Symmetry relations for the phase matrix of horizontally oriented particles

Seven symmetry relations, with a wide range of validity, are presented for the phase matrix of horizontally oriented particles. Three of these relations constitute a fundamental basis from which four others can be derived by making combinations. All seven relations can be used for many types of particles, including hexagonal plates and columns as well as spheroids, cylinders and cubes. Some applications are also pointed out.     

Scattering matrices for horizontally oriented ice crystals

Scattering matrices for horizontally oriented ice crystals are calculated with a code based on the geometric optics. The main physical regularities inherent to the scattering matrices are discussed. Degree of polarization of the scattered light is shown to be a qualitative criterion of number of photon trajectories that contribute effectively to the scattered light. The inverse scattering problem of retrieving aspect ratios of the horizontally oriented hexagonal ice plates from polarization of the scattered light in the bistatic sounding scheme has been proposed and discussed.     

随机取向六角形冰晶粒子的散射特性研究

利用离散偶极子近似方法研究卷云中随机取向六角形冰晶粒子的取向比对散射特性的影响,数值计算了在小尺度范围内随机取向六角形冰晶粒子的散射特征量,包括散射相函数、消光效率因子、不对称因子、单次散射反照率和线偏振度。研究表明:取向比对随机取向六角形冰晶粒子散射特征量的影响比较明显,并且此影响随着粒子尺度参数的变化而变化,与入射波长无关;相同尺度参量和不同取向比粒子的散射相函数的角分布曲线均有一个交点,并且随着粒子尺度参量的增加,交点所对应的散射角度值逐渐向小角度方向移动。此研究结果为气溶胶粒形检测和识别提供了理论依据。     

Scattering by randomly oriented thin ice disks with moderate equivalent-sphere size parameters

We use the T-matrix method to compute the scattering matrix for randomly oriented circular ice cylinders with diameter-to-length ratios 1 and 20 and surface-equivalent-sphere size parameters up to 12. We show that wavelength-sized, sharp-edged ice plates with extreme diameter-to-length ratios possess the same scattering properties as smooth platelike spheroids: their phase functions are similar to those of surface-equivalent compact particles, whereas all other elements of the scattering matrix are typical of Rayleigh scattering.     

Light scattering by some nematic liquid crystals due to phase transitions

New computer modelling of light scattering and its propagation through liquid crystal has been presented using T-matrix method in the structural phase transition regions. Numerical aspects of light scattering process, which are based on numerically solving Maxwell's equations, were calculated for some nematic liquid crystals. Firstly, we described in detail T-matrix method for computing light scattering from nematic liquid crystals and presented results of benchmark computations for the considered model. We reported results of extensive calculations for polydisperse, randomly oriented rod-like multilayered systems (nematic liquid crystals). Our results are associated with light scattering by ferroelectric and ferroelastic materials.     

水平层状介质并矢Green函数的递推矩阵方法

采用递推矩阵方法计算任意数目水平层状介质的并矢Green函数.根据层界面处电场和磁场的连续性条件得到3个确定Sommerfeld积分待定系数的矩阵方程组,分别对应于垂向单位电偶极子产生的TM波、水平方向单位电偶极子产生的TE波和TM波,这些方程组均可通过递推方法快速求解.只需改变3个方程组中源项元素的位置,就可以方便地得到当源点和场点在任意层时的并矢Green函数.本文给出的并矢Green函数表达式形式简洁且不含指数增加项,计算时不会出现溢出现象.     

Size and Shape Prediction of Colloidal Metal Oxide MgBaFeO Particles from Light Scattering Measurements

The size and structure of colloidal metal oxide (MgBaFeO) particles are determined using an Elliptically Polarized Light Scattering (EPLS) technique. The approach is based on a hybrid experimental/theoretical study where the experimental data are compared against predictions obtained using a T-Matrix model that accounts for particle shape irregularities. A power-law distribution function with two parameters is employed to account for the particle size distribution. The refractive index of the particles in ethyl alcohol is calculated based on the Maxwell-Garnet formula. The experiments are conducted using a second-generation nephelometer. It is shown that the current EPLS measurements can effectively be used for identification of both the shape and the size of the colloids.     

Characterization of phase transition in liquid crystals by voltaic potential difference

Our investigations show that the determination of voltaic potential differences is a useful method to characterize the phase transition N → I and I → N for a liquid-crystal (LC) mixture and for a phase transition from one liquid-crystalline phase into another. The ΔV/T curves show reversible as well as an irreversible behaviour. Moreover, the transition from the smectic into the nematic phase is demonstrated on liquid-crystalline polymers.     

Influence of hydrogen on structural and magnetic properties of the hexagonal Laves phase HoMn2

The HoMn₂ compound crystallizes in the cubic C15 or hexagonal C14 Laves phases depending on preparation. The effect of hydrogen absorption on structural and magnetic properties of HoMn₂H_x hydrides for the C14 phase has been investigated by XRD and AC/DC magnetometry in the temperature ranges of 75-380 K and 4-390 K, respectively. In addition to general features revealed by RMn₂H_x compounds (R=rare earth or Yttrium), unusual behavior of these hydrides was found. In particular, a transformation from the hexagonal to the monoclinic structure was detected, the same as that observed for cubic HoMn₂H_x compounds. The structural transformations are correlated to the magnetic behavior. The presented results are compared mainly with the properties of the cubic HoMn₂H_x hydrides as well as with those of other RMn₂H_x hydrides. Tentative magnetic and structural phase diagrams are proposed.     

Dielectric and ultrasonic investigation of phase transition in cuinp2s6 crystals

Investigation results of dielectric and ultrasonic properties of layered CuInP₂S₆ crystals are presented. At low frequencies, dielectric spectra are highly influenced by the high ionic conductivity with the activation energy of 7357.4?K (0.635?eV). The high-frequency part of the spectra is determined by relaxational soft mode. The critical slowing down and Debye-type dispersion show the order–disorder type of the phase transition. The temperature dependence of the relaxational soft mode and dielectric contribution show a quasi-one-dimensional behaviour. Ultrasonic velocity exhibits critical slowing down which is accompanied by attenuation peaks in the phase transition region. Layered CuInP₂S₆ crystals have extremely large elastic nonlinearity in the direction perpendicular to layers. The nonlinear elastic parameters substantially increases at the PT temperature.     

Influence of pressure on the electric-field-induced phase transitions in liquid crystals

Within the framework of Landau-de-Gennes formulation, we analyse the effect of pressure on electric-field-induced phase transitions in a liquid crystal which shows spontaneously an isotropic-smectic A transition. Inferring from the experimental pressure dependences on the layer spacing in smectic A phase, as well as the nematic-smectic A metastable temperature T^*_AN, we incorporated the pressure dependence in the free energy through (the surface energy term) and the coupling between the quadrupolar nematic ordering Q_ij and the smectic order parameter ψ. From the S-T phase diagram, we found that the stability of field-induced nematic phase increases with pressure, whereas the discontinuity of the transition decreases. Also, the region where paranematic phase transits directly to smectic A phase increases with pressure.     

Performance of discrete dipole approximation for prediction of amplitude and phase of electromagnetic scattering by particles

Electromagnetic scattering provides useful signatures for nonintrusive particle characterization. Scattered wave which carries characteristic information about particles is identified completely by its intensity, polarization state and phase. Recent developments in measurement techniques have enabled measurement of phase of the scattered wave which is a source of additional information about particles. In the present study, accuracy of discrete dipole approximation (DDA) in predicting amplitude and phase of scattered wave is investigated via publicly available DDSCAT code by Draine and Flatau, which is a well-established tool for DDA and has found wide range of applications in the literature due to its flexibility. DDSCAT routine is modified to enable accurate computation of phase of complex amplitude scattering matrix (ASM) elements as well as their magnitude. DDA method was implemented by using lattice dispersion relation for dipole polarizabilities, generalized prime factor algorithm for fast-Fourier transformation and pre-conditioned bi-conjugate gradient method with stabilization for the solution of the complex linear system of equations. Accuracy of ASM elements predicted by DDA is assessed on single sphere problems with various size parameters and refractive indices by validation against Mie theory solutions. Excellent agreement between predictions and exact solutions proves the reliability of the modified DDSCAT code for prediction of amplitude and phase of scattered electromagnetic wave. Applicability conditions and requirements of the present DDA application to ensure accurate prediction of complete set of scattering parameters are mapped for single spheres, on an extensive domain of size parameters and refractive indices. A correlation is presented to estimate the magnitude and phase errors associated with given size parameter, refractive index and cubic lattice subdivision. Assessment of computational time requirements for different optical constants shows that implementation of DDA with the present specifications is unfeasible for size parameters larger than 4 when Re(m)>2 and Im(m)<0.1 at the same time, due to slow convergence rate.     

About the poor decay of certain cross-correlation functions in the statistical mechanics of phase transitions in the static and dynamical regime

We introduce a method to prove poor decay of certain cross-correlation functions which are closely related to the phase transition. The methods apply both to equal and nonequal times, which gives access to the dynamical regime. We establish a criterion which displays openly what happens when the Goldstone picture breaks down. Since no rudiments of translation invariance are needed the treatment covers phases in coexistence like, e.g., liquid-gas interfaces and completely inhomogeneous systems. Furthermore a perhaps surprising connection with the breaking of time reflection invariance of the equilibrium state is established.     

Light scattering and absorption by densely packed groups of spherical particles

Light scattering by clusters of spheres is investigated using numerical light scattering simulations. We consider clusters with density of 0.1-30%. Simulations are carried out for various real part of refractive indices (i.e., 1.01, 1.10, 1.31, 1.60, and 2.00) and for two values of the imaginary part of the refractive index (0 and 0.01) of spheres in the cluster. All spheres in the cluster have the same size (kr=4, k=2π/λ, r is the radius of the sphere, λ is the wavelength of the incident light).The obtained results include behaviors of cross sections as functions of densities (up to 30%), investigation of the influence of multiple scattering inside the media on the cross sections, and influence of densities on phase matrix elements (PMEs) and parameters obtained from the PMEs such as the cross polarization ratio, degree of linear depolarization, entropy, etc.In addition, we also investigate the influence of particle size for the same total volume of the cluster on cross sections. The outer radius R of the cluster of spheres was constant and equal to 40/k in all calculations.     

Probing the material properties and phase transitions of ferroelectric liquid crystals by determination of the Landau potential

The full Landau potential of several, widely varying ferroelectric liquid-crystalline materials has been experimentally determined. Tilt angle and polarisation data is analysed across the SmA to SmC transition for varying applied electric-field amplitudes, allowing the determination of all the coefficients of the generalised Landau model of ferroelectric liquid crystals. The materials investigated encompass different materials, including low-polarisation mixtures to high-polarisation single-component materials. The materials also possess a variation in the order of the SmA to SmC phase transition from strongly first order to strongly second order. The effects of both the polarisation and order of phase transition of the system are discussed with respect to the various terms of the generalised Landau model. Further, the mechanisms behind the difference between a first- and second-order phase transition are discussed with respect to the Landau potential and the second Landau coefficient b .     

Brillouin scattering study of phase transitions in LiK0.80(NH4)0.20SO4 mixed crystals

Brillouin spectroscopy was used to study the phase transitions of LiK_0.80(NH₄)_0.20SO₄ mixed crystals in the temperature range 10-300 K. The relevant elastic stiffness coefficients were evaluated at room temperature. The quasi-longitudinal γ₁₆ and the quasi-transverse γ₁₇ mode frequencies were measured in the above temperature range. From their frequency vs. temperature curve, three different phase transitions were determined. Two of the four phases presented by the crystal were found to be ferroelastic. The observed phases are tentatively assigned through a comparison with the phase transitions undergone by LiKSO₄ and LiK_0.96(NH₄)_0.04SO₄ crystals. An anomalous behavior of the Brillouin linewidth near the 260 K phase transition was observed.     

Investigation of phase transition mechanisms of CsH3(SeO3)2 single crystals by observation of nuclear magnetic resonance

The relaxation times of the ¹H and ¹³³Cs nuclei in CsH₃(SeO₃)₂ crystals were investigated using FT NMR. The ¹³³Cs spectrum does change from seven resonance lines to one resonance line near T_m (=350 K). The presence of only one ¹³³Cs signal is due to the liquid state resulting from the melting of the crystal. The variation in the separation of the ¹³³Cs resonance lines with temperature indicates that the EFG at the Cs sites produced by the (SeO₃)²⁻ groups varies with temperature, which in turn means that the atoms neighboring ¹³³Cs are displaced. And, the T₁ for ¹³³Cs is very long and undergoes significant changes near T_m. The change in the temperature dependence of T₁ at T_m for the ¹³³Cs nuclei coincides with the melting temperature. These results are compared with those obtained for MH₃(SeO₃)₂ (M=Na, K, and Cs) crystals.     

Study of the ferroelectric–paraelectric phase transition of NaH3(SeO3)2 single crystals by H and Na NMR

The ¹H and ²³Na spin–lattice and spin–spin relaxation times of NaH₃(SeO₃)₂ single crystals grown using the slow-evaporation method were measured as functions of temperature and frequency in the ferroelectric and paraelectric phases. The changes in the symmetry of the (SeO₃)²⁻ dimers as a result of the ferroelectric–paraelectric phase transition are associated with large changes in the spin–lattice and spin–spin relaxation times, and in the number of resonance lines. The large changes in the relaxation times at 195 K indicate that the H and Na ions are significantly affected by this transition. The change in the number of resonance lines for the ¹H and ²³Na nuclei means that the orientations of the (SeO₃)²⁻ dimers and the environments of the Na ions change at T_C. Therefore, the orientations of the (SeO₃)²⁻ dimers and the environments of the Na ions play important roles in the phase transitions. In conclusion, the ferroelectric–paraelectric phase transition of NaH₃(SeO₃)₂ is accompanied by changes in hydrogen-bond structure and distortions of the (SeO₃)²⁻ and Na⁺ ion lattices, which form a slightly distorted octahedron.     

Laser Raman study of phase transformations in [N(CH3)4]2ZnCI4 single crystals

We report temperature-dependent Raman studies on single crystals of [N(CH₃)₄]₂ZnCI₄ from 300 to 10 K. The observed spectral features suggest that both the N(CH₃)₄ ⁺ and ZnCl^2- ₄ ions are distorted from their regular tetrahedral structure and occupy sites of C_s symmetry in the lattice at room temperature. From the variation of line width of some selected Raman bands and other spectral changes as a function of temperature, it is inferred that both the ZnCl^2- ₄ and—CH₃ groups have high motional freedom at room temperature and the different phase transitions up to 160 K are triggered by the gradual freezing-in of orientational freedom of these groups, while the N—C₄ tetrahedra do not play any significant role in these phase transitions. The monoclinic to orthorhombic superlattice phase transitions at 159 K is triggered by freezing-in of the orientational motions of both the ZnCl^2- ₄ and N(CH₃)⁺ ₄ groups in the lattice.