Thin <Emphasis Type="Italic">W</Emphasis>′ and <Emphasis Type="Italic">W</Emphasis> domain walls in ferroelastic Pb<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript>

A model of ferroelastic domain walls consisting of matching interlayers of crystal lattices is proposed. The dependences of the parameters of the interlayers and of the parameters of the equations for W′ and W domain walls on the crystal lattice parameters of the ferroelastic phase in Pb₃(PO₄)₂ are determined. The problem concerning the number of possible orientational states and their interaction in a polydomain crystal is considered.     

Polarized light microscopy of the ferroelastic domains of YBa2Cu3O7−x

A short overview is given on recent polarized light microscopy studies of the orthorhombic ferroelastic domains and domain structures of YBa₂Cu₃O_7-x . The optical characteristics of large domains and lamellar domains with a high density of twin walls are pointed out, both for reflected and transmitted light. The polarizing microscope has allowed to observe the ferroelastic detwinning in situ and to determine the activation energy of the ferroelastic wall movements. The question of a potential ferroelectric phase transition is also discussed.     

Domain structures in orthorhombic KNbO3 and characterisation of single domain crystals

Domain configurations in large KNbO₃ single crystals grown by a top seeded flux growth technique are studied by optical methods and etching techniques. The orientation of observed domain walls is consistent with the principles of mechanical compatibility and electrical neutrality. Experimental evidence for the existence of a new type of ferroelectric domain wall (S-wall) is presented. Miller indices of such walls are irrational and depend on spontaneous strain tensor coefficients. The preparation of large single domain crystals (up to 1/3 cm³) is described. Assessment of crystal perfection by x-ray topographic and interference methods reveals a very small mosaic spread (one minute of arc) and a good optical homogeneity.     

五磷酸钕晶体中铁弹畴界的X射线形貌研究

利用X射线衍射形貌法,研究了五磷酸钕(NdP₅O₁₄)晶体中铁弹畴界的衍射衬度。发现在μt=0.6—7范围内,畴界呈现黑的或白的衬度。畴界衍射衬度的特征可归结为(c₂-c₁=)△c∥g畴界衬度明显△c⊥g畴界衬度消失△c·g>0畴界呈黑衬度△c·g<0畴界呈白衬度利用Penuing-Polder波点迁移原理,对畴界的衬度形成原理做了定性解释。根据畴界的衍射衬度特征,定性讨论了畴界的结构特征。 关键词：     

Disorientation angles and compatible walls for phase transition hexagonal to monoclinic phase

Orientation of compatible domain walls and magnitude of disorientation angle of a ferroelastic domain twin resulting from phase transition hexagonal to monoclinic phases is expressed in crystallographic unit-cell parameters of the low-symmetry phase. These two characteristics, the orientation of the compatible wall and the disorientation angle, depend on the spontaneous strain in two single-domain states R ₁, R ₂ from which the domain twin is formed. They have been determined for all classes of the compatible domain walls as a function of the strain-tensor components [A. Authier, International Tables for Crystallography, in Physical Properties of Crystals, Chapter 3.4, Vol. D, A. Authier, ed., Kluwer Academic Publishers, Dordrecht, 2003, pp. 449–505]. If relative changes of crystal lattice are small, then the second rank symmetrical strain tensor u can be calculated from the crystallographic unit-cell parameters before and after the deformation [J.L. Schlenker, G.V. Gibbs, and M.B. Boisen Jr, Strain-tensor components expressed in terms of lattice parameters, Acta. Cryst. A 34 (1978), pp. 52–54; L. Jian and C.M. Wayman, Domain boundary and domain switching in a ceramic rare-earth Orthoniobate LaNbO_{4 ,} J. Am. Ceram. Soc. 79 (1996), pp. 1642–1648]. An alternative approach expresses the disorientation angle and orientation of the compatible domain wall [J. P?ívratská, Disorientation angle expressed in terms of lattice parameters, Ferroelectrics 291 (2003), pp. 197–204] in terms of the crystallographic unit-cell parameters of the low-symmetry phase.     

Domain wall theory of elementary excitations in anisotropic antiferromagneticS=1 chains

We present a theoretical investigation of elementary excitations in anisotropic antiferromagneticS=1 chains using the concept of domain walls in string (hidden) order. Domain walls are classified by the internal spin projectionS _dw ^z . We calculate energies and string correlation 0 functions of low lying excited states of the domain wall type in the Haldane phase and compare the results to those of numerical computations. The boundaries of the Haldane phase are determined from the instability of these excitations with respect to the ground state. The interaction between two domain walls is found to be proportional to the productS _dw ^z , S _dw ^z ₂, it is effectively repulsive 0140 for equal spin projections.     

Equations for domain walls in a coordinate system of the ferroelectric phase

Two methods are suggested for writing equations for domain walls in a coordinate system of the ferroelectric phase in ferroelastics and multiaxial ferroelectrics. The equations for domain walls in ferroelectric barium titanate and ferroelastic lead orthophosphate are derived. It is shown that suborientation states are possible in these crystals. The suggested methods make it possible to find the matrices of the transformation from the coordinate system of the paraelectric phase to a coordinate system of the ferroelectric phase for each orientation state.     

Domain boundary engineering – recent progress and many open questions

Some domain boundaries contain functionalities which do not exist in the bulk. Typical examples are (super-) conducting twin walls in WO₃, highly conducting walls in BiFeO₃ and in structural interfaces between SrTiO₃ and LaAlO₃, and ferroelectric walls in CaTiO₃. The emerging field of ‘Domain Boundary Engineering’ endeavors to generate such functional interfaces in a multitude of materials for applications in device materials. Some of the recent successes are reviewed together with suggestions for further research.     

Combined piezoresponse force microscopy and Raman scattering investigation of domain boundaries in BiFeO3 ceramics

Domain structure of BiFeO₃ ceramics has been investigated using a combination of piezoresponse force microscopy (PFM) and Raman scattering techniques. Both methods demonstrate the presence of ferroelastic domains, separated by almost parallel planar domain walls, as well as the presence of large homogeneous single ferroelastic domain regions. In addition to highly resolved domain pattern obtained by PFM, small frequency shifts of the Raman-active modes give us complementary information about the angle φ between the surface normal and the rhombohedral axis of the BiFeO₃ crystal for any measured position at the surface of the sample.     

Ferroelastic domains in lead phosphate-arsenate: An afm,X-ray diffraction,tem and Raman study

Ferroelastic domain patterns in lead phosphate-type crystals depend on their chemical composition. The intersection of ferroelastic W domain walls with the (100) surface of lead phosphate-arsenate mixed crystals has been imaged using tapping mode atomic force microscopy. Dilution of the strain leads to characteristic surface deformations which deviate from those in pure lead phosphate. In highly twinned lead phosphate-arsenate X-ray diffraction was used to show renormalization effects and scattering phenomena stemming from the twin walls. Raman-active hard modes show wall-related profile changes and low-frequency tails. Symmetry mode analysis is used to describe the displacive modes characterizing the structural distortion in lead phosphate-arsenate for the sequence K m → P2₁/c.     

Permissible domain walls in ferroelectric species

A previously developed method makes it possible to determine the orientations of domain walls in ferroelectrics which are permissible under the condition that neighbouring domains must be mechanically compatible. In this paper, the method has been applied to all 88 ferroelectric species in which the polarization is the parameter of the transition. Types of permissible walls and their orientations are listed in form of tables. Cases where no walls fulfil the compatibility conditions are shown.     

Wall and boundary free energies

The existence of wall or boundary free energies is discussed generally and analyzed explicitly for general lattice systems with scalar (real-valued) spin variables. For systems with ferromagnetic (positive) spin interaction potentials,K, in the bulk andW, for the walls, correlation inequalities and appropriate stability and tempering conditions are used to establish the existence and uniqueness of the limiting free energy per unit area,f _x(K,W), of an infinite planar wall.     

Editorial

This review contains up-to-date information about experimental and theoretical investigations of phase transitions and specific features of properties of mixed crystals involving the incipient ferroelectric KTaO₃ with the off-center Li⁺, Nb⁵⁺, Na⁺ impurities. Main attention is paid to the results of the study of the mixed systems by radiospectroscopy methods (ESR and NMR).

Theoretical criteria and experimental evidence of ferroelectric and ferroelastic phase transitions as well as of dipole and quadrupolar glass states induced by the off-center impurities are discussed. It is shown that at high enough concentrations of the off-center impurities phases with long-range order appear, but at low concentrations dipole glass states occur. At intermediate concentrations of the off-center impurities new phases appear in which the coexistence of long-range properties and those of dipole glasses is possible. These phases could be named ferroelectric or ferroelastic glasses to stress their similarity with the ferroglass phases which were discovered earlier in mixed magnetic systems. The usefulness of radiospectroscopy methods for the study of phase transitions induced by off-center impurities in mixed systems, which can be considered as model disordered systems, is underlined.

In conclusion, some questions on the physics of phase transitions in disordered systems which should be solved in the future are discussed.     

Investigation of domain behaviour in 0.7Pb(Mg1/3Nb2/3) O3-0.3PbTiO3 single crystals at different temperatures in the transmission electron microscope

Using transmission electron microscopy, in-situ changes in ferroelastic domains in 0.7Pb(Mg_1/3Nb_2/3)O₃-0.3PbTiO₃ single crystals were observed at 60 to -163°C. At -163°C, the microscopic tweed morphology of the ferroelastic domains rotated by 90°, and certain orientation changes in the mesoscopic sawtooth domains took place. At this temperature, the ferroelastic domains became coarsened and certain S-shaped mesoscopic domains were reshaped. The disappearance and/or changes in the orientations of both the sawtooth and the ferroelastic domains were reversible upon return to room temperature. On heating to 60°C, both the mesoscopic sawtooth and the microscopic tweed domains were stable below 53°C. Above 53°C, the mesoscopic walls disappeared and the contrast of the tweed domains became blurred. Upon return to room temperature from 60°C, the mesoscopic domain patterns could not be retrieved, indicating that the transformation was irreversible. The morphology of the tweeds at this temperature indicated a structural transition from a two-variant domain state to a multivariant state, eliminating mesoscopic boundaries.     

Ferroid properties and domain structure of barium titanate

Distinctive features of domain formation in ferroelectric crystals are discussed theoretically for the example of ferroelectric BaTiO₃, taking into account ferroid properties of higher order. Inclusion of ferroid properties makes it possible to refine the details of the domain formation, and in particular to explain the possible existence of charged domain walls in ferroelectric crystals. Fiz. Tverd. Tela (St. Petersburg) 39, 1634–1635 (September 1997)     

On the thickness of ferroelastic twin walls in lead phosphate Pb3(PO4)2 an X-ray diffraction study

The effective thickness of ferroelastic twin-walls (W-walls) in Pb₃(PO₄)₂ at room temperature (≈ 0.7 T _c ) was determined by X-ray diffraction. The diffraction profiles were analysed using a wall profile e=eotanh x/w where W is the effective wall thickness including the effects of wall bending and surface relaxations. The experimental value W is around 10 unit cells which is larger than expected from standard renormalization arguments. The limitations of such experimental studies are discussed.     

Domain wall theory of elementary excitations in anisotropic antiferromagneticS=1 chains

We present a theoretical investigation of elementary excitations in anisotropic antiferromagneticS=1 chains using the concept of domain walls in string (hidden) order. Domain walls are classified by the internal spin projectionS _dw ^z . We calculate energies and string correlation functions of low lying excited states of the domain wall type in the Haldane phase and compare the results to those of numerical computations. The boundaries of the Haldane phase are determined from the instability of these excitations with respect to the ground state. The interaction between two domain walls is found to be proportional to the productS _dw ^z , S _dw ^z ₂, it is effectively repulsive for equal spin projections.     

Effect of Mn doping defect on 180° domain wall in ferroelectric PbTiO3

The structures, energies, spontaneous polarized properties and charge densities of 180° domain walls with Mn doping at different lattice positions were investigated in ferroelectric PbTiO₃ (PT) using the first-principles calculations. The results show that Mn ion prefers to enter the bulk region rather than the domain wall in terms of energy minimization whether it substitutes for an A-site Pb ion or a B-site Ti ion of PT. In addition the domain wall energy has a minimum value of 124.52 mJ/m² when Mn ion substitutes for Pb ion in the bulk region. And the spontaneous polarization along z axis increasing and the charge density in the domain wall region reducing could be the essential reasons for improving PT's performance after Mn doping at A site.     

Localised spin waves and domain walls stability in four-sublattice antiferromagnet La2CuO4

Domain walls in the four-sublattice antiferromagnet La₂CuO₄ are considered. The spin waves spectrum on the single domain wall is studied. The stability of the walls and the intrawalls phase transitions are analysed.     

Hard mode Raman spectroscopy and its application to ferroelastic and ferroelectric phase transitions

The application of Raman spectroscopy for the investigation of phase transitions focused traditionally on the observation of soft modes in displacive systems. The present furthergoing study on displacive and order-disorder systems is based on the observation of systematic changes of the scattering profiles of hard modes during the phase transition. It reveals the temperature evolution of the order parameters, the role of order-parameter fluctuations and phonon density of states effects in model systems like improper ferroelastic Pb₃(P_1-x As _x O₄)₂, lead diluted ferroelastic (Pb_1-x Ba _x )₃(PO₄)₂, pure ferroelastic As₂O₅ and the relaxor ferroelectric Pb(Sc_0.5Ta_0.5)O₃. Allied with supplementary experimental techniques hard-mode Raman spectroscopy (HMRS) is an ideal method for the investigation of order-parameter coupling effects and the characterization of structural phase transitions.