Morrel H. Cohen

Free-volume model of the amorphous phase : Glass transition

Free volume vf is defined as that part of the thermal expansion, or excess volume Δv which can be redistributed without energy change. Assuming a Lennard‐Jones potential function for a molecule within its cage in the condensed phase, it can be shown that at small Δv considerable energy is required to redistribute the excess volume; however, at Δv considerably greater than some value δvg (corresponding to potentials within the linear region), most of the volume added can be redistributed freely. The transition from glass to liquid may be associated with the introduction of appreciable free volume into the system. Free volume will be distributed at random within the amorphous phase and there is a contribution to the entropy from this randomness which is not present in the entropy of the crystalline phase. According to our model all liquids would become glasses at sufficiently low temperature if crystallization did not intervene. Therefore whether or not a glass forms is determined by the crystallization kinetic constants and the cooling rate of the liquid. The experience on the glass formation is consistent with the generalization: at a given level of cohesive energy the glass‐forming tendency of a substance in a particular class is greater the less is the ratio of the energy to the entropy of crystallization.

A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads

We develop a theory for dielectric response of water‐saturated rocks based on a realistic model of the pore space. The absence of a percolation threshold manifest in Archie’s law, porecasts, electron‐micrographs, and general theories of formation of detrital sedimentary rocks indicates that the pore spaces within such rocks remain interconnected to very low values of the porosity ϕ. In the simplest geometric model for which the conducting paths remain interconnected, each grain is envisioned to be coated with water. The dielectric constant of the assembly of water‐coated grains is obtained by a self‐consistent effective medium theory. In the dc limit, this gives Maxwell’s relation for conductivity σ of the rock σ=2σwϕ/(3-ϕ), where σw is the conductivity of water. In order to include the local environmental effects around a grain, a self‐similar model is generated by envisioning that each rock grain itself is coated with a skin made of other coated spheres; the coating at each level consists of other coate...

Quadrupole Effects in Nuclear Magnetic Resonance Studies of Solids

Publisher Summary This chapter discusses quadrupole effects in nuclear magnetic resonance studies of solids. The first evidence that many nuclei possess magnetic moments came from the study of the hyperfine structure of atomic spectra in the visible region. The interaction of the nuclear magnetic moment with the magnetic field produced by the atomic electrons gives rise to a hyperfine spectrum that is relatively simple, being characterized by the well known “interval rule.” Marked departures from this interval rule do occur in a few cases, however, and some of the departures can definitely be attributed to the presence of a nuclear electric quadrupole interaction. The methods of radio-frequency spectroscopy are very well adapted for the investigation of the very small interaction energies to which nuclear moments give rise. They have led not only to much more precise determinations of nuclear magnetic moments, but also to a vastly increased knowledge of nuclear electric quadrupole effects. The first outstanding success along this line was the discovery, by the molecular beam resonance method, of the quadrupole moment of the deuteron. The field of electric quadrupole interactions in nuclear magnetic resonance can be divided roughly into two areas according to the relative magnitude of the nuclear quadrupole interactions.

ON THE FREE-VOLUME MODEL OF THE LIQUID-GLASS TRANSITION.

We have improved the free‐volume model for molecular transport in dense fluids, as developed in earlier papers, by taking account of the variable magnitude of the diffusive displacement. The development is carried through in a way which may display more clearly the relation between the free‐volume model and the Enskog theory. Implicit in the free‐volume development is the association, on the average, of a correlation factor f(a) with each magnitude, a, of the displacement. It is assumed that f(a) is a step function which is zero, because of the predominance of back scattering, for a   a.* This corresponds to dividing the displacements sharply into two categories, one “gaslike” and the other “solidlike.” Molecular dynamics computations have shown that the self‐diffusion coefficient in the hard‐sphere fluid at the highest densities is falling precipitously, with increasing density, away from the Enskog values. It appears that this density trend, which was attributed to back scattering, ...

Monoclinic and triclinic phases in higher-order Devonshire theory

Devonshire theory provides a successful phenomenological description of many cubic perovskite ferroelectrics such as BaTiO3 via a sixth-order expansion of the free energy in the polar order parameter. However, the recent discovery of a novel monoclinic ferroelectric phase in the PZT system by Noheda et al. (Appl. Phys. Lett. 74, 2059 (1999)) poses a challenge to this theory. Here, we confirm that the sixth-order Devonshire theory cannot support a monoclinic phase, and consider extensions of the theory to higher orders. We show that an eighth-order theory allows for three kinds of equilibrium phases in which the polarization is confined not to a symmetry axis but to a symmetry plane. One of these phases provides a natural description of the newly observed monoclinic phase. Moreover, the theory makes testable predictions about the nature of the phase boundaries between monoclinic, tetragonal, and rhombohedral phases. A ferroelectric phase of the lowest (triclinic) symmetry type, in which the polarization is not constrained by symmetry, does not emerge until the Devonshire theory is carried to twelfth order. A topological analysis of the critical points of the free-energy surface facilitates the discussion of the phase transition sequences.

A phase-shift model for the spatial and temporal organization of developing systems

The structure of any differentiated tissue results from a well-defined sequence of events in which the spatial and temporal organization of the developing tissue mass are intimately related. It is as though every cell has access to, and can read, a clock and a map (Wolperts positional information). A model developed in the present paper is one in which the map arises from wave-like propagation of activity from localized clocks or pacemakers. Individual cells are supposed temporally organized in the sense that biochemical events essential for the control of development recur periodically. This temporal organization of an individual cell is converted by functional coupling between cells into a spatial ordering of the temporal organization. More explicitly a periodic event is postulated which propagates outward from a pacemaker region, synchronizing the tissue and providing a time base for development. Intercellular signalling, entrainment of all cells in the tissue by the fastest cells in the pacemaker region, and a refractory period to guarantee unidirectional propagation are the essential features of the propagation; they permit the derivation of a wave equation and a set of boundary conditions. An underlying gradient of frequency of the event establishes the position of the pacemaker region and the sense of propagation. A second event which propagates more slowly than the first provides positional information in the form of a one-dimensional sequence of surfaces of constant phase difference between the two events. A third event is used to regulate the pattern of phase difference and thus establish size-independent structures. The longest trajectory orthogonal to the surfaces of constant phase difference beginning at the pacemaker region and terminating at the regulating region defines a developmental axis of definite polarity. The model is readily extended to more than one axis, i.e. multi-dimensional positional information. It has a high informational capacity and is readily applied to the discussion of particular developmental phenomena. To illustrate its utility, we discuss development and regeneration in Hydra , positional in the early amphibian embryo, and the retinal-neural tectal projection of the amphibian visual system. Specific experiments to test for the existence of the postulated periodic events and their consequences are suggested. Some preliminary experimental results on Hydra tending to confirm the model are reported. Possible detailed realizations of the model in terms of, biochemical control circuits within the cell, are conjectured and discussed to show that the formal features of the model can be realized by well-recognized biochemical processes.

Extrinsic models for the dielectric response of CaCu3Ti4O12

The large, temperature-independent, low-frequency dielectric constant recently observed in single-crystal CaCu3Ti4O12 is most plausibly interpreted as arising from spatial inhomogenities of its local dielectric response. Probable sources of inhomogeneity are the various domain boundaries endemic in such materials: twin, Ca ordering, and antiphase boundaries. The material in, and neighboring, such boundaries can be insulating or conducting. We construct a decision tree for the resulting six possible morphologies, and derive or present expressions for the dielectric constant for models of each morphology. We conclude that all six morphologies can yield dielectric behavior consistent with observations. Thus, present experimental findings are insufficient to establish the internal morphology responsible for the remarkable properties of CaCu3Ti4O12, and we suggest further experiments to distinguish among them.

First-principles study of the structure and lattice dielectric response of CaCu 3 Ti 4 O 12

Structural and electronic properties of

Review of the theory of amorphous semiconductors

{\mathrm{CaCu}}_{3}{\mathrm{Ti}}_{4}{\mathrm{O}}_{12}

The effect of grain anisotropy on the electrical properties of sedimentary rocks

are calculated using density-functional theory within the local spin-density approximation. After an analysis of structural stability, zone-center optical phonon frequencies are evaluated using the frozen-phonon method and mode effective charges are determined from computed Berry-phase polarizations. Excellent agreement between calculated and measured phonon frequencies is obtained. The calculated mode effective charges are in poorer agreement with experiment, although they are of the correct order of magnitude and the lattice contribution to the static dielectric constant is calculated to be