Mahito Mabuchi

A Theory of Frenkel Excitons Using a Two-Level-Atom Model

The principal purpose of the present paper is to develop a formal, rigorous theory of Frenkel excitons with or without interaction with an external electro-magnetic field within the framework of a two-level-atom model. Employed implicitly but extensively in exciton problems have been model systems composed of interacting two-level atoms in which only two of energy levels of a given atom, corresponding to the ground state and an excited state, endowed with a transition dipole moment, are taken into account. The most common method traditionally employed here is to treat Frenkel as well as Wannier excitons simply as Bosons. It is however to be reminded that excitons, both Frenkel and Wannier types, are neither Bosons nor Fermions. Specifically, Frenkel excitons in such a model system are to be considered as Paulions or being equivalent to S=1/2 spins. Except for the specific case of one-dimensional system with nearest-neighbour interactions only,1) the conventional procedure, in analogy with magnons in Heisenberg magnets, would be to regard excitons as a non-ideal Bose gas in which the deviation from the Bose statistics is expressed in the form of effective interactions among excitons, called kinematical interactions.2),3) The discussion along this line however is generally much involved. Furthermore, there exist intrinsic or dynamical exciton-exciton interactions, even if they are regarded as Paulions or, more generally, as electron-hole pairs. It is shown in this paper that within the framework of a two-level-atom model the model exciton Hamiltonian is rigorously expressed in the form of the Heisenberg model Hamiltonian for S=1/2 spins with long-range anisotropic exchange interactions, and that Frenkel excitons thus obtained are generally expressed as quantum-mechanical nonlinear polarization waves, the nonlinearity being characterized by the atomic level population.

Diffusivity and solubility of hydrogen and deuterium in yttrium

The diffusivity and solubility of hydrogen and deuterium in polycrystalline α-yttrium have been measured in the temperature range 1073–1373 K. The ratios of the measured diffusion coefficient of deuterium to that of hydrogen showed the classical value 1/√2. The activation energy of diffusion has been found to be 510 meV for both hydrogen and deuterium. The differences in the solubility and diffusivity between hydrogen and deuterium have been explained by using rate theory and assuming that hydrogen and deuterium atoms in yttrium are slightly anharmonic oscillators.

Auger electron spectroscopy and electron energy loss spectroscopy study of the adsorption of nitrogen on a polycrystalline zirconium surface

Auger electron spectroscopy (AES) and electron energy loss spectroscopy (EELS) were used to investigate the adsorption of nitrogen gas on a polycrystalline zirconium surface at room temperature. It was found that the adsorption of nitrogen is saturated at an exposure of ∼10 L, the thickness of the nitride formed on the specimen surface is 0.4–0.5 nm at a nitrogen exposure of 100 L, and the surface has the same large electronic density of states 4–5 eV below the Fermi energy as ZrN. The measured AES and EELS spectra are consistent with the electronic structure calculated for the Zr(0001)-(1×1)-N structure.

Auger electron, electron energy loss and secondary electron emission spectroscopic studies on the oxidation of zirconium at high temperatures and room temperature

Auger electron (AES), electron energy loss (EELS) and secondary electron emission spectroscopy (SES) have been used to investigate the surface oxidation of zirconium at room temperature and high temperatures, 773–973 K, under low oxygen pressures 1.3 × 10–5–1.3 × 10–3 Pa. The kinetic energies of the Auger and the secondary electrons and the electron energy losses by single electron excitations are explained by the electronic structure in the core and the valence states of the metal and the oxide of zirconium. The energy loss by the collective excitation of plasmon is also observed in the EELS measurement for the metal and the oxide surface. The increase in the relative peak-to-peak height of the oxygen Auger transition and of the zirconium Auger transition by oxidation at high temperatures does not depend simply on the oxygen exposure represented by the product of oxygen pressure and exposure time, i.e. exposure in Langmuir, because of the dynamic competition between surface processes and the diffusion process of oxygen into the bulk. The rate of oxide growth is found to be parabolic at high temperature (773 K) and at 1.3 × 10–5 Pa.

Measurements of Young’s modulus and the modulus of rigidity of the solid solution of hydrogen in zirconium between 300 and 1300 K

Young’s modulus (E) and the modulus of rigidity (G) have been measured for zirconium between 300 and 1300 K and for zirconium hydrides ZrHx (0<x<0.9) at 941 and 1001 K, using an apparatus capable of making in situ measurements under ultrahigh vacuum. Values of E and G have been obtained from resonance frequencies for bending and torsion vibrations of a polycrystalline zirconium wire. As the temperature increases, E and G of zirconium decrease in the α phase of an hcp structure and in the β phase of a bcc structure with an abrupt decrease at the α→β transition temperature 1135 K. As the hydrogen concentration increases, E and G of ZrHx decrease in the α phase and increase in the β phase.

High-temperature diffusion of hydrogen and deuterium in palladium

The diffusivity of hydrogen and deuterium in palladium has been measured at temperatures between 773 and 1373 K and at hydrogen and deuterium concentrations less than 10–4 H/Pd and D/Pd (atomic ratio). The measured diffusion coefficients for hydrogen (DH) and deuterium (DD) showed Arrhenius behaviour. The dependence of the ratio DDDH on temperature has been explained by a model of diffusion in which a hydrogen atom in an octahedral site of the palladium lattice can jump into the adjacent octahedral site only when local deformation of the palladium lattice assists the jump.

Electron energy-loss spectra and secondary-electron emission spectra of Zr, ZrN and ZrO2

Electron energy-loss spectra and secondary-electron emission spectra have been measured for Zr, ZrN and ZrO2. The position and shape of the measured peaks associated with 4p-elecron excitation are consistent with the multiplets calculated for zirconium ions possible in Zr, ZrN and ZrO2.

Pulse-Like Excitons and Interaction between Frenkel Excitons

Solitons and wave trains are studied in the case of low density excitons interacting with each other. It is show that the wave trains in a one-dimentional chain are related to the pulse-like excitons and that in the long wave limit the pulse-like solutions always appear in Bose systems when interactions of Bose particles are described by very short-ranged potentials. The direct interaction between two Frenkel excitons through the Coulomb interaction of composite electrons and holes is also investigated. This interaction falls as R -5 , where R is the separation of two excitons, and is weakly repulsive.

Isotope effect in the diffusion of hydrogen and deuterium in titanium, Ti88Al12 and Ti3Al

Diffusion coefficients of hydrogen and deuterium in titanium, titanium–aluminium alloy Ti88Al12 and intermetallic Ti3Al have been measured in the temperature range 873–1298 K. The activation energy for diffusion has been found to be almost the same for hydrogen and deuterium and to increase, as the aluminium content in the metals increases, from ca. 0.44 eV for titanium to ca. 0.85 eV for Ti3Al. The ratio of the measured diffusion coefficient of deuterium to that of hydrogen also increases from the classical value 1/√2 for titanium to ca. 0.8 for Ti3Al. An application of the classical rate theory to the measured ratio shows that the hydrogen atom at the saddle point of the diffusion path is more tightly bound to the metal atoms and has a larger vibration energy in Ti3Al than in titanium.

Increase in yields of secondary ions by oxidation of zirconium at high temperatures and low oxygen pressures

Secondary ion mass spectroscopy has been used to investigate the oxidation of zirconium at pressures of oxygen (6.7 × 10–5–1.3 × 10–3 Pa) and at high temperatures (773–1073 K). Existence of three sequential stages of the increase in the yields of the secondary ions Zr+, ZrO+ and ZrO+2 has been found. The increase of the yield of the Zr+ ion is interpreted to be caused by the formation of oxide at the surface. By means of resonance tunnelling theory, the reason for the increase is explained by the downward energy shift of the highest occupied electronic level of the substrate.