446 Physics and Chemistry of Glasses Vol. 44 No. 6 December 2003 Phys. Chem. Glasses., 2003, 44 (6), 446–53 Two empirical relations are reported relating to both the acoustic activation energy at low temperature and to the bulk modulus for oxide glasses, on the one hand, and to stretching force constant and atomic ring size of the network on the other. A comprehensive study was un- dertaken to examine the validity of these relations when applied to a large number of tellurite, phosphate and silicate glasses. Good agreement was obtained between experimentally measured values of elastic moduli, for the majority of the studied glasses, and those calculated theoretically according to our empirical relations. A cor- relation factor varying between 99 and 90% for phos- phate glasses, 94 and 85% for tellurite glasses and 86% for silicate glasses was obtained. The study of ultrasonic velocity and attenuation in glasses plays a significant role in understanding the structural characteristics of glass networks. Any change in the network due to lattice defects can be directly observed. Ultrasonic velocity and attenuation meas- urements have been reported in tellurite glasses, (1–10) phosphate glasses (5,11–16) and silicate glasses. (17–25) The study of ultrasonic attenuation in these glasses at low temperatures often revealed a broad absorption peak, which was attributed to a structural relaxation with a distribution of activation energies. Bridge & Patel (15,16) analysed the composition dependence of the position and overall shape of the loss peaks in terms of an as- sumed loss of the standard linear solid type, with low dispersion and a broad distribution of Arrhenius type relaxation times with temperature independent relaxa- tion strengths. They found that the acoustic loss is a property of the vitreous network as a whole rather than being due to a second order effect such as the presence of dangling bonds or polar groups, or to network holes, etc. They attributed the relaxation loss at low tempera- tures to the thermal motion of bridging oxygen atoms in asymmetric double-well potentials of atomic dimen- sions. The longitudinal and transverse double-well potentials are associated with elongated and contracted cation–anion–cation angles, respectively, as shown in Figure 1. At peak temperature T p (temperature at which maximum loss occurs), the oxygen atoms undergo structural relaxation by hopping over the barrier (ac- tivation energy) between the two wells in a thermally activated process. The relaxation time, t, depends on temperature according to the Arrhenius equation t=t -1 exp(V/kT p ), where t -1 is the classical vibration frequency (attempt frequency) for the relaxing parti- cle in either well, V the average activation energy and k Boltzmann's constant. Anderson & Bommel (23) pro- posed that in silicate glasses there are a fraction of oxygen atoms localised in double-well potentials and can move from one well to the other by a transverse motion. Strakna (27) assumed also that the two poten- tial minima of the oxygen atoms in silica glasses occur in the bond direction. The elastic moduli of pure, binary and poly-com- ponent oxide glasses have been analysed quantitatively by many authors. (2–10,12,14–19,26,28) The bulk modulus and Poisson's ratio have been calculated using the bond Theoretically calculated elastic moduli of tellurite, phosphate and silicate glasses A. Abd El-Moneim 1 Physics Department, Faculty of Science, Zagazig University, Zagazig, Egypt L. Abd El-Latif National Institute for Standards, Tersa Street, El-Haram, El-Giza, Egypt Manuscript received 11 March 2002 Revision received 7 May 2003 Accepted 14 May 2003 1 Author to whom correspondence should be addressed. Current address: Science Department, Teacher’s College in Dammam, P.O. Box 2375, Dammam: 31451, Saudi Arabia. (email: aminabdelmoneim@hotmail.com) Figure 1. (a) Schematic two dimensional representation of the structure of noncrystalline material with atomic ring size, l. Full circles represent cations and open circles represent anions. a and b are the transverse and longitudinal vibrations of the oxygen atoms. (b) Double well system with barrier height V and asymmetry, D b a a V D (a) (b)