M.Sc. Physicshttp://hdl.handle.net/10464/22502019-12-04T19:22:12Z2019-12-04T19:22:12ZEffect of rattling Phonons on Superconductivity of KOs_2O_6Tajik, Saminhttp://hdl.handle.net/10464/132092018-10-05T17:14:26ZEffect of rattling Phonons on Superconductivity of KOs_2O_6
Tajik, Samin
We model the electron coupling to anharmonic (rattling) mode in β-pyrochlore superconductor KOs2O6 by a sharply peaked electron-phonon coupling function α2F(Ω) centered at the mode energy. The strong-coupling Eliashberg equations are solved for the transition temperature Tc and the gap function ∆(ω,T) for a series of temperatures 0 < T < Tc. From these solutions, we obtain the temperature dependence of the gap edge ∆(T), the nuclear magnetic resonance (NMR) relaxation rate and the microwave conductivity for several values of the electron-phonon coupling
parameter λ. The results are compared with the available experimental results 0
for KOs2O6
Magnetic and Dielectric Properties of Cu3-xNixWO6 and Cu3W1-xMoxO6Dan, Xuhttp://hdl.handle.net/10464/130952018-10-05T17:14:26ZMagnetic and Dielectric Properties of Cu3-xNixWO6 and Cu3W1-xMoxO6
Dan, Xu
Cu3WO6 is a compound with an interesting coordination chemistry for both Cu and W. In this research, all samples were made by using the standard Solid Phase Reaction method with and without any doping. Using Powder x-ray diffraction and Rietveld analysis, we did not observe any distortion of the cubic crystal. Ni substitution for Cu, and Mo substitution for W, will act as a negative pressure on the lattice parameter of Cu3WO6. Magnetization measurements of Cu3-xNixWO6 indicate that all compounds undergo an antiferromagnetic phase transition at the Néel temperature. However, a significant change was observed in Néel temperature with Ni’s concentration. All compounds show Curie–Weiss antiferromagnetic behavior at high temperatures. The value of the 𝛍eff is close to the theoretical calculation in Cu3WO6. And the magnitude of 𝛍eff (exp) increases with Ni’s concentration. A spin-singlet ground state with energy gap at low temperatures was observed for all compounds. The energy gap 𝚫 is decreasing with the increasing concentration of Ni. The dielectric permittivity as a function of temperature and different frequency from1 kHz to 20 kHz for all samples, were investigated. A peak in dielectric loss ε'' appears between 150 K to 260 K in all samples of Cu3-xNixWO6. The peak position has a linear relationship with log10(𝑓) as a function of temperaure. The doping of Ni causes a gradual shift in the peak position. The activation energy Ea is decreasing with the increasing of Ni’s concentration.
Numerical Solutions of Laplace's Equation for Various Physical SituationsVendromin, Colinhttp://hdl.handle.net/10464/129902018-10-05T17:14:26ZNumerical Solutions of Laplace's Equation for Various Physical Situations
Vendromin, Colin
There are two projects in this thesis.
In the first project, a general method is introduced to numerically calculate the resistance of truncated resistors in cylindrical coordinates, with non-constant cross-sectional area. The problem of finding the resistance of a truncated conical resistor is given in some introductory textbooks as a simple problem. The textbook method is flawed however, and leads to the wrong answer. The textbook method assumes that the electric potential distribution inside the truncated cone is approximately equivalent to a cylindrical resistor. This assumption ignores the constricting affect that the boundary of the truncated conical resistor has on the electric potential inside. The deformation of the electric field is not accounted for by excess charge or changing magnetic fields, instead it is the result of a derivative operation called the shear of the field. Numerical solutions for the resistance of truncated conical, ellipsoidal, and hyperboloidal resistors are presented as a function of a/b, where a is the radius of the smallest cross-sectional area and b is radius of the largest. It was found that the textbook solution always underestimates the numerical value of the resistance.
In the second project, dielectric breakdown clusters were grown with a stochastic two dimensional Dielectric Breakdown Model (DBM) on a honeycomb, square, and triangle lattice, as well as on a random distribution of nodes. On the regular lattices the number of nearest neighbours was a constant at all lattice sites. For a random distribution of nodes there was variation in the number of nearest neighbours at different nodes. Some percentage of the nodes were isolated from the rest of the distribution, because they had 0 nearest neighbours. Distributions of nodes in which many of the nodes had 0 nearest neighbours indicated a medium with high density fluctuations. The motivation for this work was to study the relationship between the fractal dimension of the dielectric breakdown clusters and the number of nearest neighbours, and the density variation of the medium. The singularity spectra were calculated for the clusters, as well as their fractal dimension using box counting, and sandbox methods. It was found that the dielectric breakdown model produces monofractal clusters. As such, the dimension of the clusters can be represented by a single fractal dimension. In the DBM, the probability of a perimeter site connecting to the cluster is proportional to the strength of the local electric field raised to an exponent. If the exponent is a large positive number then perimeter sites which feel a stronger electric field are more likely to connect to the cluster. Increasing the exponent produces clusters which resemble lightning, with a fractal dimension lower than the dimension of the lattice. Similarly increasing the percentage of isolated nodes decreases the fractal dimension.
Infrared Spectroscopy Of Ba_3+y Co_1+xNb_2O_9 CeramicsIbrahim, Samiahttp://hdl.handle.net/10464/129892018-10-05T17:14:26ZInfrared Spectroscopy Of Ba_3+y Co_1+xNb_2O_9 Ceramics
Ibrahim, Samia
The dielectric properties of ceramic Ba3+y Co1+xNb2O9 where x= 0,-0.07,0.03
and y = 0, -0.03 were characterized because it might used for a wide range of
applications including wireless communication used in mobile communication,
ultra high speed local area networks, intelligent transport system and satellite
communications.
Room temperature optical re
ectivity measurements of ceramics sintered
at di erent temperatures between 1200 C to 1500 C were made covering the
spectral range between 70-8000 cm1. The Lorentz model was used to t the
re
ectance data to make extrapolations for Kramers Kronig (K-K) analysis and
to estimate the microwave properties.
K -K analysis was applied to extract the other optical response functions
from the re
ectance data ( optical conductivity and dielectric permittivity).
Powder X-Ray di raction measurements were done with 2 in the range
between 10 to 80 degree for all samples. Most samples exhibit some degree of
1:2 ordering which appears as small superlattice peaks at 17.6 and 12 degree.
All samples exhibit a small amount of impurity phases.
The main purpose of this work is to study the e ect of the density, 1:2 (
Co:Nb) ordering and concentration of Cobalt on the dielectric properties. It
was shown that density has a clear e ect on the dielectric properties. For
example 1 (50 cm1) decreased if the densjhfnadfity decreased. On the other hand
the change of the concentration of Cobalt does not have any real e ect on the
dielectric properties. 1:2 order also has an e ect on the dielectric properties.
It was observed that the scattering rate of the optical phonon was smaller in
sample exhibiting more 1:2 order.