Two-dimensional nanomaterials such as MoS 2 are of great interest both because of their novel physical properties and their applications potential. Liquid exfoliation, an important production method, is limited by our inability to quickly and easily measure nanosheet size, thickness or concentration. Here we demonstrate a method to simultaneously determine mean values of these properties from an optical extinction spectrum measured on a liquid dispersion of MoS 2 nanosheets. The concentration measurement is based on the size-independence of the low-wavelength extinction coefficient, while the size and thickness measurements rely on the effect of edges and quantum confinement on the optical spectra. The resultant controllability of concentration, size and thickness facilitates the preparation of dispersions with pre-determined properties such as high monolayer-content, leading to first measurement of A-exciton MoS 2 luminescence in liquid suspensions. These techniques are general and can be applied to a range of two-dimensional materials including WS 2 , MoSe 2 and WSe 2 .

The phenomenon of a partial 2H 1T phase transition within multiwalled WS 2 nanotubes under 5 substitutional Rhenium doping is discovered by means of high-resolution transmission electron microscopy. Using density-functional calculations for the related MoS 2 compound we consider a possible origin of this phase transition, which was known formerly only for WS 2 and MoS 2 intercalated by alkali metals. An interplay between the stability of layered or nanotubular forms of 2H and 1T allotropes is found to be intimately related with their electronic structures and electro-donating ability of an impurity. 10 65 Notes

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Typically, polarization and strain in ferroelectric materials are coupled, leading to the generally accepted direct relation between polarization and unit-cell tetragonality. Here, by means of high-resolution transmission electron microscopy we map, on the unit-cell scale, the degree of tetragonality and the displacements of cations away from the centrosymmetry positions in an ultrathin epitaxial PbZr(0.2)Ti(0.8)O(3) film on a SrRuO(3) electrode layer deposited on a SrTiO(3) substrate. The lattice is highly tetragonal at the centre of the film, whereas it shows reduced tetragonality close to the interfaces. Most strikingly, we find that the maximum off-centre displacements for the central area of the film do not scale with the tetragonality. This challenges the fundamental belief in a strong polarization-tetragonality coupling in PbTiO(3)-based ferroelectrics, at such thicknesses. Furthermore, a systematic reduction of the atomic displacements is measured at the interfaces, suggesting that interface-induced suppression of the ferroelectric polarization plays a critical role in the size effect of nanoscale ferroelectrics.

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