Moire Plane Research Articles

Characterization and Formation of Rod-Shaped (Al,Si)3Ti Particles in an Al-7Si-0.35Mg-0.12Ti (Wt Pct) Alloy

In this study, the rod-shaped particles in an Al-7Si-0.35Mg-0.12Ti (wt pct) casting alloy have been characterized using transmission electron microscopy. It is found that these particles invariably contain Ti, Al, and Si and that they have the structure of the equilibrium phase (Al,Si)3Ti. A near-rational orientation relationship is observed between the (Al,Si)3Ti particles and the α-Al matrix phase. For this orientation relationship, the long axes of the (Al,Si)3Ti rods are invariably parallel to the moire planes defined by the intersection of closest-packed planes of the (Al,Si)3Ti and α-Al phases. In contrast to the (Al,Si)3Ti or Al3Ti particles form directly from the melt act as heterogeneous nucleation sites for aluminum grains and thus grain-refined Al-Si foundry alloys, the (Al,Si)3Ti particles are found to form during solution treatment at temperatures above 673 K (400 °C). Their formation occurs in the center of aluminum grains and/or dendrites which is Ti enriched due to partitioning during solidification. The low diffusivity of Ti in α-Al allows the particles to form in the Ti-enriched areas near the center of grains as the Ti concentration is not able to be homogenized during typical solution treatment times.

Structures in irrational singular interfaces

We consider periodic good matching bands (which are centered at the O-lines) as the characteristic feature of the structures in irrational singular interfaces in the primary preferred state. This feature is shared by various structures described by different models for irrational singular interfaces, and it can be used to consolidate different descriptions. We have made a quantitative analysis on the distribution of good matching zones (GMZs) in a relationship with plane matching geometry. This analysis emphasizes that matching of one set of principal planes does not represent good lattice matching. Good lattice matching is possible only at the locations of 0-d intersections, where three sets of nonlinearly related Moire planes intersect. Matching of one or more sets of principal planes in an interface usually implies the possible presence of periodic GMZs in the interface. The analysis also explains why and in what condition a dislocation configuration can be described by the traces of Moire planes. The distribution of exact 0-d intersections can be determined based on the O-lattice theory. The approximate 0-d intersections can be used for determining a possible interfacial structure when periodic O-elements do not exist.

Edge-to-edge interfaces in Ti-Al modeled with the embedded atom method

The atomistic structure and energies of high-index interphase boundaries are explored using a combination of molecular statics and dynamics simulations with embedded atom potentials. We investigate planar boundaries between the α2 and γ phases in the Ti-Al system. The class of boundaries considered has a high-index boundary orientation; the orientation relationship between the α2 and γ phases also is high index, and a set of planes from each phase meet edge to edge at the boundary plane. For the particular case of a boundary that is commensurate in one direction and coincides with a moire plane given by the so-called “Δg” diffraction condition, the boundary is not structurally singular, but it is energetically stable and does not appear to dissociate into other low-energy configurations. Misfit compensating defects are not observed; misfit in directions other than the commensurate one appears to be distributed uniformly. The boundary energy is evaluated as a function of the orientation of the boundary plane, and the edge-to-edge (moire) boundary is found to lie in an energy cusp.

Edge-to-edge matching of lattice planes and coupling of crystallography and migration mechanisms of planar interfaces

The structure and migration mechanisms of planar interfaces are examined geometrically using the concept of edge-to-edge matching of lattice planes and the Moire plane approach derived from this concept. The selected examples of planar interfaces include those associated with rational, nearrational, or irrational orientation relationships. It is demonstrated that the orientation and structure of planar interfaces associated with these orientation relationships can be rationalized by the Moire plane approach, and that the migration of these interfaces in their normal directions can occur via successive nucleation and lateral gliding of growth ledges that are in the form of transformation disconnections, for low-index interfaces, and of Moire ledges, for high-index interfaces. It is further demonstrated that a shear, and thus a shape change, is associated with the motion of all planar interfaces defined by the edge-to-edge matching of lattice planes.

Orientation and structure of planar facets on the massive phase γ m in a near-TiAl alloy

The orientation and structure of planar facets on the γm massive phase formed in a Ti-46.5 at. pct Al alloy have been characterized using a combination of transmission electron microscopy (TEM) and electron diffraction. The planar γm/α2 interfaces are irrational with respect to both the α2 matrix phase and the γm phase, and there is neither evidence of a rational orientation relationship across such facets, nor resolution of a linear defect structure within the interface planes in conventional electron diffraction patterns and amplitude-contrast images, respectively. However, when imaged parallel to a particular direction in the interface, these irrationally oriented interfaces are invariably parallel to the Moire plane, which is defined by the intersection between two sets of closely-packed planes in the γm and α2 phases. The relationship is such that there is an effective continuity of these lattice planes across the interface and a one-dimensional coherency within the planar interface. This is interpreted to imply that such interface facets adopt a configuration of reduced energy and that they are not random and fully incoherent, as often described. It is suggested that these planar facets may migrate in a glissile manner normal to the interface plane by nucleation and rapid lateral movement within the interface plane of interfacial defects that have the form of Moire ledges, which are defined by the spacing of the Moire pattern that may be formed by overlap of the relevant crystal planes across the interface.

O-lattice analyses of interfacial misfit. I. General considerations

Abstract Misfits between lattice points of intersecting crystals and between corresponding lattice planes are analysed using O-lattice constructions referred to both direct and reciprocal spaces. O-lattice planes are described by the same expression as the ‘Moire planes’ formed by the mismatch of correlated planes, which facilitates the study of the O lattice from diffraction patterns. The normalized primary O-lattice planes (those related to the closest packed atomic planes) with the smallest interplanar spacing are considered to be planes of minimum mismatch, and hence to represent plausible low-energy interfaces. An interface of arbitrary orientation is assumed to be stepped microscopically along the primary O-lattice planes. The solution for the O-lattice cells is derived. Based on this cell structure, possible configurations of the misfit dislocations in a primary O-lattice plane are obtained; this provides a basic description of interfacial structure.