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A method to predict the orientation relationship, interface planes and morphology between a crystalline precipitate and matrix. Part I. Approach

A model based on the near-coincidence of diffraction intensity weighted reciprocal-lattice spots is proposed to determine preferred orientation relationships between two crystalline phases. The preferred orientation is found by minimizing the three-dimensional lattice mismatch, i.e. by maximizing the total overlapping intensity, between the diffraction spots of two crystals. The procedure is biased towards matching reciprocal lattice sites with high structure-factor values, which is physically equivalent to matching planes of high atomic density. In contrast to previous reciprocal-lattice models, including the diffraction intensity in the present method makes it sensitive to the types of atoms in (chemistry of) crystals. The preferred orientation relationship is then used to identify the orientations of low-energy interfaces using a Δ g approach. A Voronoi (or Wigner–Seitz) construction based on the Δ g values is further used to qualitatively estimate the equilibrium shape of the precipitate in the matrix. The model was tested by performing calculations on hypothetical Au–Cu crystals to investigate the effects of chemistry and fcc truncated-octahedral precipitates in fcc matrices in Al–Ag, Al–Xe and Al–Pb alloys. The present model has the ability to sample the entire orientation space and rationalize and compare alternate orientation relationships in a reasonable timeframe, thereby providing insight into the formation of precipitate orientation relationships and shapes.