摘要
In first-order approximation, the interaction potential function among atoms in solidsmay be expressed aswhere g_α depends on the electron structures of solids; r_α and r_(αo) express the distancesbetweell two atoms in nonequilibrium and equilibrium respectively ; α≡A, B, C, …, de-noting the quantities related to the nearest, next-near and the third near neighbours withrespect to the reference atom, and the quantity related to the lattice electron; λ_D beingthe average Debye wavelength; n is the bond strength parameter determined by the theo-retical formula derived by the author. Using the Debye model of solids, the total ener-gy E_(Tτ) of the solid at T(K) can be obtained easily. Then the functional relation ofthe lattice constant γ_(AOT) (T) with T(K) can be found out by solving the equation V(p_α,γA) - E_(Tτ) = 0 for γ_A and that of the linear thermal expansion coefficient α(T) and T(K)can be derived further. The theory has been applied to the alkali and alkaline earthmetals and the results agree well with the experimental. In the paper, we have also calculated the Gruneisen constants using the theoreticalvalues of the linear thermal expansion coefficient α(T) and that of the bulk modulus obtain-ed previously by the author, and made their comparison with the values calculated fromthe experimental data. Furthermore, the product of the melting point T_m and α(T) approx-imates the Hindnert-Sonder rule. These results demonst rate that the new type of theinteraction potential function among atoms in a solid and the electron theory of thermalexpan sion established in the paper are practical and worth further developing.
In first-order approximation, the interaction potential function among atoms in solidsmay be expressed aswhere g<sub>α</sub> depends on the electron structures of solids; r<sub>α</sub> and r<sub>αo</sub> express the distancesbetweell two atoms in nonequilibrium and equilibrium respectively ; α≡A, B, C, …, de-noting the quantities related to the nearest, next-near and the third near neighbours withrespect to the reference atom, and the quantity related to the lattice electron; λ<sub>D</sub> beingthe average Debye wavelength; n is the bond strength parameter determined by the theo-retical formula derived by the author. Using the Debye model of solids, the total ener-gy E<sub>Tτ</sub> of the solid at T（K） can be obtained easily. Then the functional relation ofthe lattice constant γ<sub>AOT</sub> （T） with T（K） can be found out by solving the equation V（p<sub>α</sub>,γA） - E<sub>Tτ</sub> = 0 for γ<sub>A</sub> and that of the linear thermal expansion coefficient α（T） and T（K）can be derived further. The theory has been applied to the alkali and alkaline earthmetals and the results agree well with the experimental. In the paper, we have also calculated the Gruneisen constants using the theoreticalvalues of the linear thermal expansion coefficient α（T） and that of the bulk modulus obtain-ed previously by the author, and made their comparison with the values calculated fromthe experimental data. Furthermore, the product of the melting point T<sub>m</sub> and α（T） approx-imates the Hindnert-Sonder rule. These results demonst rate that the new type of theinteraction potential function among atoms in a solid and the electron theory of thermalexpan sion established in the paper are practical and worth further developing.
