On Determination of Diffusion Coefficient of an Inclusion Attached to a Fixed Dislocation Using Its Thermal Motion

Abstract

In situ transmission electron microscopy observations showed that one or more liquid Pb nanoinclusions attached to a fixed dislocation segment in an Al matrix exhibit quasi-one-dimensional thermal motion localized near the dislocation line as fixed segments are traps for the nanoinclusions. The use of longitudinal component of the trajectories of their thermal motion makes it possible to determine the diffusion coefficients of individual nanoinclusions in a wide range of temperatures and sizes. To determine the diffusion coefficients, the root-mean-square displacement of a one-dimensional Brownian oscillator under the action of a linear restoring force as a function of movement time, obtained by M. von Smoluchowski, was used. However, this expression does not quite correctly describe the thermal motion of inclusion attached to a dislocation segment fixed at its ends as this expression does not take into account the deceleration of inclusion near its fixed ends that leads to underestimation of the value of the diffusion coefficient of the inclusion. In the present paper, this equation is modified. The application of the modified equation demonstrated that it described the behavior of experimental dependences of a root mean squared displacement of liquid Pb nanoinclusions attached to fixed dislocation segments in an Al matrix on the movement time quite better than the equation used before. This made it possible to significantly increase the accuracy of determination of the diffusion coefficients of the nanoinclusions.