The structures of sodium niobate between 480° and 575°C, and their relevance to soft-phonon modes

Ahtee, Maija; Glazer, A. M.; Megaw, H. D.

doi:10.1080/14786437208226972

Cited by 105 publications

(106 citation statements)

References 11 publications

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“…SrTiO 3, KMnF 3, NaNbO a, LaA10 3, are caused by the condensation of a soft normal mode of vibration associated with the rotations of the octahedra in the cubic phase, and that the eigenvectors of this mode are the same as the static displacements of the atoms in the lower-symmetry phases (e.g. Glazer & Ahtee, Glazer & Megaw, 1972;Fujii, Hoshino, Yamada & Shirane, 1974). The static displacements in SrTiO 3 and KMnF a (a°a°c-) can be attributed to the condensation of a single component of the triply-degenerate R25 mode* in which the adjacent octahedra ( Fig.…”

Section: Soft Modesmentioning

confidence: 99%

High-temperature phases of SrZrO₃

Ahtee¹,

Glazer²,

Hewat³

1978

Acta Crystallogr Sect B

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108

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The high-temperature structures of SrZrO 3 have been determined by neutron powder profile refinement, and the phase transitions described by the condensation of soft vibrational modes. At 900°C, SrZrO 3 is tetragonal, I4/mcm, with an O octahedron antiphase tilt of 6.5 ° about [001], intermediate between those found in the isomorphous phases of SrTiO 3 below 110 K and KMnF 3 below 184 K. At 760°C the structure is orthorhombic Bmmb with almost equal b o and c o axes, and not tetragonal. In addition to the antiphase tilt, now 8.5 ° about 1001 I, there is an in-phase tilt of 3.1 ° about [0101. Yet a third tilt, antiphase about 1100] and identical to that about [001], is introduced at room temperature. This series of transitions indicates that the sequence of condensation of soft modes from the high-temperature cubic phase is R25, M a and finally R25 again. In addition, the two latter transitions are first order, and are accompanied by a condensation from the X-point of the Brillouin zone, which produces atomic displacements. The unusually anisotropic thermal ellipsoids provide some additional evidence for the existence of low-frequency vibrational modes.

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Section: Soft Modesmentioning

confidence: 99%

High-temperature phases of SrZrO₃

Ahtee¹,

Glazer²,

Hewat³

1978

Acta Crystallogr Sect B

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108

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“…No known examples SrZrO 3 (973-1103 K) NaNbO 3 (793-848 K) NaTaO 3 (803-873 K) NHaMnCI 3 (128 K) PrAIO 3 ( < 135 K) Marezio, Dernier, Chenevas & Joubert (1973) Chenevas, Joubert, Marezio & Bochu (1975 Ahtee, Glazer & Megaw (1972) Ahtee & Darlington (1980) Tornero, Cano, Fayos & Martinez-Ripoll (1978) Burbank (1970) …”

mentioning

confidence: 99%

Octahedral Tilting in Perovskites. II. Structure Stabilizing Forces

Woodward¹

1997

Acta Crystallogr B Struct Sci

632

480

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The 23 Glazer tilt systems describing octahedral tilting in perovskites have been investigated. The various tilt systems have been compared in terms of their A-cation coordination and it is shown that those tilt systems in which all the A-cation sites remain crystallographically equivalent are strongly favored, when all the A sites are occupied by the same ion. Calculations based on both ionic and covalent models have been performed to compare the seven equivalent A-site tilt systems. Both methods predict that when the tilt angles become large, the orthorhombic a+b-b -tilt system will result in the lowest energy structure. This tilt system gives the lowest energy structure because it maximizes the number of short A---O interactions. The rhombohedral a-a-a-tilt system gives a structure with a slightly lower Madelung energy, but increased ion-ion repulsions destabilize this structure as the tilt angles increase. Consequently, it is stabilized by highly charged A cations and small to moderate tilt angles. The ideal cubic a°a°a° tilt system is only observed when stabilized by oversized A cations and/or M---O 7r-bonding. Tilt systems with nonequivalent A-site environments are observed when at least two A cations with different sizes and/or bonding preferences are present. In these compounds the ratio of large-to-small cations dictates the most stable tilt system.

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“…In phase R there is one displacement component and three independent tilt components. The higher phases (Ahtee, Glazer & Megaw, 1972) have no Nb displacements; phase S retains three independent tilt components, phase 7"1 has two, phase T2, one. The disappearance of the two final tilt components can be correlated with one-phonon modes.…”

Section: Other Phases Of Nanbo3mentioning

confidence: 99%

The low-temperature phase transition of sodium niobate and the structure of the low-temperature phase, N

Darlington¹,

Megaw²

1973

Acta Crystallogr B Struct Sci

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119

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Sodium niobate undergoes an antiferroelectric-ferroelectric transition (P ~ N) at temperatures below about -110°C. The ferroelectric low-temperature phase (N) is rhombohedral, with space group R3c.Though a perovskite structure, it is isostructural with LiNbO3. Using pseudocubic axes of reference, a=2 × 3"9083 (5) ~, ~= 89 ° 13 (1)' at -150°C. The NbO6 octahedra remain nearly regular, but are tilted about the triad axis; displacements of Nb atoms from the centres of octahedra are parallel to this axis. The temperature dependence of the lattice parameters of both phases, N and P, below room temperature is reported, and also that of the magnitude of the Nb displacement in the antiferroelectric phase P. Experimental details of the low-temperature work are given. Evidence used in the structure determination comes from the juxtaposition of high-angle reflexions from twin components in phase N, and the orientation of domains of phase N relative to the parent phase P. The transformation is more rapid and more complete if the parent crystal is single-domain; if it is twinned, both phases coexist for long periods down to the lowest temperatures studied. The relation of the structure to that of other niobates is discussed, and some general principles are put forward from which the occurrence of different structures and the transitions between them can be understood.

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The structures of sodium niobate between 480° and 575°C, and their relevance to soft-phonon modes

Cited by 105 publications

References 11 publications

High-temperature phases of SrZrO₃

High-temperature phases of SrZrO₃

Octahedral Tilting in Perovskites. II. Structure Stabilizing Forces

The low-temperature phase transition of sodium niobate and the structure of the low-temperature phase, N

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The structures of sodium niobate between 480° and 575°C, and their relevance to soft-phonon modes

Cited by 105 publications

References 11 publications

High-temperature phases of SrZrO3

High-temperature phases of SrZrO3

Octahedral Tilting in Perovskites. II. Structure Stabilizing Forces

The low-temperature phase transition of sodium niobate and the structure of the low-temperature phase, N

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Product

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High-temperature phases of SrZrO₃

High-temperature phases of SrZrO₃