• orientation distribution function;
  • X-ray diffraction;
  • lattice strain;
  • iron;
  • phase transformations

A novel approach to quantifying intragranular distributions is developed and applied to the α[RIGHTWARDS ARROW]ɛ phase transition in iron. The approach captures both the distribution of lattice orientation within a grain and the orientation dependence of the lattice strain. Use of a finite element discretization over a ball in Rodrigues space allows for the efficient use of degrees of freedom in the numerical approach and provides a convenient framework for gradient-based regularization of the inverse problem. Application to the α[RIGHTWARDS ARROW]ɛ phase transition in iron demonstrates the utility of the method in that intragranular orientation and lattice strain distributions in the α phase are related to the observed ɛ orientations. Measurement of the lattice strain distribution enables quantitative analysis of the driving forces for ɛ variant selection. The measurement and analysis together indicate quantitatively that the Burgers mechanism is operative under the experimental conditions examined here.