Phase decomposition is a well-known process leading to the formation of two-phase mixtures. Here we show that a strain imposed on a ferroelastic crystal promotes the formation of mixed phases and domains, i.e., strain phase separation with local strains determined by a common tangent construction on the free energy versus strain curves. It is demonstrated that a domain structure can be understood using the concepts of domain/phase rule, lever rule, and coherent and incoherent strain phase separation, in a complete analogy to phase decomposition. The proposed strain phase separation model is validated using phase-field simulations and experimental observations of PbTiO3 and BiFeO3 thin films as examples. The proposed model provides a simple tool to guide and design domain structures of ferroelastic systems.


Materials Science and Engineering


The work at Penn State is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award FG02-07ER46417 (F.X. and L.-Q.C.) and by the NSF MRSEC under Grant No. DMR-1420620 (F.X. and Y.G.). The work at Beijing Normal University is supported by the NSFC under Contract No. 51322207 and the National Key Research and Development Program of China under Contract No. 2016YFA0302300. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

International Standard Serial Number (ISSN)

2469-9950; 2469-9969

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2016 American Physical Society (APS), All rights reserved.

Publication Date

01 Dec 2016

Included in

Metallurgy Commons