College of Letters & Science
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Item 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. HugoThe 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.Item Tricritical point and tricritical exponent δ in KH2PO4(1978-01) Schmidt, V. Hugo; Western, Arthur B.; Baker, A. G.; Bacon, Charles R.Static dielectric results for a KH2PO4 crystal at pressures of 0, 2, and 2. 4 kbar are analyzed in terms of a Landau free energy expansion using the “isopol” technique. The measured exponent δ at 2. 4 kbar is consistent with the mean-field tricritical value of 5. This result and the Landau parameter values indicate a tricritical point near 2. 4 kbar.Item Exact solution in the discrete case for solitons propagating in a chain of harmonically coupled particles lying in double-minimum potential wells(1979-12) Schmidt, V. HugoSolitons of the form xn=x0tanh(ωt−kna) can propagate in a chain of harmonically coupled particles in the discrete case if the potential −1/2Axn^2+1/4Bxn^4 giving such solitions in the continuum limit is suitably modified. This modified potential is expressible in closed form, and its shape is a function of ω and k. For large ω the maximum at xn=0 becomes a minimum, giving a triple-minimum potential. Potential shapes and particle positions are illustrated for various (ω,k) combinations. The total energy and its kinetic, potential, and spring energy constituents are also expressible in closed form. In the continuum limit the total energy has the form E=(m0cS^2)/(1−v^2/cS^2)^1/2, where m0 is the soliton effective mass, v is the soliton speed, and cS is the speed of sound in the mass-spring chain.Item Semiclassical theory of proton transport in ice(1967-04) Kim, Dong-Yun; Schmidt, V. HugoA 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.Item AC Susceptibility of Biased One-Dimensional Stochastic Ising Model.(1971-06) Schmidt, V. HugoThe 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.