Lattice imperfection studies in polycrystalline materials by x-ray diffraction line-profile analysis

This review concerns our recent investigations with a series of binary fcc Ag- and Cu-base alloys (viz Ag-Ga, Ag-Ge, Ag-Al and Cu-Ga, Cu-Ge) from detailed analyses of x-ray diffraction line profiles, the importance of which has been briefly summarized. The theoretical formulations of the Warren-Averbach’s method of Fourier analysis of peak-shapes along with the methods of peak-shift and peak-asymmetry have been outlined. A preview on the significant studies carried out earlier with Ag- and Cu-base (fcc) binary alloys has been made in short. A detailed analyses on the recorded profiles in the present considerations revealed, in general, quantitative estimates of several microstructural parameters characterising the deformed state of the materials namely, propensity of stacking faults (intrinsic, extrinsic and twin faults), rms microstrains, coherent domain sizes, long-range residual stresses, lattice parameter changes, dislocation density and stacking fault energy. The results indicate a general trend of increase in the concentrations of stacking faults, primarily, of intrinsic character, with increase in solute concentrations; which are solely responsible for the observed peak-shifts as well as domain size broadening. Small asymmetry in the profiles is due to the presence of extrinsic stacking faults, relatively less in magnitude compared to the intrinsic ones while the deformation twin faults are almost absent—an observation with significance. The dislocation density, quite appreciable in magnitude, has been evaluated from the anisotropic values of the coherent domain sizes and rms microstrains. The stacking fault energies of pure Ag and Cu, an important parameter have also been estimated and compared with those obtained from electron microscopy. Annealing experiments with a Ag-5·8% Al alloy, aluminium being a precipitating solute, do not reveal any detectable evidence of solute segregation at the stacking faults. The occurrence of stacking faults in the alloy systems has been correlated with a number of physical factors involving solvent-solute types.     

Diamond-anvil cell for radial x-ray diffraction

We have designed a new diamond-anvil cell capable of radial x-ray diffraction to pressures of a few hundred GPa. The diffraction geometry allows access to multiple angles of Ψ, which is the angle between each reciprocal lattice vector g(hkl) and the compression axis of the cell. At the 'magic angle', Ψ≈54.7°, the effects of deviatoric stresses on the interplanar spacings, d(hkl), are significantly reduced. Because the systematic errors, which are different for each d(hkl), are significantly reduced, the crystal structures and the derived equations of state can be determined reliably. At other values of Ψ, the effects of deviatoric stresses on the diffraction pattern could eventually be used to determine elastic constants.     

Neutron powder diffraction and high-pressure synchrotron x-ray diffraction study of tantalum nitrides

Tantalum nitride(TaN) compact with a Vickers hardness of 26 GPa is prepared by a high-pressure and hightemperature(HPHT) method. The crystal structure and atom occupations of WC-type TaN have been investigated by neutron powder diffraction, and the compressibility of WC-type TaN has been investigated by using in-situ high-pressure synchrotron x-ray diffraction. The third-order Birch–Murnaghan equation of state fitted to the x-ray diffraction pressure–volume(P–V) sets of data, collected up to 41 GPa, yields ambient pressure isothermal bulk moduli of B'_0= 369(2) GPa with pressure derivatives of B 0= 4 for the WC-type TaN. The bulk modulus of WC-type TaN is not in good agreement with the previous result(B_0= 351 GPa), which is close to the recent theoretical calculation result(B_0= 378 GPa). An analysis of the experiment results shows that crystal structure of WC-type TaN can be viewed as alternate stacking of Ta and N layers along the c direction, and the covalent Ta–N bonds between Ta and N layers along the c axis in the crystal structure play an important role in the incompressibility and hardness of WC-type TaN.     

Multiwavelength anomalous diffraction at high x-ray intensity

The multiwavelength anomalous diffraction (MAD) method is used to determine phase information in x-ray crystallography by employing anomalous scattering from heavy atoms. X-ray free-electron lasers (FELs) show promise for revealing the structure of single molecules or nanocrystals, but the phase problem remains largely unsolved. Because of the ultrabrightness of x-ray FEL, samples experience severe electronic radiation damage, especially to heavy atoms, which hinders direct implementation of MAD with x-ray FELs. Here, we propose a generalized version of MAD phasing at high x-ray intensity. We demonstrate the existence of a Karle-Hendrickson-type equation in the high-intensity regime and calculate relevant coefficients with detailed electronic damage dynamics of heavy atoms. The present method offers a potential for ab initio structural determination in femtosecond x-ray nanocrystallography.     

Coherent x-ray diffraction imaging with nanofocused illumination

Coherent x-ray diffraction imaging is an x-ray microscopy technique with the potential of reaching spatial resolutions well beyond the diffraction limits of x-ray microscopes based on optics. However, the available coherent dose at modern x-ray sources is limited, setting practical bounds on the spatial resolution of the technique. By focusing the available coherent flux onto the sample, the spatial resolution can be improved for radiation-hard specimens. A small gold particle (size <100 nm) was illuminated with a hard x-ray nanobeam (E=15.25 keV, beam dimensions approximately 100 x 100 nm2) and is reconstructed from its coherent diffraction pattern. A resolution of about 5 nm is achieved in 600 s exposure time.     

High resolution 3D x-ray diffraction microscopy

We have imaged a 2D buried Ni nanostructure at 8 nm resolution using coherent x-ray diffraction and the oversampling phasing method. By employing a 3D imaging reconstruction algorithm, for the first time we have experimentally determined the 3D structure of a noncrystalline nanostructured material at 50 nm resolution. The 2D and 3D imaging resolution is currently limited by the exposure time and the computing power, while the ultimate resolution is limited by the x-ray wavelengths. We believe these results pave the way for the development of atomic resolution 3D x-ray diffraction microscopy.     

Enhanced x-ray phase determination by three-beam diffraction

For decades, solving the phase problem of x-ray scattering has been a goal that, in principle, could be achieved by means of n-beam diffraction (n-BD). However, the phases extracted by the actual n-BD phasing techniques are not very precise, mainly due to systematic errors that are difficult to estimate. We present an innovative theoretical approach and experimental procedure that, combined, eliminate two major sources of error. It is a high precision phasing technique that provides the triplet-phase angle with an error of about 2 degrees.     

Rietveld analysis for energy dispersive x-ray diffraction under high pressure with synchrotron radiation

Abstract

A new program has been developed for the conversion of energy-dispersive x-ray diffraction spectra obtained from powder samples at high pressure in a diamond anvil cell (DAC) into conventional pseudo angle-dispersive data. The program is compatible with a conventional Rietveld program. This allows the determination of the structural parameters of the samples investigated. Results of a synchrotron radiation study of polycrystalline SrFCl in the tetragonal phase at high pressure are presented.

Presented at the IUCr Workshop on ‘Synchrotron Radiation Instrumentation for High Pressure Crystallography’, Daresbury Laboratory 20-21 July 1991     

Characterization of multilayer systems by high-resolution x-ray diffraction

The x-ray diffraction pattern of MBE-grown Ga_1–x Al _x As/GaAs superlattices has been measured withd-spacing resolutiond/d approaching 17000, corresponding to about 8500 Å^–1. The resolution was achieved by employing a highly dispersive monochromator consisting of a pair of fivefold reflecting grooved silicon crystals which delivers about 10⁴ photons s^–1 to the sample. Detailed information like the presence of buffer layers, the molar fractionx, the numberp of layers, the superlattice periodt _p , and the component layer thicknessest ₁ ,t ₂ are extracted from the measured pattern by comparing it with the pattern calculated from the dynamical theory for layer structures. In addition, the influence of disorder on the determination of the above superlattice parameters is investigated by including two different models of disorder.     

Multiple-wave diffraction in high energy resolution back-reflecting x-ray optics

We have studied the effects of multiple-wave diffraction in a novel optical scheme recently published by Shvyd'ko et?al. utilizing Bragg diffraction of x?rays in backscattering geometry from asymmetrically cut crystals for achieving energy resolutions beyond the intrinsic width of the Bragg reflection. By numerical simulations based on dynamic x-ray diffraction and by experimentation involving two-dimensional angular scans of the back-reflecting crystal, multiple-wave diffraction was found to contribute up to several tens percent loss of efficiency but can be avoided without degrading the energy resolution of the original scheme by careful choice of azimuthal orientation of the diffracting crystal surface and by tilting of the crystal perpendicular to the dispersion plane.     

Quasi-sinusoidal single-order diffraction transmission grating used in x-ray spectroscopy

A novel design of quasi-sinusoidal single-order diffraction transmission grating (QSTG) is proposed, which can achieve a line density up to thousands line/millimeter as that of traditional transmission gratings with the current level of nanofabrication technique. We fabricate a 1000?line/mm QSTG using the new design approach, and display the calibration results of such QSTG on the soft x-ray beam of synchrotron radiation.     

Microstructure and strain films using in-plane grazing analysis of GaN epitaxial incidence x-ray diffraction

This paper investigates the major structural parameters, such as crystal quality and strain state of （001）-oriented GaN thin films grown on sapphire substrates by metalorganic chemical vapour deposition, using an in-plane grazing incidence x-ray diffraction technique. The results are analysed and compared with a complementary out-of-plane x- ray diffraction technique. The twist of the GaN mosaic structure is determined through the direct grazing incidence t of （100） reflection which agrees well with the result obtained by extrapolation method. The method for directly determining the in-plane lattice parameters of the GaN layers is also presented. Combined with the biaxial strain model, it derives the lattice parameters corresponding to fully relaxed GaN films. The GaN epilayers show an increasing residual compressive stress with increasing layer thickness when the two dimensional growth stage is established, reaching to a maximum level of-0.89 GPa.     

Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence x-ray diffraction

This paper investigates the major structural parameters,such as crystal quality and strain state of (001)-oriented GaN thin films grown on sapphire substrates by metalorganic chemical vapour deposition,using an in-plane grazing incidence x-ray diffraction technique.The results are analysed and compared with a complementary out-of-plane xray diffraction technique.The twist of the GaN mosaic structure is determined through the direct grazing incidence measurement of (100) reflection which agrees well with the result obtained by extrapolation method.The method for directly determining the in-plane lattice parameters of the GaN layers is also presented.Combined with the biaxial strain model,it derives the lattice parameters corresponding to fully relaxed GaN films.The GaN epilayers show an increasing residual compressive stress with increasing layer thickness when the two dimensional growth stage is established,reaching to a maximum level of-0.89 GPa.     

Visualizing chemical reactions in solution by picosecond x-ray diffraction

We present a time-resolved x-ray diffraction study to monitor the recombination of laser-dissociated iodine molecules dissolved in CCl4. The change in structure of iodine is followed during the whole recombination process. The deexcitation of solute molecules produces a heating of the solvent and induces tiny changes in its structure. The variations in the distance between pairs of chlorine atoms in adjacent CCl4 molecules are probed on the mA length scale. However, the most striking outcome of the present work is the experimental determination of temporally varying atom-atom pair distribution functions. Variations of the mean density of the solution during thermal expansion are also followed in real time. One concludes that not only time-resolved optical spectroscopy but also time-resolved x-ray diffraction can be used to monitor atomic motions in liquids.     

High pressure x-ray diffraction techniques with synchrotron radiation

This article summarizes the developments of experimental techniques for high pressure x-ray diffraction(XRD) in diamond anvil cells(DACs) using synchrotron radiation. Basic principles and experimental methods for various diffraction geometry are described, including powder diffraction, single crystal diffraction, radial diffraction, as well as coupling with laser heating system. Resolution in d-spacing of different diffraction modes is discussed. More recent progress, such as extended application of single crystal diffraction for measurements of multigrain and electron density distribution, timeresolved diffraction with dynamic DAC and development of modulated heating techniques are briefly introduced. The current status of the high pressure beamline at BSRF(Beijing Synchrotron Radiation Facility) and some results are also presented.