Structure of the two-dimensional incommensurate charge-density wave in(PO2)4(WO

Abstract

The incommensurate charge-density waves ͑CDW's͒ in the mϭ4 phosphate bronze (PO 2) 4 (WO 3) 2m have been studied by synchrotron-radiation x-ray scattering. The CDW is found to correspond to a 2-q state for all temperatures below the first phase transition at T c1 ϭ80 K. The second phase transition at T c2 ϭ52 K is found to involve the development of mixed second-order satellites within the primary CDW. The incommensurately modulated structure has been determined at Tϭ20 K. The structure remains orthorhombic down to T ϭ20 K. At 20 K the lattice parameters are aϭ5.294(1) Å, bϭ6.591(2) Å, and cϭ17.415(16) Å. The two-dimensional CDW is characterized by the modulation wave vectors q ជ 1 ϭ͓0.330(2),0.292(2),0.000(2)͔ and q ជ 2 ϭ(Ϫ0.330,0.292,0). The (3ϩ2)D superspace group was found as P2 1 2 1 2 1 (␣,␤,0)(Ϫ␣,␤,0). The primary CDW comprises the satellite reflections (hklm 1 m 2) with (m 1 m 2) equal to (Ϯ1,0) and (0,Ϯ1). Below T c2 additional satellite reflections develop, that correspond to (m 1 m 2)ϭϮ(1,Ϫ1). Accordingly, harmonic modulation amplitudes ͑1,0͒, ͑0,1͒, and (1,Ϫ1) were incorporated into the structure model. Refinement against 4970 observed reflection intensities resulted in a fit with Rϭ0.039. The periodic lattice distortion shows that the CDW is located at the centers of the WO 3 slabs. The CDW is interpreted in terms of the formation of clusters of six tungsten atoms, that are linked together to form larger clusters of 12 to 18 atoms.

Superspace crystallography: a key to the chemistry and properties

“…Low-dimensional bands of the WO 3 slabs cause CDW instabilities resulting in a transition into an incommensurately modulated state. The incommensurate CDW structures of the m = 4 and m = 10 compounds have been refined; in both cases, the modulation is due to two-dimensional CDW confined to the displacements of the W atoms (Lü decke et al, 2000(Lü decke et al, , 2001Roussel et al, 2000).…”

Equivalence of superspace groups

“…(b) Gao et al (1990). (e) Ludecke et al (2001); an extensive review of basic structures and CDW transitions of the phosphate bronzes (PO 2 ) 4 (WO 3 ) 2m (2 < m < 14) is given by Roussel et al (2000). (d) TTF (tetrathiafulvalene) and TCNQ (tetracyanoquinodimethane), Bouveret & Megtert (1989).…”

Crystal structure of monophosphate tungsten bronze K1.33P4W8O32 at 110 K

“…The commensurate wavevector q ~0.5a* Fig. 1 View of the structure of (PO 2 ) 4 (WO 3 ) 8 15 along b showing typical pseudo-pentagonal channels in this MPTBp. The WO 6 octahedra and PO 4 tetrahedra are indicated in light and dark grey, respectively.…”