Temperature dependence of thermal expansion of solids: A new approach in the terms of the Lambert function

Abstract The new equation for the temperature dependence of the thermal expansion of solids is explicitly presented in terms of the Lambert function. The resulting expression is suitable for a wide class of solids in the entire temperature range of the solid phase, in which, upon heating, there are no other phenomena causing changes in atomic volume, such as phase or glass transitions and the formation of vacancies. At temperatures well below the Debye temperature, the new equation provides a linear correlation between thermal expansivity and specific heat in accordance with Gruneisen's law. Whereas at intermediate temperatures not exceeding half the melting point, the [1/1] and [1/2] Pade approximants of the present equation reduce to the Gruneisen expressions in the second and third order of approximation. Unlike the previous ones, the new equation predicts a sharp increase in expansivity at high temperatures in accordance with experiment.