R. N. Thurston

Third‐Order Elastic Coefficients of Quartz

All 14 third‐order elastic coefficients of quartz have been calculated from the measured transit times for small‐amplitude ultrasonic waves as functions of applied stress. Thirty‐four different experimental runs were made, ten under hydrostatic pressure, and 24 under uniaxial stress. The data permit calculation of the 14 coefficients with 20 crosschecks. Our recommended values at 25°C, based on a least‐squares fit, are as follows, all in 1012 dyn/cm2. CoefficientValueStandard errorC111−2.100.07C112−3.450.06C113+0.120.06C114−1.630.05C123−2.940.05C124−0.150.04C133−3.120.07C134+0.020.04C144−1.340.07C155−2.000.08C222−3.320.08C333−8.150.18C344−1.100.07C444−2.76 0.17.

Boundary‐layer model of field effects in a bistable liquid‐crystal geometry

Electric‐field‐induced switching between equilibrium configurations in certain bistable liquid‐crystal geometries is governed by the motion of disclinations, propelled by elastic distortions of the equilibrium states subjected to applied fields. In this paper and the next (paper II), we describe the distortions and energies of bistable planar horizontal and vertical states, and nonplanar twist states in a tilted geometry, using exact numerical solutions of the equilibrium equations as well as a ’’boundary‐layer’’ approximation in the high‐field limit. The calculations illustrate the manner in which the distortions become concentrated in boundary layers within a coherence length from the surface, and show the convergence of the planar and nonplanar vertical states at relatively low fields. Implications for the switching mechanism are discussed. In paper II, the boundary‐layer model is used to describe the forces governing the movement of disclinations in bistable switching, producing a quantitative descrip...

Mechanically bistable liquid-crystal display structures

This paper discusses two types of mechanically bistable liquid-crystal display structures, a previously reported type [2], [3] called vertical-horizontal, and a second type, called horizontal-horizontal. In both of them, the director configuration is planar. They are distinguished by the orientation of the director plane, which is perpendicular to the major surfaces of the device in the type called vertical-horizontal, and parallel in the type called horizontal-horizontal. In both types, the bistable states may be differentiated optically by use of a polarizer and dichroic dye, and switching is accomplished electrically by exploiting the dielectric anisotropy of the ordered liquid crystal states. We show calculations of the director configurations, their energy, and optical contrast of the bistable states. The bistable states are topologically distinct, so that the switching transitions are necessarily discontinuous in character. The movement of disclinations governs the switching process, and their detachment forms the basis of stability.

Acoustic Clad Fiber Delay Lines

V. CONCLUSIONS Although the various intensities of a diffracted light wave are described in a totally different way in the Raman-Nath and in the Bragg region, the final results for the molecular parameters G and T are identical. Furthermore, we found in both the cases the same correction term containing p . This term is not negligible for the first diffraction order in the Bragg region and for higher diffraction orders in the Raman-Nath region.

Equilibrium and stability of liquid‐crystal configurations in an electric field

We describe how to choose the most stable of several equilibrium states that may exist in a liquid‐crystal cell at the same voltage V (or charge Q). Among states that exist at the same charge Q, the state with the lowest total free energy F is the most stable. Among states that exist at the same voltage V, the state with the lowest electric Gibbs function (F−QV) is the most stable. Thus the relative stability of various equilibrium states can be compared by plotting G against V or F against Q. An example is given to illustrate the importance of a correct pairing of thermodynamic functions and independent variables.

Acoustic waveguide with a cladded core geometry

A new type of acoustic waveguide analogous to the clad optical fiber waveguide is described and experimental results are given. Modes exist in this structure which confine the acoustic energy to approximately the core due to the lower acoustical velocity in this region. The waveguide is excited with specially electroded bulk shear transducers bonded to the end surfaces. In the ∼100−MHz region both radial and torsional type modes may be attractive for long−delay (near 1 msec) low−loss serial memory applications.

Unit sphere description of liquid‐crystal configurations

In any one‐dimensional liquid‐crystal configuration, the unit director n(z) generates a path on the unit sphere. Paths that satisfy the equilibrium equations are characterized by special properties that are independent of the boundary conditions. This paper explores these properties for nematic liquid crystals, and applies them to delimit the kinds of equilibrium states that are possible and to simplify calculations needed in the design of liquid‐crystal displays. The applications include simple approximate formulas for (1) the relation between the director angle at the boundary ϑb and at the midplane ϑm for twisted states, (2) the dependence on elastic constants of the critical value of ϑb below which the 180° twisted state disappears, being replaced by its topologically equivalent planar state [G. Porte and J. P. Jadot, J. Phys. 39, 213 (1978)], and (3) the region of elastic constant space for bistability of topologically equivalent planar and 180° twisted states. The unit sphere is also applied to spec...

Discovery of dc switching of a bistable boundary layer liquid crystal display

A liquid crystal display based on bistable boundary layer configurations has been shown previously [Cheng et al., Appl. Phys. Lett. 40, 1007 (1982)] to have memory, adequate contrast, low‐voltage operation, and a bistability that is relatively insensitive to changes in material properties, cell parameters, and temperature. We report here the discovery that a short, low voltage dc pulse switches the display into one or the other of its bistable states, depending on the polarity of the pulse. Experiments suggest that a storage display of this type having n lines of pels can be rewritten in (50+20n) milliseconds using voltages of less than 2 V. Consequently, a large area, low power, nonrefreshed display is possible.

Exact solutions for liquid crystal configurations and an improved boundary layer model

The director configuration in a liquid crystal cell is basic to an understanding of both the optical contrast between states and switching dynamics. This paper treats the voltage dependence of nematic liquid crystal configurations in which the director orientation depends on a single space coordinate z, and there are equal but oppositely tilted boundary conditions on the two cell surfaces at z=±d/2. In the boundary layer model, configurations are approximated by joining together pieces of ‘‘boundary layer solutions,’’ which are solutions of the equations for equilibrium configurations in a half space with the boundary condition θ=constant at only one surface and θ=dθ/dz=0 at z=∞, where θ is measured from the normal to the surface. This paper (1) indicates exact solutions that satisfy the cell boundary conditions, (2) examines their high voltage asymptotes, (3) proves that the boundary layer solutions reproduce the essential features of these asymptotes, and (4) presents a way of fitting boundary layer sol...

Multiplexing the bistable boundary layer liquid crystal display

Shorter switching times in liquid crystal devices are traditionally achieved by raising the switching voltage. However, one of the limitations in multiplexing the boundary layer display is the necessity to keep the rms switching voltage Vs on the not‐yet‐selected pels below a critical threshold voltage Vth that would hold them in an asymmetric state and prevent switching. By using a periodic square wave to simulate a sequence of bipolar switching pulses, we show that their orienting effect in a ‘‘dual‐frequency’’ liquid crystal can be prevented by simultaneously applying a voltage at a higher frequency where the dielectric anisotropy is negative. This permits Vs>Vth, and in principle allows faster multiplexing. The goal of increased speed was not achieved in our simulation experiment due to the inherently slow response of the dual‐frequency material used. Nevertheless, the demonstrated scheme will be advantageous when faster dual‐frequency materials are developed.