Multiple Diffraction Peaks Research Articles

Bragg coherent diffraction imaging by simultaneous reconstruction of multiple diffraction peaks

Bragg coherent diffractive imaging (BCDI) is a noninvasive microscopy technique that can visualize the morphology and internal lattice deviations of crystals with nanoscale spatial resolution and picometer deformation sensitivity. While BCDI has been successfully applied in various studies of materials, it is less successful for highly strained crystals. Specifically, it is difficult to correctly reconstruct the electron density of a highly strained object using conventional phase retrieval algorithms. Although various algorithms have been developed to overcome this challenge, most of them require a priori knowledge that is not always available in practice. Here we report a phase retrieval workflow that can invert diffraction patterns from multiple Bragg peaks simultaneously. The workflow is explored via simulated diffraction from crystals with various strain conditions. Reconstructions from the workflow consistently demonstrate more accurate electron density maps, in comparison with the conventional method. For highly strained crystals, the workflow improves the reliability and consistency of BCDI phase retrieval significantly.

Acoustic response of a laser-excited polycrystalline Au-film studied by ultrafast Debye–Scherrer diffraction at a table-top short-pulse x-ray source

The transient acoustic response of a free-standing, polycrystalline thin Au-film upon femtosecond optical excitation has been studied by time-resolved Debye–Scherrer x-ray diffraction using ultrashort Cu Kα x-ray pulses from a laser-driven plasma x-ray source. The temporal strain evolution has been determined from the transient shifts of multiple Bragg diffraction peaks. The experimental data are in good agreement with the results of calculations based on the two-temperature model and an acoustic model assuming uniaxial strain propagation in the laser-excited thin film.

Deviatoric deformation kinetics in high entropy alloy under hydrostatic compression

An equiatomic CoCrFeMnNi high-entropy alloy under hydrostatic compression is investigated using in-situ angular-dispersive X-ray diffraction to explore the polymorphism in high entropy alloy systems. The metallic system is of face-centered-cubic structure at ambient condition and applied hydrostatic pressures up to 20 GPa via diamond anvil cell. The angle-resolved diffraction-intensity evolutions of multiple diffraction peaks were collected simultaneously to elucidate the phase stability examinations. The phase transformation from face-centered-cubic to hexagonal-close-packed structure was evidently observed in CoCrFeMnNi alloy accompanied by a deviatoric strain subjected to the hydrostatic compression. We found lattice-asymmetric crossover before and after the phase transformation subjected to hydrostatic compression surroundings. Deviatoric strain triggers fcc-hcp phase transformation as local heterogeneity-driven lattice distortion is significant for CoCrFeMnNi alloy.

Determination of the electron-lattice coupling strength of copper with ultrafast MeV electron diffraction.

Electron-lattice coupling strength governs the energy transfer between electrons and the lattice and is important for understanding the material behavior under highly non-equilibrium conditions. Here we report the results of employing time-resolved electron diffraction at MeV energies to directly study the electron-lattice coupling strength in 40-nm-thick polycrystalline copper excited by femtosecond optical lasers. The temporal evolution of lattice temperature at various pump fluence conditions were obtained from the measurements of the Debye-Waller decay of multiple diffraction peaks. We observed the temperature dependence of the electron-lattice relaxation time which is a result of the temperature dependence of electron heat capacity. Comparison with two-temperature model simulations reveals an electron-lattice coupling strength of (0.9 ± 0.1) × 1017 W/m3/K for copper.

Irreversible phase transformation in a CoCrFeMnNi high entropy alloy under hydrostatic compression

An equal-molar CoCrFeMnNi, face-centered-cubic high-entropy alloy system is investigated using in-situ angular-dispersive X-ray diffraction under hydrostatic compression up to 20GPa via diamond anvil cell. The evolutions of multiple diffraction peaks are collected simultaneously to elucidate the phase stability field. The results indicated that an irreversible phase transformation had occurred in the high entropy alloy upon decompression to ambient pressure. A reference material (n-type silicon-doped gallium arsenide) was investigated following the same protocol to demonstrate the different deformation mechanisms. It is suggested that the atomic bonding characteristics on the phase stability may play an important role in the high entropy alloys.

Silicon waveguide polarization rotation Bragg grating with phase shift section and sampled grating scheme

We describe a Bragg grating with a phase shift section and a sampled grating scheme that converts input polarization to orthogonal polarization. A very narrow polarization-independent wavelength peak can be generated by phase shift structures and polarization-independent multiple diffraction peaks by sampled gratings. The characteristics of the device were examined by transfer matrix and finite-difference time-domain methods.

A study of lattice elasticity from low entropy metals to medium and high entropy alloys

An equal-molar CoCrFeMnNi, face-centered-cubic high-entropy alloy system and a face-centered-cubic stainless steel described as a medium-entropy system, are measured by in situ neutron-diffraction experiments subjected to continuous tension at room and several elevated temperatures, respectively. With spallation neutron, the evolution of multiple diffraction peaks is collected simultaneously for lattice-elasticity study. Temperature variation of elastic stiffness of a single face-centered-cubic-phase Ni and a single face-centered-cubic-phase Fe are compared as low-entropy metals. The CoCrFeMnNi high-entropy alloy shows distinct lattice anisotropy.

Quantum reflection and interference of matter waves from periodically doped surfaces

We show that periodically doped, flat surfaces can act as reflective diffraction gratings for atomic and molecular matter waves. The diffraction element is realized by exploiting that charged dopants locally suppress quantum reflection from the Casimir-Polder potential. We present a general quantum scattering theory for reflection off periodically charged surfaces and discuss the requirements for the observation of multiple diffraction peaks.

Growth of CdSiP2 single crystals by double-walled quartz ampoule technique

A CdSiP2 single crystal measuring 15mm in diameter and 35mm in length was grown by the modified vertical Bridgman method adopting a specially designed double-walled quartz ampoule. The as-grown crystal was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), X-ray fluorescence (XRF), infrared (IR) and visible–near infrared (VIS–NIR) spectrophotometers and X-ray photoelectron spectroscopy (XPS). It is found that multiple diffraction peaks of a (101) cleavage face are evident and parallel growth steps on the face are observed. The XRF result indicates that the chemical composition of the as-grown crystal is close to the ideal stoichiometry. The IR transmittance of a sample with 2mm thickness is about 48% in the range from 10,000 to 1500cm−1. The VIS–NIR spectrum shows that the short wave absorption edge is at about 576nm and the calculated band gap is about 2.15eV. The binding energies of the Cd 3d3/2, Cd 3d5/2, Si 3d and P 2p core levels are determined to be 411.8eV, 405.1eV, 101.1eV and 129.5eV, respectively. These results show that the quality of the as-grown crystal is good and the double-walled quartz ampoule technique is promising for the growth of high-quality CdSiP2 single crystals.

Internal Strain Behavior Exerted on YBCO Layer in the YBCO Coated Conductor

The stress/strain dependence of elastic property of the surround Cu stabilized YBCO coated conductor was precisely investigated by means of white X-ray and pulsed neutrons. Multiple diffraction peaks were observed along axial and lateral directions with the tape axis as a function of tensile load. The following unusual stress/strain behaviors exerted on the YBCO layer were made clear. Pairs of (020)/(200) and (040)/(400) were observed side by side in two rows and their diffraction intensity was almost constant with increasing tensile load. The ratio of diffraction strain to external strain became less than unity. The diffraction elastic constants estimated from (0 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> 0) diffraction peaks were larger than from ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i> 00) peaks. Their observations strongly suggest that the micro twin structure is key nanostructure to understand the microscopic elastic constant and strain obtained from the diffraction experiments.

Growth of ZnGeP&lt;sub&gt;2&lt;/sub&gt; Single Crystal by Three-Temperature-Zone Furnace

In order to meet the requirements of growing high-quality ZnGeP2, a crystal growth furnace with three-temperature-zone was designed and fabricated based on a conventional vertical two-zone tubular resistance furnace. Appropriate temperature gradients of 12~15°C/cm at the growth interface and stable thermal profile were obtained. A crack-free ZnGeP2 single crystal with size of Φ15mm×30mm was grown successfully in the furnace mentioned above. The as-grown crystal was characterized by X-ray diffraction (XRD) and Infrared (IR) spectrophotometers. It is found that there is a cleavage face of (101) and X-ray multiple diffraction peaks of the {101} faces are observed, The infrared transmission of a ZnGeP2 wafer of 3 mm thickness is about 50% in the region of 3~10μm. These results show the designed crystal growth furnace is suitable for growth of ZnGeP2 crystal, and the as-grown ZnGeP2 crystal has good structural integrity and high quality.

S28 Elastic-Plastic Deformation of a Polycrystalline Titanium Alloy Studied In Situ by Energy-Dispersive Synchrotron X-ray Diffraction

Elastic lattice strain in polycrystalline assemblies evolves as a function of applied load due to elastic and plastic deformation mechanisms. The detailed nature of this deformation is complex and depends on the local arrangement of grains, their morphology and orientation, etc. To obtain mesoscopic (intermediate) scale description of polycrystal deformation, one approach that can be adopted is to measure the average lattice strain response of grain groups sharing common orientation by diffraction as the sample is subjected to increasing uniaxial load [1]. This reveals the anisotropy of the response of individual reflections (orientation grain groups), and enables the determination of the inhomogeneous fields of elastic and eventually plastic strain, if the measurements are combined with suitable interpretation and modeling approaches. Regions of localized macroscopic plasticity may be identified, and the prediction of fatigue crack initiation may also be addressed using energy dissipation at the micro-scale [2]. In the present study in situ loading and synchrotron X-ray diffraction experiments on Ti-6Al-4V alloy were performed. Multiple diffraction peaks were obtained from the experiments and both single peak fitting and Pawley pattern refinement were used for interpretation. The calculation of stress-strain response of hkl lattice planes based on the a and c lattice parameters obtained from Pawley pattern refinement was in good agreement with the results obtained by single peak fitting. The orientation dependence of polycrystal lattice stiffness and strain is discussed and a modified profile function for pattern refinement is proposed to provide an improved description of anisotropic behavior. Diffraction peak broadening was considered and the correlation between peak width and plastic strain was found (Fig 1). The intergranular strain responses for differently oriented crystallites obtained from the diffraction experiments were compared to the crystal plasticity finite element model predictions and used for validation of the model.

Growth of AgGaS 2 single crystals by modified furnace

A crystal growth furnace with new structure was designed based on a conventional vertical resistance-wound tubular two-temperature-zone furnace in order to meet the requirements of growing high-quality AgGaS 2 single crystals. Large temperature gradients of 25–30 °C/cm at the growth interface and stable thermal profile were obtained. Integral and crack-free AgGaS 2 single crystals with fewer defects were grown successfully and reproducibly in the furnace mentioned above. A new cleavage face (1 0 1) was observed in the as-grown AgGaS 2 crystal. The crystal was characterized by using XRD and IR transmission microscopy. It is found that multiple diffraction peaks of the {1 0 1} faces are evident, and that IR transmittance is above 60%. The results show not only that the modified furnace is a new promising furnace for the growth of AgGaS 2 single crystals, but also that the quality of the grown crystal is good.

The determination of a continuum mechanics equivalent elastic strain from the analysis of multiple diffraction peaks

Stress measurement by neutron or synchrotron x-ray diffraction is a nondestructive technique that provides insights into strain and/or stress fields deep within engineering components and structures. The technique is seeing increased use for the validation of finite element process models, however, present FE models predict a continuum elastic strain rather than diffraction strains. An expression is therefore derived for a physically realistic weighting of strains obtained from multiple single peak diffraction measurements of internal elastic strain in order to determine a macroscopic equivalent elastic strain, and hence stress. A practical approach to the use of the expression is suggested. A similar expression is derived for the equivalent weighting used in Rietveld refinements, for both polychromatic and monochromatic sources, which is applicable to both neutron and x-ray diffraction. The use of these expressions is illustrated for both textured and untextured, cubic (steel) and hexagonal (titanium) symmetry polycrystals. The physically realistic weighting is different from that used in the Rietveld refinement however both provide good estimates of the macroscopic equivalent elastic strain.

Optical properties and orientation of arrays of polystyrene spheres deposited using convective self-assembly

We have prepared face centered close packed arrays of polystyrene spheres using convective self-assembly. The optical properties of the arrays of spheres were studied and revealed high quality crystals that could be prepared using this method. Optical transmission measurements over a wide spectral range reveal the presence of multiple diffraction peaks. Their use for checking the quality of the arrays is proposed. The orientation of the arrays formed was studied using optical diffraction and atomic force microscopy. Both indicate the formation of oriented crystals. This was until now only reported for epitaxial growth of colloidal crystals. The oriented crystals were used to measure their photonic band structure.

Preparation of silver behenate coatings to provide low- to mid-angle diffraction calibration

A method for the preparation of a well aligned silver behenate sample is described. Multiple (0 0 l) diffraction peaks, (0 0 1) to (0 0 48), are easily observed using a conventional laboratory X-ray diffraction instrument.

Modified growth of Cd 1− xZn xTe single crystals

Good quality Cd 1− x Zn x Te ( x=0.04) single crystals 20 mm in diameter and 45 mm in length were grown by a modified growth technique, i.e. descending ampoule with rotation. Synthesis of the polycrystalline material using the melt temperature oscillation method (MTOM) and growth of Cd 0.96Zn 0.04Te single crystals were carried out in the same quartz ampoule without transfer between the steps. The as-grown crystal was characterized by using X-ray diffraction, IR transmission microscopy, FTIR spectroscopy and scanning electron microscopy (SEM). It was found that there is a (1 1 0) cleavage face in the as-grown crystal, multiple diffraction peaks of the {1 1 0} faces were evident, the transmission of the crystal sample of 30 mm thickness is up to 62% in the range from 6500 to 400 cm −1, the absorption coefficient is 0.021 cm −1. The surface of the {1 1 0} oriented wafer showed perfect homogeneous growth steps. The results showed that not only is MTOM a new effective method for synthesizing high-purity single-phase Cd 1− x Zn x Te polycrystalline materials, but also that the modified growth technique (descending ampoule with rotation) is a new promising method for growing high-quality Cd 1− x Zn x Te single crystals. Further, the crystal grown, using the polycrystalline materials synthesized by the modified growth technique shows neither any sign of phase separation nor ordering effects or structure distortion. The quality of the crystal is good.

UMWEG-98: a program for calculation and graphical representation of multiple diffraction patterns

UMWEG-XX was designed as a software tool for taking into account multiple diffraction effects in many areas of crystal structure analysis. TheUMWEG-98 version of the program makes possible the calculation and graphical representation of multiple diffraction patterns (Renninger scans, multiple diffraction peak location plots) of forbidden and weak reflections and can be applied to synchrotron as well asKα1,2radiation. The program is written in standard Fortran90 and may be ported to Unix platforms, such as HP, Sun, Silicon Graphics and IBM, as well as to DOS and Windows platforms. The program runs without any commercial subroutine libraries. Consequently it can be used without licence problems. A current version is distributedviahttp://www.rrz.uni-hamburg.de/mpi/rossmanith. Executable (binary) files are available free of charge for academic use only.

Use of Rietveld refinement to fit a hexagonal crystal structure in the presence of elastic and plastic anisotropy

When multiple elastic diffraction peaks are obtained from an x-ray or neutron source, data analysis is commonly performed using a Rietveld refinement applied to the entire pattern, rather than simply performing single peak fits. In the simplest case the crystal structure is assumed to be ideal despite the presence of stresses which, coupled with the elastic and plastic anisotropy of individual grains, can result in a nonisotropic response of the polycrystal. A first step to account for this anisotropy in the refinement is to include an anisotropic strain parameter. In an earlier work [J. Appl. Phys. 82, 1554 (1997)] we included elastic anisotropy into a Rietveld refinement and discussed its validity in the elastic and plastic regimes for a cubic crystal structure. Here we extend the discussion to include anisotropy in hexagonal crystal structures. The agreement between single peak fits and the Rietveld refinement modeled single peak positions is considered for hexagonal close packed beryllium in the presence of an applied compressive load, in both the elastic and plastic regime (to ∼1% plastic strain). Agreement is found to be good in the elastic and early plastic regime, where only basal slip is assumed to be active. At higher loads, where prism slip and/or basal fracture are also assumed to be active, agreement is poorer for some diffraction planes. The implications for residual stress measurements are considered.

Synchrotron radiation multiple diffraction study of Al 0.304Ga 0.172In 0.524As MOVPE grown onto InP(001)

Synchrotron radiation multiple diffraction in Renninger scanning (RS) geometry is used to characterise an Al 0.304Ga 0.172In 0.524 As hetero-epitaxial layer MOVPE grown onto InP(001). (006) RS data for bulk, InP substrate and the quaternary layer were obtained using a new experimental set-up on station 7.6 at the Daresbury synchrotron radiation source. Examination of the multiple diffraction peak profiles reveal the epitaxial layers to have a higher mosaic spread than the underlying substrate materials. Measurements of the layer parallel lattice parameter a ∥ = 5.8755 ± 0.003 A ̊ , as deduced from the tetragonal distortion measured at the 6-beam case in the layer RS, agrees very well with that obtained from the 222 2̄2̄2 intensity modulation on the substrate RS MORSI (modulation on the RS intensity due to the presence of the epilayers, Greenberg and Ladell, Appl. Phys. Lett 50 (1987) 436), which gives a ⊥ = 5.877 ± 0.002 A ̊ . Simulation of the layer RS using the MULTX program is consistent with a layer normal lattice parameter a ⊥ = 5.8574 A ̊ in good agreement with the corresponding experimental data.