Oxygen Octahedral Tilts Research Articles

Size effects in multiferroicBiFeO3nanodots: A first-principles-based study

An effective Hamiltonian scheme is developed to investigate structural and magnetic properties of BiFeO3 nanodots under short-circuit-like electrical boundary conditions. Various striking effects are discovered. Examples include (a) scaling laws involving the inverse of the dots' size for the magnetic and electric transition temperatures; (b) the washing out of some structural phases present in the bulk via size effects; (c) the possibility of tailoring the difference between the Neel and Curie temperatures, by playing with the size and electrical boundary conditions; and (d) an universal critical thickness of the order of 1.6 nm below which the dots do not possess any long-range ordering for the electrical and magnetic dipoles, as well as, for the oxygen octahedral tiltings.

Influence of lanthanum doping on the morphotropic phase boundary of lead zirconate titanate

A phase diagram for morphotropic (Pb0.985La0.01)(Zr1−xTix)O3 is proposed based on a combination of X-ray and neutron powder diffraction experiments and complemented by transmission electron microscopy. Dependent on composition three regions are characterized. The stability range of tetragonal microdomains for high Ti contents, the stability range of rhombohedral microdomains for low Ti contents, and an intermediate stability range of nanodomains. All three regions exhibit a corresponding low temperature configuration. Temperature dependent diffraction revealed that lanthanum doping reduces the sensitivity of the structure to changes in temperature and composition. A continuous transition from pseudorhombohedral to tetragonal symmetry with an intermediate two-phase region at the morphotropic phase boundary is observed. A similar transition of low temperature superstructure phases from pseudorhombohedral to pseudotetragonal with an intermediate monoclinic phase governed by a continuous change in the oxygen octahedral tilt system from a−a−a− over a−a−c− to a0a0c− is identified.

Nanoscale Structural and Chemical Properties of Antipolar Clusters in Sm-Doped BiFeO3 Ferroelectric Epitaxial Thin Films

The local atomic structure and nanoscale chemistry of an antipolar phase in Bi0.9Sm0.1FeO3 epitaxial thin films are examined by an array of transmission electron microscopy (TEM) coupled with electron diffraction and electron energy-loss spectroscopy methods. The observations are tied to macroscopic properties of the films, namely, polarization-electric field hysteresis loops, dielectric constant-electric field hysteresis loops, and the dielectric loss. At room temperature, the local Sm deficiency was determined to destabilize the long-range ferroelectric state, resulting in the formation of local antipolar clusters with the appearance of PbZrO3-like antiparallel cation displacements, which give rise to 1/4{011} and 1/4{211} reflections as well as 1/2{321}, because of in-phase oxygen octahedral tilts. Aberration-corrected TEM analysis reveals that the antipolar structure is actually a lamellar of highly dense ferroelectric domains with alternating polarizations. With increasing temperature, a phase transi...

Electric-Field-Induced Paths in MultiferroicBiFeO3from Atomistic Simulations

Properties of BiFeO_{3} under an electric field are simulated using an ab initio-based approach. Complex paths and anomalous phenomena occur, depending on the direction of the field. Examples of such phenomena are the rotations of the polarization and of the axis about which the oxygen octahedra tilt; isostructural transitions; disappearance and reappearance of the tilting of the oxygen octahedra; and reentrance into specific crystallographic classes.The magnetic order parameter is not always perpendicular to the polarization, especially when the tilting of the oxygen octahedra disappears. The governing "rule" is that the magnetic order parameter remains orthogonal to the axis about which the oxygen octahedra tilt.

Structural transitions and complex domain structures across a ferroelectric-to-antiferroelectric phase boundary in epitaxial Sm-dopedBiFeO3thin films

We have investigated structural phase transitions across a ferroelectric-to-antiferroelectric phase boundary in epitaxial (001) oriented ${\text{Bi}}_{(1\ensuremath{-}\text{x})}{\text{Sm}}_{\text{x}}{\text{FeO}}_{3}$ thin films. For the ${\text{Sm}}^{3+}$ concentration of $0.1\ensuremath{\le}x\ensuremath{\le}0.14$, we observe short-range antiparallel cation displacements, verified by the appearance of localized $\frac{1}{4}{011}$ weak reflections in the selected area electron diffraction patterns. At the critical composition of $x=0.14$, the system adopts a complex nanoscale domain mixture with appearance of $\frac{1}{4}{011}$, $\frac{1}{2}{011}$, $\frac{1}{2}{010}$, and $\frac{1}{2}{111}$ reflections and an incommensurate phase bridging the rhombohedral and orthorhombic phases. For compositions $0.14<x<0.2$, orientational twin domains coupled with antiphase oxygen octahedral tilts, identified by $\frac{1}{2}{hkl}$ weak superstructure are observed. The above systematic changes in the microstructure as a function of ${\text{Sm}}^{3+}$ doping are linked to the macroscopic functional properties.

Electron-phonon interactions in perovskites containing Fe and Cr studied by Raman scattering using oxygen-isotope and cation substitution

We use temperature-dependent inelastic light scattering to study the origin of the strong multiphonon scattering of a local oxygen breathing mode present in the mixed $B$-site orthorhombic (space group $Pnma$) perovskite ${\text{LaFe}}_{0.5}{\text{Cr}}_{0.5}{\text{O}}_{3}$ but absent in isostructural ${\text{LaFeO}}_{3}$ and ${\text{LaCrO}}_{3}$. It is seen that the multiphonon scattering is critically sensitive to the presence of both Fe and Cr ions on the $B$ site. These results support our interpretation that the multiphonon scattering is activated by local electron-phonon interactions according to the Franck-Condon picture following an Fe-Cr charge transfer. Further, $^{18}\text{O}$ substitution is performed on the $x=0$, 0.04, and 0.5 compounds and clearly shows that all modes appearing above the first-order phonon-scattering region in these compounds originate from higher-order oxygen stretching vibrations. In particular this is the case for the strong second-order scattering dominating the scattering response in ${\text{LaFeO}}_{3}$. Accordingly we propose that these modes are generated by infrared-active longitudinal optical (IR LO) two-phonon and combination scattering activated by Fr\ohlich interaction. For $x=0.02$ and 0.04 the characteristic IR LO two-phonon and Franck-Condon multiphonon-scattering profiles mix. We also study the influence of isovalent cation substitution and Sr doping in $A{\text{Fe}}_{0.5}{\text{Cr}}_{0.5}{\text{O}}_{3}$ ($A=\text{La}$, Nd, and Gd) and ${\text{La}}_{1\ensuremath{-}y}{\text{Sr}}_{y}{\text{Fe}}_{0.5}{\text{Cr}}_{0.5}{\text{O}}_{3\ensuremath{-}\ensuremath{\delta}}$ ($y=0$, 0.16, and 0.5) on the strong electron-phonon coupling present in ${\text{LaFe}}_{0.5}{\text{Cr}}_{0.5}{\text{O}}_{3}$. The Franck-Condon effect in ${\text{LaFe}}_{0.5}{\text{Cr}}_{0.5}{\text{O}}_{3}$, is not significantly affected by isovalent $A$-site substitution, despite the increasing orthorhombic distortion associated with decreasing $A$-site ionic radii. On the contrary, aliovalent Sr doping causes a rapid decrease in the Franck-Condon scattering. This shows that the strong electron-phonon coupling in these compounds is highly sensitive to local lattice and electronic decoherence but insensitive to global lattice distortions. Finally, a preliminary assignment of the ${A}_{g}$ and ${B}_{2g}$ phonon modes in $A{\text{Fe}}_{0.5}{\text{Cr}}_{0.5}{\text{O}}_{3}$ ($A=\text{La}$, Nd, and Gd) is made based on the present observations and published results for ${\text{LaCrO}}_{3}$ and $A{\text{MnO}}_{3}$. The modes associated with oxygen octahedral tilt and bending vibrations are heavily influenced by the magnitude of the orthorhombic distortion.

Crystal structure of (Ba1−xLax) [Mg(1 + x)/3Nb(2−x)/3]O3 ceramics

The crystal structure of (Ba1−x La x )[Mg(1 + x)/3Nb(2−x)/3]O3 (BLMN) ceramics with 0 ≤ x ≤ 1 was investigated using X-ray diffraction (XRD) and high resolution transmission electron microscopy (HRTEM). When the La content, x, was above 0.1, the 1:2 ordered hexagonal structure found in Ba(Mg1/3Nb2/3)O3 (BMN) was transformed into the 1:1 ordered cubic structure. The 1:1 ordered cubic structure was maintained up to x = 0.7. When x exceeded 0.7, however, BLMN exhibited a 1:1 ordered monoclinic structure, rather than a 1:1 ordered cubic structure. La(Mg2/3Nb1/3)O3 (LMN) has a 1:1 ordered monoclinic P21/n structure with a = 5.6004 A, b = 5.6414 A, c = 7.9346 A, and β = 89.9819°. The monoclinic LMN has the in-phase and the anti-phase tilt of oxygen octahedra. The anti-parallel shift of A-site cations was also found in LMN.

Effective Hamiltonian study ofPbZr0.95Ti0.05O3

An effective Hamiltonian ${H}_{\mathrm{eff}}$ is constructed for ${\mathrm{PbZr}}_{0.95}{\mathrm{Ti}}_{0.05}{\mathrm{O}}_{3}.$ It is parametrized using primarily ab initio results computed in the virtual-crystal approximation. The phase diagram depends sensitively on the energetic competition between the stable orthorhombic antiferroelectric ${(A}_{O})$ and the metastable ``low temperature'' rhombohedral ferroelectric ${(F}_{R(\mathrm{LT})})$ structures at 0 K. By incorporating a temperature-dependent thermal-expansion term into ${H}_{\mathrm{eff}}$ and modifying ${H}_{\mathrm{eff}}$ to adjust the relative energies of the ${A}_{O}$ and ${F}_{R(\mathrm{LT})}$ phases, we obtain a ferroelectric phase intervening between the low-temperature antiferroelectric ground state and the high-temperature paraelectric phase, in qualitative agreement with experiments. We also discuss the temperature-dependent disordering of the oxygen octahedral tilts responsible for the experimentally observed space group of the ferroelectric phase.

Synthesis and crystal structure of Sm 2MnTiO 6

A new compound, Sm 2MnTiO 6, with a perovskite-type structure was synthesized. A Rietveld refinement of X-ray diffraction data has been carried out and the refined lattice parameters with the monoclinic space group P2 1/ n (No. 14) were a=0.54463(1), b=0.57104(1), c=0.78048(2) nm and β=90.22(2)°. The oxygen octahedra tilt by several degrees against each other. The antiferromagnetic behavior was observed below 21.0 K.

Studies of the ferroelectric domain configuration and polarization of rhombohedral PZT ceramics

The character of the ferroelectric domains in lead zirconate titanate (PbZr1-xTixO3 - PZT) ceramics has been studied using transmission electron microscopy (TEM) for compositions right across the rhombohedral phase (x = 0.06 to x = 0.45). The polarization hysteresis has also been determined for the same specimens and it has been demonstrated that the compositions between x = 0.12 and x = 0.40 show double hysteresis loops. It is shown that the occurrence of domain walls which do not correspond exactly to crystallographic planes produces generalized wedge-shaped domains, instead of the typical bands of parallel-sided domains reported in most ferroelectrics. A systematic variation in the arrangement of the domain walls as the composition progresses across the rhombohedral region is reported for the first time. This result is related to the occurrence of double hysteresis loops for these compositions. The role of oxygen octahedral tilts of the low temperature rhombohedral phase in the formation of the domains and in the hysteresis behaviour is discussed.

Dielectric characterization of the phase transitions in Pb1−y/2(Zr1−xTix)1−yNbyO3(0.03⩽x⩽0.04, 0.02⩽y⩽0.05)

The Curie temperature and the ideal thermal hysteresis of Pb1−y/2(Zr1−xTix)1−yNbyO3 (0.03 ⩽x⩽0.04, 0.02⩽y⩽0.05) ferroelectric ceramics have been investigated as a function of composition at the FRH–PC phase transition. Experimental results are analyzed using the generalized effective field approach and taking into account the composition dependence of the dimensionless parameters g and h corresponding to the second and third terms in the generalized effective field expansion. With this approach we can describe reasonably well the composition dependence of TC(x,y) at the FRH–PC transition and thermal hysteresis ΔT(x,y) in the narrow range of compositions investigated. The effects of the oxygen octahedra tilt in the dielectric constant at the FRL–FRH transition have also been investigated as a function of composition.

Dynamical Properties of the FR(LT)-FR(HT) Phase Transition in Zr-Rich Lead Zirconate Titanate Ceramics

The dielectric, elastic and piezoelectric properties of the F R(LT)-F R(HT) phase transition were investigated on Nb-doped lead zirconate titanate (PZT) Pb(Zr1-xTix)O3 ceramics (x=0.05 and 0.25). Dielectric anomaly and thermal hysteresis are observed through the F R(LT)-F R(HT) phase transition in PZT(Nb)95/5, but no anomaly appears in PZT(Nb)75/25. Two compositions show pronounced dielectric dispersions in the rhombohedral ferroelectric phases. The temperature dependences of resonance frequency (f r), elastic constant (s11 E) and Poisson's ratio(σ) show remarkable anomalies around the F R(LT)-F R(HT) phase transition in both compositions. However, the temperature range of the anomaly of PZT(Nb)75/25 is much broader than that of PZT(Nb)95/5. The electromechanical coupling factor (K p) decreases abruptly in PZT(Nb)95/5, while, in contrast, it increases gradually in PZT(Nb)75/25. These results are discussed on the basis of the coupling of M-type and R-type oxygen octahedral tilts to polarization and strain.

O3stilt and the Pb/(Zr/Ti) displacement order parameters in Zr-richPbZr1−xTixO3sfrom 20 to 500 K

Neutron diffraction and dielectric data have been collected from a polycrystalline sample of PbZr1-xTixO3 (x=0.035) to determine the temperature dependence of the two-order parameters associated with the oxygen octahedral tilt and the Pb/(Zr/Ti) displacement, respectively, through the sequence of phase transitions FRL-FRH-PC present in this mixed system. The weak coupling between tilt and polarization (displacements) is satisfactorily described within the framework of a two-order-parameters statistical theory in which the respective effective fields involve two higher-order terms in addition to a linear term.

FE3+EPR investigation of PLZT 1/65/35 and 8/65/35

Abstract X-band EPR spectra of PLZT 1/65/35 and PLZT 8/65/35 doped with 1% FE3+ were recorded at temperature range −175°C to 200°C. Three types of paramagnetic centers were found. Two of them are in strong axial and rhombic crystal field due to neighboring oxygen and lead vacancies. The other center has symmetry determined by polarization and oxygen octahedra tilt. EPR spectra of PLZT 8/65/35 are in agreement with its glassy behavior.

Incommensuration and the distorted oxygen octahedron of antiferroelectric tin-modified lead zirconate titanate

A study of the thermal-mechanical properties of incommensurate antiferroelectric tin-modified lead zirconate titanate has been performed as functions of Sn and Ti contents. Deviation from a linear temperature dependence in the thermal-expansion strain (ε) was observed below ∼400 °C. The deviation resulted from a contraction of the lattice relative to an extrapolation of a high-temperature linear behavior. Dielectric property measurements were also performed. Strong deviations from Curie–Weiss behavior were found to high temperatures, however with increasing Ti content, the degree of deviation from linearity in ε decreased, whereas that in the reciprocal dielectric constant increased. This indicates that the nonlinearity in ε does not arise due to an electrostrictive coupling of polarization fluctuations to the lattice. Rather, an oxygen octahedra tilt mechanism is proposed. The existence of 1/2 [111] superlattice reflections (F spots) to temperatures close to that of the onset of nonlinearity in ε gives support to this possibility.

Investigation of the orthorhombic structures of Pb 2MgWO 6 and Pb 2CoWO 6

Orthorhombic space group of Pb 2CoWO 6 has been determined by electron microscopy. Pb 2MgWO 6 orthorhombic structure is found very close to Pb 2CoWO 6 one. They present similar symmetries and the same thermal evolution of cell parameters. Rietveld structural refinement has been carried out on Pb 2MgWO 6 at 80K, room temperature and 350K. A significant Pb shift, relatively to cubic position, is found in the orthorhombic phase. Tilt of oxygen octahedra is also evidenced.

A transmission electron microscopy investigation of the R3m → R3c phase transition in Pb(Zr,Ti)O 3 ceramics

A transmission electron microscopy (TEM) study was performed on Pb(Zr,Ti)O 3 compositions within the R3m → R3c phase region. The low temperature phase is owing to a displacive phase transition involving oxygen octahedral tilts. The associated superlattice reflections as a result of the tilt are detectable by electron diffraction. Dark Field diffraction contrast imaging of the superlattice reflections reveals antiphase boundaries (APB) associated with the octahedral tilt domains. Interaction between the octahedral tilt antiphase boundaries and the ferroelectric domain structures of the R3c phase is studied and discussed.

Thermodynamic theory of the lead zirconate-titanate solid solution system, part IV: Tilting of the oxygen octahedra

Abstract Values of coefficients related to the tilting of the oxygen octahedra in the low-temperature rhombohedral phase of the lead zirconate-titanate (PZT) solid solution system are needed in the development of a thermodynamic theory of the PZT system. In this paper these coefficients will be determined from experimental spontaneous strain and oxygen octahedral tilt angle data. Values of the tilt angle related coefficients β1,β11, and φ are assumed to be independent of temperature, and are then related to P L, θL, and T R, where P L and θL are the spontaneous polarization and tilt angle of the low-temperature rhombohedral phase at the transition temperature T R between tilted and untilted structures. P L and θL are derived from experimental data for the PZT 90/10 composition, and used together with spontaneous strain values at this composition to determine electrostrictive (Q 44) and rotostrictive (R 44) constants. These constants are then in turn used to derive P L and θL values for other PZT compositions from spontaneous strain vs temperature at each composition, and in the final paper in this sequence to derive the β1, β11, and φ values for these compositions

A Phenomenological Theory for the PbZrO3: PbTiO3 Solid Solution System with the Spontaneous Polarization and Oxygen Octahedral Tilt Angle as Order Parameters

The Landau: Ginsburg: Devonshire (LGD) theory for the singlecell region of the PZT solid solution system developed by Amin, et al.1) has been extended to include the low temperature rhombohedral phase field, which exhibits compositions having both ferroelectric polarization and tilted oxygen octahedra. An additional term has been added to the elastic Gibbs free energy to account for this tilting. The coefficients of the energy function were determined from a combination of phase boundary requirements and experimental data. The spontaneous polarization and tilt angle were calculated as a function of composition and temperature.

Cation displacements and octahedral tilts in NaNbO3 Part II—Relationship between birefringence and structure

The relationship between birefringence and crystal structure in NaNbO3 is explained. In the antiferroelectric phases it is shown that the birefringence is a function of lattice strain and sublattice polarization, with the latter term providing the dominant contribution. The first term primarily arises out of the tilting of the anion octahedra and the second out of distortions of the octahedra induced by the off-centering of the B cations. In the paraelectric phases, in which only the tilts of oxygen octahedra are involved, the birefringence is shown to be a function of the lattice strains alone. The birefringence of PbZrO3 is also discussed briefly and compared with the results for NaNbO3.