halite) were prevalently found on trichomes and epidermis, and formed aggregates. Meanwhile, wedge-shaped crystals were deposited on epidermis and consisted of calcium and sulfur. As a result of stomatal clogging by crystal deposition on the abaxial surface, it was conceivable that plant respiration became severely hampered. Transmission electron microscopy showed degenerated cytoplasm of seawater-sprayed leaves. It was common to observe severe plasmolysis and disrupted chloroplasts with a reduced number of thylakoids in grana. These results indicate that foliar applications of seawater were sufficient to induce necrosis of Q. acutissima seedlings as an abiotic disturbance factor.

Nontoxic crystal protein from Bacillus thuringiensis demonstrates a remarkable structural similarity to β‐pore‐forming toxins

Nontoxic crystal protein from <i>Bacillus thuringiensis</i> demonstrates a remarkable structural similarity to β‐pore‐forming toxins

Melting temperature of a wedge-shaped thin crystal of tin

The melting temperature of a wedge-shaped single crystal of Sn was measured as a function of the local thickness using an in-situ heating experiment in a transmission electron microscope. The melting temperature decreases with decreasing local thickness of a wedge-shaped single crystal. The behaviour was discussed using a thermodynamic model and compared with that for particles with a free surface.

A New Measurement Method for Stokes Parameters Using a Wedge-shaped LC Device

A new optical measurement method for Stokes parameters using a wedge-shaped (WS) liquid crystal (LC) device is reported for characterizing optical elements such as LC display devices, where the WS LC device is used for one-dimensional modulation of a transmitted light through an optical element. The method is very simple and reliable and does not use any mechanical parts, so it is very useful for measuring Stokes parameters of arbitrarily polarized light.

Altering the morphology of crystals of a macromolecule without changing the unit cell (A case study of ribosome crystals)

Crystals of different morphology (needle-, rod-tetragonal- and wedge-shaped) were grown from the same solution of ribosome and in the same drop using 10–15% 2-methyl-2,4-pentanediol as a precipitant. The crystals appeared in 5–48 h. Observations of the kinetics of crystal appearance lead to the conclusion that higher supersaturation of ribosome solution produces needle-shaped crystals, while the tetragonal-rod- and the wedge-shaped crystals grow at lower supersaturation. The ribosome packing in the crystals was characterized by electron microscopy (EM). An analysis of EM ultrathin sections indicates that the unit cells, with a high degree of probability, are the same in the needle-shaped and other morphology crystals. The data obtained suggest that adjusting supersaturation of the crystallization solution may convert needle-shaped to more useful morphologies.

Theory of Imaging a Perfect Crystal under the Conditions of X-Ray Spherical Wave Dynamical Diffraction

A theory of the formation of interference patterns due to X-ray spherical wave two-beam dynamical diffraction in a perfect crystal is presented. An asymmetrical Laue case is analyzed in detail, when a polychromatic focus is realized with different distances in front of and behind the crystal. Such a property is essential for high-energy X-rays produced by synchrotron radiation sources of the third generation because of the long distance between source and object. It is shown that a monochromatic X-ray spherical wave is focused due to dynamical diffraction when a definite relation between distances and crystal thickness is held. An X-ray beam of less than 10 μm width may be obtained. A two-dimensional intensity distribution (topograph) may be registered with a wedge-shaped crystal. It shows interference fringes of different kinds depending on crystal thickness and asymmetry rate. It is also discussed how a slit in front of the crystal influences the interference pattern. An example of an interference pattern is presented under the condition of highly asymmetrical diffraction which was obtained by a computer simulation technique. Fringes of a new kind are observed and their physical nature is discussed.

Simulation of thickening growth in polymer crystallisation

The scope of this work is to investigate polymer crystallisation involving thickening growth by means of a kinetic Monte Carlo simulation. The simulation combines the lateral growth mechanism of the Sadler/Gilmer model with Hikosaka's ‘chain sliding diffusion’ mechanism for thickening growth. As a result of this coupling of lateral and thickening growth, we obtain wedge-shaped crystals if the sliding friction is not too high (‘mobile regime’) and lamellar crystals for high friction. In the mobile regime the thickening rate increases with undercooling. Thickening also increases the lateral growth rate, especially at low undercooling, since it lowers the entropic and enthalpic barriers. As a result, the activation energy of both processes takes a similar value, in agreement with experiment. For high friction, the thickening rate increases with temperature up to a maximum close to the melting point, in agreement with the observations of thickening of lamellar polymer crystals. This simple model hence captures the essence of lateral and thickening growth behaviour in polymer crystallisation.

A New Approach Towards Measuring Structure Factors and Valence-Electron Distribution in Crystals with Large Unit Cells

By focusing a probe of fast electrons above or below the specimen level in convergent-beam electron diffraction, shadow images of many reflections are recorded in one exposure. For wedge-shaped crystals, this procedure provides a means of recording thickness or Pendellosung fringes of many reflections simultaneously, which ensures that the experimental conditions with respect to thickness variations and crystallographic direction of the incident beam are the same for all reflections. Disturbing defects within the illuminated area of the specimen are immediately revealed in the shadow images of the different reflections. The approach is introduced by using strontium titanate and silicon as examples. As a case study, the technique is applied to the dense (001) reciprocal-lattice row of the superconductor YBa 2 Cu 3 O 7 to address charge transfer and electron-hole distribution by determining the amplitudes and phases of the 001 and 002 reflections. By this approach, the absolute values of the structure factors are obtained from the very thin regions where the kinematical theory applies. Based on these approximate absolute values, the signs of the structure factors in centrosymmetrical crystals are determined by comparing dynamically calculated and observed intensities in somewhat thicker crystal regions for different combinations of signs. As a third step, the structure factors are refined by comparing the calculated and experimental intensity profiles within the entire observed thickness range.

Multiple Light Scattering from Polymer-Dispersed Liquid Crystals

Measurements and Monte Carlo simulations of the angular distribution of light scattered from wedge-shaped Polymer-Dispersed Liquid Crystals (PDLCs) are reported. The simulation model is based on two length scales: the scattering mean free path and the transport mean free path. The simulation reproduces the experimental angular distribution of multiply scattered light as a function of sample thickness if the angular distribution in each scattering event is taken as a Mie distribution or as a Lorentzian in the cosine of the scattering angle. The experimental parameters are in the intermediate range where models based on either single or diffusive scattering do not apply.

HREM of nanometric tips prepared from epitaxially grown silicon whiskers

Nanometric tips prepared from Si whiskers frown epitaxially by VLS techniques were investigated by HREM. Whiskers were grown on 0.23 × 2mm (111)Si ‘butt-ends’ of plate-shaped substrates oriented in <011> using X-ray diffraction techniques. Since the tip ends are suitably thin, and in an appropriate orientation—<011>—for lattice imaging, the HREM images which are obtained display facetting at the end of the tips. SEM images of the bases of tips removed mechanically from the substrate, and also two-beam diffraction contrast TEM images show that the cross-sections of the nanometric tips prepared by a one-stage process are equilateral triangles with truncated corners. This is also confirmed by observing changes in the lattice image contrast across tips, with the appearance of characteristic half-spacing contrast at specific thicknesses typical of wedge-shaped crystals. According to HREM, the lattice is defect-free. There are two versions of tip etching (two combinations of three [111] shape-making faces). The extreme ends of the tips are atomically sharp, with an apex cone angle of 18–24°. Tips prepared by a two-stage process are characterised by a thick base and thin ‘cylindrical’, needle-shaped part 50–200 nm in diameter and 6–20 μm long. The angle which forms the needle profile of the thin part with [1¯11] growth direction is 1.5–4°. Profile imaging of the thin part reveals small steps along [111]. The ends of these tips are also atomically sharp, and resemble those prepared by a one-step etching process.