Density formula for alkali silicate glasses from annealing to glass-processing temperatures

Abstract

An additive formula is given for the computation of specific volumes of molten and compacted alkali silicate binary glasses with modifiers up to 50-mole percent and from annealing temperatures (400 0 or 500 0 C) to 1,400 0 C. The effective partial volumes, Vs, for the silica. are postUlated as (l /vs ) = 2.198+r.C8 (1723 -t), where r .. is the mole fraction of nonsilica and Cs is a constant to be evaluated from glassdensity data. This is based on the idea that silica networks can contract in volume as temperatures are lowered provided, and in proportion as, modifier ions are present in the glass. The effective partial volumes of R 20, the non silica, are assumed as linear function s of temperature but not of the fraction of silica present.Computed and observed densities agree within approximately 1 p ercent. The effective volumes of nonsilica are somewhat smaller than published estimates for the oxides themselves, as should be expected because of interpenetrations.Previous formulas for the computation of densities of glasses have related principally to variations in composition. The formula proposed by Stevels [1] 1 is based on ideas of structure and has very few constants. It assumes for restricted ranges in composition that volume is independent of the nature of the cation. As modified by Stanworth [2] it shows that volume is dependent on the size of the cations, the glass volumes being larger as cation radii are larger.The additive formula proposed by Huggins [3] has many constants, and it is notably successful. That work is of considerable interest to anyone interested in structure because Huggins finds that the addition of every cation oxide molecule linearly increases the volume of a glass per oxygen atom, regardless of previous additions. However, at least for R 20 silicate glasses, it can be shown that the linearity is not dependent on the referral to oxygen, and his corresponding partial volumes of nonsilica (not referred to oxygen) also are found to be linear if plotted against mole fraction of the added oxide. 2 The Huggins formula is of further interest because the partial volumes used for silica are almost identical in the presence of various kinds of nonsilicas and are so treated except for the presence of a few elements, notably boron. Most interesting of all in connection with the present paper, his partial molar volumes (P. M. V.) attributable to silica 3 decrease as larger amounts of modifier are added. The Huggins stepwise procedure in dealing with the silica component is roughly equivalent to the procedure mentioned by LeChatelier [13], namely an arbitrary dual 1 Figures in brackets indicate tbe literature references at tbe end oC tbis paper.• Altbough tbe Huggins partial volumes Cor silica (wbetber or not referred to oxygen) are more nearly representable by a smootb curve wben plotted against mole traction oC silica tban against tbe Si to 0 ratio (used by Huggins), tbeir better representation by segments of straigbt lines can still be shown. The Huggins special points of intersection corres...

Thermal Conductivity of Molten B2O3, B2O3–SiO2, Na2O–B2O3, and Na2O–SiO2 Systems

“…Using Eq. , the phonon mean free path of the Na 2 O/4SiO 2 system was calculated on the basis of its thermal conductivity, sound velocity, density and calculated specific heat capacity. The specific heat of the molten oxide system used in the present work was estimated by following an empirical equation:where p i is the weight fraction of the oxides, a i is a temperature constant, 0.000829 for Na 2 O and 0.000468 for SiO 2 , c i is the specific heat at 273 K, 0.223 for Na 2 O and 0.166 for SiO 2 , T is the temperature (°C), and C p,T is the specific heat capacity [cal·(g·K) −1 ] at the temperature T .…”

Vitrons as flow units in alkali silicate binary glasses

“…Little is known about the mechanism of viscous flow in silica-rich glasses and the random network theory has been inadequate for describing units of flow. According to the vitron concept [ 1 ] of modulated microregularity of structure which the writer [ 1 , 2 , 3 , 4 , 5 ] has applied in studies of simple silicate glasses, nearly one-third of the silica forms small and limited clusters of dodecahedral cages called vitrons (computed density 1.99 g/cm 3 for (Si–O) = 1.60 A) within which central bonds are strong, the structure nearly regular, and the cavities large. Only oblately deformed cages can completely unite with neighbors on all sides.…”

“… Two volume-changing processes found useful in studying the mechanism of viscous flow in glasses are: (a) stress-induced variation in fissuring near vitrons at their peripheries where the Si–O bonds are tensed and weakened, and (b) distention and modification of all silica network by added oxides. These idealized processes, readily derivable from the vitron concept of pentagonal ring structure in glass [ 1 ], 2 are sensitive to both temperature and composition and have previously been found useful [ 1 , 2 , 3 , 4 , 5 ] for understanding other properties of glasses. Viscous flow of vitrons as units in annealing ranges, and at higher processing temperatures for silica-rich glasses, is here viewed as permitted primarily by the breaking of tensed and weakened Si–O bonds in shell-like stressed tissues surrounding vitrons.…”