Molecular Dynamics Simulations of Shock-Induced Thermite Reaction

A computational framework for molecular dynamics (MD) simulations of shock-induced reactions in thermite mixtures is developed. The system under study is an Fe2O3+Al thermite mixture. An interatomic potential valid for a range of temperature is formulated for the Fe+Al+Fe2O3+Al2O3 system. The parameters in the potential are determined through the use of Helmholtz free energy within the quasi-harmonic approximation. The potential is a variable charge cluster functional and is capable of describing the multi-component behavior as well as the energetics of the association and dissociation during thermite reactions. Introduction The focus of this research is on the development of a classical molecular dynamics (MD) scheme for analyzing the mechanics and energetics of shock-induced reactions in metal powder mixtures. The model system under study is an Fe2O3+Al thermite mixture. This task requires an interatomic potential capable of describing the behavior of the individual components in the system and capable of characterizing intra-component interactions with a good description of intermediate structures. The potential should respond well to the environment an ion or an atom is subjected to during shock loading. To this end, a variable charge cluster functional potential has been developed [1]. Parameters in the potential are determined by fitting to the properties of Fe, Al, Fe-Al, Fe2O3, and Al2O3. The potential uses electronegativity equalization to account for changes in the charges of different species according to their specific local environments. This potential is capable of describing qualitative energetics of association and dissociation processes during thermite reactions. However, the parameters were determined using material data available at 0 K for Fe, Fe-Al and Fe2O3 and at 300 K for Al and Al2O3. In the current paper, we extend the fitting calculations to 0600 K for Fe and Al and to 0-900 K for Fe2O3 and Al2O3. This temperature-sensitive fitting is based on the use of the Helmholtz free energy within the quasi-harmonic approximation rather than lattice energy. The quasi-harmonic approximation limits the use of the current scheme to conditions up to the Debye temperatures of the respective components. Interatomic Potential Because of the widely different electronic configurations of the species involved, the potential model includes a term ( glue E ) similar to the modified embedded atom method (MEAM) potential which is a generalized cluster functional [2] and another term ( es E ) for electro-static interactions with environment-dependent charges. Specifically, the total energy of the system is a function of interatomic distance r and charge q in the form of ( ) ( ) ( ) , , glue es E E E = + ⋅ r r r q q (1) Here, Materials Science Forum Online: 2004-09-15 ISSN: 1662-9752, Vols. 465-466, pp 157-162 doi:10.4028/www.scientific. net/MSF.465-466.157 © 2004 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific. net. (Semanticscholar.org-11/03/20,14:30:25) ( ) ( ) ( ) 1 2 ≠ = + ∑ ∑ r glue i i ij i i j E F ρ φ (2) is the glue potential with generalized cluster functional ( ) F ρ which depends on embedding electron density ρ (cf. [3]); and ( ) ( ) 1 , 2 ≠ = + ∑ ∑ r es i i i j ij i i j E q q q q V χ (3) is the electrostatic energy with χ being the instantaneous electronegativity given as [ ] ( ) ( ) ( ) ( ) 1 2 0 0 3 3 3 1 2 12 | | . ≠ ≠     = + − = + −       −   ∑ ∑ ∫ ∫ ∫ j i j i i j i i j i j j i j i i f r f r f r Z j f f f Z d r d r d r r r r χ χ χ (4) In the above equation, 0 i χ is the ground state electronegativity. Also in Eq. (3), V is the electrostatic pair interaction potential in the form of