The structure of sodium trisilicate glass via molecular dynamics employing three-body potentials
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I. INTRODUCTION Molecular dynamics (MD) computer simulations have been used rather extensively to simulate the structure of silica and silicate glasses.1"8 Many of these studies have focused on alkali silicates1'4"7 and sodium silicates1'5"7 in particular. Until recently most MD simulations have used effective two-body potentials as the basis of atomic interactions.1"7 Although simulation results have reasonably agreed with those found experimentally,10"23 this approach is sometimes criticized because the pair potential does not take into consideration the partial covalency which is normally associated with the silica structure. Feuston and Garofalini8 have recently developed a three-body potential that introduces bond directionality in the vitreous silica structure. The three-body potential acts to restrict the deviation of the tetrahedral angle, O-si-o> from its theoretically expected value of 109.5°. The three-body potential is discussed extensively by Feuston and Garofalini in the MD study of silica glass.8 The purpose of this study was to examine the applicability of the three-body potential to sodium silicate glass. The glass structure obtained using this new empirical threebody potential has been analyzed and results have been compared with those found using two-body potentials,1"7 as well as those found through various experimental means including x-ray diffraction,1^14 XPS,1819 EXAFS,15'16 neutron scattering,17 and NMR.20"23 Section II outlines the computational procedure used in these MD simulations. Section III presents the results and discussion thereof including subsections on general structure (III.A), coordination (III.B), the bridging to non434
http://journals.cambridge.org
J. Mater. Res., Vol. 4, No. 2, Mar/Apr 1989
Downloaded: 12 Mar 2015
II. COMPUTATIONAL PROCEDURE A modified form of the Born-Mayer-Huggins (BMH) two-body potential was used to describe interactions between pairs of atoms, i and j , separated by a distance r,y as follows:
where rtj is the distance between atoms i and j , qt is the formal ionic charge, and Aip p, and ptj are constants. Details of the terms in this potential, especially with respect to the usage of the /3y term, have been presented previously.24'25 Briefly, Atj is used to obtain the appropriate cation-anion bond distance. The /3y term, rather than being the normal size dependent-species independent convergence term within the complementary error function, is a constant for cation-anion pairs, cation-cation pairs, and anion-anion pairs and is size independent. In addition to the BMH potential, a three-body contribution at central atom i and near neighbors j and k was introduced according to the following form: •ij-rf)+yif(rik-rf)
if r 9 < r ?
COS 'jik
or rik < r\
Hrip rik, djik) = 0;
(2a)
if r{j ^ r • or
rik 5= r •
(2b) where cos^ = angle subtended by r,-,- and rik with vertex at i, and A.,-, yh and r\ are constants. Additional details concern1989 Materials Research Society
IP address: 128.255.6.125
R. G. Newell, B. P. Feuston, and S. H. Garofalini: Sodi
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