Physics

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The Physics department is committed to education and research in physics, the study of the fundamental universal laws that govern the behavior of matter and energy, and the exploration of the consequences and applications of those laws. Our department is widely known for its excellent teaching and student mentoring. Our department plays an important role in the university’s Core Curriculum. We have strong academic programs with several options for undergraduate physics majors, leading to the B.S. degree, as well as graduate curricula leading to the M.S. and Ph.D. degrees. Our research groups span a variety of fields within physics. Our principal concentrations are in Astrophysics, Relativity, Gravitation and Cosmology, Condensed Matter Physics, Lasers and Optics, Physics Education, Solar Physics, and the Space Science and Engineering Lab.

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Electrical Conductivity of (NH4)2SO4 Single Crystals
(American Institute of Physics, 1963-06) Schmidt, V. Hugo
Deuteron Intrabond Motion and Ferroelectricity in KD2PO4
(American Physical Society, 1964-01) Silsbee, Henry; Uehling, Edwin A.; Schmidt, V. Hugo
The Slater theory of the ferroelectric phase transition in KH2PO4 type crystals as modified by Takagi and extended by Senko is examined again in the light of recent measurements of parameters made on KD2PO4. Making full use of the measurements, and assigning an appropriate numerical value to one adjustable parameter which is not independently measured, the theory gives a nearly correct description of the shape of the spontaneous polarization curve. Also the value obtained for the Curie constant is probably satisfactory in view of limitations of the model and uncertainty of the high-temperature experimental data. The theory fails, however, in at least one important respect; the transition entropy is overestimated. This and other discrepancies are discussed briefly.
Simple coulometer for studying protonic conduction in crystals
(1965-12) Schmidt, V. Hugo
NOTES ON EXPERIMENTAL TECHNIQUE AND APPARATUS A simple glass coulometer with mercury electrodes was designed to measure the amount of gas evolved upon passing current through single crystals, to determine the extent to which electrical conduction in these crystals is due to protons or other gas-forming ions. It is useful if at least one coulomb can be passed through the crystal in a reasonable time interval. With single crystals of KH2PO4 and Li(N2H5)SO4 in this coulometer, the ratio of hydrogen evolution rate to crystal current indicates entirely protonic conduction.
Sensitive Low Level Transistorized NMR Spectrometer Employing Frequency Modulation
(American Institute of Physics, 1966-08) Blankenburg, Fred; Knispel, Roy; Schmidt, V. Hugo
A transistorized NMR spectrometer has been developed which affords sensitivity comparable to that of the best vacuum tube spectrometers. This spectrometer has operated with sample coil voltages below 10 mV peak‐to‐peak. Frequency modulation is used to facilitate modulation at frequencies high enough to minimize effects of transistor 1/fnoise.
Semiclassical theory of proton transport in ice
(1967-04) Kim, Dong-Yun; Schmidt, V. Hugo
A method is described for calculating proton or other ion mobility which is applicable if mobility is limited by lattice scattering rather than by barrier jumping. The Boltzmann transport equation is used, with the collision term calculated from the electrostatic interactions between the mobile ion and the vibrating lattice. In particular the proton mobility in ice is calculated. The lattice vibrations are approximated by a Debye spectrum for translational vibrations of water molecules, plus an Einstein spectrum for modes in which protons vibrate almost as independent particles. Scattering by phonons somewhat below the Debye cutoff frequency is of the greatest importance in determining the mobility, and the proton modes have negligible effect. The calculated mobility agrees reasonably well with the experimental value.
Dynamical Effects of Deuteron Intrabond Jumping in KD2PO4
(American Physical Society, 1967-12) Schmidt, V. Hugo
Deuteron jumps along hydrogen bonds in KD2PO4 associated with effective motion of Slater-Takagi DPO4 and D3PO4 groups are related to the deuteron magnetic-resonance spectrum and relaxation both above and below the ferroelectric transition temperature Tc, and to the dielectric relaxation and the domain-wall mobility. Below Tc the deuterons assume ordered bond positions, but occasionally jump to the opposite positions. The correlation time for the electric-field-gradient fluctuations seen by a deuteron undergoing such motion is found to be short above Tc and even shorter below Tc. The rms amplitude of the fluctuations drops rapidly below Tc. These results are used to explain the temperature dependence of the splitting and lack of line broadening in the deuteron spectrum below Tc, and the rapid decrease of the spin-lattice transition probabilities below Tc. Relaxation data above Tc, which yielded the energies and fractional populations of DPO4 and D3PO4 groups, are reanalyzed using the recently reported field-gradient tensors at the two bond positions. The dielectric relaxation is calculated, and good agreement with the high dielectric loss measured at microwave frequencies is found. The jump time for a DPO4 or D3PO4 group is found to be near hkT, implying little correlation between successive jumps, in contrast to KH2PO4. This jump time is used in a calculation of domain-wall mobility in KD2PO4.
Observation of the 169Tm and 27Al NMR in Thulium Aluminum Garnet
(American Institute of Physics, 1969-03) Jones, E. D.; Schmidt, V. Hugo
The observations of the 169Tm and 27Al nuclear magnetic resonances(NMR) in a single crystal of cubic thuliumaluminumgarnet are reported. The 27Al MNR was studied between 1.5° and 300°K, while the 169Tm NMR was observed only for T<4°K. From a study of the angular dependences of the 169Tm NMR fields, the (ξ, η, ζ) components of the Tm3+ susceptibility tensor were found to be highly ansiotropic and in units of emu/gram‐atom, χ1=0.014, χ2=0.551, and χ3=0.03. The room temperature 27Al nuclear quadrupolar coupling constants e 2 qQ/h for the a and d sites were measured to be (0.892±0.005) and (6.155±0.005) MHz, respectively. The 27AlNMR frequency shifts for both sites were found to be angular and temperature dependent. A calculation for the observed angular dependences of the 27AlNMR frequency shifts in terms of dipolar fields is found to give reasonable agreement with experiment for the 1.5° and 300°K NMR data.
Random Motion of Deuterons in KD2PO4
(American Physical Society, 1969-04) Schmidt, V. Hugo; Uehling, Edwin A.
Magnetic resonance studies of the deuteron in KD2PO4 have been conducted which show the existence of deuteron jumping between and within hydrogen bonds. The experimental results help to explain electrical conductivity and ferroelectric phenomena in crystals of this type. Pulse magnetic resonance experiments show that the lifetime TXY against deuteron jumping between X- and Y-oriented hydrogen bonds is 15 msec at 70°C with a jump activation energy of approximately 0.58 ev. The c-axis electrical conductivity of KD2PO4 is found to have the same activation energy, with a value of 1.16×10−10 (ohmcm)−1 at 25°C. The Δm=1(P1) and Δm=2(P2) deuteron spin-lattice relaxation transition probabilities due to X−Y jumps have been calculated from the known values of TXY and the electric field gradient tensors at X and Y deuteron sites. Their magnitudes and the dependences of these magnitudes on magnetic field, temperature, and orientation are in good agreement with experiment. Further measurements of P1 and P2 separately give a component of transition probability proportional to exp(0.078 ev/kT) and independent of magnetic field. The orientation dependences of P1 and P2 for this component indicate quadrupolar relaxation due to deuteron jumps along hydrogen bonds, with a jump time of order 10−11 sec at 215°K. The existence of intrabond jumps governed by an activation energy is shown to be consistent with the Slater theory of KH2PO4 as modified by Takagi.
Ferroelectricity Experiment for Advanced Laboratory
(American Institute of Physics, 1969-04) Schmidt, V. Hugo
An experiment suitable for a junior or senior physics laboratory is described, in which the spontaneous polarization and coercive field for Rochelle salt are measured from the ferroelectric hysteresis loops, over the temperature range −18° to +24°C in which this crystal is ferroelectric. The suitability of triglycine sulfate for this experiment is discussed. The apparatus is also useful in demonstrating the relation of capacitance to electrode geometry, and in determining dielectric constants.
Deuteron NMR Study of Lithium Hydrazinium Sulfate
(1969-09) Howell, Francis L.; Schmidt, V. Hugo
The magnetic resonance spectrum of the deuterons in single crystals of LiN2D5SO4 has been studied between 78 and 458°K. The electric quadrupole coupling constants, the asymmetry parameters, and the orientations of the electric field gradient (efg) tensors relative to the crystal axes were obtained at 78°K, 193°K, 25°C, 65°C, and 95°C. The orientations of the efg tensors are considered in relation to nearby atomic sites. At 78°K the spectrum contains distinct lines due to the five deuterons of the N2D5 + ion. Between 110 and 150°K the lines due to the three deuterons of the ND3 group broaden and merge to a single pair which is still visible at 185°C. A small change with temperature in the coupling constant associated with this pair of lines is discussed. The lines due to the two deuterons of the ND2 group broaden and merge to a single pair between 0 and 50°C. These line mergers result from hindered rotation of the ND2 and ND3 groups. Estimates of the activation energies for these motions are made. These changes in the spectrum are related to the results of earlier NMR studies and to previous electrical conductivity and dielectric constant measurements.
Nuclear-Magnetic-Rosonance Study of Thulium Aluminum Garnet
(1970-03) Jones, E. D.; Schmidt, V. Hugo
The Tm169 and the Al27 nuclear magnetic resonance have been studied in cubic thulium aluminum garnet. The Tm169 results at 1.5°K give magnetic-susceptibility tensor components of χ1=0.014, χ2=0.551, and and χ3=0.030 emu/g ion, which show much more anisotropy than found previously for thulium gallium garnet. The measured Al27 paramagnetic shifts at 1.5°K agree quite well with values calculated from Tm3+-ion dipole sums. The Al27 paramagnetic shifts from 1.5 to 300°K are used to calculate the approximate temperature dependence of the Tm2+-ion susceptibility components. The room-temperature Al27 quadrupolar coupling constants ∣∣e2qQh∣∣ for the axially symmetric a and d sites are 0.892±0.005 and 6.155±0.005 MHz, respectively. The unshielded electric field gradients are calculated and compared with corresponding values for other aluminum garnets and for Fe57 sites in several iron garnets. These field gradients agree quite well with values calculated using a point-charge model.
AC Susceptibility of Biased One-Dimensional Stochastic Ising Model.
(1971-06) Schmidt, V. Hugo
The ac susceptibility for the one‐dimensional Ising model is obtained for arbitrary coupling strength in the presence of a dc bias field strong enough to align most of the dipoles in one direction. The dipole flip probability is assumed proportional to the Boltzmann factor corresponding to half the energy change resulting from the flip. The general expression for ac susceptibility is analyzed in three limiting cases: weak coupling with strong bias, strong coupling with strong bias, and strong coupling with weak bias. In the latter case, relatively long chains of anti‐aligned dipoles exist and give rise to large susceptibility.
Dielectric Properties of Lithium Hydrazinium Sulfate.
(1971-12) Schmidt, V. Hugo; Drumheller, John E.; Howell, Francis L.
The dc conductivity and ac dielectric susceptibility of normal and deuterated lithium hydrazinium sulfate have been measured over a wide temperature range at frequencies up to 9.33 GHz. Over a very large temperature and frequency range the real and imaginary parts of the susceptibility are very large (up to ε′≃ε''≃106) and vary with frequency somewhat as f−12. This unusual behavior is shown to result form the nearly one-dimensional protonic conductivity and its extreme sensitivity to barriers caused by local structural defects. Etching studies indicate that the crystal is not ferroelectric, implying that the apparent hysteresis loops result from saturation of the ac conduction.
Dipolar Relaxation of 7Li by Hindered Rotators NDxH3−x in Lithimn Hydrazinium Sulfate.
(1972-04) Parker, Robert S.; Schmidt, V. Hugo
When a hindered rotation does not change the spatial charge distribution but merely permutes the locations of nuclear magnetic moments, the resulting spin-lattice relaxation of a nearby fixed nucleus is likely to be dipolar even if this nucleus has a quadrupole moment. The dipolar relaxation rate is props rtional to the average of γ2I(I + 1) for the rotating nuclei and accordingly varies linearly with percentage of deuteration. For 7Li in LiN2H5SO4 at 14 MHz the peak is 1.8 sec− at 185°K, while in 81% deuterated LiN2D5SO4 it is 4.2 times smaller, as predicted. The ND2 group deuterons also have a peak at this temperature, and all three curves show activation energy of about 0.19 eV, as found previously for protons and deuterons within rotating NH3 and ND3 groups.
Spin-Lattice Relaxation of Al^{27} in Thulium Aluminum Garnet
(1973-05) Trontelj, Z.; Schmidt, V. Hugo
The Al27 spin-lattice relaxation time T1 has been measured between 127 and 425 °K at 8 and 14 MHz for the aluminum a and d sites in thulium aluminum garnet. Both sites exhibit T1 dips at 275 °K which are attributed to Al27-Tm169 cross relaxation. Below 190 °K the a-site T1 magnitudes and approximately ω−2 frequency dependence are explained by magnetic field fluctuations caused by the Tm3+ ion making transitions between its two lowest crystal-field levels with a correlation time near 4 × 10−12 sec.
One-dimensional model for cooperative hydrogen motion in ferroelectric crystals
(1974-01) Schmidt, V. Hugo
The static and dynamic behavior is examined for “Takagi groups” in double-minimum potential wells containing protons (or deuterons) coupled by harmonic forces. Predictions of this model are compared with observed isotope effects on domain wall mobility and dielectric relaxation in KH2PO4. The model predicts effects previously attributed to tunneling.
Comment on “dielectric study of the ferroelectric transition of KH2PO4”
(1976-08) Western, Arthur B.; Schmidt, V. Hugo
We reanalyze a.c. dielectric data taken by Eberhard and Horn for KH2PO4 near Tc, and obtain a much lower value of the critical bias field, near 300 V/cm in accord with results found by other workers.
Tricritical Point in KH_{2} PO_{4}.
(1976-11) Schmidt, V. Hugo; Western, Arthur B.; Baker, A. G.
Search for tricritical point in KH2PO4 at high pressure. I. Static dielectric behavior near critical point at zero pressure
(1977-01) Western, Arthur B.; Baker, A. G.; Pollina, R. J.; Schmidt, V. Hugo
The proposed tricritical point in KDP occurs if the critical field, Ecr, can be brought to zero by applying pressure. The Landau equation of state E = A0(T - T0)P + BP3 + CP5 gives straight-line “isopols” in the T-E plane. We obtain values for A0, B and C and thus Ecr by observing such isopols. We find A0 = 4.3 × 10-3; B = -2.35 × 10-11 C = 5.91 × 10-19 cgs esu for the crystal studied at ambient pressure. These values lead to Ecr = 232 V/cm and δPspon (Tc) = 1.82 C/cm2. High pressure results are imminent.
Hydrostatic optical cell with simple window structure for low temperature and hydrostatic pressure up to 5 kilobars
(1978) Yamada, Masayoshi; Schmidt, V. Hugo
A compact gas high‐pressure cell with four windows for optical studies of phase transitions at low temperature and hydrostaticpressure up to 5 kilobars has been made. Techniques for sealing window components are discussed