Effective Coordination Number Research Articles

Eine “misslungene” synthese: Über K 4Li[IO 6] UND K 5I 2[AuO 2

Attempting to synthesize hitherto unknown K 4Li[IO 5] by heating mixtures of K 2O and LiIO 3 ( K: Li = 2.2:1, sealed gold tube, 700 °C) we obtained (formed by disproportion) colourless transparent single crystals of the new periodate K 4Li[IO 6] and also transparent green single crystals of K 5I 2[AuO 2], a new type of iodide aurate(I). According to single crystal data K 4Li[IO 6] crystallizes in an orthorhombic form with a = 1312.2 pm, b = 998.2 pm, c = 1118.9 pm ( Z = 8, space group Pbca). Stacked layers of KLiIO 6 are characteristic, connected along [001] by further K +. K 5I 2[AuO 2] also crystallizes in an orthorhombic form ( a = 1402.7 pm, b = 720.4 pm, c = 551.1 pm, Z = 2, space group Pbam). Characteristic for this structure are linear O-Au-O groups. All K + were coordinated octahedrally by 4I − and 2O 2−, these are in the trans position. The Madelung part of the lattice energy, MAPLE, and effective coordination numbers, ECoN, are calculated and discussed.

Zur kenntnis von kubischem Rb [formula omitted]MnF [formula omitted] [1

Rb 2MnF 6 cubic (Fm3m) with a=852,7(1) pm has been isolated for the first time as light yellow, stable (when exposed to air) single crystals. X F was refined from the four circle diffractometer data (Philips PW 1100; Mo-K α; 69 I o(hkl), R=5,8 R w=3,3%]), leading to d(Mn-F) = 178.5 pm (6x). The Madelung Part of lattice Energy, MAPLE, and Effective Coordination Numbers, ECoN, are discussed.

Surface structure determination by SEXAFS: The reliability of bond lengths and coordination numbers from multi-shell analyses

Any structural determination from measurements of surface extended X-ray absorption fine structure (SEXAFS) is dependent on deriving sufficient, reliable structural parameters from experimental spectra. The reliability with which a multi-shell analysis (based on computation of the EXAFS spectrum and comparison with experimental data) can produce bond lengths and coordination numbers has been tested. Furthermore, the limitations placed on such an analysis by superimposing typical experimental levels of random noise onto the input data set has been investigated, both in terms of the number of parameters which can be reproduced and their associated errors. Significance tests have also been applied to a multi-shell analysis of experimental SEXAFS measurements of chlorine adsorbed on silver {110}. These tests on both real and simulated data show that a number of (reproducible) bond lengths may be expected from a multi-shell analysis and with a sufficient accuracy to distinguish between shells separated by as little as ≈ 0.3 A ̊ , for a maximum k of 8.7 Å −1. The effective coordination number of the nearest-neighbour shell can be reproduced within an error limit of ±0.2. Large correlations between Debye-Waller factors, coordination numbers and inelastic terms in the EXAFS amplitude place a high degree of inaccuracy, in some cases as high as ±3, on the values obtained for the effective coordination number of higher shells, which cannot by themselves be used to infer the adsorption site geometry of an adatom.

On the coordination number of self-avoiding two-dimensional random walks

A numerical value for the effective coordination number of self-avoiding random walks has recently been obtained by analytical considerations. This value differs considerably from the empirical value obtained by computer simulations. It turns out that a seemingly severe simplification in the analytical approach is not the first cause of this discrepancy.

Monte Carlo test of a hyperscaling relation for the two-dimensional self-avoiding walk

The authors simulated self-avoiding walks on the square lattice with fixed endpoints by means of a dynamic Monte Carlo algorithm. From these data they obtain an evaluation of the effective coordination number mu and the critical exponents alpha and v. They can therefore test the hyperscaling relation 2- alpha =dv with a careful estimate of systematic and statistical errors.

Superconductivity and magnetic ordering in the mixed ternary ErxY1−xRh1.1Sn3.6 system

The superconducting transition temperature Tc as well as the magnetic ordering temperature Tm have been determined in the mixed ternary compound ErxY1−xRh1.1Sn3.6 as a function of the Er concentration. Tc decreases from 3.13 K for YRh1.1Sn3.6 to 1.1K for ErRh1.1Sn3.6. Reentrant superconductivity has been found for x > 0.6. The application of the models of Abrikosov and Gorkov, Maekawa and Tachiki, and Roshen and Ruvalds to this system is discussed. Tc as function of the concentration x is best described by the model of Roshen and Ruvalds assuming a ferromagnetic interaction between the spins. The parameter I2N(0), arising from electron spin, is found to be 0.088 K. The ferromagnetic ordering temperature dependence is described by the theory of Oguchi and Ono, using an effective coordination number z = 6 and an exchange constant of J′ = 0.30 K.

Zur Kenntnis von KCrF4/On KCrF4

Abstract KCrF4 has been prepared as yellowish-green single crystals (by heating of KF, CuF2 , CrF3 ; Au-tube, 750 °C, 60d). It crystallizes in the orthorhombic crystal system (Pnma) with: a = 1573.2, b = 743.2, c = 1833.1 pm, Z = 24. The structure shows [Cr3F9F6/2]3--columns along [010], The Madelung Part of Lattice Energie, MAPLE, is calculated and discussed, along with Effective Coordination Numbers, ECoN (via Mean Fictive Ionic Radii, MEFIR). The structure is described using SCHLEGEL-diagrams.

The effective coordination number of self-avoiding two-dimensional random walks

It is demonstrated that the effective coordination number of self-avoiding random walks in a plane is given by exp(− π 2/24) = 0.66283.

A Monte Carlo simulation of the inhomogeneous Lebwohl-Lasher lattice model

Abstract A Monte Carlo computer simulation of a modified Lebwohl-Lasher model is presented. The model consists of a set of interaction centres placed at the sites of a cubic lattice. The angular part of the pair potential is a second Legendre polynomial of the relative orientation between the two particles, like that of the Lebwohl-Lasher model. Each particle interacts with its six nearest neighbours with an attractive anisotropic potential differing in strength for the four horizontal and the two vertical neighbours. Various values of the in-plane to out-of-plane coupling ratio δ have been considered, i.e. δ = 0.75, 0.5, 0.1, 0.0. The latter case corresponds to the limiting situation of a two-dimensional lattice. Systems with a 1000 particles have been simulated for δ = 0.75, 0.5 and 0.1 while a sample of 3600 particles has been investigated for the two-dimensional lattice. Comparisons are made with available simulations and with mean field theory. We find that the molecular field theory predictions worsen as the effective coordination number is decreased. Energy, specific heat, second and fourth rank order parameters have been evaluated for the various models. We also present, for the first time, a way of approximately reconstructing the pair distribution, G(r12, ω12), using maximum entropy and second and fourth rank two particle order parameters.

Ein neues quaternäres Oxocadmat: Cs2K2Cd3O5 [1] / A New Quaternary Oxocadmate: Cs2K2Cd3O5 [1

Abstract Cs2K2Cd3O5 has been prepared from mixtures of the binary oxides in a silver-tube (550 °C. 17 days). The unit cell is triclinic, P1̄ (a = 983.2, b = 918.0, c = 653.5 pm. α = 108.3°, β = 113.7°, γ = 99.9°. The crystal structure was refined to R = 5.9% and /?u = 5.8% (four-circle-diffractome­ter data, 2616 unique of 3359 measured reflexions). The Effective Coordination Numbers (ECoN) and the Madelung Part of Lattice Energy (MAPLE) are calculated and discussed.

ChemInform Abstract: Lewis Acid and Lewis Base Behaviour of a Tellurium(II) Compound: A Mercury(II) Complex of a Bis‐Telluride Ligand with a 13‐Member Macrocyclic Chelate Ring.

Abstracto‐Brombenzaldehyd (I) ergibt über das Acetal (II) den Telluroether (III), der mit Ethylendiamin (IV) zum Te‐substituierten Bis‐phenyl‐di‐ aza‐hexadien (V) führt.

Pseudo-percolation of charge carriers in molecularly doped polymers: A Monte Carlo study

Abstract Motivated by the recent work of Santos Lemus and Hirsch and of Pai, Yanus and Stolka on the concentration dependence of hole transport in selected molecularly doped polymers, a Monte Carlo computer study has been conducted. It predicts that transport should in principle exhibit percolative features without, however, showing a well-defined percolation threshold (“pseudo-percolation”). A threshold concentration c 0 for pseudo-percolation will be defined. In a van der Waals solid with exponential wavefunction overlap it decreases with decreasing wavefunction localization because of non-nearest-neighbour jumps. A relation between c 0 and the effective coordination number of the lattice, defined via overlap, is established. For c < c 0 the carrier mobility remains finite and follows approximately a power law, μ∝c m, in accord with experiment. The exponent m increases with increasing localization of the wavefunction which depends on the energetic separation between the transport levels of dopant and host.

Lewis acid and Lewis base behaviour of a tellurium(II) compound: a mercury(II) complex of a bis-telluride ligand with a 13-member macrocyclic chelate ring

The structure of 1,6-bis-2-butyltellurophenyl-2,5-diazahexa-1,5-diene (1) reveals a weak tellurium–nitrogen interaction giving the tellurium atom an effective co-ordination number of 3; with HgCl2, (1) forms the complex [HgCl2·(1)] which is monomeric with four-co-ordinate mercury(II) bonded to two chlorine and two tellurium atoms, (1) thus forming a 13-membered chelate ring.

Neue Oxide des Formeltyps A2[T3O4]: Rb2Li2SiO4 [1 ] und Rb2Li2GeO4 [2 ] / New Oxides o f the Formula Type A2[T3O4]: Rb2Li2SiO4 [1 ] and Rb2Li2GeO4 [2

Rb2Li2Si04 and Rb2Li2Ge04 were prepared from the binary oxides in closed Ni-tubes at 800 and 850 °C, respectively. Crystal structures of the isotypic compounds were determined from four-circle diffractometer data (2018 and 1509 Io(hkl), R = 8.37%, Rw = 6.39% and R = Rw = 13.68%). They crystallize triclinically, P1̄, a = 897.92(11), b = 564.73(5), c = 546.99(6) pm, α = 93.95(10), β = 111.24(9), γ = 93.75(10)° (Rb2Li2SiO4) and a = 905.4(9), b = 575.4(7), c = 560.6(7) pm, α = 94.67(9), β = 110.82(10), γ = 93.60(9)° (Rb2Li2GeO4) (Guinier-Simon-data). Z = 2. Effective Coordination Number (ECoN) and Madelung Part of Lattice Energy (MAPLE) values were calculated. The structure is described using Schlegel-diagrams.

Ein neues oxomanganat(II): KNaMnO 2

KNaMnO 2 has been prepared for the first time from the binary oxides in the form of an orange-coloured powder (550°C, 5 days, nickel or silver cylinders) and single crystals (650°C, 17 days). It crystallizes in the orthorhombic space group Cccm ( a = 9.696 A ̊ , b = 9.343 A ̊ and c = 6.936 A ̊ , Z = 8; four-circle diffractometer data; Ag K \\ ̄ ga radiation; 672 from 680 I 0( hkl); R = 7.13%, R w = 4.35%). KNaMnO 2 represents a compound of the formula type A 2[(TO) 2] 2 with K 1 [6] K 2 [6] Na 2 [4] Mn 2 [4] O 1 2 [7] O 2 2 [7] . The effective coordination numbers and the Madelung part of the lattice energy are calculated and discussed.

Ein neues oxothallat(III): K 2Na 3[TlO 4] (mit einer bemerkung zum begriff der isotypie)

Pale yellow transparent single crystals of K 2Na 3[TlO 4] (powder: lemon coloured) were freshly prepared from completely pulverized mixtures of the binary oxides (K 2O, Na 2O, Tl 2O 3) (closed silver cylinder, 550°C, 10 days). It crystallizes in space group Pnnm with a = 959.9(2) pm, b = 928.1(2) pm, c = 766.2(2) pm and Z = 4 (four-circle diffractometer data, 1444 I o ( hkl), R = 6.49%, R w = 7.69%, Ag Kα; for the parameters see the text). K 2Na 3([TlO 4)] is isotypic with Na 2Li 3[GaO 4]. The comparison with the parent type is given by a new concept. The Madelung part of lattice energy (MAPLE) and effective coordination numbers (ECoN), the latter derived from the mean effective ionic radii (MEFIR), are calculated and discussed.

The Cooper-Harrison catastrophe in the case of the multistate models for unassociated solvent structure at polarizable interfaces

The possibility of occurrence of the so-called Cooper—Harrison catastrophe has been discussed in the case of a multistate model for unassociated solvent structure at a polarizable interface by Fawcett and de Nobriga. The catastrophe is avoided when the effective coordination number, C c , is greater than 14.5. The case when C c < 14.5 has been discussed.

Adsorption isitherms for neutral organic compounds—a hierarchy in modelling Part IV. Charge of maximum adsorption—statistical mechanical basis

The charge at which adsorption of organic compounds attains a maximum (σ max M ) at an electrochemical interface is analysed using several multi-state models in a hierarchical manner. The analysis is based on statistical mechanical results for the following models: (A) two-state site parity, (B) two-state multi-site, and (C) three-state site parity. The coulombic interactions due to permanent and induced dipole effects (using mean field approximation), electrostatic field effects and specific substrate interactions have been taken into account. The simplest model in the hierarchy (two-state site parity) yields the explicit dependence of σ max M on the permanent dipole moment, polarizability of the solvent and the adsorbate, lattice spacing, effective coordination number, etc. Other models in the hierarchy bring to light the influence of the solvent structure and the role of substrate interactions, etc. As a result of this approach, the “composition” of σ max M in terms of the fundamental molecular constants becomes clear. With a view to use these molecular results to maximum advantage, the derived results for σ max M have been converted into those involving experimentally observable parameters like C 0 , C 1 , E N , etc. Wherever possible, some of the earlier phenomenological relations reported for σ max M , notably by Parsons, Damaskin and Frumkin, and Trasatti, are shown to have a certain molecular basis, viz. a simple two-state site parity model. As a corollary to the hierarchical modelling, σ max M and the potential corresponding to it ( E max ) are shown to be constants independent of θ max or c org for all models. The implication of our analysis for σ max M with respect to that predicted by the generalized surface layer equation (which postulates σ max and E max variation with θ) is discussed in detail. Finally we discuss in passing σ min M and the electrosorption valency in this context.

Adsorption isitherms for neutral organic compounds—A hierarchy in modelling: Part IV. Charge of maximum adsorption—Statistical mechanical basis

The charge at which adsorption of organic compounds attains a maximum (σ max M) at an electrochemical interface is analysed using several multi-state models in a hierarchical manner. The analysis is based on statistical mechanical results for the following models: (A) two-state site parity, (B) two-state multi-site, and (C) three-state site parity. The coulombic interactions due to permanent and induced dipole effects (using mean field approximation), electrostatic field effects and specific substrate interactions have been taken into account. The simplest model in the hierarchy (two-state site parity) yields the explicit dependence of σ max M on the permanent dipole moment, polarizability of the solvent and the adsorbate, lattice spacing, effective coordination number, etc. Other models in the hierarchy bring to light the influence of the solvent structure and the role of substrate interactions, etc. As a result of this approach, the “composition” of σ max M in terms of the fundamental molecular constants becomes clear. With a view to use these molecular results to maximum advantage, the derived results for σ max M have been converted into those involving experimentally observable parameters like C 0, C 1, E N, etc. Wherever possible, some of the earlier phenomenological relations reported for σ max M, notably by Parsons, Damaskin and Frumkin, and Trasatti, are shown to have a certain molecular basis, viz. a simple two-state site parity model. As a corollary to the hierarchical modelling, σ max M and the potential corresponding to it ( E max) are shown to be constants independent of θ max or c org for all models. The implication of our analysis for σ max M with respect to that predicted by the generalized surface layer equation (which postulates σ max and E max variation with θ) is discussed in detail. Finally we discuss in passing σ min M and the electrosorption valency in this context.

Sr 2InF 7-Sr 2[InF 7] oder Sr 2F[InF 6]? [1

The new compound Sr 2InF 7 single crystals has been prepared from a melt using single crystals, the strucutre of Sr 2InF 7 is isotypic with K 2NbF 7 [2]. Details of the structure are discussed, using the Madelung Part of Lattice Energy, MAPLE, and Effective Coordination Numbers, ECoN.