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Paper des Monats
- ja (1)
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).
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.
A pseudosymmetric description of the crystal lattice derived from a single wideangle Kikuchi pattern can have several causes. The small size (<15%) of the sector covered by an electron backscatter diffraction pattern, the limited precision of the projection centre position and the Kikuchi band definition are crucial. Inherent pseudosymmetries of the crystal lattice and/or structure also pose a challenge in the analysis of Kikuchi patterns. To eliminate experimental errors as much as possible, simulated Kikuchi patterns of 350 phases have been analysed using the software CALM [Nolze et al. (2021). J. Appl. Cryst. 54, 1012–1022] in order to estimate the frequency of and reasons for pseudosymmetric crystal lattice descriptions. Misinterpretations occur in particular when the atomic scattering factors of non-equivalent positions are too similar and reciprocal-lattice points are systematically missing. As an example, a pseudosymmetry prediction depending on the elements involved is discussed for binary AB compounds with B1 and B2 structure types. However, since this is impossible for more complicated phases, this approach cannot be directly applied to compounds of arbitrary composition and structure.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 new software is presented for the determination of crystal lattice parameters from the positions and widths of Kikuchi bands in a diffraction pattern. Starting with a single wide-angle Kikuchi pattern of arbitrary resolution and unknown phase, the traces of all visibly diffracting lattice planes are manually derived from four initial Kikuchi band traces via an intuitive graphical user interface. A single Kikuchi bandwidth is then used as reference to scale all reciprocal lattice point distances. Kikuchi band detection, via a filtered Funk transformation, and simultaneous display of the band intensity profile helps users to select band positions and widths. Bandwidths are calculated using the first derivative of the band profiles as excess-deficiency effects have minimal influence. From the reciprocal lattice, the metrics of possible Bravais lattice types are derived for all crystal systems. The measured lattice parameters achieve a precision of <1%, even for good quality Kikuchi diffraction patterns of 400 x 300 pixels. This band-edge detection approach has been validated on several hundred experimental diffraction patterns from phases of different symmetries and random orientations. It produces a systematic lattice parameter offset of up to ±4%, which appears to scale with the mean atomic number or the backscatter coefficient.
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.
An extensive set of information about the diffracting volume is carried by EBSD patterns: the crystal lattice, the reciprocal lattice, the crystal structure, the crystal symmetry, the mean periodic number of the diffracting phase, the source point from where it has been projected (projection centre), the crystal orientation, the sample topography (local tilt), the (preparation) quality of defect density of the crystal, and possible pattern overlaps. Some of this information is used regularly in conventional EBSD analyses software while others are still waiting for a more widespread application. Despite the wealth of information available, the accuracy and precision of the data that are presently extracted from conventional EBSD patterns are often well below the actual physical limits. Using a selection of example applications, we will demonstrate the gain in angular resolution possible using relatively low-resolution patterns of approximately 20k pixels in combination with pattern matching (PM) approaches. In this way, fine details in a microstructure can be revealed which would otherwise be hidden in the orientation noise.
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 elastic properties of the single-crystal nickel-base superalloy CMSX-4 used as a blade material in gas turbines were investigated by the sonic resonance method in the temperature interval between room temperature and 1300 °C. Elastic constants at such high temperatures are needed to model the mechanical behavior of blade material during manufacturing (hot isostatic pressing) as well as during technical accidents which may happen in service (overheating). High reliability of the results was achieved using specimens of different crystallographic orientations, exciting various vibration modes as well as precise measurement of the material density and thermal Expansion required for modeling the resonance frequencies by finite element method. Combining the results measured in this work and literature data the elastic constants of the gamma and gamma' phases were predicted.
This prediction was supported by measurement of the temperature dependence of the gamma'fraction.
All data obtained in this work are given in numerical or analytical forms and can be easily used for different scientific and engineering calculations.
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.