Single Crystal Wire Research Articles

The influence of electric stress on morphological changes occurring by surface diffusion on a body with anisotropic surface energy

The time evolution of the surface morphology of a long single-crystal (initially cylindrical) wire which forms the central electrode of a coaxial capacitor is discussed for mass transport by (isotropic) surface diffusion but allowing for anisotropic surface energy γ. Radial changes in the shape of the wire are shown to be retarded by the electric stress when the γ anisotropy is small. As Nichols and Mullins have shown, the wire is unstable to longitudinal perturbations; their treatment is generalized to incorporate both γ anisotropy and electric stress. The dominant wavelength in the evolving unstable axial profile is related to a γ anisotropy factor involving an out-of-plane second derivative of γ averaged over directions in the radial plane. The electric stress enhances or inhibits the instability depending upon the magnitude of this anisotropy factor. Some tentative remarks, based upon a conjectured extrapolation of the perturbation treatment developed here, are addressed to the problem of the ovulation of a semi-infinite cylinder.

The influence of crystalline anisotropy on neck growth during the sintering of zinc

Polycrystalline zinc wires of two grain sizes and zinc single crystal wires of four orientations all of them 0.010 in. in diameter were grown. Pairs of wires from each of the six groups were sintered together at 365°C for 8 hr in a pressurized dry hydrogen atmosphere and the widths of the necks formed between pairs were measured. In the single crystal pairs, the neck width depended upon the relative orientation of the basal planes in the wire with the largest width up to 2.7 times as large as the smallest. In the polycrystalline samples those with fine grain size, of the order of neck width, had small necks, while those with coarse grain size, of the order of the wire diameter, had large necks. The observed variations in the width of the neck with relative orientation and with grain size must be caused by the anisotropy of those properties of zinc which determine the rate of material transport during sintering. For sintering by diffusional flow these are specific surface free energy and diffusivity, for sintering by evaporation and condensation they are specific surface free energy and vapor pressure. Since for these mechanisms approximate equations for the rate of neck growth exist, the maximum ratios of neck width due to the anisotropies of specific surface free energies, diffusivities and vapor pressures can be estimated. They are considerably smaller than the observed ratio of up to 2.7. The remaining material transport mechanism for the early stages of sintering is plastic flow which, in zinc, is highly anisotropic, since even at temperatures near the melting point the critical resolved shear stress for slip on the basal slip system is five to ten times lower than for slip on any other system. The measured neck width of the single crystal wire pairs can be directly related to the ease of basal slip. Those pairs which are oriented so that no basal slip is possible have small necks, while those which are favorably oriented for basal slip have large necks. The small neck width in the fine-grained wires must be due to constraint which inhibits basal slip. No such constraint exists in the necks of the coarse grained wires. Material transport by plastic flow must play an important role in the sintering of the zinc wires.

Effects of surface films on the deformation of metals

The effect of a thin coating on the mechanical deformation of a single crystal wire is found to be an increase in the stress required for the initiation of easy glide; the development of pseudo-elastic defor mation prior to easy glide, during which the sample deforms as an hollow elastic cylinder with a plastic core; and the concentration of slip at relatively few slip lines. A dislocation model used to explain these observations involves the generation of dislocations by the action of sources of various initial lengths, l, with a distribution of lengths, N( l) dl, assumed to be inversely proportional to their lengths. The increase in yield strength is due to the barrier effect of the coating and the axial strain of the sample, ε x , is shown to be approximately proportional to the applied stress, expressed as resolved shear stress, τ r , in the slip direction on the slip plane. A principal feature of the dislocation model is that the critical shear stress, τ c , required for piled-up dislocations to penetrate the interfacial barrier is proportional to nτ r , where n is the number of dislocations in the pile-up. This accounts for the observation that under the level of stress where dislocation break through begins, only those few sources for which nτ r , > τ c will be able to penetrate, and consequently slip lines are reduced in number and slip is concentrated. It is also pointed out that the initial distribution of source lengths is a factor in the effect of a coating on the mechanical properties of a metallic crystal.

First- and Second-Order Stress Effects on the Superconducting Transitions of Tantalum and Tin

The shift of critical field of a single-crystal wire under uniaxial tension is studied for Ta and Sn. For Ta the shift is nonlinear and gives both the first-order critical field-stress coefficient and a particular combination of second-order coefficients. By combining with other data, the three second-order constants are estimated. The smaller first-order coefficient of Sn is found to be considerably smaller than previous estimates. Both Ta and Sn are found to satisfy a similarity condition for the coefficients, but of a less restrictive form than usual. Similarity is used to predict the behavior of jumps in elastic constant moduli at the transition in Ta. The general formal theory of the first-and second-order coefficients is formulated and many special cases are given. The general thermodynamic relations at the transition between jumps in strain and elastic constants and the various coefficients, are derived. It is shown that BCS theory implies similarity.

Thermionic Work Function of the (100) Face of a Tungsten Single Crystal

A slab with one surface cut and etched parallel to (100) crystallographic planes formed the cathode in a low power electron microscope. The electron image of the cathode was formed on a fluorescent screen with a small hole at the center. An electron collector placed behind the hole permitted a measure of the electron current passing through the hole as a function of the temperature of the cathode as measured with an optical pyrometer. The most probable value of the work function, φ, obtained after 2400 hours of outgassing in a sealed-off, gettered tube is 4.59±0.02 ev. This may be compared with 4.56 ev obtained previously by Nichols for the work function in the [100] direction of a tungsten single crystal wire.

Thermo-Electric Effect in Single Crystal Zinc

Thermal e.m.f., thermo-electric power, Peltier heat of single crystal Zn against Cu as functions of crystal orientation.---In continuation of previous work data are presented on the thermal e.m.f. against copper of six single crystal wires of zinc, of which the orientations of the main crystallographic (hexagonal) axis with respect to the wire axis, range from 11.4\ifmmode^\circ\else\textdegree\fi{} to 90\ifmmode^\circ\else\textdegree\fi{}. (The average deviation from the mean for these observations is 0.8\ifmmode^\circ\else\textdegree\fi{}.) The temperature interval is from - 182\ifmmode^\circ\else\textdegree\fi{} to 475\ifmmode^\circ\else\textdegree\fi{}C. The apparatus designed to enable measurements to be made above the melting point is described in detail.Thermo-electric power, Peltier heat, and difference of Thomson coefficients for Zn \ensuremath{\perp} against Zn\ensuremath{\parallel}.---From the data are calculated the thermo-electric power, Peltier coefficient, and difference of the Thomson coefficients for Zn \ensuremath{\perp} against Zn\ensuremath{\parallel}. The data also provide a test for the Voigt-Thomson law for the variation of the thermo-electric power with crystal orientation. The law seems to be verified within the limits of experimental error for the low temperatures, but the deviations at the high temperatures (300\ifmmode^\circ\else\textdegree\fi{}-400\ifmmode^\circ\else\textdegree\fi{}) are greater than the experimental errors are thought to be.Thermal e.m.f. of liquid Zn against single crystal and polycrystalline Zn.---Further, the thermo-electric powers of liquid Zn against solid single crystal Zn of different orien tations, and against polycrystalline Zn are given. The value-7.89\ensuremath{\mu}v. per deg. for ${e}_{l}\ensuremath{-}{e}_{s}$ for Zn (polycrystalline) having been found. A theoretical discussion of the thermo-electric effect in polycrystalline substances having different properties along only two of the crystallographic axes, leads to the formula $\overline{e}=(\frac{1}{3})$ ($2e\ensuremath{\perp}+e\ensuremath{\parallel}$), and indicates that such a polycrystalline metal wire should behave the same as a single crystal wire of orientation 54.5\ifmmode^\circ\else\textdegree\fi{}, the experimental value found being between 65\ifmmode^\circ\else\textdegree\fi{} and 70\ifmmode^\circ\else\textdegree\fi{}. It appears from this formula that polycrystalline Zn may be considered as an alloy of two parts Zn \ensuremath{\perp} and one part Zn\ensuremath{\parallel}.