Intercalated Cu+ ion dynamics in the two-dimensional layered compound Cu0.33TiSe2

$\mathrm{C}{\mathrm{u}}^{+}$ ion behavior is one of the heavily discussed topics in physical and material fields because of its unclear behavior and high potential in materials application. To provide a breakthrough in this field, comprehensive research that connects the real space and the reciprocal lattice (momentum) space is effective. Here, we investigated the $\mathrm{C}{\mathrm{u}}^{+}$ ion behavior in two-dimensional layered system $\mathrm{C}{\mathrm{u}}_{0.33}\mathrm{TiS}{\mathrm{e}}_{2}$, which shows the $\mathrm{C}{\mathrm{u}}^{+}$ disorder-order phase transition at 200 K. Inelastic x-ray scattering revealed a large change of the $\mathrm{C}{\mathrm{u}}^{+}$ ion dynamics at the phase transition. It is expected that the complex interactions are involved in the behavior of $\mathrm{C}{\mathrm{u}}^{+}$ ions intercalated in the negatively charged $\mathrm{TiS}{\mathrm{e}}_{2}$ layers by charge transfer. However, Monte Carlo simulations using a simple combination of repulsive forces between $\mathrm{C}{\mathrm{u}}^{+}$ ions well reproduce the characteristic temperature dependence of the anisotropic diffuse scattering. These insights provide a unified understanding in controlling the intercalated system.