Rodrigues-Frank representations in crystallographic characterization of microstructure

The crystallographic orientation relationships in a polycrystalline material are characterized using Rodrigues-Frank (R-F) rotation space. Crystallographic microtexture is represented by irreducible R-F subspaces found by coupling sample symmetry with crystal symmetry. For common sample symmetries and cubic crystal symmetry, it is revealed that such subspaces are geometrically folded versions of the cubic fundamental zone, the maximum orientation space required in representing cubic symmetry. Components of microtexture and mesotexture (grain misorientations) are easily visualized in this rotation space, which is directly connected to the microstructure through the sample axes, making R-F space a more intuitive representation of orientation.; The quantitative description of orientation clustering in R-F space, the orientation distribution probability (ODP), is developed by a novel method of spatial convolution sampling. Algorithms for the times-random values of microtexture or mesotexture are formulated with consideration of spatial resolution and statistical reliability.; A new method of representing fiber texture, which has a straight line trajectory in R-F space, is presented using an octant of the cubic fundamental zone. It is revealed that the fiber texture trajectories in R-F space map onto a plane, forming the analog of the commonly known stereographic inverse pole figure.; The relationship between mesotexture and microtexture is formulated and visualized in R-F space for the first time. Experimental microtexture is used to construct a hypothetical microstructure in accordance with the ODP. The physical correlation of grain orientations to the microstructure is gauged by the comparative statistical analysis of the experimental and hypothetical mesotextures, giving insight into the influence of grain boundary energy minimization.; The application of R-F space mapping and visualization for crystallographic characterization is demonstrated with two examples: an ETP copper wire and a thin film of Al-3%Ge alloy. The wire is characterized as a function of radius and the origins of the collapsed grain effect in thin films is examined.