Elastic anomalies near a surface-induced phase transition

An analysis is made of the influence of elastic degrees of freedom on a surface-induced phase transition. It is found that elastic interactions give rise to a nonlinear correction to the boundary conditions for the order parameter, with the result that the surface transition is of the second order despite the fact that a first order phase transition occurs in the bulk. The propagation of Rayleigh waves near such a transition is discussed.     

Phonon-assisted electronic excitation transfer near distortive phase transitions

An anomalous temperature dependence of the phonon-assisted electronic excitation transfer rate is to be expected near a distortive phase transition, when the energy mismatch between donor and acceptor energy levels is close to that of a soft optical mode, or an order-parameter-sensitive hard mode. In the case of electron coupling to soft acoustical modes, it is shown that the Debye model used in current theories breaks down near T_c.     

Elastic interactions between surface adatoms and between surface clusters

One major term is omitted in most conventional treatments of interactions between surface adatoms or groups of adatoms. This is the elastic interaction, in which adatoms interact through mutual distortion of the substrate. The indirect elastic interaction explains a range of observed surface phenomena in a consistent quantitative way. These phenomena include static and dynamic effects ranging from ordered structures to correlated motions of adatom clusters. It is likely also that substrate distortion is important in clean surface reconstruction. The elastic interaction is typically comparable with or larger than the indirect electronic interactions usually presumed. It follows that detailed calculations which ignore the substrate distortions produced will be of limited value only.     

Elastic interaction and the phase transition in coherent metal-hydrogen systems

We study the statistical mechanics of hydrogen dissolved in metals. The underlying model is based on the assumption that the dominant attractive interaction between the protons in the metal is of an elastic nature.

In the first part of the paper we review some general properties of the elastic interaction. We then discuss the importance of boundary conditions for the form of the elastic interaction, which turns out to be of the Curie-Weiss type with macroscopic range.

In the second part we investigate the a-a' (‘gas-liquid’) phase transition in the hydrogen lattice fluid. The long-range part of the elastic interaction is treated in mean field approximation. In the canonical ensemble as opposed to the grand canonical ensemble one finds no co-existing phases near the critical point. Instead there is a continuous transition which changes into a first-order transition at tricritical points. In the temperature-density region which normally corresponds to the two-phase co-existence region the hydrogen density is inhomogeneous and varies on a macroscopic scale.

The peculiar nature of the a-a' phase transition is due to the long-range character of the elastic interaction, which ultimately results from the requirement of coherency of the host crystal. We argue that coherent metal-hydrogen systems offer examples of real systems where the classical theory of phase transitions applies.     

Exchange interaction between single magnetic adatoms

The magnetic coupling between single Co atoms adsorbed on a copper surface is determined by probing the Kondo resonance using low-temperature scanning tunneling spectroscopy. The Kondo resonance, which is due to magnetic correlation effects between the spin of a magnetic adatom and the conduction electrons of the substrate, is modified in a characteristic way by the coupling of the neighboring adatom spins. Increasing the interatomic distance of a Cobalt dimer from 2.56 to 8.1 A we follow the oscillatory transition from ferromagnetic to antiferromagnetic coupling. Adding a third atom to the antiferromagnetically coupled dimer results in the formation of a collective correlated state.     

Anisotropic,long-range elastic interaction between adatoms

The interaction between two adatoms mediated by the elastic distortion of the substrate is calculated using the Green's functions derived by Maradudin et al. for semi-infinite hexagonal and cubic crystals. For a substrate with hexagonal symmetry with the surface parallel to the basal plane, the interaction energy is isotropic over the substrate surface, and varies as R⁻³ with the separation R of the adatoms, as in the case of an elastically isotropic substrate. The interaction between adatoms on the (100) face of cubic crystal also varies as R⁻³, but is anisotropic. In many cases, the interaction between identical adatoms is attractive along the cube axes and repulsive along directions at 45° to the axes.     

The dipole-dipole interaction between two adatoms viewed as a surface plasmon mediated interaction

The semi-classical dipole-dipole interaction law previously derived from the classical image force theory is rederived from a model hamutonian in which the dipole-dipole interaction between two adatoms is mediated by surface plasmons. From this approach it emerges that the semi-classical law is only valid in the adiabatic limit where image charges can quasi-instantaneously follow the charge fluctuations on the adsorbate. Connection with the second order perturbation theory of dipole-dipole interaction between two adatoms is also analysed.     

Elastic properties of Fe1−xO near the antiferromagnetic phase transition

The elastic constants of Fe_1?xO single crystals have been investigated near the antiferromagnetic phase transition (T_N ～ 198 K) as a function of temperature. The velocity of longitudinal and tranverse ultrasonic waves was measured by the pulse echo overlap method. A strong elastic anomaly occurs for C₄₄ whereas a small step only is observed for C₁₁.     

Oscillations in ultrasonic attenuation near a phase transition

It is shown that the oscillations in ultrasonic attenuation observed in KH₂PO₄ near phase transition temperature cannot be due to velocity changes and interference of a coherent source with the echo as suggested by Steinitz et al. recently.     

Localized charge inhomogeneities and phase separation near a second-order phase transition

Localized charge inhomogeneities and phase separation are described in the framework of the phenomenological theory of phase transitions. It is shown that Coulomb interaction determines the charge distribution and the characteristic size of the emerging inhomogeneities. Phase separation associated with charge segregation becomes possible because of a high dielectric constant and a low excess charge density in the localization region. The phase diagram of the system is calculated, and estimates are obtained for the gain in energy associated with the emerging state. The role of Coulomb interaction is exposed, and corresponding estimates are given.     

Elastic interaction of a dislocation array with a phase boundary

The equilibrium configuration of an array of dislocations in parallel equidistant slip planes under an external shear stress near a welded boundary between two isotropic half-spaces having different elastic constants is computed. For large external stress, the dislocations are arranged into an arc concave when seen from the boundary. It is concluded that such an arc is formed at the tip of a twin or of a martensitic plate near a phase boundary. The tensile stress across the boundary due to an edge dislocation array is discussed in connection with the formation of an interfacial crack.     

Transport coefficients near chiral phase transition

We analyze the transport properties of relativistic fluid composed of constituent quarks at finite temperature and density. We focus on the shear and bulk viscosities and study their behavior near chiral phase transition. We model the constituent quark interactions through the Nambu–Jona-Lasinio Lagrangian. The transport coefficients are calculated within kinetic theory under relaxation time approximation including in-medium modification of quasi-particles dispersion relations. We quantify the influence of the order of chiral phase transition and the critical end point on dissipative phenomena in such a medium.     

On correlation effects in the indirect interaction between adatoms

Starting from a nonorthogonal basis set a model Hamiltonian for the chemisorption of two adsorbates is derived. The nonorthogonality is converted into a renormalization of the matrix elements. A solution is presented which becomes exact in two limiting cases. The indirect interaction energy of two hydrogen atoms is calculated for adsorption on a semi infinite simple cubic solid described by ans-band. For the band nearly filled (parameters of Ni) a 2 × 2 structure seems to be energetically favourable.     

Collective dynamics near a phase transition in confined fluids

We performed molecular dynamics simulations in the microcanonical ensemble (MEMD) for a "simple" fluid confined between two solid substrates. From the calculation of the intermediate scattering function F(k( parallel ),t) and through the memory function formalism, we extract material ( i.e. transport and thermodynamics) coefficients in the vicinity of the liquid-gas phase transition. Our results show that approaching the limit of stability ( i.e. the spinodal), the dynamics of the system changes markedly.     

Band effects and the dipole interaction between two adatoms on a metal surface

The contribution of band effects to the adatom interaction energy is investigated to second order in perturbation theory. These are found to bring an important correction to the dipole law derived recently by Kohn and Lau.     

Generating functional models for a statistical system near a phase transition

Starting from an assumed form of the distribution function near the phase transition point, an expression for the generating functional of a statistical system suitable for describing two-phase states of matter is derived. We then obtain formulas for the partition function and correlation functions by the standard procedure.     

Elastic interaction between a dislocation and a near-by inclusion

The study of elastic interaction between a dislocation and an inclusion (i.e., a region transformed without change of elastic constants) in an elastic continuum is extended to the cases when the singular dislocation line intersects or touches the inclusion or is situated inside it. The interaction energy is shown to be a finite and continuous function of position of the inclusion. The interaction of an edge dislocation with a dilatation sphere and of a screw dislocation with a sphere transformed into ellipsoid in isotropic continuum are studied in detail. The spherical inclusion which is considered as a rough model of a point defect (e.g. of carbon atom in iron) has a maximum and minimum energy position near the dislocation line so that the binding energy can be calculated in a consistent way.