Bridging the Ruddlesden–Popper and the Dion–Jacobson series of layered perovskites: synthesis of layered oxides, A2–xLa2Ti3–xNbxO10(A = K, Rb), exhibiting ion exchange

Solid solutions of the formula, A2–xLa2Ti3–xNbxO10(A = K, Rb), exist for the range 0[less-than-or-eq]x[less-than-or-eq]1.0, bridging n= 3 members of the Ruddlesden–Popper series (A2La2Ti3O10) and the Dion–Jacobson series (ALa2Ti2NbO10). For 0[less-than-or-eq]x[less-than-or-eq]0.75, the phases possess body-centred structures characteristic of the Ruddlesden–Popper phases, while the x= 1 members are isostructural with KCa2Nb3O10(A = K) and CsCa2Nb3O10(A = Rb). Protonated derivatives, H2–xLa2Ti3–xNbxO10, which are prepared by ion exchange, retain the structural difference of the parent phases. A difference in the Brønsted acidity of the protonated derivatives revealed by intercalation experiments with organic bases seems to be related to this structural difference.

Deformation dynamics of SS-316 Between 1023-K TO 1223-K In The Framework of Cottrell-Stokes Law

Kocks' formalism for analysing steady state deformation data for the case where Cottrell-Stokes law is valid is extended to incorporate possible back stresses from solution and/or precipitation hardening, and dependence of pre-exponential factor on the applied stress. A simple graphical procedure for exploiting these equations is demonstrated by analyzing tensile steady state data for a type 316 austentic stainless steel for the temperature range 1023 to 1223 K. In this instance, the computed back stress values turned out to be negative, a physically meaningless result. This shows that for SS 316, deformation in this temperature regime can not be interpreted in terms of a mechanism that obeys Cottrell-Stokes law.

Fe-57 Mössbauer and Mo K-EXAFS Investigations of MoxFe3-xO4, an Interesting Mixed-Valent Oxide System

Ferrites of the formula MoxFe3-xO4, prepared by a soft-chemistry route, show mixed valence states of both iron and molybdenum cations. Mössbauer studies show that Fe2+ and Fe3+ ions are present on both the A and B sites, giving Fe an average oxidation state between 2+ and 3+. Molybdenum is present in the 3+ and the 4+ states on the B sites. The presence of Mo in the 3+ state has been established by determining the Mo3+-O distance (2.2 Å), for the first time, by Mo K-EXAFS. The mixed valence of Fe on both the A and B sites and of Mo on the B sites is responsible for the fast electron transfer between the cations. All the Mössbauer parameters including the line width show a marked change at a composition (x ? 0.3) above which the concentration of Fe2+A increases rapidly.

Random sequential multilayer deposition of different‐sized k mers on a one dimensional infinite substrate

Kinetics of random sequential, irreversible multilayer deposition of macromolecules of two different sizes on a one dimensional infinite lattice is analyzed at the mean field level. A formal solution for the corresponding rate equation is obtained. The Jamming limits and the distribution of gaps of exact sizes are discussed. In the absence of screening, the jamming limits are shown to be the same for all the layers. A detailed analysis for the components differing by one monomer unit is presented. The small and large time behaviors and the dependence of the individual jamming limits of the k mers and (k−1) mers on k and the rate parameters are analyzed.

Synthesis of Layered Perovskite Oxides, ACa2-xLaxNb3-xTix010 (A = K, Rb, Cs), and Characterization of New Solid Acids, HCa2-xLaxNb3-xTixOlo (0 < x d 2), Exhibiting Variable Bronsted Acidity?

Layered perovskite oxides of the formula ACa~,La,Nb3-,Ti,010 (A = K, Rb, Cs and 0 < x d 2) have been prepared. The members adopt the structures of the parent ACazNb3010. Interlayer alkali cations in the niobium-titanium oxide series can be ion-exchanged with Li+, Na+, NH4+, or H+ to give new derivatives. Intercalation of the protonated derivatives with organic bases reveals that the Bronsted acidity of the solid solution series, HC~ ~ , L ~ ,N~ ~ , T ~ ,dOep~eOnd, s on the titanium content. While the x = 1 member (HCaLaNbzTiOlo) is nearly as acidic as the parent HCazNb3010, the x = 2 member (HLazNbTizOlo) is a weak acid hardly intercalating organic bases with pKa - 11.3. The variation of acidity is probably due to an ordering of Nb/Ti atoms in the triple octahedral perovskite slabs, [Ca~,La,Nb~,Ti,0~0], such that protons are attached to NbO6 octahedra in the x = 1 member and to Ti06 octahedra in the x = 2 member.

New Approximation Algorithms for Minimum Cycle Bases of Graphs

We consider the problem of computing an approximate minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. Although in most such applications any cycle basis can be used, a low weight cycle basis often translates to better performance and/or numerical stability. Despite the fact that the problem can be solved exactly in polynomial time, we design approximation algorithms since the performance of the exact algorithms may be too expensive for some practical applications. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k >= 1, we give (2k - 1)-approximation algorithms with expected running time O(kmn(1+2/k) + mn((1+1/k)(omega-1))) and deterministic running time O(n(3+2/k) ), respectively. Here omega is the best exponent of matrix multiplication. It is presently known that omega < 2.376. Both algorithms are o(m(omega)) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Theta(m(omega) ) bound. We also present a 2-approximation algorithm with expected running time O(M-omega root n log n), a linear time 2-approximation algorithm for planar graphs and an O(n(3)) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.