Theoretical model of temperature dependence of Young’s modulus

The force applied between two atoms is fitted by a sine curve as a function of bonding distance. The Young’s modulus (E) derived from this model is analyzed for heating temperature (T) of material. The dE/dT value is controlled by the summation of kβ + dk/dT, where k is the force constant of a spring binding two atoms and β is the linear thermal expansion coefficient. The derived dE/dT equation is expressed with four factors of Cp, dCp/dT, β and dβ/dT, where Cp is the specific heat capacity under atmospheric pressure. The decrease in dE/dT is prevented in the material with a small Cp and a small dβ/dT at a given temperature. The experimentally measured dE/dT for dense mullite material (3Al2O3·2SiO2) is well explained by comparing with the proposed dE/dT curve as a function of ε/β ratio with dimension of temperature (ε: thermal strain). The theoretical equation of dE/dT is compared with the reported empirical equation to reveal the factors included in the empirical parameters treated as experimental constants.