Neutron Resonance States in Overdense Crystals

New three-body resonances appeared in the neutron scattering on two nuclei fixed in nodes of overdense crystalline lattice have been calculated for the iron group isotopes. These resonances are strongly dependent on the lattice parameters and characteristics of two-body resonances in neutron–nucleus subsystems. The effective forces created by the neutron resonance rescatterings supplement the Coulomb forces between nuclei of the crystalline lattice. These effective resonance interactions occur only at certain distances between nuclei and are accompanied by gamma radiation.     

Lattice dynamics of II–VI and III–V compounds

To study the lattice dynamics of II–VI and III–V compounds having zinc-blende structure in a model which incorporates three types of interactions: (i) central ion-ion forces (ii) bond-bending forces and (iii) long range Coulombic forces, has been developed. The model involves in total eight disposable parameters. The use of six critical point phonon frequencies, two elastic constants and the lattice equilibrium condition has been made to evaluate the consistent values of the parameters. The application of the present model has been made to calculate the phonon dispersion relations of ZnSe and InSb compounds. The comparison of theoretical results with the available experimental data has been made along the three symmetry directions [100], [110] and [111]. A reasonably good agreement is observed between theory and experiments.     

Angular forces in the lattice dynamics of b.c.c. metals

The lattice dynamics of the b.c.c. lattice has been investigated using the central and the angular forces which are in general rotationally invariant. It has been observed that the four force constants are related to three elastic constants only. Dispersion curves for sodium were calculated and were found to be in excellent agreement with experiment.     

Lattice dynamics of calcium fluoride by an angular force model

The lattice dynamics of CaF₂ has been studied on the basis of a noncentral model using CGW type angular forces. The experimental data agree with the data obtained for the dispersion curves. The model has also been used to calculate lattice specific heat and Debye-Waller factors.     

Effect of three-body forces on the lattice dynamics of noble metals

A simple method to generate an effective electron-ion interaction pseudopotential from the energy wave number characteristic obtained by first principles calculations has been suggested. This effective potential has been used, in third order perturbation, to study the effect of three-body forces on the lattice dynamics of noble metals. It is found that three-body forces, in these metals, do play an important role. The inclusion of such three-body forces appreciably improves the agreement between the experimental and theoretical phonon dispersion curves.     

A New Method for Analysis of the Fluid Interaction with a Deformable Membrane

The lattice Boltzmann cellular automaton method has been successfully extended for analysis of fluid interactions with a deformable membrane or web. The hydrodynamic forces on the solid web are obtained through computation of the fluid flow stress at the moving boundary using the lattice Boltzmann method. Analysis of solid boundary deformation or vibration due to hydrodynamic force is based on Newtonian dynamics and a molecular dynamic type approach.     

Effect of Van der Waals forces on the lattice dynamics and crystal structure of noble metals

The effect of Van der Waals forces on the lattice dynamics and crystal structure of noble metals has been studied in the formalism of Rehr, Zaremba and Kohn. When the contribution of these forces is included in the resonant model potential scheme, the phonon frequencies are lowered by 5–8% and the crystal structure is still found to be the observed one (f.c.c.) for noble metals.     

Lattice dynamical study of body-centred tetragonal indium

The phonon dispersion curves, phonon frequency distribution function as well as the lattice specific heat of body-centred tetragonal indium have been deduced using a lattice dynamical model which includes central, angular and volume forces. Six elastic constants, four zone boundary frequencies and an equilibrium condition were used in the evaluation of the force constants. It is shown that this model is elastically consistent and satisfies the symmetry requirements of the lattice, the phonon frequencies of indium deduced from it are in very good agreement with the experimental values of Reichardt and Smith and the theoretical values of Garrett and Swihart, and theθ _D values compare well with the experimental values over a wide temperature range. The apparent discrepancies in the phonon dispersion curves and theθ _D-T curves obtained from deficient models, importance of umklapp processes and the significance of angular forces in the lattice dynamical models are discussed.     

The volume pinning force for periodical interaction forces between defects and the flux line lattice

The volume pinning force for some forms of the interaction potential defect-flux line is calculated without restrictions on the vortex lattice distance and the interaction range of defects. It is shown that for larger maximum elementary interaction forces, the direct summation of pinning forces is realistic. However, if the interaction range of the defects is smaller than the vortex lattice distance, one obtains a region (about one order of magnitude) in which Labusch's quadratic dependence of the volume pinning force on the elementary interaction force is valid. In the region where the direct summation of pinning forces occur, the volume pinning force is proportional the vortex lattice distance and one obtains an additional magnetic field dependence of the volume pinning force.     

Infrared-phonon-polariton resonance of the nonlinear susceptibility in GaAs

Nonlinear probing of the fundamental lattice vibration of polar crystals is shown to reveal insight into higher-order cohesive lattice forces. With a free-electron laser tunable in the far infrared we experimentally investigate the dispersion of the second-order susceptibility due to the phonon resonance in GaAs. We observe a strong resonance enhancement of second harmonic light generation at half the optical phonon frequency, and in addition a minimum at a higher frequency below the phonon frequency. Measuring this frequency and comparison to a theoretical model allows the determination of competing higher-order lattice forces.     

Order and mobility of solid vortex matter in oscillatory driving currents

We study numerically the evolution of the degree order and mobility of the vortex lattice under steady and oscillating applied forces. We show that the oscillatory motion of vortices can favor an ordered structure, even when the motion of the vortices is plastic when the same force is applied in a constant way. Our results relate the spatial order of the vortex lattice with its mobility, and they are in agreement with recent experiments. We predict that, in oscillating applied forces, the lattice orients with a principal axis perpendicular to the direction of motion.     

Hydrogen bonds and van der waals forces in ice at ambient and high pressures

The first principles methods, density-functional theory and quantum Monte Carlo, have been used to examine the balance between van der Waals (vdW) forces and hydrogen bonding in ambient and high-pressure phases of ice. At higher pressure, the contribution to the lattice energy from vdW increases and that from hydrogen bonding decreases, leading vdW to have a substantial effect on the transition pressures between the crystalline ice phases. An important consequence, likely to be of relevance to molecular crystals in general, is that transition pressures obtained from density-functional theory exchange-correlation functionals which neglect vdW forces are greatly overestimated.     

An electron fluid model for the lattice dynamics of metals

An electron fluid model is proposed for the lattice dynamics of metals which satisfies the requirement of translational invariance and the lattice is in equilibrium without recourse to external forces. The model is applied to calculate the phonon dispersion of sodium in the symmetry directions.     

What makes a crystal «stiff» enough for the Mössbauer effect?

Summary The M?ssbauer effect is well interpreted and understood in an ideal, infinitely stiff (mathematical) lattice. However we argue that the electrostatic forces that are usually considered in solid-state physics are not adequate to support such a ?stiffness?. This difficulty is seen to been surmounted by a ?superradiant? behaviour of the plasma of nuclei of a crystal.     

Steady state convergence acceleration of the generalized lattice Boltzmann equation with forcing term through preconditioning

Several applications exist in which lattice Boltzmann methods (LBM) are used to compute stationary states of fluid motions, particularly those driven or modulated by external forces. Standard LBM, being explicit time-marching in nature, requires a long time to attain steady state convergence, particularly at low Mach numbers due to the disparity in characteristic speeds of propagation of different quantities. In this paper, we present a preconditioned generalized lattice Boltzmann equation (GLBE) with forcing term to accelerate steady state convergence to flows driven by external forces. The use of multiple relaxation times in the GLBE allows enhancement of the numerical stability. Particular focus is given in preconditioning external forces, which can be spatially and temporally dependent. In particular, correct forms of moment projections of source/forcing terms are derived such that they recover preconditioned Navier–Stokes equations with non-uniform external forces. As an illustration, we solve an extended system with a preconditioned lattice kinetic equation for magnetic induction field at low magnetic Prandtl numbers, which imposes Lorentz forces on the flow of conducting fluids. Computational studies, particularly in three-dimensions, for canonical problems show that the number of time steps needed to reach steady state is reduced by orders of magnitude with preconditioning. In addition, the preconditioning approach resulted in significantly improved stability characteristics when compared with the corresponding single relaxation time formulation.     

Flux vortices and transport currents in type II superconductors

This article is concerned with the mechanisms by which type II superconductors can carry currents. The equilibrium properties of the vortex lattice are described and the generalized driving force in gradients of temperature and field is derived using irreversible thermodynamics. This leads to expressions for thermal cross effects which can include pinning forces. The field distributions which occur in a range of situations are derived and a number of useful solutions of the critical state given. In particular, the distribution in a longitudinal field is obtained, and the conditions under which force-free configurations can break down by the cutting of vortices discussed. The effects of lattice rigidity on the summation of pinning forces is considered and it is shown that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument. Theoretical expressions are derived for the vortex pinning interaction to a number of different metallurgical defects. The theoretical models are compared critically with experimental measurements of pinning forces and other related phenomena, such as flux creep, low amplitude vortex oscillations and vortex lattice defect effects. Finally, the implications for technological materials are assessed.     

Lattice dynamics of beryllium

Phonon frequencies in beryllium along the principal symmetry directions have been determined by means of the slow neutron inelastic scattering technique. The data are analysed in terms of a six-neighbour force constant model and the force constants are evaluated. It is concluded that strong tensor forces are present in beryllium and the importance of this finding to basic theories of lattice dynamics is pointed out.     

The treatment of forces in Bloch analysis

In periodic lattice structures, wave propagation on the infinite domain can be greatly simplified by invoking the Floquet-Bloch theorem. The theorem allows a system's degrees of freedom to be reduced to a small subset contained in a repeating unit cell. The equations of motion governing this subset contain internal force terms, which must be eliminated before establishing the eigenvalue problem for the dispersion relationships. There are subtle issues with regard to the elimination of these forces, which we address in this paper. We demonstrate that for any two- or three-dimensional periodic lattice, the internal forces vanish when acted upon by the linear transformation engendered by the degree of freedom reduction.     

Änderung der Laue-Bragg-Reflexe und des Volumens eines Kristalls durch statistisch verteilte Punktfehlstellen

It is proved that from the change in length of a sample due to randomly distributed point defects, and from the corresponding change of the Laue-Bragg maxima in x-ray experiments one measures the same average lattice constant. Furthermore it is shown that a homogeneous density of point defects in a continuum gives rise to a homogeneous deformation of the crystal. The problem is also treated by lattice theory. If the lattice is harmonic and if the displacements vary slowly this corresponds to the continuum theory. The double forces of continuum theory can be determined from the coupling parameters of lattice theory.