Valence State Driven Site Preference in the Quaternary Compound Ca₅MgAgGe₅: An Electron-Deficient Phase with Optimized Bonding

Abstract

The quaternary phase Ca 5 Mg 0.95 Ag 1.05(1) Ge 5 (3) was synthesized by high-temperature solid-state techniques, and its crystal structure was determined by single-crystal diffraction methods in the orthorhombic space group Pnma -Wyckoff sequence c 12 with a = 23.1481(4) Å, b = 4.4736(1) Å, c = 11.0128(2) Å, V = 1140.43(4) Å 3 , Z = 4. The crystal structure can be described as linear intergrowths of slabs cut from the CaGe (CrB-type) and the CaMGe (TiNiSi-type; M = Mg, Ag) structures. Hence, 3 is a hettotype of the hitherto missing n = 3 member of the structure series with the general formula R 2+n T 2 X 2+n , previously described with n = 1, 2, and 4. The member with n = 3 was predicted in the space group Cmcm -Wyckoff sequence f 5 c 2 . The experimental space group Pnma (in the nonstandard setting Pmcn) corresponds to a klassengleiche symmetry reduction of index two of the predicted space group Cmcm. This transition originates from the switching of one Ge and one Ag position in the TiNiSi-related slab, a process that triggers an uncoupling of each of the five 8f sites in Cmcm into two 4c sites in Pnma. The Mg/Ag site preference was investigated using VASP calculations and revealed a remarkable example of an intermetallic compound for which the electrostatic valency principle is a critical structure-directing force. The compound is deficient by one valence electron according to the Zintl concept, but LMTO electronic structure calculations indicate electronic stabilization and overall bonding optimization in the polyanionic network. Other stability factors beyond the Zintl concept that may account for the electronic stabilization are discussed. (3) was synthesized by high-temperature solid-state techniques, and its crystal structure was determined by single-crystal diffraction methods in the orthorhombic space group Pnma − Wyckoff sequence c 12 with a = 23.1481(4) Å, b = 4.4736(1) Å, c = 11.0128(2) Å, V = 1140.43(4) Å 3 , Z = 4. The crystal structure can be described as linear intergrowths of slabs cut from the CaGe (CrB-type) and the CaMGe (TiNiSi-type; M = Mg, Ag) structures. Hence, 3 is a hettotype of the hitherto missing n = 3 member of the structure series with the general formula R 2+n T 2 X 2+n , previously described with n = 1, 2, and 4. The member with n = 3 was predicted in the space group Cmcm − Wyckoff sequence f 5 c 2 . The experimental space group Pnma (in the nonstandard setting Pmcn) corresponds to a klassengleiche symmetry reduction of index two of the predicted space group Cmcm. This transition originates from the switching of one Ge and one Ag position in the TiNiSi-related slab, a process that triggers an uncoupling of each of the five 8f sites in Cmcm into two 4c sites in Pnma. The Mg/Ag site preference was investigated using VASP calculations and revealed a remarkable example of an intermetallic compound for which the electrostatic valency principle is a critical structure-directing force. The compound is deficient by one valence electron according to the Zintl concept, but LMTO ...

Structure and Bonding of an Intergrowth Phase Ca7Ag2+xGe7–x (x ≈ 2/3) Featuring a Zintl‐Type Polyanionic Chain

“…Eu 2– x Mg 2– y Ge 3 ( x = 0.1; y = 0.5) represents an interesting case for which the electron deficiency is triggered by geometrical requirements, i.e., a high density of cations resulting in defects at cation sites. Recently, we observed that one‐electron deficiency in the quasi‐ternary phase Ca 5 MgAgGe 5 is the result of local symmetry breaking of the Ge 4 chains from C 2 h to C s which is caused by Ag/Mg partial ordering as dictated by higher Madelung's part in the lattice energy 18…”

“…Nevertheless, targeted synthesis of novel Zintl polyanions may be achievable through appropriate mixtures of chemically diverse cationic species in an adequate ratio. Such a paradigm is well reflected in the recently discovered structure series Ca 2+ n Ag 2+ x Ge 2– x + n ,17,18 in which the polarizing Ag + cation can be partially substituted by divalent Mg or trivalent Al. It represents the Ca sub‐family of the broader structural homology A 2+ n T 2 X 2+ n ( X = Si, Ge, Sn; T = transition metal; A = electropositive s ‐metal), which were rationalized by Zhao and Parthé (1989)19 as intergrowths of fragments cut from the TiNiSi‐ and the CrB‐type structures.…”

“…But, only three homologues were originally described: (1) the Hf 3 Ni 2 Si 3 type ( n = 1, space group Cmcm );20 (2) the Zr 2 CoSi 2 type ( n = 2, space group C 2/ m );21 and (3) the Sc 3 NiSi 3 type ( n = 4, space group C 2/ m ) 22. Alkaline‐earth homologues have been described only recently and, unlike these three phases mentioned, those Ca homologues often comply with the Zintl–Klemm concept 17,18,23…”

“…The latter features isolated Ge 4– , dimeric Ge 2 6– and tetrameric Ge 4 10– units, with enhanced Ag–Ge polar‐covalent interactions indicating that Ag and other late transition metals may be used as polarizing cations similar to Li or Mg 4. Interestingly, the unique representative of the n = 3 member could be obtained only by using a mixture of monovalent Ag and divalent Mg atoms, resulting in the quaternary phase, Ca 5 MgAgGe 5 18. Its structure features isolated Ge 4– and tetrameric Ge 4 10– Zintl anions, instead of the expected Ge 3 8– trimeric chain.…”

Synergistic Geometrical and Electronic Features in the Intermetallic Phases Ca2AgM2, Ca2MgM2, and Ca2GaM2 (M = Pd, Pt)

“…[25] Partial mixing of Mg and Ag in Ca 5 MgAgGe 5 also results in Ca-Ag/Mg distances between 3.18 and 3.30 Å. [26] The bridging atoms, Mg or Ag, are in turn surrounded by eight Ca in their second coordination sphere in a strongly distorted square prismatic arrangement ( Figure 1c). This is in contrast to Pd or Pt atoms forming the dimers that are each surrounded by six Ca atoms in a distorted trigonal prismatic environment with Ca-Pd/Pt distances as short as 2.966(2) or 2.975(1) Å in Ca 2 AgPd 2 or Ca 2 AgPt 2 .…”