  An investigation of the structural, thermodynamic, and electronic transport
properties of the isoelectronic chemical substitution series
Ce(Pd$_{1-x}$Ni$_x$)$_2$P$_2$ is reported, where a possible ferromagnetic
quantum critical point is uncovered in the temperature - concentration ($T-x$)
phase diagram. This behavior results from the simultaneous contraction of the
unit cell volume, which tunes the relative strengths of the Kondo and RKKY
interactions, and the introduction of disorder through alloying. Near the
critical region at $x_{\rm{cr}}$ $\approx$ 0.7, the rate of contraction of the
unit cell volume strengthens, indicating that the cerium $f$-valence crosses
over from trivalent to a non-integer value. Consistent with this picture, x-ray
absorption spectroscopy measurements reveal that while CePd$_2$P$_2$ has a
purely trivalent cerium $f$-state, CeNi$_2$P$_2$ has a small ($<$ 10 \%)
tetravalent contribution. In a broad region around $x_{\rm{cr}}$, there is a
breakdown of Fermi liquid temperature dependences, signaling the influence of
quantum critical fluctuations and disorder effects. Measurements of clean
CePd$_2$P$_2$ furthermore show that applied pressure has a similar initial
effect to alloying on the ferromagnetic order. From these results,
CePd$_2$P$_2$ emerges as a keystone system to test theories such as the
Belitz-Kirkpatrick-Vojta model for ferromagnetic quantum criticality, where
distinct behaviors are expected in the dirty and clean limits.
