Elastic Moduli, Hardness and Thermal Expansion of CaO-P₂O₅ and MgO-P₂O₅ Glasses

Abstract

Density, elastic moduli, Vickers hardness and thermal expansion coefficient for CaO-P₂O₅ (47.5-55.0mol% CaO) and MgO-P₂O₅ (47.5-57.5mol% MgO) glasses have been studied. Mean molar volumes calculated from mean molecular weight and density were compared with ideal mixed molar volumes estimated from the molar volumes of the constituent oxides in the phosphate glasses. The relationship between these two kinds of molar volumes for CaO-P₂O₅ glasses was a linear over the entire range of composition, whereas the relationship for MgO-P₂O₅ glasses was not linear with maximum deviation at the metaphosphate composition relative to the linear line for CaO-P₂O₅ glasses. The deviation decreased with a decrease in MgO content and the curve agreed with the linear line for CaO-P₂O₅ glasses about 33mol% MgO. There were definite relationships between elastic moduli (bulk modulus K, Young's modulus E, shear modulus G and Poisson's ratio ν) and mean atomic volume as follows; K=K₁V^f, E=K₂V^g, G=K₃V^h, 1+ν=K₄V^j, where f=-9.0, g=-5.1, h=-4.4, j=-0.7, for CaO-P₂O₅ glasses, f=-5.0, g=-3.4, h=-3.1, j=-0.3 for MgO-P₂O₅ glasses, There was a linear relationship between Poisson's ratio and density and also between Vickers hardness and void fraction φ for CaO-P₂O₅ glasses as well as MgO-P₂O₅ glasses; where φ=1-V₀/V_m, V₀=4/3π∑r_i³n_i, V_m: mean molar volume, r_i: ionic radius and n_i: number of i-ion. Vickers hardness decreased with increasing void fraction. Thermal expansion coefficient for compostions from 47.5 to 57.5mol% CaO or MgO increased with an increase in CaO or MgO content. The thermal expansion coefficients of CaO-P₂O₅ glasses (11.0-11.8×10^-61/K) were larger than those of MgO-P₂O₅ glasses (7.66-8.47×10^-61/K).