MOLECULAR DYNAMICS SIMULATION

Since the p io n eerin g stu d y of W oodcock et al (1976) o n the sim u latio n of vitreous silica. M olecular D ynam ics (MD) sim u latio n s have been recognized as a very useful tool for the study of stru ctu ral and rheological properties of glasses. However, com pared to the m any studies of silicates, there are few investigations of borate glasses. Because of the com plexity of the boron-oxygen bonding, bo th the ex p erim en tal and m o d ellin g tech n iq u es seem to be insufficient an d th ere is still a considerable discrepancy betw een experim ental data and sim ulations.

The first m odelling studies of borate glasses w ere initiated by Soules (1979,1980) an d Soules and V arshneya (1981). They c alcu lated the structures of vitreous B2O3 and sodium borosilicate glass. They show ed

th at in vitreous B2O3 boron atom s are trigonally coordinated to oxygen

atom s, w hile in sodium borosilicate glasses the trigonal to tetrah e d ral conversion of boron atom s accom panies the addition of sodium atom s.

These tw o aspects of their results agree well w ith the experim ental data. H ow ever, no boroxol group form ation is observed in their sim ulation.

A series of m ore detailed studies w ere carried o u t by Soppe et al (1988), Soppe and H arto g (1988), Soppe an d H a rto g (1989). T heir consistent result is that they do not find any boroxol rings. They found th at for both non-pressure scaled and pressure scaled system s, and for a v ariety of different quench rates, oxygen atom s have no ten d en cy to becom e equiplanar w ith adjacent BO3 triangles. They also attem p ted an

interesting sim ulation in w hich half of the num ber of B-O-B an d O-B-O angles w ere constrained at 120°. Even w ith such artificial constraints, they do not find any boroxol rings. They concluded th at their continuous ra n d o m n e tw o rk stru c tu re w ith o u t any boroxol rin g s rea so n a b ly reproduced the RDF of X-ray data.

A m ini et al (1981), A bram o et al (1986), Xu et al (1988) also perform ed MD sim ulations on B2O3, and on silver borate and sodium borate glasses. In none of these studies were boroxol groups found.

All of these studies have two limitations. The first is that very rapid q u e n ch in g rates (10^^ ~ 10^^ K /sec) have to be used. E ven w ith supercom puters, sim ulated quench rates are still far from the rates (less th an 1 0^ K /sec) in the real process. H ow ever, in spite of such rap id

qu ench rates, several sim ulations of silica glass hav e su cceed ed in reproducing the structures of the vitreous material.

The second lim itation is the use of p a ir-p o ten tial m o d els w ith form al charges. Pair-potential m odels succeed in m odelling m an y ionic m aterials and all the p ioneers in this field em ployed su ch m odels. H ow ever, such p air-p o ten tials m ay n o t be sufficient to express the structure and bonding of m aterials w ith partial covalency.

In order to account for covalency, H irao and Soga (1985) applied a new potential w ith the extra term -A ex p [-C (r-0 .2 3 9 )2 ] (r is the distance betw een boron atoms) for B-B interactions to sodium borate glasses. They p resu m ed th at their stru ctu re m ay include boroxol g ro u p s from the calculated population of B-O-B angles at = 120°.

The MD study of Inoue et al (1987) included three body effects and is the only one th at generates boroxol rings in B2O3 glass and diborate groups in sodium borate glass. They p u t ghost atom s (G) on the centre of gravity of both BO2 and B2O triangles. A positive po in t charge w ith a

Born-M ayer type short-range potential is assum ed to exist at G w hen the G-O potential is calculated, and a negative point charge w ith a different Born-Mayer type short-range potential is assum ed to exist at G w hen the G-B potential is calculated. These ghost atoms thus provide O-B-O and B- O-B three body potentials. Boron and oxygen atoms have form al charges, and all the other potential param eters are derived from the p o ten tial en erg y of H3B O3 by the IND O (interm ediate neglect of differential

overlap) m ethod.

They concluded that their "pseudo-atom" three-body type of m odel reproduces the RDF of M ozzi and W arren (1970) w ith the presence of boroxol rings. H ow ever, the ratio of boron atom s present in the boroxol rings is less than 22.5% and smaller than that reported (82+8% by Jellison et al 1977 and 60+20% by Johnson et al 1982). This result is encouraging in th at it show s that structures w ith boroxol rings can be reproduced by three body potentials, even if a rapid quench rate is used. It is, m oreover, in terestin g to note th at calculated B-O-B bond angles are d istrib u ted around 120°. In contrast, all pair-potential studies show B-O-B angles of - 160°. The NMR data of Jellison et al (1977) give inform ation on the B-O-B angles for oxygen atom s not included in boroxol rings. The NM R result

show s a narrow distribution centred around either 134.6° or 128.1°, close to the value of 130° used by Mozzi and W arren (1970).

On the other hand, recently Verhoef and H artog (1992) carried out MD sim ulations of B2O3 glass, using different sets of p air-p o ten tials

(Born-M ayer-Huggins type) and in some cases three-body, bond-bending term s w ere applied. For the latter a sim ple harm onic form w as used. The equilibrium angle was set as 120° for O-B-O and 130° for B-O-B. The force constant for O-B-O w as fixed so as to obtain the correct energy for the high-frequency m ode in the sim ulated infrared spectrum .

Their first conclusion is that all the m odels investigated generate continuous random netw ork glass structures w ith o u t any boroxol rings, e v en if th ree b o d y b o n d -b en d in g term s are a d d e d . T heir second conclusion is th at all the m odels rep ro d u ce the ex p erim en tal d ata reasonably well, although there are detailed discrepancies m ainly w ithin the distance range of 2 - 4 A in the RDF. Their third conclusion is th at the peak at 805 cm"l in the experim ental Raman spectra can be assigned to a b reath in g m ode of the three oxygen atom s w ith in each BO3 triangle.

H ow ever, no peak at around 805 cm '^ is experim entally observed in borate crystals w hich consist of BO3 triangles. Their fourth conclusion is

th a t th ree b o d y in teractio n s are necessary to rep ro d u c e the hig h - frequency m odes in the sim ulated infrared spectra and density of state.

To sum m arize the results of all the MD sim ulations;

(1) Pair-potential m odels can reproduce the short-range d ata of X-ray a n d N e u tro n sc atterin g w ell. H o w ev er, d isc rep a n cies rem a in for m ed iu m range distances. B-O-B angles are far from the average of the experim ental values of 130° estim ated from NMR data. Pair-potential m odels alw ays generate contin u o u s ran d o m n etw o rk s w ith o u t any boroxol rings.

(2) T hree-body p o ten tial m odels can rep ro d u ce boroxol rings, a lth o u g h th is is n o t alw ays the case. They can re p ro d u c e som e characteristics of the m edium -range order w hich are sim ilar to M ozzi an d W arren's m odel. The inclusion of the three-body p otential affects n o t only the g en eratio n of boroxol rings b u t also th e v ib ratio n a l properties of the sim ulated vitreous material.

The w ork reported later in this thesis will advance the description of the interatom ic potential m odels for B2O3 and will achieve im proved

Bond lengths

[R(B-O) in Â] Ab initio calculated values Experimental values

STO-3G 4-31G 6-31G*^ MEG MNDO

cluster basis basis basis method method Average Range

BO3- 1.419 1.435 — — — 1.37 1.34 -1.40

B (0 H )3 1.364 1.364 1.358 1.37 1.371 1.361 1.353 - 1.365

B (0 H )4 - 1.48 — 1.474 1.53 ~ 1.47 1.478

Bond angles

[B-Obr-B in degrees]

Ab initio calculated values

STO-3G 4-31G 6-31G*

Experimental values

Cluster basis basis basis Average Range

[(0 H )2 B ]0