Theory of X-ray diffraction on a lateral crystal with elastically bent lattice planes

A theory of X-ray diffraction on a lateral crystal with elastically bent lattice planes is developed within the framework of the kinematic approximation. Analytical solutions for coherent and diffuse scattering are obtained in application to high-resolution triple-axis diffractometry. The angular distribution of the intensity of coherent and diffuse scattering near a node of the reciprocal lattice are numerically simulated. It is shown that the pattern of X-ray diffraction from a crystal with a trapezoidal cross section and elastically bent lattice planes has a “butterfly” shape that was previously observed in experiment.     

X-ray diffraction study of polyphilic smectic liquid crystals

4-substituted n-5,5,6,6,7,7,8,8,9,9,10,10,10-tridecafluorodecan-1-yloxybenzene and n-5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,12-pentadecafluorododecan-1-yloxybenzene, the former with CO₂CH₃ and the latter with CO₂CH₃ and CO₂H substituents in para position, are polyphilic compounds exhibiting smectic liquid crystalline phases. The structure of these phases was studied by X-ray diffraction and modelling. The method consisted of reconstructing all possible one-dimensional electron density profiles from diffraction intensities and matching them with the profiles calculated from structural models. The method is shown to be useful in both determining molecular arrangement in the smectic phase and in phase identification itself. An S_Ad phase is found in the two esters, having interdigitated perfluorinated alkyl segments. In contrast, a double-layer S_C phase, also known as S_C2, is found in the carboxylic acid. The method used here is particularly applicable to polyphilic liquid crystals such as the present ones, which are characterized by a complex electron density profile and a high translational order parameter.     

X-ray diffraction from faulted zinc sulphide crystals undergoing phase transitions

Stacking faults in close-packed structures are not always distributed randomly. When they occur preferentially at certain layer spacings. In such cases the classical theories of X-ray scattering from randomly faulted close-packed structures break down and a probability distribution of faults has to be assumed to compute the diffraction effects. This probability distribution faults has to be assumed to compute the diffraction effects. This probability distribution depends on the mechanism of the transformation in the material being studied. By recording the diffuse intensity distribution along reciprocal lattice rows perpendicular to the faults obtained from a partially transformed crystal it is possible to determine the nature of the faults involved and derive information about the mechanism of the transformation. The application of this method to investigate the mechanism of 2H 3C and 2H 6H transformations in ZnS, Zn _x ,Cd_1-x S and Zn _x ,Mn_1-x S is discussed. A three parameter model assuming different fault probabilities for deformation faulting at larger separations (a), at three-layer separations () and at two-layer separations () has been developed, to compute theoretically the diffraction effects from the transforming crystals and explain the experimentally observed distribution of diffuse intensity in reciprocal space.     

Wide angle X-ray diffraction study of the microstructure of chain-folded polyethylene crystals

The profile of the 002 diffraction peak of polyethylene is related to microstructural parameters for the [001] direction. The parameters considered are the mean crystal thickness, distribution of thicknesses, shape function and the degree of paracrystalline disorder in the lattice.An analytical relation describing the peak profile is derived for trapezium models of the shape function. Calculations are made of peak profiles and their correlation functions for various trapezium models, levels of paracrystalline disorder and Gaussian widths for the distribution of crystal thicknesses. Particular attention is paid to the effect of these parameters on the subsidiary maxima to the 002 peak.The 002 peak of linear polyethylene (RIGIDEX 50) crystallized from solution in xylene at 70°C is analysed in terms of the above parameters. The results are interpreted in terms of the buried fold model and indicate the presence of well defined zones of highly disordered material (probably nematic) within the crystal entities.The frequency of the zones increases as the fold surfaces are approached.     

Continuous X-ray diffraction measurement of lattice rotation during tensile deformation of aluminium crystals

Results are reported of experimental measurements in which crystallographic orientation changes due to lattice rotation were continuously monitored during uniaxial tensile tests on 99.99% pure aluminium crystals. The use of an image intensifier tube, lens coupled to a fluorescent screen, permitted Laue transmission X-ray diffraction patterns to be recorded with a motion picture camera at rates as fast as 24 frames per second. In all tests, the lattice rotation caused the tensile axes to overshoot the [1 0 0]-[1 1 1] symmetry line contrary to the classical view. In general, the experimentally measured lattice rotation values lagged behind the theoretical values as derived from the idealized single slip model. No clear dependence of lattice rotation on strain rate was found, although in every test the lattice rotated fast initially with no bending evident and then the lattice rotation slowed down accompanied by considerable lattice bending.     

An X-ray diffraction topographic study of single crystals of melt-grown yttrium aluminium garnet

Melt-grown crystals of yttrium aluminium garnet usually exhibit an optically imperfect central core region associated with the formation of facets on the solid/liquid interface during growth. The nature of the optical inhomogeneity of the core region, and the general defect structure of the crystals, was investigated by the technique of X-ray diffraction topography. The core region, which showed an elastic strain effect, contained straight growth striations reflecting the development of facets. Comparison was made between undoped and neodymium-doped crystals, and between crystals grown on <111> and <110> growth axes. Impurity striations were thought to be caused by temperature oscillations in the melt ahead of the growing interface. Dislocations, which were observed in the outer regions of the crystals, were sometimes nucleated at inclusions.     

High resolution X-ray diffraction studies on unirradiated and irradiated strontium hexaferrite crystals

High-resolution X-ray diffraction technique, employing a three-crystal monochromator?Ccollimator combination is used to study the irradiation induced defects in flux grown Sr-hexaferrite crystals irradiated with 50?MeV Li³⁺ ion beams at room temperature with a fluence value of 1 × 10¹⁴ ions/cm². The diffraction curves of the irradiated crystals suggest the possibility of creation of low angle grain boundaries and other point/clusters of defects causing amorphization in the irradiated crystals. The perfection of the irradiated and unirradiated (0001) cleaved surfaces of the crystals is studied using the bulk method of X-ray topography. The topographs supplement the findings suggestive of modifications in the crystalline quality of SrFe₁₂O₁₉ on irradiation with SHI of Li^3?+?. Etching of the (0001) cleaved surfaces in H₃PO₄ at 120°C suggests that the dissolution characteristics of the surfaces get affected on irradiation with SHI of Li^3?+?, besides supporting the findings of HRXRD and X-ray topography regarding modifications in the perfection of SrFe₁₂O₁₉ on irradiation.     

High resolution X-ray diffraction studies of real structure of nearly perfect single crystals

Real structure together with composition and elemental purity of single crystals controls their properties. This paper reviews recent work carried out at the National Physical Laboratory on application of high resolution X-ray diffractometry, topography and diffuse X-ray scattering for direct observation and characterization of real structure of single crystals of silicon, gallium arsenide, diamond and LiNbO₃. A series of six multicrystal X-ray diffractometers have been designed, developed and fabricated indigenously. The most versatile of these systems is a five crystal X-ray diffractometer with state-of-the-art level resolution. These techniques and equipments have been applied in studying several interesting problems. Even in dislocation-free crystals of silicon, remarkable differences in the defect structure have been observed if the growth method was changed from float zone to Czochralski. Study of effect of externally applied electric fields and ion implantation on real structure of crystals has yielded interesting results. Images of ‘filaments’ which show nonhomogeneous distribution of electric current through semiconductors and insulators have been recorded for the first time in high resolution traverse topographs. Diffracted X-ray intensities could be modified by externally applied electric fields. It has been shown that implantation of BF ₂ ⁺ ions in silicon for producing shallow junctions does not produce homogeneous distribution of boron. The impurity is partially in clustered form. Biaxial stress introduced by thin depositions in substrate crystals are of considerable applied concern. The value and nature of stress have been determined in a number of systems. Typical results obtained on GaAs: multilayer metallizations are described. Also, degradation of perfection of substrates has been monitored. This work has shown that the stress is not homogeneously distributed and is quite anisotropic. A new high resolution X-ray diffraction technique has been developed for direct observation and study of forward diffracted X-ray beam and anomalous transmission of X-rays through ‘thin’ diamond crystals of varying degrees of perfection.     

X-ray diffraction topography investigation of the core in Bi12SiO20 crystals

The core in a large Bi₁₂SiO₂₀ crystal as well as the regions free of optical inhomogenities was examined by X-ray double-crystal diffraction topography. It was established that the observed defects in the central core are two-dimensional. The absorption of some impurities as well as the composition changes observed in this area by other authors, should be considered as a consequence of the formation of these defects.     

Investigation of ammonium diuranate calcination with high-temperature X-ray diffraction

The thermal decomposition of ammonium diuranate (ADU) in air is investigated using in situ high-temperature X-ray diffraction (HT-XRD), thermogravimetry and differential thermal analysis. Data have been collected in the temperature range from 30 to 1000 °C, allowing the observation of phase transformation and the assessment of the energy changes involved in the calcination of ADU. The starting material 2UO₃·NH₃·3H₂O undergoes a process involving several endothermic and exothermic reactions. In situ HT-XRD shows that amorphous UO₃ is obtained after achieving complete dehydration at 300 °C, and denitration at about 450 °C. After cooling from heat treatment at 600 °C, a crystalline UO₃ phase appears, as displayed by ex situ XRD. The self-reduction of UO₃ into orthorhombic U₃O₈ takes place at about 600 °C, but a long heat treatment or higher temperature is required to stabilise the structure of U₃O₈ at room temperature. U₃O₈ remains stable in air up to 850 °C. Above this temperature, oxygen losses lead to the formation of U₃O_8?x , as demonstrated by subtle changes in the diffraction pattern and by a mass loss recorded by TGA.     

Two digital X-ray imaging systems for applications in X-ray diffraction

Two digital X-ray imaging systems developed at the Rutherford Appleton Laboratory are described: the Mark I and the Mark II. Both use a bidimensionally sensitive multiwire proportional counter (MWPC) as the basic X-ray image transducer coupled, in the case of the Mark I to a Digital LSI 11–23 microcomputer system via CAMAC, and in the case of the Mark II to a Digital LSI 11–73 microcomputer system via custom-built data acquisition hardware mounted directly on the Q-bus of the microcomputer. The Mark I system provides the advantages of high speed, high sensitivity digital imaging directly into the computer with the potential for software control of the sample orientation and environment. The Mark II system adds the novel features of signal averaging and multiframe exposures. The dedicated digital memories have a resolution of 512×512 pixels of 16 bits, matching well to the spatial resolution of the xenon-filled MWPC (0.5 mm fwhm over an aperture of 200 mm×200 mm). A 512×512×4 bit video graphics system displays the images in grey scales or colour.     

Composition and conduction mechanism of the NASICON structure X-ray diffraction study on two crystals at different temperatures

The results of a single crystal X-ray structure determination of NASICON at 495K are presented. The crystal symmetry is rhombohedral at this temperature, but monoclinic at room temperature. The structure refinement yielded the following composition: Na/3.1/Zr/1.78/Si/1.24/P/1.76/0/12/. This compound with NASICON structure is not located on the NASICON section given in the literature and this leads us to propose a new compositional plane. The conduction path involves both sodium sites and could be unambiguously derived from the joint probability density (PDF) of the Na ions. The potential barrier calculated from the PDF has about the same value as the activation energies measured on NASICON ceramics above the phase transition. These results are compared with similar studies on a pure Si NASICON crystal at temperatures up to 933K where the same conduction mechanism is found.