Table of contents

The freezing behaviour of a binary hard-sphere mixture with diameter ratio 0.1 is studied within the formalism of the density functional theory (DFT). The stability of a 'sublattice-melt' (SLM) phase, wherein the large spheres are localized on crystal lattice sites and the small ones are fluid-like, is examined. The non-uniform one-particle densities of the small and large spheres in the SLM phase have been calculated. The fluid-solid phase diagram has been drawn.

Using the Car-Parrinello technique, ab initio molecular dynamics simulations are performed for liquid NaSn alloys in five different compositions (20, 40, 50, 57 and 80% sodium). The obtained structure factors agree well with the data from neutron scattering experiments. The measured prepeak in the structure factor is reproduced qualitatively for most compositions. The calculated and measured positions of all peaks show the same trend as function of the composition. The dynamic simulations also yield information about the formation and stability of Sn₄ clusters (Zintl anions) in the liquid. In our simulations of compositions with 50 and 57% sodium we observe the formation of networks of tin atoms. Thus, isolated tin clusters are not stable in such liquids. For the composition with 20% tin only isolated atoms or dimers of tin appear; 'octet compounds' of one Sn atom surrounded by four Na atoms are not observed.

The hysteresis behaviour of capillary confined CO₂ gas is studied through the positron/positronium annihilation technique. The arrangement of the confining medium (VYCOR glass) allowed simultaneous measurement of the bulk and pore confined phase behaviour. Isobaric temperature cycling showed marked hysteresis at the gas-liquid and liquid-solid phase boundaries for the confined gas. Observations at the gas-liquid transition are in agreement with capillary condensation theories and simple ideas are proposed to explain the liquid-solid transition behaviour.

Until recently the research on binary systems at high pressures was mainly focused on the phase behaviour of the fluid phases. In the last few years the interest has shifted towards other properties of the mixtures and towards the coexisting solid phases. Several exciting new discoveries have been made. In this article the recent developments in the field will be described.

A new method of analysing the experimental atom-atom pair distribution functions g_aa(r), based on the corresponding state principle, is presented. The method is first rested on nitrogen and chlorine liquids via computer simulations by exploiting intermolecular potentials that reproduce the experimental data satisfactorily. It is then applied to liquid fluorine to explain the large discrepancies we found when experimental and simulated g_aa(r) were compared. Different models involving various degrees of microscopic orientational correlation are built up; among them, only one implying no appreciable orientational order agrees with the experimental data for fluorine. This model also fits liquid nitrogen well and fails in the case of liquid chlorine; consequently, the microscopic structure of liquid fluorine must be very different from that of other liquid halogens. However, some discrepancies between model and experimental g_aa(r) of fluorine around 5 AA and spurious oscillations below 2 AA indicate that significant experimental uncertainties could affect the experimental data. The results of other models, which imply different degrees of orientational order, reported here can provide a useful guide for interpreting new experimental data.

We report a neutron diffraction experiment on liquid ⁷Li_xSi_1-x alloys (x=0.80, 0.65 and 0.57) just above the liquidus and on ⁷Li₅₇Si₄₃ at about 200 K above the liquidus. We obtained absolutely normalized and fully corrected structure factors and radial distribution functions. Which provide indications for the occurrence of chemical ordering in all three alloys. We have analysed the data by fitting models to the structure factor and to the radial distribution function, and by using the reverse Monte Carlo (RMC) method. We find strong indications for the presence of covalently bonded Si in liquid Li₆₅Si₃₅ and Li₅₇Si₄₃. The Si-Si coordination number Z_SiSi varies from about 1.5 in Li₆₅Si₃₅ to about 2 in Li₅₇Si₄₃. For c_Si>0.2, Si forms poly-anions ranging from dumbbells to large three-dimensional structures. Z_SiSi in Li₅₇Si₄₃ is not strongly temperature dependent and consequently the poly-anions are fairly stable. Covalently bonded Si is absent in liquid Li₈₀Si₂₀. The RMC modelling indicates that individual Si atoms are well separated. This suggests that the covalent character of Si in the Si-rich alloys (Li₆₅Si₃₅ and Li₅₇Si₄₃) changes to a more ionic character in Li₈₀Si₂₀.

The local orientational order in binary liquid Li-In alloys at a constant temperature has been systematically studied using molecular dynamics simulations combined with potential mapping techniques. The generalized non-local model pseudopotential theory has been chosen as the fundamental theory for our calculation. Both the orientational order parameters and pair analysis approach have been adopted to examine the characterization of structures in binary liquid Li-In alloys. It demonstrates that the mapping procedure produces a significant image enhancement of the short-range order, and the third-order invariant of the spherical harmonics is much more sensitive to the icosahedral symmetry than is the quadratic invariant. In addition, the bonded pairs with various symmetries, icosahedra, defective icosahedra, etc., formed in liquid Li-In alloys are also examined and the relationship between these quantities and compositions are investigated. The results further show that distributions of the attractive part of the potentials play an important role in characterizing liquid structures. Finally, a detailed discussion of the results has been given.

An equation for the pressure dependence of the melting temperature based on thermodynamic principles has been developed, which generalizes the Simon-Glatzel equation and describes the rising and falling melting curves as well as curves with a maximum. The parameters appearing in the equation are identified in terms of the thermodynamic values. The equation accurately approximates the melting curves of different categories of substances over a large range of melting temperatures and pressures.

We have used theoretical values of the sum rules in the information theory for the transport coefficients from work of Heyes and Powles, and have found that there is no noticeable improvement in the results for the diffusion coefficient of a Lennard-Jones fluid over their results obtained using an indirect method for the evaluation of the sum rules. We also propose a phenomenological form involving two parameters for the time development of the time correlation function. The parameters are determined from the frequency sum rules of the respective time correlation function to incorporate exactly its short-time behaviour. The values of the sum rules and Green-Kubo expressions are used to determine self-diffusion, shear viscosity and thermal conductivity of Lennard-Jones fluids over wide ranges of density and temperature. A reasonable agreement with computer simulation data is obtained for all the transport coefficients.

Using mean-field free-energy density functionals, we studied the structure of a liquid drop embedded in a vapour background of a one-component fluid, in the absence of an external field, using exponentially decaying fluid-fluid attractive interactions (characterized by an inverse range parameter lambda ) of the type employed by Sullivan. In Sullivan's original model and afterwards, lambda was specified by the arbitrary condition lambda d=1 (d is the hard-sphere diameter). Now, this choice is relaxed and the potential is allowed to have variable inverse range parameter as well as attractive forces between fluid molecules; as a result, some of the interfacial quantities vary with lambda and some do not. Those influenced by lambda are the density profiles, principal tensors, surface tensions ( gamma _mech and gamma _therm) according to the mechanical and thermodynamic routes, the radii of the dividing surfaces and the homogeneous radius; while those not influenced by lambda are the pressure difference Delta p across the drop, the density rho (0) at the drop centre, the equimolar surface tension gamma _e, and the existence of a homogeneous phase inside the drop; however large the drop may be, this behaviour of the drop depends only on the supersaturation.

Neutron diffraction measurements have been performed on a single crystal of the ammonium perovskite NH₄MnF₃ at 220 K, 80 K and 20 K. This perovskite is known to undergo a transition from cubic (Pm3m, Z=1) to orthorhombic (Pnma, Z=4) structure at T_c=182 K and an antiferromagnetic transition at T_N=75 K. In the cubic phase, the rotational structure factor method has been used to obtain the parameters of the interaction potential of the NH₄⁺ molecule with its crystal environment. In the orthorhombic phase, the refinement shows that a single orientation of the NH₄⁺ molecule in the crystal is populated. This gives rise to a fully ordered sublattice of NH₄⁺ groups related to the distortion of the perovskite and the appearance of two types of hydrogen bond. In the magnetic phase, an antiferromagnetic G_y structure is deduced with a magnetic moment of 3.6(2) mu _B.

By using our newly proposed empirical interatomic potential for silicon, the structure and some dynamical properties of the silicon cluster Si_n (10<or=n<or=24) have been studied. It is found that the results obtained are close to those from ab initio methods. From the present results, we can gain a new insight into understanding the experimental data on the Si_n clusters.

The range of validity of Landau free-energy potentials with the usual approximation of constant coefficients for terms higher than quadratic has recently been questioned (J. Phys. R Condens. Matter 1 (1989) 8327). The frequent observation in real systems, within large temperature intervals, clearly outside any possible critical region, of power laws of the type mod T_c-T mod ^b for the order parameter has also been pointed out as an indication that certain simple general features in phase transitions, not related at all to critical phenomena, are beyond the usual approximations included in a Landau free-energy expansion. In particular, the value of the exponent h has been proposed to be related to the displacive and order-disorder degree of the system. In order to elucidate these questions, the temperature dependence of the Landau free energy corresponding to the three-dimensional Phi ⁴ model has been investigated using a straightforward Monte Carlo method. Different model parameters have been considered, ranging from typical displacive parameters to those approaching a pure order-disorder system. Following its formal definition, the Landau free energy at each temperature has been directly derived from the order parameter distribution in a Metropolis statistical sample. In contrast with other numerical methods used in previous literature, no approximation is introduced in the calculation, except inherent to the numerical method employed. It is shown that the temperature dependence of the Landau potential coefficients follows smooth simple laws that are outside the usual assumptions in Landau theory and can be related to the order-disorder degree of the system. The quadratic coefficient in the Landau potential exhibits a linear temperature dependence in large temperature intervals but shows a marked change in slope about the transition temperature. The quartic coefficient is shown to depend on temperature as strongly as the quadratic coefficient having a minimum around the transition point. The strong temperature dependence of this quartic coefficient is responsible for the 'non-classical' behaviour of the order parameter, which can be described by a power law.

We found that in TmCo₂ the molecular field does not exceed the critical value necessary to induce long-range magnetic order in the Co d-electron subsystem, which is in contrast to the other heavy RCo₂ compounds. Below T_c=3.8 K a first-order magnetic phase transition at 3.4 K exists, which is due to a rearrangement of the Tm 4f magnetic moments. When substituting Tm by Gd long-range magnetic order appears in the Co d subsystem. The onset of the magnetic order in the d-electron subsystem can most clearly be seen from thermal expansion measurements. There is an increasing positive volume anomaly with increasing Gd content below T_c. The estimated magnetostriction constant lambda ₁₁₁ of TmCo₂ is -4.1*10^-3, in agreement with the single-ion model. Pronounced discontinuities at T_c are characteristic for the transport properties (resistivity and thermopower) for TmCo₂ as well as for the pseudobinary Tm_1-xGd_xCo₂ compounds. At elevated temperatures the physical properties of all these compounds are dominated by spin fluctuations.

A method is developed for an accurate evaluation of the electric field gradient (EFG) tensor in the cubic lattices of point charges. It is shown that only two values of the geometrical factors similar to the Madelung constants are necessary for calculation of all EFG components at all sites in all standard cubic crystals. The EFG tensor at all carbon atoms in the different phases of alkali-doped fullerene crystals is presented as an example. It is demonstrated that a cubic network of zero potential lines with halved lattice constant exists in perovskite crystals and some fullerites. A numerical procedure is proposed for calculation of EFG at any point of the unit cell for the arbitrary cloud of point charges. The method is based on the presentation of crystal sums by means of the McDonald functions.

We study the features of the current density distribution in a thin plate of a compensated metal under pinch-effect conditions. It is established that the current structure possesses a sign-alternating character. There exist space layers where the current flows in the opposite direction to an electric field in the sample. The current density spatial oscillations are caused by the non-linearity stipulated by the influence of a non-uniform magnetic field of the current on the metal conductivity. It is shown that the sign-alternating current distribution results in oscillations in the sample I-V characteristics. These oscillations are observed experimentally.

We have carried out a Monte Carlo simulation of the conductivity of a two-dimensional strongly localized interacting system. A plot of dlog sigma /dlogT versus T, on a double logarithmic scale, clearly shows two distinct regimes, one activated at high T and a non-activated one at low T. The conductivity exponent in this later regime is close to 1/2 , in agreement with Efros and Shklovskii's predictions (1984), although the characteristic temperature T₀'; is about a factor of two smaller than predicted.

We have calculated the magnetic susceptibility chi of the degenerate electron gas in a semiconductor superlattice placed in parallel quantizing electric (E) and magnetic (H) fields directed along the superlattice growth axis. In this case the electrons have a purely discrete energy spectrum consisting of Landau and Wannier-Stark levels. This leads to: (i) the dependence of the monotonic part of the diamagnetic susceptibility of the electron gas on the electric field; (ii) the rise of a new oscillation period of chi as a function of H different from that of the de Haas-van Alphen oscillations; and (iii) the oscillatory behaviour of chi as a function of E with a periodicity in square root E. It is shown that in weak magnetic fields the Wannier-Stark quantization results in a step-like dependence of the paramagnetic susceptibility of the electron gas on the electric field strength.

We calculate the binding of two added electrons or holes for several clusters described by the extended Hubbard model. Pairing is found only away from half filling and for the geometries which give particle-hole symmetric spectra. In these situations the intersite repulsion is essential and pairing depends on it very strongly. We conclude that small-cluster results are adequate to answer the question of whether the binding is possible only if the one-particle spectra are qualitatively similar to those of the considered lattice. Altogether, the results suggest that a purely electronic mechanism of superconductivity is not likely in alkali metal doped fullerides.

EPR spectra of Cr³⁺ ions in single crystals of KTiOPO₄ (KTP), synthesized by the flux method, have been investigated at room temperature by employing a Bruker Q-band spectrometer. From the angular dependence of the EPR pattern measured in the ab, bc, and ca planes, we have identified two Cr³⁺ centres, named A and B, which have been previously analysed by other investigators. In this study, we have newly identified four magnetically inequivalent Cr³⁺ sites for both A and B. For the four sites of both A and B, the direction cosines of the principal axes of the g as well as the second-order zero-field-splitting (ZFS) tensors are found to be given by the relationship lmn, lmn, lmn, and lmn. Using the site-rotation matrices obtained by this relationship, we calculated two sets of all spin-Hamiltonian parameters that simultaneously fitted four sites for both A and B. It is also verified that observed orientations of the principal axes for all Cr³⁺ sites are consistent with the crystallographic symmetry of KTP. Two possible origins of the centres A and B are proposed: each centre may be due to Cr³⁺ ions at crystallographically equivalent Ti sites, either Ti(1) or Ti(2), with different charge compensators, or at two different Ti sites, Ti(1) and Ti(2), without charge compensators.

Second-order non-linear optical tensor coefficients of LiNbO₃-type compounds have been obtained on the basis of crystallographic data and a bond-orbital model, which is capable of calculating single bond contributions to the second-order non-linear optical susceptibility. The tensor values thus calculated are in good agreement with experimental data. The influence of energy-band broadening on the non-linear optical susceptibility is not well accounted for in the bond-orbital model.

Raman spectra of an Rb_0.5(ND₄)_0.5D₂PO₄ (DRADP-50) mixed crystal have been carefully investigated in the 15-300 K temperature range for all fundamental polarization geometries. The spectra have been interpreted in terms of vibrational modes of principal structural units and critically discussed in comparison with published data on analogous (deuterated and protonated) compounds. Analysis of the temperature dependence of peak positions and halfwidths has made it possible to estimate two characteristic temperature regions ( approximately 200-220 K and approximately 100-120 K) where incipient cluster formation and freezing of individual structural units takes place in this compound on cooling through the dipolar glass transition.

The evolution of photoluminescence (PL) from a series of as-anodized porous silicon (PS) samples with peaks in a wide energy range has been investigated systematically during oxidation enhanced by either laser illumination or gamma -ray irradiation. Under both oxidation conditions, PL spectra initially located in the infrared-red region undergo a blue shift, while those initially located in the orange-yellow region experience a red shift. Eventually, all the peaks are pinned at fixed energies which are in an energy range narrower than that for as-anodized PS samples. These experimental results can be explained by the quantum confinement-luminescence centres model, which argues that photoexcitation proceeds in nanoscale silicon and photoemission through the luminescence centres outside nanoscale silicon, and also by assuming that during oxidation the main luminescence centres change from one kind to another and/or the relative contributions to the PL intensity from various kinds of luminescence centres vary.