Abstract: The nonlinear Schrodinger equation is solved on an infinitesimal thin ring or circle. We obtained the exact real wave functions with their corresponding energies for the ground state and the excited states. Critical values of the circle perimeter are found at which the ground state changes its structure and additional higher excited states appear. Also, the complex wave functions that correspond to energy levels with finite angular momentum are studied.

Abstract: The ternary oxides Ba8Ta4Ti3O24 and Ba10Ta7.04Ti1.2O30 were synthesized and their crystal structures and defects were studied by means of X-ray powder diffraction, electron diffraction, and high resolution electron microscopy. The crystal structure of Ba8Ta4Ti3O24 is based on the 8H (cchc)(2) close-packed stacking (a 10.0314 Angstrom, c = 18.869 Angstrom, SG P6(3)/mcm, Z = 3) and that of Ba10Ta7.04Ti1.2O30 and on the 10H (cchcc)(2) close-packed stacking (a = 5.7981 Angstrom, c = 23.755 Angstrom, SG P6(3)/mmc, Z = 1) of BaO3 layers. The structural refinements gave the following values for the R factors for Ba8Ta4Ti3O24 (Ba10Ta7.04Ti1.2O30) R(I) = 0.041 (0.039), R(P) = 0.108 (0.118), and R(wP) = 0.094 (0.099). The main feature of both structures is the presence of two types of face-sharing octahedra (FSO) with different occupancies by Ta atoms, Ti atoms, and vacancies, which results in the formation of a superstructure. It was shown that in the Ba8Ta4Ti3O24 structure these pairs of FSO occur in an ordered fashion and in the Ba10Ta7.04Ti1.2O30 structure in a disordered fashion. The existence of the wide range of solid solutions was shown to be also a consequence of the presence of one of the two types of face-sharing octahedra. (C) 1995 Academic Press, Inc,

Abstract: The present paper gives a review of results of recent studies investigating the fundamentals of the martensitic and related phase transformations in Ni-Al. For the former case, the emphasis will be on the microstructure of martensite plates. The latter include the metastable Ni2Al omega-like and stable Ni5Al3 bainitic phases. These phases will be discussed in view of their atomic structure, nucleation, growth and effect on the martensitic transformation. A separate chapter will deal with precursor effects.

Abstract: The crystal structure of the newly discovered double-Hg-layer copper oxide superconductor (Hg, Pr)(2)Ba-2(Y, Ca)Cu2O8-delta was studied as a function of chemical doping using neutron and electron diffraction and high-resolution transmission electron microscopy (HREM). Rietveld refinements of the structural parameters from neutron powder diffraction data indicate that the oxygen site O3 on the mercury plane is highly defective, being both partially occupied and displaced from the high-symmetry position. The variable concentration of oxygen vacancies partially compensates for the cation doping and, together with the O3 displacement field, makes some of the Hg atoms acquire an unusual pyramidal coordination. HREM images confirm that the structure is of the '2212' type, with very few defects. In some grains, faint superstructure reflections were evidenced by electron diffraction, suggesting that both the oxygen vacancies and the O3 displacement field may order at least on a local scale.