Strain mapping of a triple junction in nanocrystalline Pd
Harald RösnerChristian KübelYulia IvanisenkoLilia KurmanaevaSergiy V. DivinskiMartin PeterlechnerGerhard Wilde
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Disclination
Triple junction
Nanocrystalline material
Triple point
Burgers vector
Lattice (music)
The interaction between liquid and solid metals where the liquid-solid interface contains three grain boundary lines which meet in triple junction point is considered. The assumption that the liquid grooves may be formed not only along grain boundaries but along triple junctions is presented. The variation of Gibbs energy during the formation of triangle pyramidal groove along triple junction is determined. The dependence of Gibbs energy variation from groove dimensions shows that the wetting of triple junctions occurs by lower temperatures than the wetting of grain boundaries. This result allows to take into account the existence of grain size effect on the liquid phase penetration depth into the polycrystalline sample. The proposed mechanism of wetting in polycrystalline metal contains two stages: the outstrip melt penetration along triple junctions and the liquid grooving on grain boundaries forming the triple junctions. One of the processes – triple junction diffusion or liquid diffusion – may control the wetting in the polycrystalline sample.
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Volterra's definition of dislocations in crystals distinguishes edge and screw defects geometrically, according to whether the Burgers vector is perpendicular or parallel to the defect. Here, we demonstrate a distinction between screw and edge dislocations that enables a unified, purely topological means of classification. Our construction relies on the construction of real or virtual disclination-line pairs at the core of the dislocation in a smectic and can be generalized to crystals with triply-periodic order. The connection between topology and geometry is exploited.
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Triple point
Grain boundary strengthening
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Disclination
Misorientation
Triple junction
Grain boundary strengthening
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Nanocrystalline material
Triple junction
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Transition point
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The theory of disclinations contains the equation ∂iαij +ejmnθmn=0, where α and θ are the dislocation and disclination density tensors, respectively. This expression is interpreted to mean that dislocations can end on twist disclinations. A concrete example in a hexagonal crystal is discussed to illustrate this concept. It contains a 60° wedge disclination normal to the basal plane. By basic geometrical construction it is shown how a dislocation can be made to end on a jog in the wedge disclination. This jog is a small segment of twist disclination. Several ramifications of this concept are that disclinations can act as sources and sinks of dislocations, that dislocations change their Burgers vectors as they glide around disclinations, that a dislocation which crosses a disclination remains connected to it by a dislocation, that dislocations encircling a disclination must have a node, and that the local Burgers vector is not conserved on following a dislocation around a disclination.
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At the triple point of a repulsive screened Coulomb system, a face-centered-cubic (fcc) crystal, a body-centered-cubic (bcc) crystal and a fluid phase coexist. At their intersection, these three phases form a liquid groove, the triple junction. Using confocal microscopy, we resolve the triple junction on a single particle level in a model system of charged PMMA colloids in a nonpolar solvent. The groove is found to be extremely deep and the incommensurate solid-solid interface to be very broad. Thermal fluctuations hence appear to dominate the solid-solid interface. This indicates a very low interfacial energy. The fcc-bcc interfacial energy is quantitatively determined based on Young's equation and, indeed, it is only about 1.3 times higher than the fcc-fluid interfacial energy close to the triple point.
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The geometrical concept of Volterra's disclination is applied to model the inhomogeneous deformation that occurs at the triple junction of grain boundaries in deformed polycrystal. It is shown that even though the deformation is restricted to maintain the strain compatibility on the three grain boundaries meeting at the triple junction, the misfit in the dihedral angles of the three grains would occur. The angular misfit gives the angle of the equivalent disclination that is accompanied by a logarithmic stress singularity at the origin, which is similar to the stress concentration at the triple junction in deformed tricrystals.
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Triple junction
Dihedral angle
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