Determination of the elastic constants of portlandite by Brillouin spectroscopy S. Speziale a, ⁎, H.J. Reichmann a , F.R. Schilling a , H.R. Wenk b , P.J.M. Monteiro c a Deutsches GeoForschungsZentrum, Telegrafenberg, 14473 Potsdam, Germany b Department of Earth and Planetary Science, University of California, Berkeley, CA 94720-4767, U.S.A. c Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720-1710, U.S.A. ABSTRACT ARTICLE INFO Article history: Received 17 October 2007 Accepted 28 May 2008 Keywords: Ca(OH) 2 Elastic moduli Cement 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 0S =26.0(±0.3) GPa and G 0 =17.5(±0.4) GPa, respectively, while the Voigt bounds of these moduli are K 0S =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. © 2008 Elsevier Ltd. All rights reserved. 1. Introduction Portlandite, Ca(OH) 2 , is one of the most simple hydrous minerals. It has a trigonal symmetry with the space group P3̄1 (e.g. [1]) and is isostructural to brucite. The structure of portlandite is based on layers of distorted edge sharing CaO 6 octahedra stacked along the c-axis. The layers are separated by H atoms bonded with oxygens of the octahedral layer. Each oxygen atom is protonated with hydrogens dynamically disordered around the 3-fold axis with a maximum of probability density aligned along the c-axis at ambient conditions [2,3]. Portlandite is of great interest in cement and concrete research and for the cement industry because it is a primary solid phase in hydrated portland cement, representing as much as 20–25% of the cement paste's volume [4,5]. Its thermal and mechanical behavior affects the properties of cement and concrete, therefore it is important to determine the elastic properties of portlandite. The knowledge of the elastic stiffness tensor of portlandite will allow the determination of the local stress field at the interfacial transition zone between the aggregate and the cement paste where portlandite crystals tend to precipitate with a preferred orientation near the aggregate [6,7]. Furthermore portlandite has been used as an internal strain gauge in neutron diffraction experiment of frozen cement paste [8,9]. The conversion of the measured strains to stresses requires accurate values of the elastic coefficients of portlandite. Finally, due to its simple composition and structure, portlandite is an ideal model to evaluate the effect of OH on the elastic properties in more complex hydrous minerals, with implications for the understanding of the mechanisms of water recycling in the Earth's interior. Single-crystal elasticity of portlandite has been the subject of both computational and experimental studies. Laugesen [10] calculated the elastic coefficients C ij of Ca(OH) 2 by means of density functional method. Holuj et al. [11] determined the C ij utilizing Brillouin interferometry. However, the results of these two reports differ significantly in some constants, as in the case of C 13 whose experimental value is 3 times larger than the values obtained from the density functional calculations. In this paper we report the full set of elastic constants C ij at ambient conditions by means of Brillouin spectroscopy, and we resolve the existing discrepancy between experimental and first principles results. 2. Sample Single-crystals of portlandite were picked from a natural specimen, sampled in the Wessel Mine, in the Kalahari Manganese Field (South Africa). The specimen is a bulk aggregate consisting of about 10 platy crystals with almost constant orientation and maximum dimension up to 2 cm. The density of our sample material ρ = 2.242 (± 0.003) × 10 3 (kg/m 3 ) has been determined at the Deutsches GeoForschungs- Zentrum (GFZ) by powder X-ray diffraction using a STOE diffracto- meter equipped with a position sensitive detector. The incident radiation was monochromatic Cu K α1 . The unit cell parameters were Cement and Concrete Research 38 (2008) 1148–1153 ⁎ Corresponding author. E-mail address: speziale@gfz-potsdam.de (S. Speziale). 0008-8846/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.cemconres.2008.05.006 Contents lists available at ScienceDirect Cement and Concrete Research journal homepage: http://ees.elsevier.com/CEMCON/default.asp