16 resultados para fragile states
em CaltechTHESIS
Resumo:
A new geometry-independent state - a traveling-wave wall state - is proposed as the mechanism whereby which the experimentally observed wall-localized states in rotating Rayleigh-Bénard convection systems preempt the bulk state at large rotation rates. Its properties are calculated for the illustrative case of free-slip top and bottom boundary conditions. At small rotation rates, this new wall state is found to disappear. A detailed study of the dynamics of the wall state and the bulk state in the transition region where this disappearance occurs is conducted using a Swift-Hohenberg model system. The Swift-Hohenberg model, with appropriate reflection-symmetry- breaking boundary conditions, is also shown to exhibit traveling-wave wall states, further demonstrating that traveling-wave wall states are a generic feature of nonequilibrium pattern-forming systems. A numerical code for the Swift-Hohenberg model in an annular geometry was written and used to investigate the dynamics of rotating Rayleigh-Bénard convection systems.
Resumo:
Our understanding of the structure and evolution of the deep Earth is strongly linked to knowledge of the thermodynamic properties of rocky materials at extreme temperatures and pressures. In this thesis, I present work that helps constrain the equation of state properties of iron-bearing Mg-silicate perovskite as well as oxide-silicate melts. I use a mixture of experimental, statistical, and theoretical techniques to obtain knowledge about these phases. These include laser-heated diamond anvil cell experiments, Bayesian statistical analysis of powder diffraction data, and the development of a new simplified model for understanding oxide and silicate melts at mantle conditions. By shedding light on the thermodynamic properties of such ubiquitous Earth-forming materials, I hope to aid our community’s progress toward understanding the large-scale processes operating in the Earth’s mantle, both in the modern day and early in Earth’s history.
Resumo:
Part I
Studies of vibrational relaxation in excited electronic states of simple diatomic molecules trapped in solid rare-gas matrices at low temperatures are reported. The relaxation is investigated by monitoring the emission intensity from vibrational levels of the excited electronic state to vibrational levels of the ground electronic state. The emission was in all cases excited by bombardment of the doped rare-gas solid with X-rays.
The diatomics studied and the band systems seen are: N2, Vegard-Kaplan and Second Positive systems; O2, Herzberg system; OH and OD, A 2Σ+ - X2IIi system. The latter has been investigated only in solid Ne, where both emission and absorption spectra were recorded; observed fine structure has been partly interpreted in terms of slightly perturbed rotational motion in the solid. For N2, OH, and OD emission occurred from v' > 0, establishing a vibrational relaxation time in the excited electronic state of the order, of longer than, the electronic radiative lifetime. The relative emission intensity and decay times for different v' progressions in the Vegard-Kaplan system are found to depend on the rare-gas host and the N2 concentration, but are independent of temperature in the range 1.7°K to 30°K.
Part II
Static crystal field effects on the absorption, fluorescence, and phosphorescence spectra of isotopically mixed benzene crystals were investigated. Evidence is presented which demonstrate that in the crystal the ground, lowest excited singlet, and lowest triplet states of the guest deviate from hexagonal symmetry. The deviation appears largest in the lowest triplet state and may be due to an intrinsic instability of the 3B1u state. High resolution absorption and phospho- rescence spectra are reported and analyzed in terms of site-splitting of degenerate vibrations and orientational effects. The guest phosphorescence lifetime for various benzene isotopes in C6D6 and sym-C6H3D3 hosts is presented and discussed.
Resumo:
We present a theoretical study of electronic states in topological insulators with impurities. Chiral edge states in 2d topological insulators and helical surface states in 3d topological insulators show a robust transport against nonmagnetic impurities. Such a nontrivial character inspired physicists to come up with applications such as spintronic devices [1], thermoelectric materials [2], photovoltaics [3], and quantum computation [4]. Not only has it provided new opportunities from a practical point of view, but its theoretical study has deepened the understanding of the topological nature of condensed matter systems. However, experimental realizations of topological insulators have been challenging. For example, a 2d topological insulator fabricated in a HeTe quantum well structure by Konig et al. [5] shows a longitudinal conductance which is not well quantized and varies with temperature. 3d topological insulators such as Bi2Se3 and Bi2Te3 exhibit not only a signature of surface states, but they also show a bulk conduction [6]. The series of experiments motivated us to study the effects of impurities and coexisting bulk Fermi surface in topological insulators. We first address a single impurity problem in a topological insulator using a semiclassical approach. Then we study the conductance behavior of a disordered topological-metal strip where bulk modes are associated with the transport of edge modes via impurity scattering. We verify that the conduction through a chiral edge channel retains its topological signature, and we discovered that the transmission can be succinctly expressed in a closed form as a ratio of determinants of the bulk Green's function and impurity potentials. We further study the transport of 1d systems which can be decomposed in terms of chiral modes. Lastly, the surface impurity effect on the local density of surface states over layers into the bulk is studied between weak and strong disorder strength limits.
Resumo:
Part I:
The earth's core is generally accepted to be composed primarily of iron, with an admixture of other elements. Because the outer core is observed not to transmit shear waves at seismic frequencies, it is known to be liquid or primarily liquid. A new equation of state is presented for liquid iron, in the form of parameters for the 4th order Birch-Murnaghan and Mie-Grüneisen equations of state. The parameters were constrained by a set of values for numerous properties compiled from the literature. A detailed theoretical model is used to constrain the P-T behavior of the heat capacity, based on recent advances in the understanding of the interatomic potentials for transition metals. At the reference pressure of 105 Pa and temperature of 1811 K (the normal melting point of Fe), the parameters are: ρ = 7037 kg/m3, KS0 = 110 GPa, KS' = 4.53, KS" = -.0337 GPa-1, and γ = 2.8, with γ α ρ-1.17. Comparison of the properties predicted by this model with the earth model PREM indicates that the outer core is 8 to 10 % less dense than pure liquid Fe at the same conditions. The inner core is also found to be 3 to 5% less dense than pure liquid Fe, supporting the idea of a partially molten inner core. The density deficit of the outer core implies that the elements dissolved in the liquid Fe are predominantly of lower atomic weight than Fe. Of the candidate light elements favored by researchers, only sulfur readily dissolves into Fe at low pressure, which means that this element was almost certainly concentrated in the core at early times. New melting data are presented for FeS and FeS2 which indicate that the FeS2 is the S-hearing liquidus solid phase at inner core pressures. Consideration of the requirement that the inner core boundary be observable by seismological means and the freezing behavior of solutions leads to the possibility that the outer core may contain a significant fraction of solid material. It is found that convection in the outer core is not hindered if the solid particles are entrained in the fluid flow. This model for a core of Fe and S admits temperatures in the range 3450K to 4200K at the top of the core. An all liquid Fe-S outer core would require a temperature of about 4900 K at the top of the core.
Part II.
The abundance of uses for organic compounds in the modern world results in many applications in which these materials are subjected to high pressures. This leads to the desire to be able to describe the behavior of these materials under such conditions. Unfortunately, the number of compounds is much greater than the number of experimental data available for many of the important properties. In the past, one approach that has worked well is the calculation of appropriate properties by summing the contributions from the organic functional groups making up molecules of the compounds in question. A new set of group contributions for the molar volume, volume thermal expansivity, heat capacity, and the Rao function is presented for functional groups containing C, H, and O. This set is, in most cases, limited in application to low molecular liquids. A new technique for the calculation of the pressure derivative of the bulk modulus is also presented. Comparison with data indicates that the presented technique works very well for most low molecular hydrocarbon liquids and somewhat less well for oxygen-bearing compounds. A similar comparison of previous results for polymers indicates that the existing tabulations of group contributions for this class of materials is in need of revision. There is also evidence that the Rao function contributions for polymers and low molecular compounds are somewhat different.
Resumo:
Bulk metallic glasses (BMGs) maybe be considered to share some of the same inherent trade-offs as engineering ceramics. While BMGs typically exhibit high yield strengths, and while some have surprising fracture toughness, they exhibiting little to no tensile ductility, and fail in a brittle manner under uniaxial loading. Speaking broadly, there are two complimentary approaches to improving on these shortcomings: 1) create bulk metallic glass matrix composites (BMGMCs) and 2) improve the properties of a monolithic BMG. The structure of this thesis mirrors this division, with chapters 2-7 focusing on creating and processing amorphous metal matrix composites, and chapter 8 focusing on modifying the properties of a monolithic BGM by altering its configurational state through irradiation.
Resumo:
The two lowest T = 3/2 levels in 21Na have been studied in the 19F(3He, n), 20Ne (p,p) and 20Ne (p,p’) reactions, and their excitation energies, spins, parities and widths have been determined. In a separate investigation, branching ratios were measured for the isospin-nonconserving particle decays of the lowest T = 3/2 levels in 17O and 17F to the ground state and first two excited states of 16O, by studying the 15N(3He,n) 17F*(p) 16O and 18O(3He, α)17O*(n) 16O reactions.
The 19F(3He,n) 21Na reaction was studied at incident energies between 4.2 and 5.9 MeV using a pulsed-beam neutron-time-of-flight spectrometer. Two T = 3/2 levels were identified at excitation energies of 8.99 ± 0.05 MeV (J > ½) and 9.22 ± 0.015 MeV (J π = ½+, Γ ˂ 40 keV). The spins and parities were determined by a comparison of the measured angular distributions with the results of DWBA calculations.
These two levels were also obsesrved as isospin-forbidden resonances in the 20Ne(p,p) and 20Ne(p,p’) reactions. Excitation energies were measured and spins, parities, and widths were determined from a single level dispersion theory analysis. The following results were obtained:
Ex = 8.973 ± 0.007 MeV, J π = 5/2 + or 3/2+, Γ ≤ 1.2 keV,
Γpo = 0.1 ± 0.05 keV; Ex = 9.217 ± 0.007 MeV, Jπ = ½ +,
Γ = 2.3 ± 0.5 keV, Γpo = 1.1 ± 0.3 keV.
Isospin assignments were made on the basis of excitation energies, spins, parities, and widths.
Branching ratios for the isospin-nonconserving proton decays of the 11.20 MeV, T = 3/2 level in 17F were measured by the 15N(3He,n) 17 F*(p) 16O reaction to be 0.088 ± 0.016 to the ground state of 16O and 0.22 ± 0.04 to the unresolved 6.05 and 6.13 MeV levels of 16O. Branching ratios for the neutron decays of the analogous T = 3/2 level, at 11.08 MeV in 17O, were measured by the 16O(3He, α)17O*(n)16O reaction to be 0.91 ± 0.15 to the ground state of 16O and 0.05 ± 0.02 to the unresolved 6.05 and 6.13 MeV states. By comparing the ratios of reduced widths for the mirror decays, the form of the isospin impurity in the T = 3/2 levels is shown to depend on Tz.
Resumo:
PART I
The energy spectrum of heavily-doped molecular crystals was treated in the Green’s function formulation. The mixed crystal Green’s function was obtained by averaging over all possible impurity distributions. The resulting Green’s function, which takes the form of an infinite perturbation expansion, was further approximated by a closed form suitable for numerical calculations. The density-of-states functions and optical spectra for binary mixtures of normal naphthalene and deuterated naphthalene were calculated using the pure crystal density-of-state functions. The results showed that when the trap depth is large, two separate energy bands persist, but when the trap depth is small only a single band exists. Furthermore, in the former case it was found that the intensities of the outer Davydov bands are enhanced whereas the inner bands are weakened. Comparisons with previous theoretical calculations and experimental results are also made.
PART II
The energy states and optical spectra of heavily-doped mixed crystals are investigated. Studies are made for the following binary systems: (1) naphthalene-h8 and d8, (2) naphthalene--h8 and αd4, and (3) naphthalene--h8 and βd1, corresponding to strong, medium and weak perturbations. In addition to ordinary absorption spectra at 4˚K, band-to-band transitions at both 4˚K and 77˚K are also analyzed with emphasis on their relations to cooperative excitation and overall density-of-states functions for mixed crystals. It is found that the theoretical calculations presented in a previous paper agree generally with experiments except for cluster states observed in system (1) at lower guest concentrations. These features are discussed semi-quantitatively. As to the intermolecular interaction parameters, it is found that experimental results compare favorably with calculations based on experimental density-of-states functions but not with those based on octopole interactions or charge-transfer interactions. Previous experimental results of Sheka and the theoretical model of Broude and Rashba are also compared with present investigations.
PART III
The phosphorescence, fluorescence and absorption spectra of pyrazine-h4 and d4 have been obtained at 4˚K in a benzene matrix. For comparison, those of the isotopically mixed crystal pyrazine-h4 in d4 were also taken. All these spectra show extremely sharp and well-resolved lines and reveal detailed vibronic structure.
The analysis of the weak fluorescence spectrum resolves the long-disputed question of whether one or two transitions are involved in the near-ultraviolet absorption of pyrazine. The “mirror-image relationship” between absorption and emission shows that the lowest singlet state is an allowed transition, properly designated as 1B3u ← 1A1g. The forbidden component 1B2g, predicted by both “exciton” and MO theories to be below the allowed component, must lie higher. Its exact location still remains uncertain.
The phosphorescence spectrum when compared with the excitation phosphorescence spectra, indicates that the lowest triplet state is also symmetry allowed, showing a strong 0-0 band and a “mirror-image relationship” between absorption and emission. In accordance with previous work, the triplet state is designated as 3B3u.
The vibronic structure of the phosphorescence spectrum is very complicated. Previous work on the analysis of this spectrum all concluded that a long progression of v6a exists. Under the high resolution attainable in our work, the supposed v6a progression proves to have a composite triplet structure, starting from the second member of the progression. Not only is the v9a hydrogen-bending mode present as shown by the appearance of the C-D bending mode in the d4 spectrum, but a band of 1207 cm-1 in the pyrazine in benzene system and 1231 cm-1 in the mixed crystal system is also observed. This band is assigned as 2v6b and of a1g symmetry. Its anonymously strong intensity in the phosphorescence spectrum is interpreted as due to the Fermi resonance with the 2v6a and v9a band.
To help resolve the present controversy over the crystal phosphorescence spectrum of pyrazine, detailed vibrational analyses of the emission spectra were made. The fluorescence spectrum has essentially the same vibronic structure as the phosphorescence spectrum.
Resumo:
The lowest T = 2 states have been identified and studied in the nuclei 12C, 12B, 20F and and 28Al. The first two of these were produced in the reactions 14C(p,t)12C and 14C (p,3He)12B, at 50.5 and 63.4 MeV incident proton energy respectively, at the Oak Ridge National Laboratory. The T = 2 states in 20F and 28Al were observed in (3He,p) reactions at 12-MeV incident energy, with the Caltech Tandem accelerator.
The results for the four nuclei studied are summarized below:
(1) 12C: the lowest T = 2 state was located at an excitation energy of 27595 ± 20 keV, and has a width less than 35 keV.
(2) 12B: the lowest T = 2 state was found at an excitation energy of 12710 ± 20 keV. The width was determined to be less than 54 keV and the spin and parity were confirmed to be 0+. A second 12B state (or doublet) was observed at an excitation energy of 14860 ± 30 keV with a width (if the group corresponds to a single state) of 226 ± 30 keV.
(3) 20F: the lowest T = 2 state was observed at an excitation of 6513 ± 5 keV; the spin and parity were confirmed to be 0+. A second state, tentatively identified as T = 2 from the level spacing, was located at 8210 ± 6 keV.
(4) 28Al: the lowest T = 2 state was identified at an excitation of 5997 ± 6 keV; the spin and parity were confirmed to be 0+. A second state at an excitation energy of 7491 ± 11 keV is tentatively identified as T = 2, with a corresponding (tentative) spin and parity assignment Jπ = 2+.
The results of the present work and the other known masses of T = 2 states and nuclei for 8 ≤ A ≤ 28 are summarized, and massequation coefficients have been extracted for these multiplets. These coefficients were compared with those from T = 1 multiplets, and then used to predict the mass and stability of each of the unobserved members of the T = 2 multiplets.
Resumo:
The (He3, n) reactions on B11, N15, O16, and O18 targets have been studied using a pulsed-beam time-of-flight spectrometer. Special emphasis was placed upon the determination of the excitation energies and properties of states with T = 1 (in Ne18), T = 3/2 (in N13 and F17) and T = 2 (in Ne20). The identification of the T = 3/2 and T = 2 levels is based on the structure of these states as revealed by intensities and shapes of angular distributions. The reactions are interpreted in terms of double stripping theory. Angular distributions have been compared with plane and distorted wave stripping theories. Results for the four reactions are summarized below:
1) O16 (He3, n). The reaction has been studied at incident energies up to 13.5 MeV and two previously unreported levels in Ne18 were observed at Ex = 4.55 ± .015 MeV (Γ = 70 ± 30 keV) and Ex = 5.14 ± .018 MeV (Γ = 100 ± 40 keV).
2) B11 (He3, n). The reaction has been studied at incident energies up to 13.5 MeV. Three T = 3/2 levels in N13 have been identified at Ex = 15.068 ± .008 MeV (Γ ˂ 15 keV), Ex = 18.44 ± .04, and Ex 18.98 ± .02 MeV (Γ = 40 ± 20 keV).
3) N15 (He3, n). The reaction has been studied at incident energies up to 11.88 MeV. T = 3/2 levels in F17 have been identified at Ex = 11.195 ± .007 MeV (Γ ˂ 20 keV), Ex = 12.540 ± .010 MeV (Γ ˂ 25 keV), and Ex = 13.095 ± .009 MeV (Γ ˂ 25 keV).
4) O18 (He3, n). The reaction has been studied at incident energies up to 9.0 MeV. The excitation energy of the lowest T = 2 level in Ne20 has been found to be 16.730 ± .006 MeV (Γ ˂ 20 keV).
Angular distributions of the transitions leading to the above higher isospin states are well described by double stripping theory. Analog correspondences are established by comparing the present results with recent studies (t, p) and (He3, p) reactions on the same targets.
Resumo:
Some of the metallogenic provinces of the southwestern United States and northern Mexico are defined by the geographic distribution of trace elements in the primary sulfide minerals chalcopyrite and sphalerite. The elements investigated include antimony, arsenic, bismuth, cadmium, cobalt, gallium, germanium, indium, manganese, molybdenum, nickel, silver, tellurium, thallium, and tin. Of these elements, cobalt, gallium, germanium, indium, nickel, silver, and tin exhibit the best defined geographic distribution.
The data indicate that chalcopyrite is the preferred host for tin and perhaps molybdenum; sphalerite is the preferred host for cadmium, gallium, germanium, indium, and manganese; galena is the preferred host for antimony, bismuth, silver, tellurium, and thallium; and pyrite is the preferred host for cobalt, nickel, and perhaps arsenic. With respect to the two minerals chalcopyrite and sphalerite, antimony, arsenic, molybdenum, nickel, silver, and tin prefer chalcopyrite; and bismuth, cadmium, cobalt, gallium, germanium, indium, manganese, and thallium prefer sphalerite. This distribution probably is the result of the interaction of several factors, among which are these: the various radii of the elements, the association due to chemical similarities of the major and trace elements, and the degree of ionic versus covalent and metallic character of the metal-sulfur bonds in chalcopyrite and sphalerite. The type of deposit, according to a temperature classification, appears to be of minor importance in determining the trace element content of chalcopyrite and sphalerite.
A preliminary investigation of large single crystals of sphalerite and chalcopyrite indicates that the distribution within a single crystal of some elements such as cadmium in sphalerite and indium and silver in chalcopyrite is relatively uniform, whereas the distribution of some other elements such as cobalt and manganese in sphalerite is somewhat less uniform and the distribution of tin in sphalerite is extremely erratic. The variations in trace element content probably are due largely to variations in the composition of the fluids during the growth of the crystals, but the erratic behavior of tin in sphalerite perhaps is related to the presence of numerous cavities and inclusions in the crystal studied.
Maps of the geographic distribution of trace elements in chalcopyrite and sphalerite exhibit three main belts of greater than average trace element content, which are called the Eastern, Central, and Western belts. These belts are consistent in trend and position with a beltlike distribution of copper, gold, lead, zinc, silver, and tungsten deposits and with most of the major tectonic features. However, there appear to be no definite time relationships, for as many as four metallogenic epochs, from Precambrian to late Tertiary, are represented by ore deposits within the Central belt.
The evidence suggests that the beltlike features have a deep seated origin, perhaps in the sub-crust or outer parts of the mantle, and that the deposits within each belt might be genetically related through a beltlike compositional heterogeneity in the source regions of the ores. Hence, the belts are regarded as metallogenic provinces.
Resumo:
The common belief that fermions lying on linear Regge trajectories must have opposite-parity partners is shown to be false. The mechanism by which these experimentally nonexistant states are eliminated from the theory depends on the presence of fixed Regge cuts in fermion exchange amplitudes. Thus it is predicted that fermion Regge trajectories are always accompanied by fixed Regge cuts. More generally, if particles may be classified as composites of spin-1/2 (fermion) quarks, fixed cuts are expected to be present in boson exchange amplitudes as well. This result is demonstrated in the framework of the Van Hove model and a few further experimental consequences are discussed.
Resumo:
I. PHOSPHORESCENCE AND THE TRUE LIFETIME OF TRIPLET STATES IN FLUID SOLUTIONS
Phosphorescence has been observed in a highly purified fluid solution of naphthalene in 3-methylpentane (3-MP). The phosphorescence lifetime of C10H8 in 3-MP at -45 °C was found to be 0.49 ± 0.07 sec, while that of C10D8 under identical conditions is 0.64 ± 0.07 sec. At this temperature 3-MP has the same viscosity (0.65 centipoise) as that of benzene at room temperature. It is believed that even these long lifetimes are dominated by impurity quenching mechanisms. Therefore it seems that the radiationless decay times of the lowest triplet states of simple aromatic hydrocarbons in liquid solutions are sensibly the same as those in the solid phase. A slight dependence of the phosphorescence lifetime on solvent viscosity was observed in the temperature region, -60° to -18°C. This has been attributed to the diffusion-controlled quenching of the triplet state by residual impurity, perhaps oxygen. Bimolecular depopulation of the triplet state was found to be of major importance over a large part of the triplet decay.
The lifetime of triplet C10H8 at room temperature was also measured in highly purified benzene by means of both phosphorescence and triplet-triplet absorption. The lifetime was estimated to be at least ten times shorter than that in 3-MP. This is believed to be due not only to residual impurities in the solvent but also to small amounts of impurities produced through unavoidable irradiation by the excitation source. In agreement with this idea, lifetime shortening caused by intense flashes of light is readily observed. This latter result suggests that experiments employing flash lamp techniques are not suitable for these kinds of studies.
The theory of radiationless transitions, based on Robinson's theory, is briefly outlined. A simple theoretical model which is derived from Fano's autoionization gives identical result.
Il. WHY IS CONDENSED OXYGEN BLUE?
The blue color of oxygen is mostly derived from double transitions. This paper presents a theoretical calculation of the intensity of the double transition (a 1Δg) (a 1Δg)←(X 3Σg-) (X 3Σg-), using a model based on a pair of oxygen molecules at a fixed separation of 3.81 Å. The intensity enhancement is assumed to be derived from the mixing (a 1Δg) (a 1Δg) ~~~ (X 3Σg-) (X 3Σu-) and (a 1Δg) (1Δu) ~~~ (X 3Σg-) (X 3Σg-). Matrix elements for these interactions are calculated using a π-electron approximation for the pair system. Good molecular wavefunctions are used for all but the perturbing (B 3Σu-) state, which is approximated in terms of ground state orbitals. The largest contribution to the matrix elements arises from large intramolecular terms multiplied by intermolecular overlap integrals. The strength of interaction depends not only on the intermolecular separation of the two oxygen molecules, but also as expected on the relative orientation. Matrix elements are calculated for different orientations, and the angular dependence is fit to an analytical expression. The theory therefore not only predicts an intensity dependence on density but also one on phase at constant density. Agreement between theory and available experimental results is satisfactory considering the nature of the approximation, and indicates the essential validity of the overall approach to this interesting intensity enhancement problem.
Resumo:
The effect of intermolecular coupling in molecular energy levels (electronic and vibrational) has been investigated in neat and isotopic mixed crystals of benzene. In the isotopic mixed crystals of C6H6, C6H5D, m-C6H4D2, p-C6H4D2, sym-C6H3D3, C6D5H, and C6D6 in either a C6H6 or C6D6 host, the following phenomena have been observed and interpreted in terms of a refined Frenkel exciton theory: a) Site shifts; b) site group splittings of the degenerate ground state vibrations of C6H6, C6D6, and sym-C6H3D3; c) the orientational effect for the isotopes without a trigonal axis in both the 1B2u electronic state and the ground state vibrations; d) intrasite Fermi resonance between molecular fundamentals due to the reduced symmetry of the crystal site; and e) intermolecular or intersite Fermi resonance between nearly degenerate states of the host and guest molecules. In the neat crystal experiments on the ground state vibrations it was possible to observe many of these phenomena in conjunction with and in addition to the exciton structure.
To theoretically interpret these diverse experimental data, the concepts of interchange symmetry, the ideal mixed crystal, and site wave functions have been developed and are presented in detail. In the interpretation of the exciton data the relative signs of the intermolecular coupling constants have been emphasized, and in the limit of the ideal mixed crystal a technique is discussed for locating the exciton band center or unobserved exciton components. A differentiation between static and dynamic interactions is made in the Frenkel limit which enables the concepts of site effects and exciton coupling to be sharpened. It is thus possible to treat the crystal induced effects in such a fashion as to make their similarities and differences quite apparent.
A calculation of the ground state vibrational phenomena (site shifts and splittings, orientational effects, and exciton structure) and of the crystal lattice modes has been carried out for these systems. This calculation serves as a test of the approximations of first order Frenkel theory and the atom-atom, pair wise interaction model for the intermolecular potentials. The general form of the potential employed was V(r) = Be-Cr - A/r6 ; the force constants were obtained from the potential by assuming the atoms were undergoing simple harmonic motion.
In part II the location and identification of the benzene first and second triplet states (3B1u and 3E1u) is given.
Resumo:
A simple model potential is used to calculate Rydberg series for the molecules: nitrogen, oxygen, nitric oxide, carbon monoxide, carbon dioxide, nitrogen dioxide, nitrous oxide, acetylene, formaldehyde, formic acid, diazomethane, ketene, ethylene, allene, acetaldehyde, propyne, acrolein, dimethyl ether, 1, 3-butadiene, 2-butene, and benzene. The model potential for a molecule is taken as the sum of atomic potentials, which are calibrated to atomic data and contain no further parameters. Our results agree with experimentally measured values to within 5-10% in all cases. The results of these calculations are applied to many unresolved problems connected with the above molecules. Some of the more notable of these problems are the reassignment of states in carbon monoxide, the first ionization potential of nitrogen dioxide, the interpretation of the V state in ethylene, and the mystery bands in substituted ethylenes, the identification of the R and R’ series in benzene and the determination of the orbital scheme in benzene from electron impact data.