JOURNAL OF MATERIALS SCIENCE LETTERS 15 (1996) 2065 2067 Elastic modulus of tellurite glasses A. EL-ADAWY, R. EL-MALLAWANY Physics Department, Faculty of Science, Monoufia University, Egypt The elastic moduli of oxide glass systems have been shown to correlate qualitatively with chemical composition in an additive manner [1]. Soga and Anderson [2] correlated elastic moduli to atom packing density, and derived a relationship relating the elastic modulus to the volume-per-ion-pair. Phillips [3] proposed an empirical method to predict Young's modulus from chemical composition. In general, the elastic modulus of materials is related to the separation distance of atoms, and is inversely proportional to the fourth power of atomic spacings [4]. In this field, a theoretical calculation model has been presented by Makishima and Mackenzie [5, 6]. They suggested that the elastic moduli are a function of both packing density and the average strength of the chemical bonds in the glass. The importance of tellurite glasses comes from their properties: (i) Their chemical durability is quite good, and they have no hydroscopic properties [7]. (ii) TeO2 in combination with some transition metal oxides such as V205 forms stable semicon- ducting glass which is characterized by having higher electrical conductivities than identical com- positions containing B203 or P205 [8, 9]. (iii) Tellurite glasses are known as high-index optical glasses (n >2.1), possessing considerable infrared transmission up to 5.5 ~lm [10, 11]. (iv) TeO2 glasses are very easily melted, forming fluid melts at temperatures below 1000 °C, and have low transformation temperatures (250-350 °C) [12]. (v) They find application as acousto-optical ma- terial [13] and laser [14] or photochromic [15, 16] glasses. Table I summarizes previous experimental elastic moduli data for tellurite glasses in the pure, binary, ternary and quaternary form [17]. TABLEI Elastic properties of the tellurite glasses at room temperature [17] Glass formula Density Young's (kg/m 3) modulus (Pa) TeO2 5101 50.7 La203)o5 TeO2)o.9 5685 59.8 Ce02)o.1 Te02)o.9 5706 60.5 8m203)0.1TeO2)o. 9 5782 63.1 Er203)0.1W03)0.3Te02)0.6 6713 74.7 Y203 )0.03 WO3)0.2 TeO2)0.77 6018 61.6 La2 03)0.03 WO3)0.2 Te02)0.77 6027 58.8 Sm203)0.05 WO3)0.2 Te02)0.75 öl 10 64.5 Ce02)o.o5WO3)o.21 TEO2)0.74 5781 72.6 Er2O3)o.o2 WO3)o.29pbO)o.2TeO2)0.49 6813 75.9 0261-8028 © 1996 Chapman & Hall According to Makishima and Mackenzie [5], the following relations hold: E = 83.6 Vt~i GiXi (1) Vt=(P)ziViXi (2) Gt = ZiGiXi (3) Gi = Ui p~ (4) mi 4 3 vi = ~ rIN(XR~e + yR~) (5) Ci = p Vi (6) m Gt = Zi ViXi (7) where E is Young's modulus, Vt is the packing density of ions in glass, Gi is the dissociation energy per unit volume of the /th oxide component, Xi is the mole fraction of the /th oxide component, p is the density, m is the average molecular weight and RMe and R0 are the Pauling's ionic radii. There are different factors which are necessary for the calculation of Young's modulus, as listed in Table II. From these important factors, we will consider first the occupied volume of glass basic unit V/ which equals 41 × 10-3 (m 3) for TeO2. By introdu- cing modifiers with smaller volume than TeO2, the occupied volume of glass will be lower. For example, ~ equäls 28.43 × 10 3 (m 3) for La203, 17.31 × 10 -3 (m 3) for CeO2, 26.44 X 10-3 (m 3) for Sm203, 25.26 × 10-3 (m 3) for Er203, 24.26 × 10-3 (m 3) for Y203, 21.44X 10 -3 (m 3) for WO3 and 11.28 × 10-3 (m 3) for pbO. From Table II we can see that the value of the occupied volume of glass in pure TeO2 glass is 41 × 10-3 (m 3) and changes to 39.8x 10 3 (m3), 38.7× 10-3 (m 3) and 39.6× 10 3 (m 3) for different binary systems and reaches values of 33.6, 36.7, 36.8, 36.4, 35.8 and 29.1 × 10 -3 (m3) for the ternary and quaternary systems, respectively. With the same composition of the basic glass TeO2 and also of the modifiers in the binary systems, we have a wider volume with La203 than CeQ and Sm203. Also, a wider volume with La203 than CeO2, Sm203, Y203 and Er203 in ternary glass systems. This is because the ionic radius of La is larger than Ce, Sm, Y and Er modifiers in both binary and ternary glass systems. Secondly, the dissociation energy of our glass systems are calculated and listed in Table II. We can see that in binary systems, the dissociation energy of CeO2 is more than that of La203 and Sm203. The important variable for the dissociation energy 2065