Doctoral Dissertations


"A model for crystallographic transitions in perovskites is proposed. The model consists of regular octahedra sharing corners and topologically able to rotate without distortion around their three-fold axes. This model, with R3̄c symmetry (18e position) can be described in terms of a continuous rotation of angle, w, of octahedra from two ideal symmetry forms: the hexagonal close-packed and the cubic face-centered configurations. A parametric relation is derived between w and the rhombohedral cell angle, α, or the corresponding hexagonal axial ratio c/a . A wide range of atomic structures based on a framework of regular or slightly distorted octahedra sharing corners can be derived from this model. A number of compounds of composition ABX₃ are examined. In all of these the anion X lies exactly or approximately in 18e position of the R3̄c space group with the cation B midway between the AX₃ layers. The site of the cation A may be vacant, as in the case where X is fluorine. These pseudosymmetric compounds can be viewed also as being generated by an array of linear chains of rigid octahedra sharing corners . Along this chain, [phi], the bond angle (cation B - anion X - cation B) is related to the bimolecular rhombohedral cell angle, α, or equivalently, to the variable parameter, x, of the anions [x, 0, 1/4], (hexagonal set, R3̄c.) These theoretical relationships are compared graphically to some crystallographic data for a trifluoride-type series, BF₃, (B = Ru, Co, V, Fe, Ti) and a perovskite-type series, AB0₃ (A = Bi, Pb, La, Li, and B =Fe, Zr-Ti, Co, Al, Nb, Ta). The experimental data for all of these compounds are in excellent agreement with the theoretical relationships. The atomic positions of the perovskite-type compounds PbZr₀.₉Ti₀.₁O₃ and BiFe0₃ were determined using X-ray and neutron diffraction. Their octahedral framework can be considered as an early stage of a continuous trigonal rotation which is fully developed in LiNb0₃ and LiTaO₃. In this isomorphous ferroelectric series, the B cation shifts from the ideal perovskite positions and are related to the A cation shifts and the spontaneous polarization. The symmetry is then reduced to the non-centrosymmetric space group, R3c. In all of these compounds the distortion of the octahedra is a second order effect compared to the trigonal rotation. Such deformations, in agreement with the theoretical data, generate superstructure reflections which depend only on the oxygen position, and the intensity of these reflections can be correlated with the trigonal rotation, w. The temperature dependence of w for the low temperature phase of PbZr₀.₉Ti₀.₁O₃ is consistent with the existence of an unstable phonon mode at the (¹/₂¹/₂¹/₂) point at the Brillouin zone corner, as in LaAlO₃. One of the most significant aspects of this work has been to relate certain phase transitions in ferroelectric materials, such as PbZr₀.₉Ti₀.₁O₃, with intensively studied transitions in some non-ferroelectric perovskites, such as LaAlO₃ and SrTiO₃"--Abstract, pages ii-iv.


Gerson, Robert, 1923-2013

Committee Member(s)

Bell, Robert John, 1934-
Tefft, Wayne E.
James, William Joseph
Straumanis, Martin E., 1898-1973



Degree Name

Ph. D. in Physics


U.S. Atomic Energy Commission


University of Missouri--Rolla

Publication Date



xii, 77 pages

Note about bibliography

Includes bibliographical references (pages 73-76).


© 1970 Christian Michel, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Library of Congress Subject Headings

Phase transformations (Statistical physics)

Thesis Number

T 2381

Print OCLC #


Electronic OCLC #


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Physics Commons