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: Homogenised and quenched Ni65Al35 samples were heated and studied in situ in a CM20 electron microscope up to 900 degrees C. The Ni5Al3 phase first forming around 550 degrees C in the quenched L1(0) microtwinned martensite starts to decompose around 800 degrees C yielding B2 precipitates in a twinned L1(2) matrix. The latter twinning is a remainder of the microtwinning in the original room temperature martensite. Also the crystallographic relations between precipitates and matrix can be traced back to the original formation of twinned martensite plates within the austenite. Some aspects of the dynamics of the process are discussed on the basis of snap shots and video recordings.

Abstract: The new families of superconducting compounds ''1201'' (Hg0.4Pr0.6Sr2CuO4+delta), ''1212'' (Hg0.4Pr0.6Sr2(Ca1-x-ySrxPry) Cu2O6+delta), and ''1222'' (Hg0.4Pr0.6Sr2(Pr1.7Sr0.3)(2)Cu2O8+delta) all show ordering between praseodymium and mercury in the (Hg,Pr)O-delta plane, reducing the symmetry from tetragonal to orthorhombic or even to monoclinic. In the 1201 compound the ordered superstructure can be described as O-I (a(I) approximate to 2a(p), b(I), approximate to a(p), c(I) approximate to c(1201)). In the 1212 compound two distinct superstructures are identified, O-I (a(I) approximate to 2a(p), b(II) approximate to a(p), c(I) approximate to c(1212)) and O-II (a(II) approximate to 2a(p), b(II) approximate to a(p), c(II) approximate to 2c(1212)). In some compounds, such as Hg0.4Pr0.6Sr2(Ca0.4Sr0.4Pr0.2) Cu2O6+delta, the Hg-Pr ordering is only present in microdomains, but due to an ordering between Sr layers and Ca layers, the c-axis doubles and one obtains a tetragonal superstructure T-III (a(III) approximate to a(p), c(III) approximate to 2c(1212)). In the 1222 compound, ordering in the (Pr,Hg)O-delta plane is very defective; a large number of translation defects actually reduce the symmetry to triclinic. (C) 1995 Academic Press, Inc.

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: Five new layered cuprates, with a 1222-type structure, have been synthesized according to the formula (Hg(1-x)M(x))(Sr,Ba)(2) Pr2Cu2O9-delta with M = Pr, Pb, Pi, and Tl. They crystallize in a tetragonal cell with a approximate to a(p) and c approximate to 29.5 Angstrom; their structure consists in a triple intergrowth of oxygen-deficient perovskite, rock-salt-and fluorite-type layers. They are characterized by a mixed [Hg(1-x)M(x)O(1-delta)] layer in the rock-sail-type slice. The ED and HREM studies show that Tl, Bi, and Pb are statistically distributed in the mixed [Hg(1-x)M(x)O(1-delta)] layer, contrary to Pr which involves an ordering phenomenon along a. Different stacking defects are observed and discussed as well as the cleavage mode of the crystals. (C) 1995 Academic Press, Inc.

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.