May 2025
Volume 93, Issue No. 5
Here, we describe a set of experiments that enables undergraduate students to perform and understand nucleation and growth utilizing the concept of birefringence. Semicrystalline polymers, e.g., polyethylene oxide, exhibit a Maltese cross extinction pattern when they are imaged under polarizing optical microscopy with crossed polars (i.e., two polarizers whose axes are oriented at right angle to each other). This behavior is due to the birefringence of the polymer's spherulite, which is its building block, analogous to the grains of a metal. In this instructional laboratory experiment, samples of polyethylene oxide were crystallized at three different transformation temperatures of 295, 273, and 77 K. Taking advantage of the birefringence of spherulites, the dependence of the microstructure with undercooling is shown. In particular, smaller spherulite sizes were obtained with larger undercoolings. It is also shown that the temperature dependence of the resulting polymer microstructure is in agreement with the analytical model for a nucleation and growth process. Finally, a live transformation of solidification of polyethylene oxide from the melt was recorded under crossed polars at room temperature via video microscopy. The time-dependent data that describe the advancement of the phase transformation are in excellent agreement with the Avrami model.
EDITORIAL
In this issue: May 2025 by John Essick; Jesse Kinder; Claire A. Marrache-Kikuchi; Beth Parks; Donald Salisbury; Keith Zengel. DOI: 10.1119/5.0272830
PAPERS
Internal ballistics of the sling by Mark Denny. DOI: 10.1119/5.0226263
Editor's Note: The sling (not to be confused with the slingshot) is an ancient weapon in which the projectile is held by a long cord and accelerated in a circle before release, after which it could travel up to 400 m! The dynamics of the throw can be understood using ideas from introductory mechanics, so the analysis in this paper can be used to create examples and assignments for your courses.
N-body linear force law allowing analytic solutions by Joseph West; Sean P. Bartz. DOI: 10.1119/5.0226894
Editor's Note: A system of many particles interacting through a pairwise force that is linear in the particle separation has many interesting properties. The seemingly daunting N-body problem reduces to N one-body problems, where every particle oscillates around the center of mass with the same frequency. The authors show how you and your students can study the thermodynamics of both the attractive and repulsive versions of this system, simulating tens of thousands of particles in under a minute of computation time on a standard laptop.
Outcomes of teaching physics using action-adventure scenarios with minimal direct instruction by Samya Zain; Valerie A. Allison. DOI: 10.1119/5.0123007
Editor's Note: Did you ever wish that adventure movies would be more respectful of basic physics principles? Now is your chance to set things right! This paper shows how to turn undergraduate mechanics labs into thrilling adventures where students impersonate Ethan Hunt or Indiana Jones and save the world from an incoming meteorite (the role of which can be played by a ping pong ball).
Temperature as joules per bit by Charles Alexandre Bédard; Sophie Berthelette; Xavier Coiteux-Roy; Stefan Wolf. DOI: 10.1119/5.0198820
Editor's Note: Information is closely related to entropy, but information is measured in bits and entropy is measured in joules per kelvin. In this article, the authors explore the historical development of entropy and elucidate the fundamental role of information in thermodynamics, from Boltzmann's microstates to Maxwell's demon and Landauer's eraser. Since temperature is defined in terms of entropy, the authors argue that entropy should have its own unit, the bit, and that temperature should be measured in joules per bit. The engaging survey of information in thermodynamics could augment a course on thermodynamics or statistical physics, and the thought-provoking discussion of temperature and information may change the way you look at a hot cup of coffee.
A first encounter with exceptional points in a quantum model by C. A. Downing; V. A. Saroka. DOI: 10.1119/5.0155858
Editor's Note: When you solve eigenvalue problems in physics, you often run into situations in which eigenvalues and eigenvectors coincide. In other words, you encounter an exceptional point. This paper, appropriate for advanced quantum mechanics or quantum optics classes, details the consequences of the exceptional point that arises when you consider a two-level system excited by a laser beam and allow dissipation. It turns out that the exceptional point corresponds to the laser amplitude at which different crossovers occur: a crossover between oscillatory and non-oscillatory level population dynamics, a crossover between bunched and random light emission, and a crossover from a singlet to a triplet in the optical spectrum of the system.
NOTES AND DISCUSSIONS
An undergraduate laboratory experiment on nucleation and growth via polarizing optical microscopy of semicrystalline polymers by F. Scurti; L. Reynolds. DOI: 10.1119/5.0234897
Editor's Note: In this work, the authors describe an experiment that examines the nucleation and growth of a polymer film from an undercooled melt using polarized optical microscopy, where the size of the resulting birefringent domains (termed spherulites) is used to extract information about the nucleation density at different temperatures. This experiment combines principles from soft matter, solid state physics, thermodynamics, and optics and will be of interest to instructional laboratory developers wishing to introduce a low-cost materials science experiment in their curricula.
Coherent diffraction imaging in the undergraduate laboratory by J. Nicholas Porter; David J. Anderson; Julio Escobedo; David D. Allred; Nathan D. Powers; Richard L. Sandberg. DOI: Am. J. Phys. 93, 415–421 (2025) https://doi.org/10.1119/5.0245088
Editor's Note: This paper presents a visible-light coherent diffraction imaging experiment in which a downstream diffraction pattern produced by an illuminated aperture is used to reconstruct the aperture's spatial profile via a software algorithm. Relevant imaging techniques are described including the method of iterative phase retrieval. The experimental setup required for this experiment is described, along with the freely available data analysis software used. This project will be of interest to those wishing to introduce an advanced optical technique related to Fourier analysis in their instructional laboratory curriculum.
From light emission to solar power: Experiment on LED's photovoltaic behavior by Tiago V. Fernandes; Luís P. Gonçalves; Rodrigo Rito. DOI: 10.1119/5.0252410
Editor's Note: This paper describes an experiment designed to clarify the connections between light-emitting diodes (LEDs) and solar cells while introducing students to modern characterization techniques and the influence of the semiconductor bandgap energy. Electroluminescence spectra and current–voltage data under sunlight illumination are gathered on varying color LEDs, which are then analyzed to produce maximum output power as a function of bandgap energy when LEDs are operated in photovoltaic mode (i.e., mimicking solar cells). These results are compared to the predictions of Shockley–Queisser theory, which predicts the performance of solar cells as a function of the semiconductor bandgap energy. The difficulty of producing a green LED is also explored. This experiment will be of interest to instructional laboratory developers seeking to add an affordable, hands-on experiment involving semiconductor pn junctions to their offerings.
NOTES AND DISCUSSIONS
Low-cost optical heterodyne detection including interference between two independent He–Ne lasers by Michael Daam; Antje Bergmann; Carsten Rockstuhl; Ronny Nawrodt. DOI: 10.1119/5.0236809
Editor's Note: This Note describes how an inexpensive software defined radio device can be used to study beat notes of superimposed HeNe laser beams. The work presented constitutes an exciting development for making a variety of laser heterodyne experiments both feasible and more widely accessible.
Natural relationship between classical orbits and quantum Hamiltonians for the Kepler problem by Jason Tran; Leanne Doughty; James K. Freericks. DOI: 10.1119/5.0220799
Editor's Note: An innovative procedure is introduced that decouples radial position and momentum variables. The authors thereby simplify the solution of the two-body problem where the potential energy varies inversely with the separation. In addition, these new classical variables lead quickly to quantum angular momentum states. The initial analysis can provide useful mathematical insights in classical mechanics, and instructors in quantum mechanics will value this new transition to the operator formalism.
The right way to introduce complex numbers in damped harmonic oscillators by Jason Tran; Leanne Doughty; James K. Freericks. DOI: 10.1119/5.0220797
Editor's Note: Complex exponential functions are convenient for analyzing the classical harmonic oscillator, but can they be introduced to students in an intuitive way? In this note, the authors show how a method described by Max Born and Pascal Jordan in their 1930 textbook on quantum mechanics accomplishes this and reveals a deep connection between classical and quantum mechanics. The material fits naturally into undergraduate courses in classical or quantum mechanics, and could also be used in graduate courses to introduce the factorization method for exactly solvable quantum systems.
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