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Approximant-based orientation determination of quasicrystals using electron backscatter diffraction
(2020)
Orientation mapping of quasicrystalline materials is demonstrated using crystalline approximant structures in the technique of electron backscatter diffraction (EBSD). The approximant-based orientations are symmetrised according to the rotational point group of the quasicrystal, including the visualization of orientation maps using proper colour keys for quasicrystal symmetries. Alternatively, approximant-based orientation data can also be treated using pseudosymmetry post-processing options in the EBSD system software, which enables basic grain size estimations. Approximant-based orientation analyses are demonstrated for icosahedral and decagonal quasicrystals.
(Bio)geochemical cycling of gold (Au) has been demonstrated in present-day (semi)-arid, (sub)-tropical and temperate environment. Hereby biofilms on Au-bearing mineral- and Au-particle surfaces drive Au dispersion and reconcentration, thereby (trans)forming the particles. However, it is unknown if biogeochemical cycling of Au occurs in polar environments, where air temperatures can reach −40 °C and soils remain frozen for much of the year. Therefore, placer Au-particles, soils and waters were collected at two placer mining districts in arctic Finland, i.e., the Ivalojoki and Lemmenjoki goldfields. Sites were chosen based on contrasting settings ((glacio)-fluvial vs. glacial-till deposits) and depths (surface to 5m below current surface). Gold particles were studied using a combination of tagged 16S rRNA gene next generation sequencing and electron microscopic/microanalytical techniques. Across all sites a range of Au-particle morphologies were observed, including morphotypes indicative of Au dissolution and aggregation. Elevated Au concentrations indicative of Au mobility were detected in placer particle bearing soils at both districts. Typically Au-particles were coated by polymorphic biofilm layers composed of living and dead cells embedded in extracellular polymeric substances. Intermixed were biominerals, clays and iron-sulfides/oxides and abundant secondary Au morphotypes, i.e., nano-particles, microcrystals, sheet-like Au, branched Au networks and overgrowths and secondary rims. Biofilms communities were composed of Acidobacteria (18.3%), Bacteroidetes (15.1%) and Proteobacteria (47.1%), with β-Proteobacteria (19.5%) being the most abundant proteobacterial group. Functionally, biofilms were composed of taxa contributing to biofilm establishment, exopolymer production and nutrient cycling, abundant taxa capable of Au mobilization, detoxification and biomineralization, among them Cupriavidus metallidurans, Acinetobacter spp. and Pseudomonas spp., were detected. In conclusion, these results demonstrate that placer Au-particle transformation and Au dispersion occur in cold, arctic environments. This corroborates the existence of biogeochemical Au cycling in present-day cold environments.
Electron backscatter diffraction (EBSD) is a technique to obtain microcrystallographic information from materials by collecting large-angle Kikuchi patterns in the scanning electron microscope (SEM). An important fundamental question concerns the scattering-angle dependent electron energy distribution, which is relevant for the formation of the Kikuchi diffraction patterns. Here we review the existing experimental data and explore the effective energy spectrum that is operative in the generation of backscatter Kikuchi patterns from silicon. We use a full pattern comparison of experimental data with dynamical electron diffraction simulations. Our energy-dependent cross-correlation based pattern matching approach establishes improved constraints on the effective Kikuchi pattern energy spectrum, which is relevant for high-resolution EBSD pattern simulations and their applications.
A nickel-based eutectic alloy with a γ/γ'-NbC structure was directionally solidified with a planar front. The specimens were tested for creep under sawtooth thermal cycling in the temperature range from 600 to 1100°C. It has been established that the lifetime under the conditions of thermal cycling is about five times shorter than it is predicted by the linear damage accumulation rule on the basis of results of isothermal creep tests. Faster creep under thermal cycling is caused by the rapid coarsening of the γ/γ' microstructure due to the periodic partial dissolution and reprecipitation of the γ' phase in heating and cooling half-cycles.
Orientation determination does not necessarily require complete knowledge of the local atomic arrangement in a crystalline phase. We present a method for microstructural phase discrimination and orientation analysis of phases for which there is only limited crystallographic information available. In this method, experimental Kikuchi diffraction patterns are utilized to generate a self-consistent master reference for use in the technique of Electron Backscatter Diffraction (EBSD). The experimentally derived master data serves as an application-specific reference in EBSD pattern matching approaches. As application examples, we map the locally varying orientations in samples of icosahedral quasicrystals observed in a Ti40Zr40Ni20 alloy, and we analyse AlNiCo decagonal quasicrystals.
The early stages of corrosion of Fe-Cr-model alloys (2 and 9 % Cr) were investigated after exposure at 650 °C in0.5 % SO2containing gas by electron backscattered diffraction (EBSD) and transmission electron microscopy(TEM). The impact of the grain orientation of the base alloy on the orientation relations of the corrosion productsis presented. After 2 min–5 min exposure the formation of a multi-layered corrosion zone was discovered. Aclear orientation relationship between ferrite and the (Fe,Cr)3O4 spinel could be demonstrated. The obtainedresults show the importance of the grain orientation on oxidation resistance.
As humanity contemplates manned missions to Mars, strategies need to be developed for the design and operation of hospitable environments to safely work in space for years. The supply of spare parts for repair and replacement of lost equipment will be one key need, but in-space manufacturing remains the only option for a timely supply. With high flexibility in design and the ability to manufacture ready-to-use components directly from a computeraided model, additive manufacturing (AM) technologies appear extremely attractive. For the manufacturing of metal parts, laser-beam melting is the most widely used AM process. However, the handling of metal powders in the absence of gravity is one prerequisite for its successful application in space. A gas flow throughout the powder bed is successfully applied to compensate for missing gravitational forces in microgravity experiments. This so-called gas-flow-assisted powder deposition is based on a porous Building platform acting as a filter for the fixation of metal particles in a gas flow driven by a pressure difference maintained by a vacuum pump.
The temperature dependences of the periods of the crystal lattices of the γ and γ' phases, their dimensional mismatch (misfit), and volume fraction of the γ' phase of an experimental single-crystal hightemperature nickel-based alloy have been determined by X-ray diffraction analysis in the temperature range of 18–1150°C. The temperature ranges in which intense changes in the structural and phase characteristics of the alloy under study take place have been determined.
Using the method of directional solidification, single crystals of experimental nickel-based superalloys with negative, zero, and positive γ/γ' misfits are obtained. The γ' solvus, solidus, and liquidus temperatures of the alloys are determined, and the microstructures of the alloys after directional solidification, heat treatment, and creep tests are investigated. Creep tests are performed at temperatures of 800 and 1000°C. It is found that single crystals of the alloy with a negative γ/γ' misfit have the highest creep resistance and lifetime (the crystal lattice period of the γ' phase is smaller than that of the γ matrix).
Interdiffusion in the Face-Centered Cubic Phase of the Co-Al-W-Ta System Between 1090 and 1240 °C
(2018)
Interdiffusion of Al, W, Ta and Co in a Co-base alloy at temperatures between 1090 and 1240 °C has been investigated. The interdiffusion coefficients were found to be close to those reported for these elements in Ni-base alloys. Combining the diffusion simulation software DICTRA with the Ni-base diffusion databases TCNi5 and MobNi3, the interdiffusion profiles of Co, Al W, and Ta were modeled for Co9Al8W2Ta/Co diffusion couples annealed at different temperatures and for different times. The results show that interdiffusion in the Co-Al-W-Ta alloys can be modeled reasonably well using the available commercial databases for thermodynamics and kinetics of Ni-base systems.
The alloying system Co-Al-W-Ta is comprehensively investigated in the vicinity of the compositional point Co-9Al-10W-2Ta, at. pct. These investigations provided a large amount of quantitative information, which can be used for alloy development, namely, the compositional dependences of the The alloying system Co-Al-W-Ta is comprehensively investigated in the vicinity of the compositional point Co-9Al-10W-2Ta, at. pct. These investigations provided a large amount of quantitative information, which can be used for alloy development, namely, the compositional dependences of the γ‘-solvus, solidus, and liquidus temperatures; fraction of the extrinsic phases after casting; the compositional dependence of the γ/γ‘-lattice misfit; the element partitioning between γ- and γ‘-phases; and the two Phase compositional area γ/γ‘ in the Co-rich part of the Co-Al-W-Ta phase diagram at 900°C. It is shown that additions of Ta elevate the γ‘-solvus temperature and increase the γ/γ‘-lattice misfit, but adding more than about 3 at. pct Ta results in a large amount of undissolvable extrinsic phases. Additionally, two Co-Al-W-Ta alloys with lower content of W were developed and solidified as [001] single crystals for mechanical testing in a temperature range between 20 and 1200°C. These tests included measurement of the Young modulus, tensile tests with constant strain rate, and stress rupture tests. It was found that at temperatures up to about 750°C the ultimate tensile strength of Co-Al-Ta-W alloys can be at the same level or even higher than of Ni-based superalloys.
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 TKDcan be affected by changes in the order of 10−3–10-2 if excess-deficiency features are not considered in the theoreticalmodel underlying a best-fit pattern matching approach. Correspondingly, the absolute accuracy of simulation-based EBSD strain determination can suffer frombiases of a similar order of magnitude if excess-deficiency effects are neglected in the simulation model.
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 TKDcan be affected by changes in the order of 10−3–10−2 if excess-deficiency
features are not considered in the theoreticalmodel underlying a best-fit pattern matching approach. Correspondingly, the absolute accuracy of simulation-based EBSD strain determination can suffer frombiases of a similar order of magnitude if excess-deficiency effects are neglected in the simulation model.
A historical tool for crystallographic analysis is provided by the Hilton net, which can be used for manually surveying the crystal lattice as it is manifested by the Kikuchi bands in a gnomonic projection. For a quantitative analysis using the Hilton net, the projection centre as the relative position of the signal source with respect to the detector plane needs to be known. Interplanar angles are accessible with a precision and accuracy which is estimated to be ≤0.3o. Angles between any directions, e.g. zone axes, are directly readable. Finally, for the rare case of an unknown projection-centre position, its determination is demonstrated by adapting an old approach developed for photogrammetric applications.
It requires the indexing of four zone axes [uvw]i in a backscattered Kikuchi diffraction pattern of a known phase collected under comparable geometric conditions.
To visualize the varying tetragonal distortions in high carbon martensitic steels by EBSD, two different approaches have been applied on backscattered Kikuchi diffraction (BKD) patterns. A band-edge refinement technique called Refined Accuracy (RA) (Oxford Instruments) is compared with a technique called Pattern Matching (PM), which optimizes the fit to a simulated BKD signal. RA distinguishes between hypothetical phases of different fixed 𝑐∕𝑎, while PM determines a best fitting continuous 𝑐∕𝑎 by projective transformation of a master pattern. Both techniques require stored BKD patterns.
The sensitivity of the 𝑐∕𝑎-determination was tested by investigating the microstructure of a ferritic steel with an expected 𝑐∕𝑎 = 1. The influence of the Kikuchi pattern noise on 𝑐∕𝑎 was compared for a single or 40 averaged frames per measuring point, and turned out to be not significant. The application of RA and PM on the martensitic microstructure delivered qualitatively similar maps of 𝑐∕𝑎. The comparison of RA and PM shows that RA is suitably fast and precise during mapping the martensite 𝑐∕𝑎 ratio in analyses of high carbon martensite, especially for fast initial surveys. As RA leads quantitatively to higher noise in 𝑐∕𝑎, the PM analysis can be used for higher precision results.
Due to the increasing global demand for pure silver, native wire silver aggregates in very high purities are gaining more industrial attention. Up to the present, no substantial metallurgical Investigation of natural wire silver exists in the accessible literature. To convey urgently needed cross-disciplinary fundamental knowledge for geoscientists and metallurgical engineers, twenty natural wire silver specimens from eight different ore deposits have been investigated in detail for the first time by EBSD (Electron Back Scattering Diffraction), supported by light microscopy and micro-probe analyses. The improved understanding of the natural silver wire microstructure provides additional Information regarding the growth of natural silver aggregates in comparison to undesired artificial growth on electronic devices. Clear evidence is provided that natural silver curls and hairs exhibit a polycrystalline face-centered cubic microstructure associated with significant twinning. Although the investigated natural wire silver samples have relatively high purity (Ag > 99.7 wt.-%), they contain a variety of trace elements such as, S, Cu, Mn, Ni, Zn, Co and Bi, As and Sb. Additionally, Vickers micro-hardness measurements are provided for the first time which revealed that natural silver wires and curls are softer than it might be expected from conversion of the general Mohs hardness of 2.7.
Inconel 718 is a precipitation strengthened, nickel-based super alloy of interest for the Additive Manufacturing (AM) of low volume, complex parts to reduce production time and cost compared to conventional subtractive processes. The AM process involves repeated rapid melting, solidification and reheating, which exposes the material to non-equilibrium conditions that affect elemental segregation and the subsequent formation of solidification phases, either beneficial or detrimental. These variations are difficult to characterize due to the small length scale within the micron sized melt pool. To understand how the non-equilibrium conditions affect the initial solidification phases and their critical temperatures, a multi-length scale, multi modal approach has been taken to evaluate various methods for identifying the initial phases formed in the as-built Inconel 718 produced by laser-powder bed fusion (L-PBF) additive manufacturing (AM). Using a range of characterization tools from the bulk differential thermal analysis (DTA) and x-ray diffraction (XRD) to spatially resolved images using a variety of electron microscopy tools, a better understanding is obtained of how these minor phases can be properly identified regarding the amount and size, morphology and distribution. Using the most promising characterization techniques for investigation of the as-built specimens, those techniques were used to evaluate the specimens after various heat treatments. During the sequence of heat treatments, the initial as-built dendritic structures recrystallized into well-defined grains whose size was dependent on the temperature. Although the resulting strength was similar in all heat treated specimens, the elongation increased as the grain size was refined due to differences in the precipitated phase distribution and morphology.
An analytical model for forecasting the temperature dependence of γ/γ' misfit in heat-resistant nickel alloys is proposed. The model accounts for the concentration dependences of the periods of crystalline lattices of the γ and γ' phases (Vegard law), thermal expansion of the γ and γ' lattices, and dissolution of the γ' phase at high temperatures. Adequacy of calculations of misfit is confirmed by comparison with the results of measurements using methods of X-ray and neutron diffraction. The model is applied for development of a nickel alloy with positive misfit.
This paper presents the results of a study of the morphology and structure at the weld interface in a brass–Invar bimetal, which belongs to the class of so-called thermostatic bimetals, or thermobimetals. The structure of the brass–Invar weld interface was analyzed using optical microscopy and scanning electron microscopy (SEM), with the use of energy-dispersive X-ray (EDX) spectrometry and back-scattered electron diffraction (BSE) to identify the phases. The distribution of the crystallographic orientation of the grains at the weld interface was obtained using an e-Flash HR electron back-scatter diffraction (EBSD) detector and a forward-scatter detector (FSD). The results of the study indicated that the weld interface had the wavy structure typical of explosive welding. The wave crests and troughs showed the presence of melted zones consisting of a disordered Cu–Zn–Fe–Ni solid solution and undissolved Invar particles. The pattern quality map showed that the structure of brass and Invar after explosive welding consisted of grains that were strongly elongated towards the area of the highest intensive plastic flow. In addition, numerous deformation twins, dislocation accumulations and shear bands were observed. Thus, based on the results of this study, the mechanism of Cu–Zn–Fe–Ni structure formation can be proposed.
The morphology of pores partially shrunk during a half-hour HIP at temperature of 1288 °C and pressure of 103 MPa has been investigated in nickel-based superalloy CMSX-4. The investigation resulted in the following findings: surrounding the shrinking pores by a c¢-shell (Ni3Al), faceting of the pores surface by {023} and {011} planes, and formation the submicroscopic satellite pores connected by channels with the neighboring larger pores. It is assumed that the formation of the c¢-shell around the pores and the faceting of the pore surface is due to diffusion processes occurring during pore shrinkage, and therefore these findings can be considered as arguments supporting the vacancy model of pore annihilation. The submicroscopic satellite pores are expected to be the result of dividing the casting pores of a complex initial shape during their shrinking. The connecting channels are probably required for the gas to escape from the rapidly shrinking small satellite pores into the slowly shrinking large pore. Thus, it is reasonable to assume that the casting pores may contain some amount of gas.
For the precise determination of orientations in polycrystalline materials, electron backscatter diffraction (EBSD) requires a consistent calibration of the diffraction geometry in the scanning electron microscope (SEM). In the present paper, the variation of the projection center for the Kikuchi diffraction patterns which are measured by EBSD is calibrated using a projective transformation model for the SEM beam scan positions on the sample. Based on a full pattern matching approach between simulated and experimental Kikuchi patterns, individual projection center estimates are determined on a subgrid of the EBSD map, from which least-square fits to affine and projective transformations can be obtained. Reference measurements on single-crystalline silicon are used to quantify the orientation errors which result from different calibration models for the variation of the projection center.
Roaldite – Fe4N – has been identified in the São Julião de Moreira iron meteorite using electron backscatter diffraction (EBSD) and simultaneously acquired energy-dispersive x-ray spectroscopy (EDS). Mean-periodic-number images derived from raw EBSD patterns confirm this phase by an even higher spatial resolution compared to EDS.
Roaldite appears in the form of systematically and repetitively aligned plates. Despite the locally heavy plastic deformation, it is shown that the origin of the oriented precipitation of roaldite is linked to the orientation of the kamacite matrix. Roaldite can be considered to be precipitated from kamacite using an inverse Kurdjumov-Sachs (K-S) or Nishiyama-Wassermann (N-W) orientation relationship. A more accurate discrimination is impossible due to the accumulated shock deformation, which blurs the local reference orientation of kamacite. The habit plane of roaldite is found to be {112}R, which is most likely parallel to {120}K of kamacite. Some of the roaldite plates contain two orientation variants which repeatedly alternate. Their misorientation angle is about 12°.
Kirkendall porosity that forms during interdiffusion in a diffusion couple of nickel-base superalloy CMSX-10 with pure nickel is investigated. The diffusion experiments are conducted at a temperature of 1250 °C, where the strengthening ƴ'-phase ist partially dissolved. The porosity is studied by X-ray sub-μ tomography with a spatial resolution of about 0.35³ μm³ at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. It is found that depending on the distance from the interface the Kirkendall pores take different shapes: octahedral, rounded pyramidal, drop shaped, dendritic, pear shaped, and joint shapes. Such a variety of pore morphologies indicates a complex multistage process of porosity nucleation and growth under vacancy supersaturation of different degrees. The experimental findings are interpreted on the basis of the results of diffusion modeling. It is shown that the kinetics of porosity growth is essentially influenced by the dissolution of the ƴ'-phase.
The locally varying tetragonality in martensite grains of a high-carbon steel (1.2 mass percent C) was resolved by electron backscatter diffraction (EBSD) with a spatial resolution in the order of 100 nm. Compared to spatially integrating X-ray diffraction, which yielded an average tetragonality fo c/a=1.05, the EBSD measurements in the scanning electron microscope allowed to image a local variation of the lattice papameter ration c/a in the range of 1.02 ≤ c/a ≤ 1.07. The local variation of tetragonality is confirmed by two different EBSD data analysis approaches based on the fitting of simulated to experimental EBSD patterns. The resulting EBSD-based tetragonality maps are pointing to a complex interaction of carbon concentration and local lattice distortions during the formation process of martensitic structures.
Signal optimization for transmission Kikuchi diffraction (TKD) measurements in the scanning electron microscope is investigated by a comparison of different sample holder designs. An optimized design is presented, which uses a metal shield to efficiently trap the electron beam after transmission through the sample. For comparison, a second holder configuration allows a significant number of the transmitted electrons to scatter back from the surface of the sample holder onto the diffraction camera screen. It is shown that the secondary interaction with the sample holder leads to a significant increase in the background level, as well as to additional noise in the final Kikuchi diffraction signal. The clean TKD signal of the optimized holder design with reduced background scattering makes it possible to use small signal changes in the range of 2% of the camera full dynamic range. As is shown by an analysis of the power spectrum, the signal-to-noise ratio in the processed Kikuchi diffraction patterns is improved by an order of magnitude. As a result, the optimized design allows an increase in pattern signal to noise ratio which may lead to increase in measurement speed and indexing reliability.
Gold and platinum-group-metals (PGM) are cycled through Earth's environments by interwoven geological, physical, chemical and biological processes leading to the trans/neoformation of metallic particles in placers.
The placer deposit at Corrego Bom Successo (CBS, Brazil) is one of the few localities worldwide containing secondary gold- and PGM-particles. Placer gold consists of detrital particles from nearby hydrothermal deposits that were transformed in the surface environment. Processes that have affected these particles include shortdistance transport, chemical de-alloying of the primary Gold silver, and (bio)geochemical dissolution/reprecipitation of Gold leading to the formation of pure, secondary gold and the Dispersion of gold nanoparticles. The latter processes are likely mediated by non-living organic matter (OM) and bacterial biofilms residing on the particles. The biofilms are largely composed of metallophillic β- and γ-Proteobacteria. Abundant mobile gold and platinum nanoparticles were detected in surface waters, suggesting similar mobilities of these metals. Earlier hydrothermal processes have led to the formation of coarsely-crystalline, arborescent dendritic potarite (PdHg). On potarite surfaces, biogeochemical processes have then led to the formation of platinum- and palladium-rich micro-crystalline layers, which make up the botryoidal platinum palladium aggregates. Subsequently potarite was dissolved from the core of many aggregates leaving voids now often filled by secondary anatase (TiO2) containing biophilic elements. The presence of fungal structures associated with the anatase suggests that fungi may have contributed to ist formation. For the first time a primary magmatic PGM-particle comprising a mono-crystalline platinum palladium-alloy with platinum iridium osmium inclusions was described from this locality, finally defining a possible primary source for the PGM mineralisation. In conclusion, the formation of modern-day placer gold- and PGM-particles at CBS began 100s ofmillions of years ago bymagmatic and hydrothermal processes. These provided the metal sources for more recent biogeochemical cycling of PGEs and gold that led to the trans/neoformation of gold- and PGM-particles.
The derivation of a crystal structure and its phase-specific parameters from a single wide-angle backscattered Kikuchi diffraction pattern requires reliable extraction of the Bragg angles. By means of the first derivative of the lattice profile, an attempt is made to determine fully automatically and reproducibly the band widths in simulated Kikuchi patterns. Even under such ideal conditions (projection centre, wavelength and lattice plane traces are perfectly known), this leads to a lattice parameter distribution whose mean shows a linear offset that correlates with the mean atomic number Z of the pattern-forming phase. The consideration of as many Kikuchi bands as possible reduces the errors that typically occur if only a single band is analysed. On the other hand, the width of the resulting distribution is such that higher image resolution of diffraction patterns, employing longer wavelengths to produce wider bands or the use of higher interference orders is less advantageous than commonly assumed.
A band width determination using the first derivative of the band profile systematically underestimates the true Bragg angle. Corrections are proposed to compensate for the resulting offset Δa/a of the mean lattice parameters derived from as many Kikuchi band widths as possible. For dynamically simulated Kikuchi patterns, Δa/a can reach up to 8% for phases with a high mean atomic number Z, whereas for much more common low-Z materials the offset decreases linearly. A predicted offset Δa/a = f(Z) is therefore proposed, which also includes the unit-cell volume and thus takes into account the packing density of the scatterers in the material. Since Z is not always available for unknown phases, its substitution by Zmax, i.e. the atomic number of the heaviest element in the compound, is still acceptable for an approximate correction. For simulated Kikuchi patterns the offset-corrected lattice parameter deviation is Δa/a < 1.5%. The lattice parameter ratios, and the angles α, β and γ between the basis vectors, are not affected at all.1.5%. The lattice parameter ratios, and the angles , and between the basis vectors, are not affected at all.
Методом рентгеноструктурного анализа в интервале температур 18—1150 °С определены температурные зависимости периодов кристаллических решеток γ- и γ'-фаз, их размерно-го несоответствия (мисфит) и объемной доли γ'-фазы экспериментального монокристал-лического жаропрочного никелевого сплава. Определены диапазоны температур, в которых происходят интенсивные изменения структурно-фазовых характеристик исследованного сплава.