Average Surface Energy Research Articles

Generation of semigroups, and two-dimensional quantum lattice systems

We consider two types of conditions on an operator on a Banach space which ensure that it is the generator of a semigroup of contractions. First, S. Sakai's concept of commutative normal ∗-derivations of UHF algebras is generalized to “approximately commutative operators” on Banach spaces. Next we consider the situation in which the domain of the operator contains an increasing sequence of “approximately invariant subspaces,” and generalize results of A. Kishimoto and P. E. T. Jørgensen. A corollary is the existence of time development for two-dimensional quantum lattice models when the average surface energy per unit surface is uniformly bounded in the volume.

Improvements in the transverse properties of composites

Fracture surface energies of initiation (γIc) for a transverse fracture process in glass-reinforced epoxy composites have been measured and the results calculated by three different treatments and are compared with the average fracture surface energies (γFc) for the complete fracture process.

Surface energy and the secondary recrystallisation of platinum sheet

The secondary recrystallisation of thin platinum sheet at 1500°C was observed and the growth rates of the secondary crystals were measured. Only crystals with orientations close to {111} were observed to grow. The relative variation of surface energy with crystallographic orientation was measured by the twin boundary groove technique and the grain boundary energy relative to the average surface energy was evaluated from grain boundary groove angles, so that the applied driving pressure for secondary recrystallisation could be calculated. The drag force opposing grain boundary migration was estimated from the variation of grain boundary velocity with applied driving pressure and the grain boundary mobility was evaluated. The results are compared with other mobility measurements and grain boundary anchoring and drag effects are discussed.

Calculations of the Surface Energy for Some Orthorhombic Sulfates

The surface energy for the 100 faces of barium, strontium, lead, and calcium sulfates has been calculated for various sizes of very small crystals. These values, when extrapolated to infinite surface area, give for the average surface energy 994, 1110, 1062, and 574 ergs/cm2, respectively.

Variation of surface energy with crystallographic orientation in silver

Silver was heated in air at 900°C and the orientation derivatives of surface energy, 1 γ · δγ δα , were found from twin boundary groove angles for both faceted and unfaceted crystals. It is confirmed that faceting on silver is a surface energy driven process in accord with previous results. A plausible γ-plot is derived and the conditions for faceting are discussed. The ratio of the twin boundary energy to the average surface energy is very low: 0.0051 ± 0.0006.