Strip-shaped Domain Research Articles

The influence of domain structures and phase transition on transmittance of PZN–PT ferroelectric crystal

A 0.93Pb(Zn1/3Nb2/3)O3–0.07PbTiO3(PZN–PT) single crystal was grown using the flux Bridgman method and 〈0 0 1〉-oriented slides were obtained. Strip-shaped and needle-shaped domains were observed in the same PZN–PT sample by a polarizing microscope. Raman spectra and transmittance spectra of regions with different domain structures have been measured. The Raman spectra exhibit slight differences in order information in different domain regions. The transmittance of strip-shaped domain regions is higher than that of needle-shaped domain regions, which means that the domain structures play a role in optical inhomogeneity. The temperature dependence of the domains and transmittance spectra has been investigated by in situ observation. The results show that the transmittance was influenced significantly by the ferroelectric phase transition, including the domain structure.

Kinetic models of ordering in two dimensions

The approach to equilibrium of ordered superlattice structures on surfaces is analyzed. Both Monte Carlo methods as well as analytic models of interacting domain-walls are used to study the kinetics of quenched, two dimensional systems with Q degenerate equilibrium states. In particular, the growth of long-range order in the magnetic analogs of the commensurate superlattice structures found on surfaces is analyzed in a study of the kinetics of typical domain geometric that are found, when systems are quenched from high (disordered state) to low temperatures. Calculations and simulations of the time and temperature dependence of the domain sizes for the model system of isolated domains indicate that for two dimensions roughening fluctuations of the domain-walls, strongly influence the grain growth kinetics. Strip-shaped domains approach equilibrium almost entirely through these fluctuations, while circular domains shrink due to deterministic curvature, but with a rate that is strongly temperature dependent even for temperatures outside the critical region.

Variational Problems¶on Multiply Connected Thin Strips I:¶Basic Estimates and Convergence¶of the Laplacian Spectrum

Let M be a planar embedded graph whose arcs meet transversally at the vertices. Let ?(ɛ) be a strip-shaped domain around M, of width ɛ except in a neighborhood of the singular points. Assume that the boundary of ?(ɛ) is smooth. We define comparison operators between functions on ?(ɛ) and on M, and we derive energy estimates for the compared functions. We define a Laplace operator on M which is in a certain sense the limit of the Laplace operator on ?(ɛ) with Neumann boundary conditions. In particular, we show that the p-th eigenvalue of the Laplacian on ?(ɛ) converges to the p-th eigenvalue of the Laplacian on M as ɛ tends to 0. A similar result holds for the magnetic Schrodinger operator.

Variational Problems¶on Multiply Connected Thin Strips II:¶Convergence of the Ginzburg-Landau

Let M be a planar embedded graph whose arcs meet transversally at the vertices; Let ?(M) be a strip-shaped domain around M, of width M except in a neighborhood of the singular points. Assume that the boundary of ?(M) is smooth. We consider the Ginzburg-Landau energy functional for superconductivity on ?(M). We prove that its minimizers converge in a suitable sense to the minimizers of a simpler functional on M. The supercurrents in ?(M) are shown to converge to one-dimensional currents in M.

Magnetic properties, domain structure, and microstructure of anisotropic SmCo6.5Zr0.5 ribbons with C addition

The magnetic properties and the domain structure of anisotropic melt-spun SmCo6.5Zr0.5 alloys with C addition was investigated by means of x-ray diffraction (XRD), magnetic measurement, and magnetic force microscopy. The XRD analyses showed that the addition of a few percent of C led to a significant increase in the coercivity and simultaneously affected the characterization of crystalline texture of the ribbons. The easy magnetization c axis changed from parallel to the ribbon plane for SmCo6.5Zr0.5 ribbons to normal to the ribbon plane for SmCo6.5Zr0.5C0.25−0.75 ribbons. An optimal coercivity of 0.92 T was obtained for the SmCo6.5Zr0.5C0.5 ribbon spun at 5 m/s. The corresponding remanence measured normal or parallel to the ribbon plane was 7.1 kGs or 3.1 kGs, respectively. The domain structure was studied by magnetic force microscopey. A strip-shaped domain was observed on the surface of the SmCo6.5Zr0.5 ribbons and the walls lay straight and parallel. For C-doped ribbons, the domain walls formed a maze domain pattern of grains with c axis normal to the ribbon plane. Scanning electron micrographs showed that a dendrite structure was present in the SmCoZr ribbon surface, and C addition caused the above-mentioned dendrite to diminish.

Characterization of crystalline texture and magnetic properties of anisotropic melt-spun Sm(CoZr)7Cy alloy

The effect of additive C on characterization of crystalline texture and magnetic properties of anisotropic melt-spun Sm(CoZr)(7) alloy has been investigated. A few percent of C addition was found to not only significantly enhance the coercivity of the ribbons but also affect the characterization of crystalline texture. The easy-magnetization c axis is changed from parallel to the ribbon plane for SmCo6.5Zr0.5 ribbons, to normal to the ribbon plane for the SmCo6.5Zr0.5C0.5 one. Maximum energy product of SmCo6.5Zr0.5C0.5 ribbons prepared at 5 m/s, pulse magnetized to 5 T and measured normal or parallel to the ribbon plane is 8.6MGOe or 3.2MGOe, respectively. The domain structure was studied by magnetic-force microscope. A strip-shaped domain can be observed on the surface of the SmCo6.5Zr0.5 ribbons and the walls lie straight and parallel. For C-doped ribbons, the domain walls form a maze domain pattern of grains with c axis normal to the ribbon plane. Scanning electron micrography analysis showed that a dendrite structure was present in the SmCoZr ribbon surface. C addition leads to the diminishing of the above dendrite and the grains become equiaxial, The characterization of crystalline texture in C-free and C-doped ribbons has been correlated with their microstructure.

Extremal properties of quadratic differentials with strip-shaped domains in the structure of the trajectories

One considers the modulus problem for a family of homotopic classes {Hi}, in the extended complex plane , of the following types. The classes Hn consist of closed Jordan curves, homotopic to appropriate nondegenerate contours or point curves, and also of arcs with endpoints in (distinct or coinciding) distinguished points in . One establishes the relation of the indicated extremal metric problem and the problem on the extremal decomposition of in the family of systems of mutually nonoverlapping domains {Di}, associated with the family of the classes {Hi}. The results of this paper complement a previous theorem of the author [Moduli of families of curves and quadratic differentials. Trudy Mat. Inst. Akad. Nauk SSSR, Vol. 139, 1980].

Kinetics of ordering in two dimensions. I. Model systems

The approach to equilibrium of ordered superlattice structures on surfaces is analyzed. Both Monte Carlo methods as well as analytic models of interacting domain walls are used to study the kinetics of quenched, two-dimensional systems with $Q$ degenerate equilibrium states. In particular, the growth of long-range order in the magnetic analogs ($Q$-component Potts models) of the commensurate superlattice structures found on surfaces is analyzed in a study of the kinetics of typical domain geometries that are found when systems are quenched from high (disordered state) to low temperatures. Calculations and simulations of the time and temperature dependence of the domain sizes for the model system of isolated domains indicate that for two dimensions roughening fluctuations of the domain walls strongly influence the grain growth kinetics. Strip-shaped domains approach equilibrium almost entirely through these fluctuations, while circular domains shrink due to deterministic curvature, but with a rate that is strongly temperature dependent even for temperatures outside the critical region. Pinning effects in systems with $Q\ensuremath{\ge}3$ lead to extremely slow kinetics for particular domain geometries. Low-temperature quenches on a triangular lattice indicate that these pinned geometries are rarely nucleated, while quenches on a square lattice equilibrate much more slowly due to pinning. The application of the theory to superlattice grain growth on surfaces is discussed in the following paper which presents results for the kinetics of quenched systems in terms of the simple domain geometries examined here.

Fluctuations and kinetics of domain growth in two dimensions

The approach to equilibrium of an initially strip-shaped domain in $d=2$ is calculated using both a model for interacting domain walls and Monte Carlo simulations of kinetic Ising systems. The dynamics are dominated by fluctuation effects, which result in time scales for equilibrium much faster than those predicted by a deterministic theory, but slower than those of an initially curved interface.