On the Ewald method and the quartic Helmholtz free energy of an anharmonic metallic crystal

Thesis (M. Sc.) - Brock University, 1978.

Variational Monte Carlo estimation of the dissociation energy of CuH using correlated sampling

A new approach to treating large Z systems by quantum Monte Carlo has been developed. It naturally leads to notion of the 'valence energy'. Possibilities of the new approach has been explored by optimizing the wave function for CuH and Cu and computing dissociation energy and dipole moment of CuH using variational Monte Carlo. The dissociation energy obtained is about 40% smaller than the experimental value; the method is comparable with SCF and simple pseudopotential calculations. The dipole moment differs from the best theoretical estimate by about 50% what is again comparable with other methods (Complete Active Space SCF and pseudopotential methods).

Exchange energy calculation of He-He with supermolecular one-matrix

Exch~nge energy of the He-He system is calculated using the one-density matrix which has been modified according to the supermolecular density formula quoted by Kolos. The exchange energy integrals are computed analytically and by the Monte Carlo method. The results obtained from both ways compared favourably,with the results obtained from the SCF program HONDO

Electronic and magnetic properties of LaV1-xO3 /

A series of LaVi^xOs compounds (x=0.00, 0.02, 0.04, 0.06, 0.08) were prepeired using the standard solid reaction. The samples were chareicterized by X-ray diffraction (XRD), fourprobe resistivity, smd magnetic susceptibility studies. Powder X-ray diffraction analysis indicated the formation of a single-phase sample with a orthorhombic structure which was first found in GdFeOs (space group Pnma) . The Unit Cell program was used for calculating lattice peirameters from XFID data. The XRD spectnim could be indexed on a cubic lattice with Og = 2ap ~ (7.8578 to 7.9414 A). The lattice parameter was observed to increase as the Vanadium vacancy increased. Four-probe resistivity measurements exhibited semiconductor behavior for all sajnples from room temperature down to 19K. The resistivity of samples increased with increasing Vanadium vacancy. The resistivity of samples demonstrated activated conduction with an activation energy of approximately 0.2 eV. The activation energy increased with increasing lattice parameter. Field cool magnetic susceptibility measurements were performed with field of 500 G from 300 K to 5 K. These measurements indicated the presence of an antiferromagnetic transition at about 140 K. The data was fitted above Neel temperature to Ciurie-Weiss law yielding a negative parameignetic Curie temperature. This implies that antiferromagnetic ordering is present.

An investigation of geological and geochemical characteristics of late-Quaternay sediments in the Georgian Bay Region, Southern Ontario

Core samples of postglacial sediments and sediment surface samples from Shepherd Lake on the Bruce Peninsula, Harts Lake on the Canadian Shield, and two cores from Georgian Bay (core P-l in the western deep part and core P-7 in the eastern shallow part) have been analyzed for pH, grain size distribution, water content, bulk density, loss on ignition at 4500C and 11000 C, major oxides (Si02 ,A1203,!FeO,MgO,CaO, Na20,K20,Ti02 ,MnO and P205) and trace elements (Ba,Zr,Sr,y,S, Zn,Cu,Ni,Ce and Rb). The sediment in Georgian Bay are generally fine grained (fine silt to very fine silty clay) and the grain size decreases from the Canadian Shield (core p-7) towards the Bruce Peninsula (core P-l) along the assumed direction of sediment transport. This trend coincides with a decrease in sorting coefficient and an increase in roundness. Other physical characteristics, such as water content, bulk density and loss on ignition are positively correlated with the composition of sediments and their compaction, as well as with the energy of the depositional environment. Analyses of sediment surface samples from Shepherd Lake and Harts Lake indicate the influence of bedrock and surficial deposits in the watershed on pH condition that is also influenced by the organic matter content and probably I ! I man's activities. Organic matter content increases significantly in the surface sediment in these small lakes as a result of either natural eutrophication or anthropogenic organic loading. The extremely high organic matter content in Shepherd Lake sediment indicates rapid natural eutrophication in this closed basin and high biological productivity during postglacial time, probably due to high nutrient levels and shallow depth. The chemical composition of the Canadian Shield bedrock is positively correlated with the chemical characteristics of predominantly inorganic lake sediments that were derived from the Shield rocks by glacial abrasion and by postglacial weathering and erosion of both bedrock and surficial deposits. High correlation coefficients were found between organic matter in lake sediments and major oxides (Si02,AI203,.~FeO, MgO,CaO,K20 and MnO) , as well as some trace elements (Ba,Y, S,Zn,Cu,Ni and Rb). The chemical composition of sediments in Harts Lake and core P-7 in Georgian Bay on the Canadian Shield differs from the chemistry of sediments in Shepherd Lake and core P-l in Georgian Bay on the Bruce Peninsula. The difference between cores P-l and P-7 is indicated by values of Si02 , AI203 ,:LFeo,Mgo,CaO,Ba,Zr,Sr,y and S, and also by the organic matter content. This study indicates that the processes of sediment transport, depositional environment, weathering of the rocks and surficial deposits in the watershed, as well as chemical composition of source rocks all affect the chemical characteristics of lake sediments. The stratigraphic changes and variations in lake sediment chemistry with regard to major oxides, trace elements, and organic matter content are probably related to the history of glacial and postglacial lake stages of the Georgian Bay Region and, therefore, the geochemical data can make a useful contribution to a better understanding of the Late-Quaternary history of the Great Lakes.

A study of the thermal decomposition of allyl t-butyl peroxide and 3-hydroperoxy-1-propene (allyl hydroperoxide) in toluene /|nby Krishnankutty Nair V. G. -- 260 St. Catharines [Ont. : s. n.],

Kinetics and product studies of the decompositions of allyl-t-butyl peroxide and 3-hydroperoxy- l-propene (allyl hydroperoxide ) in tolune were investigated. Decompositions of allyl-t-butyl peroxide in toluene at 130-1600 followed first order kinetics with an activation energy of 32.8 K.cals/mol and a log A factor of 13.65. The rates of decomposition were lowered in presence of the radical trap~methyl styrene. By the radical trap method, the induced decomposition at 1300 is shown to be 12.5%. From the yield of 4-phenyl-l,2- epoxy butane the major path of induced decomposition is shown to be via an addition mechanism. On the other hand, di-t-butYl peroxyoxalate induced decomposition of this peroxide at 600 proceeded by an abstraction mechanism. Induced decomposition of peroxides and hydroperoxides containing the allyl system is proposed to occur mainly through an addition mechanism at these higher temperatures. Allyl hydroperoxide in toluene at 165-1850 decomposes following 3/2 order kinetics with an Ea of 30.2 K.cals per mole and log A of 10.6. Enormous production of radicals through chain branching may explain these relatively low values of E and log A. The complexity of the reaction is indicated a by the formation of various products of the decomposition. A study of the radical attack of the hydro peroxide at lower temperatures is suggested as a further work to throw more light on the nature of decomposition of this hydroperoxide.

Optimization of trial wave functions for use in quantum Monte Carlo with application to LiH

Methods for both partial and full optimization of wavefunction parameters are explored, and these are applied to the LiH molecule. A partial optimization can be easily performed with little difficulty. But to perform a full optimization we must avoid a wrong minimum, and deal with linear-dependency, time step-dependency and ensemble-dependency problems. Five basis sets are examined. The optimized wavefunction with a 3-function set gives a variational energy of -7.998 + 0.005 a.u., which is comparable to that (-7.990 + 0.003) 1 of Reynold's unoptimized \fin ( a double-~ set of eight functions). The optimized wavefunction with a double~ plus 3dz2 set gives ari energy of -8.052 + 0.003 a.u., which is comparable with the fixed-node energy (-8.059 + 0.004)1 of the \fin. The optimized double-~ function itself gives an energy of -8.049 + 0.002 a.u. Each number above was obtained on a Bourrghs 7900 mainframe computer with 14 -15 hrs CPU time.

The kinetics and mechanism of the thermal decomposition of sec-Butyl peroxide in liquid phase /|nby Sandor Szilagyi. -- 260 St. Catharines, Ont. : [s. n.],

Re~tes artd pJ~oducts of tllerma]. d,ecom.position of sec-butyl peroxide at 110 - 150°C i.n four solvents h,ave been determined. The d,ecompos i tion vJas sb.o\'\Tn to be tlnlmolecl.llar wi tho energies of activation in toluene, benzene, and cyclohexane of 36 .7-+ 1.0, 33.2 +- 1..0, 33.t~) +.. 1.0 I'(:cal/mol respectively. The activation energy of thermal decomposition for the d,et.1terated peroxide was found to be 37.2 4:- 1.0 KC8:1/1TIol in toluene. A.bo1J.t 70 - 80/~ ol~ tJJ.e' pl~od.1..1CtS could, be explained by kn01rJ11 reactions of free allcoxy raclicals J and very littJ...e, i.f allY, disPl"Opox~tiol'lation of tll10 sec-butoxy radica.ls in t116 solvent cage could be detected. The oth,er 20 - 30% of the peroxide yielded H2 and metb.:'ll etb..yl 1{etol1e. Tl1.e yield. o:f H2 "'lIas unafJ:'ected by the nature or the viscosity of the solvent, but H2 was not formed when s-t1U202 lrJaS phctolyzed. in tolttene at 35°C nor 'tl!Jrl.en the peroxide 1;'JaS tl1.ermally o..ecoJnposed. in the gas p11ase. ~pC-Dideutero-~-butYlperoxide was prepared and decomposed in toluene at 110 - 150°C. The yield of D2 was about ·•e1ne same 248 the yield. of I{2 from s-Bu202, bU.t th.e rate of decomposition (at 135°C) 1iJas only 1/1.55 as fast. Ivlecl1.anisms fOl') J:1ydrogen produ.ction are discussed, but none satisfactorily explains all the evidence.

The kinetics and mechanism of the thermal decomposition of bis diphenyl methyl and related peroxides in liquid phase /|nby C. Thankachan. -- 260 St. Catharines, Ont. : [s. n.],

Rates and products have been determined for the thermal decomposition of bis diphenyl methyl peroxide and diphenyl methyl tert* butyl peroxide at 110@~145@C* The decomposition was uniformly unimolecular with activation energies for the bis diphenyl methyl peroxide in tetrachloroethylene* toluene and nitrobenzene 26,6* 28*3f and 27 Kcals/mole respectively. Diphenyl methyl tert* butyl peroxide showed an activation energy of 38*6 Kcals/mole* About 80-90% of the products in the case of diphenyl methyl peroxide could be explained by the concerted process, this coupled with the negative entropies of activation obtained is a conclusive evidence for the reaction adopting a major concerted path* All the products in the case of diphenyl methyl peroxide could be explained by known reactions of alkoxy radicals* About 80-85% of tert butanol and benzophenone formed suggested far greater cage disproportionation than diffusing apart* Rates of bis triphenyl methyl peroxide have been determined in tetrachloroethylene at 100-120@C* The activation energy was found to be 31 Kcals/mole*

An anharmonic contribution to the Helmholtz free energy O(lambda 6)

The anharmonic contributions of order A6 to the Helmholtz free energy for a crystal in which every atom is on a site of inversion symmetry, have been evaluated The cor~esponding diagrams in the various orders of the perturbation theory have been presented The validity of the expressions given is for high temperatures. Numerical calculations for the diagrams which contribute to the free energy have been worked out for a nearest-n~ighbour central-force model of a facecentered cubic lattice in the high-temperature limit and in the leading term and the Ludwig approximations. The accuracy of the Ludwig approximation in evaluating the Brillouin-zone sums has been investigated. Expansion for all diagrams in the high-temperature limit has been carried out The contribution to the specific heat involves a linear as well as cubic term~ We have applied Lennard-Jones, Morse and Exponential 6 types of potentials. A comparison between the contribution to the free energy of order A6 to that of order A4 has been made.