Energy of Anion Polarization in Layered Structures

Abstract

I n layered structures the anion position has low local symmetry. The result are induced anion dipoles which strongly interact with each other and with all the remaining crystalline matrix. Two different sppronchcs are examined t o take account of the anion polarization energy in layered structures. The lattice energy is calculated with regard to the anion polarization term for some halides of bivalent metals (Mg, Ca, Cd, Mn, Pb). The polarization correction t o lattice energy is found to be large, 3 to 4 eV. Impurity dissolution energies are recalculated for those cases where the pure impurity component forms a layered structure: their values are found t o be positive and correct in order of magnitude.

Analytic dependence of the Madelung constant on lattice parameters for 2D and 3D metal diiodides (MI2) with CdI2 (2H polytype) layered structure

“…The data for the Madelung constants of metal diiodides MI 2 (M=Mg, Ca, Mn, Fe, Cd, Pb), with CdI 2 (2 H polytype) structure, are available in a number of publications [24,29,30,[39][40][41]. However, the parameter A M for different MI 2 compounds was calculated by applying alternative methods, with different precisions.…”

“…It should be noted that, in above cited publications [22,24,29,40,41] reporting the data for the Madelung constant, equation (1) is expressed in other form in terms of the definition of the Madelung constant:…”

“…was proposed by Herzig and Neckel [39]. However, in the case of compounds with parameters u considerably deviating form a value = u 0.25, the above dependence cannot result in precise value for constant A , M since A M is very sensitive to variations of the parameter u [24,29]. De Haan conducted a numerical analysis [40,41] for the dependence of the Madelung constant of some metal dihalides MX 2 , with CdI 2 (2 H polytype) structure, on the c a / ratio and the geometrical parameter characterizing the degree of inclination of M-X bonds with respect to the crystallographic c axis.…”

“…Especially in applications of the exfoliation methods (through-solution, mechanical, intercalation) for preparation of 2D nanolayers of MI 2 layered compounds [2,16,[19][20][21], it is of technological interest the theoretical quantification of the cohesive energy (intralayer and interlayer) both in 2D layers/nanolayers and parent 3D bulk crystals. In metal dihalides (MX 2 ) and particularly in MI 2 compounds, the chemical bonds are partially ionic and partially covalent, with dominating iconicity [22][23][24][25][26][27][28], and this results in dominating contribution of the Coulomb electrostatic energy to the total cohesive energy (cohesive energy includes also the repulsive, polarization, van der Waals, and covalent energies) [22][23][24][25]29]. In its turn, the evaluation of the Coulomb electrostatic energy assumes, besides the partial (non-formal) ionic charges, also the precise knowledge of the Madelung constant, which characterizes the type of crystallographic arrangement of constituent ions in the crystal lattice [22,24,30].…”

“…The Madelung constant (A M ) of metal dihalides (MX 2 ) and particularly of metal diiodides (MI 2 ), with the crystallographic structure of CdI 2 polytypes (2 H, 4 H, P6 3 mc, etc), is dependent on the three crystallographic lattice parameters: the lattice constants along the a and c crystallographic axes, a and c, and the fractional out-ofplane coordinate u of halogen ion (X) in a unit cell [24,25,[29][30][31][32][33][34][35][36][37][38]. It is not a simple task to obtain an analytic dependence (i.e., analytic functional form) A a c u , , M ( )from corresponding lattice summation.…”