Symmetry Of Boundaries Research Articles

The effect of kink-like defects on the twin boundaries of nanotwinned Ta under nanoindentation

To figure out the effect of kink-like defects on twin boundaries, BCC Ta with three different kinds of microstructures: single crystal (SC), perfect twin boundaries (PTB) and defective twin boundaries (DTB), are studied under nanoindentation. Both indenter load and hardness in PTB are enhanced by twin boundaries but reduced in DTB due to intrinsic kink-like defects. According to atomic surface morphology, the relative sink-in depth in DTB is lower than that in PTB but higher than that in SC. By comparing atomic images of prismatic loops in three different stages, it can be found that kink-like defects in DTB perform two opposite functions: acceleration and delay. In initial plastic stage, defective twin boundaries can accelerate pinching-off event and nucleation. In transmission stage, dislocation backward emission is advanced by defective twin boundaries. In obstruction stage, the symmetry of coherent twin boundaries will be broken and asymmetrical shear loops are formed, which will delay prismatic loops moving across twin boundaries. Dislocations of 12〈111〉 are the main factor of nanoindentation in [1¯1¯2] direction. Kink-like defects will lead to less drops in DTB on dislocation densities than that in PTB. These findings are helpful to reveal the influence of intrinsic kink-like defects in BCC nanotwinned materials.

Symmetry and polarity of antiphase boundaries in PbZrO3

The polar properties of antiphase boundaries (APBs) in PbZrO$_3$ are analyzed in detail using a recently developed layer group approach in order parameter space and compared with the results from Landau-Ginzburg free energy description. It is shown that the former approach reveals the microscopic APBs' properties, and predicts polar APB structures at particular positions inside the unit cell, which agree very well with recent experimental obsevations [Wei, et.~al. \cite{Wei2014,Wei2015}]. The systematic usage of the method is developed. In contrast with it the commonly used free energy description obscures the microscopic features but still can reflect the macroscopic properties of the APBs by taking into account the bilinear coupling of polarization and order parameter gradients. The relation between the layer group approach and the Landau-Ginzburg free energy description is discussed and two mechanisms of polarization switching inside the APBs are distinguished. It is illustrated that the polar APBs observed in PbZrO$_3$ are consistently and naturally explained by the layer group approach. This analysis is expected to have a significant impact also in other materials.

Signatures of polarity in ferroelastic domain walls and antiphase boundaries of SrTiO3 and other perovskites

In the present work we study the polar properties of domain walls using a recently developed method of combining layer group analysis with order parameter symmetry [Schranz et al. PRB 100 (2019) 184105]. Using this method we obtain a detailed overview on the microscopic and macroscopic properties of domain walls which we can quantify with results from Landau-Ginzburg-Devonshire theory. Recently, we have applied [Schranz et al. PRB 102 (2020) 184101] the method to analyse the symmetry and polar properties of ferroelastic twin walls and antiphase boundaries in SrTiO3. Here we discuss the elastic anomalies observed in SrTiO3 at various temperatures in the light of these findings.

Symmetry and Topology of Twin Boundaries and Five-Fold Twin Boundaries in Soft Crystals.

Heteroclusters constructed by tethering dissimilar nanoclusters using organic linkers resemble lipids and self-assemble into cubosomes, namely, microparticles of soft crystals composed of unique nanochannel lattices with a defined symmetry and topology. The internal porous crystal structures can be accurately characterized using transmission electron microscopy. We herein describe twin boundaries and five-fold twin boundaries in cubosomes with a double-diamond Pn3̅m structure. Our analysis indicates a clear distinction in the conformation of the skeletal unit: a centrosymmetric staggered conformation with point group D3d for the normal skeletal unit and a mirror-symmetric eclipsed one with point group D3h for the skeletal unit on the twin boundary. This symmetry distinction causes the channels to change direction and elongate slightly as they pass through the twin boundary, but the topology is maintained. For cubosomes containing five-fold twin boundaries, one of the channels is in the center of the particles seamlessly connecting the five blocks. Our conclusion is that the two distinct channel systems are still continuous. This fundamental understanding will contribute to the development of soft crystals with defined shapes and special inner nanostructures for advanced applications.

Polarity of domain boundaries in nonpolar materials derived from order parameter and layer group symmetry

Domain boundaries and other twin boundaries in crystalline materials are receiving increasing interest. They can carry unique functional properties, which in many cases are absent in the surrounding bulk material. One such property of domain boundaries can be their electric polarity. Phenomenological insight in the polarity of domain boundaries was so far based either on the knowledge of the order parameter and the form of Landau-Ginzburg free energy functional, or on the knowledge of the symmetry of the domain boundaries. In the present work we show on the concrete examples of potassium thiocyanate (KSCN) and lacunar spinel crystals, that the concept of the primary order-parameter can help to find the layer group describing the maximal possible symmetry of a given domain boundary. Combination of layer group and order parameter symmetries is then employed to clarify the nature of the polarity of domain boundaries.

TESTING OF NUMERICAL SOLUTION OF THE PROBLEM OF DETERMINING SOURCES OF MAGNETOSTATIC FIELD IN MAGNETIZED MEDIUM

Purpose. Testing of numerical solution algorithm for integral equation for calculation of plane meridian magnetostatic field source distribution at interfaces of piecewise homogeneous magnetized medium by means of electrostatic analogy. Methodology. The piecewise homogeneous medium consists of three regions with different magnetic permeabilities: the shell of arbitrary meridian section, external unlimited medium outside the shell, and the medium inside the shell. For testing external homogeneous magnetic field effect on spherical shell is considered. The analytical solution of this problem on the basis of electrostatic analogy from the solution of the problem uniform electrostatic field effect on dielectric shell is obtained. We have compared results of numerical solution of integral equation with the data obtained by means of analytical solution at the variation of magnetic permeabilities of regions of medium. Results. Integral equation and the algorithm of its numerical solution for calculation of source field distribution at the boundaries of piecewise homogeneous medium is validated. Testing of integral equations correctness for calculation of fictitious magnetic charges distribution on axisymmetric boundaries of piecewise homogeneous magnetized medium and algorithms of their numerical solutions can be carried out by means of analytical solutions of problems of homogeneous electrostatic field effect analysis on piecewise homogeneous dielectric medium with central symmetry of boundaries – single-layer and multilayer spherical shells. In the case of spherical shell in wide range of values of the parameter λk, including close to ± 1, numerical solution of integral equation is stable, and relative error in calculating of fictitious magnetic charges surface density and magnetic field intensity inside the shell is from tenths of a percent up to several percent except for the cases of very small values of these quantities. Originality. The use analytical solutions for problems of calculation of external electrostatic field effect on piecewise homogeneous dielectric bodies for testing integral equations of magnetostatics and algorithms for their numerical solutions. Practical value. The described method of testing integral equations of magnetostatics and their numerical solutions can be used for calculation of magnetic fields of spacecraft control system electromagnets.

Order-parameter symmetries of domain walls in ferroelectrics and ferroelastics

The symmetry of boundaries between ferroelectric, ferroelastic and antiphase domains is a key element for a theoretical understanding of their properties. Here, we derive this symmetry from their organic relation to the symmetry of the primary transition order parameters. The domain wall symmetries are shown to coincide with directions of the order-parameter n-dimensional vector space, corresponding to sum of the vectors associated with adjacent domain states. This property is illustrated by the determination of the domain wall maximal symmetries in BaTiO3, LaAlO3, SrTiO3 and Gd2(MoO4)3. Besides, the domain pattern in YMnO3 is interpreted as resulting from an annihilation-creation process, the annihilation of the antiphase domain walls creating six ferroelectric domain walls merging at a single point.

Optical second harmonic generation from the twin boundary of ZnO thin films grown on silicon

The symmetry of the twin boundaries of ZnO epitaxial film was detected with reflective second harmonic generation (RSHG). The twin boundaries exhibit mirror symmetry with a polar configuration across the boundary plane and yield a nonvanishing polar contribution to RSHG. The nonvanishing second-order susceptibility supports the notion that the measured RSHG originates from the planar defect, which depends on the residual stress in the thin film. We analyzed our RSHG result by correlating the macroscopic data from optic probe with the microscopic data from tunneling electron microscope.

Principles of elementary non-wave theory of field of ultrasonic transducers used for pulse-amplitude defectometry

With the exception of the symmetry of problems, fields, structures and boundaries, the asymmetry of conditions of field spreading is also important: in medium without a sound attenuation (perfect medium) and also in medium with its sound attenuation (real medium). ENTF is based on a common method of higher mathematics under initial conditions, eliminating a wave nature of processes of excitation, spreading and reflection of sound pulses. Therefore, the theory is called elementary. The direct problem of UST, solved usually using ADD-diagrams, is generally accepted to be called defectoscopy (work in the energy of field) and the inverse problem, for the solution of which the DDA-diagram has not yet been used, is called defectometry (work in the geometry of field).

The field-space perspective on hysteresis in uniaxial ferromagnets

A procedure for the analysis of hysteresis in the H space of a uniaxial ferromagnet with higher-order anisotropy is put forward. The formulation is valid to any order n in the anisotropy expansion. The critical boundaries separating stable from metastable states are cast in a formally decoupled parametric way as Hx=Hx(Mx), Hz=Hz(Mz). The analytic expressions provide the basis for the construction of generalized astroids to any order. For n>1, new features are found and interpreted in their relation to rotational hysteresis and possible spin-reorientation transitions in uniaxial materials. The shape and symmetry of the critical boundaries depend crucially on up to n−1 independent ratios of the anisotropy constants against a suitable normalizing quantity; the normalizer can be any from among the set of constants or any linear combination thereof. Self-crossing of an astroid indicates the existence of additional extrema and, hence, of complicated hystereses.

Transient acoustic cavitation in gallstone fragmentation: a study of gallstones fragmented in vivo.

The mechanism of gallstone fragmentation by shock waves in vivo is uncertain. We used scanning electron microscopy to study 9 partially fragmented stones obtained from 6 patients who underwent lithotripsy and subsequently had surgery because of incomplete fragmentation. Surface characteristics of the stone were studied using scanning electron microscopy and compared to gallstones fragmented in degassed water in vitro and to control stones obtained from patients with uncomplicated cholelithiasis. Characteristic damage caused by transient acoustic cavitation was visible in all stones fragmented in vivo and in vitro as pits 10-100 microns diameter. In these pits, cholesterol crystals were fractured, and the symmetry of crystal boundaries was damaged. In areas of more severe damage, individual pits coalesced to form craters on the stone surface. High magnification of the pit walls revealed cracks, which in some instances radiated out onto the unpitted surface of the stone. We conclude that transient acoustic cavitation plays a role in gallstone fragmentation in vivo through the mechanism of surface pitting and the formation of cracks that radiate outward from the surface pits. Measures to enhance cavitation may improve the results of gallstone lithotripsy.

Casimir effect for regions with broken symmetry of boundaries

A method is proposed for computing corrections to the Casimir force caused by a broken symmetry of the boundaries. The values of these corrections are obtained for a parallelepiped in the case of scalar and electromagnetic fields.

On the symmetry and structure of (001) twist boundaries in f.c.c. metals

Abstract In a paper published recently Bristowe and Crocker (1978) discuss the structure of (001) twist boundaries in f.c.c. metals. Computer simulation methods were used to investigate boundary structures between Coincidence related crystals. Mechanically stable structures were obtained by allowing relative displacements of the adjacent crystals as a whole and relaxation of individual atoms. Structures of the type studied are necessarily periodic, having two non-colinear translation axes in the interface plane, but Bristowe and Crocker found that favourable structures also possess rotation and screw axes. Clearly, a system of space-group classification would be very helpful for discussions of the symmetry of these and other bicrystals. The 230 conventional space groups for single crystals are inappropriate because single crystals possess three non-colinear translation axes. However, other space-group systems have been devised for objects containing one or two non-colinear translation axes and a unique pl...