title: Misfit-induced changes of lattice parameters in two-phase systems: coherent/incoherent precipitates in a matrix.
abstract: Elastic accommodation of precipitation-induced or thermally induced misfit leads to lattice-parameter changes in crystalline multi-phase systems. Formulae for calculation of such misfit-induced lattice-parameter changes are presented for the aggregate (matrix + second-phase particles) and for the individual matrix and second phase, recognizing the occurrence of either coherent or incoherent diffraction by the matrix and second-phase particles. An overview and an (re)interpretation on the above basis is presented of published lattice-parameter data, obtained by X-ray diffraction analyses of aggregates of matrix plus second-phase particles. Examples for three types of systems consisting of a matrix with misfitting second-phase particles are dealt with, which differ in the origin of the misfit (precipitation or thermally induced) and in the type of diffraction (coherent or incoherent diffraction of matrix plus second-phase particles). The experimental data are shown to be in good to very good agreement with predictions according to the current treatment.
authors.affiliation: Max Planck Institute for Intelligent Systems (formely MPI for Metals Reseach), Heisenbergstrasse 3, Stuttgart, 70569, Germany.
authors.forename: Maryam
authors.initials: M
authors.lastname: Akhlaghi
authors.affiliation: Max Planck Institute for Intelligent Systems (formely MPI for Metals Reseach), Heisenbergstrasse 3, Stuttgart, 70569, Germany; Robert Bosch GmbH Heat Treatment Processes and Heat Treatment Technology (CR/APM4), Postbox 300240, Stuttgart, 70442, Germany.
authors.forename: Tobias
authors.initials: T
authors.lastname: Steiner
authors.affiliation: Max Planck Institute for Intelligent Systems (formely MPI for Metals Reseach), Heisenbergstrasse 3, Stuttgart, 70569, Germany.
authors.forename: Sai Ramudu
authors.initials: SR
authors.lastname: Meka
authors.affiliation: Max Planck Institute for Intelligent Systems (formely MPI for Metals Reseach), Heisenbergstrasse 3, Stuttgart, 70569, Germany; Institute for Materials Science, University of Stuttgart, Heisenbergstrasse 3, Stuttgart, 70569, Germany.
authors.forename: Eric Jan
authors.initials: EJ
authors.lastname: Mittemeijer
keywords: coherent/incoherent diffraction; elastic/plastic misfit accommodation; lattice-parameter change; precipitation-induced misfit; thermally induced misfit