Lattice dynamics of copper on modified Bhatia's model

Bhatia's model is modified to consider interionic interactions out to third neighbours. The electron-ion part of the dynamical matrix is also changed. The present scheme gave excellent agreement between calculated and experimental phonon frequencies of copper.     

Lattice dynamics of black phosphorus

Phonon dispersion curves of black phosphorus are calculated using the force constant model, in which the valence force model is assumed for intralayer interatomic interactions and the axially symmetric force model for interlayer ones. Ten force constants in all are determined by “least-squares” fitting to optical Г-phonons and the symmetry relations between sound velocities. The phonon dispersion curves calculated are applied successfully to interpretation of experiments on the first and second order Raman spectra, effective Debye temperature, and inelastic neutron scattering. Large discrepancy between the calculated and observed linear compressibilities exists.     

Lattice dynamics and structural phase transitions

Results of lattice dynamics, or atomic motions in a solid, explain many of the thermodynamic properties of solids. Inelastic neutron scattering conveniently explores the atomic motions, quantized as phonons. Of particular interest are materials that undergo structural phase transitions. The soft mode theory has been successful in relating anomalous phonon behavior to structural changes in solids. One such example is the ferromagnetic shape memory alloy, Ni₂MnGa, which undergoes a sequence of phase transitions leading to a magnetic, incommensurate modulated, tetragonal phase as the ground state. The experiments, coupled with first principles calculations, provide evidence that strong electron–phonon coupling is the driving mechanism of the phase transformation.     

Wick's theorem and Fokker-Planck dynamics

The correlation and response functions are studied through a Wick's theorem for a Fokker-Planck system in a non-stationary situation. Non gaussian correlations are considered. The effect of the stochastic force is a dressing of the free correlation function.     

Mobile valence-alternation domain walls in Wolffram's red salt

A theoretical analysis of the excitation spectrum of the long-chain of Wolffram's red salt is presented. Because of the twofold degeneracy of the ground state of the dimerized chain, elementary excitations corresponding to topological solitons, or propagating domain walls are obtained. Such domain wall motions govern the charge-lattice relaxation process in Wolffram's red salt at low temperatures.     

Electronic structure of red amorphous phosphorus studied by X-ray spectroscopy

A SXS study of occupied and unoccupied 3p states of semiconducting red amorphous phosphorus is presented. It is shown that in the upper part of the valence band, partially hybridized sp spates are present among p pure states, whereas the bottom of the valence band is almost s-like. The results are discussed in connection with theoretical data available for black phosphorus.     

Effect of phosphorus content on structural properties of phosphorus incorporated tetrahedral amorphous carbon films

With phosphorus incorporated tetrahedral amorphous carbon (ta-C:P) films prepared using filtered cathodic vacuum arc technique with PH₃ as the dopant source, we investigate the effect of phosphorus content on the structural properties of the films by X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy. XPS analysis indicates that a function is established between the atomic fraction of phosphorus in the samples and the flow rate of PH₃ during deposition, and that phosphorus implantation increases the graphite-like trihedral sp² bonds deduced from fitted C 1s and P 2p core level spectra. Raman spectra of a broad range show that there are two notable features for all ta-C:P films: the first-order band centered at about 1560 cm^-1 and the second-order band between 2400 and 3400 cm^-1. The broad first-order band demonstrates that the amorphous structure of all samples does not remarkably change when a lower flow rate of PH₃ is implanted, while a higher concentration of phosphorus impurity enhances the clustering of sp² sites dispersed in sp³ skeleton and the evolution of structural ordering. Furthermore, the second-order Raman spectra confirm the formation of small graphitic crystallites in size due to a finite-crystal-size effect. PACS 81.05.Uw; 81.15.Ef; 63.50.+x     

Dynamic structural correlations and Van Hove's correlation function for liquids

The stochastic model for liquids, developed previously and applied to the evaluation of static correlations, is extended to the evaluation of the dynamic pair correlation function. This extension can be achieved by a generalization of the width function W, characterizing the spread in the distribution of correlated local structures, from a piecewise linear function of r to a piecewise linear function in the (r, t) plane.     

Lattice Green's function for the simple cubic and tetragonal lattices at arbitrary points

The lattice Green's function for the simple cubic lattice (γ = 1) and tetragonal lattice at an arbitrary point (l, m, n)

$\text{I(a;l,m,n;γ) =}\text{1}\text{π}{}^3\text{∫∫}\text{∫}\text{o}\text{π}\text{cos}\text{lx}\text{cos}\text{my}\text{cos}\text{nx}\text{a?i??γ}\text{cos}\text{x?}\text{cos}\text{y?}\text{cos}\text{x}\text{dxdydz}$

is evaluated, assuming a ? 0, γ ? 0 without loss of generality. The integral I(a; l, m, n; γ) which has singularities at a = ± γ ± 1 ± 1, is expressed in all regions of (a, γ), i.e., for (i) a > 2 + γ, (ii) 2 ? γ > a > γ(γ < 2), (iii) a <γ ? 2 (γ > 2), (iv) a < 2 ? γ (1 < γ < 2) and γ > a (0 < γ < 1), (v) |a ? γ| < 2 and a + γ > 2, in terms of Kampé de Fériet function by the method of the analytic continuation using the Mellin-Barnes type integral. The numerical values are shown in figures. The high temperature susceptibilities of the Heisenberg model of the ferro- and antiferromagnets are calculated using the results of I(a; l, m, n; γ), showing a shift from three to two dimensions and that from three to one dimensions. The correlation function of the isotropic ferromagnet is calculated and the critical index ν is observed to be 1.     

A possible unification of Newton's and Coulomb's forces

We have considered electric charge as the fourth component of the particle momentum in five-dimensional space–time. The fifth dimension has been compactified on a circle with an extremely small radius determined from the fundamental physics constants. First, we have given equations in the framework of five-dimensional special relativity and determined the corresponding reduction to four-dimensional space–time. Then, in order to obtain an appropriate charge-to-mass ratio and to avoid the Fourier modes problem, we have considered the propagation of an off-mass shell particle in the five-dimensional space–time which can be interpreted as the motion of an on-mass shell particle in the four-dimensional world we experience. As an example, we have discussed the five-dimensional kinematic equations associated with the electron-positron annihilation process into two photons. Finally, the consequences on the gravitational interaction between two elementary charged particles has been studied. As a main result, we have obtained a unification of Newton's gravitational and Coulomb's electrostatic forces.     

Weyl's association,Wigner's function and affine geometry

According to Weyl one may associate a function with a dynamical operator; these functions depend on the parameters p and q and can be displayed in a p, q manifold, the W space. In the classical limit the W space becomes the phase space parametrised by the canonical variables. The function associated in this manner with the density operator is Wigner's function. It turns out that if Wigner's function is a delta function it cannot represent the density operator of a physically realisable state unless the argument of the delta-function is linear in the parameters a and q. In all other cases Wigner's function associated with a physically realisable state has a finite width, proportional to $\text{h}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$. Consequently straightness (linear combination of p and q) has a fundamental significance in the W space. Since this property is preserved under linear inhomogeneous transformations the W space will have a geometry generated by these transformations, the affine geometry of Euler, Moebius and Blaschke. In the present note we show how this comes about, how it simplifies the semiclassical approximations of Wigner's function, and makes one understand how in the classical limit this geometry is lost, allowing to be replaced by the geometry of canonical transformations.     

The Miura transformations of Kaup's equation and of Mikhailov's equation

Two types of Miura transformations have been found. One relates Kaup's equation to Sawada-Kotera's equation and another relates the generalized Mikhailov equation to a model equation for a shallow water wave.     

The microscopic structure of bulk amorphous red phosphorus: A Raman scattering investigation

The microscopic structure of bulk amorphous red P has been investigated by Raman scattering. It is concluded that the phosphorus tubes of pentagonal cross-section present in Hittorf's P and KP₁₅ are the structural units of the amorphous red P network. Intratube and intertube correlations are responsible for intermediate range order effects. The Raman data indicate that a continuous transition from the crystalline to the amorphous state takes place for P.     

MacDonald's theorem and Milatz's theorem for multivariate stochastic processes

MacDonald's theorem, which expresses the spectral density of a randomly fluctuating variable α(t) in terms of the finite time average of that variable, α_θ(t), is generalized for multivariate processes. For purely random processes, having a white spectrum, this also yields the corresponding generalization of Milatz's theorem.     

Pressure-induced structural transition in amorphous GeO2: a molecular dynamics simulation

We studied the structural and dynamical properties of amorphous germanium dioxide (GeO₂) from low to high pressure by means of the classical molecular dynamics technique. The simulations were done in the micro-canonical ensemble, with systems at densities ranged from 3.16 to 6.79 g/cm³, using a pairwise potential. The network topology of the systems is analyzed at atomic level through partial pair correlations, coordination number and angular distributions. The dynamic properties were characterized by means of the vibrational density of states. According the density increases, a structural transformation from a short-range order, defined by a building block composed by a basic (GeO₄) tetrahedron, to a basic (GeO₆) octahedron is observed. The vibrational density of states also presents important changes when the density increases, with a low frequency band lessened, and a high density band wider and flatter.