We follow the evolution of the electronic properties of the titled homologous series when n as well as the atomic type of A and M are varied where for n = 1, A = Ca, Sr and M = Rh, Ir while for n = 3, A = Ca, Sr and M = Rh. The crystal structure of n = 1 members is known to be CaRh2B2-type (Fddd), while that of n = 3 is Ca3Rh8B6-type (Fmmm); the latter can be visualized as a stacking of structural fragments from AM3B2 (P6/mmm) and AM2B2. The metallic properties of the n = 1 and 3 members are distinctly different: on the one hand, the n = 1 members are characterized by a linear coefficient of the electronic specific heat γ ≈ 3 mJ mol−1 K−2, a Debye temperature θD ≈ 300 K, a normal conductivity down to 2 K and a relatively strong linear magnetoresistivity for fields up to 150 kOe. The n = 3 family, on the other hand, exhibits γ ≈ 18 mJ mol−1 K−2, θD ≈ 330 K, a weak linear magnetoresistivity and an onset of superconductivity (for Ca3Rh8B6, Tc = 4.0 K and Hc2 = 14.5 kOe, while for Sr3Rh8 B6, Tc = 3.4 K and Hc2 ≈ 4.0 kOe). These remarkable differences are consistent with the findings of the electronic band structures and density of state (DOS) calculations. In particular, satisfactory agreement between the measured and calculated γ was obtained. Furthermore, the Fermi level, EF, of Ca3Rh8B6 lies at almost the top of a pronounced local DOS peak, while that of CaRh2B2 lies at a local valley: this is the main reason behind the differences between the, e.g., superconducting properties. Finally, although all atoms contribute to the DOS at EF, the contribution of the Rh atoms is the strongest.
