Analysis of the elastic model application for the phosphate glasses containing gadolinium and terbium

A series of rare-earth phosphate glasses, (Gd2O3)x(P2O5)1-x with x= 0.222, 0.226, 0.229, 0.245 and (Tb2O3) x (P2O5) 1-x with x=0.226, 0.247, 0.263, 0.271 have been quantitatively studied. The room temperature of elastic moduli and Poisson’s ratio for each phosphate glass were estimated from the measured density and 15 MHz ultrasonic longitudinal and shear wave velocities. Previous experimental result shows the density and molar volume of gadolinium phosphate glasses increase as more Gd2O3 being added into the system. On the other hand, the density of terbium phosphate glasses increased however their molar volume has slightly decreases with an addition of Tb2O3. The decreases of both ultrasonic wave velocities in both glass series might be due to the microstructure and rigidity of glass network. The experimental result shows the longitudinal (L), shear (G) and bulk modulus (K) of both glasses decrease while the Young’s modulus increases as more Gd2O3 and Tb2O3 reside into the phosphate network. Theoretical elastic behaviour of both types of phosphate glasses have been quantitatively studied via the bond compression model (bc) and, Makishima and Mackenzie (m) model. Comparison between the experimental (e) and calculated theoretical elastic data of gadolinium and terbium phosphate glasses has also been carried-out. Analysis show that based on the bond compression model, as the mole fraction of Gd2O3 increase in the (Gd2O3)x(P2O5)1-x glass system, both ratio of Kbc/Ke and the atomic ring size slightly increase. However for (Tb2O3)x(P2O5)1-x glass system, the Kbc/Ke and atomic ring size decrease as Tb2O3 are added into the glass system. Based on Makishima and Mackenzie model, the elastic moduli for both glasses decrease due to the decreasing in packing density of glasses. For the bulk modulus, Km value slightly higher as compared to Ke and Kbc. The Poisson’s ratio shows a good agreement with the experimental and calculated values. The difference of variation pattern between experimental data and Makishima and Mackenzie model is relatively large, while the difference between bond compression model and experiment result is quite comparable. Therefore, it can be concluded that Makishima and Mackenzie model is not so appropriate to be applied for both types of phosphate glasses.

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