Work-hardening of Fe,Fe-0·5 wt% Si and Fe-0·9 wt% Si single crystals

Work-hardening curves of single crystals of iron and its alloys with 0·5 and 0·9 wt.% Si and paths of the tensile axis of specimens during deformation were investigated. Single crystals oriented for single glide were deformed in tension at temperatures 113, 201, 295 and 403 K at a nominal strain rate of 5·5×10^?5 sec^?1. It appears that with increasing silicon content (a) the transition between the high-temperature regime of plastic deformation (characterized by three-stage work-hardening) and the low-temperature regime is shifted to lower temperatures, (b) stage I-hardening is enhanced and (c) the flow stress level increases. These observations are explained by strong solution hardening of iron by silicon atoms which suppresses the differences between mobilities of screw and non-screw dislocations, increases the flow stress level and consequently the density of primary dislocations. As a result of this the latent hardening in the secondary slip system increases and stage I extends to a large strain.     

Temperature dependence of development of slip bands and of strain hardening in AgCl crystals

The dependence of the flow stress and the slip band density on the plastic strain has been measured at 201 K, 293 K and 363 K. The growth of deformation concentrated in an average slip band has been stated. The types of obstacles acting against the rise and development of a slip band and the temperature dependence of the strain hardening in AgCl crystals are discussed. An equation stating the dependence of the flow stress on the slip band density is presented. The hardening in AgCl crystals is classified as the stage III — hardening.     

New look at Gleason's theorem for signed measures

It is shown that the Gleason theorem holds not only for a finite but also for ann-finite signed measurem, wheren is a cardinal, defined on all closed subspaces of a Hilbert space whose dimension is a nonmeasurable cardinal 2, ifm is bounded from below on all one-dimensional subspaces.     

Dynamical systems with relaxation time

We define mathematically a class of dynamical systems that exhibit relaxation corresponding to that observed in physical systems, and then show that this class is identical with the class ofK-mixing dynamical systems.     

Effect of water of crystallization on magnetic properties of MgSO4

The object of this paper has been to determine the effect of water of crystallization on magnetic properties of MgSO₄. Changes in the magnetic properties of MgSO₄ in depenedence on the number of waters of crystallization have been established from the magnetic susceptibility changes. The value obtained by measurement differs from that calculated by the additivity law. This disagreement can be explained by the presence of the thermally independent Van Vleck's polarization paramagnetism _p .The paper brings forward calculations of _p values for the individual hydrates of MgSO₄.i H₂O fori=0, 1, ..., 7. Besides, it examines what portion of the polarization paramagnetism _pi of the overall values of _pci is due to the effect of water of crystallization. On the basis of this information the deviation from the spherical symmetry, caused by hydration of the MgSO₄ molecule, has been interpreted.     

Kinetics of the fluorescence of poly(N-vinylcarbazole) and poly(N-vinylcarbazole) with 2,4,7-trinitrofluorenone in the solid state

The fluorescence decay time measurements by the stroboscopic method have been made on films of amorphous poly(N-vinylcarbazole) (PVCA) and PVCA doped with 2,4,7-trinitrofluorenone (TNF). The obtained lifetimes of two excimer species have at 77 K and at 300 K values of about 43 ns and 9 ns, which are similar to other measurements. The kinetics of excimer fluorescence and energy transfer in PVCA films are described by a simple model of the Stern-Volmer type. It assumes the fast migration of localized singlet excitons and their trapping in two species of excimer traps.We propose a modified kinetic model for films of PVCA with TNF. In this model we assume besides the exciton migration and trapping on excimer and impurity traps also the direct energy transfer from two excimer species to charge transfer complexes of PVCA with TNF by the Förster dipole-dipole mechanism. The estimated critical distance of this transfer are about 10 Å.     

The conceptual analysis (CA) method in theories of microchannels: Application to quantum theory. Part III. Idealizations. Hilbert space representation

We illustrate the application of the conceptual analysis (CA) method outlined in Part I by the example of quantum mechanics. In the present part the Hilbert space structure of conventional quantum mechanics is deduced as a consequence of postulates specifying further idealized concepts. A critical discussion of the idealizations of quantum mechanics is proposed. Quantum mechanics is characterized as a “statistically complete” theory and a simple and elegant formal recipe for the construction of the fundamental mathematical apparatus of quantum mechanics is formulated. Our analysis may also lead to a criticism of quantum mechanics as a “strongly idealized” theory. A critical analysis of the fundamental structure of quantum mechanics seems an indispensable and natural starting point for the construction of new theories. A major technical problem in a more general application of the CA method is the lack of mathematical representation theorems for more general algebraic structures.     

On the theories of the interacting perturbations of the Reissner-Nordström black hole

A complete account of the Hamiltonian approach to the coupled perturbations of the Reissner-Nordström black hole, initiated by Moncrief, is given. All Hamiltonian equations are expressed explicitly in suitable forms; the metric and electromagnetic field perturbations are found in terms of Moncrief's gauge invariant canonical variables in the Regge-Wheeler gauge. The basic (both tetrad and coordinate) gauge invariant scalars occurring in the perturbation studies based on the Newman-Penrose formalism are then related to Moncrief's variables. The strikingly simple relations obtained enable us to show that the fundamental pair of decoupled equations, derived recently within the Newman-Penrose formalism by Chandrasekhar, can be cast into gauge invariant form, and that it can be obtained from Moncrief's formalism.It is demonstrated how the fundamental equations, supplemented by another combination of the Newman — Penrose equations, generalize the Bardeen-Press equations for uncoupled electromagnetic and gravitational perturbations of the Schwarzschild black hole.The odd and the even parityl=1 perturbations are also considered in detail. In the Appendix the relations to Zerilli's work on coupled perturbations of the Reissner-Nordström black hole are given.     

Über die Wahl der Lösungsmittelsysteme bei der papierchromatographischen Trennung organischer Verbindungen

Zusammenfassung An praktischen Beispielen wurde gezeigt, in welcher Weise die Trennung organischer Verbindungen mittels Papierchromatographie erzielt werden kann. Man ist nicht auf einige bewährte Lösungsmittel systeme allein angewiesen, sondern kann von Fall zu Fall systematisch neue und geeignete Systeme benützen. Es hat sich bewährt, sich nach den elementaren Löslichkeitsregeln für organische Stoffe zu richten, unter der Voraussetzung, daß die zu chromatographierende Verbindung in der stationären Phase gut, in der mobilen Phase dagegen weniger löslich ist. Durch Änderung der stationären Phase (Wasser, nicht wäßriges, polares Lösungsmittel, nicht polares Lösungsmittel) oder der Polarität und Zusammensetzung der mobilen Phase kann man das Wandern der Flecke am Chromatogramm beeinflussen, beliebige R_fWerte erhalten und in vielen Fällen auch eine beliebige Reihenfolge der Verbindungen am Chromatogramm erzielen.Da die Löslichkeit organischer Verbindungen von intermolekularen Kräften abhängig ist, erscheint das Problem im Zusammenhang mit strukturellen Einflüssen sehr kompliziert und muß für jeden Fall auf eigene Weise gelöst werden. Die Löslichkeitseigenschaften können weiter durch Benutzung reaktiver Lösungsmittel beeinflußt werden, die z. B. die Verbindungen in wasserlösliche Salze überführen können. Dabei ist an die möglichen Komplikationen, die bei ionisierbaren Verbindungen durch Dissoziation und Hydrolyse entstehen können, zu achten.Von den Hauptfaktoren, die eine Trennung ermöglichen können, seien die folgenden erwähnt: funktionelle Gruppen, ihre Anzahl, Polarität, gegenseitige Stellung, bzw. ihre Basizität oder Azidität, C-Atomanzahl in homologen Verbindungen, inter- und intramolekulare Wasserstoffbindungen, sterische Faktoren u. a. Es ist dann von der Art des gewählten Lösungsmittelsystems abhängig, welche der genannten Faktoren im Vordergrund stehen und welche beseitigt werden.Wenn die Löslichkeitsunterschiede der zu trennenden Stoffe zu gering sind, um gute Trennungen zu ermöglichen, ist es zweckmäßig, die Verbindungen in solche Derivate zu überführen, deren Strukturunterschiede größer sind.

---

Summary Practical examples are given to show how organic compounds can be separated by means of paper chromatography. The operator is not limited to tested solvent systems, but can use new suitable systems as the occasion demands. It has been found best to abide by the elementary rules of solubility of organic compounds, provided the compound to be chromatographed is quite soluble in the stationary phase but less soluble in the mobile phase. By altering the stationary phase (water, nonaqueous, polar solvent, non-polar solvent) or the polarity and composition of the mobile phase, the migration of the stains in the chromatogram can be influenced, selectedR _f -values can be obtained, and in many cases it is also possible to secure a desired succession of the compounds on the chromatogram.Since the solubility of organic compounds depends on intermolecular forces, the problem in connection with structural influences appears very complicated and must be solved individually for each case. Moreover, the solubility characteristics can be affected by using reactive solvents; for instance, the compounds can be converted into water soluble salts. Under such circumstances, sight must not be lost of the complications which may arise because of the dissociation and hydrolysis of ionizable compounds. The following are among the chief factors, which may make a separation possible: functional groups, their number, polarity, relative position, their basicity or acidity, C-atom number in homologous compounds, inter- and intramolecular hydrogen bonds, steric factors, etc. It then depends on the type of solvent system selected, which of these factors are predominant and which can be neglected or eliminated.If the solubility differences are too slight to permit good separations, the compounds to be separated should, if possible, be converted into derivatives whose structural differences are more pronounced.

---

Résumé Des exemples pratiques montrent comment il est possible d'effectuer la séparation de combinaisons organiques par Chromatographie sur papier. Il n'est pas uniquement fait appel à des systèmes de solvants éprouvés mais, dans certains cas, de nouveaux systèmes appropriés sont systématiquement utilisés.Il s'est avéré satisfaisant de faire appel aux règles élémentaires de solubilité des substances organiques sous réserve que la combinaison à chromatographier soit suffisamment soluble dans la phase stationnaire et moins soluble dans la phase mobile. En faisant varier la phase stationnaire (eau, solvant non aqueux, solvant polaire, solvant non polaire) ou la polarité et la composition de la phase mobile, il est possible d'influencer la migration des taches du chromatogramme, d'obtenir des valeurs deR _f désirées et, dans de nombreux cas, d'obtenir les combinaisons dans un ordre déterminé sur le chromatogramme.La solubilité des combinaisons organiques étant fonction des forces intermoléculaires il en résulte que le problème se complique considérablement dans la mesure où l'on considère les influences structurelles et que chaque cas particulier doit recevoir une solution qui lui est propre. Les propriétés de solubilité peuvent en outre être influencées par l'emploi de solvants réactifs qui peuvent transformer, par exemple les combinaisons en sels solubles dans l'eau. Il faut alors tenir compte des possibilités de complications qui peuvent apparaître par dissociation et hydrolyse des combinaisons ionisables.Parmi les principaux facteurs qui permettent une séparation, il convient de mentionner les suivants: les groupes fonctionnels, leur nombre, leur polarité, leur position relative, ou encore leur acidité ou leur basicité, le nombre d'atomes de carbone de combinaisons homologues, les liaisons hydrogène inter- et intramoléculaires, les facteurs stériques, etc. Suivant la nature du système solvant choisi pourront alors varier les facteurs dont l'effet est prépondérant et ceux dont l'effet est nul. Lorsque les différences de solubilité des substances à séparer sont trop faibles pour permettre des séparations satisfaisantes, il est commode de transformer les combinaisons en dérivés dont les différences de structure soient plus importantes.