The face number, the volume, and the surface area (boundary area) of grains are measured in recrystallized ␣-iron by serial sectioning coupled with quantitative microstructural analysis on twodimensional (2-D) sections. The sampling volume contained approximately 1000 grains whose mean grain size was ϳ15 m. The grain volume distribution decreased monotonously with increasing grain volume, whereas the surface area had a peak around one-half of the average. The distribution of the sphere equivalent radii significantly deviated from the log-normal distribution and distributions predicted from mean field theories. The peak and the mean of the face number distribution were f ϭ 11 and 12.1, respectively. The linear relationship between the face number of a central grain and the mean face number of surrounding grains, known as the Aboav-Weaire law, was observed in three dimensions. The mean radius of f-faced grains was not proportional to the face number (perimeter law in 3-D), but appeared to be related by a curve convex upward.

No abstract

The control of Cu precipitation at low temperatures, e.g., bake hardening of Cu bearing steels, has recently attracted considerable attention due to the potential of achieving good formability and high strength. An Fe-1.5 wt pct Cu alloy, solution treated and 10 pct prestrained, exhibits a two-step age-hardening behavior, i.e., a smaller, but substantial hardening around 200°C to 300°C and a major hardening around 500°C, while only the latter hardening occurs in undeformed specimens. The precipitation behavior of nanoscale Cu particles or bcc Cu clusters that plays a major role in age hardening was simulated by Cahn-Hilliard nonclassical nucleation theory and the Langer-Schwartz model. Simulation results are compared with the distribution of Cu particles observed under three-dimensional atom probe field ion microscope (3-D APFIM) and transmission electron microscope (TEM), and age hardening behavior as well. The increase in hardness in prestrained specimens at low temperatures (Յ400°C) can be ascribed to Cu particles nucleated preferentially at dislocations or to Cu particles that were formed in the matrix as early as at dislocations presumably due to excess vacancies introduced by prestraining.