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A detailed study on the effect of additional elements on the period of CuAu II was made to investigate the origin of the longperiod superlattice. Single crystals of CuAu were made by the successive evaporation of Au and Cu onto a heated NaCl substrate. A known amount of the additional element was evaporated onto the CuAu film and diffused in by appropriate annealing techniques. The effect of the addition of 16 different elements in varying concentrations on the domain size of CuAu II was determined using electron diffraction. The addition of group III elements Al, Ga, and In of up to 25 atomic percent was found to decrease the average domain size $M$ (half-period) with increasing concentration of the element (from 5 to 1.5). Sn, Mn, and Zn incorporated into CuAu also decreased the domain size. Nickel and Pd in small amounts increased the domain size, as did Ag and concentrations of Cu and Au above the stoichiometric proportion. From the analysis of all the data, a definite relation was found to exist between the electron-atom ratio and the domain size. From the experimental data, a model based upon the stabilization of alloy phases using the Brillouin zone theory was formulated to show the variation of the electron-atom ratio $\frac{e}{a}$ with the domain size $M$. This relation is given by the following formula: $\frac{e}{a}=(\frac{\ensuremath{\pi}}{12{t}^{3}}){(2\ifmmode\pm\else\textpm\fi{}\frac{1}{M}+\frac{1}{4{M}^{2}})}^{\frac{3}{2}}$. Here $t$ is a truncation factor which in most cases has a value of around 0.95. The agreement between theory and experiment is very good. In addition, the model was applied to other alloy systems where long-period superlattices are formed and was found to give a good explanation for the stabilization of these structures. The theory provides two regions depending upon the electron-atom ratio where all the predictions are reversed. The Cu-Au system and the Cu-Pd system are examples of these two regions, respectively. The theory not only predicts the variation of the domain size with the electron-atom ratio, but also predicts the concentration dependence (without changing the electron-atom ratio) and the temperature dependence, the distortion of the lattice, the appearance of one- and two-dimenional antiphase domains and other characteristics of long-period superlattices which are in accord with the experimental data on many alloy series.

The electrical conductivity of single-crystal ${\mathrm{Cu}}_{2}$O was measured in the temperature range of 1100\ifmmode^\circ\else\textdegree\fi{} to 500\ifmmode^\circ\else\textdegree\fi{}C in oxygen pressures from 152 mm to ${10}^{\ensuremath{-}5}$ mm of Hg. The $log\ensuremath{\sigma}$ vs $logP({\mathrm{O}}_{2})$ curves were found to be linear between the oxygen pressures of 50 mm and ${10}^{\ensuremath{-}2}$ mm, with an average slope of 0.1420, or approximately $\frac{1}{7}$. These curves exhibit a radical change in slope at ${\mathrm{O}}_{2}$ pressures below ${10}^{\ensuremath{-}2}$ mm.The plots of $log\ensuremath{\sigma}$ vs $\frac{1}{T}$ at constant oxygen pressure were found to be linear and the activation energies obtained from the slopes of these plots have an average value of 0.65 ev at ${\mathrm{O}}_{2}$ pressures between 50 mm and ${10}^{\ensuremath{-}2}$ mm. At ${\mathrm{O}}_{2}$ pressures of ${10}^{\ensuremath{-}3}$ mm to ${10}^{\ensuremath{-}4}$ mm, the activation energy increases sharply to a value of 1.05 ev. The activation energy obtained from the measurement of single-crystal ${\mathrm{Cu}}_{2}$O in air at temperatures from 1020\ifmmode^\circ\else\textdegree\fi{}C to 1100\ifmmode^\circ\else\textdegree\fi{}C was found to have an average value of 0.767 ev.An explanation for the physical significance of the activation energies obtained is suggested and the models proposed to explain the dependence of the electrical conductivity on the ${\mathrm{O}}_{2}$ pressure are considered.

A theory, which has been developed recently by the authors to explain the origin and characteristics of the long-period superlattice CuAu II, is used to explain, in a more general way, similar characteristics of long-period superlattices found in face-centered cubic alloys having compositions around the ${A}_{3}B$. Although there is a difference in symmetry in the atomic arrangement between the $\mathrm{AB}$- and ${A}_{3}B$-type alloys, the application of the theory can be made in a straightforward manner. It is found that one- and two-dimensional long-period superlattices can exist in the ${A}_{3}B$-type alloy systems, but that a three-dimensional one should not occur. In the case of the one-dimensional long-period superlattices, the theory can be reduced to the same form as for the CuAu II ($\mathrm{AB}$ type) case. The theory predicts correctly the period of the superlattice, e.g., those found in the Cu-Pd, Cu-Pt, Au-Cd, Ag-Mg, and Au-Zn systems, the type of antiphase, the direction of the period and the sign of the tetragonal distortion which occurs when the long-period superlattice is formed.The theory is also applied to the case of the two-dimensional superlattice, examples of which are found in the Cu-Pd, Au-Mn, and Au-Zn alloys. Since a more detailed knowledge of the electronic structure of the alloys is necessary in dealing with the two-dimensional superlattices, less quantitative information on their characteristics is obtained. However, predictions concerning the period of the structure, type of antiphase, and lattice distortion are reasonably good.An explanation is given for the possible relation between the magnitude of the truncation factor and the shape of the Fermi surface which is based on recent findings in the noble metals.