Physical Sciences and Mathematics Commons^™

Order And Harmony: Kepler’S Guiding Forces, Dan Broadbent

Faculty Publications

Adapted from the article “Order and Harmony: Kepler’s Guiding Forces” included in “Towards Mysteries of the Cosmos with Johannes Kepler – on the 450th Anniversary of His Birth,” a commemorative volume published by the Obserwatorium Atronommiczne Krolowej Jadwigi Rzepienniku Biskupim (Queen Jadwiga Observatory of Rzepiennik Biskupi Poland) December 2021. Adapted with permission.

As the subject librarian for physics and astronomy at Brigham Young University, the author has had the privilege of handling some of Johannes Kepler’s original books preserved in the university’s archives. One of the most impressive materials in the archive is a large page from Mysterium Cosmographicum that …

Historical Milestones In Astronomy: As Shown Through The Byu Special Collections Archives, Dan Broadbent

Faculty Publications

Science Research: The “Long Conversation”

• Ideas in science can take a long time to develop.
• How do they develop?

• These books document a part of a conversation that began 447 years ago and spanned a 153 year period… documenting:
• how the overall nature of the universe was worked out,
• the establishment of the scientific method, and the boundaries of religious authority,
• and culminated in Isaac Newton’s book that presented his three laws of motion that allow us to explore the universe to this day.

Fitting Parameter Uncertainties In Least Squares Fitting, R. Steven Turley

Faculty Publications

This article review the theory and practice of computing uncertainties in the fit parameters in least squares fits. It shows how to estimate the uncertainties and gives some numerical examples in Julia of their use. Examples are given and validated for both linear and nonlinear fits.

Polynomial Fitting, R. Steven Turley

Faculty Publications

This article reviews the theory and some good practice for fitting polynomials to data. I show by theory and example why fitting using a basis of orthogonal polynomials rather than monomials is desirable. I also show how to scale the independent variable for a more stable fit. I also demonstrate how to compute the uncertainty in the fit parameters. Finally, I discuss regression analysis: how to determine whether adding an additional term to the fit is justified.

Instrument For Precision Long-Term Ss-Decay Rate Measurements, M. J. Ware, Scott D. Bergeson, J. E. Ellsworth, M. Groesbeck, J. E. Hansen, D. Pace, J. Peatross

Faculty Publications

We describe an experimental setup for making precision measurements of relative ß-decay rates of ²²Na, ³⁶Cl, ⁵⁴Mn, ⁶⁰Co, ⁹⁰Sr, ¹³³Ba, ¹³⁷Cs, ¹⁵²Eu, and ¹⁵⁴Eu. The radioactive samples are mounted in two automated sample changers that sequentially position the samples with high spatial precision in front of sets of detectors. The set of detectors for one sample changer consists of four Geiger-Müller (GM) tubes and the other set of detectors consists of two NaI scintillators. The statistical uncertainty in the count rate is few times 0.01% per day for the GM …

Long-Lived Electron Spins In A Modulation Doped (100) Gaas Quantum Well, John S. Colton, D. Meyer, K Clark, D. Craft, J. Cutler, T. Park, P. White

Faculty Publications

We have measured T1 spin lifetimes of a 14 nm modulation-doped (100) GaAs quantum well using a time-resolved pump-probe Kerr rotation technique. The quantum well was selected by tuning the wavelength of the probe laser. T1 lifetimes in excess of 1 Us were measured at 1.5 K and 5.5 T, exceeding the typical T2 lifetimes that have been measured in GaAs and II-VI quantum wells by orders of magnitude. We observed effects from nuclear polarization, which were largely removable by simultaneous nuclear magnetic resonance, along with two distinct lifetimes under some conditions that likely result from probing two differently localized …

Ground-State Characterizations Of Systems Predicted To Exhibit L11 Or L13 Crystal Structures, Lance J. Nelson, Gus L. W. Hart, Stefano Curtarolo

Faculty Publications

Despite their geometric simplicity, the crystal structures L11 (CuPt) and L13 (CdPt3) do not appear as ground states experimentally, except in Cu-Pt. We investigate the possibility that these phases are ground states in other binary intermetallic systems, but overlooked experimentally. Via the synergy between high-throughput and cluster-expansion computational methods, we conduct a thorough search for systems that may exhibit these phases and calculate order-disorder transition temperatures when they are predicted. High-throughput calculations predict L11 ground states in the systems Ag-Pd, Ag-Pt, Cu-Pt, Pd-Pt, Li-Pd, Li-Pt and L13 ground states in the systems Cd-Pt, Cu-Pt, Pd-Pt, Li-Pd, Li-Pt. Cluster expansions confirm …

Stable Ordered Structures Of Binary Technetium Alloys From First Principles, Gus L. W. Hart, Ohad Levy, Junkai Xue, Shidong Wang, Stefano Curtarolo

Faculty Publications

Technetium, element 43, is the only radioactive transition metal. It occurs naturally on earth in only trace amounts. Experimental investigation of its possible compounds is thus inherently difficult and limited. Half of the Tc-transition-metal systems (14 out of 28) are reported to be phase separating or lack experimental data. Using high-throughput first-principles calculations, we present a comprehensive investigation of the binary alloys of technetium with the transition metals. The calculations predict stable, ordered structures in nine of these 14 binary systems. They also predict additional compounds in all nine known compound-forming systems and in two of the five systems reported …

Ordered Phases In Ruthenium Binary Alloys From High-Throughput First-Principles Calculations, Gus L. W. Hart, Lance J. Nelson, Michal Jahnátek, Ohad Levy, Roman V. Chepulskii, J. Xue, Stephano Curtarolo

Faculty Publications

Despite the increasing importance of ruthenium in numerous technological applications, e.g., catalysis and electronic devices, experimental and computational data on its binary alloys are sparse. In particular, data are scant on those binary systems believed to be phase-separating. We performed a comprehensive study of ruthenium binary systems with the 28 transition metals, using high-throughput first-principles calculations. These computations predict novel unsuspected compounds in 7 of the 16 binary systems previously believed to be phase-separating and in two of the three systems reported with only a high-temperature σ phase. They also predict a few unreported compounds in five additional systems and …

Guiding The Experimental Discovery Of Magnesium Alloys, Richard H. Taylor, Gus L. W. Hart, Stefano Curtarolo

Faculty Publications

Magnesium alloys are among the lightest structural materials known and are of considerable technological interest. To develop superior magnesium alloys, experimentalists must have a thorough understanding of the concentration-dependent precipitates that form in a given system, and hence, the thermodynamic stability of crystal phases must be determined. This information is often lacking but can be supplied by first-principles methods. Within the high-throughput framework, AFLOW, T = 0 K ground-state predictions are made by scanning a large set of known candidate structures for thermodynamic (formation energy) minima. The following 34 systems are investigated: AlMg, AuMg, CaMg, CdMg, CuMg, FeMg , GeMg, …

Polymer Molded Templates For Nanostructured Amorphous Silicon Photovoltaics, Lei Pei, Amy Balls, Cary Tippets, Jonathan Abbott, Matthew R. Linford, David D. Allred, Richard R. Vanfleet, Robert C. Davis, Jian Hu, Arun Madan

Faculty Publications

Here, the authors report the fabrication of transparent polymer templates for nanostructured amorphous silicon photovoltaics using low-cost nanoimprint lithography of polydimethylsiloxane. The template contains a square two-dimensional array of high-aspect-ratio nanoholes (300 nm diameter by 1 µm deep holes) on a 500X500 nm^2 pitch. A 100 nm thick layer of a-Si:H was deposited on the template surface resulting in a periodically nanostructured film. The optical characterization of the nanopatterned film showed lower light transmission at 600-850 nm wavelengths and lower light reflection at 400-650 nm wavelengths, resulting in 20% higher optical absorbance at AM 1.5 spectral irradiance versus a nonpatterned …

Diode Properties Of Nanotube Networks, David D. Allred, Bryan Hicks, Stephanie Getty

Faculty Publications

Single-walled carbon nanotubes (SWCNT) were prepared using iron catalysts deposited by indirect evaporation on silicon substrate covered with 500 nm-thick thermal oxide. Diode SWCNT devices have been fabricated using Au and Al, as the asymmetric metal contacts, and a random network of metallic and semiconducting nanotubes as the device channel. No effort was made to align the SWCNTs or to eliminate metallic nanotubes in our devices. Asymmetric voltage-current behavior was seen. Current rectification was observed in the source-drain bias range of -3 V to +3 V. Rectification was somewhat surprising since, although metallic tubes are in the minority (~ 1/3), …

Structure Maps For Hcp Metals From First-Principles Calculations, Gus L. W. Hart, Ohad Levy, Stefano Curtarolo

Faculty Publications

The ability to predict the existence and crystal type of ordered structures of materials from their components is a major challenge of current materials research. Empirical methods use experimental data to construct structure maps and make predictions based on clustering of simple physical parameters. Their usefulness depends on the availability of reliable data over the entire parameter space. Recent development of high-throughput methods opens the possibility to enhance these empirical structure maps by ab initio calculations in regions of the parameter space where the experimental evidence is lacking or not well characterized. In this paper we construct enhanced maps for …

Structure-Property Maps And Optimal Inversion In Configurational Thermodynamics, Gus L. W. Hart, Björn Arnold, Alejandro Díaz Ortiz, Helmut Dosch

Faculty Publications

Cluster expansions of first-principles density-functional databases in multicomponent systems are now used as a routine tool for the prediction of zero- and finite-temperature physical properties. The ability of producing large databases of various degrees of accuracy, i.e., high-throughput calculations, makes pertinent the analysis of error propagation during the inversion process. This is a very demanding task as both data and numerical noise have to be treated on equal footing. We have addressed this problem by using an analysis that combines the variational and evolutionary approaches to cluster expansions. Simulated databases were constructed ex professo to sample the configurational space in …

Characterization Of Optical Constants For Uranium From 10 To 47 Nm, Nicole Brimhall, Nicholas Herrick, David D. Allred, R. Steven Turley, Michael Ware, Justin Peatross

Faculty Publications

We use a laser high-harmonics-based extreme-ultraviolet (EUV) polarimeter to determine the optical constants of elemental uranium in the wavelength range from 10 to 47 nm. The constants are extracted from the measure ratio of p-polarized to s-polarized reflectance from a thin uranium film deposited in situ. The film thickness is inferred from a spectroscopic ellipsometry measurement of the sample after complete oxidation in room air. Uranium has been used as a high-reflectance material in the EUV. However, difficulties with oxidation prevented its careful characterization previous to this study. We find that measured optical constants for uranium vary significantly from previous …

Ordered Magnesium-Lithium Alloys: First-Principles Predictions, Richard H. Taylor, Gus L. W. Hart, Stefano Curtarolo

Faculty Publications

Magnesium-lithium (Mg-Li) alloys are among the lightest structural materials. Although considerable work has been done on the Mg-Li system, little is known regarding potential ordered phases. A first and rapid analysis of the system with the high-throughput method reveals an unexpected wealth of potentially stable low-temperature phases. Subsequent cluster expansions constructed for bcc and hcp superstructures extend the analysis and verify our high-throughput results. Of particular interest are those structures with greater than 13 at. % lithium, as they exhibit either partial or complete formation as a cubic structure. Order-disorder transition temperatures are predicted by Monte Carlo simulations to be …

Measured Optical Constants Of Copper From 10 Nm To 35 Nm, David D. Allred, Nicole Brimhall, Nicholas Herrick, Justin Peatross, R. Steven Turley, Michael Ware

Faculty Publications

We use laser high-order harmonics and a polarization-ratioreflectance technique to determine the optical constants of copper and oxidized copper in the wavelength range 10-35 nm. This measurement resolves previously conflicting data sets, where disagreement on optical constants of copper in the extreme ultraviolet most likely arises from inadvertent oxidation of samples before measurement.

Generating Derivative Structures From Multilattices: Algorithm And Application To Hcp Alloys, Gus L. W. Hart, Rodney W. Forcade

Faculty Publications

We present an algorithm for generating all derivative superstructures of a nonprimitive parent lattice. The algorithm has immediate application in important materials design problems such as modeling hexagonal-close-packed (hcp) alloys. Extending the work of Hart and Forcade [Phys. Rev. B 77, 224115 (2008)] (which applies only to Bravais lattices), this approach applies to arbitrary multilattices. The algorithm enumerates superlattices and atomic configurations using permutation groups rather than direct geometric comparisons. The key concept is to use the quotient group associated with each superlattice to determine all unique atomic configurations. The algorithm is very efficient; the run time scales linearly with …

Energy Current Imaging Method For Time Reversal In Elastic Media, Brian E. Anderson, Michele Griffa, Robert A. Guyer, Paul A. Johnson, Carene Larmat, Pierre-Yves Le Bas, Timothy J. Ulrich

Faculty Publications

An energy current imaging method is presented for use in locating sources of wave energy during the back propagation stage of the time reversal process. During the back propagation phase of an ideal time reversal experiment, wave energy coalesces from all angles of incidence to recreate the source event; after the recreation, wave energy diverges in every direction. An energy current imaging method based on this convergence/divergence behavior has been developed. The energy current imaging method yields a smaller spatial distribution for source reconstruction than is possible with traditional energy imaging methods.

Verifying Predictions Of The L13 Crystal Structure In Cd-Pt And Pd-Pt By Exhaustive Enumeration, Gus L. W. Hart

Faculty Publications

In 2001, S. Müller and A. Zunger [Phys. Rev. Lett. 87, 165502 (2001)] predicted a never-before-observed crystal structure in Ag-Pd. Recently, Curtarolo predicted the same structure to be stable in Pt-Cd and Pt-Pd [S. Curtarolo et. Al., CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 29, 163 (2005)]. The predicted structure is unique in several ways. though never seen in any other face-centered-cubic-based intermetallic binary compound or ordered alloy, it is relatively simple—it contains only four atoms per unit cell. Furthermore, the structure is the only one of this small size, except the L12 structure, that cannot be characterized as a simple …

Impact Of Spherical Probe Scattering On Estimation Of Acoustic Vector Quantities. (A), Curtis P. Wiederhold, Kent L. Gee, Derek C. Thomas, Scott D. Sommerfeldt, Jonathan D. Blotter

Faculty Publications

Multimicrophone probes are often used to measure energy-based acoustical quantities. In some cases, these probes consist of microphones mounted on the surface of a sphere, which, due to the high level of symmetry, permits scattering effects to be better characterized. Scattering of a plane wave incident on a rigid sphere has been modeled to observe how particle velocity and intensity calculations are affected by the presence of the sphere. These effects have been investigated for the traditional "finite-difference" method and a recently developed "wave vector" estimation method. In the computer model, 3-D surface plots were made showing the calculated error …

Resonant Microwave Cavity For 8.5-12 Ghz Optically Detected Electron Spin Resonance With Simultaneous Nuclear Magnetic Resonance, John S. Colton, L. R. Wienkes

Faculty Publications

We present a newly developed microwave resonant cavity for use in optically detected magnetic resonance (ODMR) experiments. The cylindrical quasi-TE 011 mode cavity is designed to fit in a 1 in. magnet bore to allow the sample to be optically accessed and to have an adjustable resonant frequency between 8.5 and 12 GHz. The cavity uses cylinders of high dielectric material, so-called "dielectric resonators," in a double-stacked configuration to determine the resonant frequency. Wires in a pseudo-Helmholtz configuration are incorporated into the cavity to provide frequencies for simultaneous nuclear magnetic resonance (NMR). The system was tested by measuring cavity absorption …

Effective Medium Theory, Rough Surfaces, And Moth’S Eyes, David D. Allred, Zephne Larsen, Joseph Muhlestein, R. Steven Turley, Anthony Willey

Faculty Publications

Optics in the extreme ultraviolet (XUV) have important applications in microelectronics, microscopy, space physics, and in imaging plasmas. Because of the short wavelengths involved in these applications, it is critical to account for interfacial roughness to accurately predict the reflection and absorption of XUV optics. This paper examines two possible effects of roughness on optical absorption, non-specular reflection and enhanced transmission and compares these to measured experimental data on a rough Y2O3 thin film.

Time Reversal Of Continuous-Wave, Steady-State Signals In Elastic Media, Brian E. Anderson, Robert A. Guyer, Paul A. Johnson, Timothy J. Ulrich

Faculty Publications

Experimental observations of spatial focusing of continuous-wave, steady-state elastic waves in a reverberant elastic cavity using time reversal are reported here. Spatially localized focusing is achieved when multiple channels are employed, while a single channel does not yield such focusing. The amplitude of the energy at the focal location increases as the square of the number of channels used, while the amplitude elsewhere in the medium increases proportionally with the number of channels used. The observation is important in the context of imaging in solid laboratory samples as well as problems involving continuous-wave signals in Earth.

Comment On "Generation Of Cold Low Divergent Atomic Beam Of Indium By Laser Ablation", A. Denning, A. Booth, S. Lee, M. Amonson, Scott D. Bergeson

Faculty Publications

We present measurements of the velocity distribution of calcium atoms in an atomic beam generated using a dual-stage laser back-ablation apparatus. Distributions are measured using a velocity selective Doppler time-of-flight technique. They are Boltzmann-like with rms velocities corresponding to temperatures above the melting point for calcium. Contrary to a recent report in the literature, this method does not generate a subthermal atomic beam.

Antiphase Ordering And Surface Phases In Lithium Aluminate, Richard R. Vanfleet, J. A. Simmons, D. W. Hill, M. M. C. Chou, B. H. Chai

Faculty Publications

Antiphase domains are seen in single crystal gamma lithium aluminate (gamma-LiAlO2) with 16.7 nm periodicity in the <110> direction. Alternate domains have a (1/2) [001] shift. Beta phase lithium aluminate (beta-LiAlO2) is seen to form on the surface of the as-received wafers with an epitaxial strain limited relationship with the bulk gamma phase. The orthorhombic beta phase aligns with the a and b axes (0.528 and 0.630 nm) matching with the tetragonal gamma phase's a and c axes (0.5168 and 0.6268 nm). The gamma and beta phases are seen to have different etch rates. The beta phase converts back to the …

Extreme-Ultraviolet Polarimeter Utilizing Laser-Generated High-Order Harmonics, Nicole Brimhall, Matthew Turner, Nicholas Herrick, David D. Allred, R. Steven Turley, Michael Ware, Justin Peatross

Faculty Publications

We describe an extreme-ultraviolet (EUV) polarimeter that employs laser-generated high-order harmonics as the light source. The polarimeter is designed to characterize materials and thin films for use with EUV light. Laser high harmonics are highly directional with easily rotatable linear polarization, not typically available with other EUV sources. The harmonics have good wavelength coverage, potentially spanning the entire EUV from a few to a hundred nanometers. Our instrument is configured to measure reflectances from 14 to 30 nm and has ~180 spectral resolution (lambda/delta lambda). The reflection from a sample surface can be measured over a continuous range of incident …

Recombination Fluorescence In Ultracold Neutral Plasmas, Scott D. Bergeson, F. Robicheaux

Faculty Publications

We present the first measurements and simulations of recombination fluorescence from ultracold neutral calcium plasmas. This method probes three-body recombination at times less than 1 µs, shorter than previously published time scales. For the lowest initial electron temperatures, the recombination rate scales with the density as n22, significantly slower than the predicted n3. Recombination fluorescence opens a new diagnostic window in ultracold plasmas. In most cases it probes deeply bound level populations that depend critically on electron energetics. However, a perturbation in the calcium 4snd Rydberg series allows our fluorescence measurements to probe the population in weakly bound levels that …

An Ultrahigh Stability, Low-Noise Laser Current Driver With Digital Control, Christopher J. Erickson, Marshall Van Zijll, Greg Doermann, Dallin S. Durfee

Faculty Publications

We present a low-noise, high modulation-bandwidth design for a laser current driver with excellent long-term stability. The driver improves upon the commonly used Hall–Libbrecht design. The current driver can be operated remotely by way of a microprocessing unit, which controls the current set point digitally. This allows precise repeatability and improved accuracy and stability. It also allows the driver to be placed near the laser for reduced noise and for lower phase lag when using the modulation input. We present the theory of operation for our driver in detail, and give a thorough characterization of its stability, noise, set-point accuracy …

Algorithm For Generating Derivative Structures, Gus L. W. Hart, Rodney W. Forcade

Faculty Publications

We present an algorithm for generating all derivative superstructures--for arbitrary parent structures and for any number of atom types. This algorithm enumerates superlattices and atomic configurations in a geometry-independent way. The key concept is to use the quotient group associated with each superlattice to determine all unique atomic configurations. The run time of the algorithm scales linearly with the number of unique structures found.