Non-random distribution of crystallographic orientation, lattice-preferred orientation (LPO) (or crystallographic-preferred orientation: CPO), is one of the important microstructural characteristics of rocks. LPO in naturally deformed rocks can be measured in the laboratory or LPO in rocks deformed in Earth's interior can be inferred from seismic anisotropy. If the physical processes by which LPO is formed are understood, then one can use measured or seismologically inferred LPO to infer physical processes such as a flow pattern in Earth. This chapter provides a review of the various ways of representing LPO and the physical processes for the formation of LPO including deformation-induced LPO and crystallization- (or recrystallization-) induced LPO. LPO is controlled by both the microscopic physics of deformation or the nucleation–growth of crystals and the macroscopic geometry of field in which LPO develops (finite strain ellipsoid, stress, magnetic field, heat flow etc.). The relation between LPO and deformation geometry can change with physical (and chemical) conditions of deformation.

Key words Lattice-preferred orientation (LPO), Euler angles, orientation distribution function (ODF), pole figure, inverse pole figure, J-index, M-index, Schmid–Boas relation, Taylor–Bishop–Hill model, self-consistent model, dynamic recrystallization, fabric transition.