A Data-Driven Scheme for Quantitative Analysis of Texture
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TEXTURE is a collective term for a non-uniform distribution of crystallographic orientations in a polycrystalline aggregate.[1] Since the work of Bunge[2] and Roe,[3] continuous orientation distribution function (CODF) has been a general method to represent the texture. Nowadays, plenty of research still endeavored to construct a CODF from the discrete orientation dataset as accurate as possible.[4–7] Nevertheless, the CODF is an approximation of the discrete orientation dataset. Schaeben pointed out that such an approximation did not facilitate statistical tests of uniformity against preferred orientation, or of rotational symmetry, nor a measure of the pattern of preferred orientation with some statistical significance.[8] Also, statistical tests to compare different orientation densities by their mean,
YAFEI WANG, CHENFAN YU, LEILEI XING, KAILUN LI, JINHAN CHEN, WEI LIU, and JING MA are with the State Key Laboratory of New Ceramic and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China. Contact e-mail: [email protected] ZHIJIAN SHEN is with the State Key Laboratory of New Ceramic and Fine Processing, School of Materials Science and Engineering, Tsinghua University and also with the Department of Materials and Environment Chemistry, Arrhenius Laboratory, Stockholm University, 106 91 Stockholm, Sweden. Contact e-mail: [email protected] Manuscript submitted June 9, 2019.
METALLURGICAL AND MATERIALS TRANSACTIONS A
modes, pattern of preferred orientation, etc. were missing. Therefore, the quantitative analysis of texture from discrete orientation dataset is suggested to be based on orientation statistics. Because the statistical methods are generally not applicable to the whole orientation dataset, a cluster analysis is suggested to identify the representative orientation clusters first.[8,9] The orientation cluster is the zone of high density in the orientation space, and it is called the texture component or preferred orientation by materials scientists.[8,9] On the one hand, the orientation clusters themselves represent the intrinsic pattern of the orientation dataset.[9] On the other hand, some general statistical methods can then be applied to mine more insights into the orientation cluster,[8,10,11] and more methods on orientation data are still being developed by the statistics community.[12] An essential part of statistical analysis is the quantification of uncertainty, which guides decision making on the results.[12–15] However, uncertainty is rarely quantified in construction of CODF.[15] The combination of clustering analysis and orientation statistics is a data-driven scheme for quantitative analysis of texture, which can date back to 1993 from Schaeben.[8] He also conceived a clustering algorithm based on the estimation of density, while there was no such implementation at that time. In 1996, computer scientists Ester et al. presented a clustering algorithm relying on a density-based notion of clusters,[16] which is
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