EGU23-5863, updated on 10 Jan 2024
EGU General Assembly 2023
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

Estimation of missing third-law standard entropy of apatites using the optimized Volume-based Thermodynamics

Bartosz Puzio and Maciej Manecki
Bartosz Puzio and Maciej Manecki
  • AGH University of Science and Technology; Faculty of Geology, Geophysics and Environmental Protection; Department of Mineralogy, Petrography and Geochemistry; Kraków; Poland (

The standard absolute entropies of many minerals and mineral-based inorganic materials are unknown, thereby precluding a complete insight into their thermodynamic stability. This includes many apatites. The Apatite supergroup is one of the largest groups of minerals. Consequently, they are an incomparable testing ground for finding regularities in the variation of their thermodynamic function of state, e.g., standard entropy (S°). In the early 2000’s Jenkins and Glasser [1] showed that the formula unit volume alone, Vm, can be used to estimate the standard entropy for any inorganic compound.

It was recently indicated that in terms of their thermodynamic properties, the apatite supergroup splits into distinct subgroups (populations) [2]. These subgroups are formed by Me10(AO4)6X2 with the same Me2+ cations (e.g., Pb2+, Cd2+, Ca2+, Ba2+, Sr2+) and tetrahedral AO43- anions (e.g., A=P, As, V), but with different anions at the X position (e.g., F-, Cl-, Br-, I-, OH-). We found strong linear relationships between of apatites and their Vm observed within these subgroups. A system of linear relationships (calibrated with existing experimental data) indicating high positive correlations within selected subgroups of apatites is presented in Fig. 1.

Fig. 1 Standard entropy (S°) vs. formula unit volume (Vm)for selected apatite subgroups. Errors bars are within the marker.

Table 1. Selected estimated standard entropies (S°) and calculated formation entropies (ΔS°f, el)of iodine apatites.


Estimated S° (J/mol·K)

ΔS°f, el (J/mol·K)




















Using the new estimated with high accuracy values, it is possible to calculate the Gibbs energy of formation and plot stability fields for apatites for which this has not been possible so far. Financial support for the research was provided to B.P. by the Polish National Science Centre (NCN) grant No. 2017/27/N/ST10/00776.


[1] Jenkins, H. D. B., & Glasser, L. (2003). Standard absolute entropy, values from volume or density. 1. inorganic materials. Inorganic Chemistry42(26), 8702-8708.

[2] Puzio, B., & Manecki, M. (2022). The prediction method for standard enthalpies of apatites using the molar volume, lattice energy, and linear correlations from existing experimental data. Contributions to Mineralogy and Petrology177(11), 1-34.

[3] Wang, J. (2015). Incorporation of iodine into apatite structure: a crystal chemistry approach using Artificial Neural Network. Frontiers in Earth Science3, 20.


How to cite: Puzio, B. and Manecki, M.: Estimation of missing third-law standard entropy of apatites using the optimized Volume-based Thermodynamics, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-5863,, 2023.