HIGH PRESSURE ELASTICITY AND PHASE TRANSFORMATION IN BRUCITE, MG(OH)2

Abstract

The first pressure derivatives of the second-order elastic constants ${\rm d}C^{\prime}_{IJ}/{\rm d}p$ have been calculated for brucite, Mg(OH)2 from the second- and third-order elastic constants. The deformation theory and finite strain elasticity theory have been used to obtain the second- and third-order elastic constants of Mg(OH)2 from the strain energy of the lattice. The strain energy ϕ is calculated by taking into account the interactions up to third nearest neighbors in the Mg(OH)2 lattice. ϕ is then compared with the strain dependent lattice energy from continuum model approximation to obtain the expressions of elastic constants. The complete set of six second-order elastic constants C IJ of brucite exhibits large anisotropy. Since C 33 (= 21.6 GPa), which corresponds to the strength of the material along the c-axis direction, is less than the longitudinal mode C 11 (= 156.7 GPa), the interlayer binding forces are weaker than the binding forces along the basal plane of Mg(OH)2. The 14 nonvanishing components of the third-order elastic constants, C IJK , of brucite have been obtained. All the C IJK of brucite are negative except the values of C 114 (= 230.36 GPa), C 124 (= 75.45 GPa) and C 134 (= 36.98 GPa). The absolute values of the C IJK are, in general, one order of magnitude greater than the C IJ ’s in the Mg(OH)2 system as usually expected for a crystalline material. To our knowledge, no previous data are available to compare the pressure derivatives of brucite. The pressure derivatives of the two components viz., C 14 and C 33 become negative $({\rm d}C^{\prime}_{14}/dp = -1.51\;{\rm and}\;{\rm d}C^{\prime}_{33}/{\rm d}p= -1.41)$ indicating an elastic instability in brucite while under pressure. This may be related to the phase transition of brucite largely involving rearrangements of H atoms revealed in the Raman spectroscopic, powder neutron diffraction and synchrotron X-ray diffraction studies.