Tilt Fluctuations Research Articles

Mixing twist-bend and ferroelectric nematic liquid crystals.

Twist-bend (N_{tb}) and ferroelectric (N_{F}) nematic liquid crystals exhibit several novel effects and new physical properties. Here, we report experimental studies on the phase diagram and some physical properties of binary mixtures of CB9CB and RM734 mesogens. Both N-N_{tb} and N-N_{F} phase transition temperatures and the corresponding enthalpies decrease significantly and, eventually, these transitions disappear at some intermediate compositions, stabilizing wide nematic phase (N). Temperature-dependent birefringence several degrees above the N-N_{tb} phase transition shows strong director tilt fluctuations. The critical range of the fluctuations increases with the nematic range and the critical exponent is consistent with the mean field. The spontaneous polarization of RM734 decreases drastically with the addition of CB9CB mesogen. The temperature dependence of the splay elastic constant of the mixtures' high-temperature nematic (N) phase strikingly differs from that of the pristine CB9CB and RM734 mesogens. The study shows that a small inclusion of either compound has a substantial effect on the phase diagram and physical properties.

Effects of wave-front tilt and air density fluctuations in a sensitive atom interferometry gyroscope.

We present a matter wave gyroscope with a Sagnac area of 5.92 cm2, achieving a short-term sensitivity of 167 nrad/s/Hz1/2. The atom interferometry gyroscope is driven by a π/2 - π - π - π/2 Raman pulse sequence based on an atom fountain with a parabolic trajectory. The phase-locked laser beams for Raman transitions partly propagate outside of the vacuum chamber and expose to the air when passing through the two arms of the vacuum chamber. This configuration leads to the tilt of the laser's wave-front and suffers the fluctuation of air density. The impacts on both the fringe contrast and long-term stability are experimentally investigated in detail, and effective schemes are developed to improve the performance of our atom gyroscope. The method presented here could be useful for developing large atom interferometry facilities with separated vacuum chambers.

Landau theory and giant room-temperature barocaloric effect in MF3 metal trifluorides

The structural phase transitions of MF$_3$ (M=Al, Cr, V, Fe, Ti, Sc) metal trifluorides are studied within a simple Landau theory consisting of tilts of rigid MF$_6$ octahedra associated with soft antiferrodistoritive optic modes that are coupled to long-wavelength strain generating acoustic phonons. We calculate the temperature and pressure dependence of several quantities such as the spontaneous distortions, volume expansion and shear strains as well as $T-P$ phase diagrams. By contrasting our model to experiments we quantify the deviations from mean-field behavior and found that the tilt fluctuations of the MF$_6$ octahedra increase with metal cation size. We apply our model to predict giant barocaloric effects in Sc substituted TiF$_3$ of up to about $15\,$JK$^{-1}$kg$^{-1}$ for modest hydrostatic compressions of $0.2\,$GPa. The effect extends over a wide temperature range of over $140\,$K (including room temperature) due to a large predicted rate $dT_c/dP = 723\,$K GPa$^{-1}$, which exceeds those of typical barocaloric materials. Our results suggest that open lattice frameworks such as the trifluorides are an attractive platform to search for giant barocaloric effects.

Novel tilt-curvature coupling in lipid membranes.

On mesoscopic scales, lipid membranes are well described by continuum theories whose main ingredients are the curvature of a membrane's reference surface and the tilt of its lipid constituents. In particular, Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)] have shown how to systematically derive such a tilt-curvature Hamiltonian based on the elementary assumption of a thin fluid elastic sheet experiencing internal lateral pre-stress. Performing a dimensional reduction, they not only derive the basic form of the effective surface Hamiltonian but also express its emergent elastic couplings as trans-membrane moments of lower-level material parameters. In the present paper, we argue, though, that their derivation unfortunately missed a coupling term between curvature and tilt. This term arises because, as one moves along the membrane, the curvature-induced change of transverse distances contributes to the area strain-an effect that was believed to be small but nevertheless ends up contributing at the same (quadratic) order as all other terms in their Hamiltonian. We illustrate the consequences of this amendment by deriving the monolayer and bilayer Euler-Lagrange equations for the tilt, as well as the power spectra of shape, tilt, and director fluctuations. A particularly curious aspect of our new term is that its associated coupling constant is the second moment of the lipid monolayer's lateral stress profile-which within this framework is equal to the monolayer Gaussian curvature modulus, κ¯m. On the one hand, this implies that many theoretical predictions now contain a parameter that is poorly known (because the Gauss-Bonnet theorem limits access to the integrated Gaussian curvature); on the other hand, the appearance of κ¯m outside of its Gaussian curvature provenance opens opportunities for measuring it by more conventional means, for instance by monitoring a membrane's undulation spectrum at short scales.

Two-dimensional nanoscale correlations in the strong negative thermal expansion material ScF3

We present diffuse x-ray scattering data on the strong negative thermal expansion (NTE) material ${\mathrm{ScF}}_{3}$ and find that two-dimensional nanoscale correlations exist at momentum-space regions associated with possibly rigid rotations of the perovskite octahedra. We address the extent to which rigid octahedral motion describes the dynamical fluctuations behind NTE by generalizing a simple model supporting a single floppy mode that is often used to heuristically describe instances of NTE. We find this model has tendencies toward dynamic inhomogeneities and its application to recent and existing experimental data suggest an intricate link between the nanometer correlation length scale, the energy scale for octahedral tilt fluctuations, and the coefficient of thermal expansion in ${\mathrm{ScF}}_{3}$. We then investigate the breakdown of the rigid limit and propose a resolution to an outstanding debate concerning the role of molecular rigidity in strong NTE materials.

New insights on fractures deformation from tiltmeter data measured inside the Fontaine de Vaucluse karst system

Tilt fluctuations can potentially reflect the response of hydrosystems to important rainfall. In this context, long baseline tiltmeters have been installed in an underground tunnel penetrating the Fontaine de Vaucluse karst to study the medium deformation related to solicitations exerted by water infiltrating the hydrosystem. The instruments monitor the tilt as well as its spatial variation. Northward tilts reaching a 1 μrad amplitude are observed consecutively to rainfalls. The tilt amplitude is highly correlated with the Fontaine de Vaucluse outlet flow fluctuations. The measured tilt signal is also relatively homogeneous over a 150 m length. Different types of structure likely to produce such observations are tested in order to identify their location with respect to the tiltmeters, their dimension as well as the amount of water level variation in the structure. Following rainfalls, the infiltration of water modifies the pore pressure, inducing a medium deformation. The hypothesis of an homogeneous surface loading on the Vaucluse plateau is first refuted since the related tilt is much lower than the one measured. The water supplied by rainfalls has to accumulate in discontinuities in order to generate a higher tilt. So, the deformation related to a pressure exerted on a fracture filled by water is assessed. A first study reveals the interest of the tilt homogeneity information that constrains strongly the fracture properties. Thus, the fracture must be located at a distance more than a few hundreds metres from the tiltmeters in order to produce a tilt homogeneous in space. If the fracture is initially dry, it must also be filled on a height higher than 150 m consecutive to a rainfall in order to generate a tilt amplitude in the same magnitude as the one measured. Then, we explore the influence of water level variations on the tilt produced by a fracture located at the interface between the saturated and unsaturated zones, which are thereby permanently flooded. Since several parameters of that model satisfactorily explain the field observations, we discuss how simultaneous geodetical observations could provide complementary information that would further constrain the geometry of the structure at the origin of the medium deformation.

Mn2+ doped ZnS quantum dots in ferroelectric liquid crystal matrix: Analysis of new relaxation phenomenon, faster optical response, and concentration dependent quenching in photoluminescence

Phase transitional, dielectric, electro-optical, polarizing optical microscopic, photoluminescence (PL), and Fourier transformed infrared (FTIR) spectroscopic measurements have been carried out on ZnS:Mn quantum dots (QDs) dispersed ferroelectric liquid crystal (FLC). A new dielectric relaxation mode has been envisaged in FLC material due to the presence of 0.25 wt. % ZnS:Mn (40 mol. %) QDs. The characteristics of the new mode have been compared with those of the soft mode. A significant fastening of the electro-optical response (∼75%) has been observed in the case of 0.25 wt. % ZnS:Mn (20 mol. %) QDs doped FLC material. The induction of the new relaxation mode is attributed to the flexoelectric tilt fluctuations. The induced flexoelectric polarization in the FLC medium at the vicinity of QDs might be responsible for the enhanced spontaneous polarization in the FLC/QDs mixtures. Quenching in PL for the FLC/QDs mixtures has been observed, which strongly depends on Mn content in QDs. The change in FTIR spectra for the FLC/QDs composite clearly indicates the change in molecular dynamics of the pure FLC after the dispersion of QDs. The presented results will certainly pave a way to utilize QDs for obtaining faster response of the FLC material and potential material to tune the relaxation processes.

Reconciliation of local and long-range tilt correlations in underdopedLa2−xBaxCuO4(0≤x≤0.155)

A long standing puzzle regarding the disparity of local and long range CuO6 octahedral tilt correlations in the underdoped regime of La2-xBaxCuO4 is addressed by utilizing complementary neutron powder diffraction and inelastic neutron scattering (INS) approaches. Long-range and static CuO6 tilt order with orthogonally inequivalent Cu-O bonds in the CuO2 planes in the low temperature tetragonal (LTT) phase is succeeded on warming through the low-temperature transition by one with orthogonally equivalent bonds in the low temperature orthorhombic (LTO) phase. In contrast, the signatures of LTT-type tilts in the instantaneous local atomic structure persist on heating throughout the LTO crystallographic phase on the nanoscale, although becoming weaker as temperature increases. Analysis of the INS spectra for the x = 1/8 composition reveals the dynamic nature of the LTT-like tilt fluctuations within the LTO phase and their 3D character. The doping dependence of relevant structural parameters indicates that the magnitude of the Cu-O bond anisotropy has a maximum at x = 1/8 doping where bulk superconductivity is most strongly suppressed, suggesting that the structural anisotropy might be influenced by electron-phonon coupling and the particular stability of the stripe-ordered phase at this composition. The bond-length modulation that pins stripe order is found to be remarkably subtle, with no anomalous bond length disorder at low temperature, placing an upper limit on any in-plane Cu-O bondlength anisotropy. The results further reveal that although appreciable octahedral tilts persist through the high-temperature transition and into the high temperature tetragonal (HTT) phase, there is no significant preference between different tilt directions in the HTT regime.

Orientational Fluctuations Near the Smectic A to Smectic C Phase Transition in Two “de Vries”‐Type Liquid Crystals

On the basis of thorough analysis of 2D X-ray diffraction patterns from smectic monodomains, we examine the influence of orientational fluctuations on the weakly first-order smectic A (SmA) to smectic C (SmC) transitions in two nonchiral organosiloxane "de Vries"-type liquid crystals. We find that these materials exhibit very large molecular tilt fluctuations with magnitudes of up to 35°--thus larger than the average tilt itself. This is essential to understand the underlying molecular mechanism behind the practical absence of smectic layer contraction in these materials: in the SmA phase, the nematic order parameter is very low (molecular fluctuations correspondingly high), and the expected layer shrinkage at the SmA to SmC transition is almost fully compensated by the increase in orientational order, as the fluctuations diminish with decreasing temperature. In addition to the general tilt fluctuations, we observe intrinsic soft-mode fluctuations. They have a λ-shaped temperature dependence that peaks at the SmA-SmC transition with a maximum amplitude of about 2°.

Merging of the polar and tilt instability lines near the respective morphotropic phase boundaries of PbZr1−xTixO3

The results are presented of anelastic and dielectric spectroscopy measurements on large grain ceramic PZT with compositions near the two morphotropic phase boundaries (MPBs) that the ferroelectric (FE) rhombohedral phase has with the Zr-rich antiferroelectric and Ti-rich FE tetragonal phases. These results are discussed together with similar data from previous series of samples, and reveal new features of the phase diagram of PZT, mainly connected with octahedral tilting and its coupling with the polar modes. Additional evidence is provided of what we interpret as the onset of the tilt instability, when is initially frustrated by lattice disorder, and the long range order is achieved at lower temperature. Its temperature T_IT(x) prosecutes the long range tilt instability line T_T(x) up to T_C, when T_T. It is proposed that the difficulty of seeing the expected 1/2<111> modulations in diffraction experiments is due to the large correlation volume associated with that type of tilt fluctuations combined with strong lattice disorder. It is shown that the lines of the tilt instabilities tend to be attracted and merge with those of polar instabilities. Not only T_IT bends toward T_C and then merges with it, but in our series of samples the temperature T_MPB of the dielectric and anelastic maxima at the rhombohedral/tetragonal MPB does not cross T_T, but deviates remaining parallel or possibly merging with T_T. These features, together with a similar one in NBT-BT, are discussed in terms of cooperative coupling between tilt and FE instabilities, which may trigger a common phase transition. An analogy is found with recent simulations of the tilt and FE transitions in multiferroic BiFeO3. An abrupt change is found in the shape of the anelastic anomaly at T_T when x passes from 0.465 to 0.48, possibly indicative of a rhombohedral/monoclinic boundary.

Amplitude and phase fluctuation modes of a newly synthesized anti ferroelectric liquid crystal material 4F6Bi

Frequency and temperature dependent dielectric spectroscopy of a newly synthesized anti ferroelectric liquid crystal (AFLC) material namely “(S)-(+)-(1-methylheptyloxycarbonyl)phenyl 4′-(6-perfluoropentanoyloxyhex-1-oxy) biphenyl-4-carboxylate ((S) (4F6Bi))” has been carried out in the frequency range 1 Hz to 1 MHz under planar anchoring conditions of the molecules. 4F6Bi possesses paraelectric (SmA ⁎), ferroelectrics (SmC ⁎), and wide range anti ferroelectric (SmC A ⁎) phases. The SmA ⁎ phase shows soft mode relaxation related with the tilt fluctuations. Its relaxation frequencies are highly temperature dependent and decreases with decrease in the temperature. Dielectric strength is small (~ 1.0–2.5) but increases with decrease in temperature and follows Curie–Weiss' law. The SmC ⁎ phase shows Goldstone mode with its dielectric strength slowly increasing with decreases in the temperature, and shows maximum value (~ 64) just above the SmC ⁎–SmC A ⁎ transition at 118.1 °C. Goldstone mode relaxation frequency has been found to be almost invariant with temperature (~ 3.5 kHz). Two modes of dielectric relaxation have been observed in the SmC A ⁎ phase due to anti ferroelectric ordering of molecules.

Detection of Flow Distortions and Systematic Errors in Sonic Anemometry Using the Planar Fit Method

We describe the coordinate transformations that can be used to convert the velocity components measured by a set of sonic anemometers with time-dependent tilt fluctuations into a single, time-independent coordinate system. By applying the planar fit method (PFM) to each anemometer dataset, it is possible, for planar flows, to locate the flow plane at each measurement point and compare its orientation with the topography. Installation on a ship is also considered. An application of this method to intercomparison data has led to the detection of an instrument error due to a misalignment between the assembly of the sonic transducers and the anemometer pedestal. If this error occurs, pedestal levelling does not guarantee that measurements are unbiased. A correction method is proposed and the results of two experiments are shown. Flow planarity at different levels and flow distortion caused by the mast are highlighted. The influence of the error on the evaluation of the Reynolds stresses using PFM or the double rotation method and the triple rotation method is discussed and the tilt corrected stresses calculated using the three methods compared.

A trade‐off relation between tilt and twist angle fluctuations in InN grown by RF‐MBE

AbstractIn the InN growth on sapphire substrates, it is difficult to control both of tilt and twist angle fluctuations at same time. It is necessary to understand initial growth stage such as the role of nitridation process to improve the mosaicity. Low‐temperature nitridation technique brings the drastically improvement of the tilt angle fluctuation, although the twist angle fluctuation becomes worse. Such experimental results strongly indicate that there is some trade‐off relation between the tilt and the twist angle fluctuations as a function of the nitridation condition such as the nitridation time. In this paper, we discuss about such trade‐off relation in the direct growth of InN on the nitridation sapphire substrates and also propose a simple model of initial nitridation process to explain it. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Role of molecular tilt in thermal fluctuations of lipid membranes

Long-wavelength thermal fluctuations of lipid membranes are adequately described by the Helfrich elastic model. On the other hand, fluctuations of wavelengths comparable with bilayer thickness exhibit significant deviations from the prediction of the elastic model and are typically assumed to be dominated by microscopic surface tension due to protrusion of lipid molecules into the solvent. We present evidence that the short-wavelength modes of a lipid membrane are dominated by fluctuations of the tilt of lipid molecules with respect to the membrane normal rather than the microscopic surface tension. We obtain an expression for the spectral intensity of the thermal membrane fluctuations by appealing to the Hamm-Kozlov model, which accounts for both membrane bending and lipid tilt contributions to the total membrane energy but neglects the contributions of the microscopic surface tension. The tilt and the bending fluctuations obtained from our coarse-grained molecular dynamics simulations of a dipalmitoylphosphatidylcholine lipid bilayer show good agreement with the theory. Furthermore, the obtained tilt and bending moduli are in close agreement with experimentally determined values. The magnitude of the microscopic protrusion tension estimated from our simulations is significantly smaller than that of the tilt modulus. These results indicate that the membrane fluctuations can be adequately described by a macroscopic elastic model down to scales of interlipid distance provided one accounts for the tilt fluctuations.

Polar order and tilt in achiral smectic phases

Material with the phase sequence SmA-SmAP-SmCP is studied as an example of a system in which the spontaneous electric polarization and the molecular tilt develop independently at the SmA-SmAP and the SmAP-SmCP phase transition, respectively. The temperature dependence of the spontaneous electric polarization clearly shows a strong coupling between the polarization and tilt. The system exhibits also very strong precritical polarization and tilt fluctuations. Experimental observations are explained within the theoretical model.

Local wing tilt analysis of laterally overgrown GaN by x-ray rocking curve imaging

We report on recent advances in spatially resolved x-ray diffraction, extending the technique known as rocking curve imaging down to 1–2 µm spatial resolution. Application to a set of gallium nitride samples grown by epitaxial lateral overgrowth (ELO) shows the potential of the technique. Quantitative information on crystallographic misorientations and lattice quality can be obtained by direct imaging with high lateral resolution. Results from two samples of ELO-GaN grown on different substrates are compared. Tilt in individual lateral periods of the ELO structure can be quantified. Local tilt fluctuations are distinguished from macroscopic variations (curvature). The local lattice quality can be investigated via the peak width of diffraction profiles recorded in individual camera pixels. The peak broadening previously observed in laboratory x-ray diffraction measurements is found to have (at least) two different reasons. In both cases, peak broadening does not indicate a degradation in local crystalline quality.

Three-dimensional wedge filling in ordered and disordered systems

We investigate interfacial structural and fluctuation effects occurring at continuous fillingtransitions in 3D wedge geometries. We show that fluctuation-induced wedgecovariance relations that have been reported recently for 2D filling and wetting havemean-field or classical analogues that apply to higher-dimensional systems. Classicalwedge covariance emerges from analysis of filling in shallow wedges based on asimple interfacial Hamiltonian model and is supported by detailed numericalinvestigations of filling within a more microscopic Landau-like density functionaltheory. Evidence is presented that classical wedge covariance is also obeyed forfilling in more acute wedges in the asymptotic critical regime. For sufficientlyshort-ranged forces mean-field predictions for the filling critical exponents andcovariance are destroyed by pseudo-one-dimensional interfacial fluctuations. Weargue that in this filling fluctuation regime the critical exponents describing thedivergence of length scales are related to values of the interfacial wandering exponentζ(d) defined for planar interfaces in (bulk) two-dimensional(d = 2) andthree-dimensional (d = 3) systems. For the interfacial height , with θ the contactangle and α the wedgetilt angle, we find βw = ζ(2)/2(1−ζ(3)). For pure systems (thermal disorder) we recover the known resultβw = 1/4 predicted by interfacial Hamiltonian studies whilst for random-bond disorder we predictthe universal critical exponent even in the presence of dispersion forces. We revisit the transfer matrix theory ofthree-dimensional filling based on an effective interfacial Hamiltonian model and discussthe interplay between breather, tilt and torsional interfacial fluctuations. We show that thecoupling of the modes allows the problem to be mapped onto a quantum mechanicalproblem as conjectured by previous authors. The form of the interfacial height probabilitydistribution function predicted by the transfer matrix approach is shown to be consistentwith scaling and thermodynamic requirements for distances close to and far from the wedgebottom respectively.

Latitude and magnetic flux dependence of the tilt angle of bipolar regions

Magnetogram data of 517 bipolar active regions are analyzed to study latitude, magnetic flux, polarity separation dependence of tilt angle of the active regions with well-defined bipolar magnetic configurations. The data were obtained at Huairou Solar Observing Station in Beijing during 1988 to October 2001. By statistical analysis, it is found: (1) The tilt angle (ψ) is a function of the latitude (θ). Our observed result, sinψ=0.5 sin θ, is in good agreement with that obtained by Wang and Sheeley (1991). (2) The tilt angle is a function of the magnetic flux. The tilt angle increases (decreases) with flux increasing when the flux is smaller (larger) than 5×1021 Mx. (3) The tilt angle is a function of the magnetic polarity separation. The tilt angle increases (decreases) with the separation increasing when the separation is smaller (larger) than 8×109 cm. (4) The magnetic flux (φ in 1020 Mx) is correlated to the magnetic polarity separation (d in Mm), following φ20∼d1.15. The result is close to the observed result of Wang and Sheeley (1989), φ20∼d1.3. (5) The tilt fluctuations are independent of the latitude, but depend slightly on the separation, which is similar to the result obtained by Fisher, Fan, and Howard (1995). (6) The distribution function of the ratio of net magnetic flux to total magnetic flux is almost centered around zero net flux. The imbalance of magnetic flux is lower than 10% for 47% of our samples; 31% of active regions are in imbalance of the magnetic flux between 10% and 20%.

Critical Behavior of Chiral Smectic Liquid Crystals

The phase transitions from the smectic - A phase to the ferroelectric smectic - C*, the antiferroelectric smectic - C*A and the incommensurate smectic - C*α phase are of the three dimensional (3D) XY universality class, where the soft mode condenses either at the edge, at the boundary or at a general point of the smectic Brillouin zone. High-resolution optical polarimetry and linear electro-optic response have been used to determine the temperature dependence of the order parameter in the antiferroelectric liquid crystals MHPOBC, MHP8CBC, EHPOBC, MHP10CBC and 10OTBBB1M7. The conclusions are: (i) In the smectic- A phase antiferroelectric liquid crystals exhibit unusually large tilt fluctuations, (ii) In most antiferroelectric liquid crystals, the critical exponents for tilt fluctuations are neither pure 3D XY nor Gaussian, but somewhat in between (iii) The “reconstructive” phase transitions between incommensurate, ferro-, ferri- and antiferroelectric phases are of first order. (iv) The discrete “clock” Landau model explains well the observed discontinuities, (v) The results of the resonant X-ray scattering experiment and optical polarimetry on 3 and 4-layer “clock” smectic phases are inconsistent.

Tectonic and eustatic control on Albian shallowing (Viking and Paddy Formations) in the Western Canada Foreland Basin

Late Albian shallowing in the Viking and Paddy Formations is investigated using a dynamic forward model on two cross sections through the Western Canada Foreland Basin. The model incorporates flexural loading of the evolving Cordilleran fold-and-thrust belt, sea-level changes, cratonic tilt, and in-plane stress fluctuations. The stratigraphic observations are explained either by a rapid eustatic sea-level drop or by eastward tilting of the North American craton during late Albian times. In both cases, southward increases in the vertical growth rates of the adjacent accretionary wedge are implied. Differences between the predicted stratigraphic patterns in the upper Albian formations of the western and southern parts of the Western Canada Foreland Basin demonstrate the complications arising from local tectonics in determining eustatic sea-level fluctuations from sequence stratigraphy. The models also show that changes both in the magnitudes of intraplate stress and in continental tilt forces can produce intrabasinal highs like those underlying the upper Albian formations in the basin. Furthermore, sediment loading is demonstrated to affect the stratigraphic patterns in relation to the sedimentation rate and the rate of change of accumulation space.