Nonlinear gallery expansion of randomly intercalated anharmonic bilayers

We study the combined effects of local anharmonicity and transverse layer rigidity on the nonlinear gallery expansion in ternary intercalated systems. Numerical simulations are performed using both Lennard-Jones potentials and cubic anharmonic potentials between the intercalant atoms and the host-layer atoms. The harmonic approximation is used for the host-layer deformation energy. Simulation results are compared with analytic calculations within an effective-medium approximation. We find that the gallery expansion is determined by a competition between the compressibilities of the intercalants and the transverse rigidity of the host layer. A single small impurity limit clearly brings out the role of anharmonicity. The effective-medium solution reduces to exact results in three limiting cases; for perfectly floppy and perfectly rigid host layers, and for the harmonic potential with arbitrary host-layer rigidity. While it is well known that Vegard’s law (linear expansion of the gallery spacing) is observed in the harmonic limit when the two intercalants have the same compressibility, we find that the inclusion of anharmonicity gives rise to deviations from Vegard’s law which increases with the increase in host-layer rigidity and the degree of anharmonicity.