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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. |
