Anisotropy and directional elastic behavior data obtained from the second-order elastic constants of portlandite Ca(OH)2 and brucite Mg(OH)2.

This article reports data on the anisotropy and directional elastic behavior, namely Young׳s modulus E, linear compressibility β, shear modulus μ, Poisson׳s ratio ν and wave velocities Vs1, Vs2 and Vp, of brucite (magnesium hydroxide, Mg(OH)2) and portlandite (calcium hydroxide, Ca(OH)2), calculated from their second order elastic constants at different hydrostatic compressions (Ulian and Valdrè, in press). The dataset has been obtained by ab initio quantum mechanical means, by employing density functional theory methods, in particular the B3LYP hybrid functional, all-electron Gaussian-type orbitals basis sets and a correction to take into account the effects of dispersive forces.

Specifications table

Value of the data

Elastic constants and related properties of brucite (magnesium hydroxide, Mg(OH)2) and portlandite (calcium hydroxide, Ca(OH)2) in space group settings and , useful for mechanical applications of these mineral phases.

Data obtained at the density functional theory (DFT) level, employing hybrid B3LYP functional and including a correction to take into account the contribution of dispersive forces, which could be useful for ab initio comparisons of similar materials.

The present data could be helpful for researchers involved in the mechanical properties of hydroxyl phases under the effect of applied pressure, e.g. for geological and building/cement applications.

Data

Brucite and portlandite mechanical properties variations with direction

Single-crystal elastic properties of both brucite and portlandite were calculated at T = 0 in the Cartesian space by using the second order elastic constants obtained in a previous work [1]. Two space group settings were considered, namely , where the hydroxyl groups are all oriented along the [001] direction and , which included some proton disorder in the structure. The effect of weak van der Waals interactions in both the equilibrium and hydrostatically compressed unit cells, and thus on the mechanical properties, was also taken into account. This is an important topic for both the mechanical and the surface properties for layered minerals. For the sake of clearness, in Table 1 the unit cell volumes of brucite and portlandite in each symmetry setup and their corresponding pressure are reported [1].

Table 1

Simulated unit cell volumes and the corresponding pressure values of brucite and portlandite in the space group settings and .

Model	BruciteP3¯m1		BruciteP3¯		PortlanditeP3¯m1		PortlanditeP3¯
	P (GPa)	V (Å3)	P (GPa)	V (Å3)	P (GPa)	V (Å3)	P (GPa)	V (Å3)
P01	−1.99	41.9998	−1.73	124.4219	−1.29	57.2331	−1.15	169.236
P02	−1.35	41.0678	−1.37	122.6337	−0.80	55.9663	−0.90	167.5269
P03	−0.51	40.1503	−0.63	120.0533	−0.20	54.7127	−0.43	164.5618
P00	0.08	39.6302	−0.04	118.4413	0.05	54.0043	−0.06	161.8418
P04	0.58	39.2426	0.48	117.3462	0.54	53.4761	0.26	160.1480
P05	1.95	38.3476	1.94	114.5878	1.43	52.2556	1.15	156.3257
P06	3.65	37.4628	3.75	111.8689	2.49	51.0434	2.24	152.6057
P07	5.71	36.5942	5.87	109.2402	3.76	49.8562	3.52	149.0702
P08	8.20	35.7381	8.30	106.7016	5.24	48.6894	4.96	145.7070
P09	11.19	34.8928	11.03	104.2052	6.97	47.5477	6.57	142.4289
P10	14.67	34.0735	14.00	101.8082	8.96	46.4321	8.34	139.228

Overall, the directional Young׳s modulus E, linear compressibility β, shear modulus μ, Poisson׳s ratio ν and wave velocities Vs1, Vs2 and Vp were calculated on the (xy), (xz) and (yz) planes for 44 structures and are reported in the Supplementary materials as follows:

Brucite (s.g ) – Tables S1–11;

Brucite (s.g ) – Tables S12–22;

Portlandite (s.g ) – Tables S23–33;

Portlandite (s.g ) – Tables S34–44.

The reported data can be employed, for instance, to create polar plots of the desired quantities and compare them to other theoretical or experimental results. An example of this application is reported in Fig. 1.

Fig. 1

Directional dependence of Young׳s modulus E (a), linear compressibility β(b), shear modulus μ (c), Poisson׳s ratio ν (d) and wave velocities Vs1, Vs2 and Vp on the (x,y), (x,z) and (y,z) planes, for brucite model P00 (s.g. , pressure 0.08 GPa). In (c,d) plots, solid lines are referred to the maximum values and dashed ones to the minimum ones.

Experimental design, materials, and methods

The data here presented were calculated from the results obtained by first principle simulations on periodic systems, using both the CRYSTAL14 [2] and CRYSTAL17 codes [3], which implements the Hartree–Fock and Kohn–Sham self-consistent field method. The same approach was employed to investigate the elastic behaviour of other phases containing hydroxyl groups [4].

Basis set

Multi-electron wave functions are constructed as an antisymmetrized product (Slater determinant) of monoelectronic crystalline orbitals (CO) that are linear combination of local functions (atomic orbitals, AO) centred on each atom in the system. In turn, atomic orbitals (basis set) are linear combinations of Gaussian-type functions (GTF). The all-electron basis sets employed in the present simulations for Ca2+ and Mg2+ were a 86–511 G* and a 8–511 G* basis sets [5], [6], [7], [8], [9]. For O and H atoms, a triple-ζ basis set with polarization from to the work of Ahlrichs and co-workers [10] has been adopted for both atoms.

Hamiltonian and computational parameters

The Becke [11] three-parameter (B3LYP) hybrid exchange functional in combination with the gradient-corrected correlation functional of Lee et al. [12] has been adopted for all calculations.The exchange–correlation contribution is performed over a grid of points and is the result of a numerical integration of the electron density and its gradient. The adopted pruned grid is given by 75 points and 974 angular points (XLGRID) and obtained from The Gauss–Legendre quadrature and Lebedev schemes [13]. The tolerance thresholds that control accuracy of the Coulomb and exchange integrals were set to 10−7 and 10−16, respectively [2]. The Hamiltonian matrix has been diagonalized using a Monkhorst grid of k-points of size 8 × 8 × 8 for the high symmetry models (s.g. ), whereas a 4 × 4 × 4 grid was employed for the low symmetry (s.g. ) ones.The convergence on total energy was reached when the difference between the energy of two subsequent self-consistent field cycles was less than 10−8 Ha.

Van der Waals (dispersive) forces were included with the (DFT+D2 scheme [14], which adds the following contribution to the calculated DFT energy:

The summation over all atom pairs ij and g lattice vectors excludes the self-interaction contribution (i = j) for every g. The parameters C represent the dispersion coefficient for the atom i, R is the interatomic distance between atom i in the reference cell and atom j in the neighbouring cells at distance |g| and s is a functional-dependent scaling factor. The function f is used to dump the energy correction to avoid double counting of short-range contributions to the energy and depends on the sum of atomic van der Waals radii and on a steepness parameter (d = 20). Due to the molecular nature of the DFT+D2 scheme, which tends to overestimate cohesive energy in solid crystals, the original B3LYP+D parameters where modified, setting s to 1, R(H) to 1.30 and the heavier atom van der Waals radii were scaled by a factor 1.05 (B3LYP-D* approach) [15], [16], [17].

Calculation of directional elastic properties

For the calculation of the directional dependence of the cited elastic properties, the stiffness tensor was transformed by means of:

Eq. (2), in which terms r are the direction cosines, employs the Einstein׳s summation rule. Within the Cartesian reference system, it is possible to represent a direction corresponding to an elastically significant distortion as a point on the unit sphere (unit vector a), using two angles, θ (0,π) and φ (0,2π):

For the calculation of the Young׳s modulus (E) or the linear compressibility (β), this single vector is sufficient. However, for shear modulus (μ) and the Poisson׳s ratio (ν), it is necessary to define a second vector b, placed perpendicularly to a. The second vector is characterized by a third angle, χ (0,2π), and by the coordinates:

Then, the coordinates of a and b represents the first two columns of the rotation matrix, which allow the calculation of all the components in the subvectorial space defined by directions 1 and 2 [18]:

The directional dependence of the elastic modulus and linear compressibility are defined as:whereas shear modulus and Poisson׳s ratio directional variation are given by the following formulas:

Wave velocities were calculated by solving the Christoffel׳s equation.

Subject area	Physics
More specific subject area	Directional mechanical properties of hydroxyl mineral structures calculated from their second order elastic constants at different pressures
Type of data	Table and figure
How data were acquired	Quantum mechanical simulations at the DFT/B3LYP level of theory, including dispersive forces contributions (CRYSTAL14 code)
Data format	Raw, analyzed
Experimental factors	Initial geometries were taken from experimental data available in literature
Experimental features	Quantum mechanical simulations conducted using Density Functional Theory, B3LYP functional and Gaussian-type orbitals basis sets.
	Inclusion of dispersive forces contribution via DFT-D2 scheme, corrected for the B3LYP functional (B3LYP-D* approach).
	Unit cell under different hydrostatic compression states.
Data source location	Bologna, P. Porta San Donato 1, Italy
Data accessibility	Data are displayed within this article.
Related research article	This Data in Brief article is related to the paper:
	Ulian, G. & Valdrè, G. (2018) Equation of state and second-order elastic constants of portlandite Ca(OH)2and brucite Mg(OH)2. Physics and Chemistry of Minerals, in press,doi:10.1007/s00269-018-0989-3.