The elasticity anisotropy in the basal atomic planes of Mg(OH)2 and Ca(OH)2 associated with auxetic elastic properties of the hydrogen sub-lattice

Within the framework of the Hook’s generalized law and using the experimental data for characteristic crystallographic parameters and stiffness constants available from literature, the individual elastic properties of constituent octahedral layers and interlayers of the (0 0 0 1) atomic planes in the Mg(OH)2 and Ca(OH)2 crystal lattices are theoretically quantified from intermolecular interaction energy. It is shown that, under uniaxial type of deformation applied along the (0 0 0 1) basal planes, in the “load-deformation response” the octahedral layers and interlayers exhibit the positive and negative Poisson’s ratio, respectively. Manifestation of such a type strong elastic anisotropy in the basal atomic planes and auxetic elastic behavior of the hydrogen sub-lattice (interlayers) upon applied uniaxial load result from a large difference in the strength of bonding within octahedral layers and interlayers. The intermolecular binding energy is contributed both by “hydroxyl–hydroxyl” and “metal atom–hydroxyl” dispersion interactions, whereas the Young’s modulus in the direction parallel to a (0 0 0 1) plane is practically contributed only by the former interaction. For this Young’s modulus, an approximate analytical expression is derived, which is convenient for a physical analysis and presumably is also applicable to other metal hydroxides with brucite structure. The proposed theoretical model may be extended to hydrostatic type loading of metal hydroxides for analysis of the hydrogen associated bonding under high-pressure conditions. The approach applied in this study to estimate the dispersive energy may be useful in the evaluation of the physisorption energy for system “H2–metal hydroxide” in terms of the potential application of metal hydroxides as hydrogen storage materials.

Graphical abstractTo the out-of-plane strain εxεx induced in the (0 0 0 1) atomic planes of Mg(OH)2, the contributions of constituent octahedral layers εx(1) and interlayers εx(2) are of opposite sign.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Elasticity anisotropy of rare earth metal hydroxides is theoretically analyzed. ► Elastic anisotropy within (0 0 0 1) atomic planes is studied from energy consideration. ► The out-of-plane Poisson’s ratios of octahedral layers and interlayers are of opposite sign. ► Auxeticity of the hydrogen sublattice (interlayers) results from weak interlayer bonding. ► The obtained expression for the in-plane Young’s modulus results in useful conclusions.