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 Tl(4)MQ(4) (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 P1 and Z = 5, in contrast to Tl(4)MTe(4) compounds that adopt space group R3. The unit cell parameters for Tl(4)ZrS(4) are as follows: a = 9.0370(5) ?, b = 9.0375(5) ?, c = 15.4946(9) ?, α = 103.871(1)°, β = 105.028(1)°, γ = 90.138(1)°, and V = 1183.7(1) ?(3). In contrast to the corresponding tellurides, the sulfides and selenides exhibit edge-shared MQ(6) octahedra, propagating along the c axis in a zigzag manner. All elements occur in the most common oxidation states, according to the formulation (Tl(+))(4)M(4+)(Q(2-))(4). Electronic structure calculations predict energy band gaps of 1.7 eV for Tl(4)ZrS(4) and 1.3 eV for Tl(4)ZrSe(4), which are in accordance with the large resistivity values observed experimentally.