We explore the factors stabilizing
one member of the diverse structures
encountered in Ln–T–E systems (Ln = lanthanide or similar
early d-block element, T = transition metal, E = p-block element):
the HoCoGa5 type, an arrangement of atoms associated with
unconventional superconductivity. We first probe the boundaries of
its stability range through the growth and characterization of ScTGa5 crystals (T = Fe, Co, Ni). After confirming that these compounds
adopt the HoCoGa5 type, we analyze their electronic structure
using density functional theory (DFT) and DFT-calibrated Hückel
calculations. The observed valence electron count range of the HoCoGa5 type is explained in terms of the 18-n rule,
with n = 6 for the Ln atoms and n = 2 for the T sites. The role of atomic sizes is investigated with
DFT-chemical pressure (DFT-CP) analysis of ScNiGa5, which
reveals negative pressures within the Ga sublattice as it stretches
to accommodate the Sc and T atoms. This CP scheme is consistent with
HoCoGa5-type gallides only being observed for relatively
small Ln and T atoms. These conclusions account for the relative positions
of the HoCoGa5, BaMg4Si3, and Ce2NiGa10 types in a structure map, demonstrating
how combining the 18-n and CP schemes can guide our
understanding of Ln–T–E systems.