The uncorrelated triple junction distribution function: Towards grain boundary network design

Johnson, Oliver K.; Schuh, Christopher A.

doi:10.1016/j.actamat.2013.01.025

Cited by 22 publications

(29 citation statements)

References 53 publications

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“…In the absence of spatial correlations of grain orientation, it is possible to derive an uncorrelated TJDF, which we denote T (q 12 , q 23 ), and whose coefficients may be obtained directly from those of the orientation distribution function (ODF) according to 3 (Johnson and Schuh, 2013):…”

Section: Texture and Topologymentioning

confidence: 99%

“…11, * denotes complex conjugation, and denotes integration over the entire domain, S 3 × S 3 , with respect to the appropriate invariant measure (Johnson and Schuh, 2013), which is omitted for brevity. Eq.…”

Section: Grain Boundary Network Configuration Spacementioning

confidence: 99%

“…6, the TJDF may also be expressed as a generalized Fourier series in the basis of bi-polar hyperspherical harmonics (Johnson and Schuh, 2013): …”

Section: Grain Boundary Network Configuration Spacementioning

confidence: 99%

“…In previous work, we introduced a general triple junction distribution function (TJDF) as the core of a design strategy for grain boundary networks (Johnson and Schuh, 2013). The TJDF provides a statistical description of grain boundary network connectivity that facilitates adaptation of the existing design framework to grain boundary network design.…”

Section: Introductionmentioning

confidence: 99%

“…The TJDF provides a statistical description of grain boundary network connectivity that facilitates adaptation of the existing design framework to grain boundary network design. Expressed in the context of the spectral framework of Johnson and Schuh (2013), the TJDF provides a bridge between crystallographic texture and grain boundary network topology. These tools allow one to rigorously bound the universe of all possible grain boundary network configurations.…”

Section: Introductionmentioning

confidence: 99%

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The triple junction hull: Tools for grain boundary network design

Johnson

Schuh

2014

Journal of the Mechanics and Physics of Solids

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Grain boundary engineering (GBE) studies have demonstrated significant materials properties enhancements by modifying the populations and connectivity of different types of grain boundaries within the grain boundary network. In order to facilitate rigorous design and optimization of grain boundary networks, we develop theoretical tools that are based upon a spectral representation of grain boundary network statistics. We identify the connection between a local length scale, embodied by triple junctions, and a global length scale, associated with the grain boundary network configuration as a whole. We define the local state space for triple junctions, A (3) , and enumerate its symmetries. We further define the design space for grain boundary networks, M (3)H , characterize its important geometric properties, and discuss how its convexity permits grain boundary network design. We also investigate the extent to which the control of texture alone allows one to probe the full design space.

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Section: Texture and Topologymentioning

confidence: 99%

Section: Grain Boundary Network Configuration Spacementioning

confidence: 99%

“…6, the TJDF may also be expressed as a generalized Fourier series in the basis of bi-polar hyperspherical harmonics (Johnson and Schuh, 2013): …”

Section: Grain Boundary Network Configuration Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The triple junction hull: Tools for grain boundary network design

Johnson

Schuh

2014

Journal of the Mechanics and Physics of Solids

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Kinetics of triple-junctions in eutectic solidification: a sharp interface model

2014

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The kinetics of triple-junctions (TJs) in eutectic solidification is modeled by the thermodynamic extremum principle (TEP). It consists of two parts. First, TJs as the interaction of interfaces follow the interface kinetics according to which the temperature and concentration at the TJs are determined. This interface part of TJ kinetics is closely related to the eutectic point in the kinetic phase diagram. Second, TJs have their specific kinetics according to which their morphology (e.g., the contact angles in two dimensions) is determined. Using a new solution of solute diffusion in liquid, the TJ kinetics is incorporated into the current lamellar eutectic growth model. The model is applicable to the concentrated alloy systems and can be extended to any kind of eutectics. Simulation results of the rapid solidification of a lamellar Ni 5 Si 2 -Ni 2 Si (c-d) eutectic show that both parts of TJ kinetics can play important roles in eutectic solidification and need to be considered to improve the current eutectic theory.

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Inferring grain boundary structure–property relations from effective property measurements

Johnson

Demkowicz

et al. 2015

J Mater Sci

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Grain boundaries strongly affect many materials properties in polycrystalline materials. However, very few structure-property models exist for grain boundaries, due in large part to the complicated and poorly understood way in which the properties of grain boundaries vary with their crystallographic structure. In the present work, we infer grain boundary structure-property correlations from measurements of the effective properties of a polycrystal. We refer to this approach as grain boundary properties localization. We apply this technique to a simple model system of grain boundary diffusivity in a two-dimensional microstructure, and infer the properties of low-and highangle grain boundaries from the effective diffusivity of the grain boundary network. The generalization and use of these methods could greatly reduce the computational and experimental effort required to establish structure-property correlations for grain boundaries. More broadly, the technique of properties localization could be used to infer the properties of many microstructural constituents in complex microstructures.

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The uncorrelated triple junction distribution function: Towards grain boundary network design

Cited by 22 publications

References 53 publications

The triple junction hull: Tools for grain boundary network design

The triple junction hull: Tools for grain boundary network design

Kinetics of triple-junctions in eutectic solidification: a sharp interface model

Inferring grain boundary structure–property relations from effective property measurements

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