The Basic and the Charge Density Wave Modulated Structures of NbS3-II

Abstract

The basic and the charge density wave (CDW) structures of the monoclinic $Nb{S}_3-II$ polymorph were studied by synchrotron x-ray diffraction, ab-initio calculation, simulation of electron diffraction patterns and by atomic-resolution transmission electron and low-temperature scanning tunneling microscopies. It is shown that the basic structure belongs to the space group $P{2}_1/m$ and is described with a unit cell, formed of four pairs of symmetry-related trigonal prismatic (TP) columns ($a_0$ = 0.96509(8) nm, $b_0$ = 0.33459(2) nm, $c_0$ = 1.9850(1) nm, ${\beta }_0$ = 110.695(4) deg), with all Nb and S atoms in $2e$ special positions. The two CDWs, with $\overrightarrow{q_1}$ = (0, 0.298,0) and $\overrightarrow{q_2}$ = (0, 0.352, 0), form their own modulation unit cells ($a_m$ = $2a_0$, $b_m$ = $b_0/q_{jb}$, $c_m$ = $c_0$, ${\beta }_m$ = ${\beta }_0$) and are ordered pairwise along adjacent isosceles TP columns. The symmetries of both $\overrightarrow{q_j}$ modes belong to the space group $Cm$ and are related according to the $2a$ special positions. If considered as long-period commensurate, the entire modulated structure with both CDWs included is best described with an enlarged unit cell ($a$ = $2a_0$, $b$ = $37b_0$, $c$ = $c_0$, $\beta$ = ${\beta }_0$), with all Nb and S atoms in $1a$ positions of the space group $P1$.

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