Twinning on pyramidal planes in hexagonal close packed crystals determined along with other defects by X-ray line profile analysis

A systematic procedure is developed to evaluate the frequency of {10.1} < 10.(2) over bar > and {11.2} < 11.(3) over bar > compressive twins and {10.2} < 10.(1) over bar > and {11.1} <(1) over bar(1) over bar .6 >. tensile twins together with dislocation densities, active slip systems and crystallite size in hexagonal close packed (hcp) metals. The effect of pyramidal twinning on X-ray line broadening in hcp metals is fundamentally different from the effect of twinning on close packed planes in face centred cubic (fcc) crystals. Therefore, the usual theoretical descriptions developed previously for fcc crystals cannot be used for pyramidal twinning in hcp crystals. The profile functions of sub-reflections for this type of twinning are derived to be the sum of a symmetrical and an antisymmetrical Lorentzian function. Sub-profile properties are parameterized and the parameter files are incorporated into the convolutional multiple whole profile (CMWP) procedure. The extended procedure, eCMWP, is applied to determine pyramidal twin frequencies together with dislocation densities, active slip systems and crystallite size in Mg deformed at different temperatures, in commercial purity Ti deformed at high temperature and in high-purity Ti deformed at room temperature.