A unique distortion in K1/3Ba2/3AgTe2: X-ray diffraction determination andelectronic band structure analysis of its incommensurately modulated structure

The incommensurately modulated structure of a square Te-net, namely that of K1/3Ba2/3AgTe2, is determined from single-crystal X-ray diffraction data w ithin a (3+1)D higher dimension formalism, The phase is shown-to crystalliz e in the monoclinic symmetry, P2(1)(alpha 0 gamma) superspace group with th e following lattice parameters; a = 4.6441(10) Angstrom, b = 4.6292(22) Ang strom, c = 23.765(9) Angstrom and beta = 101.28(2)degrees with q = 0.3248(6 )a* - 0.071(8)c*, that is, in a symmetry different from that reported for t he average structure (tetragonal) or that assumed from electron diffraction measurements (orthorhombic). After the Introduction of a crenel function f or the Te displacive description, the refinement converged to a residual fa ctor R = 0.033 for 2583 observed reflections and 115 parameters (R = 0.024 and 0.101 for 1925 main reflections and 658 first-order satellites, respect ively). The [Ag-2-Te-2] and the Ba/K layers are found to be only weakly mod ulated. The modulation of the square Te-net is, however, both substantial a nd unique. Namely, it results in two different units: a "V"-shaped Te-3 tri mer and a "W"-shaped Te-5 pentamer. To examine both unit types, which are s egregated in domains that aperiodically alternate within the Te layers, fir st principles electronic band structure calculations were carried out for t hree model commensurate structures using the tight-binding linear-muffin-ti n-orbital method (LMTO). The calculations show that the distorted structure s of V-pattern (model 2) and W-pattern (model 3) are more stable than the a verage structure (model 1) and that the V-pattern distortion provides a sli ghtly larger stabilization than does the W-pattern distortion, The Fermi su rface calculated for the average structure shows nesting vectors that are c onsistent with the occurrence of the V- and W-pattem distortions in the Te layers. However, these vectors do not predict the observed modulation vecto r of the incommensurately distorted structure, because the stabilization en ergy associated with the distortion is not mainly dominated by the energy l owering of the occupied band levels near the Fermi level.