arXiv subjects

Kenneth G. Libbrecht

Publications and source records attributed to Kenneth G. Libbrecht.

At least 19 recordsLinked to original sources

arXiv2026

Notes from the Physics Teaching Lab: Rubidium Atomic Spectroscopy

We describe a series of rubidium spectroscopy experiments that can be done using the Teachspin Diode Laser Spectroscopy instrument, which is commercially available and is already being used in physics teaching labs at over 150 universities. Our goal here is to provide a detailed examination of the capabilities of this instrument, including numerous examples of measurements and data analysis, presented as a supplement to the Teachspin users manual. Our hope is that instructors using this product or similar diode-laser-based Rb spectroscopy systems will find the experiments described here useful for designing and implementing the curricula in their own physics teaching labs.

physics.ed-ph↗

arXiv2026

Notes from the Physics Teaching Lab: A Magneto-Mechanical Harmonic Oscillator

We describe a magnetically driven torsional oscillator that is well suited for teaching the physics of simple harmonic motion using a collection of hands-on, quantitative experiments. The mechanical Q of the system can be tuned using eddy-current damping, while optical read-outs provide electronic signals than can be recorded using nothing more than a basic digital oscilloscope. The 40-Hz oscillator is described by simple harmonic motion to high accuracy, providing many satisfying comparisons between theory and experiment.

physics.ed-ph↗

arXiv2026

Notes from the Physics Teaching Lab: Optical Pumping

We describe a series of experiments done using a commercially available optical pumping apparatus that is currently being used in physics teaching labs at over one hundred universities. Our focus here is to provide an extensive and detailed examination of the capabilities of this instrument, including numerous examples of measurements and data analysis, presented as a supplement to the manufacturers user manual. Our hope is that instructors using this or similar optical pumping instruments will find the experiments described here useful for designing and implementing the curricula in their own physics teaching labs.

physics.ed-ph↗

arXiv2025

Notes from the Physics Teaching Lab: Diode Laser Spectroscopy at 658 nm

We describe a teaching-lab experiment that applies basic optical spectroscopy to examine the physics of semiconductor diode lasers. By using a low-power visible laser, this experiment is suitable for use in an open lab environment, where students assemble the spectrometer optics themselves as part of the project. A small holographic grating disperses light onto a camera driving a large display monitor, providing a high-resolution, real-time look at the laser output spectrum. Observing this spectrum as a function of injection current, diode temperature, and optical feedback reveals several features of the laser internal optical resonator and semiconductor properties. While teaching about the intrinsically quantum phenomenon of laser physics, this experiment also provides a hands-on experience that gives students a practical familiarity working with lasers, optics, and imaging technologies.

physics.ed-ph↗

arXiv2025

Notes from the Physics Teaching Lab: NMR Experiments at 21 Gauss

We describe a series of laboratory experiments that can be performed with the Quantum Control apparatus sold by TeachSpin, which uses pulsed NMR techniques to observe the precession of protons in a liquid water sample. With a uniform background magnetic field of 21 Gauss, the protons precess at about 90 kHz, yielding numerous relatively simple observations and measurements that are well suited to undergraduate physics teaching labs. Our goal in this paper is to document some of these experiments in detail, thereby making it easier for instructors to choose material that is best suited for their curricula.

physics.ed-ph↗

arXiv2023

A Taxonomy of Snow Crystal Growth Behaviors: 2. Quantifying the Nakaya Diagram

This paper presents a matrix of 206 snow crystal growth observations as a function of temperature and water vapor supersaturation in air, each illustrating the morphology and size of a crystal forming on the tip of an isolated c-axis ice needle after a known growth time. Because each complex structure emerged from a simple, well-defined seed crystal under known environmental conditions, this data set is well suited for making comparisons with three-dimensional computational models. These observations thus provide a needed extension of the well-known Nakaya diagram, as they allow a quantitative evaluation of model predictions over a broad range of growth conditions. I also briefly discuss computational methods along with an initial model of the most relevant microphysical processes governing snow crystal growth. My overarching goal with this new data set is to facilitate the development of quantitative computational growth models that can eventually reproduce the remarkable diversity of morphological structures seen in snow crystal formation.

cond-mat.soft↗

arXiv2023

A Comprehensive Model of Snow Crystal Faceting

Crystal faceting can emerge via two broad physical mechanisms: anisotropic attachment kinetics on growing crystals and anisotropic surface energies on near-equilibrium crystals. For the case of the ice/vapor system, anisotropic attachment kinetics is the dominant faceting mechanism, while the possible occurrence of equilibrium faceting has been debated for many decades. In this investigation we examine ice/vapor faceting at low supersaturations over the temperature range -15C -2C, thus suggesting that snow crystal faceting is caused by anisotropic attachment kinetics even at extremely slow growth rates.

cond-mat.mtrl-sci↗

arXiv2021

Snow Crystals

This monograph reviews our current understanding of the physical dynamics of ice crystal growth, focusing on the spontaneous formation of complex structures from water vapor (called snow crystals) as a function of temperature, supersaturation, background gas pressure, and other extrinsic parameters. Snow crystal growth is a remarkably rich and rather poorly understood phenomenon, requiring a synthesis of concepts from materials science, crystal-growth theory, statistical mechanics, diffusion-limited solidification, finite-element modeling, and molecular surface processes. Building upon recent advances in precision measurement techniques, computation modeling methods, and molecular dynamics simulations of crystalline surfaces, I believe we are moving rapidly toward the long-sought goal of developing a full physical model of snow crystal formation, using ab initio molecular dynamics simulations to create a semi-empirical characterization of the nanoscale surface attachment kinetics, and then incorporating that into a full computational model that reproduces the growth of macroscopic crystalline structures. Section 1 of this monograph deals mainly with the material properties of ice Ih in equilibrium, including thermodynamics quantities, facet surface structures, terrace step energies, and crystal twinning behaviors.

cond-mat.mtrl-sci↗

arXiv2021

A Taxonomy of Snow Crystal Growth Behaviors: 1. Using c-axis Ice Needles as Seed Crystals

I describe a new approach to the classification of snow crystal morphologies that focuses on the most common growth behaviors that appear in normal air under conditions of constant applied temperature and water-vapor supersaturation. The resulting morphological structures are generally robust with respect to small environmental changes and thus should be especially amenable to computational modeling. Because spontaneous structure formation depends on initial conditions, the choice of seed crystal can be an important consideration, and I have found that slender c-axis ice needles provide an exceptionally good starting point for this series of investigations. A sharp needle tip exposes a single basal surface that often simplifies subsequent morphological development, and the absence of a nearby substrate allows for the exploration of a broad range of supersaturations with well-controlled boundary conditions. The overarching goal of this endeavor is to facilitate detailed quantitative comparisons between laboratory ice-growth experiments and corresponding computational models, which will should greatly improve our understanding of the ice/vapor molecular attachment kinetics as well as our ability to model diffusion-limited growth dynamics in the ice/vapor system. This specific case-study of water ice connects broadly to many areas in aqueous chemistry, cryobiology, and environmental science, while the physical principles of molecular attachment kinetics and diffusion-limited growth apply more generally to other systems in crystal growth and materials science.

cond-mat.mtrl-sci↗

arXiv2021

Toward a Comprehensive Model of Snow Crystal Growth: 8. Characterizing Structure-Dependent Attachment Kinetics near -14 C

In this paper I examine snow crystal growth near -14 C in comparison with a comprehensive model that includes Structure-Dependent Attachment Kinetics (SDAK). Analyzing a series of ice-growth observations in air, I show that the data strongly support the model, which stipulates that basal growth is described by classical terrace nucleation on faceted surfaces in this temperature region. In contrast, prism growth exhibits a pronounced "SDAK dip" that substantially reduces the nucleation barrier on narrow prism facets (relative to that found on broad prism facets). I use these measurements to further characterize and refine the SDAK model, which effectively explains the robust formation of platelike snow crystals in air near 14 C.

cond-mat.mtrl-sci↗

arXiv2021

Triangular Snowflakes: Growing Structures with Three-fold Symmetry using a Hexagonal Ice Crystal Lattice

Snow crystals growing from water vapor occasionally exhibit morphologies with three-fold (trigonal) symmetry, even though the ice crystal lattice has a molecular structure with six-fold symmetry. In extreme cases, thin platelike snow crystals can grow into faceted forms that resemble simple equilateral triangles. Although far less common than hexagonal forms, trigonal snow crystals have long been observed both in nature and in laboratory studies, and their origin has been an enduring scientific puzzle. In this paper I describe how platelike trigonal structures can be grown on the ends of slender ice needles in air with high reliability at -14 C. I further suggest a physical model that describes how such structures can self-assemble and develop, facilitated by an edge-sharpening instability that turns on at a specific combination of temperature and water-vapor supersaturation. The results generally support a comprehensive model of structure-dependent attachment kinetics in ice growth that has been found to explain many of the overarching behaviors seen in the Nakaya diagram of snow crystal morphologies.

cond-mat.mtrl-sci↗

arXiv2020

Toward a Comprehensive Model of Snow Crystal Growth: 10. On the Molecular Dynamics of Structure Dependent Attachment Kinetics

I examine the molecular dynamics of ice growth from water vapor, focusing on how the attachment kinetics can be augmented by edge-dependent surface diffusion. Although there are significant uncertainties in developing an accurate physical model of this process, it is possible to make some reasonable estimates of surface diffusion rates and admolecule density enhancements, derived from our basic understanding of ice-crystal growth processes. A quantitative model suggests that edge-dependent surface diffusion could substantially enhance terrace nucleation on narrow faceted surfaces, especially at the onset of surface premelting. This result supports our hypothesized mechanism for structure-dependent attachment kinetics, which readily explains the changes in snow crystal growth morphology with temperature depicted in the well-known Nakaya diagram. Many of the model features described here may be amenable to further quantitative investigation using existing computational models of the molecular structure and dynamics of the ice surface.

cond-mat.mtrl-sci↗

arXiv2020

Toward a Comprehensive Model of Snow Crystal Growth: 9. Characterizing Structure-Dependent Attachment Kinetics near -4 C

In this paper I examine snow crystal growth near -4 C in comparison with a comprehensive model that includes Structure-Dependent Attachment Kinetics (SDAK). Together with the previous paper in this series that investigated growth near 14 C, I show that a substantial body of experimental data now supports the existence of pronounced 'SDAK dips' on basal surfaces near -4 C and on prism surfaces near -14 C. In both cases, the model suggests that edge-associated surface diffusion greatly reduces the nucleation barrier on narrow facet surfaces relative to that found on broad facets. The remarkable quantitative similarities in the growth behaviors near -4 C and -14 C suggest that these two SDAK features arise from essentially the same physical mechanism occurring at different temperatures on the two principal facets. When applied to atmospheric snow crystal formation, this comprehensive model can explain the recurrent morphological transitions between platelike and columnar growth seen in the Nakaya diagram.

cond-mat.mtrl-sci↗

arXiv2020

Toward a Comprehensive Model of Snow Crystal Growth: 7. Ice Attachment Kinetics near -2 C

I examine a variety snow crystal growth experiments performed at temperatures near -2 C, as a function of supersaturation, background gas pressure, and crystal morphology. Although the different experimental data were obtained using quite diverse experimental techniques, the resulting measurements can all be reasonably understood using a single comprehensive physical model for the basal and prism attachment kinetics, together with particle diffusion of water vapor through the surrounding medium and other well-understood physical processes. As with the previous paper in this series, comparing and reconciling different data sets at a single temperature yields significant insights into the underlying physical processes that govern snow crystal growth dynamics.

cond-mat.mtrl-sci↗

arXiv2019

A Versatile Apparatus for Measuring the Growth Rates of Small Ice Prisms from the Vapor Phase

I describe an adaptable apparatus for making precision measurements of the growth of faceted ice prisms from water vapor as a function of temperature, supersaturation, and background gas pressure. I also describe procedures for modeling growth data to disentangle a variety of physical effects and better understand systematic errors and measurement uncertainties. By enabling precise ice-growth measurements over a broad range of environmental conditions, this apparatus is well suited for investigating the molecular attachment kinetics at the ice/vapor interface, which is needed to understand and model snow crystal growth dynamics.

cond-mat.mtrl-sci↗

arXiv2019

Toward a Comprehensive Model of Snow Crystal Growth: 6. Ice Attachment Kinetics near -5 C

I examine a variety of snow crystal growth measurements taken at a temperature of -5 C, as a function of supersaturation, background gas pressure, and crystal morphology. Both plate-like and columnar prismatic forms are observed under different conditions at this temperature, along with a diverse collection of complex dendritic structures. The observations can all be reasonably understood using a single comprehensive physical model for the basal and prism attachment kinetics, together with particle diffusion of water vapor through the surrounding medium and other well-understood physical processes. A critical model feature is structure-dependent attachment kinetics (SDAK), for which the molecular attachment kinetics on a faceted surface depend strongly on the nearby mesoscopic structure of the crystal.

cond-mat.mtrl-sci↗

arXiv2019

A Quantitative Physical Model of the Snow Crystal Morphology Diagram

I describe a semi-empirical molecular model of the surface attachment kinetics governing ice crystal growth from water vapor as a function of temperature, supersaturation, and crystal mesostructure. An important new hypothesis in this model is surface-energy-driven molecular diffusion enabled by a leaky Ehrlich-Schwoebel barrier. The proposed surface-diffusion behavior is sensitive to facet width and surface premelting, yielding structure-dependent attachment kinetics with a complex temperature dependence. By incorporating several reasonable assumptions regarding the surface premelting behavior on basal and prism facets, this model can explain the overarching features of the snow crystal morphology diagram, which has been an enduring scientific puzzle for nearly 75 years.

cond-mat.mtrl-sci↗

arXiv2016

Toward a Comprehensive Model of Snow Crystal Growth: 5. Measurements of Changes in Attachment Kinetics from Background Gas Interactions at -5 C

We present measurements of the diffusion-limited growth of ice crystals from water vapor at a temperature of -5 C, in air at a pressure of $p_{air}=1$ bar. Starting with thin, c-axis ice needle crystals, the subsequent growth morphologies ranged from solid prismatic columns to hollow columns to complex "fishbone" dendritic structures as the supersaturation was increased. We modeled the simpler morphologies using analytical techniques together with a cellular-automata method that yields faceted crystalline structures in diffusion-limited growth. We found that the molecular attachment coefficient $α_{prism}$ on faceted prism surfaces in air at -5 C is substantially lower than that measured at low background air pressure. Our data show that increasing $p_{air}$ from 0.01 to 1 bar reduces $α_{prism}$ by nearly two orders of magnitude at this temperature. In contrast, we find that $α_{basil}$ is essentially unaffected by air pressure over this range. These and other measurements indicate that ice surfaces near the melting point undergo a series of complex structural and dynamical changes with temperature that remain largely unexplained at even a qualitative level.

cond-mat.mtrl-sci↗