Theoretical Diffraction Research Articles

Surface morphology and thermal figure of merit of a new compound thin film

The third nonlinear optical properties of a new compound 4,4′-bis(3-methoxy benzylidene amino) biphenyl doped poly-methyl methacrylate (PMMA) have been studied using Z-scan technique. Experiments are performed using a continuous waveguide (cw) diode laser at 532 nm wavelength and 0.68 kW/cm2 laser intensity. The optical power limiting behavior of sample doped PMMA was also investigated. It also shows a very good optical limiting behavior with a limiting threshold of 4.7 mW. We attribute the nonlinear absorption and optical limiting property of the sample film to two photon absorption effect at 532 nm. The experimental evidences of observing diffraction pattern in compound 4,4′-bis(3-methoxybenzylideneamino) biphenyl doped PMMA has been present. The refractive index change, Δn, and nonlinear refractive index, n 2 determined from the number of observed ring. We obtained good values of Δn = 105.154 × 10−4and n 2 = 154.154 × 10−7 cm2/W. Variation of refractive index with temperature, dn/dT, and figure of merit, H, are found to be 8.858 × 10−6 1/°C and 5.316 × 10−6, respectively. This large nonlinearity is attributed to a thermal effect resulting from linear absorption. Theoretical diffraction pattern that agree well with experimental one are generated using a wave theory.

Decomposition of the γ phase in as-cast and quenched U–Zr alloys

An investigation of the decomposition of the high temperature γ phase in as-cast and quenched U–Zr alloys was conducted. Differential scanning calorimetry data clearly showed δ⇌γ transformations in alloys with <10 wt% Zr while XRD data did not contain any peaks which uniquely identify it's presence. Since δ phase forms via ω transformation, a comparison of the theoretical diffraction patterns for ω and δ revealed that the intensities of the peaks which uniquely identify the existence of δ when α-U is present, were either very weak, or were zero in ω, suggesting that the ambiguity can be explained if the phase present in these alloys is ω as opposed to δ. Our data are consistent with the presence of δ and ω in as-cast and quenched U–50Zr alloy, respectively, and (α+ω) in rest of the as-cast and quenched alloys. Based on the experimental data, the transformation sequence from γ phase in U–Zr alloys is proposed.

Prospects for electron beam aberration correction using sculpted phase masks

Technological advances in fabrication methods allowed the microscopy community to take incremental steps towards perfecting the electron microscope, and magnetic lens design in particular. Still, state of the art aberration-corrected microscopes are yet 20–30 times shy of the theoretical electron diffraction limit. Moreover, these microscopes consume significant physical space and are very expensive. Here, we show how a thin, sculpted membrane is used as a phase-mask to induce specific aberrations into an electron beam probe in a standard high resolution TEM. In particular, we experimentally demonstrate beam splitting, two-fold astigmatism, three-fold astigmatism, and spherical aberration.

Abinitio Prediction of Martensitic and Intermartensitic Phase Boundaries in Ni-Mn-Ga.

Despite the importance of martensitic transformations of Ni-Mn-Ga Heusler alloys for their magnetocaloric and shape-memory properties, the martensitic part of their phase diagrams is not well determined. Using an abinitio approach that includes the interplay of lattice and vibrational degrees of freedom we identify an intermartensitic transformation between a modulated and a nonmodulated phase as a function of excess Ni and Mn content. Based on an evaluation of the theoretical findings and experimental x-ray diffraction data for Mn-rich alloys, we are able to predict the phase diagram for Ni-rich alloys. In contrast to other mechanisms discussed for various material systems in the literature, we herewith show that the intermartensitic transformation can be understood solely using thermodynamic concepts.

Структура и свойства алмазоподобной фазы, получаемой из тетрагональных графеновых слоев

Using the density functional theory method in the generalized gradient approximation in this article, crystal structure and properties of the carbon diamond-like LA10 phase, in which all the atomic positions are crystallographically equivalent, were calculated. The diamond-like LA10 phase structure can be theoretical derived by polymerization of tetragonal L4-8 graphene layers, consisting of fourmembered and eightmembered structural units. The LA10 crystalline phase lattice belongs to a tetragonal crystal system with I41/amd space group symmetry. The body-centered tetragonal unit cell has the following parameters: a = 3.581 Å, c = 8.611 Å, and Z = 16 atoms. Band structure and electron density of states calculations showed that the diamond-like LA10 phase is a wide-gap semiconductor with a band gap of 5.0 eV to 6.1 eV. Furthermore, the LA10 phase should have high strength characteristics: the Knoop hardness is equal to 72.3 GPa, the bulk modulus is 351 GPa. It is also established that the LA10 phase should be stable under normal conditions, as the sublimation energy of this phase is only 6.9% less than the corresponding energy of cubic diamond. The most probable synthetic way to obtain the LA10 phase is a strong static compression of graphite, consisting of tetragonal polymorphic variety graphene, perpendicular to the graphene layers. This diamond-like phase can be experimentally identified by a theoretical powder X-ray diffraction pattern, calculated in this work. The calculated X-ray pattern is quite different from the X-ray patterns cubic diamond and lonsdaleite, but is very close to the X-ray pattern hexagonal graphite.

Engaging with theoretical diffraction in teacher education

ABSTRACTThis article presents a study in which we began with a question ‘how to teach theoretical reflectivity in teacher education’, and ended with a sentence ‘there is theoretical diffraction in teacher education’. The research presented in this paper took place in the context of a university course in which we have been involved for the past two years. During the course we simultaneously aimed to teach theoretical reflection and to analyse what was happening as we taught theoretical reflection. For two years we asked: What are students doing while we are trying to engage them in theoretical reflection? We noted that students are engaged in theory, but not in ways easily readable to the educators, and that the process could be called theoretical diffraction rather than reflection. Theoretical diffraction during the course was patterned by existing discursive practices: (1) disciplining emotions and focusing on control and answers; (2) personalising school as the teacher, and personally defending it; and (3) prioritising practice over theory and seeing both as dogma.

Structural and dielectric studies of Mg2+ substituted Ni–Zn ferrite

AbstractPolycrystalline ferrites having the chemical formula Ni0.65−xZn0.35MgxFe2O4 (0 ⩽ x ⩽ 0.2) were prepared by solid state reaction route in steps of x = 0.04. The effect of incorporation of diamagnetic divalent magnesium at expense of nickel on the structural properties of these ferrites has been studied. The proposed cation distribution was derived from theoretical X-ray diffraction intensity calculations. These intensity calculations were done by varying the concentration of magnesium ions over two sites in the lattice. For a certain amount of magnesium concentration, the calculated and observed X-ray diffraction intensities were found to be in good agreement. Site occupancy of divalent diamagnetic magnesium was established from this cation distribution. The octahedral environment facilitates magnesium to enter the B-site at about 95 % and the remaining 5 % occupy tetrahedral sites (A-sites). The movements of cations between tetrahedral and octahedral sites as a result of magnesium substitution were discussed in the view of structural parameters, such as tetrahedral and octahedral bond lengths, cation-cation and cation-anion distances, bond angles and hopping lengths, which were calculated using experimental lattice constants and oxygen parameters. All structural parameters showed slight deviations from ideal values. Among all magnesium substituted samples, the ones with x = 0.12 exhibited insignificant variation in view of structural properties. Dielectric measurements were conducted at a standard frequency of 1 kHz. Large values of the recorded dielectric constants displayed typical characteristics of bulk ferrites. Both dielectric constant and loss values showed mixed variations, attributed to the loss of zinc ions during the sintering process.

Focused Ion Beam Micromachining Enables Novel Optics for X-ray Microscopy

X-ray microscopy is a strong analytical tool with a plethora of applications in physics, materials science and life sciences [1]. In many high resolution X-ray microscopes, a focusing optic such as a Fresnel zone plate (FZP) is utilized as a lens to form an image. The FZP is a diffractive optic composed of a series of concentric rings (zones) of radially varying grating period, where the width, Δr, of the outermost zone determines the resolution. Synchrotron radiation facilities are required as bright and coherent X-ray sources as the FZPs are usually quite limited in diffraction efficiency. The diffraction efficiency depends on FZP properties such as geometry, material, structure thickness and on the outermost zone width for small Δr. Conventional FZP profiles are binary and can have up to 10-40 % diffraction efficiency for ideal absorption and phase reversal zone plates, respectively. In practice the efficiencies are lower due to fabrication difficulties and errors. Electron beam lithography (EBL), the usual fabrication method, allows fabrication of binary FZPs with ultra-high resolution via processes of ever increasing complexity. However, due to the scattering of electrons within the resist, it is very difficult to fabricate ultra-high resolution FZPs with high structural thicknesses to achieve high aspect ratios. This, so called, proximity effect limits the aspect ratio, restricting the utilization of high resolution FZPs to softer X-ray energies. One special type of refractive/diffractive X-ray optic is the kinoform lens, with a continuous 3D surface profile. Ideally, it has a theoretical diffraction efficiency of 100 %. While in a real lens absorption would hinder 100 % efficiency, diffraction efficiencies well above 40 % are already demonstrated [2] using these lenses. Nevertheless, in order to fabricate these kinoforms, researchers resorted to step approximations using several consecutive overlay EBL steps, which is complicated and lead to much lower efficiencies than theoretically expected due to the vulnerability of the optics to fabrication errors amplified by error accumulations. To solve the issues that are intrinsic limitations of the EBL-FZPs we introduced novel, precise and mostly direct methods relying on the FIBs. The powerful method potentially allows for higher resolutions than EBL [3] and precise 3D sculpting capability enables the realization of highly efficient X-ray optics with high fidelity [4]. We have used a standard multi-purpose FIB instrument (Nova 600 NanoLab, DualBeam, FEI) to fabricate binary FZPs, kinoform lenses and multilayer FZPs (Figure 1).

Surface Structure of Bi(111) from Helium Atom Scattering Measurements. Inelastic Close-Coupling Formalism.

Elastic and inelastic close-coupling (CC) calculations have been used to extract information about the corrugation amplitude and the surface vibrational atomic displacement by fitting to several experimental diffraction patterns. To model the three-dimensional interaction between the He atom and the Bi(111) surface under investigation, a corrugated Morse potential has been assumed. Two different types of calculations are used to obtain theoretical diffraction intensities at three surface temperatures along the two symmetry directions. Type one consists of solving the elastic CC (eCC) and attenuating the corresponding diffraction intensities by a global Debye–Waller (DW) factor. The second one, within a unitary theory, is derived from merely solving the inelastic CC (iCC) equations, where no DW factor is necessary to include. While both methods arrive at similar predictions for the peak-to-peak corrugation value, the variance of the value obtained by the iCC method is much better. Furthermore, the more extensive calculation is better suited to model the temperature induced signal asymmetries and renders the inclusion for a second Debye temperature for the diffraction peaks futile.

Ion implantation of the 4H SiC epitaxial layers and substrates with 2 MeV Se+ and 1 MeV Al+ ions

The implantations were performed in 4H silicon carbide homoepitaxial layers deposited on (00.1) substrates with 8° offcut, and reference 4H‐SiC substrates. The 2 MeV Se+ ions and 1 MeV Al+ ions were implanted with four fluences subsequently increased by the factor of 4–5×. The samples were studied by means of X‐ray diffraction topography, high‐resolution diffractometry, specular X‐ray reflectometry, and Rutherford backscattering spectrometry\channeling method. The dislocation density in the samples evaluated from the diffraction topographs did not exceed 5 × 103 cm−2. The representative roughness values evaluated from the reflectometric measurements was 2.3 ± 0.1 nm for the substrates and less than 1.4 ± 0.1 nm for the epitaxial layers.A significantly higher damage level in the case of 2 MeV Se+ ions in comparison with 1 MeV Al+ ion and a linear increase of the strain with the fluence was indicated, but the highest doses of selenium ions caused the amorphization of the implanted layer. It was also possible to obtain a good fitting of the theoretical and experimental diffraction curves approximating the strain profiles by the distribution of the point defects calculated with the SRIM 2008 code. It was confirmed that the maximum coming from surface damages observed in channeling spectra of the virgin substrate wafers was significantly higher than in the case of epitaxial layers. Copyright © 2015 John Wiley &amp; Sons, Ltd.

A Mechanochromic Luminescent Dye Exhibiting On/Off Switching by Crystalline-Amorphous Transitions.

A mechanochromic luminescent dye based on a simple aminomaleimide skeleton was readily synthesized in a one-pot process. It exhibited an on/off mechanochromic luminescent switching property dependent on external stimuli, unlike a traditional mechanochromic color change. The green emission was turned on by grinding in a mortar and turned off by heating or treatment with dichloromethane. In the crystalline state, two molecules were stacked by cofacial π-π interactions, which caused concentration self-quenching. The crystalline-to-amorphous transition induced by grinding removed cofacial π-π stacking, which led to intensive emission. Crystallizing processes recovered the cofacial π-π stacking, resulting in elimination of the emission. Theoretical calculations and X-ray diffraction analyses revealed that the dye molecule was distorted in the crystalline state; thus even a mechanical stimulus caused the crystalline-to-amorphous transition.

Straightforward understanding of the structures of metastable α″ and possible ordered phases in uranium–niobium alloys from crystallographic simulation

Crystallographic simulation is carried out in the present work to understand the respective structure of metastable α″ and possible ordered phases, which could be the prerequisite for revealing the low-temperature aging mechanism underlying the α″ phase in U–Nb alloys. The space group of No. 11 with C-type lattice is found to describe the structure of α″ phase in a straightforward way, avoiding the mistaken or indirect indexation and analysis of structural data. The obtained theoretical diffraction pattern of α″ phase shows clearly the phenomenon of peak splitting, in which the Bragg positions also agree well with the experimental observation. Additional peaks are observed at the low diffraction angles for the possible ordered phases in U–Nb alloys through simulation on the proposed two types of structures, which need to be carefully detected by the uniting of multiprobe diffraction. The correlation between ordered structures and stress-strain response is also deduced and discussed. The present work would provide some enlighten to the integrity of the phase diagram and the understanding of low-temperature aging mechanism in U–Nb alloys.

Using the parallel stacked mirror model to analytically describe diffraction in the planar volume reflection grating with finite absorption

The parallel stacked mirror (PSM) model of grating diffraction is extended to include a complex refractive index for the case of an unslanted reflection geometry at oblique incidence and for the &#x3C3;-polarization. The well-known theoretical upper diffraction efficiency limit applicable to reflective absorption gratings described by Kogelnik&#x2019;s coupled-wave theory, is shown to be directly derivable from the PSM model. Analytical formulae for the diffraction efficiency of phase, absorption, and mixed harmonic-index gratings are compared with numerical computations using a rigorous coupled-wave description. A conventional truncated coupled-wave description, similar to Kogelnik&#x2019;s approach, is also derived from the harmonic-index rigorous coupled-wave equations by limiting the propagating modes to a signal and reference wave and by ignoring second-order derivatives. At low to moderate average loss the PSM theory is observed to provide a somewhat better fit to the rigorous coupled-wave calculations, and this is particularly evident for gratings that are dominated by phase modulation. As the average absorption coefficient is increased, all three models show the diffractive response sharpening around Bragg resonance and the characteristic sideband structure attenuating and then disappearing altogether, giving rise to a broader spectral behavior away from resonance. At high average loss, the truncated coupled-wave model is observed to very marginally outperform PSM. However, overall the PSM model is found to provide an exceedingly good description of the general mixed-phase-absorption unslanted reflection grating with finite average loss.

Short-range order in disordered transition metal oxides, carbides, and nitrides with the B1 structure

A method has been proposed for the simulation of the atomic structure of disordered phases of nonstoichiometric transition metal oxides, carbides, and nitrides with the B1 structure taking into account the shortrange order in the arrangement of structural vacancies. The simplest structural models constructed with allowance for pair correlations between vacancies within the first four coordination spheres have been considered. A computer simulation of the atomic structure of disordered phases with the inclusion of the shortrange order has been performed. For each stru ctural model, the maximum possible concentration of vacancies and the shortrange order parameters at diffe rent concentrations have been calculated. For a fur� ther experimental verification, the influence of the shortrange order on the shape of the Xray scattering spectrum has been investigated by calculating the theoretical Xray diffraction patterns according to the Debye formula. The influence of the shortrange order on the total energy of the disordered phases has been analyzed by ab initio methods. It has been shown that, in some cases, the proposed structural models of the shortrange order are energetically favorable as compar ed to the model of statistical arrangement of vacan�

Magnetism, electronic structure and half-metallic property of transition metal (V, Cr, Mn, Fe, Co) substituted Zn3P2 dilute magnetic semiconductors: An ab-initio study

Abstract The ab-initio electronic structure calculations are used to investigate the half-metallic property, structural stability, spin dependent density of states and magnetism of transition metal (V, Cr, Mn, Fe, Co) substituted Zn 3 P 2 . Our results show the half-metallic ground state and ferromagnetic (antiferromagnetic) stability for small concentrations (2.5% and 5%) of transition metal atom substitution considered in our study. The structural and magnetic stability of the substituted compounds have been investigated through the calculation of the heat of formation and analyzing the minimum total energies corresponding to the ferromagnetic, antiferromagnetic and nonmagnetic phases. The substituted transition metal atom is found to give rise to magnetism of these compounds and half-metallic property is observed in many cases. We have used the spin, orbital and atom projected density of states to investigate this point and studied the nature of bonding in these systems using the charge density contours. We have observed from our calculations, magnetically stable phases and large values of the magnetic moments in these compounds and it suggests that these compounds may be useful materials for semiconductor spintronic devices. We have further calculated the theoretical X-ray diffraction pattern of these compounds.

Diffraction model of peristrophic multiplexing with spherical reference wave.

Multiplexing recording is a primary contributor to determining the recording density in holographic data storage. Therefore, many different kinds of recording methods have been proposed. Among them, the method that utilizes spherical waves as reference waves is characterized by the ability to enable multiplexing recording only by moving (shifting or rotating) the recording medium. In our research, we propose a theoretical diffraction model of peristrophic multiplexing with a spherical reference wave and evaluate the diffraction efficiency; this multiplexing recording method has incorporated spherical reference waves in rotation of the media. Additionally, we verify the effectiveness of the model by comparing it with experimental results.

Fine-tuning the theoretically predicted structure of MIL-47(V) with the aid of powder X-ray diffraction

The structural characterization of complex crystalline materials can be simplified by closely comparing theoretical and experimental diffraction patterns.

All-phase target reconstruction method for coherent field imaging

Received signal processing and target reconstruction technique plays a key role in coherent field imaging, and directly influences the quality of the reconstructed image of a target. Based on all-phase fast Fourier transformation (FFT) spectrum analysis theory, a new processing and reconstruction method is proposed. By directly extracting the phase and amplitude information from all-phase FFT spectrum of the return signal, the proposed all-phase target reconstruction method is capable of inhibiting the frequency error caused by many factors, thus reconstructing the target image more precisely. The validity of the proposed method is proved by a coherent field imaging system in outdoor environments, and it has a better reconstruction performance than a traditional method. The resolution of the reconstructed target is close to a theoretical diffraction limit.

Pressure-induced metallization of dense (H₂S)₂H₂ with high-Tc superconductivity.

The high pressure structures, metallization, and superconductivity of recently synthesized H2-containing compounds (H2S)2H2 are elucidated by ab initio calculations. The ordered crystal structure with P1 symmetry is determined, supported by the good agreement between theoretical and experimental X-ray diffraction data, equation of states, and Raman spectra. The Cccm structure is favorable with partial hydrogen bond symmetrization above 37 GPa. Upon further compression, H2 molecules disappear and two intriguing metallic structures with R3m and Im-3m symmetries are reconstructive above 111 and 180 GPa, respectively. The predicted metallization pressure is 111 GPa, which is approximately one-third of the currently suggested metallization pressure of bulk molecular hydrogen. Application of the Allen-Dynes-modified McMillan equation for the Im-3m structure yields high Tc values of 191 K to 204 K at 200 GPa, which is among the highest values reported for H2-rich van der Waals compounds and MH3 type hydride thus far.

Beyond the diffraction limit of optical/IR interferometers

Context. As previously demonstrated on Achernar, one can derive the angular radius, rotational velocity, axis tilt, and orientation of a fast-rotating star from the differential phases obtained by spectrally resolved long baseline interferometry using earth-rotation synthesis.Aims. We applied this method on a small sample of stars for different spectral types and classes, in order to generalize the technique to other rotating stars across the H-R diagram and determine their fundamental parameters.Methods. We used differential phase data from the AMBER/VLTI instrument obtained prior to refurbishing its spectrometer in 2010. With the exception of Fomalhaut, which has been observed in the medium-resolution mode of AMBER (λ /δλ ≈ 1500), our three other targets, Achernar, Altair, and δ Aquilae offered high-resolution (λ /δλ ≈ 12 000) spectro-interferometric data around the Brγ absorption line in K band. These data were used to constrain the input parameters of an analytical, still realistic model to interpret the observations with a systematic approach for the error budget analysis in order to robustly conclude on the physics of our 4 targets. We applied the super resolution provided by differential phases φ diff to measure the size (equatorial radius R eq and angular diameter ⌀eq ), the equatorial rotation velocity (V eq ), the inclination angle (i ), and the rotation axis position angle (PArot ) of 4 fast-rotating stars: Achernar, Altair, δ Aquilae, and Fomalhaut. The stellar parameters of the targets were constrained using a semi-analytical algorithm dedicated to fast rotators SCIROCCO.Results. The derived parameters for each star were R eq = 11.2 ± 0.5 R ⊙ , V eq sini = 290 ± 17 km s-1 , PArot = 35.4° ± 1.4°, for Achernar; R eq = 2.0 ± 0.2 R ⊙ , V eq sini = 226 ± 34 km s-1 , PArot = −65.5° ± 5.5°, for Altair; R eq = 2.2 ± 0.3 R ⊙ , V eq sini = 74 ± 35 km s-1 , PArot = −101.2° ± 14°, for δ Aquilae; and R eq = 1.8 ± 0.2 R ⊙ , V eq sini = 93 ± 16 km s-1 , PArot = 65.6° ± 5°, for Fomalhaut. They were found to be compatible with previously published values from differential phase and visibility measurements, while we were able to determine, for the first time, the inclination angle i of Fomalhaut (i = 90° ± 9°) and δ Aquilae (i = 81° ± 13°), and the rotation-axis position angle PArot of δ Aquilae.Conclusions. Beyond the theoretical diffraction limit of an interferometer (ratio of the wavelength to the baseline), spatial super resolution is well suited to systematically estimating the angular diameters of rotating stars and their fundamental parameters with a few sets of baselines and the Earth-rotation synthesis provided a high enough spectral resolution.