Determination of the elastic constants of portlandite by Brillouin spectroscopy

Abstract

The single crystal elastic constants C ij and the shear and adiabatic bulk modulus of a natural portlandite (Ca(OH) 2) crystal were determined by Brillouin spectroscopy at ambient conditions. The elastic constants, expressed in GPa, are: C 11 = 102.0(± 2.0), C 12 = 32.1(± 1.0), C 13 = 8.4(± 0.4), C 14 = 4.5(± 0.2), C 33 = 33.6(± 0.7), C 44 = 12.0(± 0.3), C 66 = ( C 11– C 12)/2 = 35.0(± 1.1), where the numbers in parentheses are 1σ standard deviations. The Reuss bounds of the adiabatic bulk and shear moduli are K 0 S = 26.0(± 0.3) GPa and G 0 = 17.5(± 0.4) GPa, respectively, while the Voigt bounds of these moduli are K 0 S = 37.3(± 0.4) GPa and G 0 = 24.4(± 0.3) GPa. The Reuss and Voigt bounds for the aggregate Young's modulus are 42.8(± 1.0) GPa and 60.0(± 0.8) GPa respectively, while the aggregate Poisson's ratio is equal to 0.23(± 0.01) . Portlandite exhibits both large compressional elastic anisotropy with C 11/ C 33 = 3.03(± 0.09) equivalent to that of the isostructural hydroxide brucite (Mg(OH) 2), and large shear anisotropy with C 66/ C 44 = 2.92(± 0.12) which is 11% larger than brucite. The comparison between the bulk modulus of portlandite and that of lime (CaO) confirms a systematic linear relationship between the bulk moduli of brucite-type simple hydroxides and the corresponding NaCl-type oxides.