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The characterization of really unknown phases typically uses 70 to 150 reflectors for lattice metric calculation. The determination of the lattice parameters follows with 4% accuracy. Including a Z correction up to 1% can be reached. The precision of the lattice parameters ratios (a:b:c) is, however, better than 0.1%.
Electron Back Scatter Diffraction (EBSD) is a very versatile analytical technique allowing for the characterization of material structure. Historically, diffraction images (Kikuchi patterns) registered during EBSD analysis were solved using Hough/Radon transformation. The last decade brought several novel techniques of experimental pattern analysis, focusing entirely on image analysis routines such as pattern matching, or various variants of High-Resolution EBSD. However, all the above-mentioned techniques require prior knowledge of the material structure to perform orientation analysis. The recently presented algorithm employed in Crystallographic Analysis of Lattice Metric (CALM) software, effectively removes this limitation enabling a standard-less analytical approach in EBSD systems. At its core, the CALM technique couples accurate detection of the Kikuchi bands position, with a rigid construction of reciprocal lattice resulting from translational crystal symmetry. A unique characteristic of the methodology also gives an opportunity for application in the analysis of continuous lattice changes, for example tetragonality mapping. During mapping, however, the geometry of the gnomonic projection (represented by the projection center) is continuously altered decreasing overall algorithm efficiency. The work presents an analysis of the projection center in terms of precision and accuracy.
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.
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).
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 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.
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.
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.