Deep ice cores from polar ice sheets enable reconstructions of Earth’s past climate. Ice-core records are therefore crucial for projecting future climate change, however, our ability to interpret them relies on our understanding of polycrystalline-ice microstructures and mechanics. In turn, these microstructures enable modeling of ice flow and large-scale effects of ice-sheet evolution. Since drilling began in the 1950s, the ice textures and climate proxies developed to decipher ice-core records have been analyzed in one- or two-dimensional (2D) spaces, necessitated by the analytical instruments of core-processing lines and laboratories. Here we develop a three-dimensional (3D), non-destructive approach to textural analysis that preserves the natural context of ice and complements standard methods. Our method combines lab-based absorption and diffraction contrast tomography to simultaneously visualize, measure, and spatially correlate ice grains and air bubbles from volumetric and 3D crystallographic perspectives, both lost during traditional sample preparations. We evaluate the representation of 3D versus 2D data and discuss how access to both c- and a-axis directions of grains may help constrain micromechanical models. We also built a specially designed cooling device for the laboratory X-ray system to extend observational volumes by several orders of magnitude over previous synchrotron-based measurements.

The 3D microstructure of a second-generation single-crystal nickel-based superalloy, Ren & eacute; N5, has been analyzed using laboratory-based X-ray diffraction contrast tomography (lab-based DCT). This experiment has demonstrated the precise capabilities of lab-based DCT in resolving subgrain boundaries with a misorientation angle of less than 1 degrees, achieving an angular accuracy as fine as 0.1 degrees. The performance of the lab-based DCT has been compared with standard and widely used electron backscatter diffraction (EBSD) analysis. Obtaining the 3D microstructure non-destructively enabled the segmentation of the network of nickel-based single-crystal dendrites, opening up new opportunities for studying crystal mosaicity.

The development of 3D non-destructive X-ray characterization techniques in home laboratories is essential for enabling many more researchers to perform 3D characterization daily, overcoming the limitations imposed by competitive and scarce access to synchrotron facilities. Recent efforts have focused on techniques such as laboratory diffraction contrast tomography (LabDCT). LabDCT allows 3D characterization of recrystallized grains with sizes larger than 15-20 µm, offering a boundary resolution of approximately 5 µm using commercial X-ray computed tomography (CT) systems. To enhance the capa-bil-ities of laboratory instruments, we have developed a new laboratory-based 3D X-ray micro-beam diffraction (Lab-3DµXRD) technique. Lab-3DµXRD combines the use of a focused polychromatic beam with a scanning-tomographic data acquisition routine to enable depth-resolved crystallographic orientation characterization. This work presents the first realization of Lab-3DµXRD, including hardware development through the integration of a newly developed Pt-coated twin paraboloidal capillary X-ray focusing optics into a conventional X-ray micro-computed tomography (µCT) system, as well as the development of data acquisition and processing software. The results are validated through comparisons with LabDCT and synchrotron phase contrast tomography. The findings clearly demonstrate the feasibility of Lab-3DµXRD, particularly in detecting smaller grains and providing intragranular information. Finally, we discuss future directions for developing Lab-3DµXRD into a versatile tool for studying materials with smaller grain sizes and high defect densities, including the potential of combining it with LabDCT and µCT for multiscale and multimodal microstructural characterization.

Minerals are crystalline solids manifesting various symmetries in their ordered structures despite high-energy defects seated in their atomic templates. Twin boundaries are imperfections affording energy reduction through reflection, rotation, or inversion of the crystal lattice, forming symmetrical intergrowths. Quartz is one of many minerals that twins as a rule, yet its most common twin is rarely seen without destructive analysis. Disguised as one crystal, this penetrative twin abides by the Dauphiné Law, appearing in 2D as patchworks of irregular domains to roughly triangular sectors. The physical basis for such diverse morphologies remains inconclusive. However, because twins are related by a rotational symmetry that disrupts quartz’s piezoelectric property, their enigma and ubiquity have plagued quartz’s profound technological role in society for over a century. Here we noninvasively map twins and find their boundaries ideally manifest as a 3D waveform oscillating in harmony with α-quartz’s elastic anisotropy. While maximizing elastic strain energy, the sinusoid minimizes internal energy by equipoising twins’ softer and stiffer parts that are transposed in r- and z-rhombohedra, such that oscillations correspond to the threefold c-axis symmetry mirrored in Young’s modulus. This helps explain twin diversity and invites new appraisals of quartz’s microstructural behavior from geological and engineering perspectives.

<p>The relationship between Raman peak intensity and crystal orientation via knowledge of the: Raman tensor of a given vibrational mode, incident laser light and Raman scattered light polarisation vectors is well established. Thanks to Loudon’s work in 1964 the Raman tensor structure is known for all 32 crystal classes[1]. Many researchers have exploited this to determine Raman tensor coefficients to study the nature of semiconductor and covalently bonded materials e.g.[2,3] using polarised Raman microscopy with the aim to determine crystal orientation locally.<br /><br />In 2019 Ilchenko et al. demonstrated the feasibility of quantitatively mapping crystallographic orientation of polycrystalline materials in 2D, and in 3D exploiting the confocal nature of a Raman microscope[4]. The novelty of this work overcomes the need to serially collect Raman spectra at each map pixel for multiple combinations incident and scattered polarization needed to compute the local crystal orientation. A new generation of this technology, quantitative Raman imaging of crystallographic orientation (qRICO), rapidly collects Raman spectra of up to 20 combinations of incident and scattered polarization in a simultaneous manner.<br /><br />Development work using ideal semiconductor materials has demonstrated that qRICO delivers the ability to produce crystallographic images of sample microstructures with sample stage step / pixel sizes down to 0.5 µm, contiguous scanning areas on the order of 10 x 10 cm and crystal orientation accuracy better than 2°. Thus, qRICO provides access to a very wide range of the microstructure length scales seen in geological materials and is amenable to typical geological specimen dimensions and shapes. Fundamentally qRICO is not limited to polished planar sample surfaces and is not restricted to surface studies for transparent materials.<br /><br />In this work, in addition to non-natural polycrystalline materials, we will present high resolution as well as large area map examples of orientation mapping results on natural diamonds containing defect structures, polycrystalline quartz particles and multiphase petrographic thin slices. These examples will be used to illustrate the potential of qRICO for understanding geological materials in terms of grain boundaries, phase boundaries, orientation gradients, and crystallographic orientations and texture in relation to the conventional information contained in the underlying Raman spectra such as chemical gradients and internal stress.<br /><br />[1]  R. Loudon, The Raman effect in crystals, Adv. Phys. 13 (1964) 423–482. https://doi.org/10.1080/00018736400101051.<br />[2]  C. Kranert, C. Sturm, R. Schmidt-Grund, M. Grundmann, Raman tensor elements of β-Ga2O3, Sci. Rep. 6 (2016) 35964. https://doi.org/10.1038/srep35964.<br />[3]  X. Zhong, A. Loges, V. Roddatis, T. John, Measurement of crystallographic orientation of quartz crystal using Raman spectroscopy: application to entrapped inclusions, Contrib. Mineral. Petrol. 176 (2021) 89. https://doi.org/10.1007/s00410-021-01845-x.<br />[4] O. Ilchenko, Y. Pilgun, A. Kutsyk, F. Bachmann, R. Slipets, M. Todeschini, P.O. Okeyo, H.F. Poulsen, A. Boisen, Fast and quantitative 2D and 3D orientation mapping using Raman microscopy, Nat. Commun. 10 (2019) 5555. https://doi.org/10.1038/s41467-019-13504-8.</p>

Three new advanced acquisition strategies for lab-based diffraction contrast tomography are presented. They are named Helical Phyllotaxis, Helical Phyllotaxis Raster, and Helical Phyllotaxis HART and enable grain mapping of longer, larger, high-aspect ratio samples. The implementation of these advanced acquisition strategies combines a golden angle rotation with vertical and horizontal translations to perform a seamless data collection that has a uniform sample illumination both angularly and spatially. Reconstruction of the corresponding data is equally seamless, simultaneously using all data to reconstruct the full illuminated volume without the need for registration or stitching of data subsets or sample subvolumes. Examples of performing Helical Phyllotaxis and Helical Phyllotaxis Raster scans on a selection of samples, which have either been mapped previously or come from the same batch of samples, show a substantial reduction in data collection time and/or a significant improvement in grain statistics. The Helical Phyllotaxis HART (high-aspect ratio tomography for plate-like samples) strategy enables investigations of a hitherto inaccessible class of sample geometries comprising industrially relevant materials like rolled metal sheets and electrical steels. The advanced acquisition strategies take lab-based non-destructive 3D grain mapping to the next level of throughput, grain statistics and versatility and hold great promise for integrated computational materials science and engineering applications. While the throughput warrants 4D studies of materials microstructural evolution, a representative sample volume is a prerequisite for successful model predictions of the evolution, and the versatility enables studies of samples or components under more realistic in situ or in operando conditions.

Electrical steels with high Si contents are widely used in electrical power transformers, motors and generators. Texture is the most important property for electrical steel as the orientations of grains have strong influences on the magnetization and electrical resistance of the materials. Lab-based diffraction contrast tomography (lab-based DCT) is a recently developed X-ray-based technique that can map the grain morphology and crystallographic orientation nondestructively in 3D. The capability of lab-based DCT in characterizing the grain structure of both non-oriented and grain-oriented electrical steels provides important complementary information to commonly used techniques such as X-ray diffraction (XRD) and electron backscattered diffraction (EBSD) in terms of full 3D grain mapping and significant grain statistics. In this work, we will present several case studies of using lab-based DCT to characterize the grain structure of both non-oriented and oriented electrical steels, with discussion on how this non-destructive 3D technique will contribute to the texture analysis in electrical steels.

The efficiency of large second phase particles to stimulate nucleation of recrystallization in commercially cold rolled (25%) AA5182 aluminium sheet is investigated by laboratory multimodal X-ray tomography. The spatial distributions of 11434 particles and 742 nuclei are determined non-destructively in 3D in the same sample volume. Our work confirms that particle stimulated nucleation is the dominant nucleation mechanism, but it is also found that PSN nuclei stimulated from small particles and non-PSN nuclei can grow to large sizes. These results and the observed orientation distributions of the PSN and other nuclei are discussed in relation to existing theories. IMPACT STATEMENT The efficiency of the nucleation mechanism called particle stimulated nucleation is quantified in 3D by a non-destructive experimental approach.

The mechanism of recrystallization texture development of cold-rolled metal and steel largely depends on the material chemical composition, cold-rolling reduction, and annealing treatment conditions. To clarify the mechanism, it is important to identify the locations where recrystallization starts and progresses within cold-rolled materials. Using laboratory diffraction contrast tomography (LabDCT), three-dimensional (3D) crystal orientation mapping corresponding to different stages of recrystallization has been successfully performed for pure iron sheets that were severely cold-rolled and heated at different temperatures. In cold-rolled iron with 99.2% reduction, the deformation texture was a strong alpha-fiber (RD//< 110 >). During annealing in the temperature range of 773-973 K, recrystallized grains were formed with textural components of {100}, {211}, {111} and {411}, and the alpha-fiber changed to the {100} < 012 > component. Recrystallized grains were generated at rather random locations within the sample. The size of recrystallized grains in the center region was 20-30% larger than that in the surface region. These results suggest that the nucleation is driven by the large strain caused by severe rolling. The number of recrystallization sites was larger in the surface region than in the center region and the competition of selective growth among recrystallized grains was more severe in the surface region, resulting in a smaller grain size. The volume data of the 3D crystal orientation mapping obtained by LabDCT provided crucial information for understanding the recrystallization mechanism including the nucleation and/or selective growth.

Non-destructive orientation mapping is an important characterization tool in materials science and geoscience for understanding and/or improving material properties based on their grain structure. Confocal Raman microscopy is a powerful non-destructive technique for chemical mapping of organic and inorganic materials. Here we demonstrate orientation mapping by means of Polarized Raman Microscopy (PRM). While the concept that PRM is sensitive to orientation changes is known, to our knowledge, an actual quantitative orientation mapping has never been presented before. Using a concept of ambiguity-free orientation determination analysis, we present fast and quantitative single-acquisition Raman-based orientation mapping by simultaneous registration of multiple Raman scattering spectra obtained at different polarizations. We demonstrate applications of this approach for two- and three-dimensional orientation mapping of a multigrain semiconductor, a pharmaceutical tablet formulation and a polycrystalline sapphire sample. This technique can potentially move traditional X-ray and electron diffraction type experiments into conventional optical laboratories.

A method for reconstructing the three-dimensional grain structure from data collected with a recently introduced laboratory-based X-ray diffraction contrast tomography system is presented. Diffraction contrast patterns are recorded in Laue-focusing geometry. The diffraction geometry exposes shape information within recorded diffraction spots. In order to yield the three-dimensional crystallographic microstructure, diffraction spots are extracted and fed into a reconstruction scheme. The scheme successively traverses and refines solution space until a reasonable reconstruction is reached. This unique reconstruction approach produces results efficiently and fast for well suited samples.

Crystallographic imaging (i.e.imaging of crystallites/grains in polycrystalline materials) is primarily known from electron microscopy, and particularly the introduction of the electron back-scattering diffraction (EBSD) technique in the early 1990's, has made it a routine tool for research and/or development related to metallurgy, functional ceramics, semi-conductors, geology etc.The ability to image the grain structure in such materials is instrumental for understanding and optimization of material properties and processing.However, the destructive nature of 3D EBSD prevents the technique from directly evaluating the microstructure evolution when subject to either mechanical, thermal or other environmental conditions.

Laboratory diffraction contrast tomography (LabDCT) enables the user to reconstruct three-dimensional (3D) grain maps of polycrystalline materials. For each grain, the size, orientation, and 3D morphology including the number of faces can be derived. Since the technique is non-destructive, LabDCT opens up new possibilities for studies of microstructural evolution at the level of individual grains. The LabDCT setup is integrated on a commercial X-ray microscope, enabling correlation of the resulting grain map with complimentary information on, e.g., cracks, porosities, and inclusions. Here, the LabDCT principle is introduced, and recent materials science applications are presented. The first example on liquid metal embrittlement highlights the correlation of grain boundary properties and complimentary absorption information on grain boundary wetting. It is shown that the grain boundary energy determines whether wetting occurs or not. The second example is on grain growth. The grain statistics in this study, more than 1200 grains at two different time steps, were large enough to capture rare events such as abnormal grain growth and the annihilation of a grain with only three faces.

Laboratory diffraction contrast tomography (LabDCT) is a laboratory-scale x-ray microtomography technique that can be used to non-destructively map grains and grain boundaries in 3D. The fidelity of grain mapping significantly depends on the quality of grain reflections obtained from the illuminated volume of the specimen. In this article, we report the application of a novel forward modeling approach to improve the reliability of grain mapping. Through this approach, a comparison between the obtained grain reflections and simulated grain reflections can be used to perform a self-fitting operation. This can be used to optimize instrumental parameters and iteratively improve the quality of reconstruction. To demonstrate the effectiveness of the forward modeling approach, LabDCT was used to map the grains in a polycrystalline specimen of the magnesium alloy AZ91E and iteratively improve reconstruction quality significantly.

To be useful in numerical simulations of e.g. deformation processes, EBSD datasets of crystallographic orientations have to be downsized by several orders of magnitude yet preserving the orientation density function approximately. The objective is either to preserve the overall shape of the initially kernel estimated orientation density function and in particular its non-negativity, or to preserve the unbiased estimates of the first Fourier coefficients up to a given finite order. Methods are presented how to construct a much smaller set of weighted orientations such that their kernel density estimate approximates the initial estimate. To preserve its overall shape the de la Vallée Poussin kernel is applied as it is the only known non-negative kernel with a finite Fourier series expansion avoiding truncation errors. If the first Fourier coefficients are to be preserved the Dirichlet kernel applies as it is the only kernel providing unbiased estimates of the Fourier coefficients up to any given finite order. The weights are determined numerically by resolving a least squares or a maximum likelihood problem. Due to the linearity of kernel density estimation and the Fourier transform the approaches in spatial and spectral domain are related to each other in a unique complementary way. For an exemplary practical application we use a large EBSD dataset of about 80.000 orientations from a recrystallized low alloyed Zirconium sheet. Our methods reduce the size of the dataset by about \(99.75\,\%\) to the order of 200 weighted orientations supporting a secondary approximate distribution with a volume portion of crystallites oriented differently than initially of less than \(10\,\%\).

Journal Article 3D Mapping Grain Morphology and Grain Orientations by Laboratory Diffraction Contrast Tomography Get access Leah Lavery, Leah Lavery Carl Zeiss X-ray Microscopy, Pleasanton, CA, United States Search for other works by this author on: Oxford Academic Google Scholar Nicolas Gueninchault, Nicolas Gueninchault Xnovo Technology, Køge, Denmark Search for other works by this author on: Oxford Academic Google Scholar Hrishikesh Bale, Hrishikesh Bale Carl Zeiss X-ray Microscopy, Pleasanton, CA, United States Search for other works by this author on: Oxford Academic Google Scholar Christian Holzner, Christian Holzner Carl Zeiss X-ray Microscopy, Pleasanton, CA, United States Search for other works by this author on: Oxford Academic Google Scholar Florian Bachmann, Florian Bachmann Xnovo Technology, Køge, Denmark Search for other works by this author on: Oxford Academic Google Scholar Erik Lauridsen Erik Lauridsen Xnovo Technology, Køge, Denmark Search for other works by this author on: Oxford Academic Google Scholar Microscopy and Microanalysis, Volume 23, Issue S1, 1 July 2017, Pages 48–49, https://doi.org/10.1017/S1431927617000927 Published: 04 August 2017

This paper presents the background for the calculation of anisotropic piezoelectric properties of single crystals and the graphical display of the results in two or three dimensions, and the calculation of the aggregate properties from constituent crystals and the texture of the aggregate in a coherent manner. The texture data can be obtained from a wide range of sources, including pole figure diffraction and single orientation measurements (electron backscattered diffraction, electron channelling pattern, Laue Pattern, optical microscope universal-stage). We consider the elastic wave propagation in piezoelectric crystals as an example of the interaction of electrical (2nd rank tensor), piezoelectric (3rd rank tensor) and elastic properties (4th rank tensor). In particular, we give explicit formulae for the calculation of the Voigt averaged tensor from individual orientations or from an orientation distribution function. For the latter we consider numerical integration and an approach based on the expansion into spherical harmonics. We illustrate the methods using single crystals, polycrystalline quartz measured using electron channelling patterns and ideal Curie limiting groups applied to quartz aggregates. This paper also serves as a reference paper for the mathematical tensor capabilities of the texture analysis software MTEX.