Elastic effects in intercalation compounds: Comparison of lithium in graphite andTiS2

We compare the concentration dependence of stage-1 package thicknesses for the intercalation compound families ${\mathrm{Li}}_{\mathrm{x}}$ ${\mathrm{C}}_6$ and ${\mathrm{Li}}_{\mathrm{x}}$ ${\mathrm{TiS}}_2$ in order to study the influence of host elastic properties on staging. In both families the data suggest that local host-layer distortions around isolated intercalates are important, an elastic model based on rigid layers giving a poor fit. The decay lengths for local distortions are 5 and 7 Å, respectively, for graphite and ${\mathrm{TiS}}_2$. We argue that a more concentrated strain field associated with the smaller decay length gives rise to a larger value of $U_0$, the effective in-plane two-body attractive potential, for Li in graphite relative to ${\mathrm{TiS}}_2$. This in turn explains qualitatively why ${\mathrm{Li}}_{\mathrm{x}}$ ${\mathrm{C}}_6$ exhibits high stages at 300 K for various x while ${\mathrm{Li}}_{\mathrm{x}}$ ${\mathrm{TiS}}_2$ is restricted to stage 1.