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A method for intragranular orientation and lattice strain distribution determination
Author(s) -
Barton Nathan R.,
Bernier Joel V.
Publication year - 2012
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889812040782
Subject(s) - lattice (music) , discretization , materials science , finite element method , finite strain theory , phase transition , statistical physics , condensed matter physics , inverse , mathematical analysis , mathematics , physics , geometry , thermodynamics , acoustics
A novel approach to quantifying intragranular distributions is developed and applied to the α→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→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.