Lattice and grain boundary self-diffusion coefficients of radioactive nickel 63 into high purity nickel have been measured over the temperature range 650°–475°C. The lattice diffusion coefficients, measured by radioactive counting of the surface, are given by DL=1.9 exp(−66 800/RT) cm2sec−1in agreement with previous measurements at higher temperatures. The grain boundary diffusion coefficients, determined from activity-penetration data, are similarly given by DB=0.07 exp(−27 400/RT) cm2sec−1and found to be independent of grain diameter in the range of about 0.03 to 0.07 mm.

The theory of two-dimensional instability of laminar flow of water over solid surfaces is extended to include the effects of heat transfer. The equation that governs the stability of these flows to Tollmien-Schlichting disturbances is the Orr-Sommerfeld equation “modified” to include the effect of viscosity variation with temperature. Numerical solutions to this equation at high Reynolds numbers are obtained using a new method of integration. The method makes use of the Gram-Schmidt orthogonalization technique to obtain linearly independent solutions upon numerically integrating the “modified Orr-Sommerfeld” equation using single precision arithmetic. The method leads to satisfactory answers for Reynolds numbers as high as Rδ* = 100,000. The analysis is applied to the case of flow over both heated and cooled flat plates. The results indicate that heating and cooling of the wall have a large influence on the stability of boundary-layer flow in water. At a free-stream temperature of 60 deg F and wall temperatures of 60, 90, 120, 135, 150, 200, and 300deg F, the critical Reynolds numbers Rδ* are 520, 7200, 15200, 15600, 14800, 10250, and 4600, respectively. At a free-stream temperature of 200F and wall temperature of 60 deg F (cooled case), the critical Reynolds number is 151. Therefore, it is evident that a heated wall has a stabilizing effect, whereas a cooled wall has a destabilizing effect. These stability calculations show that heating increases the critical Reynolds number to a maximum value (Rδ* max = 15,700 at a temperature of TW = 130 deg F) but that further heating decreases the critical Reynolds number. In order to determine the influence of the viscosity derivatives upon the results, the critical Reynolds number for the heated case of T∞ = 40 and TW = 130 deg F was determined using (a) the Orr-Sommerfeld equation and (b) the present governing equation. The resulting critical Reynolds numbers are Rδ* = 140,000 and 16,200, respectively. Therefore, it is concluded that the terms pertaining to the first and second derivatives of the viscosity have a considerable destabilizing influence.

The elastic constants of single crystals of magnesium and of dilute alloys of magnesium with lithium have been measured at 298°K using the pulse-echo technique. The alloys covered the range of 1.841-2.0 electrons per atom. All fundamental elastic constants decrease with increasing lithium content. In terms of Cf l (dC/dx) the values are c u , (-0.411); i(cn-Ci2), (-0.235); Cn+ci2+2c 8 3-4cia, (-0.400) per atom fraction of lithium. These values are corrected for the change in lattice parameter upon alloying by using experimental data on the pressure derivatives of the elastic constants of pure magnesium. The remaining effect is due to alloying alone (change in the electron-atom ratio) and is still negative for all three shear constants. In terms of Co -1 (dC/dx) Vt c/a the values are c u , (-0.827); J(cn-Cu), (-0.589); Cn-\-Ci2+2czz-4ci 3 , (-0.886) per atom fraction of lithium. These results may be interpreted as indicating, first, a decrease in the long-range electrostatic forces because of the decrease in the average ion-core charge, and second, a decrease in the Fermi stiffness. The decrease in the Fermi stiffness is attributed to: (1) an increase in the volume of electron holes-a hole contributes negatively to the Fermi stiffness-and a decrease in the volume of the overlap electrons in the Brillouin-zone structure with decreasing electron-atom ratio; (2) the transfer (under shear) of electrons from those faces receding from the origin of the Brillouin zone to those approaching it. The over-all effect of this transfer phenomenon is also to decrease the Fermi stiffness.A simple procedure for classifying d-band states is proposed and applied to the d bands of Cu. It is found that most of the spectral structure arises from covalent d-d interactions, with s-d hybridization playing a minor but significant role.

The coefficient of self-diffusion in annealed and prestrained nickel single crystals, Du, determined in the temperature range 948° to 1023°K by radioactive counting of the surface is Du=1.9 exp(−66 800/RT) cm2sec−1. The coefficient of self-diffusion in annealed and prestrained fine-grained nickel crystals, Du′, in the same temperature range is independent of the degree of prestrain: Du′=1.1×10−7 exp(−32 300/RT) cm2sec−1. The coefficient of self-diffusion in nickel single crystals undergoing plastic deformation, Dd, was determined for strain rates ranging from 0.01 to 0.1035 h−1 in the same temperature range. Dd appears to vary with strain but eventually reaches an asymtotic value D̄d. At a constant temperature, D̄d/Du is almost linearly dependent on the strain rate ε: D̄d/Du=1+Kε̇, where K is 162, 225, and 470, (h−1) for temperatures 1023°, 973°, and 948°K, respectively.

Neglecting temperature fluctuations, assuming viscosity is only temperature dependent, and assuming all other fluid properties are constant, the two-dimensional linearized parallel flow stability problem is adequately treated by modifying the Orr-Sommerfeld equation to include viscosity variations with temperature. The resulting equation is used to study the spatial stability of stagnation water boundary layer with heat transfer. The mean flow with free-stream temperature T∞ = 60°F and wall temperature Tw ranging from 32 to 200°F is computed numerically, from the boundary layer equations with variable fluid properties. It is found that heating stabilizes the boundary layer and cooling destabilizes it. At Tw≅196°F the neutral curve degenerates to a singular point at frequency ω = 5×10−7 and Reynolds number Rδ* = 30.7×103. All disturbances become completely damped for Tw>196°F. It appears that the effect of viscosity μ is larger than the effect of its first derivative μ′ on stability, and that the effect of μ″ is negligible compared with the effect of μ′.

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The linearized spatial stability of adiabatic flat plate flow to the first mode of oblique disturbances is computed numerically, using finite difference techniques, in the Mach number range M=1.6 to 6.0. The most unstable wave angle ψ is found in the range ψ=46° to 60°. Stability maps, in the form of curves of constant spatial amplification rate, are presented on the frequency-Reynolds number diagram. The critical x-Reynolds number is found to decrease monotonically with M, and is best fit with the expression R1/2x=579.34 M−1.18. This decrease is found to correspond with the outward displacement of the minimum critical layer and the ‘‘inflection’’ point, y at (U′/T)′=0, from y=0.248 and 0.231 at M=1.6 to 0.754 and 0.842 at M=6.0. No transition from viscous to inviscid instability is found with increasing Mach number, rather viscous instability persists to M=6.0. Some of the results agree with those obtained earlier by Mack, but others differ, particularly computations for M>3.0.