Birefringence and optical activity of CuAlSe2 single crystals

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 56, No. 1, pp. 81–85, January, 1992.     

Commensurate incommensurate phase transitions

there are two types of Commensurate-Incommensurate Phase Transitions : t_I between the basic structure and the incommensurate phasis and t_L between the inc. phasis and the lock in phasis. They both have connected structures. So that, they must verify the relation between crystallographic groups in accordance with Landau's Theory. But we have to consider the three phases in the superspace - as we do at an ordered-disordered magnetic transition-because the inc. phasis ins't a crystal in the physical space; e.g., in order to cancel the “middle range order” of the inc. phasis at t_I, we are led to assume the grey (point) group to the basic structure in the superspace. Now both inc. phase and basic structure verify the connection between point-groups in the superspace in the same way as both para and ferro phases do at a ferroic transition in the physical space. We also show that the same type of relation is possible at t_L and we give the order parameter at both t_I and t_L.     

On the satellite extinction in incommensurate phase

For ZnP₂ and CdP₂ crystals in incommensurate phase selective superstructure X-ray reflections are observed. As shown a phason and amplitudon excitation modes do not result in this selective extinction of satellites. Apparently, it is associated with a modulation wave form in the incommensurate phase. The X-ray spectrum peculiarity of incommensurate crystals is discussed taking into consideration systematic and selective extinction of satellites.     

Birefringence and phase transitions in liquid crystals

The birefringence of liquid-crystalline phases is the result of the parallel order of molecules exhibiting a polarizability anisotropy. The magnitude and sign of the birefringence are determined by the structure and order of the liquid-crystalline phase types as well as by the polarizability properties of the constituent molecules. The characteristic change of the birefringence at phase transitions between liquid-crystalline phases indicates more or less pronounced structural changes. The temperature dependence of the birefringence is due to the temperature change of the molecular order.

It is shown that the structural variety of the liquid crystalline state is reflected by a big variety of their optical anisotropy properties.     

On the incommensurate phase in modulated Heisenberg chains

Using the density matrix renormalization group method (DMRG) we calculate the magnetization of frustrated S=1/2 Heisenberg chains for various modulation patterns of the nearest neighbour coupling: commensurate, incommensurate with sinusoidal modulation and incommensurate with solitonic modulation. We focus on the order of the phase transition from the commensurate dimerized phase (D) to the incommensurate phase (I). It is shown that the order of the phase transition depends sensitively on the model. For the solitonic model in particular, a k-dependent elastic energy modifies the order of the transition. Furthermore, we calculate gaps in the incommensurate phase in adiabatic approximation. Received: 9 March 1998 / Accepted: 17 April 1998     

Birefringence and anisotropic optical absorption in porous silicon

The refractive indices and the coefficients of optical absorption by free charge carriers and local vibrations in porous silicon (por-Si) films, comprising nanometer-sized silicon residues (nanocrystals) separated by nanometer-sized pores (nanopores) formed in the course of electrochemical etching of the initial single crystal silicon, have been studied by polarization-resolved IR absorption spectroscopy techniques. It is shown that the birefringence observed in por-Si is related to the anisotropic shapes of nanocrystals and nanopores, while the anisotropy (dichroism) of absorption by the local vibrational modes is determined predominantly by the microrelief of the surface of nanocrystals. It is demonstrated that silicon-hydrogen surface bonds in nanocrystals can be restored by means of selective hydrogen thermodesorption with the formation of a considerable number of H-terminated surface Si-Si dimers.     

Dynamic mechanical relaxation and loss in the incommensurate phase of quartz

The dynamic mechanical properties of quartz have been studied as a function of temperature across the α-β phase transition and in the vicinity of the incommensurate (IC) phase on cooling from the β phase. The mechanical response of the IC phase shows strong anelasticity for measurement of Young's modulus (closely related to C(11) in our geometry) with modulated stress driven at 1 Hz. The dynamic shear modulus does not show similar strong effects in its imaginary component, although a very weak anomaly is barely detectable in the real part of the modulus. Our results indicate that the incommensurate microstructures within the quartz transition interval are susceptible to dilatational stress with relaxation times around 1 s.     

Dynamics of NaNO2 in the paraelectric and in the incommensurate phase

On the basis of a microscopic model with translation-rotation coupling, a set of coupled dynamic equations is derived. The corresponding resonances are studied in the paraelectric and in the incommensurate phase. The theory gives a qualitative explanation of inelastic neutron scattering results.     

Theoretical study of the magnetism in the incommensurate phase of TiOCl

Going beyond a recently proposed microscopic model [D. Mastrogiuseppe, A. Dobry, arXiv:0810.3018v1] for the incommensurate transition in the spin-Peierls TiOX (X=Cl, Br) compounds, in the present work we start by studying the thermodynamics of the model with XY spins and adiabatic phonons. We find that the system enters an incommensurate phase by a first order transition at a low temperature T_c1. At a higher temperature T_c2 a continuous transition to a uniform phase is found. Furthermore, we study the magnetism in the incommensurate phase by density matrix renormalization group (DMRG) calculations on a one-dimensional Heisenberg model where the exchange is modulated by the incommensurate atomic position pattern. When the wave vector q of the modulation is near π, we find local magnetized zones (LMZ) in which spins abandon their singlets as a result of the domain walls induced by the modulated distortion. When q moves far away enough from π, the LMZ disappear and the system develops incommensurate magnetic correlations induced by the structure. We discuss the relevance of this result regarding previous and future experiments in TiOCl.     

Features of the optical response of dielectric crystals with incommensurate phases

The constitutive relation describing the optical response of dielectric crystals in incommensurately modulated phases is derived for the plane-wave range of modulation. The symmetry properties of modulation corrections to the permittivity tensor of such crystals are analyzed with allowance for spatial dispersion. These properties are dictated by the Onsager principle for a nonabsorbing medium and by the mesoscopic periodicity of the medium. It is shown that the basic results are consistent with the general conventional approach in crystal optics of spatially inhomogeneous media.     

Soft mode at an incommensurate structural phase transition

We show within the RPA approximation that a soft mode is associated with an incommensurate structural phase transition in a simple microscopic model of two level ions interacting with the phonons of a crystal.