X-Ray Mapping and Interpretation of Scatter Diagrams

Electron beam induced quantitative X-ray mapping has become a very useful characterisation tool for determining the elemental distribution in materials, whether using energy dispersive spectroscopy or wavelength dispersive spectroscopy. The X-ray intensity distributions of the elements from an X-ray map allow us to generate two dimensional and ternary scatter diagrams thus converting spatial information into concentration dimensions, which is an important tool for displaying the spatial relationships of elements or correlated elements (phases) in materials. To best understand how to use this tool, we need to understand the production and features of the scatter diagram. The type of clustering observed in the scatter diagram, whether oval, linear or spherical, can give the major and trace element distributions within phases as well as qualitative and quantitative phase information. This paper demonstrates the generation of scatter diagrams, properties of scatter diagrams, interpretation of scatter diagrams and the advantages of scatter diagrams through the use of examples.     

Multinomial permutations on a circle

Multinomial permutations on a circle are considered in the framework of combinatorics. Different cases are presented and shown to agree with previously derived formula for the number of cyclic necklaces. Two applied examples are discussed with a view to illustrate the implications of derived formulas. Copyright © 2006 John Wiley & Sons, Ltd.     

Wave-vector diagrams for two-dimensional photonic crystals

Photonic crystals exhibit band gaps, meaning that electromagnetic fields cannot propagate in them for specific ranges of wavelengths and directions. The calculation of band structure diagrams has been intensively studied and is now well understood. In contrast to that, so-called wave-vector diagrams (i.e. dispersion surfaces, depicting the loci of all relevant wave vectors at a fixed wavelength) are less known and used. In principle, they show how the effective index of the structure depends on the direction of propagation. A method to calculate explicitly wave-vector diagrams for two-dimensional photonic crystals is derived which leads finally to quadratic eigenvalue problems. Results for square and triangular lattices are presented and some applications are discussed.     

Quantitative theory of living free‐radical polymerization. III. Calculation of copolymerization products' spinodal

The problem of finding conditions of the loss of thermodynamic stability by the reaction system was solved on the basis of the developed theory of living free‐radical copolymerization. The spinodal's calculations were carried out for a significant number of systems differing in the values of kinetic, stoichiometric, and thermodynamic parameters. Analysis of the results of such calculations revealed some regularities in the spinodal curves' behavior and permitted us to classify their possible topological types. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 892–902, 2003     

亚双曲型广义Cartan矩阵的分类

本文解决了一类非双曲型的不定型（亚双曲型）广义Ｃａｒｔａｎ矩阵的分类问题．证明了亚双曲型矩阵的阶数范围，并做出了阶数为３，５，６的亚双曲型广义Ｃａｒｔａｎ矩阵的Ｄｙｎｋｉｎ图．     

New results for virial coefficients of hard spheres inD dimensions

We present new results for the virial coefficientsB _k for κ<- 10 for hard spheres in dimensionsD = 2,..., 8.     

The phase diagram of a single polymer chain: New insights from a new simulation method

We present simulation results for the phase behavior of a single chain for a flexible lattice polymer model using the Wang-Landau sampling idea. Applying this new algorithm to the problem of the homopolymer collapse allows us to investigate not only the high temperature coil–globule transition but also an ensuing crystallization at lower temperature. Performing a finite size scaling analysis on the two transitions, we show that they coincide for our model in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil–globule transition. As a consequence, also the many chain phase diagram of this model can be predicted to consist only of gas and crystal phase in the limit of infinite chain length. This behavior is in agreement with findings on the phase behavior of hard-sphere systems with a relatively short-ranged attractive square well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2542–2555, 2006     

Topological order in the phase diagram for high-temperature superconductors with point defects

Applying a Lindemann like criterion obtained previously by Kierfeld et al. [J. Kierfeld, T. Nattermann, T. Hwa, Phys. Rev. B 55 (1997) 626], we estimate the magnetic field and temperature for a high-T_c superconductor, at which a topologically ordered vortex glass phase becomes unstable with respect to a disorder-induced formation of dislocations. The employed criterion is shown to be equivalent to a conventional phenomenological Lindemann criterion including the values for the numerical factors, i.e., for the Lindemann number. The positional correlation length of the topologically ordered vortex glass is calculated.     

Specific features of the thermodynamics of activation in the LaNi<Subscript>5</Subscript>-H<Subscript>2</Subscript> and CeNi<Subscript>5</Subscript>-H<Subscript>2</Subscript> systems

Using heat conducting Tian—Calvet calorimetry and volumetric measurements, the first hydrogen absorption—desorption cycles in the LaNi₅-H₂ and CeNi₅-H₂ systems were studied. The pressure—composition isotherms were plotted, the equilibrium pressures of hydrogen along the absorption and desorption branches and in the region of hysteresis for different activation steps were determined, and the enthalpies of phase transitions α → β and β → α were calculated. The profiles of the heat evolution curves were analyzed. It was concluded that the mechanism of the reactions studied changes upon activation.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 134–139, January, 2005.     

Thermodynamic simulation of four-component carnallite type systems

Summary The standard method ofPitzer for predicting the solubility isotherms of systems in which solid phases with a constant composition crystallize is applied to cases when mixed crystals are formed. The four-component carnallite type systems RbCl-CsCl-MgCl₂-H₂O, RbCl-KCl-MgCl₂-H₂O, and RbCl-RbBr-MgCl₂-MgBr₂-H₂O and the corresponding subsystems are thermodynamically simulated at 25°C. It is established that the solubility diagrams consist of crystallization regions of the simple saltsMX,MX, MgX ₂·6H₂O, and MgX₂·6H₂O and of the corresponding carnallite type double salts with the composition 1:1:6. A method of calculation of the integralGibbs energy of mixingG ^mix(s) of crystals formed in water-salt systems has been proposed. The results on the systems RbCl-KCl-H₂O, RbCl-RbBr-H₂O, and MgCl₂-MgBr₂-H₂O are compared with experimental data from the literature and with values calculated using various models.

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Thermodynamische Simulation von Vierkomponentensystemen des Carnallit-Types

Zusammenfassung DiePitzer-Methode zur Voraussage der Löslichkeitsisothermen in Mehrstoffsystemen, in welchen feste Phasen mit konstanter Zusammensetzung auskristallisieren, wurde auch für Fälle angewendet, bei denen sich Mischkristalle bilden. Die Vierstoffsysteme RbCl-CsCl-MgCl₂-H₂O, RbCl-KCl-MgCl₂-H₂O und RbCl-RbBr-MgCl₂-MgBr₂-H₂O, aus welchen Carnallit-Typ-Mischkristalle auskristallisieren, und die dazugehörigen Dreistoff-Randsysteme wurden bei 25°C simuliert. Man stellt fest, daß die Löslichkeitsdiagramme sowohl Kristallisationsbereiche der einfachen SalzeMX,M'X, MgX ₂·6H₂O und MgX ₂·6H₂O als auch der entsprechenden carnallitartigen Doppelsalze mit der Zuzammensetzung 1:1:6 umfassen. Eine Methode zur Berechnung derGibbs-EnergieG ^mix(s) für die in Wasser-Salz-Systemen gebildeten Mischkristalle wird vorgeschlagen. Die für die Systeme RbCl-KCl-H₂O, RbCl-RbBr-H₂O und MgCl₂-MgBr₂-H₂O erhaltenen Ergebnisse werden mit experimentellen Literaturdaten und Resultaten von Berechnungen aufgrund verschiedener Modelle verglichen.