A model for the lattice dynamics of b.c.c. transition metals

Recent ideas proposed by Fielek for the lattice dynamics of f.c.c. noble and transition metals have been extended to b.c.c. transition metals. Phonon dispersion curves, calculated on the basis of this model, for chromium are in fairly good agreement with experimental ones and are far better than those reported so far.     

Interatomic forces in the b.c.c. transition metals

Using information obtained from X-ray scattering data, a model for the charge density in the transition metals is constructed. In this model the charge density is given by the sum of the charges situated at the ionic and bond centre sites. Within this framework, expressions for the second order elastic constants and the phonon frequencies in the cubic transition metals are obtained. These quantities have been calculated with and without the bond charge contributions for iron. The comparison with the experimental results shows that the introduction of bond charges, and hence angularity in the force-fields, in iron leads to distinctly better agreement with experiment. From a study of the elastic constants of the other b.c.c. transition metals some observations as to the nature of the angular force fields are made.     

Mean-square atomic displacements in f.c.c. crystals

The mean-square displacements of volume atoms, surface atoms and atoms near a vacancy are calculated for f.c.c. metals and rare gas solids, using a simple series expansion of the Wallis formula. We employ a model with rotationally invariant bond bending forces, unlike the de Launay model used by Masri and Dobrzynski. For atoms near a vacancy and for rare gas solids this method has been applied for the first time. The calculations are done to the R⁴ term in the expansion. The inclusion of the R⁴ term together with temperature-dependent elastic constants give results which are in better agreement with experiment. For rare gas solids Lindemann ratios calculated by this method agree closely with the values obtained from elaborate computations as well as those deduced from entropy data. The present calculation also supports the view that the melting of solids is initiated at the crystal surfaces and in the neighbourhood of vacancies.     

Strengthening at nanoscaled coherent twin boundary in f.c.c. metals

This paper analyses slip transfer at the boundary of nanoscaled growth twins in face-centred cubic (f.c.c.) metals for strengthening mechanism. The required stress for slip transfer, i.e. inter-twin flow stress, is obtained in a simple expression in terms of stacking fault energy and/or twin boundary (TB) energy, constriction energy and activation volume. For nanotwinned Al, Cu and Ni, inter-twin flow stress versus twin thickness remarkably shows Hall–Petch relationship. The Hall–Petch slope is rationalized for various reactions of screw and non-screw dislocations at the TB. Additionally, strengthening at the boundary of nanoscaled deformation twins in f.c.c. metals is analysed by evaluating required twinning stress. At small nanograin size, the prediction of deformation twin growth stress shows inverse grain-size effect on twinning, in agreement with recent experimental finding.     

Orientation dependence of screw dislocation motion in b.c.c. transition metals

A tight-binding type electronic theory is used to calculate the Peierls stress of the screw dislocation in b.c.c. transition metals. The repulsive core-core interaction energies are simulated by Born-Mayer type potentials as well as the modified Born-Mayer potentials. It is shown that there are essential differences in the orientation dependence of the screw dislocation motion among the transition metals, in agreement with experiments.     

Rotational Brownian dynamics simulations of non-interacting magnetized ellipsoidal particles in d.c. and a.c. magnetic fields

The rotational Brownian motion of magnetized tri-axial ellipsoidal particles (orthotropic particles) suspended in a Newtonian fluid, in the dilute suspension limit, under applied d.c. and a.c. magnetic fields was studied using rotational Brownian dynamics simulations. The algorithm describing the change in the suspension magnetization was obtained from the stochastic angular momentum equation using the fluctuation-dissipation theorem and a quaternion formulation of orientation space. Simulation results are in agreement with the Langevin function for equilibrium magnetization and with single-exponential relaxation from equilibrium at small fields using Perrin's effective relaxation time. Dynamic susceptibilities for ellipsoidal particles of different aspect ratios were obtained from the response to oscillating magnetic fields of different frequencies and described by Debye's model for the complex susceptibility using Perrin's effective relaxation time. Simulations at high equilibrium and probe fields indicate that Perrin's effective relaxation time continues to describe relaxation from equilibrium and response to oscillating fields even beyond the small field limit.     

Lambda spectra in 11.6A GeV/c Au-Au collisions

E896 has measured Lambda production in 11.6A GeV/c Au-Au collisions over virtually the whole rapidity phase space. The midrapidity p(t) distributions have been measured for the first time at this energy and appear to indicate that the Lambda hyperons have different freeze-out conditions than protons. A comparison with the relativistic quantum molecular dynamics model shows that while there is good shape agreement at high rapidity the model predicts significantly different slopes of the m(t) spectra at midrapidity. The data, where overlap occurs, are consistent with previously reported measurements.     

Electronically induced lattice instabilities in b.c.c. Zr

Electronically induced lattice instabilities in metals are discussed by means of an accurate determination of the generalized susceptibility function, χ(q), from a KKR band structure and Fermi surface determined for b.c.c. Zr. We describe how the detailed behavior of χ(q) for b.c.c. Zr may be related to the omega phase upon alloying with Nb or upon application of pressure to the b.c.c. lattice.     

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.     

ππ scattering amplitudes within the sub-threshold triangle

The on-shell ππ scattering amplitudes within and on the boundary of the subthreshold triangle (0 ≤ s ≤ Σ, 0 ≤ t ≤ Σ, 0 ≤ u ≤ Σ ≡ 4μ²) are investigated. Interior Dispersion Relations, when combined with experimental ππ phase shifts, inelasticities, and scattering lengths, provide an almost perfect tool for this study. The general results obtained are in striking agreement with the chiral model of Weinberg.     

New phase transition into the b.c.c. structure in antimony at high pressure

X-ray diffraction study of Sb has been made under the pressure of up to 43 GPa. A new phase transition from the Sb(III) into a b.c.c. phase occurs at about 28 GPa. The b.c.c. phase is found to be stable for the wide range of pressure from 28 GPa to at least 43 GPa.     

Collective sea-gull effect in πp interactions at 250 GeV/c

A collective “sea-gull” effect is observed for a system of fast hadrons produced in the fragmentation regions of nondiffractive π⁺p-interactions at 250 GeV/c. The effect is not reproduced by the FRITIOF fragmentation model in its details. It is demonstrated that hard-like processes, both in the collision phase and in the fragmentation phase, are not properly treated in the model.     

Radiation transfer in absorbing-scattering liquids—II. Comparisons of measurements with predictions

Comparisons have been made between measured and predicted results for the radiation field in both highly absorbing and scattering aqueous suspensions with a highly reflecting or absorbing bottom. Predictions were based on a discrete ordinate solution to the equation of transfer, with the requisite properties (extinction coefficient, absorption coefficient and scattering phase function) obtained from measurements performed on samples extracted from the suspensions. All trends in the data were predicted by the model, although poor numerical agreement was obtained for suspensions of large albedo and extinction coefficient. The disagreement is attributed to the effect of multiple scattering on the property measurements.     

New aspects on the thermodynamic functions of iron

It is shown that the phase transformations of iron can be simply explained if all phases are attributed equal magnetic entropies at high temperatures corresponding to directional disorder of local moments. It is also pointed out that the b.c.c. or f.c.c. stabilization in iron alloys is consistent with a rigid band model for the conduction electrons.     

Pion-nucleon phase shifts below 270 MeV

Pion-nucleon phase shifts below 270 MeV are derived from fixed t-dispersion relations using as input the π⁺p total cross sections measured by Bugg et al. below 290 MeV and CERN phase shifts above that energy. No particular high-energy model is needed.

It is pointed out that the predicted d-wave phase shifts — in contradiction to those belonging to earlier phase-shift solutions — are in good agreement with partial-wave dispersion relations and recent information on the helicity amplitudes describing the process . Furthermore our prediction for the P₁₃ wave has very recently got strong support from the work by Bugg et al. on pion-nucleon charge-exchange scattering.     

B.c.c.-f.c.c. allotropy, F-bands,and metallization in xenon and krypton

APW-Xα calculations of a f.c.c.-b.c.c. phase transition in Xe prior to metallization give P ? 950 kbar, contrary to the 820 kbar result of Hama and Matsui; their use of non-touching APW spheres (f.c.c.) may be the crucial difference. Hartree-Fock plus correlation calculations in Kr indicate that f-bands play no role in rare gas crystal metallization.     

Simulation of thermally-induced processes of diffusion and phase formation in layered metal-metalloid systems

A physical model of thermally induced processes of diffusion and phase formation in layered metal-metalloid systems is offered. The software for the model is created, which allows one to quantitatively describe the kinetics of these processes under arbitrary modes of annealing. The results of theoretical computations are compared with the data of experimental studies of a ⁵⁷Fe:O⁺ layered implantation system using the methods of M?ssbauer spectroscopy. The agreement between the numerical and experimental results indicates that the nature of phase transformations in the investigated system is determined by a change in the local concentration of the metalloid during its interstitial diffusion and corresponds to peculiarities of the phase equilibrium diagram of the Fe-O binary system.     

ρ-Meson coupling to the nucleon in the chiral bag model

The vector and tensor couplings of the ρ-meson to the nucleon are calculated by assuming the indirect coupling of the ρ-meson to the nucleon, through the pion cloud of the chiral bag model. Qualitative agreement with experiment is found at reasonable bag radii for both versions of the model: the cloudy bag model with pions in the interior, and the standard model with pions excluded from the bag.     

Impurity scattering on the Fermi surface of aluminum

A calculation is described for the anisotropic relaxation time due to impurity scattering on the Fermi surface of aluminum. The Bloch states and the Fermi surface are obtained from Ashcroft's 4-OPW model, while the scattering potentials are obtained from locally re-screened form factors. Numerical results reveal that strong anisotropicsin the electronic lifetime arise for s-like impurities such as Si and Ge. A phase shift model is introduced to explain these anisotropies. The predicted anisotropies appear to be in reasonable agreement with experimental values for the Dingle temperature. The relaxation time for d.c. conductivity is obtained from iterative solution of the Boltzmann equation.