Kinetic Equations for Local Concentrations of Reactants in Spatially Inhomogeneous Solutions

Spatially inhomogeneous dilute solutions of reactants placed in a continual solvent (Waite approach) are examined. Based on the familiar non-Markovian kinetic equations of the Integral Encounter Theory, the Markovian kinetic equations were first obtained that allowed for the force action of reactants on each other due to binary encounters in solution during reactant macroscopic displacement. It has been shown that the value of “collisional integral” of reactants determined by their stochastic motion is small as compared to the “collisional integral” with the solvent molecules in the frame of the binary approach to the description of the solvent evolution. Nevertheless, taking account of the encounters of reactants with each other may turn out to be of primary importance, since it results in new physical effects.

Dislocation/Twin/Interface Interactions during Deformation of PST TiAl Single Crystals, an AFM Study

ABSTRACTPST TiAl crystals oriented such that the deformation axis lies in the (111) interfacial planes have been deformed in compression. This deformation produces so-called “channeled flow” in which the strain perpendicular to the (111) interfaces is zero, while the other two strains are equal and opposite in sign. Thus the sample simply shortens axially and spreads laterally in the channels defined by the (111) interfacial planes. We have examined the fine structure of deformation bands on the free surface of these deformed samples using AFM to see how the deformation processes interact with the boundaries. By measuring the offset angle at the surface we have been able to show that not only is the macroscopic displacement vector parallel to the lamellar boundaries, but the total shear vector in each layer is also parallel to the lamellar boundaries. However these deformation bands have very different characters, requiring complex deformation processes at the boundaries in order to satisfy this requirement. Some consist of either just super dislocations or just ordinary dislocations with Burgers vectors lying in the interface. But others consist of a special combination of twinning and ordinary dislocations in fixed ratio, such that the net shear vector also lies in the boundary, even though the individual twinning and dislocation shear directions are inclined to it. This results in deformation that is homogeneous and completely ‘channeled’ inside each lamella with no shear vector perpendicular to the lamellar boundaries. We have also shown that the cooperative twinning and slip is homogeneous on the nano-scale, i.e., the twinning and slip occurs in the same volume of material.