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 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 Anomalies of hypersound velocity and attenuation in ferroelectric tris-sarcosine calcium chloride (TSCC) for small-angle and right-angle Brillouinscattering and Brillouin backscattering(1986-07) Wang, J. T.; Schmidt, V. HugoThe Brillouin spectra of ferroelectric tris-sarcosine calcium chloride have been observed using small-angle and right-angle scattering and also backscattering. For different-frequency phonons along the same direction, analogous anomalies in the sound velocity and the attenuation are seen. The smallest angle we have achieved is 7.48°. The temperature and frequency dependences of the sound velocity are discussed. The fact that the linewidth maximum for [001] phonons occurs somewhat below Tc seems to indicate that the anomalies are due to piezoelectric coupling induced by spontaneous polarization below Tc. For [010] phonons the elementary relaxation times which relate to the energy are estimated as τE0=5.25×10−13 sec above Tc and τE0=3.32×10−12 sec below Tc. The phonon attenuations are also estimated and compared with the observed ones. For the [001] phonons the elementary relaxation time is estimated as τ0=5.25×10−14 sec, in good agreement with the value obtained from right-angle Brillouin scattering.