Density functional theory investigation of titanium-tungsten superlattices: Structure and mechanical properties

Sven P. Rudin

Phys. Rev. B 86, 184104 – Published 9 November 2012

Abstract

Titanium (Ti) exhibits the body-centered crystal structure only at high temperatures. The temperature range of this so-called $β$ -Ti phase can be expanded by alloying Ti with tungsten (W). Rather than placing the W atoms in the $β$ -Ti crystal at random, this work applies density functional theory calculations to explore the consequences of an orderly placement in Ti/W superlattice structures. In all examples the W layer remains bcc-like. The stacking direction of the Ti/W superlattice drives the core of the Ti layer toward either a locally hcp- or $ω$ -Ti structure, though the latter is mechanically unstable for all but the thinnest W layers. The relative thicknesses of the W and Ti layers as well as the stacking direction influence the formation energies, which consistently fall within a range corresponding roughly to room temperature. Superlattices allow a choice of stacking direction and layer thicknesses, both strongly influencing the material's strength, though not improving the mechanical properties as observed for Ti with randomly placed W particles.

Received 10 September 2012

DOI:https://doi.org/10.1103/PhysRevB.86.184104

Authors & Affiliations

Sven P. Rudin

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

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Vol. 86, Iss. 18 — 1 November 2012

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Figure 1
Geometries of optimized Ti/W superlattices with 9 Ti and 9 W monolayers for (a) [001], (b) [011], and (c) [111] stacking. Small and large spheres represent the Ti and W atoms, respectively. For all stacking directions the W atoms’ local environment remains essentially bcc-like, while a displacement of the Ti atoms away from bcc-like toward hcp-like or $ω$ -like becomes apparent in the core of the Ti layer. The displacements occur perpendicular to the [001] and [011] stacking directions (toward hcp) and parallel to the [111] stacking direction (toward $ω$ ).Reuse & Permissions
Figure 2
Calculated diffraction patterns for Ti/W superlattices. Solid lines represent Ti/W superlattices; dashed lines represent systems with only Ti or W. (a) The diffraction patterns for W-rich superlattices closely approximate the [011] peak of bcc W (with $a = 3.17$ Å). (b) The diffraction patterns for Ti-rich superlattices resemble those of strained hcp and $ω$ -Ti. (c) The diffraction pattern for the Ti $_{9}$ /W $_{9}$ [001] superlattice centers around a large peak at 40.1 $^{\circ}$ stemming from {019} planes in a tetragonally strained bcc W system. This pattern changes little when nine monolayers of the strained bcc W alternate with a vacuum layer of the same thickness (SL1); the large peak shifts to 39.6 $^{\circ}$ only when the strained bcc W appears as part of a superlattice (SL2) with the same period as the Ti $_{9}$ /W $_{9}$ [001] superlattice.Reuse & Permissions
Figure 3
Calculated gamma-point phonons for Ti/W superlattices with [111] stacking, nine ( $n_{Ti} + n_{W} = 9$ ) monolayers, and two atoms per monolayer. The frequencies are plotted with a Gaussian smearing of 0.02 THz. (Each superlattice unit cell corresponds to three stacked $ω$ -Ti unit cells with some Ti atoms replaced by W and allowed to relax.) (a) Titanium in the $ω$ structure. (b) $ω$ -Ti with one of two atoms in a honeycomb layer replaced by W. (c) $ω$ -Ti with one hexagonal layer replaced by W. (d) $ω$ -Ti with W replacing a hexagonal layer and one of two atoms in an adjacent honeycomb layer. (e) $ω$ -Ti with a honeycomb layer replaced by W.Reuse & Permissions
Figure 4
Optimized unit cell parameters for 18 atomic layer Ti/W superlattices as a function of number of W atomic layers. (a) The in-plane lattice vectors span the base angle. (b) The lattice constant ratio compares the lattice constant in the stacking direction to the in-plane lattice constant; the plotted ratios are divided by nine for [001] and [011] stacking and by six for [111] stacking. Dotted lines serve to guide the eye. Horizontal lines indicate the ideal values of the unit cell parameters for the bcc and hcp structures at the W-rich and Ti-rich ends, respectively.Reuse & Permissions
Figure 5
Calculated formation energy for 18 atomic layer Ti/W superlattices as a function of number of W atomic layers. The formation energy describes the energy needed to form the superlattices relative to bcc W and hcp Ti. Dotted lines serve to guide the eye.Reuse & Permissions
Figure 6
Calculated tensile stress-strain curves for 18-atomic layer Ti/W superlattices with (a) one, (b) nine, and (c) 17 W monolayer(s). For comparison, solid lines show the stress calculated for hcp Ti, $ω$ Ti, and bcc W with strain applied in the crystallographic directions corresponding to their orientation in the superlattices.Reuse & Permissions

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