VictorJuiz/thesis huggingface dataset:
The theory of the absorption edge in semiconductors

The thesis is concerned with optical absorption by a semiconductor due to the excitation of electrons from the valence band to the conduction band giving rise to the phenomenon of the absorption edge. In treating the final state of the semiconductor in such an absorption process it is shewn that the system Bay be considered as a two particle one in which the excited electron in the conduction band is bound to the hole left behind in the valence band, which behaves in many ways like a positively charged particle. A bound system of this type is called an exciton. The theory of the exciton is developed in some detail in the effective mass approximation for the case of a semiconductor with spherical energy bands. The effect of an externally applied uniform magnetic field is calculated.
Using the exciton wave-function derived in this way, a general expression for the absorption coefficient due to exciton creation in a magnetic field is obtained. The evaluation of this formula requires a knowledge of the wave-functions of the hydrogen atom in a magnetic field. For special cases, e.g. zero magnetic field it is shewn how the general absorption coefficient formula leads to expressions previously derived by other authors.
The ware-equation for the hydrogen atom in a magnetic field in solved by a perturbation theory approach for the case where the magnetic field energy is larger than the Coulomb energy, a case of some importance in semiconductors since the Coulomb interaction is reduced by the dielectric constant and the electron or hole effective masses are usually small. Both bound and free states of the exciton are considered, and formal expressions for f-values and absorption coefficients are presented.
These formal expressions are evaluated numerically for some important cases. The positions and intensities of the lowest observable absorption lines are calculated when the electronic transition from the valence band to the conduction band is either allowed or forbidden, and the values of the absorption coefficients close to the absorption edge are determined.
Finally the accuracy of the perturbation theory method used is assessed and recent experimental work on the absorption edge is discussed.
An investigation of the properties of nuclear levels by nuclear orientation

Nuclear alignment has been on established technique in nuclear physics for some years and the majority of the experiments have employed the methods suggested by Bleaney (1951) and by Rose (1949) and Gerter (1948). The former is simpler since it requires no external fields. For this method the nucleus must be the core of a paramagnetic ion which is included in a crystal with suitable internal fields. The alignment arises through anisotropic hyperfine structure (S(off)=[illegible fraction]) or isotropic hyperfine structure with a finite splitting of the electronic levels caused by the crystalline field (D≠OS≥1). Certain nuclear states will become predominantly populated at very low temperatures which can conveniently be produced by adiabatic demagnetisation of an ion incorporated in the same salt.
Paramagnetism arises through vacancies in the 3f and 4d electronic shell so that those nuclei studied fall in the iron-transition and rare-earth groups. The former can be conveniently incorporated with the salts of the Tutton series (double sulphates) or the double nitrates, both of which have been extensively studied. However, the Tutton salts have two ions per unit cell giving rise to two alignment axes inclined at about 70° while for some of the iron group elements (e.g. Co++, Mn++) the double nitrates have two positions in the unit cell with different hyperfine constants
Following the successful cooling of nickel-zinc fluosilicate by adiabatic demagnetisation (Hill, Meyer & Milner 1959) it was realised that this salt which has one ion per unit cell might be suitable for nuclear orientation and indeed have some advantages over the other salts. All the principal experiments described in this thesis have been performed with nickel-zinc fluosilicate.
The angular distribution of the gamma-radiation from an aligned nucleus is not in general isotropic, the anisotropy depending on the degree of alignment and decay characteristics of the isotope. Thus by measuring the anisotropy it is possible to deduce values for some of the nuclear parameters such as the angular moments and magnetic moment of the levels involved.
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Thermochemical and spectroscopic studies of bond energies in simple molecules

The gaseous alkali halide molecules are of interest because they constitute a group particularly susceptible to theoretical interpretation. It does not seem to be too far from the truth to regard them as systems of simple polarizable ions.
An important molecular property is the dissociation energy, D(MX). In the case of the alkali halides, this may be determined either by spectroscopic or by thermochemical methods. However, although analyses of their ultraviolet absorption spectra have given fair estimates of the dissociation energies, the method of analysis is here liable to systematic errors and is best used to get relative values. The most reliable estimates of the energies of dissociation are therefore to be obtained from the thermochemical cycle which may be written
D(MX) = - Qf(MX) - ΔsH(MX) + ΔsH(M) + ½D(X ).....(1)
The quantities least well known in equations (1) for the alkali halides are often the heats of sublimation, ΔsH298(MX), of the salts. There is at present available in several cases information only on the vapour pressure above the liquids at relatively high temperatures, and the corrections to give ΔsH298 are large and uncertain, and more so since the only values commonly known for the heats of fusion are derived from rather scanty information on freezing points in binary systems.
On these grounds, the merits of determining ΔsH298 by measuring the vapour pressures above the crystal at relatively low temperatures are obvious, in addition it has recently become clear that the interpretation of measurements at higher pressures is not simple. There is now good evidence, both from electron impact studies, and from the observations of molecular beams, that the vapours of the alkali halides consist by no means exclusively of monomers, MX, but also contain appreciable proportions of polymers, especially of (MX)2. It would be expected that at the low vapour pressures obtaining above the crystal, dimerisation would be relatively unimportant, and that reliable values of ΔsH298 for the monomer species might be obtained by simple treatments. In fact, the results given below may be taken to indicate that this is the situation for caesium and rubidium fluorides, but that in lithium, sodium, and, to a larger extent in potassium fluorides, dimerisation is significant even at pressures in the range 10-4 to 10-2 mm.
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(i) auxiliary cofactors in the metabolism of citrate by yeast ; (ii) biochemical studies of intestinal mucins

The properties of factors present in boiled yeast juice which stimulate the oxidative breakdown of citrate in baker's yeast have been investigated. The activity has been shown to reside predominantly in the nucleotide fractions (i.e., pyridine codehydrogenases) and to a lesser extent in the ammonium salts present in whole yeast cells. The activity of the Citrate Oxidation Factor (COF) concentrated from yeast extracts and described by Foulkes (Biochem. J. 54 323 (1953)) was attributable entirely to the ammonium content of COF preparations.
This activating effect of ammonium ions is accompanied by their removal from the assay system and the simultaneous production of glutamic acid. Correlation of the uptake of ammonium ion with the increased citrate metabolism indicates that the activity of the ammonium salts lies in their ability to promote the reductive amination of α-oxoglutarate. The mechanism(s) whereby this serves to stimulate the further breakdown of citrate to oxoglutarate involves the mediation of the pyridine codehydrogenases (DPN, TPN).
These findings are discussed in relation to the known functioning of individual stains of the tricarboxylic acid cycle and to possible alternative pathways for the oxidation of citrate in yeast.
A study has been made of the incorporation of 35S into rabbit duodenal mucin after intravenous administration of Na235SO4 and DL35S-methionine. Within 1 hour, 35S-sulphate and 35S-methionine were present in the nondialysable mucosubstances which constitute the viscosity-raising agents of the mucin. The maximum incorporation of both the sulphate and the methionine into these mucosubstances was found after a period of 4 hours. Following the administration of Na235SO4, appreciable amounts of inorganic 35SO4" and a dialysable ester 35sulphate were excreted into the mucin.
The influence of cortisone on mucin production was studied using these isotopically-labelled compounds. In contract to the many reports in the literature concerning the inhibitory effect of cortisone on the biosynthesis or sulphated mucosubstances in mesenchymal tissues, cortisone acetate was found to have no appreciable influence on the biosynthesis of the (epithelial) mucosubstances in duodenal mucin. Some studies on the composition of the duodenal mucosubstances of both pig and rabbit are also reported.
In part III the development and use of a micromethod for the estimation of 3-15μg. inorganic and esterfied sulphate is described. This method was developed in response to the necessity of determining the microquantities of total sulphate present in small volumes (<1 ml.) of various radioactive mucin fractions, in order to evaluate their respective specific radioactivities. In principle, the sulphate is quantitively precipitated by benzidine, filtered in situ and the benzidine contained in the microprecipitate determined colorimetrically by diazotisation and coupling with thymol.
Enzyme studies in the tricarboxylic acid cycle

The purpose of this investigation was to obtain a highly purified preparation of aconitase and to study the properties of the purified enzyme. The thesis describes
The method of purification
The activation of aconitase by Fe24 and reducing agents
The effect of pH on the enzyme activity
The study of the Kinetics of the enzyme
The effect of fluorocitric acid on the enzyme activity
The effect of other inhibititors on the enzyme activity.
The results may be briefly summarised as follows:
A preparation of aconitase with a higher specific activity than previously reported has been obtained. The preparation was stable. Electrophoretic analysis showed that the aconitase protein formed 75-80% of the total protein present. The results obtained during the fractionation were consistent, with the idea that aconitase activity is associated with a single species of protein molecule. The final enzyme preparation possessed little activity in the absence of Fe2+ and a reducing agent. The activity could be increased 70-fold by the presence of these substances. The results indicate that the active form of the enzyme is an enzyme-Fe2+-activator complex.
from a study of the effects of pH on the reactions catalysed by aconitase and of the reaction Kinetics, it was concluded that the same catalytic centre of the aconitase protein is concerned in all the reactions
Aconitase was inhibited in a competitive fashion by 'natural' fluorocitric acid, whilst synthetic fluorocitric acid inhibited it competitively and irreversibly. Whereas pchloromercuribenzoate inhibited aconitase in the presence of substrate, o-phenanthroline, 2:2'- dipyridyl and versene inhibited only in the absence of substrate. Cyanide and azide did not inhibit the enzyme.
Radiometric measurements of atmospheric temperature

A review of current problems and phenomena requiring further study in Atmospheric Physics is given, with particular reference to the upper atmosphere, defined as the region above 25 km. The conclusion is that an extended program of observations with very wide coverage and high accuracy is required, and that only satellite-borne instruments can do this economically. The particular difficulties associated with making accurate measurements at high levels are discussed, and the possibility of employing a number of conventional spectroscopic techniques is considered and finally rejected. The method of using a cell of carbon dioxide, the pressure of which is periodically modulated, as the spectroscopic element, as suggested by J. T. Houghton and C. D. Rodgers in 1965, is evaluated theoretically and shown to be capable of a temperature discrimination of 1°K with adequate height resolution at altitudes up to 70 km.
The rest of the thesis is concerned mainly with the design of suitable instrumentation. Three different prototypes using different pressure-modulation techniques and different optical systems were tried until a sufficiently sensitive and reliable design was achieved, suitable for a satellite instrument. This consists of an optical system using a germanium window and one germanium field lens together with a conical light-pipe and a wide band interference filter to isolate the band; an experimental pyroelectric detector developed by Mullard Ltd. is used. Pressure modulation is achieved by the use of a light alloy piston mounted on beryllium-copper spider springs and magnetically driven by cross-connected Helmholtz coils. Special electronics are used to maintain a constant amplitude of the piston. Modulating the pressure of the absorbing gas also modifies its absorption coefficient, chopping the centres of spectral lines in the selected band, and generating an a.c. signal at the detector. The intensity of this signal is related to the temperature of the emitting gas. The distribution of the emitting gas along the line of sight can be computed by the use of spectral models and data on the band, but it was also measured directly by an experiment based on the Curtis-Godson approximation and using a simulated atmosphere in a large tank. The final design was incorporated into a flight prototype designed to be carried to 40 km. by a large balloon. The balloon radiometer had an in-flight calibration system together with voltage, current and temperature 'housekeeping' measurements all multiplexed for use with single channel eight-bit digital telemetry. The final two chapters deal with the flights of the balloon instruments, and the reduction of the data and its comparison with simultaneous measurements made by conventional radio-sonde. The results confirm the predictions of the theory, and it is concluded that a powerful new technique is available for the study of the Upper Stratosphere and Mesosphere.
The study of chemiluminescent reactions in the gas phase

The two lowest lying singlet electronic states of molecular oxygen O2(1Δg) and O2(1Σg+) are present in the atmosphere and undergo optical transitions to the ground state molecule giving rise to the atmospheric bands:
O2(1Σg+) ↔ O2(3Σg-) (O,O) 762 nm
and the infra-red atmospheric bands:
O2(1Δg) ↔ O2(3Σg-) (O,O) 1268 nm.
Possible mechanisms for the production of the excited species were studied in the laboratory. The reactions were carried out in time resolved flow systems and the species observed by their optical emission with the aid of photomultipliers and photo conductors in conjunction with phase sensitive detection circuitry.
The ultra violet photolysis of ozone with λ = 253.7 nm was studied as a source of O2(1Σg+) and O2(1Δg). O2(1Δg) was observed in the photolysis of ozone-oxygen mixtures with λ = 253.7 nm and its production was attributed to the energy transfer process:
O(1D) + O2(3Σg-) → O(3P) + O2(1Δg).
O2(1Σg+) was observed in a system involving the photolysis of oxygen with λ = 147 nm by an analogous reaction:
O(1D) + O2(3Σg-) → O(3P) + O2(1Σg+)
The atom recombination reaction:
O(3P) + O(3P) + M → O2(singlet) + M
and the chemi luminescent reaction:
NO + O3 → NO2 + O2 + hν
were studied but found not to produce significant quantities of excited molecular oxygen.
The excited species have relatively long lifetimes and generally undergo physical or chemical deactivation reactions in preference to radiative transitions. The reactions of O2(1Σg+) and O2(1Δg) with ozone:
O3 + O2(1Σg+) → 2O2 + O(3P)
O3 + O2(1Δg) → 2O2 + O(3P)
and the quenching reactions:
O2(1Σg+) + M → O2 + M
where M = O2, N2 and Ar were studied and rate constants evaluated. A value for the efficiency of deactivation of O2(1Σg+) at a pyrex surface was also obtained and the rate of the energy pooling process O2(1Δg) + O2(1Δg) → O2(1Σg+) + O2(3Σg-) was estimated.
The rates of the following O(1D) atom reactions:
O(1D) + N2 → O(3P) + N2
O(1D) + Ar → O(3P) + Ar
O(1D) + O3 → O2 + O2
O(1D) + O2 → O2(1Σg+) + O(3P)
O(1D) + O2 → O2(1Δg) + O(3P)
were estimated.
Calculations were carried out to test the importance of the various mechanistic schemes studied as sources of excited singlet oxygen in the atmosphere, In addition the major loss processes of excited oxygen molecules and atoms were calculated and the results compared with atmospheric data.
Sylow subgroups of index 2 in their normalizers

The following theorem is proved:
Theorem Let G be a finite group, P a Sylow p-subgroup of G, p odd. Suppose
|N(P)/P⋅C(P)| = 2;
cl(P) ≤ 2 .
Then
if G is perfect, then P is necessarily cyclic;
if P is not cyclic, then either 0p(G) < G, or 02(G) < G with G = 0p,(G)⋅N(P).
A unified proof is given as far as possible, but the proof eventually splits into three cases, with hypothesis (2) strengthened by one of:
|P′| = p,
P is abelian but not cyclic, or
|P′| > p.
Different methods are in fact required for each case.
Several corollaries are also discussed.
Studies in photoionisation

The studies in photoionisation in molecules presented in this thesis were accomplished by the technique of Photoelectron Spectroscopy. The gaseous molecules are irradiated by photons of discreet energy (hν), sufficient to eject electrons, and through the analysis of the kinetic energies (En) of the photoelectrons the ionisation energies (In) can be determined from Einstein's photoelectric equation
En = hν - In
Ionisation phenomena and the means of relating the information to electronic structure and dimensional changes are discussed. The techniques used to study electronic processes in the vacuum ultra-violet are outlined and the advantages, limitations in the experimental aspects and interpretation of data compared. The features of significance in photoelectron spectroscopy are discussed both from the theoretical and experimental viewpoint. The instrumental development since the initial work in the early sixties is reviewed and the experimental criteria outlined. The modifications carried out in conjunction with this work and the experimental details are presented.
In the lowest ionisation process in phosphine and phosphorous trifluoride an extensive vibrational progression is discernible. The sufficiently high quality data allows a detailed discussion of the geometry of these ions, barriers to inversion and potential functions. The analysis suggests that the ground ionic state of phosphorous trifluoride is very probably strictly planar, while that of phosphine is pyramidal with a very small barrier to inversion. The higher ionisation energies are discussed in view of-the spectral detail and a molecular orbital scheme.
In the study of steric inhibition of resonance in substituted benzenes, it is shown that through the correlation of Π-energy levels in series of related molecules, electronic and steric effects can be separated and the relative importance of the latter estimated.
In biphenyls an empirical correlation between certain bands in the spectra and dihedral angle is.noted and its use in conformational studies emphasised.
The variation of the photoelectron Π-ionisation energies in biphenyls, phenyl ethylenes, anilines, phenols and related molecules is rationalised on a semi-quantitative basis by a Hückel-type theory based on the interaction of semi-localised Π-MOs. The dihedral angles in sterically hindered, or rigidly held, phenyl ethylenes and anilines can then be inferred. The validity of the semi-empirical treatment is demonstrated by the success in reproducing the photoelectron data. Discussion of the Franck-Condon envelopes gives support to the assignment of the Π-MOs, indicating geometrical changes. In the anilines the deduction is that nitrogen is non-planar.
Features of interest in the individual molecules are also discussed. Correlation diagrams are used extensively to illustrate the trends, choice of basis set parameters, and to summarise the assignments.
Excitations in impure magnetic crystals

In this thesis we consider two types of magnetic system, the ferromagnet and the antiferromagnet, containing substitutional impurities. The Heisenberg Hamiltonian is used and the spin-waves are examined by means of Green function equations of motion; the coherent potential approximation (CPA) is employed to obtain expressions for self-energies which are approximately valid for all impurity concentrations. In each case, an extension of the usual CPA is made: in Part I the impurities are described by scattering potentials with matrix elements on several lattice sites, and in Part II the effects of clusters of defects are included.
In Part I, we discuss the dilute ferromagnet, and attempt to obtain an estimate of the critical concentration of magnetic ions by considering the long-wavelength spin-waves. The self-energy is calculated in such a way as to sum coherently the scattering of spin-waves from all sites affected by one impurity, although correlations between pairs of defects are neglected. We examine solutions for a single non-magnetic impurity and for small impurity concentrations; it emerges from these considerations that it is essential that the resonance which the non-magnetic ions produce at zero energy should be kept there by any approximation which is to be of use in describing the low-energy spin-waves. A generalized form of the CPA, suitable for extended defect matrices, is developed and used to derive expressions for the self-energy; detailed numerical results are presented. We find that although the CPA behaves well over most of the spin-wave band, it fails to describe the zero-energy resonance correctly, and this failure prevents us from deducing a value for the critical concentration. Two attempts to avoid this difficulty are described: the first uses defect Green functions to fix the energy of the resonance, the second moves it away from zero and outside the spin-wave band, but neither enables us to estimate the critical concentration. We also discuss a magnetic analogue of the percolation bond problem, to which the application of the CPA is successful.
In Part II we apply the CPA to a calculation of the spin-wave energies in antiferromagnets containing either magnetic or non-magnetic impurities. Each site is allowed to have any possible number of impurities among its nearest neighbours; in order to deal with this we extend the CPA to deal with a large number of different defect types. Variations in the transverse interactions are not included in the CPA, but are treated in an approximate way afterwards. Expressions for the neutron scattering and Raman cross sections are derived in order to permit a detailed comparison of theory with experiment. The results of numerical calculations for three systems are presented: (Mn,Co)F2, K(Mn,Co)F3 and (Mn,Zn)F2. These are compared with experimental data, and excellent agreement is found; in particular, the neutron scattering results agree extremely well, the line-shapes and widths being accurately described by the theory.