Lattice Parameter Ratio Research Articles

Structure and energy of crystal interfaces

Abstract The variational method developed by Fletcher and Adamson is applied to calculate the energy of the interface between (100) faces of two cubic crystals for arbitrary relative twist displacements and for lattice parameter ratios between 0·6 and 2·0. A simplified interatomic potential is used for this calculation and this shows only a small number of cusped energy minima.

Low-Energy Electron-Diffraction Study of the Clean (100), (111), and (110) Faces of Platinum

The structures of the (111), (100), and (110) crystal faces of platinum were studied as a function of temperature in the range 300°—1769°C (melting point). The (111) and (100) substrates are stable while the (110) face shows faceting above 600°C. Several surface structures were found to exist on the stable platinum substrates. These have well-defined temperature ranges of stability. There are two types of surface structures, ordered and disordered. Both types appear to be the property of the clean platinum substrates. The ordered structures appear during annealing, after ion bombardment at lower temperatures (<900°C). They exhibit long-range order and their stability ranges overlap on a given substrate. These structures are believed to be due to ordered arrays of vacancies in the substrate plane which, under proper conditions, show remarkable stability. A high, nonequilibrium concentration of defects at the surface may be necessary to induce their formation. The disordered surface structures appear at high temperatures, above the stability range of most of the ordered structures. They are characterized by ringlike diffraction features which develop gradually as a function of increased heating time or temperature. The formation of these structures is irreversible and they can only be removed by ion bombardment. Near the melting point, the ring patterns remain the only diffraction features of the presumably greatly disordered surfaces. The ratio of lattice parameters assigned to the diffraction rings on each substrate indicate that they can be due to domains of (111) surface structures. These hexagonal structures appear on all of the platinum surfaces, are freely rotated in the substrate plane, and show an ∼11% contraction with respect to the inter-planar spacing in the ordered (111) face. The disordered close-packed-hexagonal structure seems to be the stable high-temperature surface phase of platinum.

Electrical resistivity, elastic modulus, and debye temperature of titanium diboride

Electrical-resistivity measurements on single and polycrystalline specimens of TiB 2 at 293° and 77°K indicated a metallic-bonding mechanism. The average resistivity for single crystal TiB 2 is 6.6μΩ-cm at 293° and 1.1μΩ-cm at 77°K. Anisotropy of the resistivity values with respect to the c- and a-axes of TiB 2 ( c a = 1.067 ) was not observed. The random electrical resistivity of hot-pressed specimens ranged from 9.1 μΩ-cm at 293°K to 2.2 μΩ-cm at 77°K. Anisotropy in elastic and shear moduli was determined to follow the lattice-parameter ratio. Debye-temperature values were calculated from average rod-velocity measurements on single-crystal bar and rod-shaped specimens resulting in θ − v 0( m) = 952° and 964°K, respectively. For polycrystalline TiB 2 the Debye temperature calculated from rod-velocity measurements ranged from 1100–1130°K.

Aging Reactions in Precipitation Hardenable Stainless Steel

The physical metallurgy of a precipitation hardenable stainless steel—17-4 PH—is reviewed. Electron micrographs are presented describing the microstructure of 17-4 PH as a function of aging time and temperature. Phase composition and X-ray diffraction data quantitatively relate lattice parameter, nonuniform microstrain, and austenite-ferrite ratio with heat treatment.

Recrystallization behavior of solid solutions of metals

1. The main factor affecting the re crystallization temperature of solid solutions is the relation between the lattice constants of solvent and solute elements: solute elements with lattice parameters larger than those of the solvent, increase the recrystallization temperature but decrease it when the lattice parameter ratio is reversed. 2. Curves relating the RTT to the concentration of solid solution are determined by the nature of the solute element and its concentration: they rise at small concentrations (or fall in the case of Si); there is a stabilization of recrystallization temperature at medium concentrations and another increase at still higher alloy contents. 3. The second increase of the RTT of the investigated alloys is apparently controlled by diffusional processes which retard recrystallization.