Studies on the Hydrolytic Behavior of Zirconium(IV)

The stability constants of zirconium(IV) hydrolysis species have been measured at 15, 25, and 35 °C [in 1.0 mol-dm^–3 (H,Na)ClO₄] using both potentiometry and solvent extraction. In addition, the solubility of [Zr(OH)₄(am)] has been investigated in a 1 mol-dm^–3 (Na,H)(ClO₄,OH) medium at 25 °C over a wide range of –log [H⁺] (0-15). The results indicate the presence of the monomeric species Zr(OH)³⁺, Zr(OH)₂ ²⁺, Zr(OH)₃ ⁺, and Zr(OH)₄ ⁰(aq) as well as the polymeric species Zr₄(OH)₈ ⁸⁺ and Zr₂(OH)₆ ²⁺. The solvent extraction measurements required the use of acetylacetone. As such, the stability constants of zirconium(IV) with acetylacetone were also measured using solvent extraction. All stability constants were found to be linear functions of the reciprocal of temperature (in kelvin) indicating that H ^o and S ^o are both independent of temperature (over the temperature range examined in the study). The results of the solubility experiments have shown four distinctly different solubility regions. In strongly acidic solutions, the solubility is controlled by the formation of polynuclear hydrolysis species in solution whereas in less acidic solution the formation of mononuclear hydrolysis species becomes dominant. The largest portion of the solubility curve is controlled by equilibrium with aqueous Zr(OH)₄ ⁰(aq) where the solubility is independent of the proton concentration. In alkaline solutions, the solubility increases due to formation of the zirconate ion. The middle region was used to determine the solubility constant (log *K _s10) of Zr(OH)₄(s). From the data in the alkaline region, a value of the stability of the zirconate ion has been determined. This is the first time that the possible evidence for the zirconate ion has been identified in aqueous solution that has previously been found only in the solid phase.     

Spectral analysis of multichannel MRS data

The use of phased-array receive coils is a well-known technique to improve the image quality in magnetic resonance imaging studies of, e.g., the human brain. It is common to incorporate proton (1H) magnetic resonance spectroscopy (MRS) experiments in these studies to quantify key metabolites in a region of interest. Detecting metabolites in vivo is often difficult, requiring extensive scans to achieve signal-to-noise ratios (SNR) that provide suitable diagnostic results. Combining the MR absorption spectra obtained from several receive coils is one possible approach to increase the SNR. Previous literature does not give a clear overview of the wide range of possible approaches that can be used to combine MRS data from multiple detector coils. In this paper, we consider the multicoil MRS approach and introduce several signal processing tools to address the problem from different nonparametric, semiparametric, and parametric perspectives, depending on the amount of available prior knowledge about the data. We present a numerical study of these tools using both simulated 1H MRS data and experimental MRS data acquired from a 3T MR scanner.     

Die Struktur von blauen Goldsolen

Zusammenfassung Die Eigenschaften verschiedener Arten von blauen Goldsolen wurden besprochen. Die durch Reduktion einer neutralen oder alkalischen Aurichloridlösung erhaltenen blauen Sole wurden nach verschiedenen Methoden untersucht: Keimmethode, magnetische Doppelbrechung usw. Es darf geschlossen werden, daß diese Sole wenigstens zum Teil aus einem der Oxyde des Goldes bestehen.     

Treewidth computation and extremal combinatorics

For a given graph G and integers b,f ≥0, let S be a subset of vertices of G of size b+1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every graph on n vertices contains at most $n\left( {_b^{b + f} } \right)$ such vertex subsets. This result from extremal combinatorics appears to be very useful in the design of several enumeration and exact algorithms. In particular, we use it to provide algorithms that for a given n-vertex graph G

1. compute the treewidth of G in time O(1.7549 ⁿ ) by making use of exponential space and in time O(2.6151 ⁿ ) and polynomial space
2. decide in time O(n ⁵· $_{k + 2}^{\left\lceil {(2n + k + 8)/3} \right\rceil } $ ) if the treewidth of G is at most k
3. list all minimal separators of G in time O(1.6181 ⁿ ) and all potential maximal cliques of G in time O(1.7549 ⁿ ).

This significantly improves previous algorithms for these problems.     

Twenty-third MAX-lab User Meeting

The 23^rd Annual User Meeting for MAX-lab users was held at Scandic Star Hotel in Lund, Sweden, on November 8-10, 2010. The meeting was, as in previous years, jointly organized by MAX-lab and the MAX-lab Association for Synchrotron Radiation Users (FASM). From the start in the late 1980s these meetings have grown with the user community of MAX-lab, and with increasing interest in the development of MAX IV, the coming synchrotron radiation facility in Sweden (http://www.maxlab.lu.se/maxlab/max4/index.html.), this growth has accelerated. The last four meetings have hosted around 300 participants, with a new record number of 342 registered participants and 26 commercial exhibitors at this meeting!     

Status of the MAX IV Laboratory

On the day of the 2016 summer solstice, June 21, MAX IV, the new synchrotron radiation facility in Lund, Sweden, will be inaugurated. MAX IV is setting a new standard in terms of emittance, thereby providing beamlines with the best possible brilliance and coherence. At the same time, MAX IV continues a more than three-decades-long successful history of Swedish synchrotron-radiation-based research. The activities at the present MAX-lab, which officially started when the MAX I storage ring opened for users in 1986, have been concluded with a “last beamdump” ceremony for the MAX II and MAX III storage rings on December 13, 2015, Saint Lucy's Day. In Sweden, the winter solstice is celebrated with a festival of light.     

How quantitative is the concept of maximum overlap?

A criterion based on the concept of maximum overlap has been used as an optimizing principle to obtain approximate all valence electron wave functions for a variety of molecules. By means of this procedure, the wave functions are obtained without the use of parameters, semiempirical data, or integral approximations. Even though there are obvious errors in such an approach, the charge densities and dipole moments calculated from these wave functions have a surprising degree of validity. It does appear, though, that the results will be most reasonable for strongly covalent molecules, where large amounts of charge migration are not involved.

---

Zusammenfassung Ein Kriterium auf Grund der Konzeption der maximalen Überlappung wurde als Optimalisierungsprinzip verwendet, um Wellenfunktionen für alle Valenzelektronen einer ganzen Reihe von Molekülen zu finden. Auf diesem Weg werden keine Parameter, semiempirische Daten oder Integral-näherungen benötigt. Trotz der offensichtlichen Vernachlässigungen sind die erhaltenen Ladungsdichten und Dipolmomente erstaunlich gut. Allerdings scheint es, als ob die Ergebnisse bei ausgeprägt kovalenten Molekülen am besten wären, wo größbere Ladungsverschiebungen nicht auftreten.

---

Resumé Utilisation d'un critère fondé sur le concept du recouvrement maximum comme principe pour obtenir des fonctions d'onde pour tous les électrons de valence de toute une variété de molécules. A l'aide de ce procédé les fonctions d'onde sont obtenues sans l'emploi de paramètres, de données semi-empiriques ou d'approximation d'intégrales. Quoique cette approche comporte des erreurs évidentes, les densités de charge et les moments dipolaires calculés à partir de ces fonctions d'onde ont un degré de validité surprenant. Il apparaît néanmoins que les résultats seront d'autant plus raisonnables que les molécules seront plus covalentes et ne comporteront pas de transferts de charges importants.

---

---

This work was supported in part by the National Science Foundation, Grant NSF-GP-16666.

---

IBM Graduate Fellow.     

Hydrogen in oxides

The paper reviews the history and present understanding of protons in oxides; their defect chemistry, thermodynamics, and transport. Focus is put on correlations between hydration thermodynamics and other materials properties which may help to predict proton uptake and proton conduction in oxides. Also effects of defect association and the particular problem of high grain boundary resistance in high temperature proton conductors are addressed. In the second part, a number of experimental observations attributed to the presence of hydride ions under mildly reducing conditions are discussed in relation to the unlikelihood that general thermodynamic considerations predict of finding these species under such conditions.