Density functional studies are performed on the structures, stabilities, electronic properties, and polarizabilities of the Ga13M(M = Li, Na, K, and Rb) clusters, which have closed electronic shell structures, enhanced stabilities, large HOMO-LUMO energy gaps, high vertical ionization potentials, and low vertical electron affinities. All of these properties are characteristic of a magic cluster and can be well understood by the jellium model. Therefore, we strongly suggest Ga13M(M = Li, Na, K, and Rb) are magic clusters and promising as building blocks in developing cluster-assembled materials. The calculated vertical electron affinity of Ga-13 is close to that of bromine, implying it would be like a halogen atom in the Ga13M molecule. The static linear polarizabilities and first-order hyperpolarizabilities of Ga13M clusters are significantly larger than those of Ga-13 because of their lower symmetries and higher delocalization of p electrons. (C) 2013 Elsevier B.V. All rights reserved.
Lichkova, N. V.
Zagorodnev, V. N.
Okhrimchuk, A. G.
Butvina, L. N.
Irzhak, D. V.
Karandashev, V. K.
We have demonstrated for the first time the possibility of preparing high-purity and praseodymium- and dysprosium-doped solid solutions based on lead halides and alkali metals: Rb1 - x Cs (x) Pb2Cl5, Rb1 - x Cs (x) Pb2Br5, Rb1 - x K (x) Pb2Cl5, and RbPb2Cl5 - y Br (y) . According to X-ray diffraction data, Rb1 - x Cs (x) Pb2Cl5 and Rb1 - x Cs (x) Pb2Br5 crystals in the solid solution range are isostructural with the constituent double salts RbPb2Cl5 and RbPb2Br5, respectively. The double salt Rb0.5K0.5Pb2Cl5 is isostructural with KPb2Cl5, and the double mixed salt RbPb2Cl2.5Br2.5 is isostructural with RbPb2Br5. The Pr3+ and Dy3+ concentrations in crystals of the solid solutions and mixed salts were determined by inductively coupled plasma mass spectrometry (ICP-MS). In the Rb1 - x (Cs, K) (x) Pb(2)Hal(5) (Hal = Cl, Br) solid solutions, the dopants were observed to be nonuniformly distributed over the host. According to ICP-MS analysis data and absorption spectra, the Pr3+ and Dy3+ concentrations in the RbPbCl2.5Br2.5 crystals were higher than those in RbPb2Br5.
The classification of exact solutions, including solitons and elliptic solutions, to the generalized K(m, n) equation by the complete discrimination system for polynomial method has been obtained. From here, we find some interesting results for nonlinear partial differential equations with generalized evolution.
We define the notion of admissible pair for an algebra A, consisting on a couple (Gamma, R), where Gamma is a quiver and R a unital, splitted and factorizable representation of Gamma, and prove that the set of admissible pairs for A is in one to one correspondence with the points of the variety of twisting maps T(A)(n) := T (K(n), A). We describe all these representations in the case A = K(m).
From solutions containing 2-17 wt % TiO2 at the molar ratios M/Ti =3D 1-4, F/Ti =3D 2-4, and PO (4) (3-) /Ti =3D 0.5-10 under mild conditions, fluoro- and oxo(hydroxo) fluorophosphate titanates were isolated: crystalline M2TiF6 (M =3D K, Rb, Cs) and K2Ti2O2.5F2PO4 center dot 2H(2)O, and amorphous K3Ti4O(OH)F-7(PO4)(3) center dot 5H(2)O, Cs2Ti3O2F7PO4 center dot 6H(2)O, and CsTi3O3F4PO4 center dot 3H(2)O. In a mixture with M2TiF6 and KCl, phosphate-ion-containing crystalline phases of unidentified composition were detected. The phases were studied by elemental, crystal-optical, X-ray powder diffraction, thermal, IR spectroscopic, and electron microscopic analyses. Annealing fluorophosphate titanates gives a mixture of MTiOPO4 and TiO2. All the mentioned alkali metal fluorophosphates contain the tetrahedral ion PO (4) (3-) and titanium polyhedra with bonds Ti-F and Ti-O; some of them also contain bridging oxygen connecting titanium atoms: Ti-O-Ti; i.e., these substances are polymeric.
The set of all non-increasing nonnegative integer sequences pi = (d(v (1)), d(v (2)), aEuro broken vertical bar, d(v (n) )) is denoted by NS (n) . A sequence pi a NS (n) is said to be graphic if it is the degree sequence of a simple graph G on n vertices, and such a graph G is called a realization of pi. The set of all graphic sequences in NS (n) is denoted by GS (n) . A graphical sequence pi is potentially H-graphical if there is a realization of pi containing H as a subgraph, while pi is forcibly H-graphical if every realization of pi contains H as a subgraph. Let K (k) denote a complete graph on k vertices. Let K (m) -H be the graph obtained from Km by removing the edges set E(H) of the graph H (H is a subgraph of K (m) ). This paper summarizes briefly some recent results on potentially K (m) -G-graphic sequences and give a useful classification for determining sigma (H, n).