Using variable temperature total x-ray scattering and large-scale structure modeling, we study the temperature and composition evolution of lattice distortions and charge density waves (CDWs) in the archetypal strongly correlated system $\mathrm{RENi}{\mathrm{C}}_2$ ($\mathrm{RE}=\mathrm{Dy}$, Tb, Gd, and Sm). Joint analysis of reciprocal and real space data reveals the presence of strong lattice distortions that, depending on the RE species and temperature, appear periodic or remain local, forming a complex CDW phase diagram. Apparently, the CDWs in $\mathrm{RENi}{\mathrm{C}}_2$ materials arise from a common to the system lattice instability involving diverse distortion modes that persist when magnetic order also sets in at very low temperature. The results support the notion that intrinsic lattice distortions are important to the emergence of exotic electronic phases in strongly correlated systems and call for their further investigation using the advanced approach adopted here.

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• Charge density waves
• Strongly correlated systems
• Monte Carlo methods
• X-ray pair-distribution function analysis