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The Impact of Short-range Forces on Defect Production from High-energy Collisions Roger Earl Stoller, Artur Tamm, Laurent K Béland, German D. Samolyuk, George Malcolm Stocks, Alfredo Caro, Lyudmila V. Slipchenko, Yu. N. Osetsky, Alvo Aabloo, Mattias Klintenberg, and Yang Wang J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.5b01194 • Publication Date (Web): 25 Apr 2016 Downloaded from http://pubs.acs.org on April 28, 2016
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The Impact of Short-range Forces on Defect Production from High-energy Collisions R. E. Stoller1, A. Tamm2,3, L. K. Beland1, G. D. Samolyuk1, G. M. Stocks1, A. Caro3, L. V. Slipchenko4, Yu. N. Osetsky1, A. Aabloo2, M. Klintenberg5, and Y. Wang6 1
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 3781, USA 2
IMS Lab, Institute of Technology, University of Tartu, 50411 Tartu, Estonia
3
Materials Science and Technology Division, Los Alamos National Laboratory Los Alamos NM 87544, USA 4
Department of Chemistry, Purdue University, West Lafayette, IN 47906
5
Department of Physics and Astronomy, Uppsala University, SE-75120 Uppsala, Sweden 6
Pittsburgh Supercomputer Center, Carnegie-Mellon University, Pittsburgh, PA 15213, USA
Format-corrected revision submitted to Journal of Chemical Theory and Computation 21 April 2016 (Revision submitted 28 March 2016) (Original submission 17 December 2015)
Research sponsored by the Office of Basic Energy Sciences, U.S. Department of Energy, under contract DE-AC05-00OR22725 with UT-Battelle, LLC. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes.
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The Impact of Short-range Forces on Defect Production from High-energy Collisions R. E. Stoller1, A. Tamm2,3, L. K. Beland1, G. D. Samolyuk1, G. M. Stocks1, A. Caro3, L. V. 6 Slipchenko4, Yu. N. Osetskiy1, A. Aabloo2, M. Klintenberg5, and Y. Wang 1
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 3781, USA 2
IMS Lab, Institute of Technology, University of Tartu, 50411 Tartu, Estonia
3
Materials Science and Technology Division, Los Alamos National Laboratory Los Alamos NM 87544, USA 4
Department of Chemistry, Purdue University, West Lafayette, IN 47906
5
Department of Physics and Astronomy, Uppsala University, SE-75120 Uppsala, Sweden
6
Pittsburgh Supercomputer Center, Carnegie-Mellon University, Pittsburgh, PA 15213, USA Abstract Primary radiation damage formation in solid materials typically involves collisions between
atoms that have up to a few hundred keV of kinetic energy. During these collisions, the distance between two colliding atoms can approach 0.05 nm. At such small atomic separations, force fields fitted to equilibrium properties tend to significantly underestimate the potential energy of the colliding dimer. To enable molecular dynamics simulations of high-energy collisions, it is common practice to use a screened Coulomb force field to describe the interactions and to smoothly join this to the equilibrium force field at a suitable interatomic spacing. However, there is no accepted standard method for choosing the parameters used in the joining process, and our results prove that defect production is sensitive to how the force fields are linked. A new procedure is presented that involves the use of ab initio calculations to determine the magnitude and spatial dependence of the pair interactions at intermediate distances, along with systematic criteria for choosing the joining parameters. Results are presented for the case of nickel, which demonstrate the use and validity of the procedure. 1. Introduction Molecular dynamics (MD) simulations are widely used to investigate atomistic and molecular phenomena including applications from biology1 to materials science.2,3 Although MD simulations can be used to elucidate the details of many processes on this scale, the primary limitation of the approach is the accuracy with which the force field (alternately interatomic potential), describes the relevant phenomena.2,4,5 This is a particularly difficult issue when the
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application of interest involves atoms that are far from their equilibrium positions because the force fields are typically determined by material properties at or near equilibrium. Among the most common properties used in fitting force fields for metals are the lattice parameter, elastic constants, and point and extended defect formation energies. When metals and alloys are exposed to irradiation by high-energy particles, a process known as a displacement cascade can be initiated.6 Most simply, this cascade can be visualized as a series of elastic collisions that proceeds after a given atom has been struck by an incident ion (or high-energy neutron in the case of fission reactor materials). The initial atom, which is called the primary knock-on atom (PKA), will recoil with a given amount of kinetic energy, which it dissipates in a sequence of collisions with other atoms. These secondary knock-on atoms will in turn lose energy to third and subsequently higher order knock-ons until all of the energy initially imparted to the PKA has been dissipated. This simple description ignores the fraction of the energy that may be transferred to the electrons in the material. Although the physics is slightly different, similar events are commonly observed on billiard tables. In this context, the most important difference between a rack of billiard balls and atoms in a crystalline solid is the binding forces that arise from the presence of the electrons and other atoms. As a result, a certain minimum kinetic energy must be transferred to an atom before it can be displaced from its lattice site. This is referred to as the displacement threshold energy and is in the range of 20 to 40 eV for most metals.7 The collisions of interest to most ion implantation and radiation damage studies involve PKA kinetic energies up to at least a few hundred keV. Collisions at such energies bring atoms very close together, with the colliding dimer eventually reaching potential energies of a few 100 eV. This is well above the energy range corresponding to equilibrium bonding, which is a few (negative) eV. Force fields fitted to equilibrium properties do not accurately describe the interactions at these short distances and high energies, substantially underestimating the potential energy of the two colliding atoms. At those short distances, collisions may be considered binary, in the sense that most of the potential energy of the system comes from the colliding dimer, with negligible contributions from the other adjacent atoms.5 In the context of modern many-body force fields used for MD simulations, this fact justifies describing the shortrange part of the force field with a pair interaction part alone, with little or no contribution from the many-body embedding term. For example, see the description the embedded atom model (EAM) or the Finnis-Sinclair force fields.9 This pair contribution has to be extrapolated from the equilibrium distances where it was fitted to properties of the solid, to shorter distances where it
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has to reproduce a binary collision potential. Figure 1 illustrates this concept with the example of two repulsive pair components from commonly used force fields for iron9,11 and nickel10 along with the binary screened-Coulomb “universal” potential obtained by Ziegler, Biersack, and Littmark (ZBL), which is considered an accurate function for high energy collisions.12 It is common practice to smoothly join the ZBL potential to the equilibrium pair force field in order to adequately describe the whole range of distances and energies. The procedure used by Calder and Bacon11 is illustrated in Figure 1(a) in which two functions were used in this intermediate region join the Finnis-Sinclair and ZBL pair potentials. The curve labeled Spline in Figure 1(b) was obtained using the so-called overlay function in LAMMPS as described in the Supporting Material. The purpose of this paper is to show that one of the most important results of molecular dynamics simulations of high-energy collision cascades, i.e. stable defect production, significantly depends on the value of the repulsive force field precisely in the matching region between ZBL and equilibrium distances. By comparing results obtained in the conventional way and using our newly developed procedure that is based on fitting accurate first principles energy evaluations in this spatial domain, the necessity of using particular care in this matching region is demonstrated. A procedure which involves the use of ab initio calculations to determine the spatial dependence of the close-pair atomic interactions is described, and systematic criteria are defined for choosing the parameters needed to join the equilibrium force field to a ZBL potential. Results are presented for the case of nickel, which demonstrate the use and validity of the procedure. The revised force field provides the same values for equilibrium properties, notably interstitial defects, as the initial one, but the energy and forces obtained for closely spaced pairs of atoms that arise in radiation damage studies are improved. Moreover, the procedure provides a systematic approach that can be followed for any metal or alloy force field. 2. High energy collisions In order to determine the interatomic spatial domain explored during a collision cascade, a series of MD simulations were carried out over a wide range of energies and temperatures using a version of the Finnis-Sinclair iron force field9 which was modified by Calder and Bacon11 to link with the ZBL. The results shown in Figure 2 demonstrate that for PKA up to 100 keV at 1200K the minimum interatomic distance approaches 0.05 nm. Comparing these values with Figure 1(b), it is clear that many collisions occur in the transition region between the equilibrium and the ZBL components. It is to be expected then that the value of the force field in this region would affect the outcome of the simulation. Previous work involving low energy (
