Second-order Structural Transition in (Ca0.5Sr0.5)3Rh4Sn13

(Ca0.5Sr0.5)3Rh4Sn13 is a member of the substitution series (CaxSr1–x)3Rh4Sn13 which has recently been argued to feature a structural quantum critical point at xc = 0.9. In the stoichiometric compound Sr3Rh4Sn13, the structural transition at T* ≈ 138 K has been shown to be second-order. Moving towards xc, we examine the character of the structural transition in (Ca0.5Sr0.5)3Rh4Sn13 (i.e. x = 0.5, T* ≈ 55 K) using electrical resistivity, heat capacity and X-ray scattering. The absence of the thermal hysteresis in specific heat around T*, and the continuous evolution of the superlattice reflection detected by X-ray diffraction are consistent with the scenario that the structural transition associated with a modulation vector q = (0.5 0.5 0) in (Ca0.5Sr0.5)3Rh4Sn13 remains second-order on approaching the quantum critical point.