Kinematical Diffraction Research Articles

Piezoelectricity in La0.85Ce0.15MnO3 layer of BiFeO3/ La0.85Ce0.15MnO3 based ferroelectric/semiconductor oxide superlattice

Superlattice comprising of ferroelectric (FE) and non-ferroelectric (non-FE) material has been developed to induce a ferroelectric response in the non-ferroelectric layer. In this study, a superlattice thin film comprising of BiFeO3 (BFO) as FE oxide and La0.85Ce0.15MnO3 (LCMO) as semiconducting non-FE oxide is fabricated and investigated the FE and piezoelectric responses in LCMO. We observed the piezoelectric response of individual layers using time-resolved X-ray microdiffraction experiment under an external electric field. Piezoelectric response of individual layers was resolved by comparing it with the values obtained from kinematic diffraction calculation. Piezoelectric coefficient (d33) of LCMO monolayer is found to be approximately 27 pm/V, which is a similar value as that of the BFO layer.

Determination of atomic positions and polar direction in half-Heusler material Sb1-xSnxTi1-y-zHfyZrzCo using electron channeling

Variation of electron-induced x-ray emission with the crystal direction of an incoming electron beam (channeling) is used to study the crystal site preference of different elements in a promising thermoelectric half-Heusler material. This material has Sb, Co and Ti as the main constituting elements, with lower contents of Hf, Zr and Sn. It is confirmed experimentally, in accordance with previous assumptions, that Sb and Sn occupy one of the octahedral sites, 4a (0, 0, 0), Ti, Zr and Hf the other octahedral site, 4b (½, ½, ½), and Co atoms occupy the tetrahedral site, 4c (¼, ¼, ¼) in the cubic spacegroup F4¯3m with lattice constant a = 0.598 ± 0.001 nm. Furthermore, a strong asymmetry along the polar directions is observed, which is as it should be in a half-Heusler material, when the Co atoms have a strong preference for one of the two sets of tetrahedral sites. Such asymmetries can not be observed by kinematical diffraction according to Friedel’s law, thus demonstrating that the observation of element characteristic signals under channeling conditions is a unique technique for determining the sense of polar directions and distinguishing crystal symmetry alternatives in small crystal grains and nanocrystals.

Diffraction from twisted nanowires: helicity revealed by anisotropy

The helical nature of twisted nanowires is studied by simulated X-ray diffraction. It is shown that this helicity is revealed by the anisotropy, which can be both an elastic anisotropy, through the warping displacement generated by torsion, or a shape anisotropy of the cross section. To support the analytical calculations, based on the kinematic theory of diffraction by helices, atomistic simulations of copper nanowires are performed.

Effect of Sn Doping on the Crystallization Kinetics of Amorphous TlInS2 Films

The crystallization of amorphous Sn-doped TlInS2 films into three polymorphs has been studied by kinematic electron diffraction. The results demonstrate that the crystallization of 30-nm-thick amorphous films produced by thermal evaporation in high vacuum can be described by the Avrami–Kolmogorov equation: Vτ = V0[1–exp(–kτm)]. Kinematic electron diffraction patterns of the TlIn1–хSnxS2 films have been used to assess the effect of doping with Sn on the growth dimensionality and the activation energy for the crystallization of the amorphous films and the unit-cell parameters of the resultant crystalline materials. Doping extends the temperature range and effective activation energy for the crystallization of the amorphous films.

Diffuse X-ray scattering from local chemical inhomogeneities in InGaN layers

Diffuse X-ray scattering from random chemical inhomogeneities in epitaxial layers of InGaN/GaN was simulated using linear elasticity theory and kinematical X-ray diffraction. The simulation results show the possibility of determining the r.m.s. deviations of the local In content and its lateral correlation length from reciprocal-space maps of the scattered intensity. The reciprocal-space distribution of the intensity scattered from inhomogeneities is typical and it can be distinguished from other sources of diffuse scattering such as threading or misfit dislocations.

Structure, Elastic Constants and XRD Spectra of Extended Solids under High Pressure

ABSTRACTWe present results of evolutionary simulations based on density functional calculations of a potentially new type of energetic materials called extended solids: P-N and N-H. High-density structures with covalent bonds generated using variable and fixed concentration methods were analysed in terms of thermo-dynamical stability and agreement with experimental X-ray diffraction (XRD) spectra. X-ray diffraction spectra were calculated using a virtual diffraction algorithm that computes kinematic diffraction intensity in three-dimensional reciprocal space before being reduced to a two-theta line profile. Calculated XRD patterns were used to search for the structure of extended solids present at experimental pressures by optimizing data according to experimental XRD peak position, peak intensity and theoretically calculated enthalpy. Elastic constants has been calculated for thermodynamically stable structures of P-N system.

Simulation of kinematic Kikuchi diffraction patterns from atomistic structures

One of the limitations of atomistic simulations is that many of the computational tools used to extract structural information from atomic trajectories provide metrics that are not directly compatible with experiments for validation. In this work, to bridge between simulation and experiment, a method is presented to produce simulated Kikuchi diffraction patterns using data from atomistic simulations, without requiring a priori specification of the crystal structure or defect periodicity. The Kikuchi pattern simulation is based on the kinematic theory of diffraction, with Kikuchi line intensities computed via a discrete structure factor calculation. Reciprocal lattice points are mapped to Kikuchi lines using a geometric projection of the reciprocal space data. This method is validated using single crystal atomistic models, and the novelty of this approach is emphasized by simulating kinematic Kikuchi diffraction patterns from an atomistic model containing a nanoscale dislocation loop. Deviations in kinematic Kikuchi line intensities are explained considering the displacement field of the dislocation loop, as is done in diffraction contrast theory.

Quantitative disentanglement of coherent and incoherent laser-induced surface deformations by time-resolved x-ray reflectivity

We present time-resolved x-ray reflectivity measurements on laser excited coherent and incoherent surface deformations of thin metallic films. Based on a kinematical diffraction model, we derive the surface amplitude from the diffracted x-ray intensity and resolve transient surface excursions with sub-Å spatial precision and 70 ps temporal resolution. The analysis allows for decomposition of the surface amplitude into multiple coherent acoustic modes and a substantial contribution from incoherent phonons which constitute the sample heating.

Threefold rotational symmetry in hexagonally shaped core-shell (In,Ga)As/GaAs nanowires revealed by coherent X-ray diffraction imaging.

Coherent X-ray diffraction imaging at symmetric hhh Bragg reflections was used to resolve the structure of GaAs/In0.15Ga0.85As/GaAs core-shell-shell nanowires grown on a silicon (111) substrate. Diffraction amplitudes in the vicinity of GaAs 111 and GaAs 333 reflections were used to reconstruct the lost phase information. It is demonstrated that the structure of the core-shell-shell nanowire can be identified by means of phase contrast. Interestingly, it is found that both scattered intensity in the (111) plane and the reconstructed scattering phase show an additional threefold symmetry superimposed with the shape function of the investigated hexagonal nanowires. In order to find the origin of this threefold symmetry, elasticity calculations were performed using the finite element method and subsequent kinematic diffraction simulations. These suggest that a non-hexagonal (In,Ga)As shell covering the hexagonal GaAs core might be responsible for the observation.

Observation of sagittal X-ray diffraction by surface acoustic waves in Bragg geometry

X-ray Bragg diffraction in sagittal geometry on a Y-cut langasite crystal (La3Ga5SiO14) modulated by Λ = 3 µm Rayleigh surface acoustic waves was studied at the BESSY II synchrotron radiation facility. Owing to the crystal lattice modulation by the surface acoustic wave diffraction, satellites appear. Their intensity and angular separation depend on the amplitude and wavelength of the ultrasonic superlattice. Experimental results are compared with the corresponding theoretical model that exploits the kinematical diffraction theory. This experiment shows that the propagation of the surface acoustic waves creates a dynamical diffraction grating on the crystal surface, and this can be used for space-time modulation of an X-ray beam.

CADEM: calculate X-ray diffraction of epitaxial multilayers.

Epitaxial multilayers and superlattice (SL) structures are gaining increasing importance as they offer the opportunity to create artificial crystals with new functionalities. These crystals deviate from the parent bulk compounds not only in terms of the lattice constants but also in the symmetry classification, which renders calculation of their X-ray diffraction (XRD) patterns tedious. Nevertheless, XRD is essential to get information on the multilayer/SL structure such as, for example,out-of-plane lattice constants, strain relaxation and period length of the crystalline SL. This article presents a powerful yet simple program, based on the general one-dimensional kinematic X-ray diffraction theory, which calculates the XRD patterns of tailor-made multilayers and thus enables quantitative comparison of measured and calculated XRD data. As the multilayers are constructed layer by layer, the final material stack can be entirely arbitrary. Moreover, CADEM is very flexible and can be straightforwardly adapted to any material system. The source code of CADEM is available as supporting material for this article.

Effects of Domain Boundaries on the Diffraction Patterns of One-Dimensional Structures

Motivated by diffraction experiments on the (2√3 x √3) R30◦ reconstructed Si(111) surface due to deposition of rare earth elements (Dy, Tb) and silicide formation, we analyse the splitting and non-splitting of superstructure diffraction spots. For this purpose, we model diffraction patterns for one-dimensional structures generated by the binary surface technique and use supercell models to keep the analysis simple. Diffraction patterns are calculated in the framework of the kinematical diffraction theory, and they are analyzed as a function of the domains and domain boundaries. Basic properties of the diffraction pattern are analyzed for model systems of a two-fold and a three-fold periodicity. The rules derived from these calculations are applied to the “real-world” system of Si(111)-(2√3 × √3) R30◦-RESix (RE = Dy or Tb). Depending on the combination of domains and domain boundaries of different types, a plethora of different features are observed in the diffraction patterns. These are analyzed to determine the sizes of both domain boundaries and domains from experimentally observed splitting of specific superstructure spots.

Strain-induced quasi-one-dimensional rare-earth silicide structures on Si(111)

After deposition of rare-earth elements (Dy, Tb) on Si(111) at elevated temperatures, a formerly unknown $\left(2\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\right)R{30}^{\ensuremath{\circ}}$ reconstruction is observed by low-energy electron diffraction, while scanning tunneling microscopy measurements exhibit a $\left(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\right)R{30}^{\ensuremath{\circ}}$ reconstruction. On the basis of density-functional theory calculations, the structure of the larger unit cell is explained by periodically arranged subsurface Si vacancies. The vacancy network in the first subsurface layer has a $\left(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\right)R{30}^{\ensuremath{\circ}}$ periodicity, while strain is released by a $\left(2\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\right)R{30}^{\ensuremath{\circ}}$ Si vacancy network in the second subsurface layer. In addition, this vacancy network forms quasi-one-dimensional structures (striped domains) separated by periodically arranged antiphase domain boundaries. The diffraction spot profiles are explained in detail by kinematic diffraction theory calculations, and average domain widths are deduced.

Experimental evidence of transition between dynamical and kinematical diffraction regimes in ion-implanted Si observed through X-ray multiple-beam diffraction mappings

In this paper, the dependence of a Laue diffraction streak on the crystalline perfection of Xe-implanted Si(001) substrates is presented, based on the observation in the X-ray multiple diffraction (XRMD) mappings, as an experimental evidence of the transition between dynamical and kinematical diffraction regimes. A direct observation of the implanted region by transmission electron microscopy revealed an amorphous Si layer, which recrystallizes into a heavily twinned and faulted microstructure after thermal treatment at 800 °C. Besides the lattice damages, the annealing induces the formation of Xe bubbles. Both singularly affect the XRMD pattern, primarily the four-fold streaks profile of the (000)(002)(11¯1¯)(11¯3) four-beam simultaneous case when compared with the pristine Si pattern, highlighting the intra- and inter-block diffractions and the role played by the primary extinction effect. Such features provide information on the dominant diffraction regime. The findings are also discussed and compared to the conventional reciprocal space mappings via the asymmetric Si(113) reflection.

Investigation of Penetration Depth and Defect Image Contrast Formation in Grazing Incidence X-ray Topography of 4H-SiC Wafers

Synchrotron X-ray Topography has been shown to be a vital tool for the nondestructive characterization of defects in 4H-SiC crystals [1-2]. Techniques utilizing reflection geometry are particularly useful for discerning defects at different depths below the crystal surface. For example, in studying defects in SiC pin diode structures, which typically comprise a buffer layer homoepitaxially grown on a substrate, with the drift layer grown on top of the buffer layer, it is important to be able to discriminate the depth at which particular defect configurations reside. This is particularly important for the characterization of defects resulting from relaxation processes such as interfacial dislocations and half loop arrays [3]. There are generally two approaches adopted depending of the level of perfection of the crystal. In deformed regions (such as around dislocation cores) the penetration depth is simply determined by photoelectric absorption. In perfect regions it is determined by extinction. Extinction contrast predicts particularly shallow penetration depths in these geometries, whereas kinematical theory predicts much deeper penetration depths. However, even under the kinematical diffraction conditions, the penetration depth calculated theoretically by just considering a dislocation as a single line is much smaller than the value measured experimentally. In our study we compared two models involving different diffracting volumes. In one model, the volume is defined by the misorientation larger than the FWHM of the rocking curve in the vicinity of the dislocation core. In another model, the contrast is naturally formed by simulating the photoelectric absorption profile of the diffraction beam according to the local lattice plane tilt by assuming the dislocation image formation is dominant by orientation contrast. We will present a comparison between measured penetration depths in grazing incidence geometry with these two approaches and develop an optimized model to explain our observations. [1] Muller, G.S., et al., Volume production of high quality SiC substrates and epitaxial layers: Defect trends and device applications. Journal of Crystal Growth, 2012. 352(1): p. 39-42. [2] Dudley, M., et al., Characterization of 100 mm diameter 4H-Silicon carbide crystals with extremely low basal plane dislocation density, Material Science Forum,2001. 65: p. 353-356. [3] Wang, H., Dudley, M., et al., Studies of the Origins of Half-Loop Arrays and Interfacial Dislocations Observed in Homoepitaxial Layers of 4H-SiC. Journal of Electronic Materials, 2015. 44(5): p. 1268-1274

Electron diffraction study of the plastic relaxation of MgO epitaxially grown on BCC FeV(001) alloys by varying the lattice mismatch

The epitaxial growth of MgO on Fe1−xVx buffer layers with adjustable lattice parameter is studied by electron diffraction (RHEED) in real time. At the onset of plastic relaxation in the MgO layer, a clear splitting of the diffraction rods is observed in 〈110〉 directions, as well as an increase in their length in the 〈100〉 directions. Splitting along 〈100〉 is also made visible through image background subtraction. These features originate from the surface strain above misfit dislocations, as previously proposed to account for satellite spots in LEED measurements. This explanation is supported by simulations of the diffraction patterns using kinematic diffraction theory. Observation of the diffraction rods splitting is shown to be a powerful way to check the presence of dislocations in MgO tunnel barriers and to accurately determine the critical thickness of plastic relaxation.

Investigation of Penetration Depth and Defect Image Contrast Formation in Grazing Incidence X-ray Topography of 4H-SiC Wafers

Techniques utilizing the grazing incidence geometry are particularly useful for discerning defects at different depths below the crystal surface particularly for 4H-SiC epitaxial wafers. The penetration depths calculated theoretically by just considering a dislocation as simple line defect are much smaller than those measured experimentally. In our study we have developed and compared two models involving different diffracting volumes to account for this discrepancy. In one model, the image contrast is formed by simulating the density map of the diffracted beam according to the local lattice plane tilt assuming the dislocation image formation is dominated by orientation contrast. In the second model, diffracting volume for kinematical diffraction is defined by the surface over which the effective misorientation associated with the dislocation is equal to the rocking curve width of dislocations with different Burgers vectors. By comparing between measured penetration-depths in grazing incidence geometry with these two approaches, our study show that both model play a role in dislocation contrast formation mechanism.

The displacement disorder of atoms in diamond crystals revealed by X-ray imaging plate detector

Cylindrical Imaging Plate Area Detector of Rigaku (IPD) was used to register the X-ray diffraction patterns from diamond crystals grown by Chemical Vapor Deposition (CVD) process. The analysis revealed a deviation from cubic diamond lattice symmetry. X-ray diffraction patterns have been taken by oscillation and stationary crystal methods. Due to high resolution, sensitivity and speed, the IPD detector, allows registration of scattering in the vicinity of Bragg reflections such as broadening, splitting, and satellite reflections. These details were recognized via comparison with the diffraction pattern from a nearly perfect natural diamond crystal and a single crystal of silicon, which were used as diffraction standards. We report data on highly oriented diamond film (HOD) on (001) Si. Powder diffraction patterns show a split of the 111 diffraction line. The line at 2.056Å corresponds to cubic diamond, and the other line at 2.036Å is assigned to a disordered polytype. Two superstructure spots were located at 4.076Å and 4.092Å. Creation of this polytype during growth annihilates desired heteroepitaxy. The issues of lattice disorder, specifically for diamond crystals, are discussed in the framework of kinematical theory of X-ray diffraction.

On the role of secondary extinction in the measurement of the integrated intensity of X-ray diffraction peaks and in the determination of the thickness of damaged epitaxial layers

The integrated intensity of X-ray diffraction reflections has been measured for a series of epitaxial layers of AIII nitrides (GaN, AlN, AlGaN) grown on different substrates (sapphire, SiC) and characterized by different degrees of structural perfection. It has been shown that, despite a high density of dislocations and a significant broadening of the diffraction peaks, the obtained values are not described by the kinematic theory of X-ray diffraction and suggest the existence of extinction. The results have been analyzed on the basis of the Darwin and Zachariasen extinction models. The secondary extinction coefficients and the thicknesses of epitaxial layers have been determined using two orders of reflection both in the Bragg geometry (0002 and 0004) and in the Laue geometry (\(10\bar 10\)) and \(10\bar 20\)). It has been demonstrated that the secondary extinction coefficient is the greater, the smaller is the broadening of the diffraction peaks and, consequently, the dislocation density. It has been found that, for epitaxial layers with a regular system of threading dislocations, the secondary extinction coefficient for the Laue reflections is substantially greater than that for the Bragg reflections.

Polarization angular-resolved transmission spectroscopy of opal films

In this paper, we investigated the angular behavior of light transmission through opal films over a broad range of wavelengths and angles. The opal films were prepared using the capillary deposition method (CDM). The observation of many well-defined diffraction peaks indicates that the CDM results in opal films with high quality. Peaks overlapping at normal incidence split when samples are rotated. The angular shift of these peaks was found to satisfy the kinematical diffraction theory very well. Furthermore, the variation of intensity with incident angle can be interpreted in terms of a simplified dynamical diffraction theory. Moreover, the presence of two differently oriented domains in CDM-made opal films is essential in discussing the measured spectra. These domains can be assigned to parallel microscopic stripes of ABC and ACB type fcc structures. Angular-resolved spectroscopy with polarized incident light shows interesting polarization dependence of light propagation inside opals.