### Abstract

The incommensurately modulated structure of a square Te-net, namely that of K(1/3)Ba(2/3)AgTe_{2}, is determined from single-crystal X-ray diffraction data within a (3+1)D higher dimension formalism. The phase is shown to crystallize in the monoclinic symmetry, P2_{1}(α0γ) superspace group with the following lattice parameters: a = 4.6441(10) Å, b = 4.6292(12) Å, c = 23.765(9) Å, and β = 101.28(2)°with q = 0.3248(6)a* - 0.071(8)c*, that is, in a symmetry different from that reported for the average structure (tetragonal) or that assumed from electron diffraction measurements (orthorhombic). After the introduction of a crenel function for the Te displacive description, the refinement converged to a residual factor 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, respectively). The [Ag_{2}-Te_{2}] and the Ba/K layers are found to be only weakly modulated. The modulation of the square Te-net is, however, both substantial and unique. Namely, it results in two different units: a 'V'-shaped Te_{3} trimer and a 'W'-shaped Te_{5} pentamer. To examine both unit types, which are segregated in domains that aperiodically alternate within the Te layers, first principles electronic band structure calculations were carried out for three model commensurate structures using the tight-binding linear-muffin-tin-orbital method (LMTO). The calculations show that the distorted structures of V-pattern (model 2) and W-pattern (model 3) are more stable than the average structure (model 1) and that the V-pattern distortion provides a slightly larger stabilization than does the W-pattern distortion. The Fermi surface calculated for the average structure shows nesting vectors that are consistent with the occurrence of the V- and W-pattern distortions in the Te layers. However, these vectors do not predict the observed modulation vector of the incommensurately distorted structure, because the stabilization energy associated with the distortion is not mainly dominated by the energy lowering of the occupied band levels near the Fermi level.

Original language | English |
---|---|

Pages (from-to) | 1398-1409 |

Number of pages | 12 |

Journal | Inorganic Chemistry |

Volume | 39 |

Issue number | 7 |

DOIs | |

Publication status | Published - Apr 3 2000 |

### Fingerprint

### ASJC Scopus subject areas

- Inorganic Chemistry

### Cite this

_{2}: X-ray diffraction determination and electronic band structure analysis of its incommensurately modulated structure.

*Inorganic Chemistry*,

*39*(7), 1398-1409. https://doi.org/10.1021/ic991457g

**A unique distortion in K(1/3)Ba(2/3)AgTe _{2} : X-ray diffraction determination and electronic band structure analysis of its incommensurately modulated structure.** / Gourdon, O.; Hanko, Jason; Boucher, F.; Petricek, V.; Whangbo, M. H.; Kanatzidis, Mercouri G; Evain, M.

Research output: Contribution to journal › Article

_{2}: X-ray diffraction determination and electronic band structure analysis of its incommensurately modulated structure',

*Inorganic Chemistry*, vol. 39, no. 7, pp. 1398-1409. https://doi.org/10.1021/ic991457g

_{2}: X-ray diffraction determination and electronic band structure analysis of its incommensurately modulated structure. Inorganic Chemistry. 2000 Apr 3;39(7):1398-1409. https://doi.org/10.1021/ic991457g

}

TY - JOUR

T1 - A unique distortion in K(1/3)Ba(2/3)AgTe2

T2 - X-ray diffraction determination and electronic band structure analysis of its incommensurately modulated structure

AU - Gourdon, O.

AU - Hanko, Jason

AU - Boucher, F.

AU - Petricek, V.

AU - Whangbo, M. H.

AU - Kanatzidis, Mercouri G

AU - Evain, M.

PY - 2000/4/3

Y1 - 2000/4/3

N2 - The incommensurately modulated structure of a square Te-net, namely that of K(1/3)Ba(2/3)AgTe2, is determined from single-crystal X-ray diffraction data within a (3+1)D higher dimension formalism. The phase is shown to crystallize in the monoclinic symmetry, P21(α0γ) superspace group with the following lattice parameters: a = 4.6441(10) Å, b = 4.6292(12) Å, c = 23.765(9) Å, and β = 101.28(2)°with q = 0.3248(6)a* - 0.071(8)c*, that is, in a symmetry different from that reported for the average structure (tetragonal) or that assumed from electron diffraction measurements (orthorhombic). After the introduction of a crenel function for the Te displacive description, the refinement converged to a residual factor 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, respectively). The [Ag2-Te2] and the Ba/K layers are found to be only weakly modulated. The modulation of the square Te-net is, however, both substantial and unique. Namely, it results in two different units: a 'V'-shaped Te3 trimer and a 'W'-shaped Te5 pentamer. To examine both unit types, which are segregated in domains that aperiodically alternate within the Te layers, first principles electronic band structure calculations were carried out for three model commensurate structures using the tight-binding linear-muffin-tin-orbital method (LMTO). The calculations show that the distorted structures of V-pattern (model 2) and W-pattern (model 3) are more stable than the average structure (model 1) and that the V-pattern distortion provides a slightly larger stabilization than does the W-pattern distortion. The Fermi surface calculated for the average structure shows nesting vectors that are consistent with the occurrence of the V- and W-pattern distortions in the Te layers. However, these vectors do not predict the observed modulation vector of the incommensurately distorted structure, because the stabilization energy associated with the distortion is not mainly dominated by the energy lowering of the occupied band levels near the Fermi level.

AB - The incommensurately modulated structure of a square Te-net, namely that of K(1/3)Ba(2/3)AgTe2, is determined from single-crystal X-ray diffraction data within a (3+1)D higher dimension formalism. The phase is shown to crystallize in the monoclinic symmetry, P21(α0γ) superspace group with the following lattice parameters: a = 4.6441(10) Å, b = 4.6292(12) Å, c = 23.765(9) Å, and β = 101.28(2)°with q = 0.3248(6)a* - 0.071(8)c*, that is, in a symmetry different from that reported for the average structure (tetragonal) or that assumed from electron diffraction measurements (orthorhombic). After the introduction of a crenel function for the Te displacive description, the refinement converged to a residual factor 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, respectively). The [Ag2-Te2] and the Ba/K layers are found to be only weakly modulated. The modulation of the square Te-net is, however, both substantial and unique. Namely, it results in two different units: a 'V'-shaped Te3 trimer and a 'W'-shaped Te5 pentamer. To examine both unit types, which are segregated in domains that aperiodically alternate within the Te layers, first principles electronic band structure calculations were carried out for three model commensurate structures using the tight-binding linear-muffin-tin-orbital method (LMTO). The calculations show that the distorted structures of V-pattern (model 2) and W-pattern (model 3) are more stable than the average structure (model 1) and that the V-pattern distortion provides a slightly larger stabilization than does the W-pattern distortion. The Fermi surface calculated for the average structure shows nesting vectors that are consistent with the occurrence of the V- and W-pattern distortions in the Te layers. However, these vectors do not predict the observed modulation vector of the incommensurately distorted structure, because the stabilization energy associated with the distortion is not mainly dominated by the energy lowering of the occupied band levels near the Fermi level.

UR - http://www.scopus.com/inward/record.url?scp=0034599286&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034599286&partnerID=8YFLogxK

U2 - 10.1021/ic991457g

DO - 10.1021/ic991457g

M3 - Article

C2 - 12526442

AN - SCOPUS:0034599286

VL - 39

SP - 1398

EP - 1409

JO - Inorganic Chemistry

JF - Inorganic Chemistry

SN - 0020-1669

IS - 7

ER -