Submitted Abstracts

Spring Meeting of the Illinois Section of AAPT
April 23-24, 2004, University of Illinois, Urbana-Champaign, Illinois

This file is automatically updated by the Web server after anyone submits an abstract by using the Online - Call for Papers. These abstracts will also appear in the detailed program for the meeting.  * Indicates participation in the Student Research Symposium.  Last update:  April 17, 2004.

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Papers to be Presented on Friday Afternoon

World Year of Physics 2005: News from the Montreal Preparatory Conference, March 2004. Patricia Sievert, Northern Illinois University, DeKalb, IL 60115. According to the physics2005.org Web site, “The World Year of Physics (WYP 2005) is a worldwide celebration of physics and its importance in our everyday lives.” What’s planned internationally, nationally, or regionally to celebrate physics? As one of 50 international participants in the WYP 2005 - Secondary Preparatory Conference in Montreal, March 19-21, 2004, I’d like to share our plans. I’ve been involved with the American Physical Society’s efforts to use WYP 2005 to increase the public’s appreciation of physics since being invited to participate in their Physics on the Road Conference in 2003. As the Outreach Coordinator for the Department of Physics at NIU, I’d also like to share our WYP 2005 efforts in northern Illinois.

Our SECRET. Elisabeth Langford, Springfield Southeast High School, Springfield, IL 62703. In the fall of 2003 an extracurricular activity, Southeast Cosmic Ray Experimental Team, SECRET, was formed for interested students of the Springfield Southeast High School to begin to work with CosRayHS, a NSF project directed by Prof. Julia Thompson [U of Pittsburgh, UMSL]. The researchers, having access to scintillation counters for two and one half months, began their study by taking random measurements of cosmic rays in and around the vicinity of school, to determine if a difference existed in the number of cosmic rays detected in different areas. They found that a difference in the number of cosmic rays occurred in different levels of the building. The hypothesis was that as the amount of materials above the counters increased the cosmic ray count would decrease. The researchers made measurements at the twenty-eight-story Hilton Hotel, in Springfield, Illinois and at the Radisson Hotel in St. Louis, Missouri. Although the detector was not sophisticated enough to determine the particle composition, the results to date are consistent with an initial loss of the electron component, and a slower loss of the remaining muons, as expected from their respective energy loss mechanisms.

Encounters with Viki and Quantum Mechanics. James E. Clark. I was privileged to meet Victor Weisskopf or Viki as he was known to his friends and acquaintances, three times in the 1980s and early 1990s. In my discussion I will consider how Viki influenced my understanding of quantum mechanics. Viki was an advocate of Niels Bohr's notion of complementarity and the Copenhagen interpretation of quantum mechanics. The Copenhagen interpretation draws a line or region of demarcation between measuring instruments represented by classical physics and an atom that interacts with a photon, governed by quantum mechanical laws. Influenced by Viki and my study of Bohr's and Heisenberg's works, I have come to believe that the Copenhagen interpretation of quantum mechanics is valid and complete. I will contrast one of my encounters with Viki, with an encounter reported by David Mermin in his reference frame article that appeared in Physics Today, February, 2004, pages 10-11.

Aether and the Talking Wires. Kay Yandell, Keith Andrew , Univ. of Wisconsin-Madison, Eastern Illinois University, Charleston, IL 61920. The early history of the telegraph, circa 1833, set the stage for a paradigm shift that would not manifest itself until 1905 with the development of relativity by Einstein and the disappearance of the aether of antiquity. This change provides valuable insights into the evolution of scientific and social thought that can play a central role in presenting this material to students at all levels. We look at some of the earliest experiments involving wires, including the “Mile of Monks,” the “Test of Tears,” and the “Mystery of the Grounding Wire.” This couples with the parallel development of the railroad and the establishment of a time standard, which was accompanied by an inherent and prevalent personal mysticism that meshed well with naïve aether concepts and a pragmatic employment need that came to a peak with the widespread employment of women as telegraphers during the Civil War period. We review documents from the period, which indicate that the rapid technological development of the wire based telegraph, the so-called “talking wires,” was viewed with great suspicion and when the role of women in the work force was viewed as problematic and a challenge to gender standards.

Novel N-Body Orbits for Constrained Potentials Including the Unusual Figure Eight Three Body Orbit. Jan M. Dudzik, Oak Lawn High School, Oak Lawn, IL 60453. Keith Andrew, Eastern Illinois University, Charleston, IL, 61920. Recently new n-body planar orbits have been discovered which are linearly stable. These orbits correspond to small n, generally n<20, and exhibit unexpected patterns with respect to the initial conditions. Here we shall examine numerical solutions to the three-body problem and the restricted three-body problem for three body potentials that are the sum of three two body potentials. Then for an everywhere attractive three body potential with non-collinear and collision less orbits with a strictly monotone decreasing test function there exist linearly stable bound states that are not chaotic. For the right initial conditions these orbits can be mapped numerically and visualized. We will display a number of these cases corresponding to the three body problem, restricted three body problem, the chaotic restricted three body problem and the new stable bound state orbits to exhibit some of their special features and to take note of a number of open questions dealing with simple orbital problems.

Evaluating Multiple-Choice Exams in Large Introductory Physics Courses. Michael Scott, University of Illinois, Urbana-Champaign, Urbana, IL 61801. The reliability and validity of multiple-choice exams have been extensively studied for “professionally” written exams such as the SAT and GRE, and even the Force Concept Inventory. Much of the success of these multiple-choice exams is attributed to the careful construction of each question, as well as each response. In a study at the University of Illinois, Urbana-Champaign, we investigated the reliability and validity of our multiple-choice exams written for and administered in our large, introductory physics courses. The reliability is found using standard statistical methods. To determine the test’s validity, we compared student ranking for a subset of students based on their multiple-choice score, graded explanations, and student interviews. In this talk we will share with you our findings and discuss whether or not multiple-choice exams are a reliable and valid way to rank students.

Nonlinear Dynamics and Liberal Arts Majors. Brian K. Clark, Illinois State University, Normal, IL 61790-4560. The typical physics course delivered to liberal arts majors concentrates on introducing students to the laws of physics with applications and examples drawn from topics including astronomy, lasers, and optics, for example. As nonlinear processes become increasingly important in the nonsciences, student should receive an introduction to major concepts in nonlinear processes. During the first attempt to teach nonlinear dynamical concepts to freshman liberal arts majors at Illinois State University, a heavily graphical approach was used and seemed to be well received by the students. The course material uses the logistic equation and a ball bouncing on a vibrating table as primary examples. I discuss some of the difficulties encountered by students.

* Use of the Magnetic Force Microscope (MFM) for Domain Wall Imaging and Sensitivity Correlation in Magnetoelastic Transducers. Mark S. Boley, Greg Sollenberger, and Jason Wilson, Physics Department, Western Illinois University, Macomb, IL 61455. In this study, we created two distinct portions of the torque transducer ring or shaft in which a high degree of oppositely polarized circumferential magnetization was maintained with a saturated alignment of the magnetic domains. This sensory area produced a field signal linearly proportional to the applied torque. The ring sample was constructed of a steel alloy of 18% nickel in iron (known as C250), while the shaft samples used were steel alloys of 0.5% chromium and 0.3% nickel, 0.5% chromium and 4% nickel, 3.5% chromium, 5% chromium, and 12% chromium and 0.3% nickel (known as O-1, Kapstar, S-7, A-2, and D-2 respectively). We then used the magnetic force probe of our AFM, in an imaging technique known as MFM, to determine the width and sharpness of the domain wall transition region between the two oppositely polarized regions of both types of sensors and their relative depth of magnetic alignment. We found the domain wall transition region to be much wider and to change in a more gradual manner in the shaft sensors. However, following the heat treatment of the shaft-type sensors, the width of their domain walls began to approach that of the ring-type sensor. We also found that the relative height of the domain wall signals compared to the background signals was in direct correlation with the torque load sensitivity numbers measured for each of the samples.

* Improving the Magnetoelastic Sensitivity of a 5% Chromium Tool Steel Torque Sensor via Heat Treatment. Mark S. Boley, Ryan T. Gordon, Jacob R. Hoberg, Christopher C. Jurs, and Doug A. Franklin, Physics Department, Western Illinois University, Macomb, IL 61455. We have produced a torque sensor from type A-2 tool steel for industrial torque transfer applications in a 0.75 inch outer diameter hollow shaft by magnetically polarizing two adjacent sections of the shaft with oppositely directed circumferential magnetization. The resultant field signal, found to be linear with applied torque up to 15 N-m, emanated from the domain wall formed between the two regions and was easily detected with a Gaussmeter. A two-step heat treatment, consisting of a rapid quench from a temperature higher than the Curie temperature of the ferromagnetic steel in order to erase magnetic history, followed by a slow cool from a lower temperature to restore desired magnetic and mechanical properties, was then applied to the samples. This resulted in an increase in torque-load sensitivity (field signal in mG per unit applied shear stress in lb/in² or psi) from 48.2 mG/psi to 59.2 mG/psi, a remarkably improved linearity of the signal, and a more reliable re-zeroing of the sensor following removal of the applied torque. Simultaneously, the magnetic hysteresis properties of the samples were studied prior and subsequent to the heat treatments. The axial coercive force was found to decrease from 50 Oe to 40 Oe following heat treatment, with the percent of decrease in excellent correlation to the percent of increase in the sensitivity found above, while the circumferential coercive force remained above 40 Oe, which is sufficient to guarantee integrity of the magnetically polarized regions comprising the sensor.

* Coupled Chaotically Driven Impact Oscillators. Adam D. Hall, Jacob R. Hutchcraft, Brian K. Clark, and Epaminondas Rosa, Jr., Department of Physics, Illinois State University, Normal, IL 61790-4560. We describe the behavior of a two-impact oscillator system. An impact oscillator is essentially a system driven with a periodic forcing function, such as a ball bouncing on a harmonically oscillating table. In our case, a table of infinite mass drives ball 1. Ball 1 is then used to drive ball 2, where the mass of ball 1 is infinitely larger than the mass of ball 2. The relationship between the trajectories of the two oscillators is studied for the cases in which both ball trajectories are periodic, ball 1 is periodic and ball 2 is chaotic, and when both ball trajectories are chaotic. We show that ball 2 will typically have the same periodicity as ball 1, but can act as a linear amplifier of small perturbations. We also discuss phase synchronization between the two balls.

* Adaptive Delayed Feedback Control of a Chaotic Impact Oscillator. Jacob R. Hutchcraft, Adam D. Hall, B. K. Clark, and Epaminondas Rosa, Jr., Illinois State University, Normal, IL 61790-4560. Impact oscillators are a class of nonautonomous systems that include moving machinery parts, machine noise, induced vibration in fluids, moored ships, particle accelerators, transportation, separation of granular solids, and biological systems. The electronic bouncing ball is a representative impact oscillator that is an electronic analog of a mechanical ball bouncing on a driven vibrating table. The electronic version is convenient for study because it is a relatively noise free system, can operate at almost any frequency compared to the relatively low frequencies for the mechanical ball, and does not have added mechanical constraints usually required for real balls [1]. It is desirable to have a control mechanism that does not require in situ or extensive computational analysis before control can be initiated as in the Ott, Grebogi and Yorke (OGY) method [2]. Ideally control should be initiated at an arbitrary time, without waiting for the system trajectory to enter a defined window about the desired controlled orbit. Pyragas [3] has introduced a modified version of the OGY approach, delayed feedback control (DFC). Our lab group has developed an addaptive delayed feedback control (ADFC) based electronic circuit that can be initiated at an arbitrary time without the need of associated computational analysis. Experimental results are compared to computer simulations in which ADFC was successfully implemented to convert chaotic trajectories of the electronic bouncing ball to controlled periodic trajectories. We discuss the experimental implementation of the ADFC algorithm based on perturbations to the table amplitude rather than the table frequency, which is a more common approach. We show that our algorithm also addresses the potential shortfalls of simple DFC methods. [1] B. K. Clark, E. Rosa, Jr., A. D. Hall, and T. R. Shepherd, Phys. Lett. A 318, 514(2003). [2] E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990). [3] K. Pyragas, Phys. Lett. A 170, 421 (1992).

* Mössbauer Studies of Field-Induced Phase Transitions in Ru[NH₃]₆FeCl₆. Kelly Lave and Charles E. Schulz; William Reiff (Dept. of Chemistry, Northwestern University, Boston), Knox College, Galesburg, IL 61401. Mössbauer Spectroscopy was used to observe field-induced phase transitions in Ru[NH₃]₆FeCl₆. This system has been observed to undergo antiferromagnetic transitions with T_N ~ 5.2K. When a strong external magnetic field was applied at 4.2K, the Mössbauer data indicate that a spin flop transition occurs with an applied field between 4T and 6T. A further transition to field-induced paramagnetism occurs at 8T. Consistent with the phase diagram, these transitions occur at lower fields when the temperature is decreased.

Papers to be Presented on Saturday Morning

* Nonlinear Refraction of Olive Oil Using Z-scan and Intensity Scan Techniques. Daniel Probst, Jennifer Esker, and Abdulatif Hamad, Southern Illinois University Edwardsville, Edwardsville, IL 62026. We studied the nonlinear refractive properties of olive oil using the single beam z-scan and single beam intensity scan along with a pump-probe intensity scan techniques. We used the intensity scan and z-scan to compare the induced change in the index of refraction that we extracted from the results of both techniques. The pump-probe intensity scan was used to determine the decay rate of the induced lens. The large induced change of index of refraction arose from thermal lensing and mass diffusion. The pump beam induced a divergent lens in the olive oil and this effect could be seen by monitoring the beam size in the far field.

* Uncovering Students’ Conceptual Hierarchy of Lunar Phases. Aaron Hines and Rebecca Lindell, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1654. According to cognitive theory, to encourage the development of a scientific understanding, instructors need to be able determine if their students have a mental model of phenomena, how deeply rooted these mental models are, as well as how structured they are. The majority of research to date has focused on the discovery of the different mental models of specific phenomena, as well as how deeply rooted these mental models are. In this research project we utilized data obtained from the national field test of the Lunar Phases Concept Inventory (LPCI) to investigate the conceptual hierarchy across the eight different concept dimensions investigated by the LPCI by employing the psychometric theory of item response. Item response theory (IRT) looks for patterns of item response based upon underlying latent traits typically total score. Rather than use the typical total score to estimate the latent trait, this research utilized the understanding of the different dimensions of lunar phases as the latent trait. Preliminary results of this research will be reported.

* Magnetic Birefringe in Liquid Crystalline and Liquid Crystalline-like Materials. Jason Reeves, Knox College, Galesburg, IL 61401. Fluctuations in molecular orientation, called nematic fluctuations, in the isotropic phase of cyanobiphenyls near the isotropic liquid-to-crystal phase transition were investigated experimentally using magnetically induced birefringence. Experiments were done on short-chain cyanobiphenyls which exhibit no stable liquid crystalline (nematic) phase, and the results compared to data from a previous light scattering experiment exploring the same phenomenona. Experimental results from both experiments suggest that nematic fluctuations exist above the isotropic-crystal transition despite the absence of a nematic phase in these materials. The theoretical description of the temperature-dependence of the fluctuations in liquid crystals (Landau-de Gennes theory) is in qualitative agreement with the experimental data. Estimates of the minimum supercooling temperatures were comparable for the two experiments.

* Resonant Electron States in Atoms. John Henderson, Q. Charles Su, Rainer Grobe, Illinois State University, Normal, IL 61790-4560. We explain resonant states created in atomic hydrogen by a relatively weak laser field and a strong magnetic field. We use a two-vector model to explain the resonance due to velocity diffusion during the time evolution caused by the relativistic mass increase. To understand the more complicated circumstances when cyclotron frequency of the applied magnetic field is only a fraction of the laser frequency we systematically analyze the effect of kinematic relativity, the magnetic component of the laser field, and the electric component of the laser field on the fractional cycloatom resonance. The understanding here is crucial in generalizing the model to two electron systems and making better suggestions for any experimental verifications.

* Electron-electron Correlation in Relativistic Ionization of Helium. Peter J. Peverly, Q. Charles Su, Rainer Grobe, Illinois State University, Normal, IL 61790-4560. We investigate the combined effect of relativity and electron-electron repulsion in the presence of a Coulombic nuclear binding force and strong laser and static magnetic fields. We discuss single and double ionization for helium and compare the corresponding probabilities with those obtained for hydrogen and the helium positive ion under identical conditions. The complicated interplay of relativity, electron correlation and Coulomb interaction under the cycloatomic resonance conditions reveal features that could open up an interesting area of research for further investigations.

* Understanding the Universal Profile of Nonlinear Resonance. Kareem Carr, Q. Charles Su, Rainer Grobe, Illinois State University, Normal, IL 61790-4560. The impact of relativity on the maximum velocity of a driven harmonic oscillator under near resonant conditions is investigated. We find that the shape of the resonance profile is characterized by a very abrupt asymmetric drop as a function of the frequency of the external force field. We explore the corresponding orbits within a small amount of deviation to either side of the drop and find that the separation between the orbits in phase space diverges exponentially for certain periods of time followed by periods of exponential convergence. The physics of such a non-linear behavior seems to be universal both in the velocity as well as the coordinate variables.

* Computer Modeling of Light Scattering in Random Media. Matthew Narter, Sunish Menon, Q. Charles Su, Rainer Grobe, Illinois State University, Normal, IL 61790-4560. For system of randomly arranged plane-parallel dielectric layers with randomly varying index of refraction and width, we compare the reflection coefficient derived from the Maxwell equations with that of the Boltzmann theory. For a strictly monochromatic field this coefficient is an oscillatory function of the laser frequency. We show how suitable frequency or ensemble averaging permits a comparison of the two theories. The calculation of the usual Boltzmann scattering coefficient from microscopic parameters can be improved to permit a better agreement with the exact Maxwell data.

* Coherence and De-coherence in a Light-Mirror System. Rebecca Wenning, Q. Charles Su, Rainer Grobe, Illinois State University, Normal, IL 61790-4560. We investigate how the presence of mirrors around scattering samples may lead to an enhancement in the detection efficiency and thus the quality of the reconstructed image embedded in the sample. The effect of the mirror is studied for a simple example of a bi-directional scattering system. The transmitted or reflected signals are obtained analytically and are compared directly with the corresponding data without a mirror.

* Observation of Laser Light Scattering in Turbid Samples. Michael S. Bell, George Rutherford, Q. Charles Su, Rainer Grobe, Illinois State University, Normal, IL 61790-4560. We have explored experimentally and theoretically the propagation of a light pulse in a heterogeneous medium. From the theoretical point of view the process can be modeled by assuming that the laser photons perform a random walk type motion. We have developed a Monte-Carlo algorithm to simulate a laser pulse in a time-dependent turbid medium such as milk. The computer simulations are designed to get a better understanding of how spatial in-homogeneities that are embedded inside the milk modify the propagation dynamics and how they can be detected. I will also describe our first experiments to measure the scattering coefficient of milk for various concentrations by measuring the scattered or absorbed light intensity as a function of the source-detector spacing.

* Image Recovery from Turbid Media. Kimberly McGill, Q. Charles Su, Rainer Grobe, Illinois State University, Normal, IL 61790-4560. We use intensity modulation as a control to recover the depth information of an unknown object imbedded in a random scattering medium. Upon analyzing the transmission signal of incoming light carrying a different modulation frequency, I used matrix inversion computer algorithms to reconstruct the unknown image. I will discuss the details of such an implementation and sample tests made with my computer simulations. Parameters for a sharp image recovery and problems of loss of image due to numerical errors will be discussed.

Student Difficulties with Equations in Physics. Eugene Torigoe, Gary Gladding, Tim Stelzer, University of Illinois Urbana-Champaign, Urbana, IL 61801. The ability to correctly apply equations in physics poses a major barrier to understanding in our classes. One of the reasons students have difficulties may be related to a confusion between algebra and arithmetic. Algebraic equations express relationships between variables, while arithmetic equations express a process to solve for an unknown. Some of the student difficulties with equations in physics may be related to arithmetic approaches to problems that require an understanding of algebraic relations. In my talk I will discuss observed student difficulties with the use of equations from this perspective.

Student Confusion Hidden from the Instructor. Adam Feil, University of Illinois, Urbana, IL 61801. When running a small group physics discussion section, instructors must move from table to table, offering students help and asking questions. Instructors usually move on to the next table after they are satisfied with a group’s explanations of the question at hand; however, students can sometimes fool an instructor into believing they understand a question when they are actually still somewhat confused. A video clip of such an event will be shown, and the surprisingly positive learning outcome will be discussed.

A Geometric View of Contiguous Relations. M.L. Horner, Lenore Horner, Edwardsville, IL 62026. Taking a geometric view of contiguous relations for hypergeometric functions has two principle goals: to facilitate the construction of new contiguous relations from known relations and to put the known relations in perspective as to their interrelations and their relations to the set of all possible contiguous relations. First, I show how arbitrary contiguous relations can be derived easily from a few relations. Second, I show that the generalized contiguous relations of Rainville, Gottschalk and Maslen, and Niukkanen are insufficient to directly obtain contiguous relations for the particular case of the ₂F₀ hypergeometric functions. Based on these results, I conclude that the geometric view of contiguous relations can yield practical insights into the classification of contiguous relations as well as facilitating the derivation of arbitrary relations.

Either Day Will be Fine

Physics with Balloons. Cecilia Vogel, Augustana College, Rock Island, IL 61201. Balloons are an inexpensive tool for teaching that can be used in a wide variety of ways. I have used balloons for demonstrations and lab experiments in mechanics, thermodynamics, electrostatics, general relativity, optics, and acoustics. Some of the more novel applications will be discussed in this talk.

CCD Observations of Bright Asteroids. Lee Carkner, Tyler Coleman, Augustana College, Rock Island, IL 52722. Observations of several bright asteroids performed with the 14–inch telescope of Augustana College’s Carl Gamble Observatory and an SBIG ST-6 CCD camera will be presented. From our exposures we have been able to obtain accurate astrometric and photometric data allowing determination of positions and light curves. From these light curves we have been able to determine the rotation periods. Data analysis using web based resources will be discussed as well as future plans to apply these methods to the observation of newly discovered asteroids including potentially dangerous Near Earth Objects (NEO’s).

The Illinois Articulation Initiative Physics Major Recommendations. Michael R. Fortner, Northern Illinois University, DeKalb, IL 60115. The Illinois Articulation Initiative (IAI) is designed to improve course transfers for students moving between institutions in Illinois. In 2001 the Steering Committee convened a Physics Panel to add recommendations and course descriptions for physics majors using the IAI. Early in 2004 the Panel's recommendations were adopted by the IAI and IBHE. The recommendations include a sequence of introductory calculus-based courses through twentieth-century "modern" physics. The course descriptions for the sequence are compatible with both three- and four-course sequences and are written with the expectation that many students may not complete the entire sequence before transfering to another institution. The recommendation relies on the previous work done by other panels for supporting courses in mathematics and chemistry.

* Mathematical simulations of a mechanical analogue to RF ion trapping. Brad Norkewicz, James Rabchuk, John Chisholm (Department of Mathematics), Western Illinois University, Macomb, IL 61455. RF Paul traps use radio-frequency voltages to trap ions for mass spectrometry, quantum computing and other applications. The simplest trap configuration involves hyperbolic electrodes, which lead to a saddle-shaped potential for the ion which is “rotating” at twice the frequency of the applied voltages. Wolfgang Paul, who developed the Paul trap, suggested that a mechanical analogue of this trap would be a ball on a rotating saddle. We have investigated this analogue using mathematical simulations in Maple and Mathematica. We are particularly interested in determining the effect that friction and rolling have on the trap characteristics. We have shown that introducing friction in the model greatly reduces the range of frequencies over which the “rotating saddle” would continue to trap the ball.

* Lightning and Atmospheric Laser Radiation. Erick Blomberg, Highland Community College, Freeport, IL 61032. Blumlein and T.E.A. lasers demonstrate that simple air can be made to lase at atmospheric pressure and lases readily at slightly lower pressures. For this reason it seems possible that atmospheric discharges may produce pulses of laser light. The objective of this project is to simulate atmospheric discharges against different conditions to determine what atmospheric factors could induce or inhibit lasing, and ultimately learn if lightning can produce laser radiation.

* Using a 14% Chromium Stainless Steel to Produce a Highly Sensitive Magnetic Torque Sensor for both Large and Small Scales. Mark S. Boley, Jacob R. Hoberg, Jason T. Orris, Christopher C. Jurs, and Doug A. Franklin, Physics Department, Western Illinois University, Macomb, IL 61455. We have produced a large scale (0.75 inch) and a small scale (0.25 inch) torque sensor from type ESR-420 stainless steel for industrial torque transfer or small scale medical applications by appropriately polarizing two adjacent sections of the shafts with oppositely directed circumferential magnetization. The resultant field signal, found to be linear with applied torque up to 15 N-m, emanated from the domain wall formed between the two regions and was easily detected with a Gaussmeter. A two-step heat treatment, consisting of a rapid quench to room temperature from 1038°C, followed by a slow 3-day cool from 871°C to restore desired magnetic and mechanical properties, was applied to the samples to enhance performance. The torque- load sensitivity (field signal in mG per unit applied shear stress in lb/in² or psi) was found to be remarkably linear and as high as 237 mG/psi, with excellent re-zeroing capability, making it an ideal candidate for the small-scale applications where weak signals are usually a plaguing problem. Simultaneously, the magnetic hysteresis properties of the samples were studied prior and subsequent to the heat treatments. The axial coercive force was found to remain consistently low around 5-6 Oe throughout heat treatment, in correspondence with the large sensitivity values, while the circumferential coercive force remained around 25-27 Oe, which is sufficient to guarantee integrity of the magnetically polarized regions comprising the sensor at both scale levels.

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