The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (S{sub N}) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and S{sub N} regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor S{sub N} is well suited for by themselves. The fully coupled Monte Carlo/S{sub N} technique consists of defining spatial and/or energy regions of a problem in which either a Monte Carlo calculation or an S{sub N} calculation is to be performed. The Monte Carlo region may comprise the entire spatial region for selected energy groups, or may consist of a rectangular area that is either completely or partially embedded in an arbitrary S{sub N} region. The Monte Carlo and S{sub N} regions are then connected through the common angular boundary fluxes, which are determined iteratively using the response matrix technique, and volumetric sources. The hybrid method has been implemented in the S{sub N} code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the response …

An analytical/numerical study of the breakup, burning, and ignition of liquid fuels injected transversely into a hot air stream is conducted. The non-reacting liquid jet breakup location is determined by the local sonic point criterion first proposed by Schetz, et al. (1980). Two models, one employing analysis of an elliptical jet cross-section and the other employing a two-dimensional blunt body to represent the transverse jet, have been used for sonic point calculations. An auxiliary criterion based on surface tension stability is used as a separate means of determining the breakup location. For the reacting liquid jet problem, a diffusion flame supported by a one-step chemical reaction within the gaseous boundary layer is solved along the ellipse surface in subsonic crossflow. Typical flame structures and concentration profiles have been calculated for various locations along the jet cross-section as a function of upstream Mach numbers. The integrated reaction rate along the jet cross-section is used to predict ignition position, which is found to be situated near the stagnation point. While a multi-step reaction is needed to represent the ignition process more accurately, the present calculation does yield reasonable predictions concerning ignition along a curved surface.

The data engineers and scientists use to determine if the groundwater supply is contaminated are derived from analysis of samples taken largely from monitoring wells. For these data to be reliable several factors must be considered. One factor is the integrity of the monitoring well. In this project, emphasis has been placed on the potential impact on water quality caused by diffusion across the threaded joints of PVC pipe. In this study, the diffusion of trichloroethylene across several common types of threaded joints (i.e., square flush, modified ACME, modified ACME stub, and ACME) has been measured. Samples were obtained from the water inside the pipe sections and analyzed for trichloroethylene by gas chromatography. Breakthrough occurs within days of the samples being placed in the baths. The softened PVC joints of the pipes in the pure trichloroethylene split before the first sample interval of 1.5 weeks. The data show great variability in casting joints from the same manufacturer, and indicate a need for increased precision in the manufacturing of the PVC pipe joints. A one-dimensional diffusion model is used to determine an equivalent gap size through which the diffusion occurs. Flow rates through the threaded joints are calculated by using the …

The effect of incubation temperature on the post-hatching growth and performance capacities of the common snapping turtle, Chelydra serpentina was investigated in the laboratory. Turtle eggs were collected from four sites in New York State and randomly assigned to four incubation temperature treatments to produce males (constant 26{degree}C and downshifted 30-26-30{degree}C) and females (constant 30{degree}C and upshifted 26-30-26{degree}C) under constant and altered temperature regimes. The incubation conditions resulted in 92% males from the constant 26{degree}C group and 93% males from the downshifted group. 100% females resulted from both the constant 30{degree}C group and the upshifted group. Turtles hatching from eggs incubated constantly at 26{degree}C were significantly larger than hatchlings from eggs incubated at a constant 30{degree}C or downshifted. Hatchlings were raised in individual aquaria at 25{degree}C and fed earthworms and fish. After a 9-month growth period, turtles which had been incubated at a constant 30{degree}C gained significantly more mass than did turtles from eggs which had been downshifted or upshifted. There was no extended effect of incubation condition on Post-hatching performance and learning ability as measured by righting and feeding responses. Thus, the mass gain differences seen in this study suggest that physiological differences do result as the consequence of …

Properties of small lithium clusters with sizes ranging from n = 1 to 5 atoms were investigated using quantum Monte Carlo (QMC) methods. Cluster geometries were found from complete active space self consistent field (CASSCF) calculations. A detailed development of the QMC method leading to the variational QMC (V-QMC) and diffusion QMC (D-QMC) methods is shown. The many-body aspect of electron correlation is introduced into the QMC importance sampling electron-electron correlation functions by using density dependent parameters, and are shown to increase the amount of correlation energy obtained in V-QMC calculations. A detailed analysis of D-QMC time-step bias is made and is found to be at least linear with respect to the time-step. The D-QMC calculations determined the lithium cluster ionization potentials to be 0.1982(14) [0.1981], 0.1895(9) [0.1874(4)], 0.1530(34) [0.1599(73)], 0.1664(37) [0.1724(110)], 0.1613(43) [0.1675(110)] Hartrees for lithium clusters n = 1 through 5, respectively; in good agreement with experimental results shown in the brackets. Also, the binding energies per atom was computed to be 0.0177(8) [0.0203(12)], 0.0188(10) [0.0220(21)], 0.0247(8) [0.0310(12)], 0.0253(8) [0.0351(8)] Hartrees for lithium clusters n = 2 through 5, respectively. The lithium cluster one-electron density is shown to have charge concentrations corresponding to nonnuclear attractors. The overall shape …

Optical properties and electronic structures of disordered Ag{sub 1- x}In{sub x}(x = 0.0, 0.04, 0.08, 0.12) and Ni{sub 1-x}Cu{sub x} (x = 0.0, 0.1, 0.3, 0.4) alloys and ordered AuGa{sub 2}, PtGa{sub 2}, {beta}{prime}-NiAl, {beta}{prime}-CoAl, CeSn{sub 3}, and LaSn{sub 3} have been studied. The complex dielectric functions have been determined for Ag{sub 1-x}In{sub x}, Ni{sub 1-x}Cu{sub x}, AuGa{sub 2}, and PtGa{sub 2} in the 1.2--5.5 eV region and for CeSn{sub 3} and LaSn{sub 3} in the 1.5--4.5 eV region using spectroscopic ellipsometry. Self-consistent relativistic band calculations using the linearized-augmented-plane-wave method have been performed for AuGa{sub 2}, PtGa{sub 2}, {beta}{prime}-NiAl, {beta}{prime}-CoAl, CeSn{sub 3}, and LaSn{sub 3} to interpret the experimental optical spectra.

Ultrasonic techniques have recently been applied to the texture characterization in polycrystalline aggregates of hexagonal crystals. The basis of this application lies in the relations between the elastic constants {bar C}{sub ij} of the aggregates, which can be inferred from ultrasonic wave velocity measurements, and the orientation distribution coefficients. This communication present such relations for aggregates which possess orthotopic material symmetry and hexagonal crystal symmetry for Voigt, Reuss, and Hill averaging methods in a unified and concise representation.

The kinetics of the reactions of C{sub 2}H{sub 5} radical with Co(NH{sub 3}){sub 5}X{sup 2+}, Ru(NH{sub 3}){sub 5}X{sup 2+}, and Co(dmgH){sub 2} (X) (Y) (X = Br, Cl, N{sub 3}, SCN; Y = H{sub 2}O, CH{sub 3}CN) complexes were studied using laser flash photolysis of ethylcobalt complexes. The kinetics were obtained by the kinetic probe method. Some relative rate constants were also determined by a competition method based on ethyl halide product ratios. The kinetics of colligation reactions of a series of alkyl radicals with {beta}-Ni(cyclam){sup 2+} were studied using flaser flash photolysis of alkylcobalt complexes. Again, the kinetics were obtained by employing the kinetic probe competition method. The kinetics of the unimolecular homolysis of a series of RNi(cyclam)H{sub 2}O{sup 2+} were studied. Activation parameters were obtained for the unimolecular homolysis of C{sub 2}H{sub 5}Ni(cyclam)H{sub 2}O{sup 2+}. Kinetic and thermodynamic data obtained from these reactions were compared with those for the {sigma}-bonded organometallic complexes. The kinetics of the unimolecular homolysis of a series of RNi(cyclam)H{sub 2}O{sup 2+} complexes were studied by monitoring the formation of the oxygen insertion product RO{sub 2}Ni(cyclam)H{sub 2}O{sup 2+}. The higher rate constants for the reactions of alkyl radicals with oxygen in solution, as compared with …

This thesis describes a number of diverse experiments whose common theme is to elaborate some aspect of DNA supercoiling. The torsion elastic constant of DNA is measure as a function of superhelix density using the technique of picosecond Time Resolved Fluorescence Polarization Anisotropy (FPA) of intercalated ethidium bromide. The results agree with theories which predict that the anisotropy decay should vary with the square root of the relative viscosity. This experiment furthermore demonstrates a sensitivity of FPA to a change in torsion elastic constant of less than 10%. A number of covalently closed DNA samples, ranging in superhelix density from = {minus}0.123 to {plus}0.042, are then examined. A novel method for measuring changes in local supercoiling on a large PNA molecule which is sensitive to changes in supercoiling of regions of chromosomal DNA as short as 1 kilobase in length is presented. Study of chromosomal supercoiling regulating anaerobic gene expression in the facultative photosynthetic bacterium, Rhodobacter capsulatus showed that no stable change in chromosomal supercoiling upon a shift from aerobic respiratory growth to anaerobic photosynthetic conditions. Studies to detect transient changes in DNA supercoiling indicate that DNA downstream from heavily transcribed genes for the photosynthetic reaction center are relaxed or …

This thesis encompasses two separate research projects. The first project, described in Chapter 2 was a project investigating the fatigue behavior of thermoset Fiber Composite (FC) sandwich wall ties. The second research project detailed in this thesis was a project studying the bond and tensile properties of FC rod and FC fibers.

Resistivity measurements have been performed for electric characterization of the compounds Ba{sub 5}Sb{sub 3} and Ba{sub 5}Sb{sub 3}Cl, both with the Mn{sub 5}Si{sub 3} structure type, along with Ca{sub 5}Bi{sub 3} and Ca{sub 5}Bi{sub 3}F, both with the {beta}-Yb{sub 5}Sb{sub 3} structure type. These measurements were taken as a function of temperature using the four probe method on pressed polycrystalline pellets of the compounds. A sealed apparatus was developed for containing these air-sensitive compounds throughout the experiments. By a simple electron count, one extra electron in both Ba{sub 5}Sb{sub 3} and Ca{sub 5}Bi{sub 3} should occupy a conduction band, giving these compounds a metallic character. In the cases of Ba{sub 5}Sb{sub 3}Cl and Ca{sub 5}Bi{sub 3}F, the extra electron should bond to the halide, both filling the valence band and giving rise to semiconducting character. Ca{sub 5}Bi{sub 3}, Ca{sub 5}Bi{sub 3}F, and Ba{sub 5}Sb{sub 3}Cl were found to comply with the electron count prediction. Ba{sub 5}Sb{sub 3}, however, was found to be a semiconductor (E{sub g} = 0.30 eV) with a larger band gap than its corresponding chloride (E{sub g} = 0.09 eV).

The electrocatalysis of oxygen-transfer reactions is discussed in two parts. In Part I, the reduction of iodate (IO{sub 3}{sup {minus}}) is examined as an example of cathodic oxygen transfer. On oxide-covered Pt electrodes (PtO), a large cathodic current is observed in the presence of IO{sub 3}{sup {minus}} to coincide with the reduction of PtO. The total cathodic charge exceeds the amount required for reduction of PtO and IO{sub 3}{sup {minus}} to produce an adsorbed product. An electrocatalytic link between reduction of IO{sub 3}{sup {minus}} and reduction of PtO is indicated. In addition, on oxide-free Pt electrodes, the reduction of IO{sub 3}{sup {minus}} is determined to be sensitive to surface treatment. The electrocatalytic oxidation of CN{sup {minus}} is presented as an example of anodic oxygen transfer in Part II. The voltametric response of CN{sup {minus}} is virtually nonexistent at PbO{sub 2} electrodes. The response is significantly improved by doping PbO{sub 2} with Cu. Cyanide is also oxidized effectively at CuO-film electrodes. Copper is concluded to serve as an adsorption site for CN{sup {minus}}. It is proposed that an oxygen tunneling mechanism comparable to electron tunneling does not occur at the electrode-solution interface. The adsorption of CN{sup {minus}} is therefore considered to …

Data are presented for the first time on exclusive Pomeron-Pomeron interactions which produce a neutral strange and neutral antistrange particle pair in a central system X. In this paper, the system, X, is identified as one of the following neutral combinations; K{sub s}{sup 0}K{sub s}{sup 0}, K{sub s}{sup 0}K{sup {plus minus}}{pi}{sup {minus plus}}, {Lambda}{sup 0}{bar {Lambda}}{sup 0}, {Lambda}{sup 0}{bar {Lambda}}{sup 0}*. These data were obtained in proton-proton collisions at {radical}s = 62 GeV at the CERN ISR. The triggering systems used to obtain these data are described, followed by a description of the data. The central system mass distributions are presented along with differential mass cross section estimates. A broad enhancement is seen in the K{sub s}{sup 0}K{sub s}{sup 0} system at a mass of 1.2 GeV, and is likely to have the quantum numbers J{sup PC} = 0{sup ++}. Total cross section estimates of 1.3 {plus minus} .64 {mu}b in the K{sub 2}{sup 0}K{sub s}{sup 0} system, . 44 {plus minus} .14 {mu}b in the K{sub s}{sup 0}K{sup {plus minus}}{pi}{sup {minus plus}} system, .20 {plus minus} .14 {mu}b in the {Lambda}{sup 0}{bar {Lambda}}{sup 0} system, and .13 {plus minus} .06 {mu}b in the {Lambda}{sup 0}{bar {Lambda}}{sup 0}* system are …

Proton magnetic resonance spectroscopy, or nuclear magnetic resonance (NMR) of hydrogen, has been applied to investigate silica-supported Group VIII monometallic and Group VIII-Group IB bimetallic catalysts and alumina- and silica-supported platinum-rhenium bimetallic catalysts. Two adsorbed states of hydrogen, i.e., irreversible and reversible hydrogen, on the surfaces of monometallic Ru, Pt, and Cu particles and bimetallic Ru-Group Ib, Pt-Group Ib, and Pt-Re particles were observed directly via proton NMR. The same amounts of the irreversible hydrogen adsorbed on pure Ru catalysts were measured by both proton NMR and the volumetric technique. The electronic environments on surfaces of monometallic catalysts are sensitive to changes in metal dispersion, state of adsorbed hydrogen, and residual chlorine. Surface compositions for the Ru--Cu and Pt--Cu bimetallic catalysts were determined by NMR of adsorbed hydrogen. 297 refs., 96 figs., 19 tabs.

An angle-resolved photoemission study of the normal and superconducting states in Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8} was performed. Measurements in the normal state show bands dispersing through the Fermi level from at least 350 meV below E{sub F}. The Fermi level crossings are consistant with local-density band calculation, including a point calculated to be of Bi-O character. Additional measurements were made where bands crossed the Fermi level between 100 and 250K, along with measurements on an adjacent Pt foil. The Fermi edges of both materials agree to within the noise. Below the Fermi level, the spectra show correlation effects on the form of an increased effective mass. The shape of the spectra can be explained by a lifetime-broadened photohole and secondary electrons. The effective inverse photohole lifetime is linear in energy. A superconducting gap has been measured at a number of points where there is density at the Fermi level in the normal state. By proper modeling, a gap of 24 meV was obtained for all these points, including points of Cu-O and Bi-O character respectively, according to band calculation. The lack of gap anisotropy in the basal plane suggests that pinning in this material is not d-wave pairing.

We have studied the interactions of water and perfluorodiethyl ether on Ru(100) in order to model the effects of surface structure and humidity on the bonding and decomposition of perfluoroalkyl ether lubricants with metal surfaces. In order to understand the interactions on Ru(100), we have first investigated the interactions of each of these adsorbates alone on the clean surface. The interactions of water with Ru(100) have been studied using both thermal desorption spectroscopy (TDS) and electron energy loss spectroscopy (EELS). From these studies we conclude that a small amount of water dissociates on this surface (5--10% of a monolayer), but water is adsorbed in a predominantly molecular form on this surface with an increasing degree of hydrogen-bonding with increasing coverage. The effects of hydrogen and oxygen coadsorption on the interactions of water with this surface have also been studied using TDS. Finally, the interactions of coadsorbed water and perfluorodiethyl ether on Ru(100) have been investigated using TDS.

Measurements of the normal state magnetic susceptibility {chi}(T) of YBa{sub 2}Cu{sub 3}O{sub 7}, Bi{sub 1.8}Pb{sub 0.2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}}, and Bi{sub 2{minus}x}Pb{sub x}Sr{sub 2}Ca{sub 2}Cu{sub 3}O{sub 10+{delta}} (x = 0.2 and 0.25) were carried out. All {chi}(T) data show negative curvature below {approximately}2{Tc}. The data for YBa{sub 2}Cu{sub 3}O{sub 7} are in excellent agreement with a new calculation of the superconducting fluctuation diamagnetism. From the analysis, we infer s-wave pairing and microscopic parameters are obtained. For {chi}(T) of YBa{sub 2}Cu{sub 3}O{sub 7}, part of the negative curvature is inferred to arise from the normal state background. We find a strong temperature dependent anisotropy {delta}{chi} {equivalent to} {chi}{sub c} {minus} {chi}{sub ab} and estimate the normal state spin contributions to {chi}(T). The heat capacity C(T) of YBa{sub 2}Cu{sub 3}O{sub 7} is reported for 0.4 K < T < 400 K in zero and 70 kG magnetic fields. In addition to the feature associated with the onset of the superconductivity at {Tc}, two anomalies in C(T) were observed near 74 K and 330 K, with another possible anomaly near 102 K; the temperatures at which they occur correlate with anomalies in {chi}(T) and ultransonic measurements. The occurrence of the anomaly at {approx …

The production of the neutral technicolor pseudo Goldstone bosons, P{sup 0}{prime}and P{sub 8}{sup 0}{prime}, at large transverse momentum in pp collisions, pp {yields} g(q)P{sup 0}{prime} (P{sub 8}{sup 0}{prime})X has been investigated in reactions at a high energy collider such as the SSC. The major two-body and three-body decay modes in tree diagrams are investigated in detail. The t{bar t} decay channel would dominate both the decays of P{sup 0}{prime} and P{sub 8}{sup 0}{prime} if it is allowed. Otherwise, gg and 3g will be the dominant decay modes unless the mass of the P{sup 0}{prime} and P{sub 8}{sup 0}{prime} are below 40 GeV, where b{bar b} becomes dominant. According to the QCD backgrounds, which we have also investigated in detail in this work, the signal for t{bar t} is much larger than the background and will be the ideal signal for detecting these bosons. However, in the absence of the t{bar t} channel, the {tau}{bar {tau}} mode can be used to identify P{sup 0}{prime} up to m{sub P} = 300 GeV in the transverse momentum range P{sub {perpendicular}} {approx lt} 100 GeV. Similarly, the b{bar b} decay mode can serve us a signal to identify P{sub 8}{sup 0}{prime} up to m{sub …

Results covering burn intensities in the nW to {mu}W/cm{sup 2} range, of dispersive hole growth kinetics are reported for Oxazine 720 in glycerol glasses and polyvinyl alcohol polymer films and their deuterated analogues. A theoretical model which employs a distribution function for the hole burning rate constant based upon a Gaussian distribution for the tunnel parameter is shown to accurately describe the kinetic data. This model incorporates the linear electron-phonon coupling. A method for calculating the nonphotochemical quantum yield is presented which utilizes the Gaussian distribution of tunnel parameters. The quantum yield calculation can be extended to determine a quantum yield as a function of hole depth. The effect of spontaneous hole filling is shown to be insignificant over the burn intensity range studied. Average relaxation rates for hole burning are {approximately}8 orders of magnitude greater than for hole filling. The dispersive kinetics of hole burning are observed to be independent over the temperature range of these experiments, 1.6 to 7.0 K. 6 refs., 20 figs., 1 tab.

The reactive o-quinodimethanes, 1,2-dimethylene-1,2-dihydronaphthalene (9) and o-xylylene (1) were observed by flow {sup 1}H NMR spectroscopy at room temperature. The {sup 1}H NMR spectrum of 9 was obtained in the absence of precursor and dimers. However, the {sup 1}H NMR spectrum of the more reactive 1, generated in a similar manner from (o-((trimethylsilyl)methyl)benzyl)trimethylammonium iodide (5.) could be obtained only in the presence of its stable (4 + 2) and (4 + 4) dimers. The dimerization kinetics of 3-methyl- (5{prime}), 3,6-dimethyl- (11), 3-isopropyl- (12), and 3,6-diisoproply-1,2-xylylene (13) in acetonitrile (CH{sub 3}CN) were studied by stopped-flow UV-visible spectroscopy. Fluoride ion induced 1,2-elimination from 2-elimination from 2-trimethylsilylbenzocyclobutenyl-1 mesylate (26) was used to generate the reactive molecule benzocyclobutadiene (1{prime}) in CD{sub 3}CN, which was observed by flow {sup 1}H NMR spectroscopy at room temperature. The {sup 1}H NMR spectrum (in CD{sub 3}CN) of 1,2-dimethylene-1,2-dihydrothiophene (1{double prime}), obtained by fluoride ion induced 1,4-elimination from 3-(trimethylammoniummethyl)-2-(trimethylsilylmethyl)thiophene iodine was observed by flow {sup 1}H NMR spectroscopy at room temperature. The dimerization rate of 1{double prime} in CH{sub 3}CN, generated in the same manner, was measured by UV-visible spectroscopy. 166 refs., 7 figs., 7 tabs.

As a continuation of the research on bcc Gd-Mg alloy system by Herchenroeder and Gschneidner, the metastable bcc Gd-Cd alloys were studied with the emphasis on their metallurgical and magnetic properties. An essentially single phase alloy could be retained for Cd concentrations from 15 at. % Cd to 19 at. % Cd, which is in the vicinity of the eutectoid composition of {beta}Gd in the Gd-Cd system. The lattice constants obtained for these alloys were used to determine the lattice constant of pure bcc Gd by extrapolation to 0 at. % Cd. Good agreement between this extrapolated value and that obtained from Gd-Mg alloys by using the same method suggested the validity of such extrapolation method. Thermal stability of these metastable bcc Gd-Cd alloys was examined by using differential thermal analysis (DTA).

The use of platinum(II) complexes as tags and probes for biomolecules is indeed advantageous for their reactivities can be selective for certain purposes through an interplay of mild reaction conditions and of the ligands bound to the platinum. The use of {sup 195}Pt NMR as a method of detecting platinum and its interactions with biomolecules was carried out with the simplest model of platinum(II) tagging to proteins. Variable-temperature {sup 195}Pt NMR spectroscopy proved useful in studying the stereodynamics of complex thioethers like methionine. The complex, Pt(trpy)Cl{sup +}, with its chromophore has a greater potential for probing proteins. It is a noninvasive and selective tag for histidine and cysteine residues on the surface of cytochrome c at pH 5. The protein derivatives obtained are separable, and the tags are easily quantitated and differentiated through the metal-to-ligand charge transfer bands which are sensitive to the environment of the tag. Increasing the pH to 7.0 led to the modification by Pt(trpy)Cl{sup +}of Arg 91 in cytochrome c. Further studies with guanidine-containing ligands as models for arginine modification by Pt(trpy)Cl{sup +} showed that guanidine can act as a terminal ligand and as a bridging ligand. Owing to the potential utility of Pt(trpy)L{sup n+} as …

There has been much recent interest in the photochemistry and photophysics of transition metal polypyridine complexes due to the possibility of their use in solar energy conversion systems. The excited state of these compounds are known to undergo useful electron transfer and energy transfer reactions. This work attempts to elucidate the mechanism of the quenching of *CrL{sub 3}{sup 3+} (where L = 2,2{prime}-bipyridine, 4,4{prime}-dimethyl-2,2{prime}-bipyridine, 1,10-phenanthroline, 5-chloro-1,10-phenanthroline, 5-methyl-1,10-phenanthroline) by oxalate ions in neutral pH. Evidence suggests an ion-pairing pre-equilibrium followed by rate limiting electron transfer to produce CrL{sub 3}{sup 2+} and CO{sub 2}{sup {minus}} can then react with ground state chromium(III) species to produce another mole of the reduced product or it can produce a secondary transient as in the case of phenanthroline and substituted phenanthroline complexes. The secondary transient reacts to produce CrL{sub 3}{sup 2+} in a subsequent reaction. 85 refs., 24 figs., 7 tabs.

A method for determining the location and possible existence of symmetry elements in Patterson superposition maps has been developed. A comparison of the original superposition map and a superposition map operated on by the symmetry element gives possible translations to the location of the symmetry element. A reciprocal space approach using structure factor-like quantities obtained from the Fourier transform of the superposition function is then used to determine the best'' location of the symmetry element. Constraints based upon the space group requirements are also used as a check on the locations. The locations of the symmetry elements are used to modify the Fourier transform coefficients of the superposition function to give an approximation of the structure factors, which are then refined using the EG relation. The analysis of several compounds using this method is presented. Reciprocal space techniques for locating multiple images in the superposition function are also presented, along with methods to remove the effect of multiple images in the Fourier transform coefficients of the superposition map. In addition, crystallographic studies of the extended chain structure of (NHC{sub 5}H{sub 5})SbI{sub 4} and of the twinning method of the orthorhombic form of the high-{Tc} superconductor YBa{sub 2}Cu{sub 3}O{sub 7-x} are …