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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.
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.
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.
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.
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.
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.