Polarizable potentials for metals: The density readjusting embedded atom method (DR-EAM)

Hemanta Bhattarai, Kathie E. Newman, and J. Daniel Gezelter

Phys. Rev. B 99, 094106 – Published 15 March 2019

Abstract

In simulations of metallic interfaces, a critical aspect of metallic behavior is missing from the some of the most widely used classical molecular dynamics force fields. We present a modification of the embedded atom method (EAM) which allows for electronic polarization of the metal by treating the valence density around each atom as a fluctuating dynamical quantity. The densities are represented by a set of additional fluctuating variables (and their conjugate momenta) which are propagated along with the nuclear coordinates. This “density readjusting EAM” (DR-EAM) preserves nearly all of the useful qualities of traditional EAM, including bulk elastic properties and surface energies. However, it also allows valence electron density to migrate through the metal in response to external perturbations. We show that DR-EAM can successfully model polarization in response to external charges, capturing the image charge effect in atomistic simulations. DR-EAM also captures some of the behavior of metals in the presence of uniform electric fields, predicting surface charging and shielding internal to the metal. We further show that it predicts charge transfer between the constituent atoms in alloys, leading to novel predictions about unit cell geometries in layered $L 1_{0}$ structures.

Received 6 February 2019

DOI:https://doi.org/10.1103/PhysRevB.99.094106

Physics Subject Headings (PhySH)

Metals

Embedded atom model Molecular dynamics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Hemanta Bhattarai and Kathie E. Newman

Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA

J. Daniel Gezelter^*

Department of Chemistry & Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA

^*gezelter@nd.edu

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Issue

Vol. 99, Iss. 9 — 1 March 2019

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Images

Figure 1
$V_{self} (q)$ for Copper. In the traditional harmonic model (dashed line), the self potential is parameterized using the ionization potential (IP) and electron affinity (EA), and charge states are integer multiples of electron charge (circles). In DR-EAM, oxidation states are separated by $\sim 0.4 e$ (squares), and the self potential is fit using a sixth-order polynomial (solid red line).
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Figure 2
DR-EAM self potential $V_{self} (q)$ for FCC, BCC and HCP metals. The symbols are gas phase ion energies referenced to the neutral atom (with charges scaled by 0.4). Lines are Eq. (5) with coefficients given in Table 2. The region between $- 0.4 < q < 0.4$ is enlarged in the Supplemental Material [77] in Fig. S1.
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Figure 3
Structures of the ordered alloys $L 1_{0}$ (left) and $L 1_{2}$ (right). $L 1_{0}$ structures present alternating layers of A and B atoms, so any charge transfer between the two elements will result in modification of the $c / a$ ratio exhibited by the crystal.
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Figure 4
The response of an 18-layer DR-EAM Platinum (111) slab exposed to an external uniform electric field (0.01 V/Å along the $z$ axis). The average charge in each layer (top) displays a nearly linear dependence on the $z$ coordinate of the layer. The dipole density(middle), in units of $\frac{e}{2 A}$ , is approximately constant in the interior of the slab. The net electric field (bottom) exhibits a nearly complete screening in the interior of the slab. Only the outermost atomic layers feel the full external field, while the response of the DR-EAM densities effectively screens the interior. The model has an effective penetration depth of 2–3 atomic layers before complete screening is recovered.
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Figure 5
Configurational energies as a function of the distance $(d)$ of a point charge from the surface are fit to find an offset $δ$ of the image charge surface from the top layer of atoms, and a scaling parameter $(s \sim 2)$ to understand how closely DR-EAM captures classical image effects.
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Figure 6
Effective interaction potential [Eq. (30)] for a point charge model of a Chloride ion $(q = - 1)$ approaching a Copper (111) surface (simulated using DR-EAM) above three different binding sites (atop, three-fold hollow, and bridge). On the right, we show the induced density changes in the metal (represented by changes in the atomic partial charges). Parameters for the fits of the effective interaction potential (dashed lines) are given in Table 7.
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