Study of the extraction of phosphomolybdic acid by radiotracers and application to the titration of phosphorus in steels

We studied the extraction of phosphomolybdic acid labelled with⁹⁹Mo and³²P and of other species extracted. From the influence of the acidity and of the concentration of excess molybdenum on the distribution coefficient of phosphorus, we propose the following equilibrium for the formation of phosphomolybdate in our experimental conditions $$12/7H_6 Mo_7 O_{24} + H_3 PO_4 \rightleftharpoons PMo_{12} O_{40}^{3 - } + 3H^ + + 36/7H_2 O.$$ We show that the best yield of extraction is obtained with isobutyl acetate. From the relation between the quantities of molybdenum and phosphorus extracted, extraction of “free” molybdenum has been shown. It can be eliminated by washing the organic phase with a 5M HNO₃ solution. Subsequently we test a method using radioactive molybdenum, proposed by J. E. KENNEY and M. P. MENON¹ for the titration of phosphorus in steels. Because of the presence of interfering elements (Nb, Zr, Ti, V, Si, etc.) specific conditions for the extraction of phosphomolybdic acid have to be found for the application of this method to steels.     

Cyclopropylidenecyclanes - IV Comportement inattendu du E-tétraméthyl-2,2,2′,2′ Bicyclopropylidène vis à vis d'halogénocarbènes.

(E) 2,2,2′,2′-tetramethylcyclopropylidene undergoes a double addition of dibromocabene leading to a tetrabromobicyclo [5.1.0] octene derivative.     

Electromagnetic waves near perfect conductors. I. Multiple scattering expansions. Distribution of modes

An expansion is established for the Green functions describing electromagnetic waves in the presence of a perfectly conducting boundary. Each term represents a process for which the wave scatters several times on the boundary and propagates freely in between. This multiple scattering expansion reduces to ray optics in the high frequency limit, and thus provides a general framework to study diffraction corrections. It also allows one to evaluate quantities averaged over the spectrum. Some symmetry properties of the expansion are exhibited, in particular, the replacement of magnetic fields by electric fields results in a change of sign at each scattering. Convergence is proven for any smooth boundary in the domain Im k ? | Re k | of complex wavenumbers k. The continuation of the convergence domain around k = 0 is shown to depend upon the topology of the boundary. The multiple scattering expansion method is applied to determine the distribution of electromagnetic eigenmodes in a conducting cavity. The density of modes ?(k) is analyzed in terms of closed classical rays, bouncing off the walls with mirror reflections. Paths of zero length yield the smooth part of ?, expanded as $\text{π}{}^{\mathrm{?2}}\text{[Vk}{}^2\text{-}\text{2}\text{3}\text{∫ dα / R}$ + $\text{O}$(k^?2)] where V is the volume of the cavity, and ∫ dα/R is the integral over the boundary of the mean curvature. Paths of finite length L yield contributions to the density ?(k), of the form Im(a exp ikL) appearing as regular oscillations in the bunching of eigenmodes. For an analytic boundary, inclusion of complex classical rays renders exact the analysis of the eigenmodes in terms of closed paths. As a consequence, the high temperature expansion for the energy of a small blackbody is obtained.     

Exact partition functions and correlation functions of multiple Hamiltonian walks on the Manhattan lattice

This is a general and exact study of multiple Hamiltonian walks (HAW) filling the two-dimensional (2D) Manhattan lattice. We generalize the original exact solution for a single HAW by Kasteleyn to a system ofmultiple closed walks, aimed at modeling a polymer melt. In 2D, two basic nonequivalent topological situations are distinguished. (1) the Hamiltonian loops are allrooted andcontractible to a point:adjacent one to another, and, on a torus,homotopic to zero. (2) the loops can encircle one another and, on a torus, canwind around it. Forcase 1, the grand canonical partition function and multiple correlation functions are calculated exactly as those of multiple rooted spanningtrees or of a massive 2Dfree field, critical at zero mass (zero fugacity). The conformally invariant continuum limit on a Manhattantorus is studied in detail. The melt entropy is calculated exactly. We also consider the relevant effect of free boundary conditions. The number of single HAWs on Manhattan lattices with other perimeter shapes (rectangular, Kagomé, triangular, and arbitrary) is studied and related to the spectral theory of the Dirichlet Laplacian. This allows the calculation of exact shape-dependent configuration exponents y. An exact surface critical exponent is obtained. Forcase 2, nested and winding Hamiltonian circuits are allowed. An exact equivalence to thecritical Q-state Potts model exists, whereQ ^1/2 is the walk fugacity. The Hamiltonian system is then always critical (forQ<-4). The exact critical exponents, in infinite numbers, are universal and identical to those of theO(n=Q ^1/2) model in its low-temperature phase, i.e. are those of dense polymers. The exact critical partition functions on the torus are given from conformai invariance theory. These models 1 and 2 yield the two first exactly solved models of polymer melts.     

Superconducting quark matter

In asymptotically dense quark matter, colored glue forces cause an unusual variant of superconductivity. Instead of pairing, the quarks clump in groups of six. We investigate the gap equation in the weak coupling limit, and find the leading behavior of the energy gap and the critical temperature as functions of the renormalized coupling constant.     

Hétérocycles contenant du phosphore. XXXII. Etude de l'action des phosphorhydrazides sur les orthoesters,l'anhydride acétique et l'acide formique

The reaction of phosphodi- or trihydrazides with orthoesters affords mainly 2,3,4,5-tetrahydro-1,2,4,5,3-tetrazaphosphorines and sometimes 4-amino-1,2,4,3-triazaphospholidines. These 1,2,4,5,3-tetrazaphosphorines present a prototropy which explains different pathways of the reaction of these derivatives with formaldehyde or acetone, The structure of all heterocycles which were obtained was established by nmr spectra.