Rigidity of randomly intercalated layered solids. II. Gallery structure of multilayers

We have investigated the gallery structure of intercalated multilayer systems ${\mathit{A}}_{1\mathrm{-}\mathit{x}}$${\mathit{B}}_{\mathit{x}}$L, assuming that the intercalants A and B are randomly distributed in each gallery flanked by host layers L. We allow for the correlation between the intercalants in different galleries denoted as interlayer correlation (ILC). The gallery structure is characterized by an average gallery height, by fluctuations in the gallery height from site to site, and by a complete height distribution function. These quantities have been studied by constructing a harmonic spring model which accounts for the layer rigidity, differential size, and compressibilities of the intercalants, and incorporating the ILC through a one-dimensional Ising-spin model. We have obtained exact solutions for this model for arbitrary ILC when the two intercalants have the same compressibilities (${\mathit{k}}_{\mathit{A}}$=${\mathit{k}}_{\mathit{B}}$). In this limit, we show that Vegard’s law is obeyed for all values of the transverse rigidity of the host layers. In the general case (${\mathit{k}}_{\mathit{A}}$≠${\mathit{k}}_{\mathit{B}}$), we have developed an effective-medium theory whose results are in excellent agreement with computer simulations.