New stereology for the recovery of grain-boundary plane distributions in the crystal frame

A new experimental method is given for recovering the probability-distribution function S, ((n) over cap (A)\Deltag). The function S-v ((n) over cap (A)\Deltag) is the grain-boundary area per unit volume as a function of grain-boundary plane orientation ((n) over capA), given a lattice misorientation (Deltag) between the adjoining grains. The grain-boundary normal ((n) over capA) is expressed in the crystal frame in which the misorientation Deltag originates. The proposed method recovers the three-dimensional S-v ((n) over cap (A)\Deltag) function using data taken from two-dimensional section planes. The method requires the measurement of many grain-boundary trace (in-plane) angles and lengths associated with grain boundaries of lattice misorientation. All such boundary traces may be observed from a single section plane if the crystallographic texture is sufficiently random. In heavily textured microstructures, the method requires the researcher to observe traces from multiple oblique section planes cut through the material. A method of quantitatively estimating whether the texture is sufficiently random is given. Simulations on both textured and nontextured microstructures demonstrate the validity of the method. Experimentally, the new method is used to analyze boundaries of misorientation (Sigma3) observed in 304 stainless steel. Calculated grain-boundary plane-probability functions are shown to be consistent with what is already known.