A comparison of methods for the estimation of the enthalpy of formation of rare earth compounds.

Rare earth elements are helping drive the global transition towards a greener economy. However, the way in which they are produced is far from being considered green. One of the major obstacles to developing greener production methods and the design of novel processes and materials involving rare earth elements is the limited thermodynamic data available. In the present work, we apply a suite of methods to estimate the enthalpy of formation of several rare earth compounds, including a new method based on a linear relationship, established by the authors. Experimental values of the enthalpy of formation of LnCl3, LnOCl, LnPO4, Ln2O2S, Ln2O2CO3 and NaLnO2 were collated and used to assess the accuracy of the different methods, which were then used to predict values for compounds for which no data exists. It is shown that Mostafa et al.'s group contribution method and the linear relationship proposed by the authors give the lowest mean absolute error (<9%). The volume based thermodynamics (VBT) method yields estimates with absolute mean errors below 16.0% for LnPO4 and Ln2O2S, but above 26.0% for other compounds. Correction of the VBT method using an improved estimate of the Madelung energy for the calculation of the lattice enthalpy decreases the absolute mean error below 12.0% for all compounds except LnPO4. These complementary methods provide options for calculating the enthalpy of formation of rare earth compounds, depending on the experimental data available and desired accuracy.