Guoquan Liu

Applied stereology in materials science and engineering

A general view of the role of stereology in materials science and engineering (MSE), is followed by a discussion of applied stereology for one‐, two‐ and multi‐phase structures, and by examples of stereology applications to MSE, such as the impact of stereology on the creation and evolution of modern high–strength, low‐alloy steels. The present state and prospects of applied stereology in MSE are informally discussed. It is demonstrated that, without stereology, materials science cannot evolve into a truly quantitative science, and that the needs of both materials scientists and materials engineers should be met by the continuing cooperation of those who develop stereological methods and those who apply them.

Topological correlations of three-dimensional grains

Topological correlations of three-dimensional grains were investigated by Monte Carlo-Potts model simulation. The result shows that, unlike first nearest neighbors (the Aboav-Weaire law [D. Aboav, Metallography 3, 383 (1970) and D. Weaire, Metallography 7, 157 (1974)] holds), there appears to be very little correlation between grains and their second and third nearest neighbors (on average), i.e., the average number of faces of second nearest neighbors, m2, and third nearest neighbors, m3, are independent of faces f of the center grain (nearly m2 = 14.984 and m3 = 14.489). This result indicates that long range correlations beyond first nearest neighbors may have negligible effect on the growth of center grains and thus provides support to a topologically averaged growth law that only considered the non-random first nearest-neighbor interactions.

On the sampling of three-dimensional polycrystalline microstructures for distribution determination

How to sample three‐dimensional microstructure and effectively reduce experimental error is a challenging problem. Taking seven single‐phase polycrystalline structures generated by 400×400×400 Potts Monte Carlo simulation as the study object, effects of sampling strategy on the determination of various characteristic parameters of the grain size distribution and grain topology distribution are studied. The mean voxel value (or volume) of individual grains in the three‐dimensional simulated microstructure varies from 4.56×104 to 1.0×103, and the number of grains contained in the structure varies from 63 901 to 1403. The results show that, a minimum of 200 sampled grains can ensure the relative error to be less than 5% for determination of the mean grain volume, the mean grain face number and the coefficient of variance of the distribution of grain size and the grain face number. Whereas for the coefficient of the skewness and the kurtosis of grain size distribution or grain face number distribution, a minimum of 800 sampled grains are required for the same error level. However, if some exceptional big grains appear, e.g. a grain larger than with eight multiples of mean grain volume and/or three multiples of mean grain face number, abnormal values of the two parameters would be resulted, even the number of examined grains is over 1000.

STEREOLOGICAL CHARACTERIZATION OF PARTICLE CONTIGUITY

Some parameters used to characterize fictitious features not existing in the real microstructure, such as the total length in a unit volume of the intersection curves made by the interface between the particles of secondary phase with the fictitious grain boundary surface of the matrix phase, are useful for the quantitative characterization of particle–profile contiguity on grain boundary surfaces, and can be determined in an unbiased way from measurements on random planes of polish. It is shown that the contiguity parameters C3D proposed by Gurland, LV‐type by Cahn & Hilliard and CGB by Liu, all accessible stereologically, have different physical meanings and provide different kinds of quantitative information on particle contiguity. The reversed stereology principle is applicable to contiguity parameters C3D and CGB, since their estimators are comparable. The contiguity analysis carried out for isothermal austenite‐ferrite phase transformation processes occurring in five series of low‐carbon Ti–B or V–Ti–B steels has confirmed the feasibility of the methods proposed.

Reconstruction of three-dimensional grain structure in polycrystalline iron via an interactive segmentation method

Using a total of 297 segmented sections, we reconstructed the three-dimensional (3D) structure of pure iron and obtained the largest dataset of 16254 3D complete grains reported to date. The mean values of equivalent sphere radius and face number of pure iron were observed to be consistent with those of Monte Carlo simulated grains, phase-field simulated grains, Ti-alloy grains, and Ni-based super alloy grains. In this work, by finding a balance between automatic methods and manual refinement, we developed an interactive segmentation method to segment serial sections accurately in the reconstruction of the 3D microstructure; this approach can save time as well as substantially eliminate errors. The segmentation process comprises four operations: image preprocessing, breakpoint detection based on mathematical morphology analysis, optimized automatic connection of the breakpoints, and manual refinement by artificial evaluation.

Topological correlations of grain faces in polycrystal with experimental verification

How grain faces are arranged in three-dimensional grain structures is one of the outstanding problems in physics, biology and materials science. Based on the topological analysis of 477 real pure iron grains and 6093 Monte Carlo simulated grains, two forms of topological correlations are studied. The first correlation is Riviers relation (Philos. Mag. B, 52 (1985) 795), in which the average number of edges of faces neighboring to e-edged faces on f-faceted grains is related to e and f; and the second correlation is the one derived in the current paper, in which a typical e-edged face in a polycrystal is a function of the average number of edges of its neighboring faces M(e). Both correlations are verified by experimental and simulation data.

CRYSTALLINE PLATE-LIKE SIO2 PRECIPITATES IN SILICON AND THEIR RELATION WITH NEW DONORS

Czochralski grown silicon annealed at 750° C has been investigated with high-resolution electron microscopy, Hall effect and infrared measurement. Crystalline plate-like precipitates were observed and identified asβ-cristobalite. The structure of the coherent interface of the new phase and its connection with the origin of the new donor are discussed.

Matrix description of the complete topology of three-dimensional cells

A new, efficient method based on a series of matrices is introduced to completely describe the detailed topology of individual domains and their topology evolution in three-dimensional cellular structures. With this approach, we found a lot of new topological grain forms which are never reported before, i.e., there are total 8 and 32 topological forms for 7- and 8-faced grains respectively, other than the reported 7 and 27. This method is proved to be a practical tool to predict all possible grain forms efficiently. Moreover, a connectivity index of grain forms serves as a new convenient differentiator of different multicellular structures.