Silver-tracer diffusion in Cu2O

The diffusion of¹¹⁰Ag in Cu₂O has been measured by a serial-sectioning technique as a function of temperature (700–1132°C) and oxygen partial pressure (6 × 10^?6 ?8 × 10^?2 atm). The data are fit to the defect model for Cu₂O developed by the authors in the preceding paper. Silver ions have a larger impurity-vacancy binding free energy and/or a larger jump frequency for the singly charged cation vacancies relative to that for the neutral cation vacancies. The activation enthalpies for the diffusion of copper and silver ions in Cu₂O are nearly equal, but the absolute value of D¹_Ag is about three times larger than D¹_Cu even though the silver ion is 31% larger than the copper ion.     

Cation self-diffusion and the isotope effect in Mn1−δO

Diffusion of ⁵⁴Mn in Mn_1?δO single crystals has been measured by a serial sectioning technique as a function of temperature (1000–1500°C) and deviation from stoichiometry (0.00003 < δ < 0.12). The value of m in the expression varies from about 6 at low Po₂ at all temperatures to a value approacing 2 at high Po₂ and high temperatures, thus suggesting that diffusion occurs by doubly charged vacancies at low Po₂ with increasing contributions from singly charged and neutral vacancies as Po₂ (and vacancy concentration) increases. For δ near 0.1, the values of D fall below the values extrapolated from smaller defect concentrations. The isotope effect for cation self-diffusion was measured by simultaneous diffusion of ⁵²Mn and ⁵⁴Mn in Mn_1?δO (0.0004 < δ < 0.116) at 1300 and 1500°C. The measured values of fΔK are independent of temperature within experimental error, and decrease from a value of 0.70 at low defect concentrations to 0.37 for large values of δ. The isotope-effect results suggest that diffusion occurs by single non-interacting vacancies at low defect concentrations; defect-defect interactions become important for δ ? 0.01. The defect-defect interactions may involve essentially individual defects or may result in defect clusters; the similarity between the present isotope-effect results and those for Fe_1?δ0 suggests that defect clustering plays a significant role in mass transport in Mn_1?δO at large values of δ.     

Energy transfer in rare earth-doped CaWO4 after red edge excitation

Host sensitized energy transfer in CaWO₄ doped with Eu³⁺ and Sm³⁺ is investigated using pulsed laser time-resolved spectroscopy techniques. The excitation is into the long wavelength tail of the absorption edge and the results indicate that this selectively excites tungstate ions which are located next to activator impurity ions. The subsequent energy transfer is found to be consistent with a single step, nearest neighbor process. Both electric dipole-dipole and exchange interactions can predict strong enough transfer to account for the observed rates. These results are compared to those obtained previously for broad band excitation into the highest energy absorption bands of CaWO₄ crystals.     

Isotopic ion exchange separation of radioisotopes using an acetone-water-hydrochloric acid system

Isotopic ion exchange for the rapid separation of radioactive mixtures has been further extended through the use of an acetone-water-hydrochloric acid system. Distribution data were obtained for 27 elements in the range of 15–90% acetone, 0.3N HCl indicating a number of new separations. The approach was used for the separation of several radioisotopes from short half-life magnesium matrix for activation analysis. The separations were completed in less than 5 minutes. Research supported by the Advanced Research Projects Agency.     

Chromium tracer diffusion in NiO crystals

Diffusion of ⁵¹Cr in NiO single crystals in air has been studied by the tracer-sectioning technique. In the temperature range 1192–1642°C, the diffusion coefficient can be expressed by the Arrhenius expression D=D_oexp(-Q/RT), with D_o=(8·6±1·2)×10^?3 cm²/sec and Q=67·4±1·1 kcal/mole. The use of a high specific-activity tracer and a special configuration for the diffusion anneal prevented the self-dopling effect found by Seltzer and the evaporation of chromium from the sample surface. The present results, in conjunction with published results on nickel self-diffusion in NiO and interdiffusion in the NiO?Cr₂O₃ system, are used to determine a chromium ion-vacancy binding energy of about 5 kcal/mole in pure NiO.     

Inelastic scattering studies on 50Cr

The inelastic scattering of protons, deuterons, τ and α from⁵⁰Cr has been studied. Spins, parities and transition strengths have been inferred for many states. The 1.89 MeV 4⁺state is excited by a double-excitation process, but more weakly than expected for a two-phonon state. A weak 5^? state is found at 4.37 MeV, and a 5⁺ state is inferred at 3.792 MeV.     

On sensitivity in optimal control problems

Two types of interpretations of multipliers in both static and dynamic optimization problems are described. It is snown that the Lagrange multipliers encountered in mathematical programming problems and the auxiliary functions arising in Pontryagintype optimal control problems sometimes have highly analogous interpretations as rates of change of the optimal attainable value of an objective function, or in some cases as bounds on average rates of change.