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A modified embedded atom method potential for the titanium–oxygen system
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Modelling Simul. Mater. Sci. Eng. 23 015006 (http://iopscience.iop.org/0965-0393/23/1/015006) View the table of contents for this issue, or go to the journal homepage for more
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Modelling and Simulation in Materials Science and Engineering Modelling Simul. Mater. Sci. Eng. 23 (2015) 015006 (18pp)
doi:10.1088/0965-0393/23/1/015006
A modified embedded atom method potential for the titanium–oxygen system W J Joost, S Ankem and M M Kuklja Department of Materials Science and Engineering, University of Maryland, College Park, MD 20782, USA E-mail:
[email protected] Received 29 July 2014, revised 25 October 2014 Accepted for publication 7 November 2014 Published 16 December 2014 Abstract
Small concentrations of impurity atoms can affect the behavior of metal alloys in many ways of interest to the science and engineering community. In some cases, such as for oxygen (O) interstitials and twins or dislocations in titanium (Ti) alloys, these interactions can be difficult to study experimentally due to the small time and length scales of the governing mechanisms. Theory and atomic-scale modeling offers a path toward understanding materials at very high resolution using a variety of techniques ranging from ab initio methods such as density functional theory (DFT) to empirical potential methods such as the Modified Embedded Atom Method (MEAM). In this study we present the first published MEAM potential for the Ti–O system; the potential is fit to experimental measurements and DFT calculations for the lattice constants, elastic constants and thermodynamic characteristics of several Ti–O structures with O concentration between 0 and 50 at%. We validate the effectiveness of the new potential by successfully reproducing properties such as lattice constants, elastic constants and diffusion energy barriers for other structures. In doing so, we have calculated and report properties for two new stable structures of TiO: a CsCl structure and a zinc blende structure. We also report the first theoretical study on the effects of O concentration on the elastic constants of hexagonal close packed Ti without the confounding effects of changing supercell size. Overall, this new potential will enable interrogation of Ti and O interactions at time and length scales below those available experimentally and above the range accessible by DFT. Keywords: titanium, oxygen, interatomic potential, potential fitting (Some figures may appear in colour only in the online journal)
0965-0393/15/015006+18$33.00
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Modelling Simul. Mater. Sci. Eng. 23 (2015) 015006
W J Joost et al
1. Introduction
Titanium (Ti) and its oxides have broad technical relevance as structural, electronic and functional materials. Titanium oxides, particularly TiO2 , are used in many industrial and commercial applications including pigments and as electronic materials [1]. Structural Ti alloys exhibit excellent strength, toughness, corrosion resistance and high temperature stability and have thus been the subject of extensive metallurgical research for several decades [2]. The Ti–O system is unique from most metal-gaseous element combinations in several important ways. For example, a larger number of phases exist—structural information is reported for at least 26 different Ti–O structures—and the solubility of O in hexagonal close packed (hcp) Ti is up to 33 at% at room temperature [3]. The high solubility of O in metallic Ti presents unique opportunities for tailoring the mechanical behavior of Ti alloys; O is a known α stabilizer that generally increases strength while reducing ductility in Ti [4]. Further, the presence of O interstitials may affect the deformation characteristics of Ti alloys by impeding the growth of twins. Prior experimental work combined with a crystallographic model suggests that O interstitial sites are not conserved during the shearing process associated with twin growth and the interstitials thus interfere with twin growth in body centered cubic (bcc) Ti [5]. In addition, recent experimental evidence indicates that {1 0 1¯ 2} twin growth rate in hcp Ti is decreased by the presence of O interstitials, with implications for room temperature creep and structural performance [6–8]. Very recent DFT calculations by Ghazisaeidi and Trinkle provide additional clarity on the relationship between O interstitials and twins in hcp Ti, demonstrating that both attractive and repulsive O interstitial sites exist in the vicinity of a twin boundary and the calculated energy of these sites is sensitive to supercell size [9]. Creep and deformation in Ti alloys is of critical importance for numerous applications and while many experimental measurements and ab initio calculations have been dedicated to studying the Ti–O system, a gap exists in our ability to probe behavior at length scales and timescales below those accessible experimentally and above those accessible using first-principles techniques. Simulations using classical potentials provide an opportunity to explore material behavior at atomic length scales, while the modest computational requirements allow simulation of millions of atoms for practically meaningful times. Here we present a new modified embedded atom method (MEAM) potential that can be used for atomistic calculations of the Ti–O system. The potential is fit to the lattice constants, cohesive energies and elastic constants of rock salt TiO, α TiO (monoclinic) and Ti3 O2 (hexagonal), the relative site energies of the three most prevalent O interstitial sites in hcp Ti and the diffusion barrier for one of the many diffusion pathways of O in hcp Ti. The performance of the new potential is demonstrated by calculating the properties of many Ti–O structures and comparing to experimental and ab initio results.
2. Computational methods
We employed two computational techniques: the MEAM for which a Ti–O interatomic potential is the objective of this study and DFT in order to produce fitting targets and validation tests for the MEAM potential. In total, we calculated properties for 11 different Ti–O structures in order to conduct a robust survey of bond distances, angles, O concentrations and other important characteristics. The relevant input and output files for the DFT and MEAM relaxation calculations for all of the structures reported here are available via the NIST Computational File Repository [10]. 2
Modelling Simul. Mater. Sci. Eng. 23 (2015) 015006
W J Joost et al
Table 1. Summary of structures and DFT settings used to determine fitting targets in this study. The k-point characteristics are indicated as (G) for gamma-centered.
Structure name
Lattice system
Ti atoms
O atoms
k-point mesh
Rock salt TiO α TiO Ti3 O2 hcp-diffusion
Cubic Monoclinic Hexagonal Hexagonal
4 10 12 96
4 10 8 1
17 × 17 × 17 (G) 7 × 5 × 11 (G) 3 × 3 × 11 (G) 2 × 2 × 2 (G)
2.1. Density functional theory
We performed all DFT calculations in the Vienna Ab-initio Simulation Package (VASP) [11–14], employing projector augmented wave (PAW) pseudopotentials [15, 16] and the Perdew–Burke–Ernzerhof generalized gradient approximation (GGA-PBE) [17]. The cut-off energy for all calculations was held at 520 eV. For relaxation calculations we used a stopping criterion of
