College of Letters & Science
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The College of Letters and Science, the largest center for learning, teaching and research at Montana State University, offers students an excellent liberal arts and sciences education in nearly 50 majors, 25 minors and over 25 graduate degrees within the four areas of the humanities, natural sciences, mathematics and social sciences.
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Item Short-range interaction explanation of ferroelectric, antiferroelectric and proton glass behavior in pure RDP, ADP, and mixed RDP-ADP crystals respectively(1985-01) Schmidt, V. Hugo; Wang, J. T.; Schnackenberg, P. T.A unified model is presented for Rb1-x(NH4)xH2PO4 crystals over the whole range x=0 (RDP) to x=1 (ADP). Two short-range interactions are postulated. One is the Slater energy ε0 which is kept at the value for RDP for all x. The other is an interaction εa between two hydrogens in O-H...O bonds across an NH4+ ion from each other. It is responsible for the off-center positions observed for ammonium ions in the antiferroelectric phase of ADP. Its strength is assumed proportional to x. By minimizing the free energy, one finds a range of x for which no transition occurs, but instead proton glass behavior sets in. Fox x near 0 and 1 respectively, first-order ferroelectric and antiferroelectric transitions are predicted. Both phase boundaries are close to those observed experimentally.Item Thermal Properties of the Frustrated Rb0.52(ND4)0.48D2PO4 System at Low Temperatures(1985-01) Lawless, W. N.; Schmidt, V. HugoSpecific heat and thermal conductivity data, 1.5–35 K, are reported on the mixed (frustrated) ferroelectric-antiferroelectric crystal Rb0.52(ND4)0.48D2PO4. A glasslike linear term in the specific heat is resolved below 5 K and ascribed to random electric fields caused by the random distribution of Rb ions, in good agreement with the theory of McWhan et al. A maximum in C/T3 at 13.5 K is attributed to dispersionless motions of the deuterium ions, by analogy with KDP. In contrast to the specific heat, the thermal conductivity is not glasslike, displaying a maximum at 12.5 K of 37 mW cm-1K-1. At lower temperatures, the behavior of the thermal conductivity is tentatively ascribed to resonant phonon scattering from the Rb–ND4 system. The Debye temperature for the crystal is 303 K, in reasonably good agreement with extrapolations based on θD for KDP.Item Anisotropy in Anomalies of Hypersound Velocity and Attenuation in Ferroelectric TSCC(1985-01) Hikita, T.; Wang, J. T.; Schnackenberg, P. T.; Schmidt, V. HugoFrom Brillouin shift and linewidth of longitudinal phonons propagating along the [100] and [001] directions of TSCC, the polarization relaxation time was calculated to be τ=3.1×10-12/(Tc-T) sec below the transition temperature Tc. The anomalies in the longitudinal phonons of the [010] propagation were carefully examined using an annealed crystal of excellent quality. No essential difference was observed between the velocities of a normal and high quality crystals. The relaxation time was deduced as a function of temperature from the observed anomalies in the velocity and linewidth. Spectra are observed for nearly forward scattering from the q\varparallel[010] phonons.Item Review of order-disorder models for KDP-family crystals(1987-03) Schmidt, V. HugoThe various order-disorder-type models for crystals in the KDP (potassium dihydrogen phosphate) family are reviewed, beginning with the Slater-Takagi-Senko model, continuing with tunneling additions by Blinc and Svetina, and analyzing the pressure-induced tricritical point in the Slater-Takagi-Senko model. The possibility of a deuteration-induced tricritical point at atmospheric pressure in RDP (rubidium dihydrogen phosphate) is explored. The Ishibashi model for ADP (ammonium dihydrogen phosphate) is reviewed, and finally various theories and computer simulations for the mixed RDP-ADP crystal system are discussed in terms of their prediction of the observed ferroelectric and antiferroelectric transitions and proton glass behavior.Item Brillouin scattering near the ferroelectric phase transition in TSCC(1985-06) Hikita, T.; Schnackenberg, P. T.; Schmidt, V. HugoBrillouin spectra from longitudinal phonons in ferroelectric tris-sarcosine calcium chloride (TSCC) propagating along [100], [010] and [001] have been measured as functions of temperature. Large anomalies were found in the Brillouin shift and linewidth in the [100] and [001] phonons. These anomalies are interpreted as arising from the linear coupling of the polarization and phonons. From the the temperature where the linewidth is maximum, the relaxation time of the polarization fluctuations is estimated to be τ = 3.1×10−12/(Tc−T) sec, where Tc is the ferroelectric transition temperature. We also observed anomalies in Brillouin shift and linewidth of the [010] phonons which propagate along the ferroelectric axis. These anomalies are interpreted as coming from electrostrictive coupling. The energy relaxation time was estimated to be τE=2.5×10−10/(T−Tc) sec in the paraelectric (PE) phase and τE=1.0x10−9/(T−Tc) sec in the ferroelectric (FE) phase, by comparing our Brillouin results with those f the ultrasonic measurements.Item Comment on “dielectric study of the ferroelectric transition of KH2PO4”(1976-08) Western, Arthur B.; Schmidt, V. HugoWe 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.Item Soft modes and proton tunneling in PbHPO4, squaric acid and KH2PO4, type ferroelectrics(1984-01) Blinc, Robert; Schmidt, V. HugoIt is pointed out that the huge observed differences in the soft mode frequencies of KH2PO4, PbHPO4, CsH2PO4 and squaric acid do not necessarily reflect a large difference in the proton 0—H———O tunneling frequencies but rather result from a difference in the short range correlations renormalizing the single proton O——H—O tunneling frequency.Item EPR study of the symmetry breaking effect in ferroelectric cesium dihydrogen phosphate doped with Cr5+ ions(1984-11) Waplak, S.; Schmidt, V. HugoThe (PO4)3− units in a CsH2PO4 (CDP) crystal were replaced in a small fraction of sites by (CrO4)3− groups and the EPR of the Cr5+ center was investigated. Splitting of the EPR line appears at T∗c=245 K, 91 K higher that the ferroelectric transition temperature Tc=154 K. The electronic wave function of Cr5+ (3d1) is identified as dx2−y2. The dx2−y2 function couples with the near protons and the reorientation of this unit in the two possible configurations occurs in the paraelectric phase and breaks the symmetry far above Tc. The observed correlation time 10−9 sec and associated activation energy ΔU=0.215 eV are discussed.Item PVF2 bimorphs as active elements in wind generators(1983-11) Schmidt, V. Hugo; Klakken, M.; Darejeh, HadiThe application to wind electric generation of bimorphs constructed of two sheets glued back-to-back of the piezoelectric polymer poly(vinylidene fluoride), or PVF2, is discussed. First, some fundamentals of piezoelectric behavior and of cantilever beam oscillations are reviewed. Then test results are presented for electrically driven PVF2 bimorphs oscillating in air and in vacuum, from which damping factors are derived. Next, two particular vertical axis wind generator designs are described employing such oscillating cantilever bimorphs which are forced into oscillation by the alternating direction of the wind forces acting on them during each rotor revolution. Wind tunnel test results for both designs are presented. Finally, the effect of possible improved polymer properties on generator output and cost is discussed.Item Dielectric observation of a probably antiferroelectric high pressure phase in the ferroelectric Tris-Sarcosine Calcium Chloride (TSCC)(1980-09) Schmidt, V. HugoDielectric susceptibility and ferroelectric hysteresis measurements on TSCC show that the 2nd-order paraelectric-ferroelectric (PE-FE) phase boundary beginning at (130.8 K, 1 bar) runs with pronounced curvature to (176.8 K, 5.03 kbar), where a new phase of low dielectric susceptibility appears. This phase is hypothesized to be antiferroelectric (AFE) with 3 possible structures: orthorhombic (P212121, piezoelectric) or monoclinic (P21/a or P21/n, centrosymmetric). The FE-AFE phase boundary was determined down to (81.0 K, 2.60 kbar) and the PE-AFE boundary up to (225.5 K, 6.82 kbar). Both the FE-AFE and PE-AFE transitions are of 1st order over the range studied.
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