Calculation of the Madelung constant for estimating the ionic bond energy in oxide crystals with cubic, tetragonal, and rhombic crystal systems

Background. The Madelung constants play an important role in the study of properties and behavior of crystalline solids as it relates the electrostatic potential of ionic crystal lattices with their parameters. Current research in this field aim to increase the speed of calculation, to develop of new algorithms with better series convergence, and to calculate the Madelung constants for more complex crystal structures. Recent calculations of the Madelung constants are focused on implementations of the Harrison method and methods developed on its basis, for example, on the Harrison-Sychev method. The purpose of this work is to apply the Harrison-Sychev method to a calculation of the Madelung constant, which is required to estimate the ionic bond energy in oxides and natural aluminosilicates contained in clays. Clay was chosen as the research object as it is used as a basis for many functional materials. Analysis of changes of binding energy within elementary latices caused by phase transitions in oxides is of a special interest.
Materials and methods. Clay is a dispersed system consisting of chemical compounds with an amorphous and crystalline structure. This research discusses the crystals of oxides that are part of the chemical composition of montmorillonite clays. Evaluation of the ionic bond energy in oxides with cubic, tetragonal, and rhombic crystal systems using the Born-Lande formula involves calculation of the Madelung constants. The Harrison-Sychev method was used in this research.
Results. The work presents an application of the improved Harrison (Harrison-Sychev) method for oxide crystals with a cubic crystal system, which are found in montmorillonite clay. The implementation of the Harrison-Sychev method for oxide crystals with tetragonal and rhombic crystal system is described in details. The Madelung constants are calculated for the tetragonal cell of titanium oxide and calcium chloride with a rutile structure. Theoretical and experimental data were compared and they were found to agree for a low value of the relative error. It is shown that the Harrison-Sychev method is suitable for calculation of the Madelung constants for crystals with a tetragonal crystal system.
Conclusions. The calculation results agree with the experimental data with a low value of the relative error. This allows one to claim that the improved Harrison-Sychev method is suitable for calculation of the Madelung constants for crystals with a tetragonal syngony.