Isotropic and anisotropic physical properties of quasicrystals

Since quasicrystals have positional and orientational long-range order, they are essentially anisotropic. However, the researches show that some physical properties of quasicrystals are isotropic. On the other hand, quasicrystals have additional phason degrees of freedom which can influence on their physical behaviours. To reveal the quasicrystal anisotropy, we investigate the quasicrystal elasticity and other physical properties, such as thermal expansion, piezoelectric and piezoresistance, for which one must consider the contributions of the phason field. The results indicate that: for the elastic properties, within linear phonon domain all quasicrystals are isotropic, and within nonlinear phonon domain the planar quasicrystals are still isotropic but the icosahedral quasicrystals are anisotropic. Moreover, the nonlinear elastic properties due to the coupling between phonons and phasons may reveal the anisotropic structure of QCs. For the other physical properties all quasicrystals behave like isotropic media except for piezoresistance properties of icosahedral quasicrystals due to the phason field.     

Molecular dynamics simulations of thermodynamics,elastic constants and solid solution strengths for Mg-Gd alloys

The thermal and mechanical properties of Mg-Gd intermetallics MgGd, MgGd₂ and MgGd₃ are studied using a modified analytical embedded atom method. Calculated results agree well with the available experimental data and other theoretical results. The results on the elastic constants suggest that thermal softening behavior is observed as the temperature increases and the bulk moduli of ordered phases are larger than that of elemental Mg above 300 K. The heat capacities of MgGd, Mg₂Gd and Mg₃Gd are 22.91, 23.04 and 23.09 J mol K^-1, respectively, at 300 K. Furthermore, the addition of Gd gives rise to an increase of c/a. With the same content of Gd, the ratio c/a remains unchanged with increasing temperature, whereas this phenomenon does not occur in pure Mg, which indicates that the temperature-independent c/a restrains the occurrence of non-basal slip and twinning. Hence the addition of Gd can enhance the strength of Mg, in good agreement with experimental observation.     

TiC lattice dynamics from ab initio calculations

Ab initio calculations and a direct method have been applied to derive the phonon dispersion curves and phonon density of states for the TiC crystal. The results are compared and found to be in a good agreement with the experimental neutron scattering data. The force constants have been determined from the Hellmann-Feynman forces induced by atomic displacements in a supercell. The calculated phonon density of states suggests that vibrations of Ti atoms form acoustic branches, whereas the motion of C atoms is confined to optic branches. The elastic constants have been found using the deformation method and compared with the results obtained from acoustic phonon slopes. Received 23 February 1998     

Elastic Green's function of icosahedral quasicrystals

The elastic theory of quasicrystals considers, in addition to the “normal” displacement field, three “phason” degrees of freedom. We present an approximative solution for the elastic Green's function of icosahedral quasicrystals, assuming that the coupling between the phonons and phasons is small. Received: 18 December 1997 / Accepted: 6 March 1998     

Magneto-phonon contribution into the Young's modulus of gadolinium

Theoretical and experimental investigation has been made of the magnetic contribution to the Young's modulus of rare earth ferromagnet gadolinium. Experimental study includes measurements of the Young's modulus as a function of temperature, magnetic field and magnetization of gadolinium. Theoretical analysis is based on the account of phonon anharmonicity which gives rise to the dependence of Debye temperature on magnetization. Spontaneous magnetic contribution to the Young's modulus of Gd is found to be proportional to the squared magnetization of the metal. The magnetic contribution is also induced by magnetizing magnet due to the paraprocess. Received: 9 April 1996 / Revised: 26 January 1998 / Accepted: 26 February 1998     

Melting of the cooperative Jahn-Teller distortion in LaMnO 3 single crystal studied by Raman spectroscopy

We have studied the behavior of the Raman phonons of a stoichiometric LaMnO₃ single crystal as a function of temperature in the range between 77 K and 900 K. We focus on the three main phonon peaks of the Pbnm structure, related to the tilt, antisymmetric stretching (Jahn-Teller mode) and stretching modes of Mn-O octahedra. The phonon frequencies show a strong softening that can be fit taking into account their renormalization because of three phonon anharmonic effects in the pseudoharmonic approximation. Thermal expansion effects, in particular the variation of Mn-O bond lengths with temperature, are not relevant above 300 K. On the contrary, phonon width behavior deviates from the three phonon scattering processes well bellow T _c . The correlation between the magnitude of the cooperative Jahn-Teller distortion, that disappears at 800 K, and the amplitude of the Raman phonons in the orthorhombic phase is shown. Nevertheless, Pbnm phonons are still observable above this temperature. Phonon width and intensity behavior around T _c can be explained by local melting of the orbital order that begins quite below T _c and by fluctuations of the regular Mn-O octahedra that correspond to dynamic Jahn-Teller distortions. Received 25 January 2001 and Received in final form 14 March 2001     

Ab initio lattice dynamics and elastic constants of ZrC

Ab initio calculations and a direct method are applied to derive the phonon dispersion relations and phonon density of states for the ZrC crystal. The results are in good agreement with neutron scattering data. The force constants are determined from the Hellmann-Feynman forces induced by atomic displacements in a 222 supercell. The elastic constants are found using the deformation method and successfully compare with experimental data. Received 2 July 1999 and Received in final form 26 November 1999     

Mobility and conductivity of ionic and bonded defects in hydrogen-bonded chains with nonlinear interactions

The proton conductivity and the mobility arising from motions of the ionic and bonded defects, in hydrogen-bonded molecular systems are investigated by means of the quantum mechanical method. Our two component model goes beyond the usual classical harmonic interaction by inclusion of a quartic interaction potential between the nearest-neighbor protons. Among the rich variety of soliton patterns obtained in this model, we focus our attention to compact kink (kinkon) solutions to calculate analytically, the mobility of the kinkon-antikinkon pair and the specific electrical-conductivity of the protons transfer in the hydrogen-bonded systems under an externally applied electrical-field through the dynamic equation of the kinkon-antikinkon pair. For ice, the mobility and the electrical conductivity of the proton transfer obtained are about 5.307×10^-7 m²  V^-1  s^-1 and 6.11×10^-4 Ω^-1 m^-1, respectively. The results obtained are in qualitative agreement with experimental data.     

Soliton patterns and breakup thresholds in hydrogen-bonded chains

The dynamics of protons in hydrogen-bonded quasi one-dimensional networks are studied using a diatomic lattice model of protons and heavy ions including a φ⁴ on-site substrate potential. It is shows that the model with linear and nonlinear coupling of the quartic type between lattice sites for the protons admits a richer dynamics that cannot be produced with linear couplings alone. Depending on two types of physical boundary conditions, namely of the drop or condensate type, and on conditions requiring the presence of linear and nonlinear dispersion terms, soliton patterns of compact support, whether with a peak, drop, bell, cusp, shock, kink, bubble or loop structure, are obtained within a continuum approximation. Phase trajectories as well as analytical studies provide information on the disintegration of soliton patterns upon reaching some critical values of the lattice parameters. The total energies of soliton patterns are computed exactly in the continuum limit. We also show that when anharmonic interactions of the phonon are taken into account, the width and energy of soliton patterns are in qualitative agreement with experimental data.     

c-director relaxation around a vortex of strength +1 in free-standing smectic-C films

The relaxation of director fields in freely suspended smectic films is studied experimentally by means of polarizing microscopy, and analyzed by solving the torque balance equation under appropriate initial and boundary conditions. We consider in particular the role of anchoring conditions of the c-director at particles and defects in the film. The structure of regular relaxation patterns allows to determine the elastic anisotropy of smectic materials. The splay elastic constant can exceed the bend constant by a factor of two and more. A remarkable consequence of this anisotropy is the stick-slip-like relaxation around a central defect of topological strength s = + 1.     

Non-linear elastic behavior of light fibrous materials

Light fibrous materials composed of elastic fibers display a non-linear elastic behavior, where the non-linearity is due to the increase in the number of contacts between fibers under compression. Testing glass wool under compression up to 95% shows such a strongly non-linear behavior. A model is proposed to account for the divergence of the compressive stress as the strain approaches a threshold compression , with . Quantitative analysis of the experimental data on glass wool is fully consistent with this result. Received 2 February 1999     

Finite-temperature thermophysical properties of fcc-Ca

At an extreme environment, such as high-temperature and high-pressure, harmonic theory has obvious limitations, where the anharmonic effects are influential in determining bulk properties of the materials. In this regard, necessity for incorporating anharmonicity through vibrational contribution and thermally excited electrons to the total free energy at finite temperatures is illustrated taking an example of divalent fcc-Ca. In this regard, we have employed a coupling scheme of combining recently proposed mean-field potential (MFP) with the local pseudopotential to obtain vibrational contribution to the total free energy. To access the applicability of the present coupling scheme, we have calculated temperature variation of several thermodynamical properties. Static EOS, shock Hugoniot and temperature along principal Hugoniot are also estimated. Results are satisfactorily compared with the other theoretical and experimental data and the use of local pseudopotential in conjunction with the MFP approach is justified.     

Molecular Dynamics as a tool to interpret macroscopic amorphization-induced swelling in silicon carbide

We present here an investigation of the irradiation-induced swelling of SiC using Classical Molecular Dynamics simulations. Heavy ion irradiation has been assumed to affect the material in two steps: (a) creation of local atomic disorder, modeled by the introduction of extended amorphous areas with various sizes and shapes in a crystalline SiC sample at constant volume (b) induced swelling, determined through relaxation using Molecular Dynamics at constant pressure. This swelling has been computed as a function of the amorphous fraction introduced. Two different definitions of the amorphous fraction were introduced to enable meaningful comparisons of our calculations with experiments and elastic modeling. One definition based on the displacements relative to the ideal lattice positions was used to compare the Molecular Dynamics results with data from experiments combining ion implantations and channeled Rutherford Backscattering analyses. A second definition based on atomic coordination was used to compare the Molecular Dynamics results to those yielded by a simplified elastic model. The simulation results using the lattice-based definition of the amorphous fraction compare very well with the experimental results. This proves that the modeling in two steps chosen for the creation of the amorphous regions is reasonable. Moreover, the results show very clearly that SiC swelling does not scale linearly with the amorphous fraction introduced. Two swelling regimes are observed relatively to the size of the amorphous area. Comparison of the elastic model with the Molecular Dynamics results using the coordination-based definition of the amorphous fraction has also enabled us to shed light on the swelling mechanisms and has shown that amorphization-induced swelling exhibits an elastic behavior. Furthermore, scalings for the swelling as a function of the two amorphous fractions considered, which can be used by larger scale models, have been determined. Finally, our study shows that classical Molecular Dynamics calculations enable one to connect the results of the available experiments with the elastic calculations and to get further insight into the swelling mechanisms.     

Far-infrared optical properties of YVO4 single crystal

Near-normal incident infrared reflectivity spectra of a (001) YVO₄ single crystal have been measured at different temperatures in the frequency region between 100 and 6000 cm^-1. The reflectivity spectra are analyzed with the factorized form of the dielectric function, and the dielectric properties and optical conductivity of the YVO₄ crystal are obtained. From the TO/LO splitting, effective charges at different temperatures are calculated to study the ionicity of YVO₄. The internal modes of the VO₄^3- ion and the external modes of the Y(VO₄) lattice are compared with SiO₄^4- in zircon and with other rare-earth vanadates.     

Sonic stop-bands for cubic arrays of rigid inclusions in air

Extensive band structures have been computed for cubic arrays of rigid spheres and cubes in air. Complete stop bands are obtained for the face-centered-cubic (fcc) structure; however, there is no gap for the body-centered-cubic (bcc) and simple-cubic (sc) structures. These gaps start opening up for a filling fraction of (27%) for spherical (cubic) inclusions and tend to increase with the filling fraction, exhibiting a maximum at the close-packing. We also propose a tandem structure that allows the achievement of an ultrawideband filter for environmental or industrial noise in the desired frequency range. This work is motivated by the recent experimental measurement of sound attenuation on the sculpture, by Eusebio Sempere, exhibited at the Juan March Foundation in Madrid (Nature 378, 241 (1995)) and complements the corresponding theoretical work (Appl. Phys. Lett. 70, 3218 (1997)). Received: 24 October 1997 / Revised: 1 December 1997 and 26 January 1998 / Accepted: 6 March 1998     

Structural and elastic properties of Zr<Subscript>2</Subscript>AlX and Ti<Subscript>2</Subscript>AlX (X = C and N) under pressure effect

Using first-principles density functional calculations, the effect of high pressures, up to 20 GPa, on the structural and elastic properties of Zr₂AlX and Ti₂AlX, with X = C and N, were studied by means of the pseudo-potential plane-waves method. Calculations were performed within the local density approximation to the exchange-correlation approximation energy. The lattice constants and the internal parameters are in agreement with the available results. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline Zr₂AlX and Ti₂AlX aggregates. We estimated the Debye temperature of Zr₂AlX and Ti₂AlX from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Zr₂AlC, Zr₂AlN and Ti₂AlN compounds, and it still awaits experimental confirmation.     

Lehmann effect in a compensated cholesteric liquid crystal: Experimental evidence with fixed and gliding boundary conditions

In a recent letter (Europhys. Lett. 80, 26001 (2007)), we have shown that a compensated cholesteric liquid crystal (in which the macroscopic helix completely unwinds) may be subjected to a thermomechanical torque (the so-called Lehmann effect), in agreement with previous findings of éber and Jánossy (Mol. Cryst. Liq. Cryst. Lett. 72, 233 (1982)). These results prove that one must take into account the chirality of the molecules and the absence of inversion symmetry at the macroscopic scale when deriving the constitutive equations of the phase at the compensation temperature. In this paper, we present the details of our experimental work and a new experiment performed in a sample treated for planar gliding anchoring. The latter experiment, coupled with a numerical simulation, supports the existence of a thermomechanical coupling in a compensated cholesteric.     

Neural network learning dynamics in a path integral framework

Using the local-density approximation, calculating the Hellmann-Feynman forces and applying the direct method, the phonon dispersion relations for the rutile-like structure of crystalline SnO₂ have been derived for the first time. The phonon frequencies at the point agree very well with Raman and infrared data and other phenomenological model calculations. The LO/TO splitting is estimated by calculating phonons from an elongated supercell. The computations under pressure reveal a soft mode of B_1g symmetry which leads to a ferroelastic phase transition. The pressure-dependence of the lattice constants and the Grüneisen parameters of the modes are calculated. Received 18 July 1999     

Ab initio study of phonons and structural stabilities of the perovskite-type MgSi{O_3}

Using the local-density approximation, calculating the Hellmann-Feynman forces, applying the direct method and deriving the phonon dispersion relations, the stability of the perovskite-like structures of MgSiO₃ at T =0 have been studied. The cubic Pmm phase shows a dispersion-less soft phonon branch spreading from the R to M points of the cubic Brillouin zone. This soft branch persists up to high pressures of 150 GPa. The low-symmetry phases I4/mcm and Imma, P4/mbm can be considered as a result of the soft mode condensation at the M and R points, respectively. These phases prove to be unstable at T =0. The experimentally observed Pmnb phase is a consequence of the intersection of Imma and P4/mbm space groups. Thus, it can be regarded as a simultaneous condensation of two soft modes: one at the M and a second at the R high-symmetry points of the cubic Brillouin zone. The phonon dispersion relations of Pmnb show that this phase is stable and its optical phonons appear above 4.0 THz only. Received 15 October 1999 and Received in final form 14 January 2000