${\mathrm{EuPd}}_2{\mathrm{Si}}_2$ serves as an ideal system to probe the interplay between lattice dynamics and electronic instabilities through its tunable valence transition, which is responsive to temperature, pressure, and magnetic field. Here, we focus on investigating the origin of the temperature-induced europium valence instability in pristine ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$, alloyed ${\mathrm{EuPd}}_2{\mathrm{Si}}_{1.95}{\mathrm{Ge}}_{0.05}$, and ${\mathrm{EuPd}}_2{\mathrm{Si}}_{1.9}{\mathrm{Ge}}_{0.1}$ and its correlation with structural responses. Compared with the parent compound ${\mathrm{EuPd}}_2{\mathrm{Si}}_2$ which exhibits the europium valence transition at $T_v$ = 143 K, magnetic susceptibility measurements reveal a systematic shift in $T_v$ with Ge substitution, decreasing to 87 K for ${\mathrm{EuPd}}_2{\mathrm{Si}}_{1.95}{\mathrm{Ge}}_{0.05}$. Temperature-dependent synchrotron x-ray diffraction confirms phase coexistence between $\mathrm{E}{\mathrm{u}}^{2+}\mathrm{P}{\mathrm{d}}_2\mathrm{S}{\mathrm{i}}_{2-x}\mathrm{G}{\mathrm{e}}_x$ and $\mathrm{E}{\mathrm{u}}^{3+}\mathrm{P}{\mathrm{d}}_2\mathrm{S}{\mathrm{i}}_{2-x}\mathrm{G}{\mathrm{e}}_x$ phases across the valence transition for all samples measured ($x=0$, 0.05, 0.10). The pronounced increase in the full width at half maximum well above $T_v$ reflects the gradual nature of the transformation and highlights the role of structural strain in stabilizing the coexisting phases, supporting the presence of a phase-segregated ground state, in contrast to a homogeneous intermediate-valence or mixed-valence state. The variation in $T_v$ across different compositions correlates with changes in lattice parameters, highlighting the robust coupling between the structural and electronic degrees of freedom. The phase diagram suggests an inverse linear relationship between the lattice parameter and $T_v$, suggesting a possible predictive framework for estimating transition temperatures in other chemically substituted variants of this family.

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• Electronic phase separation
• Phase separation
• Phase transitions
• X-ray diffraction