Density functional theory calculations of the turbostratically disordered compound $[(\mathrm{SnSe}){}_{1+y}{]}_{m}({\mathrm{VSe}}_{2}){}_{n}$

Density functional theory calculations of the turbostratically disordered compound $[(SnSe)_{1 + y}]_{m} ({VSe}_{2})_{n}$

Sven P. Rudin and David C. Johnson

Phys. Rev. B 91, 144203 – Published 30 April 2015

Abstract

Among composite materials that layer constituent substances of nanoscale thicknesses, ${[(SnSe)}_{1 + y}]_{m} ({VSe}_{2})_{n}$ emerges as an example where the constituents retain incommensurate lattice structures. Perpendicular to the stacking direction, the system exhibits random translations and random rotations on average, i.e., turbostratic disorder, with local regions showing twelvefold diffraction patterns. Earlier theoretical work on these structures showed that combining density functional theory with an empirical treatment of the van der Waals interaction gave structural parameters in good agreement with experiment, but no attempt was made to examine the relative orientations. Here we approximate the extended system with one extended constituent and one finite constituent, which allows the treatment of all relative orientations on equal footing. The calculations show how the twelvefold periodicity follows from how the ions of the SnSe layer lock in with favored positions relative to the ${VSe}_{2}$ layer, and the associated energy scale supports arguments for the overall turbostratic disorder. The success of this approximation in describing the structural parameters of the extended ${[(SnSe)}_{1 + y}]_{m} ({VSe}_{2})_{n}$ system encourages its use for other properties and for other similar systems with other chemistries.

Received 25 February 2015

DOI:https://doi.org/10.1103/PhysRevB.91.144203

Authors & Affiliations

Sven P. Rudin

Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

David C. Johnson

Department of Chemistry and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 91, Iss. 14 — 1 April 2015

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Top view of typical (a) high- and (b) low-symmetry unit cells employed in the current calculations. This current work approximates the incommensurate ${[(SnSe)}_{1 + y}]_{m} ({VSe}_{2})_{n}$ structures with infinite ${VSe}_{2}$ planes that sandwich finite SnSe islands (initially given a NaCl-like crystal structure with differing $z$ components for Sn and Se in the stacking direction). The cell is defined in the plane by $N_{V}^{2} {VSe}_{2}$ unit cells (shown in red are the V sites for a $4 \times 4$ cell). Over this lies a layer of SnSe (gray and green ions), situated with (1) an angle $δ$ between the two layers' lattice vectors and (2) a relative in-plane offset d between the center of the cell and the central Se and Sn ions.
Reuse & Permissions
Figure 2
Optimized structural parameters for SnSe islands sandwiched between ${VSe}_{2}$ layers as a function of island size and for a sequence of unit cell sizes given by the ${VSe}_{2}$ grid. Solid horizontal lines show the experimental value. The parameters are averaged over the appropriate ions or bonds in the unit cell. Calculations optimize optimally placed initial structures [ $δ = 15^{\circ}, d = (0, 0)$ ; see text].
Reuse & Permissions
Figure 3
Calculated energies for a SnSe “dimer” (island with zero radius) sandwiched between $4 \times 4 {VSe}_{2}$ layers with offsets scanned across a ${VSe}_{2}$ unit cell. Structures are not relaxed. The minimum occurs at $d = (0, 0)$ , where the dimer sits centered over a Se triangle and in line with a V ion (inset); the maximum is at $d = (- 1 / 3, - 1 / 3)$ , where the dimer sits centered in a V triangle with the Sn ion adjacent to a Se ion (inset). The latter geometry but with the dimer's Se ion adjacent to a Se ion (not shown) occurs at $d = (+ 1 / 3, + 1 / 3)$ , where the energy surface exhibits a third point with zero slope.
Reuse & Permissions
Figure 4
(a) Calculated energies for SnSe islands with 69 Sn (Se) ions sandwiched between $12 \times 12 {VSe}_{2}$ layers at $δ = 0^{\circ}$ (blue) and $δ = 15^{\circ}$ (red) with offsets scanned across a ${VSe}_{2}$ unit cell and (b) energy calculated by adding the energies of 69 dimer systems (Fig. 3) with the SnSe dimer located at in-plane positions of the 69 Sn (Se) ions. Structures are not relaxed.
Reuse & Permissions
Figure 5
Calculated average, maximum, and minimum energies of scans across $d$ for SnSe islands sandwiched between ${VSe}_{2}$ layers. The structures are not relaxed. A comparison of the results for islands with 13 Sn (Se) ions calculated in unit cells with $10 \times 10$ and $12 \times 12 {VSe}_{2}$ at $δ = 0^{\circ}$ and $δ = 15^{\circ}$ shows minor differences but not on a scale relevant to current conclusions (both unit cells are large enough to keep periodic versions of the islands well separated).
Reuse & Permissions
Figure 6
Calculated energy maxima and minima at $δ = 15^{\circ}$ , relative to average energy, for SnSe islands sandwiched between ${VSe}_{2}$ layers. The structures are not relaxed. The dashed lines represent linear fits with slopes of +24 meV/dimer and $- 26$ meV/dimer.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Density functional theory calculations of the turbostratically disordered compound $[(SnSe)_{1 + y}]_{m} ({VSe}_{2})_{n}$

Sven P. Rudin and David C. Johnson

Phys. Rev. B 91, 144203 – Published 30 April 2015

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review B

covering condensed matter and materials physics

Density functional theory calculations of the turbostratically disordered compound [(SnSe)1+y]m(VSe2)n

Sven P. Rudin and David C. Johnson

Phys. Rev. B 91, 144203 – Published 30 April 2015

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Density functional theory calculations of the turbostratically disordered compound $[(SnSe)_{1 + y}]_{m} ({VSe}_{2})_{n}$