Hypersonic wave anomalies in Cs3H(SeO4)2 at the transitions above room temperature

The elastic properties of Cs3H ( SeO4 ) ₂ are investigated by Brillouin spectroscopy in the temperature range 20-220 covering the two transitions III II and II I occurring at and , respectively. Phase I is known to be a protonic conductive one. Discontinuities of elastic constants are generally observed at both transitions, implying first orderness. In phases II and I, a slight broadening of the Brillouin lines is detected. The results are discussed in comparison with compounds of the families XHSeO4 (X = NH4, Rb and Cs) and CsH2BO4 (B = As and P) which also undergo a transition to a superionic phase. In the conductive phase, it appears that the lattice anharmonicity is weaker in Cs3H ( SeO4 ) ₂ than in these other compounds. Received 16 October 1998     

Elastic anomalies and orientational glass transition in Na(CN) Cl mixed crystals. A Brillouin spectroscopic study

High performance Brillouin spectroscopy (BS) has been used to study the elastic properties (static and dynamic) of the orientational glassy state of Na(CN)_xCl_1-x samples ). The temperature behaviour of the elastic properties reveals a more complex scenario for the orientational glass transition than generally believed. The shear elastic constant shows the well-known c ₄₄ ( T ) anomaly, indicated by a minimum, found in other cyanide mixed crystals. The results obtained for the hypersonic attenuation are in clear contradiction with the dynamic character of the c ₄₄ ( T )-minimum. The temperature behaviour of the longitudinal elastic constant c₁₁ of very dilute Na(CN)_xCl_1-x samples shows two striking features: i) Similar to the anomalous temperature behaviour of c ₄₄ ( T ), lowering the temperature c ₁₁ ( T ) first decreases, goes through a minimum and then rises again. The minimum takes place at a temperature above the temperature, , where c ₄₄ ( T ) reaches its minimum value. ii) A kink-like anomaly of c ₁₁ ( T ) is observed at lower temperatures. This second anomaly is similar to the classical one observed in canonical glasses at their glass transition temperature . Received 8 April 1999 and Received in final form 3 June 1999     

Prediction of cell variations with pressure of ionic layered crystal Application to the matlockite family

Compounds belonging to the matlockite family are ionic layered crystals. Some previous experimental studies on these compounds demonstrated the correlation between the difference in bond strength translating the layered properties and the anisotropic coordination of the highly polarizable halogen anion. In the present paper, we present a model to estimate the anisotropic compressibilities of matlockites which could be generalized to other ionic layered compounds. The compressibilities of each individual polyhedron which built the sheet of an ionic layered crystal are determined from a simple relation based on a semi-empirical relation obtained by Hazen et al., involving the electrical charge of the ions and the interatomic distances. The electrical charge of the anions are taken to be direction-dependent and are modulated by the anion polarizability value. Finally, to validate the model, the calculated compressibilities are compared with previously published data, but also with new high pressure experimental data obtained by X-ray absorption spectroscopy up to 20 GPa on SrFCl and SrFBr at the K edge of the strontium and by X-ray diffraction up to 30 GPa on SrFBr and PbFBr. Present estimations give results which differ from the experimental values by less than 15%. Received 26 October 1998     

Brillouin spectroscopy on monodomains of thin polycrystalline layers of molecular crystals

An unconventional Brillouin-spectroscopic technique is proposed to determine elastic stiffness tensor coefficients of molecular crystals. With 90A Brillouin measurements on thin monodomains of melt-crystallized films (about 30 μm thickness) the need to grow large single crystals is avoided. Measurements on sym-difluorotetrachloroethane and perfluoroeicosane are presented.     

Structural and elastic properties under pressure effect of the cubic antiperovskite compounds ANCa3 (A = P, As, Sb, and Bi)

Using first-principles density functional calculations, the effect of high pressures, up to 40 GPa, on the structural and elastic properties of ANCa₃, with A = P, As, Sb, and Bi, were studied by means of the pseudo-potential plane-waves method. Calculations were performed within the local density approximation and the generalized gradient approximation for exchange-correlation effects. The lattice constants are in good 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 modulus, Poisson's ratio and Lamé's constants for ideal polycrystalline ANCa₃ aggregates. By analysing the ratio between the bulk and shear moduli, we conclude that ANCa₃ compounds are brittle in nature. We estimated the Debye temperature of ANCa₃ from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of PNCa₃, AsNCa₃, SbNCa₃, and BiNCa₃ compounds, and it still awaits experimental confirmation.     

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     

Analytical solution of 1D Ising-like systems modified by weak long range interaction

It is well-known that 1D systems with only nearest neighbour interaction exhibit no phase transition. It is shown that the presence of a small long range interaction treated by the mean field approximation in addition to strong nearest neighbour interaction gives rise to hysteresis curves of large width. This situation is believed to exist in spin crossover systems where by the deformation of the spin changing molecules, an elastic coupling leads to a long range interaction, and strong bonding between the molecules in a chain compound leads to large values for nearest neighbour interaction constants. For this interaction scheme an analytical solution has been derived and the interplay between these two types of interaction is discussed on the basis of experimental data of the chain compound which exhibits a very large hysteresis of 50 K above RT at 370 K. The width and shape of the hysteresis loop depend on the balance between long and short range interaction. For short range interaction energies much larger than the transition temperature the hysteresis width is determined by the long range interaction alone. Received 26 November 1998     

Brillouin scattering study of transverse elastic waves in the α, incommensurate and β phases of AlPO4

Transverse and pseudo-transverse elastic waves have been studied in several scattering geometries in order to investigate the temperature dependences of C E ₆₆ and C E ₁₄ over the range 300-1100 K, including the transitions near 860 K. These results complete those on C E ₄₄ we have obtained in a previous work. All these constants display discontinuities at the lock-in transition. In the phase, the results are analysed in term of lowest order couplings between strains (e) and the order parameter (Q). The main features are described by the lowest order biquadratic e2Q2 coupling, in particular for C E ₄₄ in a large temperature range. However, it appears that a contribution of the next coupling term arises for C E ₆₆ below K and that the first two lowest order terms have to be taken into account even just below the lock-in transition in the case of C E ₁₄ . The temperature dependence of Q has been deduced and it can be well described in the framework of Landau's theory. Received: 2 October 1997 / Received in final form: 3 December 1997 / Accepted: 29 January 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     

Equation of state of cubic hafnium(IV) nitride having Th3P4 -type structure

Pressure dependence of the specific volume, V(P), of the recently discovered high-pressure compound Hf₃N₄ having cubic Th₃P₄-type structure (c- Hf₃N₄) has been measured at room temperature up to 43.9 GPa in a diamond anvil cell using energy-dispersive X-ray powder diffraction combined with synchrotron radiation. A least-square fit of the Birch-Murnaghan equation of state to the experimental V(P)-data yielded for c- Hf₃N₄ the bulk modulus of and its first pressure derivative of . For fixed at 4 the bulk modulus of c- Hf₃N₄ was determined to be . The obtained B₀-value is only insignificantly below that estimated in preliminary measurements. Existing theoretical predictions for B₀ scatter around the present experimental data. The observation of a high bulk modulus of c- Hf₃N₄ supports the suggestion that this compound could have high hardness.     

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.     

Light scattering by transverse waves in supercooled liquids and application to metatoluidine

We discuss the hydrodynamic equations which describe the shear dynamics of a liquid composed of anisotropic molecules, both in its normal and its supercooled phases. We use these equations to analyze 90 depolarized light scattering experiments performed in the supercooled phase of a glass forming liquid, metatoluidine, and show that the information extracted from this analysis is consistent with independent shear viscosity measurements performed on that liquid in the same temperature range. Received 28 April 1998     

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     

Structural and dynamical properties of aqueous suspensions of NaPSS (HPSS) at very low ionic strength

Results on the structural and dynamical properties of aqueous solutions of NaPSS (HPSS) are reported. Most samples of previous measurements, including our own, are contaminated by the presence of (temporal) aggregates. The emphasis of this paper lies on investigations of well purified samples at very low ionic strength where interacting effects are maximum. As previously reported, this can be achieved by pumping the suspension through ion exchange resin by means of a tube-pump, using filters of pore size. Information has been extracted from static and dynamic light scattering and viscosity measurements. A second maximum is observed in the scattering curves versus wavenumber for the first time. It is discussed on the basis of two current models describing the structure of charged macromolecules. The short time dynamics reflects the measured intensity. Detailed viscosity data in comparison of those of rodlike (TMV), slightly flexible so-called fd virus particles (length 880 nm) are used to confirm the interpretation of the light scattering results. The recently observed maximum in the reduced viscosity could be confirmed. Received: 5 May 1997 / Revised: 1 September 1997 / Accepted: 10 November 1997     

The elastic behavior of entropic "fisherman's net”

A new formalism is used for a Monte Carlo determination of the elastic constants of a two-dimensional net of fixed connectivity. The net is composed of point-like atoms each of which is tethered to six neighbors by a bond limiting the distance between them to a certain maximal separation, but having zero energy at all smaller lengths. We measure the elastic constants for many values of the ratio between the maximal and actual extensions of the net. When the net is very stretched (), a simple transformation maps the system into a triangular hard disks solid, and we show that the elastic properties of both systems coincide. We also show that the crossover to a Gaussian elastic behavior, expected for the non-stressed net, occurs when the net is looser (). Received 9 February 2000 and Received in final form 14 May 2000     

Strength of magnesium oxide under high pressure: evidence for the grain-size dependence

X-ray diffraction patterns from magnesium oxide compressed in a diamond anvil cell up to 55 GPa have been recorded and the differential stress (a measure of compressive strength) and grain-size (crystallite size) determined as a function of pressure from the line-width analysis. The strength agrees well with the uniaxial stress component (another measure of compressive strength) derived earlier from the line-shift data. The strength increases while the crystallite size decreases steeply as the pressure is raised from ambient to ∼10 GPa. The increase in strength is much smaller at higher pressures. The strength-pressure data are explained by combining the grain-size dependence of strength and the shear-modulus scaling law. The dependence of strength on grain-size has not been considered in the past in the discussion of high-pressure strength data.     

Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model

We present a new model of rubber elasticity where linear forces act to constrain the fluctuations of the eigenmodes of the phantom model. The model allows us to treat the constrained junction and the tube model within the same, transparent formalism, does not require any further approximations, and is particularly suited for the analysis of simulation data for (strained) model polymer networks. As an interesting side result we show that in order for the model to be consistent, the constraints (but not the mean polymer conformations!) have to deform affinely, a severe restriction that might also apply to other models. Complementary, we prove in analogy to the derivation of the virial theorem that introducing constraints into the phantom network Hamiltonian leads to extra terms in addition to the usual Doi-Edwards formulas for the polymer contribution to the stress tensor which vanish only for affinely deforming constraints. Received: 28 November 1997 / Received in final form and accepted: 31 March 1998     

Mechanical properties of carbon nanotubes

A variety of outstanding experimental results on the elucidation of the elastic properties of carbon nanotubes are fast appearing. These are based mainly on the techniques of high-resolution transmission electron microscopy (HRTEM) and atomic force microscopy (AFM) to determine the Young’s moduli of single-wall nanotube bundles and multi-walled nanotubes, prepared by a number of methods. These results are confirming the theoretical predictions that carbon nanotubes have high strength plus extraordinary flexibility and resilience. As well as summarising the most notable achievements of theory and experiment in the last few years, this paper explains the properties of nanotubes in the wider context of materials science and highlights the contribution of our research group in this rapidly expanding field. A deeper understanding of the relationship between the structural order of the nanotubes and their mechanical properties will be necessary for the development of carbon-nanotube-based composites. Our research to date illustrates a qualitative relationship between the Young’s modulus of a nanotube and the amount of disorder in the atomic structure of the walls. Other exciting results indicate that composites will benefit from the exceptional mechanical properties of carbon nanotubes, but that the major outstanding problem of load transfer efficiency must be overcome before suitable engineering materials can be produced. Received: 17 May 1999 / Accepted: 18 May 1999 / Published online: 29 July 1999     

Pressure and temperature variation of the depolarized light scattering spectra of the fragile glass-former liquid salol

The pressure and temperature dependences of the depolarized light scattering spectra of salol have been measured at isobaric condition P = 1 bar for T between 328 and 393 K, and at isothermal condition T = 343 K for P between 1 and 625 bar, i.e. outside the metastable liquid region. The experimental results for both the α- and β-relaxations can be well described by the Mode Coupling Theory. The independence of the power-law parameters a, and consequently b and γ, from the thermodynamic variables T and P is demonstrated.The critical temperature T _c at 1 bar and the critical pressure P _c at T = 343 K have been determined from the normal liquid state. Received 2 May 2000     

Orientational diffusivities measured by Rayleigh scattering in a lyotropic calamitic nematic () liquid crystal phase: the backflow problem revisited

Using a light-beating technique we have measured the damping time of thermal fluctuations of the nematic director for the so called cylindrical or calamitic nematic (N_C) phase of the lyotropic system K-laurate/decanol/. By varying the scattering angle in suitable geometries, we have been able to estimate the orientational diffusivities associated to the three pure deformations of splay, twist and bend. A former measurement made in the disk-like N_D phase of the same system yielded a large deviation between the splay and twist diffusivities. The effect was then attributed to induced flows, or backflow, which could be responsible for the reduction of the splay viscosity. In fact, this is the analogous effect, for disks, to the one recognized since long time ago arriving for rod-like molecules in a classical nematic, though in this case it is associated with bend deformations. The analogy comes about thanks to the interchange of the role played by disks and cylinders for, respectively, splay and bend fluctuations.The measurements reported here provide a new test on the applicability of the backflow model to a nematic system composed of micelles, that is, aggregates made of amphiphilic (surfactant) molecules, in its cylindrical-like variant, i.e. the N_C phase. In addition, the comparative study made here with the previous results existing in the literature for the N_D phase, allows us to conjecture on structural issues concerning lyotropic nematics. Received: 29 April 1998 / Revised: 19 August 1998 / Accepted: 31 August 1998