arXiv subjects

P. Fraundorf

Publications and source records attributed to P. Fraundorf.

30 records · Page 2Linked to original sources

arXiv2001

Lattice parameters from direct-space images at two tilts

Lattices in three dimensions are oft studied from the ``reciprocal space'' perspective of diffraction. Today, the full lattice of a crystal can often be inferred from direct-space information about three sets of non-parallel lattice planes. Such data can come from electron-phase or Z contrast images taken at two tilts, provided that one image shows two non-parallel lattice periodicities, and the other shows a periodicity not coplanar with the first two. We outline here protocols for measuring the 3D parameters of cubic lattice types in this way. For randomly-oriented nanocrystals with cell side greater than twice the continuous transfer limit, orthogonal +/-15 deg and +/-10 deg tilt ranges might allow one to measure 3D parameters of all such lattice types in a specimen from only two well-chosen images. The strategy is illustrated by measuring the lattice parameters of a 10 nm WC_{1-x} crystal in a plasma-enhanced chemical-vapor deposited thin film.

cond-mat.mtrl-sci↗

arXiv2001

The core structure of presolar graphite onions

Of the ``presolar particles'' extracted from carbonaceous chondrite dissolution residues, i.e. of those particles which show isotopic evidence of solidification in the neighborhood of other stars prior to the origin of our solar system, one subset has an interesting concentric graphite-rim/graphene-core structure. We show here that single graphene sheet defects in the onion cores (e.g. cyclopentane loops) may be observable edge-on by HREM. This could allow a closer look at models for their formation, and in particular strengthen the possibility that growth of these assemblages proceeds atom-by-atom with the aid of such in-plane defects, under conditions of growth (e.g. radiation fluxes or grain temperature) which discourage the graphite layering that dominates subsequent formation of the rim.

astro-ph↗

arXiv2001

Ten-nanometer surface intrusions in room temperature silicon

Defects ~10 nm in size, with number densities ~10^{10} cm^{-2}, form spontaneously beneath ion-milled, etched, or HF-dipped silicon surfaces examined in our Ti-ion getter-pumped transmission electron microscope (TEM) after exposure to air. They appear as weakly-strained non-crystalline intrusions into silicon bulk, that show up best in the TEM under conditions of strong edge or bend contrast. If ambient air exposure is <10 minutes, defect nucleation and growth can be monitored {\em in situ}. Possible mechanisms of formation are discussed.

cond-mat.mtrl-sci↗

arXiv2001

An experience model for anyspeed motion

Simple airtrack simulations, like those now possible with web-based 3D environments, can provide explorers of any age with experiential data sufficient to formulate their own models of motion. In particular, with a compressable spring, two gliders, a moving clock and two gate pairs with timers (pre and post collision), Newton's laws (or one's own version thereof) may emerge (or be tested) in the lab. With a high speed simulation, one may find instead Minkowski's spacetime version of Pythagoras' theorem (the metric equation) in the data, along with ``anyspeed'' expressions for momentum and kinetic energy.

physics.ed-ph↗

arXiv1999

Heat capacity in bits

Information theory this century has clarified the 19th century work of Gibbs, and has shown that natural units for temperature kT, defined via 1/T=dS/dE, are energy per nat of information uncertainty. This means that (for any system) the total thermal energy E over kT is the log-log derivative of multiplicity with respect to energy, and (for all b) the number of base-b units of information lost about the state of the system per b-fold increase in the amount of thermal energy therein. For ``un-inverted'' (T>0) systems, E/kT is also a temperature-averaged heat capacity, equaling ``degrees-freedom over two'' for the quadratic case. In similar units the work-free differential heat capacity C_v/k is a ``local version'' of this log-log derivative, equal to bits of uncertainty gained per 2-fold increase in temperature. This makes C_v/k (unlike E/kT) independent of the energy zero, explaining in statistical terms its usefulness for detecting both phase changes and quadratic modes.

cond-mat.stat-mech↗

arXiv1998

Some minimally-variant map-based rules of motion at any speed

We take J. S. Bell's commendation of ``frame-dependent'' perspectives to the limit here, and consider motion on a ``map'' of landmarks and clocks fixed with respect to a single arbitrary inertial-reference frame. The metric equation connects a traveler-time with map-times, yielding simple integrals of constant proper-acceleration over space (energy), traveler-time (felt impulse), map-time (momentum), and time on the clocks of a chase-plane determined to see Galileo's original equations apply at high speed. Rules follow for applying frame-variant and proper forces in context of one frame. Their usefulness in curved spacetimes via the equivalence principle is maximized by using synchrony-free and/or frame-invariant forms for length, time, velocity, and acceleration. In context of any single system of locally inertial frames, the metric equation thus lets us express electric and magnetic effects with a single frame-invariant but velocity-dependent force, and to contrast such forces with gravity as well.

physics.ed-ph↗

arXiv1998

Teaching Newton with anticipation(...)

Care making only clock-specific assertions about elapsed-time, and other ``space-time smart'' strategies from the perspective of a selected inertial map-frame, open doors to an understanding of anyspeed motion via application of the metric equation.

physics.ed-ph↗

arXiv1997

The instrument response function in air-based scanning tunneling microscopy

The distinction between point and line resolution in transmission electron microscopy (TEM) arises because an ability to image sub-0.2 nm fringes is a necessary, but not a sufficient, condition for imaging individual atoms. In scanned tip microscopy, as in TEM, empirical data on instrument response should precede assertions about point resolution. In the ``slow scan limit'', time-domain noise and geometry effects decouple, and tip shape can take on the role of a 2-dimensional impulse response function. We indicate here that nuclear track pits can be used to quantitatively measure tip geometry with nanometer-scale resolution in three dimensions, that stationary tip images provide a robust measure of time-domain instabilities, and that when these data are taken before and after imaging an unknown, images with instrument response quantitatively constrained by experiment are possible. Specimen-induced tip effects also become measurable in situ.

physics.ins-det↗

arXiv1997

Localizing periodicity in near-field images

We show that Bayesian inference, like that used in statistical mechanics, can guide the systematic construction of Fourier dark-field methods for localizing periodicity in near-field (e.g. scanning-tunneling and electron-phase-contrast) images. For crystals in an aperiodic field, the Fourier coefficient Ze^{i phi} combines with a prior estimate for background amplitude B to predict background phase (beta) values distributed with a probability p(beta - phi | Z,phi,B) inversely proportional to the amplitude P of the signal of interest, when this latter is treated as an unknown translation scaled to B.

cond-mat.stat-mech↗

arXiv1996

A one-map two-clock approach to teaching relativity in introductory physics

This paper presents some ideas which might assist teachers incorporating special relativity into an introductory physics curriculum. One can define the proper-time/velocity pair, as well as the coordinate-time/velocity pair, of a traveler using only distances measured with respect to a single ``map'' frame. When this is done, the relativistic equations for momentum, energy, constant acceleration, and force take on forms strikingly similar to their Newtonian counterparts. Thus high-school and college students not ready for Lorentz transforms may solve relativistic versions of any single-frame Newtonian problems they have mastered. We further show that multi-frame calculations (like the velocity-addition rule) acquire simplicity and/or utility not found using coordinate-velocity alone.

physics.ed-ph↗

arXiv1996

Non-coordinate time/velocity pairs in special relativity

Motions with respect to one inertial (or ``map'') frame are often described in terms of the coordinate time/velocity pair (or ``kinematic'') of the map frame itself. Since not all observers experience time in the same way, other time/velocity pairs describe map-frame trajectories as well. Such coexisting kinematics provide alternate variables to describe acceleration. We outline a general strategy to examine these. For example, Galileo's acceleration equations describe unidirectional relativistic motion {\it exactly} if one uses $V=\frac{dx}{dT}$, where $x$ is map-frame position and $T$ is clock time in a chase plane moving such that $γ^{\prime }=γ\sqrt{\frac 2{γ+1}}$. Velocity in the traveler's kinematic, on the other hand, has dynamical and transformational properties which were lost by coordinate-velocity in the transition to Minkowski space-time. Its repeated appearance with coordinate time, when expressing relationships in simplest form, suggests complementarity between traveler and coordinate kinematic views.

gr-qc↗

arXiv1995

Three Self-Consistent Kinematics in (1+1)D Special Relativity

When introducing special relativity, an elegant connection to familiar rules governing Galilean constant acceleration can be made, by describing first the discovery at high speeds that the clocks (as well as odometers) of different travelers may proceed at different rates. One may then show how to parameterize any given interval of constant acceleration with {\em either}: Newtonian (low-velocity approximation) time, inertial relativistic (unaccelerated observer) time, or traveler proper (accelerated observer) time, by defining separate velocities for each of these three kinematics as well. Kinematic invariance remains intact for proper acceleration since $m a_o = dE/dx$. This approach allows students to solve relativistic constant acceleration problems {\em with the Newtonian equations}! It also points up the self-contained and special nature of the accelerated-observer kinematic, with its frame-invariant time, 4-vector velocities which in traveler terms exceed Newtonian values and the speed of light, and of course relativistic momentum conservation.

gr-qc↗