M.Sc. Physics

Permanent URI for this collectionhttps://hdl.handle.net/10464/2250

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Open Access
mKdV Loop Travelling Waves and Interactions of Loop Solitons
(Brock University) Maan, Jaskaran; Department of Physics
The modified Korteweg-de Vries (mKdV) equation is an integrable nonlinear evolution equation which has applications in modeling various physical phenomena. It also describes the curvature of curve which undergoes a certain non-stretching geometrical evolution in the Euclidean plane. This curve motion finds applications in various areas, such as describing the dynamics of inelastic rope, modeling the evolution of the boundary of vortex patch (swirling region) in thin, sheet-like layer of incompressible fluid, and understanding the behavior of electrons quantized in thin-layered materials by studying the boundaries of electron cloud densities under strong electromagnetic fields. This study focuses on mKdV curve motions called loop solutions. One class arises from soliton, heavy-tail (rational), and periodic solutions of the mKdV equation. These loop solutions exhibit intriguing symmetrical shapes: the soliton and heavy-tail cases describe a single loop which is open, and asymptotically straight or circular, respectively; the periodic case describes both open and closed loops which can have multiple crossings. Additionally, a class of colliding loop solutions are obtained from the 2-soliton solution of the mKdV equation. The collisions show interesting interaction patterns. A summary of different types of patterns will be given by categorizing the various shapes that occur during the interaction, which depend on the speed ratio of the initial two loops. Analytical and numerical methods are employed to determine the loop solutions for both classes, as well as the conditions determining interaction type in the case of collision. These findings contribute to a deeper understanding of the mKdV equation and solitons.
Open Access
Localized Vibrational Modes in High-Entropy Oxides
(Brock University) Wilson, Connor Mackenzie; Department of Physics
The existence of localized vibrational modes in the high-entropy oxide (MgCoNiCuZn)O is investigated using classical lattice dynamics. New empirical interatomic potentials for the cation-oxygen interactions in (MgCoNiCuZn)O are developed and are shown to yield superior agreement with the experimental crystal structures, dielectric constants, and phonon frequencies of the parent binary oxides. Various probes for localization are calculated and suggest (MgCoNiCuZn)O supports localized modes beyond a high-frequency mobility edge in the vibrational density-of-states.
Open Access
Exotic gap structures in multiband superconductors
(Brock University) Nanchian, Hooman; Department of Physics
The symmetry-based approach is a capable method in the theory of superconductivity. To understand how the gap function transforms under the point group operation, one needs to know the transformation properties of the single-electron states. Accord- ing to the Ueda-Rice prescription, the transformation of the Bloch states, under the operation of a point group element, is described by the pure spin-1/2 rotation matrices, even in the presence of spin-orbit coupling. In the presence of spin-orbit coupling, we show that the Bloch states in a centrosymmetric and non-magnetic crystal are not the eigenstates of the pure spin-1/2 operators. In this case, the transformation of the Bloch states depends on the symmetry of the bands participating in the pairing. This transformation is not necessarily equivalent to the transformation of the pure spin-1/2 Bloch states. In this work, we study a hexagonal multiband superconductor with a D6h point group in the presence of spin-orbit coupling. We discovered that the Bloch states in some specific bands do not transform like pure spin-1/2 states. This behavior of the electron bands leads to an exotic gap nodal structure that we study in two pairing channels. In an interband s-wave pairing, some nodes appear in the gap structure of the superconductor. In an interband i-wave pairing, the gap nodes move by changing the strength of the interband pairing. The pseudospin symmetry-based approach, presented in the textbooks, does not predict these results.
Open Access
Low-dimensional purple and blue bronzes: Crystal growth, characterization and optical properties
(Brock University) Ahmadi, Mohammad; Department of Physics
The molybdenum oxide bronzes are a family of charge-density-wave (CDW) conductors with distinctive properties originating from their low-dimensional crystal structure and associated Fermi surface instabilities. Single crystals of potassium blue and purple bronzes and sodium purple bronze have been synthesized using a temperature flux technique and XRD measurement was deployed to investigate the formation of the correct phase. Optical spectroscopy and electrical resistivity measurements were carried out on sodium purple bronze and potassium blue bronze. Sodium purple bronze crystals were found to exhibit a clear anisotropy in their natural cleavage (a-b) plane. Electrical resistivity measurements were performed along the different crystallographic directions which displayed two distinct metallic axes perpendicular to each other in the a-b plane. The optical conductivity obtained from Kramers-Kronig analysis of reflectance spectroscopy data was in good agreement with the resistivity measurements. The two in-plane metallic axes undergo CDW transitions at two different temperatures Tp, suggesting a distinction in electronic and phononic subsystems along each axis. Potassium blue bronze samples exhibit various temperature dependent anomalies in the electrical resistivity measurements, which are associated with CDW instability in this compound. The absolute values of resistivity at room temperature along both in-plane crystallographic axes, were compared to the literature to verify the accuracy of our measurement techniques. The ac-current effects on linear and non-linear regimes of resistivity were closely investigated, and the results support the sliding of the CDW, and the existence of a small-threshold field ET of CDW depinning in this sample. Hysteresis in resistivity, which has been detected in many CDW compounds, has been observed in our measurements and is associated with the instability of the CDW possibly due to the presence of defects.
Open Access
Optical Study of (Nb0.5In0.5)0.02 Ti0.98O2 Crystals
(Brock University) Cosco, Mike; Department of Physics
This work was a study of pure TiO2Rutile crystals, as well as Rutile crystals 2% co-doped with Indium and Niobium (2-NITO). There is much interest surrounding co-doped TiO2re-cently, with several papers published on ’colossal permittivity’ in the lower frequency ranges (10^2-10^6Hz range). The aim of this work was to study the optical and Raman modes of pure and co-doped crystals to determine the effects co-doping has on these modes. Infrared reflectance along with Raman Spectroscopy were used for this purpose. In order to determine the dielectric function from the infrared data, the Factorized Model and Kramers-Kronig analysis were used. Since TiO2has a tetragonal unit cell, infrared measurements of both the a and c axes of both doped and undoped crystals were done. Thea-axis is known to have 3 optical modes, whereas the c-axis only has one. However an additional mode was seen in all spectra, believed to be caused by anharmonicity. In addition, the 136cm−1mode observed in polycrystalline conductivity spectra of 5 and 10-NITO lines up directly with the A2u mode and the 793cm−1 mode also appears in single crystal TiO2, meaning these are not new modes. However the 447cm−1 and 654cm−1 modes do not appear in our data, and are likely a result of higher percentage co-doping. The effect of co-doping was observed to be an overall decrease in the reflectance of TiO2. We also observed sizable increases inγtofor all modes in 2-NITO. In addition, the dielectric permittivity decreases below the first phonon mode; suggesting that the enhanced permittivity observed at lower frequencies is not caused by co-doped changes to phonon modes. All expected Raman-active modes were observed, however due to poor data resolution some of the peak positions appear to be slightly different than previously measured. Our Raman spectra showed new structures at around 300cm−1and 700cm−1 in the (100) surface spectra, it is possible these are combination lines.
Open Access
High Temperature Method Of Measuring Electrical And Magnetic Properties Of Europium Doped Nickel Oxide
(Brock University) Torabi, S. Parisa; Department of Physics
The measurement of the magnetic moment of materials as a function of temperature in modern AC or DC magnetometers normally has a limited high temperature range up to 400 K. To overcome this problem one needs to design ovens which can handle high temperatures. The highest Curie temperature observed in materials is in pure Co which is about 1400 K. However, most materials and compounds show Tc below 800 K. My thesis research topic is to study the substitution of Ni ions by rare earth ions in NiO. The NiO is a semiconductor which exhibits antiferromagnetism below 520 K, which makes it suitable for applications; to name a few, rechargeable batteries, and p-type transport conducting lms. In this study, Ni ions were substituted by 2, 5, and 8 percent of Eu ions. The effect of substitution on the semiconducting properties of Ni1-xEuxO was studied as function of temperature from room temperature to 1000 K. To study the magnetic properties and the effect of Eu substitution on the Neel temperature of Ni1-xEuxO we adapted two ovens for high temperature measurements of AC susceptibility by using the ac modulation technique implementing a lock-in ampli er and the DC susceptibility using the SQUID magnetometer. To check the reliability of these two ovens we also examined the ferromagnetic transition temperatures of Bismuth Ferrite samples as function of Co substitutions for Fe.
Open Access
Electronic and Magnetic Properties of MAX Phase (Cr1-xGdx)2AlC and Er3AlC Alloy
(Brock University) Albandri, Huriyyah A; Department of Physics
Bulk samples of (Cr1-xGdx)2AlC with X = 0, 0.0025, 0.01, 0.025, 0.05 and Er3AlC compound were synthesized using the arc melting technique. The samples were characterized by X-ray diffraction, magnetic susceptibility, and four probe resistivity measurements to study their magnetic and electronic properties. Using Rietveld analysis for X-ray diffraction, it was determined that the parent compound Cr2AlC exhibits a side phase of Cr7C3. The substituted samples were found to have secondary phases of Cr7C3 and GdCr3.5Al8.5 which slightly increase on increasing substitution of Cr3+ by Gd3+. The change of the concentration of Gadolinium does not have any real effect on the lattice parameter of (Cr1-xGdx)2AlC. Er3AlC contains secondary phases of ErAl2 and ErC0.6. The MAX phase Cr2AlC and the Gadolinium substituted samples show complex magnetic behaviour. The magnetization measurements show that Cr2AlC has an unusual magnetic behavior above 70 K which does not obey the Curie-Weiss law. The sample with X = 0.0025 also does not obey the Curie-Weiss law at high temperature. The susceptibility data shows that samples with X = 0.01, 0.025, and 0.05 obey the Curie-Weiss law, and the magnitude of the effective magnetic moments decreases while increasing the value of X. The susceptibility data of Er3AlC obey the Curie-Weiss law; and the effective moment is 9.1 ± 0.005 𝛍B. The resistivity measurement of the parent sample Cr2AlC indicates metallic behavior. In the Gd-substituted samples, we observed a Kondo Effect from the resistivity data. The resistivity of Gd-substituted samples increases with increasing Gadolinium concentration. We also observed metallic behavior in the Er3AlC resistivity.
Open Access
Resistivity of Single Crystal Molybdenum Dioxide
(Brock University) BAUER, KURTIS; Department of Physics
The chemical vapour transport method was used to grow molybdenum oxide single crystals so that their electrical properties could be analyzed. Satisfactory single crystal samples of MoO2 and Mo4O11 were grown successfully using I2 as a transport agent. Crystal growths using TeCl4 as a transport agent were also performed, though with mixed results. This approach yielded MoO2, MoO3, and Mo9O26, but this produced samples of a quality not suitable for single crystal analysis. Measurements performed on these samples yielded unique results, due to their mixed oxide nature, but as the composition of each sample was inconsistent, even between crystals from the same growth, little can be said about them definitively. Rubidium doped single crystal growths were also attempted, to build on previous polycrystalline Rb doped sample research, however no growths successfully included measurable amounts of Rb. While resistivity and heat capacity measurements performed on MoO2 did identify a phase transition in the area of 267K reported by other researchers, there was however no evidence found to support a reported 220K electronic transition [1]. In Mo4O11 two previously identified 109K and 30K charge density wave transitions were observed in the DC resistivity. When AC resistivity measurements were performed the 30K transition was not apparent. Instead, a divergence of the cooling and warming curves not seen in the DC experiments occurred above 200K, with previously unseen peaks appearing at 285K and 250K when cooling from 400K.
Open Access
Deformations of Maxwell gauge field theory
(Brock University) Frank, James; Department of Physics
Deformations of Maxwell gauge theory are studied in 2+1 dimensions. Unlike in previous work in the literature, no Lagrangian structure is assumed for possible deformations, and instead the requirement of gauge invariance of the deformed field equations under the deformed gauge symmetry is used. The results yield a new nonlinear generalization of Maxwell gauge theory. A non-abelian extension of this theory is also obtained.
Open Access
Travelling Wave Solutions on a Non-zero Background for the Generalized Korteweg-de Vries Equation
(Brock University) Nayeri, HamidReza; Department of Physics
In presenting this thesis, we try to find all non-periodic travelling waves of the generalized Korteweg-de Vries (gKdV) equation u_t +\alpha u^p u_x +\beta u_{xxx}=0 using an energy analysis method. Since the power p in the gKdV equation is arbitrary, we consider positive integer values for $p$. We first check the method for two cases where p=1 and p=2 which are known as the KdV and the mKdV equations, respectively. Then, we look at the general case where p greater than or equal 3 is arbitrary. By applying the energy analysis method on the KdV and the mKdV equations, we will find an explicit form of solitary waves on a non-zero background. Afterwards, we reparametrize the derived solutions in terms of speed and the background size to interpret these solutions physically. We also look at some limiting cases in which heavy-tailed and kink waves arise in the mKdV equation. At last, we split up the gKdV equation into two cases of odd and even $p$ powers and apply a similar derivation. In each case, the implicit solutions are introduced and characterized by their features.
Open Access
An Analogue of the Laplace-Runge-Lenz Vector for Timelike Geodesics in Schwarzschild Spacetime
(Brock University) Fazio, Jordan; Department of Physics
In Schwarzschild spacetime, the timelike geodesics are the trajectories of free, massive particles, orbiting a singularity at the origin r = 0. In this work we derive four scalar first integrals of timelike geodesics in Schwarzschild spacetime. Two of the first integrals, corresponding to energy and angular momentum, are well-known. The other two first integrals, an angular quantity and a temporal quantity, are not as well-known. Using the freedom to shift first integrals by a constant value we set a ‘zero-point’ for each of the four first integrals. By choosing a natural point on a non-circular trajectory such as a turning point or inertial point to set the zero-point value, the angular and temporal first integrals will correspond respectively to the angle and time of the chosen zero-point. We then take the Newtonian limit of the angular and temporal first integrals, and show that using a natural choice of zero-point they provide a generalization of the classical Laplace-Runge-Lenz (LRL) vector. We then evaluate the angular first integral for each type of timelike geodesic in Schwarzschild spacetime. In most cases we are able to choose a turning or inertial point to set a zero-point. For an unbound or asymptotic trajectory which falls into the singularity of the metric at r = 0, however, we find that we must take a different point, such as the point where the trajectory crosses the horizon at r = 2M, which we call the ‘horizon point.’ For the case of a precessing elliptic orbit we find that the angular first integral is multi-valued, with the zero-point jumping each time the trajectory crosses an apoapsis. It is found that the angular and temporal first integrals provide a relativistic generalization of the classical LRL vector, where we the first integrals correspond to a larger class of physically meaningful points compared to Newtonian orbits and where the LRL vector and angular and temporal first integrals may always correspond to the periapsis.
Open Access
Electronic and Magnetic Properties of Pyrochlore (Eu(1-x)Dyx)2Ir2O7
(Brock University) Amir, Zainab Mohamed; Department of Physics
The pyrochlore (Eu(1-x)Dyx)2Ir2O7 for x = 0, 0.25, 0.50, 0.75, and 1.0 were prepared using solid-state reaction method. As the Dy concentration increases, the X-ray results indicate a systematic decrease of the cubic lattice parameter of (Eu(1-x)Dyx)2Ir2O7. We observed metal insulator transition in all compounds in addition two new anomalies at high temperatures in specifi c heat and resistivity results. The origin of these anoma- lies have not yet been identifi ed. The metal insulator transition temperature TMI of (Eu(1-x)Dyx)2Ir2O7 increases with the reduction in the lattice parameter. In the mag- netic susceptibility results, the effective magnetic moment increases with the increment of the Dy substitution for Eu ions. The magnetic fi eld dependence of resistivity was in- vestigated for all samples, negative and positive magnetoresistance effects are discussed.
Open Access
Investigation into the Magnetoelectric Effect and Magnetic Properties of Iron-doped Cobalt Molybdate
(Brock University) Pula, Mathew; Department of Physics
The plausibility of revealing linear magnetoelectric coupling is investigated in the cobalt molybdate (Co2Mo3O8). Recently, Wang et al.[Scientific Reports. 2015;Vol. 5:Article 12268] showed that iron molybdate(Fe2Mo3O8) can be induced into a ferrimagnetic state from a nominal antiferromagnetic state via application of a magnetic field. As such, it may be possible that cobalt molybdate exhibits a similar effect intrinsically or with addition of iron dopant. Single crystals of the hexagonal molybdate (Co(1-x)Fe(x))2Mo3O8 (x=0, 0.25, 0.5, 0.75, 1) were synthesized via chemical vapour transport. The magnetic properties were investigated along the polar axis and in the basal plane. Despite doping with iron, no metamagnetic phase transition was present in (Co(1-x)Fe(x))2Mo3O8 (x=0.25, 0.5, 0.75). Low field measurements of the susceptibility reveal the presence of an anisotropic ferromagnetic-like moment, which is suppressed at moderate fields. This is believed to be a product of an exchange-bias-like phenomena, which is not fully understood. The magnetocapacitance was measured along the c-axis for x=(0.25, 0.5). Co1.5Fe0.5Mo3O8 exhibits the conventional magnetodielectric effect, with a proportionality constant of 5.1(0.3) x10^(-14) Oe^(-2) at 40K, while the capacitance of Co1Fe1Mo3O8 shows linear dependency on H, with slope -6.99(0.07) x10^(-9) Oe^(-1) at 49K.
Open Access
A critical analysis of the 2H NMR data in chlorhexidine-containing model membranes
(Brock University) Talo, Hoda; Department of Physics
Deuterium nuclear magnetic resonance spectroscopy was used to study the in uence of chlorhexidine on the internal molecular motions of phospholipid model membranes. Mixtures of dimyristoylphosphocholine (DMPC) and chlorhexidine (CHX) were investigated at several DMPC:CHX molar ratios (1:0,10:1,3:1). Extensive numerical analysis of previously acquired data identi ed the di erences in the temperature-dependence of the order parameters characterizing the rapid molecular motions (on the NMR scale) in both the fatty acid chains of DMPC and in the saturated methylene bridge of CHX. The results are consistent with the known localization of CHX in the membrane determined by neutron scattering [1] and con rmed by molecular dynamics simulations reported earlier [2]. The NMR results indicate that chlorhexidine undergoes di erent motions than those of the bulk lipids in the membrane. The study used a Tikhonov-regularization-based numerical deconvolution technique (dePakeing) that allowed simultaneous determination of the order parameter and of the orientational distribution of domains in the powder sample, partially oriented by the external magnetic eld. Both appeared to suggest an anomalous result in a narrow temperature region for the 3:1 sample, perhaps the existence of a new re-entrant phase, but this conclusion could not be made from the limited data available, and requires a further investigation.
Open Access
Effect of rattling Phonons on Superconductivity of KOs_2O_6
(Brock University) Tajik, Samin; Department of Physics
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
Open Access
Magnetic and Dielectric Properties of Cu3-xNixWO6 and Cu3W1-xMoxO6
(Brock University) Dan, Xu; Department of Physics
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.
Open Access
Numerical Solutions of Laplace's Equation for Various Physical Situations
(Brock University) Vendromin, Colin; Department of Physics
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.
Open Access
Infrared Spectroscopy Of Ba_3+y Co_1+xNb_2O_9 Ceramics
(Brock University) Ibrahim, Samia; Department of Physics
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 cm􀀀1. 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 cm􀀀1) 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.
Open Access
Effect of Topological Morphology on Optical Filtering Properties of Porous Silicon
(Brock University) Beniac, Thomas; Department of Physics
Macroporous silicon samples of differing topological porous properties were manufactured by way of electrochemical etching. Different etching parameters (etching current, time, electrolyte concentration) were used on four different (in terms of crystal orientation and resistivity) types of samples in order to obtain a series of samples of differing pore topology. It is known that macroporous silicon acts as a high-wavelength pass filter in the infrared regime. FTIR spectroscopy was performed on each of these samples in order to obtain an optical cutoff wavenumber for each sample. Furthermore, SEM analysis was performed in order to determine the number of pores per unit area on the surface as well as the percentage of the surface that was covered in pores for each sample. Furthermore, the average linear dimension per pore was determined using these values. Finally, the average pore-to-pore distance was also estimated on each sample. These four sets of measurements were performed in order to find a relationship between the optical and topological properties of macroporous silicon. It was found that there is a relationship between pore number density and cutoff; the cutoff wavenumber increases as the pore number density is increased. Additionally, a correlation between the pore spacing and the cutoff was also determined; the cutoff wavelength increases as the pore spacing increases. It was expected that there would be a correlation between the average linear dimension per scattering element as is seen in other types of scattering filters; however such a trend was only observed for one of the sample types. This suggests that the scattering mechanism by which porous silicon filters operate differs between samples of significantly differing surface topology. In addition to this, the temperature-dependence of the cutoff was investigated. Through low-temperature optical analysis using FTIR spectroscopy and liquid helium as a coolant, it was determined that the cutoff wavenumber exhibits no temperature-dependence below 100 K. For higher temperatures, the measurements performed were inconclusive. This was due to the thermal expansion at higher temperatures of the copper sample holder coupled with the inhomogeneity of the surface structure of each of the silicon filters.
Open Access
Preparation of Single Crystal Molybdenum Bronzes and Polycrystalline Rubidium Molybdenum Oxide
(Brock University) Hicks, Darren; Department of Physics
Lithium purple bronze (LiPB) Li0.9Mo6O17 was studied extensively in the 1980’s and has recently regained interest in the research community. The mechanism for the metal-insulator (M/I) transition at ∼25 K and superconductivity at ∼2 K is still unknown. The temperature gradient flux technique has been used to grow single crystal LiPB. A large superconducting LiPB single crystal was grown (di- mensions: 4.7×3.0×1.2 mm3) and characterized and will be referred to throughout this work as ‘I33sc2’. For the non-superconducting single crystal oriented along the b-crystallographic axis, we found the maximum value of the energy gap to be 2 meV±0.1 meV at 9.16 K, which is different from the accepted literature value of ∼1 meV at 5-6 K [1,2]. Furthermore, heavier alkali metals (Na, K and Rb) were used in the temperature gradient flux technique. Small lilac brown single crystals were found in all three growths. In particular, the rubidium growth yielded polyhedral (denoted as ‘POLY’, having approximate dimensions: 0.5 × 0.3 × 0.3 mm3) and small bar shaped (denoted as ‘SBAR’, having approximate dimensions: 1×0.1×0.1 mm3) lilac brown single crystals which exhibited anomalous properties in the re- sistivity and specific heat. The anomalous properties include a M/I transition at 250 K and a small phase transition in the resistivity at 94 K. These lilac brown single crystals were studied with powder X-ray diffraction (XRD) and match very closely with molybdenum dioxide MoO2, however with slightly larger ‘a’ and ‘b’ lattice parameters. These lilac brown crystals are being further characterized with single crystal XRD. Polycrystalline rubidium molybdenum dioxide Rb0.03MoO2−δ was then grown to further understand what rubidium doping (if any) these lilac brown single crystals have. The resistivity of polycrystalline Rb0.03MoO2−δ has a M/I transition at 250 K, similar to the lilac brown single crystals, but lacks a phase transition at 94 K. Unlike the lilac brown single crystals, the slope of the M/I transition at 250 K is strongly affected by thermal cycling. Furthermore, poly- crystalline Rb0.03MoO2−δ shows signs of a small superconducting volume fraction. This material is under further investigation.

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