In order to understand the structure and dynamics of hot dense hydrogen, a tight-binding model for hydrogen is developed by fitting the energies of the hydrogen molecule and various crystal structures of solid hydrogen. Pair correlation functions and self-diffusion coefficients obtained from tight-binding molecular-dynamics simulations on relatively large systems for long time scales compare very well with density-functional molecular-dynamics results at various densities (0.1–3 g ${\mathrm{cm}}^{\mathrm{-}3}$) and temperatures (0.1–5 eV).

A theory of the nucleation of crystalline particles in disordered media is proposed accounting for small statistical fluctuations in microscopic structural parameters, which are shown to affect considerably the thermodynamic barrier to nucleation. As a result, the classical nucleation rate exponent -W/kT takes the correction Γ(W/kT${)}^3$ at high temperatures, where Γ depends both on the correlation radius of the disorder and its amplitude; this correction may be significant. At low temperatures the nucleation-rate exponent remains finite in the case of uncorrelated disorder, while it is proportional to ${\mathit{T}}^{\mathrm{-}1/3}$ at T→0 in the case of strongly correlated disorder. The implications of these findings for nucleation in glasses are discussed.

Two models are presented which we have used to reproduce experimental data, such as Raman excitation profiles and the dispersion of the depolarization ratio of totally symmetric fundamentals, in the excitation range of resonance Raman scattering of cis-polyacetylene. The first model works in the diabatic approach of the vibronic coupling theory, and considers a solvent-induced symmetry lowering as a probable mechanism for inducing scattering of totally symmetric motions into a forbidden electronic transition. The second one is based on the theory developed by Korenowski, Ziegler, and Albrecht and assumes that even dipole-forbidden electronic states are possible sources for the Raman-intensity enhancements and for the dispersion of depolarization ratios when a vibrational mixing mode produces vibronic coupling between forbidden and allowed electronic states. Both models seem to be suitable, even if with some differences, for fitting our experimental results for two totally symmetric motions of a soluble form of cis-polyacetylene.

Both stationary and moving intrinsic anharmonic gap modes are generated in a perfect one-dimensional diatomic chain. Within the rotating-wave approximation, the eigenfrequency, eigenvector, and energy of such a localized packet can be found from differential-difference equations. A connection between the anharmonic system treated here and the harmonic one is that since the effective force constants are determined by the eigenvector of the particular localized mode, they can be viewed as renormalized force constants in a harmonic lattice. For the diatomic chain the even-parity anharmonic mode is unstable against conversion to an odd-parity mode while the odd-parity mode shows long term stability, in contrast with the result found earlier for a monatomic chain. Part of the mean energy of the odd-parity gap mode is associated with kinetic and potential terms of the ac vibration while the rest resides in a localized dc distortion of the lattice. Strongly localized gap modes can be approximated by the dynamics of a triatomic molecule. For larger vibrational amplitudes and associated dc distortions, the potential for the gap mode becomes double valued and the rotating-wave approximation fails. When the interaction of intrinsic gap modes with stationary anharmonic mass defect impurity modes is examined in numerical simulation studies, a variety of scattering results are found depending on the mass defect magnitude and the site in the diatomic chain. Two important features of the trajectories are that the gap mode is trapped at the mass defect when the vibrational frequencies of the moving mode and the anharmonic defect mode are near resonance and that the scattering is elastic when the frequencies are far apart.

A Fourier approach is applied for calculating the pulsed-field-gradient-spin-echo amplitude M(k,t) of a fluid in a porous medium with a periodic microgeometry. The method is most effective for long times t, but works quite well down to times that are short enough so that asymptotic short-time approximations of the diffusion process are still valid. The method can be applied regardless of the value of the porosity or the shape of the periodic pore space. Preliminary results are presented for simple cubic arrays of spherical obstacles in a fluid.

The Europium compound ${\mathrm{Eu}}_2$${\mathrm{BaCoO}}_5$ has been studied by means of Raman and x-ray-absorption spectroscopies. The eigenfunctions and frequencies of the optical normal modes have been calculated from an adequate potential showing good accordance with the observed phonons. In addition to Raman-allowed normal modes, several infrared and luminescence bands are observed between 10 and 300 K. The temperature dependence of these processes has allowed us to determine the complex interrelation between these two kinds of elementary excitations. A broad luminescence band (at 2.3 eV) is tentatively attributed to electronic transitions between ${\mathrm{Co}}^{2+}$ 3d crystal-field levels in the gap of the material. The mixing of these quasiatomic levels with apical oxygen orbitals, along the very short Co-O(2) bonds in the chains, can be the reason for the simultaneous enhancement of the intensities of the luminescence band and of the apical oxygen infrared modes through a resonant electron-phonon coupling. From the dependence of the phonon frequencies and the analysis of the extended x-ray-absorption fine structure spectra with the temperature it can be concluded that on decreasing the temperature the a axis becomes shorter, while the other two axes remain nearly unchanged. The emission spectrum in the visible range has been observed and interpreted in the frame of the crystal-field theory. We have studied the dependence of the intensity of the electronic transitions between 4f levels of the europium ions with the temperature and the energy of the exciting light. From the behavior of the ${\mathrm{Eu}}^{3+}$ luminescence peaks it has been possible to determine the processes of excitation and emission, which are shown to involve lattice phonons. The crystal-field parameters of the ${\mathrm{Eu}}^{3+}$ ions have been calculated from the energies of the lower terms of the ion.

The variational-cumulant-expansion (VCE) method is adopted to calculate the Heisenberg model. The free energy of the model is expanded to the third order, and the analytical formulas for the critical temperature ${\mathit{T}}_{\mathit{c}}$ are given for each order. The first order of VCE corresponds to the mean-field theory, the second order gives the same result for ${\mathit{T}}_{\mathit{c}}$ as the 1/z expansion, and the third order gives a more complicated correction. As a comparison, the results of the two-dimensional (2D) Ising model for VCE to the seventh order are shown. We carry out a trial to predict the critical temperature of the infinite order of the VCE, and get a very accurate result for the 2D Ising model. A prediction of ${\mathit{T}}_{\mathit{c}}$ for the Heisenberg model is also made.

We have investigated the spin dynamics of the nearly ideal one-dimensional S=1 antiferromagnet Ni(${\mathrm{C}}_2$${\mathrm{H}}_8$${\mathrm{N}}_2$${)}_2$${\mathrm{NO}}_2$${\mathrm{ClO}}_4$ (NENP) by inelastic neutron scattering. The measurements have been performed as a function of both the wave vector (in the vicinity of the antiferromagnetic point q=π) and the magnetic field, for field configurations parallel (up to 5 T) or perpendicular to the chain axis (up to 10 T). Our experimental results at low temperature are in good quantitative agreement with most theoretical predictions (both analytical and numerical) established for the spin-1 Haldane-gap system in presence of finite orthorhombic anisotropy: nonmagnetic singlet ground state, three gaps in the excitation spectrum corresponding to the excited triplet (${\mathrm{\Delta }}_{\mathit{y}}^0$≊1.05 meV, ${\mathrm{\Delta }}_{\mathit{x}}^0$≊1.23 meV, ${\mathrm{\Delta }}_{\mathit{z}}^0$≊2.5 meV), finite correlation lengths at T=0 (${\xi }_{\mathit{x}\mathit{y}}$/d≊8,${\xi }_{\mathit{z}}$/d≊4) and unconventional field dependencies. The evolution with field of the various modes and their respective polarization have been determined experimentally and are compared to recent field-theory treatments of the S=1 anisotropic antiferromagnetic chain together with numerical calculations on finite-size systems. We present results concerning the field dependencies of the correlation lengths, both in field parallel and perpendicular to the chain axis, which are not fully understood from the existing theories.

Structural and magnetic properties of stage-1, stage-2, and stage-3 ${\mathrm{CuCl}}_2$ graphite intercalation compounds (GIC’s) were studied by means of x-ray, electron- and neutron-diffraction, dc magnetic susceptibility, and electron spin resonance (ESR) measurements. The ${\mathrm{Cu}}^{2+}$ ions form an isosceles triangular lattice with one short side and two longer sides. The in-plane dc magnetic susceptibility shows Curie-Weiss behavior above 150 K, a broad maximum around 62–65 K, indicative of low-dimensional magnetic correlations, and a Curie-type behavior below 20 K, attributable to paramagnetic inhomogeneities in the sample. The temperature and magnitude of the susceptibility maximum are more consistent with a two-dimensional Heisenberg antiferromagnet than a one-dimensional model, suggesting that the distortion from an equilateral triangular lattice is not an important factor in the magnetic behavior of ${\mathrm{CuCl}}_2$ GIC’s. ESR measurements indicate that the local magnetic symmetry of ${\mathrm{Cu}}^{2+}$ spins is tetragonal. The angular dependence of the ESR linewidth at 4.2 K is explained by the combined effects of a canting of the tetragonal axis from the c axis and a weak anisotropy in the Landé g factor that favors spins to lie in the intercalate plane. No magnetic phase transition is observed from dc magnetic susceptibility down to 1.5 K and magnetic neutron scattering above 0.5 K.

The magnetic behavior of Co-Mn and Ni-Mn alloys is typical of competing interaction systems with regions of ferromagnetism and antiferromagnetism enclosing an intermediate concentration region in which only magnetic short-range order (MSRO) occurs. Neutron diffuse scattering measurements were made on alloys from this intermediate region to characterize the MSRO and to determine the associated magnetic moments. Diffuse peaks indicative of antiferromagnetic short-range order were observed and average sublattice moments were determined by comparison of the integrated diffuse peak intensities with the cross section for Bragg scattering from the alloys with assumed antiferromagnetic long-range order. The average sublattice moment of the Co-Mn alloys is appreciably smaller than that for the Ni-Mn alloys. Recent local density calculations indicate vanishing moments for Ni and Co atoms in fcc antiferromagnets with large wave vectors. If this applies to these alloys, then all of the moment resides at the Mn sites and corresponds to about 1${\mathrm{\mu }}_{\mathit{B}}$/Mn for the Co-Mn alloys and 4${\mathrm{\mu }}_{\mathit{B}}$/Mn for Ni-Mn alloys. This moment difference for these otherwise similar systems is attributed to a moment-volume instability of the type more commonly associated with fcc Fe.

A magnetic field may alter the flexural resonant frequencies of a vibrating reed that possesses an anisotropic magnetic susceptibility. The phenomenon’s magnitude is a function of the field strength, the length of the reed, the radius of gyration of the reed’s cross section, the Young’s modulus of the material, the vibrational mode observed, the magnetic susceptibility tensor, and the field’s orientation relative to the principal susceptibility directions and the reed’s plane of vibration. This effect can allow a direct and extremely sensitive measure of magnetic anisostropy of nonferromagnetic materials.

Correlated-f-electron systems have a wide range of f-electron delocalization varying from ‘‘almost localized’’ to ‘‘almost itinerant.’’ Previously, techniques to calculate hybridization and exchange Coulomb interaction in the f-electron systems have been developed from the ‘‘core point of view.’’ Such a procedure is appropriate for ‘‘almost localized’’ systems, i.e., typically cerium systems where the electrons of interest are 4f. Here techniques for the same purposes are discussed, and that to calculate hybridization is developed in detail, from a ‘‘band point of view’’ in order to treat ‘‘almost itinerant’’ systems, i.e., typically light actinide systems where the electrons of interest are 5f such as uranium systems. Calculations have been done for uranium monopnictides and monochalcogenides. Results on magnetic ordering are in good agreement with experiment. Validity and limitations of the two points of view are discussed in regard to their application to realistic systems.

The field-induced magnetism in ${\mathrm{UGe}}_3$ and ${\mathrm{URh}}_3$ has been studied by means of first-principles calculations. The calculated induced moments on the U and Rh sites agree well with experimental work on ${\mathrm{URh}}_3$. Also, the calculated field-induced magnetic form factor of ${\mathrm{URh}}_3$ compares favorably with experiment. In the case of ${\mathrm{UGe}}_3$ the agreement between theory and experiment is less satisfactory. Even though the calculated induced moment on the U site is rather close to measurement, the calculated Ge moment is substantially smaller than derived experimentally.

We analyze the motion of a single hole on a Néel background, neglecting spin fluctuations. Brinkman and Rice studied this problem on a cubic lattice, introducing the retraceable-path approximation for the hole Green’s function, exact in a one-dimensional lattice. Metzner et al. showed that the approximation also becomes exact in the infinite-dimensional limit. We tackle this problem by resumming the Nagaoka expansion of the propagator in terms of nonretraceable skeleton paths dressed by retraceable-path insertions. This resummation opens the way to an almost quantitative solution of the problem in all dimensions and, in particular, sheds light on the question of the position of the band edges. We studied the motion of the hole on a double chain and a square lattice, for which deviations from the retraceable-path approximation are expected to be most pronounced. The density of states is mostly adequately accounted for by the retraceable-path approximation. Our band-edge determination points towards an absence of band tails extending to the Nagaoka energy in the spectra of the double chain and the square lattice. We also evaluated the spectral density and the self-energy, exhibiting k dependence due to finite dimensionality. We find good agreement with recent numerical results obtained by Sorella et al. with the Lanczos spectra decoding method. The method we employ enables us to identify the hole paths which are responsible for the various features present in the density of states and the spectral density.

The time dependence of the density operator for two coupled spin-1 nuclei, such as dideuterium ${\mathrm{D}}_2$ and dinitrogen ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}_2^{}{}_{}{}^{}$, under the second rank intramolecular dipolar and the first rank spin-rotation Hamiltonians has been derived. It is shown that the relaxation rates for the ortho and para species are not identical. We report the five independent rates for the para and the 21 independent rates for the ortho species. Due to cross-relaxation between spin orders which precess at a common frequency, the relaxation for the ortho configuration is not always single exponential. There are 15 cross-relaxation terms between certain spin orders for the ortho species in the slow-motion regime. The complexity of our coupled spin system is discussed for the solid and the Jeener-Broekaert echo sequences. The Zeeman spin-lattice relaxation rates ${\mathit{R}}_{10}$ for ortho- and para-dideuterium have been measured experimentally in patially oriented nematic solvents at 304 K using ${}_{}{}^2{}_{}{}^{}\mathrm{NMR}$. The solvents used are PCH-7, 1132 and a 55 wt.% 1132/EBBA mixture. These oriented solvents make it possible to separate the resonances of the ortho and para configurations thereby facilitating the ${\mathit{R}}_{10}$ determination directly without multiexponential analysis. The ${\mathit{R}}_{10}$ of para-dideuterium is about twice that of ortho-dideuterium in all experiments. Using our calculated expressions for ${\mathit{R}}_{10}$ based on quadrupolar, dipolar, and spin-rotation interactions, and performing the proper averaging over the rotational states, we obtain excellent agreement with our experimental results. Good agreement has been obtained with published low-temperature studies as well.

The electronic structure of U${\mathit{T}}_2$${\mathrm{Si}}_2$, where T=Cr, Mn, Fe, Co, Ni, Cu, Ru, Rh, Pd, Os, is determined by means of self-consistent density-functional calculations in the local approximation treating the U 5f states as band states. A pronounced trend in the hybridization strength is exposed and is deduced to give rise to the different magnetic properties of the compounds. In agreement with experiment, the nonmonotonic behavior in the subseries containing 3d elements is reproduced, especially the state of ${\mathrm{UFe}}_2$${\mathrm{Si}}_2$ which is nonmagnetic in contrast to the other 3d members. The underlying physics of this fact is explained. Furthermore, special features of the heavy-fermion system ${\mathrm{URu}}_2$${\mathrm{Si}}_2$ are discussed.

We use a quantum O(N) nonlinear σ model to describe one-dimensional quantum Heisenberg antiferromagnets with integer spin S. A large-N analytical treatment of this effective theory leads to definite predictions for thermodynamic quantities in the low-temperature regime. We obtain the Haldane gap as a function of the temperature and note a trend similar to that found in the compound NENP. The specific heat and magnetic susceptibility are also obtained and comparison with exact numerical results for the S=1 spin chain allows us to determine the domain of validity of our approximation. By a calculation at subleading 1/N order we compute the quasiparticle lifetime. Results are given on-shell, for the width observed at the quasiparticle pole as seen in neutron-scattering experiments, and also off-shell, for the NMR relaxation rate ${\mathit{T}}_1^{\mathrm{-}1}$. The phenomenological interacting boson model is compared with our approach. We discuss the effects of anisotropy and compare our results with present experiments on NENP.

The ordering process in a nearly one-dimensional anisotropic ferromagnetic system is studied by utilizing the modified Ginzburg-Landau equation. In the early stages the process is dominated by the formation of Bloch walls. Then, annihilation of domains follows, which promotes the growth of magnetic domains. By deriving the equation of motion for the assembly of Bloch-wall positions, we study the temporal evolution of the scattering function both from the numerical and the theoretical standpoint. It is found that the average domain size increases logarithmically in time and the scattering function asymptotically takes the exponential form in the later stages. This can be quantitatively well explained by the kink dynamics. Furthermore, the temporal evolution of the distribution function for domain sizes is numerically obtained. We find that it can be well approximated fundamentally by the exponential law.

We perform a finite-size analysis of the longitudinal and transverse structure factors ${\mathit{S}}_{\mathit{j}}$(p,γ,N),j=1,3 in the ground state of the one-dimensional spin-1/2 XXZ model. Comparison with the exact results of Tonegawa for the XX model yields excellent agreement.

X-ray- and polarized-neutron-diffraction measurements have been carried out on a single crystal of hexagonal ${\mathrm{Y}}_2$${\mathrm{Fe}}_{17}$ in order to determine the details of the structural disorder and local-Fe-moment distribution. The crystal structure as determined by X-ray diffraction indicates a disordered variant of the ${\mathrm{Th}}_2$${\mathrm{Ni}}_{17}$ structure with formation of dumbbell Fe sites around Y sites 2b and 2c. These act to induce weak distortions on the nearby 12k and 12j Fe sites. For this particular crystal with a refined stoichiometry of ${\mathrm{Y}}_2$${\mathrm{Fe}}_{17.3}$, only the 12j Fe site was found to decompose into two subsites. The magnetization density has been measured by polarized-neutron diffraction and fitted to a multipole model of the Fe moments. The calculated Fe magnetic moments are in good agreement with recent electronic band-structure calculations.