Orientational Phase Diagram Research Articles

Effect of rotating magnetic field on orientational dynamics of ferrocholesteric liquid crystals

We present numerical and analytical results describing the dynamics of a helical orientational structure of a ferrocholesteric liquid crystal, i.e., dilute suspension of ferromagnetic nanoparticles in a cholesteric liquid crystal, under the action of a rotating magnetic field. We employ the continuum theory to show how rotating magnetic field can untwist the helical ferrocholesteric structure and induce a ferrocholesteric–ferronematic transition. We analyze the non-stationary and stationary rotation regimes of the helical structure of a ferrocholesteric in a magnetic field. For weak fields, small and large rotational velocities the analytical expressions are obtained for the pitch of the ferrocholesteric helix. In the stationary rotational regime the orientational phase diagram of the ferrocholesteric–ferronematic transition is constructed for different values of magnetic field and angular velocities. It is shown that with increasing these parameters the transition field decreases. The dependence of a ferrocholesteric pitch on the magnetic field and its angular velocity at various material parameters is numerically obtained. We derive the analytical expression describing the divergence law for the pitch of a helix in the pre-transition region.

Cholesteric–nematic transition induced by a rotating magnetic field

We study theoretically the unwinding of helical orientational structure of a cholesteric liquid crystal under rotating magnetic field action. We analyze the non-stationary rotation regime of the orientational structure at the initial stages of the cholesteric helix unwinding in weak magnetic fields. For small deformations of the orientational structure we analytically obtain the dependence of the pitch of the cholesteric helix on the strength and rotation velocity of a magnetic field. For the stationary rotation regime in a magnetic field, the orientational phase diagram of the cholesteric–nematic transition is constructed. We study numerically and analytically the dependences of the cholesteric helical pitch on the strength and rotation velocity of the magnetic field. We reveal that in the narrow range of rotating magnetic field strength, the reentrant cholesteric–nematic–cholesteric orientational transitions take place. We show that in the stationary rotation regime, an increase in the rotation velocity of the field leads to a decrease in the cholesteric–nematic transition field. In the absence of rotation, our results are reduced to the well-known for static magnetic fields.

Investigation of the Direction of Spontaneous Magnetisation at 0 K in HoCo2 and TmFe2

The direction of spontaneous magnetisation at 0 K across a phase orientation boundary in rare-earth laves phase compounds is computed as a function of the ratio of magnetic to electrostatic interactions. The phase boundary and range of parameters used for the computation correspond to the portion of the orientational phase diagram where experimental data can be obtained. In the series of pseudo-binary compounds (Gdx Ho1-x )Co2 and (Yx Ho1-x )Co2 the range of parameters covers the continuous transition from the <100> to the <110> orientations. The nmr measurements on this series show that the direction of spontaneous magnetisation is at intermediate orientation between the <100> and <110> directions. The material TmFe2, which is in the vicinity of a discontinuous orientational boundary, is also discussed.

Orientational phase diagram of the epitaxially strained Si(001): Evidence of a singular (105) face

By exploiting the misfit strain of Ge on Si epitaxy, we examine the significant changes induced by surface stress in the polar structural phase diagram of Si(001) surfaces. Under compressive strain, the atomic and mesoscale structures of the vicinal Si(001) surfaces are converted into a new singular (105) face which does not exist on the strain-free equilibrium shape of Si and Ge. The observed structural modifications of substrates have far-reaching implications for the Stranski-Krastanov evolutionary path of three-dimensional islanding.

A Ground State Monte Carlo Approach for Studies of Dipolar Systems with Rotational Degrees of Freedom

We have developed a path integral ground state Monte Carlo (PIGSMC) algorithm for quantum simulations of rotating dipolar molecules, using a highly accurate sixth-order algorithm. The method allows us to calculate unbiased estimates of ground state properties of dipolar molecules in a variety of geometries, with or without an external electric field. To demonstrate the capability of the approach, we calculate the orientational phase diagram of a one dimensional lattice system of rotating point dipoles in the absence of any external electric fields. We find that for finite lattice size, this system exhibits an order–disorder transition at finite dipolar interaction strength in contrast to the well-known orientational disorder of the corresponding one dimensional O(3) quantum rotor models. Comparison of the quantum Monte Carlo results with a self-consistent field estimate of the phase transition shows the emergence of an ordered phase at non-zero dipolar strength, confirming the symmetry breaking role of the anisotropic dipole–dipole interaction.

Orientational Ordering of ortho–para Mixtures of Crystals of Homonuclear Diatomic Molecules: Theoretical Evidence for Reentrance

We have developed a theoretical formalism to calculate the orientational phase diagram of ortho–para (or odd-J/even-J) mixtures of homonuclear diatomic molecules in the low-pressure solid phases. In particular, our formalism allows for the explicit disorder present in such mixtrues. While the formalism is general, here we apply it to the quantum anisotropic planar rotor model, a two-dimensional model of coupled rotors. Our calculated phase diagram, separating phases of disorder and short-range order is reentrant, when an equilibrium mixture of odd-J/even-J species is considered. A reentrant phase diagram separating states of disorder and long-range order is known to exist in all-J species in both two and three dimensions. The phase diagram we find for the thermal mixture of odd-J/even-J species exhibits reentrance over a wider range of coupling constants than the corresponding all-J species. We also investigate systems where the odd-J fraction is fixed as a function of temperature. We find that even 1% odd-J mixture exhibits a phase diagram different from the pure even-J case, indicating that the even-J molecules play important role in orientational ordering.

Observation of double- to single-domain transition on the Eu/Si(1 0 0) surface by LEED and STM

The orientational phase diagram and morphology of the Eu-adsorbed Si(1 0 0) surface miscut by 0.4° have been studied by low-energy electron diffraction and scanning tunneling microscopy. We demonstrate that the original double-domain configuration with single-layer steps on the Si(1 0 0) substrate can be drastically broken at 0.4 monolayer (ML) of Eu. At this coverage, the ordered domain pattern formed by topographically non-equivalent terraces with Eu-induced 2 × 3 and “2 × 1” (so-called “wavy” structure) reconstructions is found, while no orthogonal 3 × 2 and “1 × 2” domains are observed. A model of the single-domain surface is proposed. The origin of the double- to single-domain transition found for the Eu/Si(1 0 0) system is discussed.

Orientational ordering of short LC rods in an anisotropic liquid crystalline polymer glass

The orientational phase diagram and ordering of guest liquid crystalline (LC) rods in a host liquid crystalline polymer (LCP) matrix quenched below the glass transition is determined by field theory. Microscopic anisotropic interactions can align the LC rods to each other and also align LCP matrix side chains and the LC rods in the plane normal to the local LCP chain contour. Our numerical analysis suggest ways to exploit host entropy, anisotropy of microscopic interactions and manipulate properties of LC rods for modern applications. We predict a nematic–nematic discontinuous orientational transition from a guest stabilized to a guest–host stabilized region and a reentrant transition from a guest stabilized nematic region to a host only stabilized regime. A detailed analysis of phase boundaries transitions and ordering is presented.

Domain structure of (011) crystalline garnet ferrite plates

The domain structure in (011) crystalline garnet ferrite plates is studied with allowance for induced uniaxial anisotropy and two-constant cubic anisotropy. It is shown that the inclusion of the second constant of cubic anisotropy greatly affects the orientational phase diagram and also the topology of magnetic inhomogeneities in a given magnet. It is found, in particular, that 180°non-Bloch domain walls may appear in a certain range of combined anisotropy constants, causing a continuous change in the wall orientation.

Step bunching on the vicinal GaN(0001) surface

Nominally $2\ifmmode^\circ\else\textdegree\fi{}$ vicinal GaN(0001) surfaces exhibit monolayer-height steps at $990\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ in the metal-organic chemical vapor deposition environment. Real-time x-ray scattering observations at $715--990\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ indicate that there is a tendency for step bunching during growth. Below $850\ifmmode^\circ\else\textdegree\fi{}\mathrm{C},$ step bunches nucleated during growth remain and coarsen after growth, while above $850\ifmmode^\circ\else\textdegree\fi{}\mathrm{C},$ the surface reverts to monolayer-height steps after growth. Surfaces vicinal toward the ${11\ifmmode\bar\else\textasciimacron\fi{}00}$ and the ${112\ifmmode\bar\else\textasciimacron\fi{}0}$ planes exhibit similar behavior. We suggest a simple equilibrium surface orientational phase diagram for vicinal GaN(0001) that is consistent with these observations.

Influence of external stresses with [formula omitted] upon magnetization processes of cubic ferromagnets

The paper attempts a theoretical research into the effects of a magnetic field upon the basic state of a cubic ferromagnet which also features a uniaxial anisotropy induced by external stresses with σ ∥[0 0 1] . The presence of external fields and elastic stresses has been shown to substantially modify the magnet's orientational phase diagram and to bring about an appearance of new magnetic phases and phase transformations between them. In particular, the magnetic field H∥[1 1 0] may induce an isostructural phase transition between the angular phases.

Energetics of Si(001)

A classical thermodynamic description of a surface requires the introduction of a number of energetic parameters related to the surface steps. These parameters are the step free energy, the kink creation energy, and the energetic and entropic interactions between steps. This review will demonstrate how a statistical analysis of scanning tunneling microscopy images of stepped surfaces can provide appropriate values of these fundamental energetic parameters. The Si(001) surface is used as a model system. In order to illustrate the significance of these energetic parameters, two morphological surface phase transitions are discussed, namely, the thermal roughening transition and the orientational phase diagram.

Anchoring and orientational wetting of nematic liquid crystals on self-assembled monolayer substrates: An evanescent wave ellipsometric study

An evanescent wave ellipsometric technique is used to study the orientational wetting of ${4}^{\ensuremath{'}}$,4- alkylcyanobiphenyls $(n\mathrm{CB},n=5--9)$ at the interface with a series of self-assembled monolayers. Brewster angle measurements are interpreted in terms of a global orientational wetting phase diagram ${(T,n,h}_{1}),$ where T denotes temperature, n is the alkyl chain length, and ${h}_{1}$ is the cosine of the contact angle of water with the monolayer. At temperatures below the isotropic-nematic phase transition temperature ${T}_{\mathrm{IN}},$ an anchoring transition from planar to homeotropic alignment occurs as the surface of the monolayer is made more hydrophobic. Homeotropic anchoring of the nematic director at $T<{T}_{\mathrm{IN}}$ is associated with complete orientational wetting on approaching the isotropic-nematic phase boundary from temperatures above ${T}_{\mathrm{IN}}.$ The anchoring-wetting transition shifts to less hydrophobic surfaces as n increases.

Orientational phase diagram of the stepped Au(001) surface

We report an X-ray scattering study of the structure and morphology of a stepped Au(001) surface between room temperature and bulk melting. At high temperatures, between 1170 and 1220 K, the vicinal Au(001) surface appears rough. Below T 0 = 1170 K, there is a facetting transition: hexagonally reconstructed (001) facets appear in coexistence with unreconstructed, stepped domains. The tilt angle of the stepped domains increases with decreasing temperature, exhibiting a power-law behavior versus reduced temperature. The phase behavior of the hexagonally reconstructed domains follows that observed on nominally unstepped Au(001) surfaces. At T 1 = 992 K, there is a second facetting transition at which the stepped domains reconstruct to form a rotated and corrugated, quasi-hexagonal structure. The corrugation is threefold commensurate with the average terrace width, consistent with a 2° magic vicinal phase. The orientational phase diagram of vicinal Au(001) is deduced and found to be qualitatively similar to that of vicinal Pt(001), although with intriguing differences.

Faceting kinetics of stepped Si(113) surfaces: dynamic scaling and nano-scale grooves

Time-resolved synchrotron X-ray scattering studies are presented of the faceting kinetics of stepped silicon surfaces misoriented by 2.1° and 1.3° from the cubic [113] direction towards the [001] direction. Following a quench from the high-temperature one-phase region of the orientational phase diagram into the two-phase coexistence region, originally-uniformly-distributed steps rearrange to form a grooved superstructure. Time-resolved surface X-ray scattering measurements reveal the behavior of the grooved surface morphology as a function of time. For times up to several hundred seconds after a quench, the behaviors of the specular and diffuse scattering intensity support a dynamic scaling description of the surface morphology. Specifically, the surface is found to be self-similar in time, with a characteristic groove side ( L) varying as a power-law versus time (t): L = L ot ф with a coarsening exponent of ф = 0.164 ± 0.021 ⋍ 1 6 . ф = 1 6 is consistent with a theory which focuses on thermally fluctuating step bunches and takes their collisions as the key growth mechanism. At later times, the groove size approaches a limiting value which depends on the stepped phase misorientation angle. This is consistent with the behavior expected for faceted surfaces in the case that elastic effects are important [V.I. Marchenko, Zh. Eksp. Teor. Fiz. 81 (1981) 1141].

Theory of tricriticality for miscut surfaces.

We propose a theory for the observed tricriticality in the orientational phase diagram of Si(113) misoriented towards [001]. The systems seems to be at or close to a very special point for long range interactions.

Faceting of Stepped Silicon (113) Surfaces: Step Unbinding, Dynamic Scaling, and Nano-Scale Grooves

AbstractX-ray scattering studies are reviewed of the faceting kinetics of stepped silicon (113) surfaces misoriented towards [001]. Following a quench from the one-phase region of the orientational phase diagram into the coexistence region, initially-uniformly-distributed steps rearrange to form a grooved superstructure. Our measurements reveal the behavior of the grooved surface morphology as a function of time. The surface is found to be self-similar in time, with a characteristic groove size (L) varying as a power-law versus time (t): L = L0tøwith a coarsening exponent of ø = 0.164 ± 0.021 ≃ 1/6, consistent with a theory for the kinetics of faceting which focuses on thermally fluctuating step bunches and their collisions. At later times, the groove size approaches a limiting value which depends on the stepped phase misorientation angle, as expected for faceted surfaces in the case that elastic effects are important.

Faceting, tricriticality, and attractive interactions between steps in the orientational phase diagram of silicon surfaces between [113] and [55 12

An X-ray scattering study is presented of the orientational phase diagram of Si surfaces misoriented by up to 5.2° from the cubic [113] direction towards [111], and for temperatures between 300 and 1500 K. At the highest temperatures (above 1200 K), the surface is uniformly stepped. In this region, the intensity of near-specularly scattered X-rays increases with decreasing temperature, suggesting a corresponding increase in the surface roughness as a result of a direct attractive interaction between steps. For temperatures below a tricritical point of T′ t = 1200 K, there occurs a two-phase region in which (113) facets appear in coexistence with stepped phase regions. For temperatures below a triple point at T′ 3 = 1180 K, coexistence between (113) facets and (55 12) facets is found. These results pertain to the sample heating current directed towards [332̄]. For heating currents directed in the opposite direction, there occurs an electric-field-induced instability, which has a significant effect on the high-temperature morphology.

Attractive step-step interactions, tricriticality, and faceting in the orientational phase diagram of silicon surfaces between

A synchrotron x-ray scattering study is presented of the orientational phase diagram of Si surfaces misoriented by up to 6\ifmmode^\circ\else\textdegree\fi{} from the cubic [113] direction towards [001] and for temperatures between 300 and 1500 K. At the highest temperatures (above 1223 K), the surface is uniformly stepped. In this region, the intensity of near-specularly scattered x rays increases with decreasing temperature, suggesting a corresponding increase in the surface roughness. Specifically, the temperature dependence of the intensity of the near-specular diffuse scattering may be described as a power law versus reduced temperature: ${\mathit{I}}_{\mathit{D}}$\ensuremath{\sim}${\mathit{t}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}\ensuremath{\lambda}}$, with \ensuremath{\lambda}=0.76\ifmmode\pm\else\textpm\fi{}0.2 (${\mathit{t}}_{\mathit{s}}$(\ensuremath{\theta})=[T-${\mathit{T}}_{\mathit{s}}$(\ensuremath{\theta})]/${\mathit{T}}_{\mathit{s}}$(\ensuremath{\theta}), where ${\mathit{T}}_{\mathit{s}}$(\ensuremath{\theta}) is spinodal temperature for surface misorientation \ensuremath{\theta}). Below ${\mathit{T}}_{\mathit{t}}$=1223\ifmmode\pm\else\textpm\fi{}40 K, there is a two-phase region in which (113) facets appear in coexistence with the stepped phase. We identify ${\mathit{T}}_{\mathit{t}}$ as a tricritical point. The misorientation angle at the phase boundary separating one- and two-phase regions may be also described as a power law versus reduced temperature: \ensuremath{\theta}=${\mathrm{\ensuremath{\theta}}}_{0}$${\mathit{t}}^{\mathrm{\ensuremath{\beta}}}$, with \ensuremath{\beta}=0.42\ifmmode\pm\else\textpm\fi{}0.10 [t=(${\mathit{T}}_{\mathit{t}}$-T)/${\mathit{T}}_{\mathit{t}}$]. The behavior of the intensity of the diffuse scattering above ${\mathit{T}}_{\mathit{t}}$ and of the phase boundary below ${\mathit{T}}_{\mathit{t}}$ can be understood qualitatively on the basis of a mean-field theory incorporating a direct attractive interaction between steps. However, the observed tricritical exponents are not given correctly. For temperatures between a triple point at ${\mathit{T}}_{3}$=1134\ifmmode\pm\else\textpm\fi{}40 and 300 K, coexistence between the (113) facet and the (114) facet is found.

Tricriticality in the orientational phase diagram of stepped Si(113) surfaces.

An x-ray scattering study is presented of the orientational phase diagram of Si surfaces misoriented by up to 6\ifmmode^\circ\else\textdegree\fi{} from the cubic [113] direction towards [001] and for temperatures between 300 and 1500 K. At the highest temperatures, the surface is uniformly stepped. Below ${\mathit{T}}_{\mathit{t}}$=1223 K, there is a two phase region in which (113) facets appear in coexistence with the stepped phase. We identify ${\mathit{T}}_{\mathit{t}}$ as a tricritical point. For temperatures between a triple point at ${\mathit{T}}_{3}$=1134 K and 300 K, coexistence between the (113) facet and the (114) facet is found.