Interferometric measurement of the resonant absorption and refractive index in rubidium gas

We present a laboratory demonstration of the Kramers-Kronig relation between the resonant absorption and refractive index in rubidium gas. Our experiment uses a rubidium vapor cell in one arm of a simple Mach-Zehnder interferometer. As the laser frequency is scanned over an atomic resonance, the interferometer output is affected by variations of both the absorption and refractive index of the gas with frequency, all of which can be calculated in a straightforward manner. Changing the vapor density and interferometer phase produces a family of different output signals. The experiment was performed using a commercially available tunable diode laser system that was designed specifically for the undergraduate physics laboratory. As a teaching tool this experiment is reliable, fun, and instructive, while it also introduces the student to some sophisticated and fundamental physical concepts

Crystal Growth in the Presence of Surface Melting: Novel Behavior of the Principal Facets of Ice

We present measurements of the growth rates of the principal facet surfaces of ice from water vapor as a function of supersaturation over the temperature range -2 C > T > -40 C. Our data are well described by a dislocation-free layer-nucleation model, parameterized by the attachment coefficient as a function of supersaturation \alpha(\sigma) = Aexp(-\sigma_0/\sigma). The measured parameters A(T) and \sigma_0(T) for the basal and prism facets exhibit a complex behavior that likely originates from structural changes in the ice surface with temperature, in particular the onset and development of surface melting for T > -15 C. From \sigma_0(T) we extract the terrace step energy \beta(T) as a function of temperature for both facet surfaces. As a basic property of the equilibrium ice surface, the step energy \beta(T) may be amenable to calculation using molecular dynamics simulations, potentially yielding new insights into the enigmatic surface structure of ice near the triple point

Measurements of Growth Rates of (0001) Ice Crystal Surfaces

We present measurements of growth rates of the (0001) facet surface of ice as a function of water vapor supersaturation over the temperature range $-2$ $\geq T\geq -40$ C. From these data we infer the temperature dependence of premelting on the basal surface and the effects of premelting on the ice growth dynamics. Over this entire temperature range the growth was consistent with a simple 2D nucleation model, allowing a measurement of the critical supersaturation $\sigma _{0}(T)$ as a function of temperature. We find that the 2D nucleation barrier is substantially diminished when the premelted layer is partially developed, as indicated by a reduced $\sigma _{0},$ while the barrier is higher both when the premelted layer is fully absent or fully developed

Cloud chambers and crystal growth: Effects of electrically enhanced diffusion on dendrite formation from neutral molecules

We present an extension of the solvability theory for free dendrite growth that includes the effects of electrically enhanced diffusion of neutral polar molecules. Our theory reveals a new instability mechanism in free dendrite growth, which arises when electrically enhanced diffusion near the dendrite tip overwhelms the stabilizing influence of surface tension. This phenomenon is closely related to the growth instability responsible for the visualization of charged particle tracks in cloud chambers, and is expected for enhanced diffusion of neutral molecules, but not for the case of ionic diffusion. Above a threshold applied potential, the crystal growth can no longer be described by the usual solvability theory, and requires a new physical mechanism to limit the growth velocity. We also describe experimental observations of the free dendrite growth of ice crystals from water vapor in supersaturated normal air. These observations demonstrate the calculated growth instability, which results in the rapid growth of branchless ice needles with a tip velocity 5–50 times the normal dendrite tip velocity. The production of clean ice needles is useful for the study of ice crystal growth from vapor, allowing the controlled growth of isolated single-crystal samples. This instability mechanism may find further application in crystal growth from a wide variety of polar molecules

Electrically Induced Morphological Instabilities in Free Dendrite Growth

We describe a new instability mechanism in free dendrite growth, which arises from electrically enhanced diffusion of polar molecules near the dendrite tip. For a small applied potential, the dendrite tip velocity increases slowly with potential, as is described by an extension of normal solvability theory. Above a threshold potential, however, capillarity is insufficient to stabilize growth. We present observations that confirm this instability, which brings about a transition from enhanced normal dendrite growth to a rapidly growing needle morphology with strongly suppressed sidebranching

Electrically Enhanced Free Dendrite Growth in Polar and Non-polar Systems

We describe the electrically enhanced growth of needle crystals from the vapor phase, for which there exists a morphological instability above a threshold applied potential. Our improved theoretical treatment of this phenomenon shows that the instability is present in both polar and non-polar systems, and we provide an extension of solvability theory to include electrical effects. We present extensive experimental data for ice needle growth above the electrical threshold, where at $T=-5$C high-velocity shape-preserving growth is observed. These data indicate that the needle tip assumes an effective radius} $R^{\ast}$ which is nearly independent of both supersaturation and the applied potential. The small scale of $R^{\ast}$ and its response to chemical additives suggest that the needle growth rate is being limited primarily by structural instabilities, possibly related to surface melting. We also demonstrate experimentally that non-polar systems exhibit this same electrically induced morphological instability

A basic lock-in amplifier experiment for the undergraduate laboratory

We describe a basic experiment for the undergraduate laboratory that demonstrates aspects of both, the science and the art of precision electronic measurements. The essence of the experiment is to measure the resistance of a small length of brass-wire to high accuracy using a simple voltage divider and a lock-in amplifier. By performing the measurement at different frequencies and different drive currents, one observes various random noise sources and systematic measurement effects

Search Interfaces for Mathematicians

Access to mathematical knowledge has changed dramatically in recent years, therefore changing mathematical search practices. Our aim with this study is to scrutinize professional mathematicians' search behavior. With this understanding we want to be able to reason why mathematicians use which tool for what search problem in what phase of the search process. To gain these insights we conducted 24 repertory grid interviews with mathematically inclined people (ranging from senior professional mathematicians to non-mathematicians). From the interview data we elicited patterns for the user group "mathematicians" that can be applied when understanding design issues or creating new designs for mathematical search interfaces.Comment: conference article "CICM'14: International Conference on Computer Mathematics 2014", DML-Track: Digital Math Libraries 17 page

Macroscopic coherence effects in a mesoscopic system: Weak localization of thin silver films in an undergraduate lab

We present an undergraduate lab that investigates weak localization in thin silver films. The films prepared in our lab have thickness, $a$, between 60-200 \AA, a mesoscopic length scale. At low temperatures, the inelastic dephasing length for electrons, $L_{\phi}$, exceeds the thickness of the film ($L_{\phi} \gg a$), and the films are then quasi-2D in nature. In this situation, theory predicts specific corrections to the Drude conductivity due to coherent interference between conducting electrons' wavefunctions, a macroscopically observable effect known as weak localization. This correction can be destroyed with the application of a magnetic field, and the resulting magnetoresistance curve provides information about electron transport in the film. This lab is suitable for Junior or Senior level students in an advanced undergraduate lab course.Comment: 16 pages, 9 figures. Replaces earlier version of paper rejected by Am. J. Phys. because of too much content on vacuum systems. New version deals with the undergraduate experiment on weak localization onl