  The discovery of the 1144-phase, e.g. CaKFe$_4$As$_4$, creates opportunities
to build novel intermetallics with alternative stacking of two parent
compounds. Here we formalize the idea and introduce a concept, namely
hetero-crystals (HC), to describe a unique class of bulk crystalline solids
with such $A$-$B$ stacking (including 1144-phases and beyond). HC generalizes
hetero-structures from few-layer or thin-film semi-conductors to bulk
intermetallics. We illustrate the HC concept with the example of 1144-phases.
Theoretically, four families of phosphides \textit{AB}(TM)$_4$P$_4$ (TM=Fe, Ru,
Co, Ni) are investigated by first-principles calculations, wherein
configurational, vibrational and electronic degrees of freedom are considered.
It predicts a variety of stable 1144-phases (especially Ru- and Fe-phosphides).
Stability rules are found and structural/electronic properties are discussed.
Experimentally, we synthesize high-purity CaKRu$_4$P$_4$ as a proof of
principle example of such a HC. The synthetic method is simple and can be
applied to other HC. Moreover, HC alludes to a new strategy to explore complex
multi-component compounds, facilitated by a new phase diagram coordinated by
collective descriptors.
