December 1965Viscosity and Density of Boron Trioxide 613 fixed composition decreases with increasing temperature The variation of activity shown in Fig. 3 , however, is, by virtue of the choice of standard states, relative to the activity in pure Na20 a t the same temperature. In reality the oxygen ion activities in pure sodium monoxide and in silicate or borate melts of fixed composition, all decrease with increasing temperature (daoZ-/dT is negative). The data in Fig. 3 now add to this knowledge and demonstrate that dao"/dT is approximately the same for the silicates and pure sodium monoxide but is numerically smaller €or the borates. Consequently, with pure sodium monoxide as the standard state, the activity of oxygen ions in silicate melts appears to be virtually indcpendent of tempcrature whereas for borate melts a positive value of da$-/dT is observed. IIence, a relation similar to Fig. 3 of Ref. 2 would have resulted for the present calculations if sodium monoxide a t some fixed temperature had been chosen as the skandard state instead of sodium monoxide at the tcinperature of interest.It is possible to rationalize the results as follows: Fincham and RichardsonlO postulated that since oxygen can exist in silicate melts in only three fornis (singly bonded 0-, doubly bonded 0", and oxygen ions 02-), the equilibrium between these tlirec forms can be exprcssed as follows:This forward reaction parallels the polymerization reaction, and the viscosity data indicate that, for a melt of given composition, increasing temperature favors depolymerization. IIence, it lollows that increasing temperature favors the back reaction of reaction (7) and thus reduces the oxygen ion activity as demonstrated in Figs. 5 and 2 of Refs. 1 and 2, respectively. The prescnt data would indicate therefore, that for binary borate and silicate melts with identical N N~~o , the complex borate ions are of greater thermal stability than the complex silicate ions. This is supported by the fact that the temperature coefficient of viscosity is greater in silicate melts. It does not follow, however, that the same degree of complexity exists in both melts. In fact the lower viscosities o€ the borate melts indicate that they are distinctly less complex than the silicate melts of the same quantitative compositions.Extensive and accurate viscosity values for molten BzOo a r e reported over the continuous range from 20 poises (at 1400°C) to 101Opoises (at 318°C). T h e measurements were made with a wide-range rotating-cylinder viscometer. The melts were pretreated by bubbling superdry nitrogen through them to ensure a minimum water content. Above 800°C the temperature dependence of the viscosity curve obeyed the Arrhenius equation ; below 800°C the curvature was smooth showing no breaks. At the low temperatures, although its curvature decreased, the viscosity curve did not obey the Arrhenius equation. Densities were determined between 41 l" and 1400°C. Over this range the volume expansion coefficient changed by 1 order of magnitude Prcsentcd in part at

The viscosity of B.Oa glass was measured from 10 1L I0 14 P by the fiber-elongation method and found to be Arrhenius with an activation energy of 94 kcal/mol. These new data were combined with previously reported rotation data (10 L lO 10 P) and gave a smooth plot. The complete viscosity data were used to test the equations of the best-known viscosity theories but no reasonable fits were found. Therefore, an examination of the validity of the basic assumptions underlying these theories was made. As a result of this study, it was found that the temperature dependence of the viscosity is not controlled by structural effects such as free volume, configuration entropy, etc., but by activation energy effects in the viscous flow process. The onset of the non-Arrhenius region is a direct consequence of the appearance of a symmetric distribution of relaxation times and/or a distribution of activation energies which cannot be explained by existing viscosity theories. Finally, all theories are in error in predicting that the viscosity goes to infinity (in the annealing region) much faster than the measured values indicate.

Time·index of refraction iso th erm s for a boros ilica te glass in th e tran sfo rmation region hav e bee n es tabli shed. By co mparin g two qu enc hed glasses of the sa me index , o ne qu e nc hed after attaining equilibrium at a given te mpe ra ture a nd the oth e r qu e nc hed from a te mperature at wh ic h t he s peci men was approach ing a hi ghe r valu e of index , c urves similar to th e one obtained by Ritland in co mparin g rate cooled a nd qu e nched spec im e ns are developed.Key Word s: Ann ealing, boros ilicate glass, glass, tim e· ind ex of refrac tio n iso th e rm s, tran sform a· ti on ra nge , index of refraction .

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The viscos ity o f a soda -lime-sili ca g lass has bce n m eas urcd a t t he Nat io na l B urcau of Stand a rd s a nd se ven oth er la bo ratories. D ete rmin atio ns wc rc mad e in t hc ra nge of 102 t o 10 15 p oises. The rotat in g cy lind er was u sed at t he hig her t em pcrat urcs (800 to 1450 °C) a nd t hc fib er elongation m et hod at t he lower te mpcratur es (52 0 t o 658°C) . T hc rcsul Ls ha ve bee n critically eva lu ated a nd t il e g lass has bee n issu ed as Stand a rd Sam p lc No . 710. This glass is a va ila ble fr om t he Nat ion a l Bureau of Standa rds.