Orientation Of Domain Walls Research Articles

Internal friction and elastic softening in polycrystallineNb3Sn

The vibrating-reed technique was used to measure internal friction and Young's modulus of polycrystalline ${\mathrm{Nb}}_{3}$Sn in the form of composite Nb-${\mathrm{Nb}}_{3}$Sn tapes from 6 to 300 K. In tapes with only small residual strain in the $A15$ layers, a dramatic increase in internal friction with decreasing temperature is observed with an abrupt onset at \ensuremath{\sim}48 K. The internal friction ${Q}^{\ensuremath{-}1}$ between 6 and 48 K is believed to be associated with stress-induced motion of martensitic-domain walls. In this temperature range, ${Q}^{\ensuremath{-}1}$ is approximately proportional to the square of the tetragonal strain of the martensitic phase; ${Q}^{\ensuremath{-}1}\ensuremath{\propto}{(\frac{c}{a}\ensuremath{-}1)}^{2}$. With residual compressive strains of \ensuremath{\sim}0.2%, the internal friction associated with domain-wall motion is considerably reduced. This is attributed to a biasing of domain-wall orientation with residual stress, which reduces wall motion induced by the (much smaller) applied stress. The transformation temperature, however, is unchanged (within \ifmmode\pm\else\textpm\fi{} 1 K) by residual strains of up to 0.2%. Young's modulus exhibits substantial softening on cooling from 300 to 6 K. This softening is substantially reduced in the presence of small residual compressive strains, indicating a highly nonlinear stress-strain relationship as previously reported for V $_{3}\mathrm{Si}$.

Natural spin resonance (with various domain wall orientations) in mixed garnets Y3−xGdxFe5O12

Natural spin resonances (NSR) well separated from the domain wall relaxation are presented in YGdIG samples. It is shown that even in dynamical conditions the complementary term to K1 in the total anisotropy cannot be explained by the dipolar energy. The natural stress value is found to be of the order of 109 dyn cm-2. Experiments with applied dc fields confirm the gyromagnetic nature of NSR.

Phenomenological approach to structural phase transitions in trigonal double molybdates and tungstates

Structural phase transitions are investigated in crystals of the isostructural compounds MRA2 (M alkali metal, R trivalent metal, A anion (MoO4)2- or (WO4)2-). A group-theoretical analysis of possible transitions is carried out. It is shown that the transitions are of pure ferroelastic nature, occur between centrosymmetric phases: D (C or C) C, and may proceed continuously. Changes of the macroscopic crystal properties, behaviour of elastic waves, and permissible orientations of domain walls in various phases are studied. [Russian Text Ignored].

Domain-wall orientations and domain shapes of ferroelectric TGS and TGSe crystals

Wall-energy density as a function of wall orientation has been calculated on the basis of Zhirnov-type domain-wall theory. The equilibrium wall-orientations and the domain shapes which are consistent with the experimental observations have been successfully brought about for TGS and TGSe crystals. Two preferential orientations in TGSe are mainly due to the tri-critical nature of the ferroelectric phase transition.

A symmetry approach to domain structures

Whereas the symmetry of the order parameter is specified by operations preserved at the transition, domains are determined by lost symmetry operations. The number and the relations between domains and domain pairs can be found by grouping the lost operations into left and double cosets. Different types of domains, rotational (e.g., ferroelectric, ferroelastic) and translational ones, are related to maximal subgroups retaining a characteristic domain property. The interface between domains is treated as a two-dimensional residue of the parent phase and is described by two-sided plane groups. The existence, orientation and charge of coherent stress-free domain walls between ferroelastic domains can also be determined from left coset decompositions. Junctions and interactions of antiphase boundaries, domain walls and imperfect dislocations are considered. Annihilation of antiphase boundaries by moving domain walls, the creation of antiphase boundaries by reacting domain walls and the selective interactions of dislocations with antiphase boundaries and domain walls are demonstrated on the example of gadolinium molybdate. Goldstone modes as a dynamical counterpart of domain structures in systems described by continuous symmetry groups are briefly mentioned.

Domain-wall orientations in ferroelastics

The orientations of domain walls in ferroelastic materials are theoretically investigated. The procedure followed is based on the same criterion of spontaneous strain compatibility defined by Fousek and Janovec for ferroelectric crystals. Two given domains in a ferroelastic are found to be separated by a planar wall whose orientation belongs to a set of two mutually perpendicular orientations. Domain walls are not always crystallographically prominent planes of fixed indices ($W$ planes) and can instead be determined by the relative magnitude of the components of the second-rank tensor representing the spontaneous strain (${W}^{\ensuremath{'}}$ walls). In the latter case the orientation is expected to be temperature dependent. It is also shown that symmetry considerations are sufficient to find all $W$ planes. According to the considered ferroelastic species the pair of permissible walls between two domains can be two $W$ planes, or a $W$ plane and a ${W}^{\ensuremath{'}}$ plane, or two ${W}^{\ensuremath{'}}$ planes. The situation where no permissible walls are expected is of particular interest and is examined in known crystals. The predicted orientations of walls are given for the 94 species of full ferroelastics. Available experimental data of the literature are all consistent with our results.

Symmetry of secondary ferroics. II

In an earlier paper (Part I), the symmetry requirements for the secondary ferroic phenomena of ferrobielectricity, ferrobimagnetism and ferromagnetoelasticity and ferromagnetoelectricity were considered, and examples of materials illustrating the behavior discussed. In this second paper, the phenomena of ferrobielasticity and ferroelastoelectricity are considered. It is shown that there are 5 ferrobielastics, 15 ferroelastoelectric and 10 ferrobielastic-ferroelastoelectric species in which the primary ferroic effects are forbidden by symmetry. For α-quartz and other secondary ferroics it is suggested that the orientation of twin or domain walls which effect state switching under stress are dictated by strain compatibility between the contiguous domain states involved.

Symmetry of secondary ferroics. I

Although at present there are only a few well documented examples, secondary ferroic phenomena may prove to be rather common, since the symmetry requirements are not especially stringent. In this paper, the conditions for ferrobielectricity, ferrobimagnetism, ferromagnetoelasticity and ferromagnetoelectricity are discussed. It is shown that ferrobielectricity can be expected in antiferroelectric ferroelastic classes with substantial dielectric anisotropy. Nickel oxide and other antiferromagnetic ferroelastics with anisotropic magnetic susceptibility show ferrobimagnetism. Evidence for ferromagnetoelastic domains is found in CoF 2 and FeCO 3 , while Cr 2 O 3 shows ferromagnetoelectric switching. Of the 90 magnetic point groups, 35 are potentially ferromagnetoelastic and 40 potentially ferromagnetoelectric. In a companion paper (Part II) to be published, symmetry restrictions for ferrobielasticity and ferroelastoelectricity will be considered, and the conditions which determine the orientation of domain walls in secondary ferroics examined.

A Quantitative Study of the Stabilization Field for 180° Walls in Iron Single Crystal Sheets Containing Solute Nitrogen

AbstractThe strength of the stabilization field for 180° walls in [100] (011) iron single crystal sheets is derived theoretically and compared with experimental results. An initial magnetization curve after the stabilization of domain walls has taken place is derived using a model in which the reversible and irreversible magnetization processes are separately taken into account. The theoretical maximum value of the stabilization field is shown to be equal to the magnetic field at which the initial magnetization curve shows a first sudden discontinuous increase in induction. Effects of domain wall orientation and magnetostriction on the strength of the stabilization field are calculated. Calculations show that the 180° walls parallel to the (011) plane can be displaced irreversibly at the weekest magnetic field. These theoretical results are satisfied by experiment. A breakaway motion of domain walls is proposed for the sudden discontinuous increase in induction in the stabilized initial magnetization curves. The flexibility of domain walls contributes to the breakaway motion of domain walls.

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.

Observations of ferroelectric domains in boracites

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Orthoferrite crystal flux-growth morphology and perfection effects

Abstract Orthoferrite single crystal growth in PbO-PbF 2 and Pb0-PbF 2 -B 2 O 3 fluxed melts has been studied with particular attention being given to crystal morphology and perfection. Dendritic structures and bands (striae) were observed and are discussed in terms of possible {110} and {001} crystal growth modes. Optically visible bands are associated with variations in the lead impurity but not with the silicon impurity which is constant throughout these crystals. These bands impede bubble domain motion selectively, according to the relative band and domain wall orientations, but not as seriously as grain boundaries or twins. On the basis of these considerations, the effects of bands can be minimized by selecting crystal platelets grown in a {001} mode when the net magnetization is oriented 〈001〉.

The Orientation of Domain Walls in Twinned Ferroelectric Crystals

Due to the spontaneous deformations of ferroelectric crystals in their ferroelectric phases, twins (domains) may be separated only by those composition planes (domain walls) which satisfy the mechanical compatibility conditions; such planes are in an infinite crystal called permissible walls. A mathematical treatment is proposed which makes it possible to find all permissible walls in any ferroelectric species. It is shown that different types of permissible walls exist: W∞ walls with arbitrary orientation, crystallographically prominent Wf walls, and S walls whose indices depend on PS and the electromechanical coefficients. The orientations of such S walls are necessarily temperature dependent. Two particular domains may be separated by a W∞ wall or by one of two mutually perpendicular permissible walls of Wf and/or S type. In a number of species, however, there are pairs of domains between which no wall is permissible. It is shown that the occurrence of W∞ and Wf walls can be predicted from the symmetry properties of the paraelectric phase. The properties of S walls are discussed in detail. Among the known ferroelectrics, S walls are most likely to exist in MASD and in boracites. The available data on nickel-chlorine boracite suggest that S walls have been observed in this material.

Domain Wall Orientations in Silicon-Iron Crystals

The stable orientation of a 180° ferromagnetic domain wall in a cubic crystal with <100> easy directions is calculated as a function of crystal orientation for a sheet specimen with a <100> direction parallel to the surface. The effect of the second crystal anisotropy constant K2 on the domain wall energy is considered and shown to be negligible if |K2| <K1. If the crystal surface is a {110} plane, there are two equivalent stable domain wall positions, with the wall making an angle of ±32° with the normal to the specimen surface. If the crystal surface is a {100} plane, the domain wall lies normal to the surface. These results are changed if a stress is applied to the sample. Experimentally determined domain wall orientations agree with the calculated positions.