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A detailed investigation of BaNi2(As,P)2 single crystals usinghigh-resolution thermal-expansion, heat-capacity,Young-modulus and resistivitymeasurements is presented. The experimental data are complemented bydensity-functional calculations. The phase diagram of BaNi2(As,P)2 is shown tobe much richer than suggested by the original data of Kudo et al. [Phys. Rev.Lett. 109, 097002 (2012)]. The transition to the commensuratecharge-density-wave (C-CDW) is always preceded by a four-fold symmetry-breakingtransition associated with the long-range ordering of a strongly fluctuatingunidirectional incommensurate charge-density wave (I-CDW). Significantprecursors above the I-CDW and C-CDW transitions are seen in the thermalexpansion and resistivity and are particularly evident in the temperaturedependence of the $c/a$ ratio of the lattice parameters. Heat-capacitymeasurements of the crystals with a higher P content and a higher criticaltemperature of 3.2 K uncover a Debye-like behavior of a soft-phonon mode with avery low Debye temperature of roughly 15 K. Associated with this soft phononare unusually large thermal-expansion anomalies, resulting in logarithmicallydiverging uniaxial phonon Grueneisen parameters. Young-modulus data of thesehigher-Tc crystals exhibit a significant softening in both B1g and B2gchannels, which is argued to be incompatible with nematic criticality and israther associated with a broad phase transition to an hitherto unknownstructure. Possible origins of the increase in the superconducting criticaltemperature with P-substitution are discussed.

Charge-density-wave transitions, phase diagram, soft phonon and possible electronic nematicity: a thermodynamic investigation of BaNi2(As,P)2