Crystal growth, Raman scattering and optical properties of the superconductor Cd2Re2O7(16O, 18O)/

Using the Physical Vapor Transport method, single crystals of Cd2Re207 have been grown, and crystals of dimensions up to 8x6x2 mm have been achieved. X-ray diffraction from a single crystal of Cd2Re207 has showed the crystal growth in the (111) plane. Powder X-ray diffraction measurements were performed on ^^O and ^^O samples, however no difference was observed. Assigning the space group Fd3m to Cd2Re207 at room temperature and using structure factor analysis, the powder X-ray diffraction pattern of the sample was explained through systematic reflection absences. The temperatiure dependence of the resistivity measurement of ^^O has revealed two structural phase transitions at 120 and 200 K, and the superconducting transition at 1.0 K. Using Factor Group Analysis on three different structiures of Cd2Re207, the number of IR and Raman active phonon modes close to the Brillouin zone centre have been determined and the results have been compared to the temperature-dependence of the Raman shifts of ^^O and ^*0 samples. After scaling (via removing Bose-Einstein and Rayleigh scattering factors from the scattered light) all spectra, each spectrum was fitted with a number of Lorentzian peaks. The temperature-dependence of the FWHM and Raman shift of mode Eg, shows the effects of the two structurjil phase transitions above Tc. The absolute reflectance of Cd2Re207 - '^O single crystals in the far-infrared spectral region (7-700 cm~^) has been measured in the superconducting state (0.5 K), right above the superconducting state (1.5 K), and in the normal state (4.2 K). Thermal reflectance of the sample at 0.5 K and 1.5 K indicates a strong absorption feature close to 10 cm~^ in the superconducting state with a reference temperature of 4.2 K. By means of Kramers-Kronig analysis, the absolute reflectance was used to calculate the optical conductivity and dielectric function. The real part of optical conductivity shows five distinct active phonon modes at 44, 200, 300, 375, and 575 cm~' at all temperatures including a Drude-like behavior at low frequencies. The imaginary part of the calculated dielectric function indicates a mode softening of the mode 44 cm~' below Tc.

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

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

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

An analysis of the methyl rotation dynamics in the So (x' A) and T (a A) states of thioacetaldehyde from Pyrolysis jet spectra /

Jet-cooled, laser-induced phosphorescence excitation spectra (LIP) of thioacetaldehyde CH3CHS, CH3CDS, CD3CHS and CD3CDS have been observed over the region 15800 - 17300 cm"^ in a continuous pyrolysis jet. The vibronic band structure of the singlet-triplet n -* n* transition were attributed to the strong coupling of the methyl torsion and aldehydic hydrogen wagging modes . The vibronic peaks have been assigned in terms of two upper electronic state (T^) vibrations; the methyl torsion mode v^g, and the aldehydic hydrogen wagging mode v^^. The electronic origin O^a^ is unequivocally assigned as follows: CH3CHS (16294.9 cm"'' ), CH3CDS (16360.9 cm"'' ), CD3CHS (16299.7 cm"^ ), and CD3CDS (16367.2 cm"'' ). To obtain structural and dynamical information about the two electronic states, potential surfaces V(e,a) for the 6 (methyl torsion) and a (hydrogen wagging) motions were generated by ab initio quantum mechanical calculations with a 6-3 IG* basis in which the structural parameters were fully relaxed. The kinetic energy coefficients BQ(a,e) , B^(a,G) , and the cross coupling term B^(a,e) , were accurately represented as functions of the two active coordinates, a and 9. The calculations reveal that the molecule adopts an eclipsed conformation for the lower Sq electronic state (a=0°,e=0"') with a barrier height to internal rotation of 541.5 cm"^ which is to be compared to 549.8 cm"^ obtained from the microwave experiment. The conformation of the upper T^ electronic state was found to be staggered (a=24 . 68° ,e=-45. 66° ) . The saddle point in the path traced out by the aldehyde wagging motion was calculated to be 175 cm"^ above the equilibrium configuration. The corresponding maxima in the path taken by methyl torsion was found to be 322 cm'\ The small amplitude normal vibrational modes were also calculated to aid in the assignment of the spectra. Torsional-wagging energy manifolds for the two states were derived from the Hamiltonian H(a,e) which was solved variationally using an extended two dimensional Fourier expansion as a basis set. A torsionalinversion band spectrum was derived from the calculated energy levels and Franck-Condon factors, and was compared with the experimental supersonic-jet spectra. Most of the anomalies which were associated with the interpretation of the observed spectrum could be accounted for by the band profiles derived from ab initio SCF calculations. A model describing the jet spectra was derived by scaling the ab initio potential functions. The global least squares fitting generates a triplet state potential which has a minimum at (a=22.38° ,e=-41.08°) . The flatter potential in the scaled model yielded excellent agreement between the observed and calculated frequency intervals.