We use probes of three different length scales to examine symmetry of (1–x)Pb(Mg1/3Nb2/3)O₃-xPbTiO₃ (PMN-xPT) single crystals in the morphotropic phase boundary (MPB) region at composition x = 0.31 (PMN-31% PT). On the macroscopic scale, x-ray diffraction (XRD) shows a mixture of strong and weak diffraction peaks of different widths. The closest match to XRD peak data is made with monoclinic Pm (MC) symmetry. On the local scale of a few nanometers, convergent beam electron diffraction (CBED) studies, with a 1.6-nm electron probe, reveal no obvious symmetry. These CBED experimental patterns can be approximately matched with simulations based on monoclinic symmetry, which suggests locally distorted monoclinic structure. A monoclinic Cm (MA or MB)-like symmetry could also be obtained from certain regions of the crystal by using a larger electron probe size of several tens of nanometers in diameter. Thus the monoclinic symmetry of single crystal PMN-31%PT is developed only in parts of the crystal by averaging over locally distorted structure on the scale of few tens of nanometers. The macroscopic symmetry observed by XRD is a result of averaging from the local structure in PMN-31%PT single crystal. The lack of local symmetry at a few nanometers scale suggests that the polarization switching results from a change in local displacements, which are not restricted to specific symmetry planes or directions.
Kim, Kyou-Hyun, et al. "Symmetry of piezoelectric (1–x)Pb(Mg<sub>1/3</sub>Nb<sub>2/3</sub>)O₃-xPbTiO₃ (x=0.31) single crystal at different length scales in the morphotropic phase boundary region." Physical Review. B, Condensed Matter and Materials Physics, vol. 86, no. 18, Nov. 2012. https://doi.org/10.1103/PhysRevB.86.184113
Kim, Kyou-Hyun, Payne, David A., & Zuo, Jian-Min (2012). Symmetry of piezoelectric (1–x)Pb(Mg<sub>1/3</sub>Nb<sub>2/3</sub>)O₃-xPbTiO₃ (x=0.31) single crystal at different length scales in the morphotropic phase boundary region. Physical Review. B, Condensed Matter and Materials Physics, 86(18). https://doi.org/10.1103/PhysRevB.86.184113
Kim, Kyou-Hyun, Payne, David A., and Zuo, Jian-Min, "Symmetry of piezoelectric (1–x)Pb(Mg<sub>1/3</sub>Nb<sub>2/3</sub>)O₃-xPbTiO₃ (x=0.31) single crystal at different length scales in the morphotropic phase boundary region," Physical Review. B, Condensed Matter and Materials Physics 86, no. 18 (2012), https://doi.org/10.1103/PhysRevB.86.184113
@article{osti_1101855,
author = {Kim, Kyou-Hyun and Payne, David A. and Zuo, Jian-Min},
title = {Symmetry of piezoelectric (1–x)Pb(Mg<sub>1/3</sub>Nb<sub>2/3</sub>)O₃-xPbTiO₃ (x=0.31) single crystal at different length scales in the morphotropic phase boundary region},
annote = {We use probes of three different length scales to examine symmetry of (1–x)Pb(Mg1/3Nb2/3)O₃-xPbTiO₃ (PMN-xPT) single crystals in the morphotropic phase boundary (MPB) region at composition x = 0.31 (PMN-31% PT). On the macroscopic scale, x-ray diffraction (XRD) shows a mixture of strong and weak diffraction peaks of different widths. The closest match to XRD peak data is made with monoclinic Pm (MC) symmetry. On the local scale of a few nanometers, convergent beam electron diffraction (CBED) studies, with a 1.6-nm electron probe, reveal no obvious symmetry. These CBED experimental patterns can be approximately matched with simulations based on monoclinic symmetry, which suggests locally distorted monoclinic structure. A monoclinic Cm (MA or MB)-like symmetry could also be obtained from certain regions of the crystal by using a larger electron probe size of several tens of nanometers in diameter. Thus the monoclinic symmetry of single crystal PMN-31%PT is developed only in parts of the crystal by averaging over locally distorted structure on the scale of few tens of nanometers. The macroscopic symmetry observed by XRD is a result of averaging from the local structure in PMN-31%PT single crystal. The lack of local symmetry at a few nanometers scale suggests that the polarization switching results from a change in local displacements, which are not restricted to specific symmetry planes or directions.},
doi = {10.1103/PhysRevB.86.184113},
url = {https://www.osti.gov/biblio/1101855},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
issn = {ISSN PRBMDO},
number = {18},
volume = {86},
place = {United States},
publisher = {American Physical Society},
year = {2012},
month = {11}}
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 281, Issue 1301https://doi.org/10.1098/rsta.1976.0024