Conoscopic Figure Research Articles

Practice of the visual determination of the direction of light polarization plane rotation in the gyrotropic uniaxial single crystals

When studying and applying crystals of the middle category, it is necessary to take into account the manifestations of anisotropy of their properties, in particular, optical anisotropy. One of the manifestations of optical anisotropy is the rotation of the polarization plane (gyrotropy effect), which is observed in the direction of the optical axis of such crystals. The plane of polarization of light can rotate clockwise and counterclockwise. To determine the direction of rotation of the polarization plane, simple visual methods can be used based on studies of samples in converging polarized light – observations of conoscopic figures. In general, the type of conoscopic figures depends on the relative position of the polarizers, the wavelength of light in the system, the cut of the single crystal perpendicular to which the light propagates, the thickness of the sample and the birefringence. The direction of rotation of the polarization plane can be determined by еру change of the type of conoscopic figure of a sample of a gyrotropic crystal cut perpendicular to the optical axis: change of the central spot color during the analyzer rotation; the extinction of the central spot when observing a conoscopic figure using light filters; the direction of movement of the rings in monochromatic light; observation of Airy patterns. According to the experience of working in our laboratory “Single crystals and Stocke on their Base”, the simplest, most operational and unambiguous visual method for determining the direction of rotation of the polarization plane is the observation of Airy figures. A conoscopic pattern in the form of Airy figures (a four-way spiral) occurs when observing in converging polarized light a combination of two superimposed samples of gyrotropic crystals cut perpendicular to the optical axis, rotating the plane of polarization of light in opposite directions. To use this method, a well-known sample of a gyrotropic crystal cut perpendicular to the optical axis is required.

Petrographic structures and Hardy – Weinberg equilibrium

The article is devoted to the most narrative side of modern petrography – the definition, classification and nomenclature of petrographic structures. We suggest a mathematical formalism using the theory of quadratic forms (with a promising extension to algebraic forms of the third and fourth orders) and statistics of binary (ternary and quaternary, respectively) intergranular contacts in a polymineralic rock. It allows constructing a complete classification of petrographic structures with boundaries corresponding to Hardy – Weinberg equilibria. The algebraic expression of the petrographic structure is the canonical diagonal form of the symmetric probability matrix of binary intergranular contacts in the rock. Each petrographic structure is uniquely associated with a structural indicatrix – the central quadratic surface in n-dimensional space, where n is the number of minerals composing the rock. Structural indicatrix is an analogue of the conoscopic figure used for optical recognition of minerals. We show that the continuity of changes in the organization of rocks (i.e., the probabilities of various intergranular contacts) does not contradict a dramatic change in the structure of the rocks, neighboring within the classification. This solved the problem, which seemed insoluble to A.Harker and E.S.Fedorov. The technique was used to describe the granite structures of the Salminsky pluton (Karelia) and the Akzhailau massif (Kazakhstan) and is potentially applicable for the monotonous strata differentiation, section correlation, or wherever an unambiguous, reproducible determination of petrographic structures is needed. An important promising task of the method is to extract rocks' genetic information from the obtained data.

Electronic intervalence Fe2+ + Ti4+ → Fe3+ + Ti3+ charge-transfer transition in ilmenite

The optical absorption spectrum of natural ilmenite was measured on a narrow translucent rim zone of a thin polished slide of thickness ca. 0.004 mm, mounted with epoxy resin upon a supporting glass plate. The color of the material in the zone is dark red. At conoscopic observation between crossed Nicols, it displays a very dark, vague, off-centered conoscopic figure. Unpolarized optical absorption spectrum of ilmenite, measured in the transparent zone, consists of a very intense high-energy absorption edge which covers a major part of the visible range and causes the dark-red color of ilmenite. On the edge tail, which extends far to the NIR range, there is an intense, broad, asymmetric, vaguely structured absorption band with maximum at around 7000 cm−1. On the account of high iron and titanium contents (0.82 and 0.86 apfu, respectively), it may confidently be attributed to Fe2+/Ti4+ IVCT transition, though its energy is unusually low compared to other Fe2+, Ti4+-bearing minerals studied so far. This most probably proved that the effect of lowering of energy of IVCT bands with increasing number of ion pairs, established by Amthauer and Rossman (Phys Chem Miner 11:37–51 1984), on Fe2+/Fe3+ IVCT bands also takes place in case of electronic Fe2+/Ti4+ IVCT transition in ilmenite.

Conoscopic figure: a complex consequence of a not so simple phenomenon

Observation of conoscopic figures through a special microscope is widely used as an experimental method for determination of optical properties of anisotropic materials. The conoscopic figure appears when a divergent light passes through an anisotropic material sandwiched between crossed polarizers. The complex pattern of bright and dark areas appears due to different polarization states of light. The pattern gives information about optical axes and birefringence of the material and allows for deduction of microscopic structures at the origin of such properties. Due to the complexity of the figure, the method is often used following recipes. This contribution presents a series of experiments that provide students with experiences needed for construction and comprehension of optical phenomena that contribute to the complexity of the conoscopic figure.

Two crystal plates variable phase retarder system

The system of two crystal plates with the particular orientation of optical axis and location plates relatively to each other can be used as adjustable retarder with specific properties. The phase difference between ordinary and extraordinary beams depends on plates thickness an angle between plates and incidence angle of light on two plates system. Under certain conditions system is characterized by a special direction – pseudo optical axis. This direction can be detected experimentally by observing the interference picture – conoscopic figure of optical system.

Nematic biaxiality in a bent-core material

The results of a recent investigation of the nematic biaxiality in a bent-core mesogen (A131) are in apparent disagreement with earlier claims. Samples of mesogen A131 used in the two studies were investigated with polarized optical microscopy, conoscopy, carbon-13 NMR, and crossover frequency measurements. The results demonstrate that textural changes associated with the growth of biaxial nematic order appear at ∼149 °C. The Maltese cross observed in the conoscopic figure gradually splits into two isogyres at lower temperatures indicating phase biaxiality. Presence of the uniaxial to biaxial nematic phase transition is further confirmed by temperature trends of local order parameters based on 13C chemical shifts in NMR experiments. Frequency switching measurements also clearly reveal a transition at 149 °C. Differences between the two reports appear to be related to the presence of solvent, impurities, and/or adsorbed gases in samples of A131 used in the study of Van Le [Phys. Rev. E 79, 030701 (2009)].

Conoscopic observation of director reorientation during Poiseuille flow of a nematic liquid crystal

Director reorientation under pressure driven (Poiseuille) flow is observed conoscopically for the liquid crystal 5CB aligned at an azimuthal angle of 45° to the direction of flow. A polyimide surface treatment (AL 1254) is used to promote planar homogeneous alignment and rubbed to produce an initial azimuthal alignment angle ϕ0. Conoscopic interference figure rotation is documented as a function of flow rate and compared to that produced from numerical models using Leslie–Ericksen–Parodi theory. Model and data show excellent agreement.

Analysis of the conoscopic measurement for uniaxial liquid-crystal tilt angles

Conoscopy as an optical method for accurate measurement of crystal tilt angles from interference figures is analyzed for the special case of uniaxial crystals. The displacement of interference figures is related to the crystal tilt angle in an explicit, noniterative manner that is accurate to within ~2%. The analysis applies to uniaxial nematic liquid-crystal monodomains and homogeneous crystals when a symmetrical center of the conoscopic interference figure is visible. The equations developed are also used to derive other previously reported expressions that are approximations with a limited range of applicability.

Induced Smectic Phase Formed by New Liquid Crystalline Binary Systems Consisting of Main Chain Polymer and Twin Compound

Abstract The thermal and mesomorphic properties of the new liquid crystalline binary systems, consisting of a nematic main chain liquid crystalline polymer and a nematic twin liquid crystal, have been studied. The liquid crystalline binary systems formed an induced smectic A phase, which was characterized by a uniaxial conoscopic figure, a fan texture, and a broad X-ray scattering peak at the wide angle.

Optical anisotropy of polyimide

AbstractOptical anisotropy of polyimide films prepared from polyamic acid solutions was investigated by conoscopic observation and refractive index measurements. The conoscopic figure (crossed pattern) characteristic of a negative uniaxial crystal with its optic axis perpendicular to the film plane was observed for samples imidized on substrates. Uniaxial drawing of a polyamic acid cast film with 40 wt % solvent gave a highly oriented sample with an elongation of more than 80%. This sample had a conoscopic figure characteristic of a positive uniaxial crystal with its optic axis equivalent to the molecular c axis (parallel to the film plane). A large optical anisotropy (bire‐fringence 0.18) was observed in the film plane. The TE‐mode refractive index (parallel to the film plane) ranged from 1.64 to 1.82 at a wavelength of 633 nm according to the sample rotation. These values corresponded to the refractive indices perpendicular and parallel to the c axis, respectively. The optical system change of the polyimide film was explained in terms of the uniaxial orientation of the in‐plane oriented molecular c axis.

Molecular Orientational Structures in Ferroelectric, Ferrielectric and Antiferroelectric Smectic Liquid Crystal Phases as Studied by Conoscope Observation

Molecular orientational structures in MHPOBC were studied by means of conoscope observation. Contrary to a ferroelectric response of the conoscope to an electric field in the smectic C* phase, the conoscopic figure in the antiferroelectric smectic CA* phase does not shift its center and is biaxial with its optic plane perpendicular to the field direction. This conoscope change is only due to a dielectric contribution, indicating the existence of the inherent threshold in the electric field induced transition to the ferroelectric phase. In between the ferroelectric and antiferroelectric phases, a kind of ferrielectric phase was clearly distinguished in the field response of the conoscopic figure; the shift of the conoscope center perpendicular to the applied field and the biaxial optic plane parallel to the field suggest a novel molecular orientational structure.

Properties of morphotropic phase boundary lead barium niobate (PBN) compositions

Abstract Investigations of the polarization mechanisms in tungsten bronze ferroelectric, Pb1−xBaxNb2O6, in particular of the morphotropic phase boundary compositions, have been carried out for both ceramics and bulk crystals by means of electrical, optical, and electron microscopic methods. It is demonstrated by optical conoscopic interference figure that electric field can switch the crystal from one ferroelectric phase to the other for compositions close to the morphotropic phase boundary. A TEM study in the temperature range from—180°C to room temperature revealed the presence of ferroelectric domains and discommensurate structures associated with octahedral rotations in the PBN crystals and ceramics. In the light of above observed experimental data, the polarization mechanisms of the morphotropic phase boundary compositions are discussed.

Determination of the direction of the crystal optical axis of ground uniaxial precious stones by means of polarized‐light microscope photometry

SUMMARYThe direction of the crystal optical axis of a uniaxial microscopic object is determined on the basis of the known correlation between this direction, the displacement of isogyres of the conoscopic figure, and the rotation of the microscope stage. It is shown that the use of photoelectric equipment for indicating the displacement, a stepping motor controlled by a microprocessor for rotating the stage, and a desk calculator for processing the photometric data provides a more convenient and accurate determination than classicial procedures, involving visual inspection and manual operation. The method is particularly suitable for uniaxial crystals of the size and shape of precious stones.

Dependence of Temporal Behavior of Conoscopic Figures in Nematic Liquid Crystals on Film Thickness

The time required to form the conoscopic figure in nematic liquid crystals after the electric field is turned on and off is studied temporally, varying the thickness of the twisted film. The effect of the film thickness on the temporal behavior of the conoscopic figure is remarkable. The film thickness at which the conoscopic figure can be formed fastest is about 9 or 14 µm under 1 V/µm and the formation of the conoscopic figure depends strongly on the electric field strength. Reformation and rotatory motion of the conoscopic figure are observed after the electric field is turned off, and figures similar to those of a biaxial crystal are observed in films of thickness greater than 20 µm.

Dependence of Temporal Behavior of Conoscopic Figures in Nematic Liquid Crystals on Initial Alignment

How the bound force between the boundary surface and the aligned liquid crystal molecules affects the formation of the conoscopic figure after the electric field is turned on and turned off is studied in twisted thin film and homogeneous thin film. The formation of the conoscopic figure depends strongly on the initial basic alignment (twisted or homogeneous) and depends on the elastic modulus, but its temporal behavior depends only slightly on the pretilt angle (3 degrees or 30 degrees) and the coefficient of viscosity. The temporal change of the deformations obtained in the experiment is compared with the change in the deformations calculated from a Voigt model in the rheological theory, and qualitative agreement is obtained.

Conoscopic Study of Liquid Crystal after Application and Removal of the External Electric Field

The temporal changes of conoscopic figures of electrically driven twisted nematic liquid crystal film are observed using a commonly available video camera. The unavoidable time lag effect of 16 ms of the lower side area of the image field of video camera compared with the upper side area which is caused by the finite scan time of the video camera is decreased to 2 ms by introduction of a “montage method”. By this method, the conoscopic figures are observed during a period of 0∼16 ms after turning on and turning off of the external electric field. The general behavior of L.C. molecules during this time interval confirm results reported in the previous paper (Jpn. J. Appl. Phys. 21 (1982) L616). Crystal optical consideration of the observed conoscopic figure is presented.

Viscoelastic twist properties of some nematic liquid crystalline azoxybenzenes

The static and dynamic behavior of the Frederiks transition for twist of a uniform planar nematic sample in an external magnetic field has been studied by monitoring the associated conoscopic figure. In particular, the decay of this figure after the field has been switched off is considered in detail in order to obtain results for the twist viscosity γ1. Results for the twist elastic constant K2 and for the viscosity γ1 are reported for the homologous series of p, p′-dialkylazoxybenzenes. K2 is found to be smaller than both K1 and K3, while K2 varies little along the series. The temperature dependence of γ1 can be described by a combination of an activated process and a term depending on the orientational order parameter.

Biaxiality in relation to visible twinning in experimentally deformed calcite

Moderate to strong biaxiality (2V = 10 °–45 °) in experimentally deformed calcite (in single crystals and in marble) is attributed to overlap between one or two thin {01¯12} twin lamellae and the enclosing host. A perfectly centered conoscopic figure (section normal to [0001]) is perceptibly asymmetric about the trace of the optic axial plane. This asymmetry is pronouned in thick sections (> 0.04 mm) and completely distrupts the biaxial configuration of the figure if the overlapping lamella exceeds about 0.0025 mm in thickness. In sections somewhat oblique to [0001] and cut at 20 ° or less to the plane of twinning the conoscopic figure may appear to be perfectly biaxial-expecially in thin sections (∼ 0.02 mm) enclosing thin (∼ 0.001 mm) but still visible twins.