Response to "Comment on 'A versatile thermoelectric temperature controller with 10 mK reproducibility and 100 mK absolute accuracy"' [Rev. Sci. Instrum. 80, 126107 (2009)]

The preceding comment by Sloman points out that the absolute accuracy of a temperature controller may be compromised by thermistor self-heating. We measured the self-heating of the thermistor used in our temperature controller, verifying a systematic error of nearly 200 mK. However, this error is reduced by over an order of magnitude with a slight change in our original circuit design. With this change, our controller does achieve an absolute temperature accuracy of 100 mK, limited mainly by the stated absolute accuracy of the thermistor used in the circuit

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

A versatile thermoelectric temperature controller with 10 mK reproducibility and 100 mK absolute accuracy

We describe a general-purpose thermoelectric temperature controller with 1 mK stability, 10 mK reproducibility, and 100 mK absolute accuracy near room temperature. The controller design is relatively simple and could be readily modified for use in different experimental circumstances. We also describe a time-domain numerical model that allows one to characterize the stability and transient behavior of the system being controlled, even in the presence of elements with highly nonlinear responses

A Dual Diffusion Chamber for Observing Ice Crystal Growth on c-Axis Ice Needles

We describe a dual diffusion chamber for observing ice crystal growth from water vapor in air as a function of temperature and supersaturation. In the first diffusion chamber, thin c-axis ice needles with tip radii ~100 nm are grown to lengths of ~2 mm. The needle crystals are then transported to a second diffusion chamber where the temperature and supersaturation can be independently controlled. By creating a linear temperature gradient in the second chamber, convection currents are suppressed and the supersaturation can be modeled with high accuracy. The c-axis needle crystals provide a unique starting geometry compared with other experiments, and the dual diffusion chamber allows rapid quantitative observations of ice growth behavior over a wide range of environmental conditions

The physics of snow crystals

We examine the physical mechanisms governing the formation of snow crystals, treating this problem as a case study of the dynamics of crystal growth from the vapour phase. Particular attention is given to the basic theoretical underpinnings of the subject, especially the interplay of particle diffusion, heat diffusion and surface attachment kinetics during crystal growth, as well as growth instabilities that have important effects on snow crystal development. The first part of this review focuses on understanding the dramatic variations seen in snow crystal morphology as a function of temperature, a mystery that has remained largely unsolved since its discovery 75 years ago. To this end we examine the growth of simple hexagonal ice prisms in considerable detail, comparing crystal growth theory with laboratory measurements of growth rates under a broad range of conditions. This turns out to be a surprisingly rich problem, which ultimately originates from the unusual molecular structure of the ice surface and its sensitive dependence on temperature. With new clues from precision measurements of attachment kinetics, we are now just beginning to understand these structural changes at the ice surface and how they affect the crystal growth process. We also touch upon the mostly unexplored topic of how dilute chemical impurities can greatly alter the growth of snow crystals. The second part of this review examines pattern formation in snow crystals, with special emphasis on the growth of snow crystal dendrites. Again we treat this as a case study of the more general problem of dendritic growth during diffusion-limited solidification. Since snow crystals grow from the vapour, we can apply dendrite theory in the simplified slow-growth limit where attachment kinetics dominates over capillarity in selecting the tip velocity. Although faceting is quite pronounced in these structures, many aspects of the formation of snow crystal dendrites are fairly well described using a theoretical treatment that does not explicitly incorporate faceting. We also describe electrically modified ice dendrite growth, which produces some novel needle-like structures