Application of [Lambda] to the fourth perturbation theory in calculating the equation of state of rare gas solids and fcc metals

We have calculated the thermodynamic properties of monatomic fcc crystals from the high temperature limit of the Helmholtz free energy. This equation of state included the static and vibrational energy components. The latter contribution was calculated to order A4 of perturbation theory, for a range of crystal volumes, in which a nearest neighbour central force model was used. We have calculated the lattice constant, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the adiabatic and the isothermal bulk modulus, and the Gruneisen parameter, for two of the rare gas solids, Xe and Kr, and for the fcc metals Cu, Ag, Au, Al, and Pb. The LennardJones and the Morse potential were each used to represent the atomic interactions for the rare gas solids, and only the Morse potential was used for the fcc metals. The thermodynamic properties obtained from the A4 equation of state with the Lennard-Jones potential, seem to be in reasonable agreement with experiment for temperatures up to about threequarters of the melting temperature. However, for the higher temperatures, the results are less than satisfactory. For Xe and Kr, the thermodynamic properties calculated from the A2 equation of state with the Morse potential, are qualitatively similar to the A 2 results obtained with the Lennard-Jones potential, however, the properties obtained from the A4 equation of state are in good agreement with experiment, since the contribution from the A4 terms seem to be small. The lattice contribution to the thermal properties of the fcc metals was calculated from the A4 equation of state, and these results produced a slight improvement over the properties calculated from the A2 equation of state. In order to compare the calculated specific heats and bulk moduli results with experiment~ the electronic contribution to thermal properties was taken into account~ by using the free electron model. We found that the results varied significantly with the value chosen for the number of free electrons per atom.

Investigation of the composition of linear alkylbenzenes with emphasis on the identification and quantitation of some trace compounds using GS/MS system in both electron impact and chemical ionization modes

Linear alkylbenzenes, LAB, formed by the Alel3 or HF catalyzed alkylation of benzene are common raw materials for surfactant manufacture. Normally they are sulphonated using S03 or oleum to give the corresponding linear alkylbenzene sulphonates In >95 % yield. As concern has grown about the environmental impact of surfactants,' questions have been raised about the trace levels of unreacted raw materials, linear alkylbenzenes and minor impurities present in them. With the advent of modem analytical instruments and techniques, namely GCIMS, the opportunity has arisen to identify the exact nature of these impurities and to determine the actual levels of them present in the commercial linear ,alkylbenzenes. The object of the proposed study was to separate, identify and quantify major and minor components (1-10%) in commercial linear alkylbenzenes. The focus of this study was on the structure elucidation and determination of impurities and on the qualitative determination of them in all analyzed linear alkylbenzene samples. A gas chromatography/mass spectrometry, (GCIMS) study was performed o~ five samples from the same manufacturer (different production dates) and then it was followed by the analyses of ten commercial linear alkylbenzenes from four different suppliers. All the major components, namely linear alkylbenzene isomers, followed the same elution pattern with the 2-phenyl isomer eluting last. The individual isomers were identified by interpretation of their electron impact and chemical ionization mass spectra. The percent isomer distribution was found to be different from sample to sample. Average molecular weights were calculated using two methods, GC and GCIMS, and compared with the results reported on the Certificate of Analyses (C.O.A.) provided by the manufacturers of commercial linear alkylbenzenes. The GC results in most cases agreed with the reported values, whereas GC/MS results were significantly lower, between 0.41 and 3.29 amu. The minor components, impurities such as branched alkylbenzenes and dialkyltetralins eluted according to their molecular weights. Their fragmentation patterns were studied using electron impact ionization mode and their molecular weight ions confirmed by a 'soft ionization technique', chemical ionization. The level of impurities present i~ the analyzed commercial linear alkylbenzenes was expressed as the percent of the total sample weight, as well as, in mg/g. The percent of impurities was observed to vary between 4.5 % and 16.8 % with the highest being in sample "I". Quantitation (mg/g) of impurities such as branched alkylbenzenes and dialkyltetralins was done using cis/trans-l,4,6,7-tetramethyltetralin as an internal standard. Samples were analyzed using .GC/MS system operating under full scan and single ion monitoring data acquisition modes. The latter data acquisition mode, which offers higher sensitivity, was used to analyze all samples under investigation for presence of linear dialkyltetralins. Dialkyltetralins were reported quantitatively, whereas branched alkylbenzenes were reported semi-qualitatively. The GC/MS method that was developed during the course of this study allowed identification of some other trace impurities present in commercial LABs. Compounds such as non-linear dialkyltetralins, dialkylindanes, diphenylalkanes and alkylnaphthalenes were identified but their detailed structure elucidation and the quantitation was beyond the scope of this study. However, further investigation of these compounds will be the subject of a future study.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

On the anharmonic, multi-phonon, Debye-Waller contributions to the phonon-limited resistivity of metals : applications to Na and K

The anharmonic, multi-phonon (MP), and Oebye-Waller factor (OW) contributions to the phonon limited resistivity (;0) of metals derived by Shukla and Muller (1979) by the doubletime temperature dependent Green function method have been numerically evaluated for Na and K in the high temperature limit. The anharmonic contributions arise from the cubic and quartic shift of phonons (CS, QS), and phonon width (W) and the interference term (1). The QS, MP and OW contributions to I' are also derived by the matrix element method and the results are in agreement with those of Shukla and Muller (1979). In the high temperature limit, the contributions to;O from each of the above mentioned terms are of the type BT2 For numerical calculations suitable expressions are derived for the anharmonic contributions to ~ in terms of the third and fourth rank tensors obtained by the Ewald procedure. The numerical calculation of the contributions to;O from the OW, MP term and the QS have been done exactly and from the CS, Wand I terms only approximately in the partial and total Einstein approximations (PEA, TEA), using a first principle approach (Shukla and Taylor (1976)). The results obtained indicate that there is a strong pairwise cancellation between the: OW and MP terms, the QS and CS and the Wand I terms. The sum total of these contributions to;O for Na and K amounts to 4 to 11% and 2 to 7%, respectively, in the PEA while in the TEA they amount to 3 to 7% and 1 to 4%, respectively, in the temperature range.

On the formulation and the calculation of the harmonic contributions to the Debye-Waller factor in metals (sodium)

The algebraic expressions for the anharmonic contributions to the Debye-Waller factor up to 0(A ) and 0 L% ) £ where ^ is the scattering wave-vector] have been derived in a form suitable for cubic metals with small ion cores where the interatomic potential extends to many neighbours. This has been achieved in terms of various wave-vector dependent tensors, following the work of Shukla and Taylor (1974) on the cubic anharmonic Helmholtz free energy. The contribution to the various wave-vector dependent tensors from the coulomb and the electron-ion terms in the interatomic metallic potential has been obtained by the Ewald procedure. All the restricted multiple whole B r i l l o u i n zone (B.Z.) sums are reduced to single whole B.Z. sums by using the plane wave representation of the delta function. These single whole B.Z. sums are further reduced to the •%?? portion of the B.Z. following Shukla and Wilk (1974) and Shukla and Taylor (1974). Numerical calculations have been performed for sodium where the Born-Mayer term in the interatomic potential has been neglected because i t is small £ Vosko (1964)3 • *n o^er to compare our calculated results with the experimental results of Dawton (1937), we have also calculated the r a t io of the intensities at different temperatures for the lowest five reflections (110), (200), (220), (310) and (400) . Our calculated quasi-harmonic results agree reasonably well with the experimental results at temperatures (T) of the order of the Debye temperature ( 0 ). For T » © ^ 9 our calculated anharmonic results are found to be in good agreement with the experimental results.The anomalous terms in the Debye-Waller factor are found not to be negligible for certain reflections even for T ^ ©^ . At temperature T yy Op 9 where the temperature is of the order of the melting temperature (Xm) » "the anomalous terms are found to be important almost for all the f i ve reflections.

Studies in the mass spectra of perfluoroaromatic derivatives of phosphorus and some selected transition metals

The mass spectra and fragmentation of a variety of fluoroaromatic compounds of Group V and some selected transition elements are discussed in some detail, aided by data from metastable defocussed experiments. Results of ,studies on the coupling reaction using unstable organotitanium chloride intermediate species are reported. The preparation of some 5-substituted octafluorodibenzophospho1es is also discussed. Rearrangements under electron bombardment resulting in the loss of heteroatom-fluoride fragments are discussed in the light of presently accepted mechanisms for these processes as are rearrangements observed in compounds involving thionophosphoryl bonds ( p=s ).

Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen models

Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately as the presence of the free electron gas renders the total energy strongly dependent on the electron density. The embedded atom method (EAM) addresses this issue by replacing part of the total energy with an explicitly density-dependent term called the embedding function. Finnis and Sinclair proposed a model where the embedding function is taken to be proportional to the square root of the electron density. Models of this type are known as Finnis-Sinclair many body potentials. In this work we study a particular parametrization of the Finnis-Sinclair type potential, called the "Sutton-Chen" model, and a later version, called the "Quantum Sutton-Chen" model, to study the phonon spectra and the temperature variation thermodynamic properties of fcc metals. Both models give poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. We identify the power law decay of the electron density with distance assumed by the model as the main cause of this behaviour and show that an exponentially decaying form of charge density improves the results significantly. Results for Sutton-Chen and our improved version of Sutton-Chen models are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen parameter. For the sake of comparison we have also considered two other models where the distance-dependence of the charge density is an exponential multiplied by polynomials. None of these models exhibits the instability against thermal expansion (premature melting) as shown by the Sutton-Chen model. We also present results obtained via pure pair potential models, in order to identify advantages and disadvantages of methods used to obtain the parameters of these potentials.

Investigating Microbial Trace-fossils and Abiotic Alteration in Hydrovolcanic Tuffs of the Fort Rock Volcanic Field, Oregon

Microbial ichnofossils in volcanic rocks provide a significant record of subsurface microbes and potentially extraterrestrial biosignatures. Here, the textures, mineralogy, and geochemistry of two continental basaltic hydrovolcanic deposits - Reed Rocks and Black Hills - in the Fort Rock Volcanic Field (FRVF) are investigated. Methods include petrographic microscopy, micro and powder X-ray diffraction, SEM/BSE/EDF imaging, energy dispersive spectroscopy, stable isotopes, and X-ray fluorescence. Petrographic analysis revealed granular and tubular textures with biogenic morphologies that include terminal enlargements, septate divisions, branching forms, spiral filaments, and ovoid bodies resembling endolithic microborings described in ocean basalts. They display evidence of behaviour and a geologic context expressing their relative age and syngenicity. Differences in abiotic alteration and the abundance/morphotype assemblage of putative microborings between the sites indicate that water/rock ratio, fluid composition and flux, temperature and secondary phase formation are influences on microboring formation. This study is the first report of reputed endolithic microborings in basalts erupted in a continental lacustrine setting.

Surfaces de Riemann compactes et formule de trace d'Eichler

Dans ce mémoire, nous étudierons quelques propriétés algébriques, géométriques et topologiques des surfaces de Riemann compactes. Deux grand sujets seront traités. Tout d'abord, en utilisant le fait que toute surface de Riemann compacte de genre g plus grand ou égal à 2 possède un nombre fini de points de Weierstrass, nous allons pouvoir conclure que ces surfaces possèdent un nombre fini d'automorphismes. Ensuite, nous allons étudier de plus près la formule de trace d'Eichler. Ce théorème nous permet de trouver le caractère d'un automorphisme agissant sur l'espace des q-différentielles holomorphes. Nous commencerons notre étude en utilisant la quartique de Klein. Nous effectuerons un exemple de calcul utilisant le théorème d'Eichler, ce qui nous permettra de nous familiariser avec l'énoncé du théorème. Finalement, nous allons démontrer la formule de trace d'Eichler, en prenant soin de traiter le cas où l'automorphisme agit sans point fixe séparément du cas où l'automorphisme possède des points fixes.

Spectroscopie Raman de complexes de fer(II) et fer(III) à transition de spin

Les transitions de spin provoquent des changements de propriétés physiques des complexes de métaux du bloc d les subissant, notamment de leur structure et propriétés spectroscopiques. Ce mémoire porte sur la spectroscopie Raman de composés du fer(II) et du fer(III), pour lesquels on induit une transition de spin par variation de la température ou de la pression. Trois complexes de fer(II) de type FeN4(NCS)2 avec des comportements de transition de spin différents ont été étudiés : Fe(Phen)2(NCS)2 (Phen : 1,10-Phénanthroline), Fe(Btz)2(NCS)2 (Btz : 2,2’-bi-4,5-dihydrothiazine) et Fe(pyridine)4(NCS)2. Un décalage de l’ordre de 50 cm-1 est observable pour la fréquence d’étirement C-N du ligand thiocyanate des complexes FeN4(NCS)2, lors de la transition de spin induite par variation de la température ou de la pression. Il est possible d’utiliser cette variation de fréquence afin de tracer un profil de transition. Quatre complexes isomères de type FeL222(CN)2 (L222 : 2,13- diméthyl-6,9-dioxa-3,12,18-triazabicyclo[12.3.1]-octadéca-1(18),2,12,14,16-pentaène) ont également été étudiés. Un taux de décalage de l’ordre d’environ 0,03 cm-1/K est observé pour plusieurs bandes du complexe FeL222(CN)2. La bande à 1415 cm-1 disparaît à plus haute température au profit d’une bande à 1400 cm-1. Pour le complexe de chiralité R,R’, les bandes à 1008 cm-1 et 1140 cm-1 se déplacent vers des fréquences plus élevées à partir de 223 K. Les transitions de spin sont observées dans certains complexes de fer(III). Dans cette famille de composés, le complexe Fe(EtDTC)3 (EtDTC : N,N-diéthyldithiocarbamate) a été étudié . Aucun changement n’a été observé dans l’intensité des bandes d’étirement fer-soufre sur les spectres à température variable. Cependant, la bande Fe-S associée à la forme bas-spin à 530 cm-1 augmente en intensité au profit de la bande associée à la forme haut-spin à 350 cm-1 lors des mesures à haute pression, passant d’un rapport d’amplitude de 50% à pression ambiante à 80% à 21 kbar. Un dédoublement de la bande d’étirement C-N du ligand dithiocarbamate à 1495 cm-1 est également observé à des pressions supérieures à 5 kbar. Une comparaison des changements des fréquences de vibration de tous les complexes est effectuée.

Effects of diverse plant species on the bioavailability of contaminants in soil

La phytoremédiation constitue une technologie alternative pour le traitement de sols contaminés en métaux. Toutefois, la biodisponibilité des métaux dans le sol peut limiter l’efficacité de cette approche. Nous émettons l’hypothèse que diverses espèces de plante, caractérisées par systèmes racinaires différents, peuvent affecter différemment la biodisponibilité des éléments traces (ET) dans le sol. Une étude utilisant un dispositif expérimental en bloc aléatoire complet avec cinq réplicats a été conduite entre le 6 juin et le 3 septembre 2014, sur le site du Jardin botanique de Montréal. Dans ce contexte, l’impact de la présence de huit espèces de plantes, herbacées ou ligneuses, sur le pool labile de six métaux (Ag, Cu, Pd, Zn, Ni et Se) dans la rhizosphère de celles-ci a été étudié. Après trois mois de culture, la biomasse aérienne et souterraine de chaque espèce a été mesurée et la concentration en ET dans les tissus des plantes a été analysée. La fraction labile de ces ET dans la rhizosphère (potentiellement celle qui serait biodisponible) de même que d’autres paramètres édaphiques (le pH, la conductivité, le pourcentage de matière organique et le carbone organique dissous (COD)) ont aussi été mesurés et comparés en fonction de la présence d’une ou l’autre des espèces utilisées. Les résultats montrent que pour la plupart des plantes testées, les plus fortes concentrations en ET ont été trouvées dans les racines alors que les plus faibles niveaux s’observaient dans les parties aériennes, sauf pour le Ni dans le Salix nigra. Ceci suggère que le Ni peut être extrait du sol par des récoltes régulières des tiges et des feuilles de cette espèce de saule. Les pools labiles de l’Ag, Ni et du Cu dans la rhizosphère étaient significativement et différemment affectés par la présence des plantes. Toutefois, la présence des plantes testées n’a pas affecté certains paramètres clés de la rhizosphère (ex. le pH, conductivité, et le pourcentage de matière organique). À l’opposé, les niveaux de COD dans la rhizosphère de toutes les plantes testées se sont révélés supérieurs en comparaison des témoins (sols non plantés). De plus, une corrélation positive a pu être établie entre la concentration disponible du Ni et la concentration en COD. Une relation similaire a été déterminée pour le Cu. Ceci suggère que certains systèmes racinaires pourraient modifier les niveaux de COD et avoir un impact indirect sur les pools labiles des ET dans le sol.

Dynamics And Speciation Of The Heavy Metals In The Lower Reaches Of Chithrapuzha- A Tropical Tidal River

The proposed study is an attempt to quantify and study the seasonal and spatial variations in the distribution of Cr, Mn, Fe, Co, Ni, Cu, Zn, Cd and Pb among the various geochemical phases in the surficial sediments of Chitrapuzha river. The study also estimates the concentration of heavy metals in dissolved, particulate and sediments and their variation in seasonal and spatial distribution. Chitrapuzha River originates as a small stream from the upper reaches of high ranges in the eastern boundary of Kerala, passes through the valley and finally joints in the Cochin backwaters. Numerous industrial units located along the banks of the river discharge treated and untreated effluents into the water. These are long standing local complaints about water pollution causing fish mortality and serious damage to agricultural crops resulting in extensive unemployment in the area. The river is thus of considerable social and economic importance.

Evanescent Wave Fibre Optic Sensors for Trace Analysis of Fe3+ in Water

In this communication, we discuss the details of fabricating an off-line fibre optic sensor (FOS) based on evanescent wave absorption for detecting trace amounts of Fe3+ in water. Two types of FOS are developed; one type uses the unclad portion of a multimode silica fibre as the sensing region whereas the other employs the microbent portion of a multimode plastic fibre as the sensing region. Sensing is performed by measuring the absorption of the evanescent wave in a reagent medium surrounding the sensing region. To evaluate the relative merits of the two types of FOS in Fe3+ sensing, a comparative study of the sensors is made, which reveals the superiority of the latter in many respects, such as smaller sensing length, use of a double detection scheme (for detecting both core and cladding modes) and higher sensitivity of cladding mode detection at an intermediate range of concentration along with the added advantage that plastic fibres are inexpensive. A detection limit of 1 ppb is observed in both types of fibre and the range of detection can be as large as 1 ppb–50 ppm. All the measurements are carried out using a LabVIEW set-up.

Evanescent wave fibre optic sensors for trace analysis of Fe3+ in water

In this communication, we discuss the details of fabricating an off-line fibre optic sensor (FOS) based on evanescent wave absorption for detecting trace amounts of Fe3+ in water. Two types of FOS are developed; one type uses the unclad portion of a multimode silica fibre as the sensing region whereas the other employs the microbent portion of a multimode plastic fibre as the sensing region. Sensing is performed by measuring the absorption of the evanescent wave in a reagent medium surrounding the sensing region. To evaluate the relative merits of the two types of FOS in Fe3+ sensing, a comparative study of the sensors is made, which reveals the superiority of the latter in many respects, such as smaller sensing length, use of a double detection scheme (for detecting both core and cladding modes) and higher sensitivity of cladding mode detection at an intermediate range of concentration along with the added advantage that plastic fibres are inexpensive. A detection limit of 1 ppb is observed in both types of fibre and the range of detection can be as large as 1 ppb–50 ppm. All the measurements are carried out using a LabVIEW set-up.

Evanescent wave fibre optic sensors for trace analysis of Fe3+ in water

In this communication, we discuss the details of fabricating an off-line fibre optic sensor (FOS) based on evanescent wave absorption for detecting trace amounts of Fe3+ in water. Two types of FOS are developed; one type uses the unclad portion of a multimode silica fibre as the sensing region whereas the other employs the microbent portion of a multimode plastic fibre as the sensing region. Sensing is performed by measuring the absorption of the evanescent wave in a reagent medium surrounding the sensing region. To evaluate the relative merits of the two types of FOS in Fe3+ sensing, a comparative study of the sensors is made, which reveals the superiority of the latter in many respects, such as smaller sensing length, use of a double detection scheme (for detecting both core and cladding modes) and higher sensitivity of cladding mode detection at an intermediate range of concentration along with the added advantage that plastic fibres are inexpensive. A detection limit of 1 ppb is observed in both types of fibre and the range of detection can be as large as 1 ppb–50 ppm. All the measurements are carried out using a LabVIEW set-up.