Network Structure of Oxide Glasses Containing Alkali & Other Ions by Diffraction and MD Simulations
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EXPERIMENT Neutron diffraction Neutron diffraction was measured by the time of flight method with pulsed neutrons. The structure factor S(Q) up to Qmax = 30 A: was obtained. The measurement was carried out using the HIT-II facility in the National Institute of High-Energy Physics, Tsukuba. The function S(Q) was Fourier transformed to yield radial distribution function, which was expressed in the form of 2;t 2rp(r). Molecular dynamics Structural models of the glasses with the same composition as those for the diffraction measurements were constructed by MD simulation. In the case of silicate glasses, a Born-Mayer type two-body potential set was used. In borate or tellurite glasses, a three-body potential was used in addition to the Born-Mayer type pair potential. The Born-Mayer potential is expressed as,
(Iij= 1 ZiZje2 + Bijexp(-r) 4x0 rij pij
(1)
where r is interatomic distance, Z is charge, B and p are empirical constants. The three-body potential is explained below for more complex tellurite glasses: In order to consider the anisotropic nature of Te-O, a suitable potential was invented by modifying the Keating type potential [1], which was applied to O-Te-O and Te-O-Te angles. This potential describes the three-body interaction as,
357 Mat. Res. Soc. Symp. Proc. Vol. 455 01997 Materials Research Society
(lijk = C(COS0ijk -
cos0O) 2 g(0ijk) exp[ix / (rij - a) + X / (rjk - a)] (for rij, rjk < a)
(2)
where,
g(0jk)= 1-q
/ cosOjk -
cos 00
2
1+1coso] )
(3)
In these two equations, C is a constant and a is a cutoff radius of rij and r*. A variable Oijk represents an angle of a central j-th atom held between the other i-th and k-th atoms, and 00 is the ideal angle. When g(Oijk) = 1, eq. (2) corresponds to the original potential form of Keating, which always has an unstable maximum at 180'. Tellurite glasses are generally thought to consist of TeOx polyhedra with O-Te-O angles of about 900 and 180', which requires an appropriate modification of the Keating type potential. The factor g(Oijk) expressed in eq. (3) was introduced to lower the potential energy at 180'. A parameter q in g(Oijk), ranging in 0 - 1, regulates potential height at the angle. In order to improve the concept of MD for glasses containing alkali ions, it is necessary to include polarization effect induced at each ion. The concept of polarization is quite important, if the mixed alkali effect is taken into consideration. The potential of induced electronic polarization can be written as
.
=
ctE,2
(4)
assuming point dipoles in local electric fields, where ct1 is isotropic atomic polarizability and Ej is the local electric field at atom i. The variable Ej includes electrostatic interaction from all surrounding atoms, which can be deduced from the gradient of the Coulombic potential, the first term in eq. (1). Atomic forces are obtained directly as the negative gradient of the total potential energy, = --Vi('PAIR +. +
ID),
(5)
where fi represents the force on atom i.
RESULTS and DISCUSSION 1. Silicate glasses The basic structural uni
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