TY - JOUR
T1 - Permissible domain walls in monoclinic ferroelectrics. Part II. The case of MC phases
AU - Biran, Ido
AU - Gorfman, Semën
N1 - Publisher Copyright:
© 2024 International Union of Crystallography. All rights reserved.
PY - 2024/5/1
Y1 - 2024/5/1
N2 - Monoclinic ferroelectric phases are prevalent in various functional materials, most notably mixed-ion perovskite oxides. These phases can manifest as regularly ordered long-range crystallographic structures or as macroscopic averages of the self-assembled tetragonal/rhombohedral nanodomains. The structural and physical properties of monoclinic ferroelectric phases play a pivotal role when exploring the interplay between ferroelectricity, ferroelasticity, giant piezoelectricity and multiferroicity in crystals, ceramics and epitaxial thin films. However, the complex nature of this subject presents challenges, particularly in deciphering the microstructures of monoclinic domains. In Paper I [Biran & Gorfman (2024). Acta Cryst. A80, 112–128] the geometrical principles governing the connection of domain microstructures formed by pairing MAB type monoclinic domains were elucidated. Specifically, a catalog was established of ‘permissible domain walls’, where ‘permissible’, as originally introduced by Fousek & Janovec [J. Appl. Phys. (1969), 40, 135–142], denotes a mismatch-free connection between two monoclinic domains along the corresponding domain wall. The present article continues the prior work by elaborating on the formalisms of permissible domain walls to describe domain microstructures formed by pairing the MC type monoclinic domains. Similarly to Paper I, 84 permissible domain walls are presented for MC type domains. Each permissible domain wall is characterized by Miller indices, the transformation matrix between the crystallographic basis vectors of the domains and, crucially, the expected separation of Bragg peaks diffracted from the matched pair of domains. All these parameters are provided in an analytical form for easy and intuitive interpretation of the results. Additionally, 2D illustrations are provided for selected instances of permissible domain walls. The findings can prove valuable for various domain-related calculations, investigations involving X-ray diffraction for domain analysis and the description of domain-related physical properties.
AB - Monoclinic ferroelectric phases are prevalent in various functional materials, most notably mixed-ion perovskite oxides. These phases can manifest as regularly ordered long-range crystallographic structures or as macroscopic averages of the self-assembled tetragonal/rhombohedral nanodomains. The structural and physical properties of monoclinic ferroelectric phases play a pivotal role when exploring the interplay between ferroelectricity, ferroelasticity, giant piezoelectricity and multiferroicity in crystals, ceramics and epitaxial thin films. However, the complex nature of this subject presents challenges, particularly in deciphering the microstructures of monoclinic domains. In Paper I [Biran & Gorfman (2024). Acta Cryst. A80, 112–128] the geometrical principles governing the connection of domain microstructures formed by pairing MAB type monoclinic domains were elucidated. Specifically, a catalog was established of ‘permissible domain walls’, where ‘permissible’, as originally introduced by Fousek & Janovec [J. Appl. Phys. (1969), 40, 135–142], denotes a mismatch-free connection between two monoclinic domains along the corresponding domain wall. The present article continues the prior work by elaborating on the formalisms of permissible domain walls to describe domain microstructures formed by pairing the MC type monoclinic domains. Similarly to Paper I, 84 permissible domain walls are presented for MC type domains. Each permissible domain wall is characterized by Miller indices, the transformation matrix between the crystallographic basis vectors of the domains and, crucially, the expected separation of Bragg peaks diffracted from the matched pair of domains. All these parameters are provided in an analytical form for easy and intuitive interpretation of the results. Additionally, 2D illustrations are provided for selected instances of permissible domain walls. The findings can prove valuable for various domain-related calculations, investigations involving X-ray diffraction for domain analysis and the description of domain-related physical properties.
KW - X-ray diffraction
KW - ferroelastic domains
KW - monoclinic symmetry
UR - http://www.scopus.com/inward/record.url?scp=85192113768&partnerID=8YFLogxK
U2 - 10.1107/S2053273324002419
DO - 10.1107/S2053273324002419
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C2 - 38683644
AN - SCOPUS:85192113768
SN - 0108-7673
VL - 80
SP - 293
EP - 304
JO - Acta Crystallographica Section A: Foundations and Advances
JF - Acta Crystallographica Section A: Foundations and Advances
IS - Pt 3
ER -