Exact analytical solution for the Kissinger equation: Determination of the peak temperature and general properties of thermally activated transformations

• Exact solution of the Kissinger equation for the peak temperature.
• Analytical solution for experimental and theoretical purposes.
• Analytical solution for numerical purposes.

A key parameter of many transformations when heated at a constant rate is the peak temperature, i.e., the temperature at which the transformation rate is at its maximum. The most universal approach to determine the peak temperature for thermally activated transformations is the Kissinger equation. In this paper, we solve Kissinger equation to deduce the exact dependence of the peak temperature on the heating rate. This analytical solution is based on the Lambert W-function. In addition, an approximate solution is derived that is used to infer general properties of thermally activated processes and to obtain a test to check the validity of Kissinger method.