DOI: 10.15125/bath-00314
title: Supporting data for article "Strain-induced phonon shifts in tungsten disulfide nanoplatelets and nanotubes"

description: The relationship between structure and properties has been followed for different nanoscale forms of tungsten disulfide (2H-WS2) namely exfoliated monolayer and few-layer nanoplatelets, and nanotubes. The similarities and differences between these nanostructured materials have been examined using a combination of optical microscopy, scanning and high-resolution transmission electron microscopy (SEM and HRTEM) and atomic force microscopy (AFM). Photoluminescence (PL) and Raman spectroscopy have also been used to distinguish between monolayer and few-layer material. Strain induced phonon shifts have been followed from the changes in the positions of the A1g and E2g1 Raman bands during uniaxial deformation. This has been modelled for monolayer using density functional theory (DFT) with excellent agreement between the measured and predicted behaviour. It has been found that as the number of WS2 layers increases for few-layer crystals or nanotubes, the A1g mode hardens whereas the E2g1 mode softens. This is believed to be due to the A1g mode, which involves out of plane atomic movements, being constrained by the increasing number of WS2 layers whereas easy sliding reduces stress transfer to the individual layers for the E2g1 mode, involving only in-plane vibrations. This finding has enabled the anomalous phonon shift behaviour in earlier pressure measurements on WS2 to be resolved, as well as similar effects in other transition metal dichalcogenides, such as molybdenum disulfide (MoS2), to be explained.

This dataset contains supporting data for the density functional theory calculations which were the part of this work carried out at the University of Bath.The two zipped files contain all the input files supplied to the Quantum Espresso package for the two cases of pure hydrostatic strain and pure shear strain.
description: See R. M. Martin, "Electronic Structure: Basic Theory and Practical Methods", Cambridge UP, for a tutorial introduction to the computational methodology, plus citations in the associated article to the publications of the authors of the Quantum Espresso code.
description: The two zipped files contain all the input files supplied to the Quantum Espresso package for the two cases of pure hydrostatic strain and pure shear strain applied to a WS2 monolayer. 

Use is as follows: 

For each strain, the WS2 monolayer structure is relaxed so that atomic positions (specifically the sulphur atom heights) can respond. A final self-consistent calculation is then carried out for the relaxed structure. The phonon modes are then calculated at the Gamma and M points. After each phonon calculation, the acoustic sum rule is imposed as described in the Quantum Espresso documentation. From the phonon values obtained at each strain, the rates of shift of phonon frequency with hydrostatic and shear strains can be calculated and these can be combined with the experimentally deduced amounts of shear and hydrostatic deformation (taking into account the Poisson's ratio of the matrix applying the distortion, which causes the experimental strain state not to be a pure one) as detailed in the associated publication and the related earlier paper PHYSICAL REVIEW B 87, 081307(R) (2013).

The input files are representative ones: a large number of calculations were carried out exploring different choices of pseudopotential and convergence criteria and not all results were presented in the paper. The input files given produced well-converged results and a good match to the zero-strain experimental phonon frequencies.
description: Further relevant documentation may be found in the following resources.

   Quantum ESPRESSO Foundation, and MaX Centre of Excellence,   n.d.   Quantum ESPRESSO.            Available from: https://www.quantum-espresso.org/.