Web Site of Adam Morawiec

Downloads

Methods for quantitative characterization of
three-dimensional grain boundary networks
in polycrystalline materials

Cover

See also related publications

Abstract:

It is well known that grain boundaries have an impact on properties of polycrystalline materials. The most basic aspect of boundary analysis is boundary geometry. Geometry of a boundary is described by five so-called macroscopic boundary parameters, i.e., by relative orientation between abutting grains and inclination of the boundary plane. Recent progress in development of experimental techniques for three-dimensional orientation mapping (e.g., electron backscatter diffraction combined with precise serial sectioning) has made it possible to determine all five geometric parameters for significant numbers of boundaries. The resulting data sets are sufficiently large for carrying out statistical studies of boundaries. It turns out that boundary characterization with all five boundary parameters taken into account is far more complex compared to that limited solely to grain misorientations. This dissertation is devoted to development of effective tools for geometric characterization of individual boundaries and quantitative analyses of entire boundary networks.

Several types of geometrically characteristic grain boundaries are distinguished. Based on all five parameters, boundaries can be classified, e.g., as tilt, twist, symmetric, or 180°-tilt. Two questions related to this classification are addressed: 1. Does a boundary having given parameters belong – within an assumed tolerance – to any of these groups? 2. What are the area-fractions of characteristic boundaries in a boundary network? To answer them, applicability of various approaches to recognizing the boundary types are considered. E.g., it is shown that the widespread idea of decomposition of a boundary into its tilt and twist components is not suitable for analysis of experimental (error-affected) data. Other solutions are either inefficient or provide incomplete information. Therefore, new reliable and fast-to-calculate parameters describing geometry of boundaries are defined. Then, using these parameters, the frequencies of occurrence of characteristic boundaries are estimated for the first time for real materials (ferritic steel and nickel-based superalloy IN100).

A basic characteristic of a boundary network in a given polycrystal is a distribution of boundaries with respect to their macroscopic parameters. To avoid artifacts caused by the currently used computation method, it is proposed to utilize the kernel density estimation technique and to determine boundary distributions based on distance functions defined in the five-dimensional space of boundary parameters. Based on diverse example distributions obtained for several metals with both face-centered and body-centered structures (pure Ni, the Ni-based alloy, and ferrite), it is shown that with new computational approach, the resulting distributions are clearly more accurate. A scheme of interpretation of the distributions is also proposed. It includes evaluation of their statistical reliability and identification of their symmetries. Besides that, charts allowing for verification whether extrema in such distributions correspond to boundaries of characteristic geometry are obtained using two complementary methods (analytical and numerical). Kernel density estimation is also adapted to computation of boundary-plane distributions independent of misorientations. Such distributions are studied in both crystallite and laboratory reference frames. The distribution functions given in the crystallite frame are used for investigation of populations of boundary planes in pure Ni and alloy IN100. The distribution functions in the laboratory frame have not been considered before; the functions of this kind are computed for the above-mentioned metals as well as for yttria.

In parallel to developing the aforementioned methods themselves, a package of computer programs including implementations of the new approaches has been created. Its features are briefly described.

Contents:

1 Introduction

2 State of the field
    2.1 Mathematical foundations
        2.1.1 Space of grain boundaries
        2.1.2 Equivalent boundary representations
        2.1.3 Metrics in the boundary space
    2.2 Boundaries of characteristic geometry
        2.2.1 Decomposition into tilt and twist components
        2.2.2 Tilt/twist component parameter
        2.2.3 Distances to the nearest tilt and twist boundaries
        2.2.4 Fractions of tilt and twist boundaries
    2.3 Grain boundary distributions
        2.3.1 Partition-based method
        2.3.2 Boundary-plane distributions
        2.3.3 Misorientation distribution functions
        2.3.4 Locations of characteristic boundaries
        2.3.5 Symmetries of functions of macroscopic boundary parameters
    2.4 Grain boundary energy
        2.4.1 Relative energies from geometry of triple junctions
        2.4.2 Molecular-dynamics simulations
    2.5 Computer programs related to boundary analysis
    2.6 Problem statement
        2.6.1 Shortcomings of parameters describing boundary characters
        2.6.2 Artifacts originating from the partition-based method
        2.6.3 Incomplete interpretation of boundary distributions
        2.6.4 Capabilities missing in the existing software

3 Objectives of this work

4 Reconstruction of boundary networks

5 Methods for quantifying the character of a boundary
    5.1 Tilt and twist characters
        5.1.1 Applicability of Fortes decomposition
        5.1.2 Extreme values of the TTC parameter
        5.1.3 Example: tilt and twist boundaries in Small IN100
    5.2 Symmetric and 180°-tilt characters
        5.2.1 Parameters αS and αL as substitutes of the distances
        5.2.2 Example: symmetric and 180°-tilt boundaries in SmallIN100
        5.2.3 Example: characteristic boundaries in Ferrite
    5.3 Locations of characteristic points in the boundary space
        5.3.1 Analytical method
        5.3.2 Numerical searches
        5.3.3 Example: CSL misorientations for the Oh symmetry
        5.3.4 Example: WC/WC boundaries in WC-Co composites

6 New approach to computation of boundary distributions
    6.1 Use of kernel density estimation
    6.2 Five-parameter distributions for selected materials
        6.2.1 Nickel (CMU)
        6.2.2 Nickel (UGent)
        6.2.3 Big IN100
        6.2.4 Ferrite
    6.3 Boundary-plane distributions
        6.3.1 Examples

7 GBToolbox

8 Final remarks
    8.1 Comments on determination of the boundary character
    8.2 Understanding boundary distribution

9 Summary
    9.1 Conclusions
    9.2 Closing remarks

Acknowledgments

Appendix A Data sets

Appendix B Charts for interpreting functions of macroscopic parameters

Bibliography

Known errors:
- p. 85:   is "... are divided by 4 × n_S × V_p and 4 × V_p, respectively.",   should be    "... are divided by 4 × n_S × V_p and 2 × V_p, respectively."