Crystal Structures, Electronic Structures, and Physical Properties of Tl₄MQ₄ (M = Zr or Hf; Q = S or Se)

The ternary thallium chalcogenides of the general formula Tl4MQ4 (M = Zr or Hf; Q = S or Se) were obtained from high-temperature reactions without air. These sulfides and selenides are isostructural, crystallizing in the triclinic system with space group P1̅ and Z = 5, in contrast to Tl4MTe4 compounds that adopt space group R3̅. The unit cell parameters for Tl4ZrS4 are as follows: a = 9.0370(5) Å, b = 9.0375(5) Å, c = 15.4946(9) Å, α = 103.871(1)°, β = 105.028(1)°, γ = 90.138(1)°, and V = 1183.7(1) Å3. In contrast to the corresponding tellurides, the sulfides and selenides exhibit edge-shared MQ6 octahedra, propagating along the c axis in a zigzag manner. All elements occur in the most common oxidation states, according to the formulation (Tl+)4M4+(Q2−)4. Electronic structure calculations predict energy band gaps of 1.7 eV for Tl4ZrS4 and 1.3 eV for Tl4ZrSe4, which are in accordance with the large resistivity values observed experimentally.