The presence of phonon instabilities that leads to the formation of charge modulations in kagome metals has allowed their classification based on the atomic displacements of the imaginary modes. Here, we use diffuse and inelastic x-ray scattering (IXS), backed by Monte Carlo simulations to describe a type-I instability in the kagome metal ${\mathrm{Yb}}_{0.5}{\mathrm{Co}}_3{\mathrm{Ge}}_3$. We find that the in-plane displacement of Co in the kagome plane drives a structural transition with the appearance of new Bragg peaks at odd $L$. The in-plane odd Bragg reflections are surrounded by an anisotropic hexagonal diffuse scattering, characteristic of a highly frustrated triangular lattice, that can be modeled following a combination of an Ising model and Lennard-Jones potential. The inelastic spectra reveal no softening but an anomalous broadening of the $\mathrm{\Gamma }$–$A$ low energy acoustic mode, and demonstrate that the structural phase transition in ${\mathrm{Yb}}_{0.5}{\mathrm{Co}}_3{\mathrm{Ge}}_3$ is of an order-disorder transformation type. Our results allow disentangling the structural ordering from the geometric frustration-induced correlated disorder in kagome lattices, and highlight the power of combined diffuse scattering and IXS to differentiate between displacive and order-disorder scenarios.

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• Phase transitions
• Phonons
• Kagome lattice
• Inelastic X-ray scattering
• Monte Carlo methods
• X-ray diffuse scattering