Diffuse Intensity Distribution Research Articles

Median based algorithm for sub-pixel estimation of extrema positions of diffuse light reflection signal

It has been proposed to utilize the median algorithm for determination of the extrema positions of diffuse light reflectance intensity distribution by a discrete signal of a photodiode linear array. The algorithm formula has been deduced on the base of piecewise-linear interpolation for signal representation by cumulative function. It has been shown that this formula is much simpler for implementation than known centroid algorithm and the noise immune Blais and Rioux detector algorithm. Also, the methodical systematic errors for zero noise as well as the random errors for full common mode additive noises and uncorrelated noises have been estimated and compared for mentioned algorithms. In these terms, the proposed median algorithm is proportionate to Blais and Rioux algorithm and considerably better then centroid algorithm.

Kikuchi pattern simulations of backscattered and transmitted electrons

We discuss a refined simulation approach which treats Kikuchi diffraction patterns in electron backscatter diffraction (EBSD) and transmission Kikuchi diffraction (TKD). The model considers the result of two combined mechanisms: (a) the dynamical diffraction of electrons emitted coherently from point sources in a crystal and (b) diffraction effects on incoherent diffuse intensity distributions. Using suitable parameter settings, the refined simulation model allows to reproduce various thickness- and energy-dependent features which are observed in experimental Kikuchi diffraction patterns. Excess-deficiency features are treated by the effect of gradients in the incoherent background intensity. Based on the analytical two-beam approximation to dynamical electron diffraction, a phenomenological model of excess-deficiency features is derived, which can be used for pattern matching applications. The model allows to approximate the effect of the incident beam geometry as a correction signal for template patterns which can be reprojected from pre-calculated reference data. As an application, we find that the accuracy of fitted projection centre coordinates in EBSD and TKD can be affected by changes in the order of - if excess-deficiency features are not considered in the theoretical model underlying a best-fit pattern matching approach. Correspondingly, the absolute accuracy of simulation-based EBSD strain determination can suffer from biases of a similar order of magnitude if excess-deficiency effects are neglected in the simulationmodel.

Ni cluster formation in low temperature annealed Ni50.6Ti49.4

Various low temperature treatments of Ni[Formula: see text]Ti[Formula: see text] have shown an unexpected effect on the martensitic start temperature. Periodic diffuse intensity distributions in reciprocal space indicate the formation of short pure Ni strings along the [Formula: see text]111[Formula: see text] directions in the B2 ordered lattice, precursing the formation of Ni4Ti3 precipitates formed at higher annealing temperatures.

A modulation wave approach to the order hidden in disorder.

The usefulness of a modulation wave approach to understanding and interpreting the highly structured continuous diffuse intensity distributions characteristic of the reciprocal spaces of the very large family of inherently flexible materials which exhibit ordered 'disorder' is pointed out. It is shown that both longer range order and truly short-range order are simultaneously encoded in highly structured diffuse intensity distributions. The long-range ordered crystal chemical rules giving rise to such diffuse distributions are highlighted, along with the existence and usefulness of systematic extinction conditions in these types of structured diffuse distributions.

A modulation wave approach to the long range order hidden in nominal 'disorder'

While the definition of a crystal in terms of pure point diffraction/sharp Bragg reflections only is undoubtedly an excellent approximation for many crystalline materials, there exists a large and growing family of phases for which such a description is grossly inadequate: namely crystalline materials whose reciprocal spaces exhibit highly structured, continuous, diffuse intensity distributions which are essentially long range ordered in at least one or more dimensions (see e.g. Fig.1). To gain insight into both the local order, as well as the long range order, hidden in disordered materials of this type it is very helpful, if not essential, to use the language of modulated structures. An approach of this type automatically emphasizes the close relationship between the crystallography of disordered structures and aperiodic crystallography in general. In this contribution, the use of such an approach to understand the often highly structured shapes of such diffuse distributions, the characteristic extinction conditions frequently associated with them and the long range crystal chemical rules underlying their existence will be highlighted. Fig.1: <11-2> and <-110> zone axis electron diffraction patterns of (a) β-cristobalite and (b) SiO2-tridymite.

Diffuse Scattering Intensity Distribution Associated with Static and Dynamic Atomic Position Fluctuations

Diffuse scattering is a general phenomenon associated with various nanoscale disorders omnipresent in crystalline solids. While it contains rich information on structural disorders, interpretation and analysis of diffuse scattering pose a great challenge because it usually contains contributions from multiple types of disorders and their respective contributions are difficult to separate. In order to extract useful information from diffuse scattering, concerted efforts in high-quality diffuse scattering intensity measurement, quantitative data analysis, theoretical interpretation, and computer simulations are required. In this theoretical work, the diffuse scattering intensity distribution associated with static and dynamic atomic position fluctuations is formulated to effectively combine with our concurrent experimental and computational works. In particular, the theoretical formulation is used to interpret diffuse scattering originated from phonon softening in precursor state of a shape-memory alloy, and, as examples of static atomic position fluctuations, diffuse scattering phenomena of modulated phases and nanotwin microstructures are also discussed.

Morphology, structure, optical, and electrical properties of AgSbO3

The morphology of defect pyrochlore-type, AgSbO3 microparticle/nanoparticles obtained via solid state reaction evolve from irregular to Fullerene-like polyhedra before finally decomposing into metal-organic framework-5 like particles with increase in sintering temperature. The defect pyrochlore-type AgSbO3 particles are slightly Ag deficient while the valence of the antimony ion is shown to be +5 giving rise to a probable stoichiometry of Ag1−xSbVO3−x/2, with x∼0.01–0.04. A highly structured diffuse intensity distribution observed via electron diffraction is interpreted in terms of correlated displacements of one-dimensional (1D) silver ion chains along ⟨110⟩ directions. A redshifting in the absorption edges in UV-visible absorption spectra is observed for samples prepared at sintering temperatures higher than 1000 °C and attributed to the surface plasma resonance effect associated with small amounts of excess metallic Ag on the Ag1−xSbVO3−x/2 particles. An electrical properties investigation of the silver antimonate samples via dielectric, conductivity, and electric modulus spectroscopy shows a prominent dielectric relaxation associated with grain boundaries. The silver ion conductivity is associated with correlated displacements of 1D silver ion chains along ⟨110⟩ directions.

Coupled Li 1+/Nb 5+ and O 2−/F − ordering on the Na and Cl sites of the average NaCl structure of Li 4NbO 4F

The average, as well as the cation and anion ‘disordered’, crystal structure of Li 4NbO 4F has been carefully investigated via coupled neutron and X-ray powder diffraction studies as well as via electron diffraction studies. The existence of a spectacular highly structured diffuse intensity distribution in the latter provides strong evidence for coupled Li 1+/Nb 5+ and O 2−/F − ordering on the Na and Cl sites of the average NaCl structure of Li 4NbO 4F. Bond valence sum calculations have been used to investigate local crystal chemistry as well as to suggest plausible local crystal chemical constraints while ab initio DFT based theoretical calculations of a 2×2×2 supercell have been carried out in order to provide additional insight into the local crystal chemistry of this compound.

Electric field induced anomalies in ferroelectricK2SeO4

The lock-in transition of K2SeO4 at 93.2 K was studied using high-resolutionγ-ray diffraction, in situ dielectric measurements and neutron scattering. The phasetransition shows a coexistence regime of 1.0 K with clearly resolved incommensurate andcommensurate satellite reflections. Within a temperature interval of several K above thelock-in transition, strong third order satellites are observed, indicating a pronouncedsquaring of the modulation wave. Under the influence of high electric fields an intermediatephase is observed, which is characterized by a diffuse intensity distribution. Inaddition, the dielectric permittivity exhibits two maxima, indicating the existence oftwo separate phase transitions. This behaviour is attributed to distortions of thediscommensuration lattice and pinning of the discommensurations by accumulatedcharged defects. It seems to be characteristic for modulated ferroelectrics of theA2BX4 group, since a similar behaviour is also found in isostructuralRb2ZnCl4 andK2ZnCl4. The soft-modedynamics close to Tc is found to be essentially independent of the electric field and not affected by thediscommensuration lattice.

Structural disorder in BZN-based pyrochlores

Careful structural investigations have been carried out on the Bi1.5ZnNb1.5O7 based dielectric system (of A 2 B 2O7 pyrochlore structure type) in an attempt to understand the origin and tolerance of relaxor behavior in such materials. A highly structured, characteristic diffuse intensity distribution was observed in electron diffraction patterns, which arises from static disordering caused by local short range ordering of Bi and Zn ions on the pyrochlore A sites and associated structural relaxation of the O’A 2 sub-structure. This structural disordering is not affected by B site substitution of the Nb5+ ions by Sn4+ or Ti4+ ions. The result is of significance for optimizing the dielectric properties of bismuth-based advanced ceramics.

Structured diffuse scattering, local crystal chemistry and metal ion ordering in the (1 − x )MgS · x /3Yb2S3, 0 ≤ x ≤ ∼ 0.45, ‘defect’ NaCl system

Rare earth sulfide solid solutions of ‘defect’ NaCl average structure type exhibit excellent colour characteristics and thus represent good prospects for use in the paints and plastics industry. As the colour characteristics of such systems are closely related to the local distribution of rare earth ions, it is important to know as much as possible about the latter. In this contribution, the reciprocal space shape of a highly structured, diffuse intensity distribution observed in a (1 −x)MgS · xYb2/3S, x = 0.30, sample is used to show that the smallest polyhedral building blocks of the average NaCl structure type should each have, as far as possible, the same composition as the overall macroscopic composition. Local crystal chemical considerations suggest that both the Yb3+ ions and the vacancies □ would prefer to be opposite Mg2+ ions.

The local crystal chemistry and dielectric properties of the cubic pyrochlore phase in the Bi 2O 3[sbnd]M2+O [sbnd]Nb 2O 5 ( M2+=Ni 2+ and Mg 2+) systems

The composition, dielectric properties and inherent displacive disorder of a Bi-based, misplaced-displacive cubic pyrochlore phase found in two ternary Bi 2O 3 M 2+O Nb 2O 5 ( M=Ni and Mg) systems has been investigated. The dielectric permittivities (up to 1 MHz) of (Bi 0.825Ni 0.125□ 0.05) 2(Ni 0.25Nb 0.75) 2O 7 and (Bi 0.835Mg 0.085□ 0.08) 2(Mg 0.235Nb 0.765) 2O 7 at room temperature are found to be 116 and 151, respectively, while the dielectric loss tangents are 0.00065 and 0.00042, respectively, at 100 kHz. A highly structured characteristic diffuse intensity distribution apparent in electron diffraction is reported in both cases and partially interpreted in terms of large amplitude, β-cristobalite-type tetrahedral rotations of the O’ A 2 tetrahedral framework sub-structure of the ideal pyrochlore structure type. Bond valence sum calculations are used to investigate the local crystal chemistry responsible for this displacive disorder.

Cluster chemistry in the solid state: Structured diffuse scattering, oxide/fluoride ordering and polar behaviour in transition metal oxyfluorides

Oxide/fluoride ordering in three families of ‘disordered’ transition metal oxyfluoride compounds is carefully investigated and used to obtain insight into why the constituent inherently acentric octahedral units do not usually order in a long range ordered polar sense. Observed highly structured diffuse intensity distributions are used in each case to analyze the local crystal chemistry and orientational ordering rules governing the way in which the dipole moments from the individual polar pseudo-octahedral units add together. The common local oxide/fluoride ordering rules, the consequences of these rules for polar behaviour on the local scale as well as the role of configurational entropy and energy minimization in suppressing long range polar order are highlighted.

As–As dimerization, Fermi surfaces and the anomalous electrical transport properties of UAsSe and ThAsSe

A temperature dependent electron diffraction study has been carried out on UAsSe to search for evidence of As–As dimerization at low temperature. A highly structured characteristic diffuse intensity distribution, closely related to that recently reported for ThAsSe, has been observed at low temperature and interpreted in terms of a gradual charge density wave type phase transition upon lowering of temperature involving disordered As–As dimerization within (001) planes. Plausible models of the proposed As–As dimerization have been obtained using a group theoretical approach. Electronic band structure calculations of ThAsSe and UAsSe have been used to search for potential Fermi surface nesting wave-vectors. The results are in good agreement with the experimentally observed diffuse intensity distributions in both cases.

Crystal chemistry on a lattice: The case of BZN and BZN-related pyrochlores

This paper uses a diagnostic, highly structured diffuse intensity distribution to investigate the local crystal chemistry of (Bi 1.5Zn 0.5− δ )(Zn 0.5Nb 1.5)O 7− δ (BZN) as well as Sn 4+ and Ti 4+, B site substituted, BZN-related pyrochlore phases. The structured diffuse distribution of the B site substituted material is found to be remarkably similar to that observed for BZN itself. In the special case of (Bi 1.5Zn 0.5)(Ti 1.5Nb 0.5)O 7 (BZNT), the continuous G±〈10 l〉* type diffuse streaking characteristic of BZN-related pyrochlores has virtually condensed out to give just G±〈001〉* “satellite reflections” and a P-centred, close to a superstructure phase of average pyrochlore unit cell dimensions. Bond valence sum considerations are used to investigate the local crystal chemistry of this BZNT phase and to derive a plausible model for this superstructure phase. Monte Carlo modelling is used to confirm the plausibility of the model proposed. The underlying crystal chemistry of BZN and BZN-related pyrochlores is shown to result from strong local Bi/Zn ordering rules and associated large amplitude structural relaxation.

Disorder, structured diffuse scattering and the transmissionelectron microscope

Abstract A review of the application of electron microscopy to disordered materials exhibiting sharp, highly structured diffuse intensity distributions is given from a modulation wave approach perspective. Structurally useful diffraction phenomena such as polarization, overall diffuse distribution shape and pseudo-extinction conditions are highlighted. The dangers of multiple scattering are emphasized before two particular such systems, substitutionally disordered solid solutions and inherently flexible framework structures are considered in more detail.

Compositionally modulated Fermi surfaces, structured diffuse scattering and ternary derivatives of 1T-TaS 2

Ternary derivatives of 1T-TaS 2 have been synthesized and the variation in the highly structured diffuse intensity distributions characteristic of such materials carefully monitored to investigate the effect that such substitution has upon the band structures and Fermi surfaces (FSs) of the materials. Removal of d electrons via the replacement of Ta ions with lower valent transition metal ions leads to a systematic increase in the radii of the characteristic structured diffuse intensity distribution. Extended Hückel tight binding calculations of the FSs of the doped samples are carried out and used to predict possible nesting wave-vectors. The results are in reasonably good agreement with the radii of the experimentally observed diffuse intensity distributions.

Effects of grazing incidence conditions on the x-ray diffuse scattering from self-assembled nanoscale islands

Grazing incidence small-angle x-ray scattering and grazing incidence x-ray diffraction from SiGe nanoscale islands grown on Si(001) substrate were investigated. Experiments and corresponding theoretical simulations based on the distorted-wave Born approximation were carried out. The strain field inside and in the vicinity of the SiGe islands was calculated in the framework of linear elasticity theory using the numerical finite element method. The diffuse intensity pattern in reciprocal space reveals a well-resolved fine structure with prominent maxima and a complicated fringe pattern. The distribution of diffuse intensity in reciprocal space strongly depends on the angle of incidence with respect to the sample surface. The results obtained substantiate the important role of basically five (grazing incidence small-angle x-ray) and nine (grazing incidence diffraction) scattering channels that have to be considered for a complete understanding of the scattering scenario. A refined island model concerning shape, size, and Ge composition was elaborated.

‘Soft’ phonon modes, structured diffuse scattering and the crystal chemistry of Fe-bearing sphalerites

Electron diffraction has been used to carefully investigate the reciprocal lattices of a range of iron-bearing sphalerites looking for evidence of Fe clustering and/or Fe/Zn ordering in the form of either additional satellite reflections or a structured diffuse intensity distribution accompanying the strong Bragg reflections of the underlying sphalerite-type average structure. While a highly structured diffuse intensity distribution in the form of transverse polarized { 110 } * sheets of diffuse intensity has been detected and found to be characteristic of all compositions, it does not appear to arise from Fe clustering and/or Fe/Zn ordering. Rather inherently low frequency, and therefore strongly thermally excited, phonon modes propagating along reciprocal space directions perpendicular to each of the six 〈110〉 real space directions of the average structure are suggested to be responsible for these { 110 } * sheets of diffuse intensity. Monte Carlo simulation (for a range of Zn–S, Zn–Zn and S–S interaction strengths) and subsequent Fourier transformation is used to confirm the existence of these low-frequency phonon modes of distortion as well as to show that they are an intrinsic, predictable property of the corner-connected tetrahedral structure of sphalerite. The low-frequency phonon modes involve coupled (Zn, Fe) and S motion in one-dimensional strings along 〈110〉 real space directions.

Disorder, structured diffuse scattering and the transmissionelectron microscope

A review of the application of electron microscopy to disordered materials exhibiting sharp, highly structured diffuse intensity distributions is given from a modulation wave approach perspective. Structurally useful diffraction phenomena such as polarization, overall diffuse distribution shape and pseudo-extinction conditions are highlighted. The dangers of multiple scattering are emphasized before two particular such systems, substitutionally disordered solid solutions and inherently flexible framework structures are considered in more detail.