Infrared spectra of jennite and tobermorite from first-principles

Cement and Concrete Research 60 (2014) 11–23

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Infrared spectra of jennite and tobermorite from first-principles Alexandre Vidmer ⁎, Gabriele Sclauzero, Alfredo Pasquarello Chaire de Simulation à l'Echelle Atomique (CSEA), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

a r t i c l e

i n f o

Article history: Received 19 June 2013 Accepted 12 March 2014 Available online 29 March 2014 Keywords: Calcium–silicate–hydrate (C–S–H) (B) Crystal structure (B) Density functional theory (DFT)

a b s t r a c t The infrared absorption spectra of jennite, tobermorite 14 Å, anomalous tobermorite 11 Å, and normal tobermorite 11 Å are simulated within a density-functional-theory scheme. The atomic coordinates and the cell parameters are optimized resulting in structures which agree with previous studies. The vibrational frequencies and modes are obtained for each mineral. The vibrational density of states is analyzed through extensive projections on silicon tetrahedra, oxygen atoms, OH groups, and water molecules. The coupling with the electric field is achieved through the use of density functional perturbation theory, which yields Born effective charges and dielectric constants. The simulated absorption spectra reproduce well the experimental spectra, thereby allowing for a detailed interpretation of the spectral features in terms of the underlying vibrational modes. In the far-infrared part of the absorption spectra, the interplay between Ca and Si related vibrations leads to differences which are sensitive to the calcium/silicon ratio of the mineral. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Concrete is a widely used building material, but its microscopic structure is not yet fully understood [1]. The main binding phase in most types of concrete consists of calcium silicate hydrates (C–S–H) and is responsible for its strength properties [2]. Therefore, it is important to characterize the microscopic structure of C–S–H. Since the C–S–H in concrete are poorly crystalline, their atomic structure cannot be solved by X-ray diffraction experiments (XRD) [3]. Moreover, the calcium to silicon (C/S) ratio can vary from 1.2 to 2.1 in a given cement paste [4]. To overcome these difficulties, research has focused on several crystalline model systems of given C/S ratio which show similar structural arrangements as C–S–H. Through XRD experiments, Bernal et al. showed similarities between C–S–H in cement paste and tobermorite, a mineral that can be found in nature [5]. Similarly, the mineral jennite is often considered to describe the properties of C–S–H with higher C/S ratios [6]. Jennite and tobermorite are both mostly composed of Ca–O sheets connected on both sides by infinite silicate chains named ‘dreierketten’ [1]. These chains give rise to typical signatures identifying twofold coordinated Si tetrahedra in both nuclear magnetic resonance [7,8] and Raman spectroscopy [9] experiments. The Ca\O sheets in jennite are corrugated [10] giving a C/S ratio much larger than that of tobermorite (1.5 for jennite vs. 0.83 or less for tobermorite). Tobermorite and jennite structures generally serve as starting point for the construction of C–S–H models [8,3,11], which are then used to advance our understanding of this phase. These minerals have been the object of extensive experimental investigation in the last decade. ⁎ Corresponding author. Tel.: +41 21 69 33436. E-mail address: [email protected] (A. Vidmer).

http://dx.doi.org/10.1016/j.cemconres.2014.03.004 0008-8846/© 2014 Elsevier Ltd. All rights reserved.

Merlino, Bonaccorsi and co-workers have characterized the structures of tobermorite 11 Å [12], tobermorite 14 Å [13], and jennite [10] through XRD experiments. The proposed protonation scheme of O atoms in jennite has been confirmed later by first-principles molecular dynamics [14]. Structural properties and elastic constants have been investigated through first-principles methods for jennite and various forms of tobermorite [15]. Infrared (IR) spectroscopy techniques have also been used to investigate C–S–H of various C/S ratios [16]. IR spectroscopy is an analytical technique which is sensitive to vibrational modes, thereby indirectly providing information on the local atomic structure. To interpret the IR spectra obtained for C–S–H, analogous spectra were obtained for jennite and tobermorite [16]. IR spectra of C–S–H with a C/S ratio greater than 1.7 were found to show similarities with that of jennite, whereas those with C/S ratios lower than 1.7 resembled that of tobermorite. Theoretical modeling of infrared spectra has remained limited. The IR spectrum of tobermorite 14 Å has only been studied through semiempirical simulations [17]. First-principles calculations of infrared spectra have been performed on small molecular clusters intended to model C–S–H [18]. However, IR spectra of tobermorite and jennite minerals have so far not been achieved through first-principles simulations. In this work, we model the infrared absorption spectra of jennite, tobermorite 14 Å, and tobermorite 11 Å through first principles in order to provide a detailed description of the underlying active vibrational modes. For tobermorite 11 Å, we consider both the anomalous and the normal structure [12]. In particular, we aim at understanding to what extent this knowledge can be used to infer structural properties of C–S–H from their infrared spectra. Our investigation is composed of several parts. First, a fully geometrically optimized structure is obtained for each mineral and compared with previous experimental and

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A. Vidmer et al. / Cement and Concrete Research 60 (2014) 11–23

theoretical studies. In particular, we analyze the structural properties leading to specific vibrational signatures. Next, the vibrational frequencies and modes are calculated and analyzed in terms of atom-specific contributions. The vibrational modes are also distinguished by considering their projections on the tetrahedra composing the silicate chains, the oxygen atoms in differing environments, the water molecules, and the OH groups. The infrared spectra are obtained by considering the coupling between the vibrational modes and an electric field. The simulated infrared spectra are found to give a good description of their experimental counterparts, allowing us to establish a correspondence between calculated and measured peaks. This correspondence provides the basis for the interpretation of the experimentally observed peaks in terms of the underlying vibrations. Finally, we highlight specific features in the absorption spectra of each mineral and relate them to their underlying structural properties. The relevance of the present results for the interpretation of the infrared spectra of C–S–H is discussed. The article is organized as follows. In Section 2, we describe the methods used for the calculation of IR spectra and give the computational parameters. In Section 3, we describe the structures obtained upon full geometrical optimization. In Section 4, we present and analyze the vibrational modes. The IR spectra and their interpretation are given in Section 5. In Section 6, the spectra of various minerals are compared and the conclusions are drawn. 2. Methods The simulations in this work are performed within density functional theory (DFT) [19,20] using the plane-wave implementation in the QUANTUM ESPRESSO (QE) suite of electronic structure codes [21]. We use the generalized-gradient approximation (GGA) to the exchangecorrelation functional as proposed by Perdew, Burke, and Ernzerhof [22]. The interaction of the valence electrons with the nuclei and the core electrons is described through ultrasoft pseudopotentials (US-PP) [23]. All the US-PP are taken from the official website of QE. The Ca 3s and 3p semi-core states are included among the valence states. After detailed convergence tests, the kinetic energy cutoffs are set at 50 and 550 Ry for the wave functions and the electron charge density, respectively [24,25]. For the optimization of the structures, we simultaneously minimize the forces acting on the atoms and the stress acting on the cell. For the tobermorite structures, the initial atomic positions and cell parameters are taken from experimental data [12,13], while we find it more convenient to start the jennite optimization from previous coordinates found from first-principles [14]. The structural optimizations are continued until each component of the atomic forces is below 0.006 eV/Å and each component of the stress tensor is below 0.1 kbar. Jennite is simulated using a triclinic cell with two k-points along the shortest direction of the cell (b axis, see also Table 1). Tobermorite cells are simulated through monoclinic cells with 2 k-points along the two shortest directions (axes a and b). Convergence with respect to k-point sampling and size of the basis set is carefully checked.

A finite-difference method is used to build the force-constant matrix. To obtain the numerical derivatives of the forces, each atom is displaced by + Δx and −Δx along the three Cartesian directions. The size of the displacements results from a trade-off: it needs to be large enough to avoid numerical errors, but small enough to remain in the harmonic region of the potential. The value of the displacement is set at Δx = 0.05 Å. For jennite, we check that the vibrational density of states obtained in this way closely agrees with that obtained through density functional perturbation theory [21,26]. To simulate the infrared spectra, the coupling with an electric field is achieved within density functional perturbation theory [21,26]. We calculate the Born effective charge tensors of each atom in our model systems. The Born effective charge tensor is defined as the variation of the polarization induced by a given atomic displacement [26]: Z I;ij ¼ Ω

∂P i ; ∂r Ij

ð1Þ

where Pi is the polarization along direction i, rIj is the displacement of ion I along j, and Ω is the volume of the unit cell. The high frequency dielectric constant is given by: ij

ϵ∞ ¼ δij þ 4π

∂P i ; ∂E j

ð2Þ

where Ej is the electric field along direction j. It is convenient to introduce the oscillator strengths: n

Fi ¼

X Ij

ξnIj  Z I;ij pffiffiffiffiffiffi ; MI

ð3Þ

where ξnIj corresponds to the displacement of atom I along j in the vibrational mode n and MI is the mass of ion I. The real part of the dielectric function in the long wavelength limit can be written as [27–29]: 4π X jF j ; 3Ω n ω2 −ω2n n 2

ϵ1 ðωÞ ¼ ϵ∞ −

ð4Þ

and the imaginary part as:

ϵ2 ðωÞ ¼

 n 2 4π2 X  F  δðω−ωn Þ: 3Ω n 2ωn

ð5Þ

The frequency-dependent refractive index can then be expressed in terms of the dielectric functions: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u tϵ1 ðωÞ þ ϵ1 ðωÞ2 þ ϵ2 ðωÞ2 nðωÞ ¼ : 2

ð6Þ

Table 1 Calculated cell parameters of jennite and tobermorite structures compared to experimental data [10,13,12]. The present results are also compared with previous DFT calculations (DFT-GGA) obtained with a single k-point [15]. α, β, and γ are the angles between axes b and c, a and c, and a and b, respectively.

Jennite

Tobermorite 14 Å

Tobermorite 11 Å (anomalous)

Tobermorite 11 Å (normal)

Present DFT-GGA [15] Expt. [10] Present DFT-GGA [15] Expt. [13] Present DFT-GGA [15] Expt. [12] Present Expt. [12]

a (Å)

b (Å)

c (Å)

α

β

γ

10.66 10.70 10.58 6.64 6.87 6.74 6.82 6.80 6.74 6.82 6.73

7.31 7.34 7.27 7.41 7.43 7.43 7.47 7.51 7.39 7.46 7.37

10.97 10.89 10.93 28.18 28.49 27.99 22.70 22.57 22.49 22.67 22.68

100.87° 102.11° 101.30° 90.00° 89.96° 90° 90° 89.83° 90° 90.27° 90°

97.86° 95° 96.98° 89.99° 90.05° 90° 90° 89.05° 90° 89.12° 90°

109.31° 109.82° 109.65° 121.66° 123.47° 123.25° 123.22° 123.43° 123.25° 123.24° 123.18°

A. Vidmer et al. / Cement and Concrete Research 60 (2014) 11–23

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Finally, the IR absorption spectrum is obtained through [28] α ðωÞ ¼

ω ϵ ðωÞ; cnðωÞ 2

ð7Þ

Ca2

where c is the speed of light. 3. Structures In this section, we focus on the structures of the minerals considered in this work, i.e. jennite, tobermorite 14 Å, and tobermorite 11 Å in both its anomalous and normal form. Nominally, jennite is triclinic and the tobermorite minerals are monoclinic. These minerals are modeled through simulation cells corresponding to the basic unit cell, containing 69, 104, 88, and 87 atoms, respectively. Their respective space groups are P1, B11b, and B11m. For each mineral, we perform a full relaxation of the cell parameters and the atomic positions within the unit cell. The optimized cell parameters are shown in Table 1, while the detailed atomic positions are given in the Supplemental material [30]. In tobermorite 14 Å and in the normal form of tobermorite 11 Å, some atomic sites in the basic unit cell show partial occupation which cannot be described through a simulation cell corresponding to the basic unit cell. In these cases, only some of these sites are occupied such that the stoichiometric formula is respected. This modeling approach breaks the nominal symmetry of the unit cell and is at the origin of the small deviations of the angles α and β from 90° in Table 1. Focusing on the cell parameters in Table 1, we observe that differences between experimentally derived parameters and our results are around 1%. We notice that the lengths of the lattice vectors obtained from the optimization are generally slightly larger than the experimental ones, which is a typical feature of GGA functionals [31]. However, the lengths of a and b in tobermorite 14 Å and the length of c in normal tobermorite are slightly shorter than experimental results. All the minerals in the present study share the same layered structure: they are all composed by ribbons of edge-sharing calcium polyhedra, i.e. Ca atoms surrounded by six or seven O atoms. All minerals also show chains of Si tetrahedra, corresponding to Si atoms coordinated by four oxygen atoms. These chains are usually called dreierkette silicate chains and have a periodicity of three tetrahedra. Two of these tetrahedra share edges with Ca polyhedra, while the third one does not share edges with any Ca polyhedron [32]. The former are called ‘paired tetrahedra’, while the latter is called ‘bridging tetrahedron’ because it belongs to the structure which links adjacent Ca\O layers. For jennite, this can be recognized in Fig. 1.

Ca3 Si3

Ca5

Ca3 Si1 Ca4 O8 Si1 Si2

O8 Si1 Ca1

Si2

Si1 Si3

3.1. Jennite The chemical formula of jennite is Ca9Si6O18(OH)6·8H2O and its density is 2.325 g/cm3. The detailed structure of jennite was solved by Bonaccorsi et al. [10]. In particular, they proposed a protonation scheme in which the H atoms are exclusively found in water or attached to O atoms bound to Ca, as opposed to a previous suggestion by Cong and Kirkpatrick by which some OH groups are attached to Si atoms [33]. The protonation scheme proposed by Bonaccorsi and coworkers was successfully validated by Churakov using first-principles molecular dynamics [14]. We therefore use the atomic coordinates in Ref. [14] as starting point for our structural relaxations. In Fig. 1, we show the structure of jennite obtained from the optimization of the atomic positions and cell parameters (cf. Table 1). In the figure, Ca polyhedra and Si tetrahedra are labeled according to the corresponding central atom. In this structure, Si2 and Si3 are the paired tetrahedra, while Si1 is the bridging tetrahedron. The Ca5 octahedron is not sharing any edge with other polyhedra and is located at a high symmetry position. In jennite, only single silicate chains occur implying that there are no connections between tetrahedra belonging to different chains. The O8 atom belongs to the bridging tetrahedron. Since it has

Ca2

O8 Ca5

Fig. 1. Atomic structure of jennite as seen along crystal axes b (top part) and a (bottom part). Ca polyhedra (in red) and Si tetrahedra (in blue) are labeled according to their central atom. The paired tetrahedra are Si2 and Si3, while the bridging tetrahedron is Si1. The unit cell is indicated by dashed lines.

no other Si or Ca neighbors, it is a strong proton acceptor. Indeed, the bond distance between O8 and the nearest H atoms of water molecules is about 1.5 Å, which is shorter than typical hydrogen-bond lengths in liquid water (1.8 Å [34]). In Table 2, we report Ca\O and Si\O bond lengths. Compared to experiment, the error is below 3% in most cases. The bond lengths are generally overestimated as usual in the GGA [31], but in a few cases we record underestimations. Overall, our results are consistent with previous density-functional simulations [14]. Some of the largest deviations from experiment (5%) occur for Si2\O4 and Si2\O5, confirming the large deviations obtained in a previous study [14]. However, unlike in the study of Ref. [14], we also find a rather large deviation (3.5%) for the Ca4\O7 bond length.

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A. Vidmer et al. / Cement and Concrete Research 60 (2014) 11–23

Table 2 Ca\O and Si\O bond lengths (in Å) in the jennite structure. Results obtained in this work are compared to previous DFT calculations obtained with the BLYP functional at a temperature of 0 K [14] and to experimental results [10]. Atoms with the same denomination are related by inversion symmetry. W stands for the O atom in a water molecule.

Ca1

Ca2

Ca3

Ca4

Ca5

Si1

Si2

Si3

O1 O11 O12 O4 O10 O4 O3 O9 O11 O3 O2 O14 O1 O2 O4 O12 O10 O10 O2 O9 O11 O13 O9 O3 O7 O12 W1 W2 O8 O6 O5 O1 O5 O3 O7 O4 O6 O10 O9 O7

Present

BLYP [14]

Expt. [10]

2.40 2.36 2.39 2.44 2.47 2.51 2.35 2.37 2.37 2.41 2.32 2.50 2.36 2.33 2.41 2.45 2.47 2.48 2.34 2.34 2.34 2.51 2.56 2.56 2.87 2.47 2.41 2.35 1.62 1.67 1.65 1.62 1.65 1.63 1.66 1.63 1.66 1.63 1.63 1.66

2.39 2.35 2.38 2.47 2.48 2.47 2.36 2.36 2.37 2.36 2.32 2.51 2.37 2.33 2.41 2.43 2.45 2.45 2.34 2.44 2.34 2.50 2.44 2.50 2.82 2.46 2.39 2.33 1.62 1.67 1.65 1.62 1.65 1.63 1.66 1.63 1.66 1.62 1.62 1.65

2.35 2.35 2.38 2.43 2.41 2.49 2.33 2.35 2.35 2.35 2.36 2.54 2.34 2.33 2.36 2.39 2.46 2.47 2.34 2.36 2.40 2.45 2.48 2.51 2.77 2.50 2.36 2.36 1.61 1.66 1.66 1.66 1.57 1.61 1.65 1.71 1.61 1.62 1.63 1.65

3.2. Tobermorite 14 Å The chemical formula of tobermorite 14 Å is Ca5Si6O16(OH)2·7H2O, and its density is about 2.23 g/cm3. The atomic positions and cell parameters as determined through XRD experiments [13] are used as starting point for the structural relaxation of this crystal. The relaxed structure is shown in Fig. 2. The unit cell is composed by two layers of Ca polyhedra ribbed by dreierkette silicate chains with one Ca polyhedron in the interlayer region (Ca2). Ca2 is connected to the layers by the bridging tetrahedron Si2. The protonation scheme differs from that of jennite. In tobermorite 14 Å, OH groups are attached to one Si and one Ca atom, while in jennite they are bound to two Ca atoms. O atoms having one Si and one Ca neighbor but which do not belong to an OH group always form hydrogen bonds of small length (~ 1.5– 1.6 Å) with a H atom of a neighboring water molecule. Bond distances are shown in Table 3. Compared to experimental data, Ca\O bond lengths show larger deviations than for jennite, especially for the interlayer Ca2 polyhedron. The origin of these larger deviations is unclear, but could result from the fact that the experimental data are obtained at finite temperature whereas the structure in the simulation is fully relaxed. The enhanced importance of thermal effects might be due to the lower density in the interlayer region of tobermorite 14 Å, which should allow for vibrational modes of lower frequency and thus facilitate alternative structural arrangements. Si\O bond lengths show the same kind of agreement as in jennite.

3.3. Tobermorite 11 Å Tobermorite 11 Å comes in two different varieties, anomalous tobermorite 11 Å and normal tobermorite 11 Å [12]. The difference between the two is the presence (normal tobermorite) or absence (anomalous tobermorite) of an additional Ca atom (Ca2) in the interlayer. The structures of both forms of tobermorite 11 Å are closely related to the one of tobermorite 14 Å, as the former can be obtained by heating the latter at 90–120 °C [35]. Upon further heating at 300 °C, the basal spacing of the normal form shrinks to 9 Å, while the one of the anomalous form remains unaffected [36]. After the heating process, the additional Ca atom present in the normal form is no longer properly coordinated as its neighboring water molecules are lost. In order to complete its coordination, this Ca atom binds to O atoms present in the complex layers, which is achieved by a shrinking of the basal spacing [12]. The structure of anomalous tobermorite 11 Å is shown in Fig. 3. Its chemical formula is Ca4Si6O15(OH)2·5H2O and its density is 2.38 g/cm3. The upper and lower silicate chains are connected together by the bridging tetrahedron Si2 and form a so-called double silicate chain. The protonation scheme is similar to that of tobermorite 14 Å. Bond lengths in the Ca\O layers and in the silicate chains of anomalous tobermorite are shown in Table 4. Our Si\O bond lengths are in very good agreement with experimental measurements [12] and previous simulations at ambient temperature [37]. Except for a 5% overestimation of the Ca1\W6 distance, all Ca\O bond lengths agree within 2%. Overall, we also record a good general agreement with the previous simulations in Ref. [37]. However, we remark that we find significant differences for some Ca\O bond lengths, e.g. the two Ca\O4 bond lengths differ appreciably in our study, while they coincide in the structure of Ref. [37]. The chemical formula of normal tobermorite 11 Å is Ca4.5Si6O16 (OH)·5H2O. To model this structure, one Ca atom is added and two H atoms belonging to OH groups are removed per unit cell as compared to its anomalous counterpart. Ca2 can occupy four different sites. Thus, by using a supercell encompassing several unit cells, one could alternate the occupied Ca2 site between cells and obtain the same concentration of Ca in both interlayers, as done by Churakov in his first-principles simulations [37]. In this work, we only use a single unit cell implying that Ca2 always occupies the same site. Upon optimization of the structure, a change in the protonation scheme takes place. One of the hydrogen atoms which initially belonged to a water molecule (W3) is found to detach and bind to an O atom of a Si tetrahedron (O6, corresponding to an OH group in anomalous tobermorite). The resulting structure thus acquires two additional OH groups and loses one H2O molecule. This local transformation might be caused by the small separation between the Ca2 atom and its periodic images when a single unit cell is adopted for modeling normal tobermorite 11 Å. Bond distances are shown in Table 5. Deviations with respect to experiment are generally below 3%, but reach 5% for a few bond lengths, mirroring the same kind of deviations noticed in Ref. [37]. Additionally, the Ca2\W3 and Ca2\O1 bond lengths show exceptionally large deviations of 7% and 12%, respectively. These discrepancies might result from the small periodicity of our simulation cell. 4. Vibrational properties In this section, we address the vibrational properties of jennite and various tobermorite minerals. In Fig. 4, we show their vibrational density of states (v-DOS) and their respective projections onto atomic species. We only consider frequencies up to 1700 cm−1. The vibrational modes at higher frequencies are entirely due to water and are strongly dominated by thermal effects. Their description is thus beyond the scope of the present work, in which the vibrational modes are studied within the harmonic approximation. All the v-DOSs in Fig. 4 are quite similar up to 300 cm−1, especially those of the two tobermorites. In this range of frequencies, the main contribution comes from the Ca and O atoms forming the Ca\O ribbons,

A. Vidmer et al. / Cement and Concrete Research 60 (2014) 11–23

15

Ca3

Ca1 Ca1

Si1

Ca2 Si2 Si1 Ca3

Ca3

Si1 Si3

Si2

Si2

Si2 Si1 Si3

Ca1

Ca2

Fig. 2. Atomic structure of tobermorite 14 Å as seen along crystal axes b (left side) and a (right side). Atoms are represented following the same conventions as in Fig. 1. The paired tetrahedra are Si1 and Si3, while the bridging tetrahedron is Si2.

Table 3 Bond lengths (given in Å) in tobermorite 14 Å, compared to experimental data [13].

Ca1

Ca2

Ca3

Si1

Si2

Si3

O9 O8 O3 O4 O4 O3 OH6 O5 O5 W2 W3 W1 W1 W6 O4 O9 O8 O3 O9 O8 O4 O3 O2 O1 O5 O1 O7 OH6 O7 O8 O9 O2

Present

Expt. [13]

2.39 2.42 2.48 2.41 2.53 2.51 2.52 2.28 2.60 2.51 2.43 2.33 2.36 2.58 2.35 2.42 2.42 2.38 2.45 2.74 1.62 1.62 1.66 1.67 1.60 1.66 1.63 1.67 1.66 1.62 1.62 1.67

2.27 2.29 2.33 2.38 2.53 2.56 2.74 2.26 2.33 2.36 2.36 2.36 2.55 2.39 2.45 2.47 2.47 2.53 2.55 2.62 1.59 1.60 1.61 1.69 1.57 1.59 1.63 1.66 1.62 1.63 1.65 1.74

which present the same geometrical arrangement in tobermorite 14 Å and tobermorite 11 Å. There are no vibrational Ca modes at higher frequencies. Above 400 cm−1 and up to 1200 cm−1, the vibrational spectra have contributions from rocking, bending, and stretching modes of the O\Si\O groups in the dreierkette chains. In jennite and tobermorite 14 Å, an important contribution from H modes in water and OH groups is present between 400 and 1200 cm−1, while in tobermorite 11 Å their contribution is less pronounced because of the lower water content. All the v-DOSs present a gap between 1200 and 1500 cm−1 followed by an isolated peak at about 1600 cm−1. This peak is almost entirely due to displacements of H atoms and originates from the bending modes of the water molecules, as we could easily verify by visual inspection. Apart from these broad similarities, the three minerals show several peculiar features that cannot easily be identified through simple projections onto atomic species. To understand their origin, we analyze the contributions to the v-DOS from selected atoms or groups of atoms. In the following, we present projected v-DOSs for each crystal separately and identify on their basis the origin of specific peaks in the v-DOS. The more significant peaks (or groups of peaks) in each structure are labeled. A table at the end of this section summarizes the identified microscopic origin of various vibrational features. This table is instrumental for the interpretation of the infrared spectra in Section 5.

4.1. Jennite To understand in detail the origin of the vibrational features of jennite, we perform extensive projections of its v-DOS onto silicon tetrahedra (SiO4), oxygen atoms, OH groups, and water molecules in Fig. 5. We denote by J1–12 the main features resulting from these decompositions.

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A. Vidmer et al. / Cement and Concrete Research 60 (2014) 11–23

Ca3 Ca3 Si3 W3

Si3

Si2 O6

Si1 W3 Si2

O6

Si1 Si3 Ca3

Ca3

Ca1

Fig. 3. Atomic structure of anomalous tobermorite 11 Å as seen along crystal axes b (left side) and a (right side). Possible sites for Ca2 are shown as black crosses. Atoms are represented following the same conventions as in the previous figures. Bridging tetrahedra (Si2) of different layers are linked together forming double silicate chains.

Projections onto individual SiO4 groups are presented in Fig. 5a and are named according to the central Si atom: Si1 for the bridging tetrahedron, and Si2 and Si3 for the paired tetrahedra. In the frequency range up to 550 cm−1, one observes J1 and J3 due to deformations of Si tetrahedra and Ca polyhedra. The group of peaks named J4 in the

Table 5 Bond lengths (given in Å) of normal tobermorite 11 Å compared to a previous firstprinciples study and to experiment.

Ca1 Table 4 Bond lengths (given in Å) in anomalous tobermorite 11 Å compared to a previous firstprinciples study and to experiment.

Ca1

Ca3

Si1

Si2

Si3

O4 O8 O3 O9 O3 O4 W6 O4 O8 O3 O9 O8 O9 O6 O1 O2 O3 O4 O1 O5 O6 O7 O2 O7 O8 O9

Present

BLYP 300 K [37]

Expt. [12]

2.39 2.39 2.45 2.46 2.49 2.68 2.64 2.42 2.42 2.41 2.42 2.56 2.55 2.61 1.66 1.66 1.62 1.61 1.62 1.61 1.66 1.63 1.66 1.67 1.62 1.62

2.33 2.31 2.42 2.38 2.42 2.33 2.51 2.36 2.40 2.36 2.40 2.40 2.40 2.49 1.67 1.65 1.62 1.61 1.62 1.61 1.66 1.63 1.65 1.66 1.61 1.62

2.37 2.36 2.40 2.41 2.49 2.65 2.51 2.40 2.41 2.40 2.40 2.56 2.52 2.56 1.65 1.64 1.60 1.61 1.61 1.60 1.65 1.61 1.64 1.65 1.60 1.60

Ca2

Ca3

Si1

Si2

Si3

O4 O8 O3 O9 O3 O4 W6 O6 O2 W2 W1 W3 O1 O7 O4 O8 O3 O9 O8 O9 O6 O1 O2 O3 O4 O1 O5 O6 O7 O2 O7 O8 O9

Present

BLYP 300 K [37]

Expt. [12]

2.39 2.39 2.45 2.44 2.49 2.65 2.58 2.29 2.42 2.36 2.38 2.26 3.22 2.94 2.43 2.42 2.41 2.42 2.60 2.54 2.60 1.67 1.66 1.62 1.61 1.63 1.63 1.63 1.64 1.66 1.68 1.62 1.62

2.49 2.34 2.46 2.40 2.46 2.49 2.58 2.37 2.38 2.37 2.36 2.36 2.75 2.77 2.42 2.48 2.39 2.48 2.48 2.48 2.52 1.70 1.68 1.64 1.63 1.70 1.68 1.64 1.63 1.68 1.69 1.64 1.63

2.36 2.35 2.35 2.41 2.53 2.61 2.50 2.35 2.35 2.28 2.49 2.44 2.87 2.88 2.35 2.42 2.40 2.42 2.57 2.51 2.53 1.64 1.64 1.62 1.60 1.67 1.61 1.68 1.71 1.67 1.62 1.60 1.60

A. Vidmer et al. / Cement and Concrete Research 60 (2014) 11–23

a

a

b

b

c

c

17

Fig. 4. Total (solid line) and projected (broken lines) vibrational densities of states (v-DOSs) for (a) jennite, (b) tobermorite 14 Å, and (c) anomalous tobermorite 11 Å. The projected densities give the contributions of the atomic species according to their participation to the vibrational modes. The partial densities add up to give the total density. A Gaussian broadening of 28 cm−1 has been used to smooth the curves.

Fig. 5. Vibrational density of states (v-DOS) of jennite projected onto (a) SiO4 tetrahedra, (b) O atoms in the silicate chains and in the Ca\O layer, and (c) OH groups and water molecules. In (a), we distinguish the three inequivalent tetrahedra (Si1, Si2, and Si3) and include projections on all the atoms belonging to these structural units. In (b), the O atoms are distinguished according to their nearest neighbor configuration (see text), but the projection is only performed onto the O atoms.

intermediate frequency range from 550 to 800 cm−1 is mostly due to the bending of O\Si\O units, while the structure of peaks J8–10 in the 800–1100 cm− 1 range can be attributed to the stretching of Si\O bonds. This frequency ordering of the different modes involving Si\O bonds is consistent with the analysis of the v-DOS of vitreous silica [38]. The projected v-DOSs of the two paired tetrahedra (Si2 and Si3) are very similar, whereas those of the bridging tetrahedron (Si1) show some distinct features: its contribution to J1 appears shifted to lower frequencies while its contribution to J3 is characterized by a double peak structure. Furthermore, the Si1 projection gives rise to a barely visible shoulder (J11) at about 1100 cm−1. In Fig. 5b, we show projections on O atoms distinguished according to their local environment. In all Si tetrahedra there are two O atoms that link different tetrahedra and thus have two Si neighbors (O\Si2). In the bridging tetrahedron, one of the two remaining O atoms is the special O8 atom (see Fig. 1), while the other has one Si and two Ca neighbors. In the paired tetrahedra instead, the other two O atoms both have one Si and three Ca neighbors. The projections onto oxygen atoms having one Si and two or three Ca neighbors are combined and named O\SiCax. We also consider projections onto O atoms in the Ca\O layer that do not belong to any Si tetrahedron. These oxygen atoms (OH\Cax) have two or three Ca neighbors and form OH groups. One notices that J1 originates from coupled deformations of Si tetrahedra and Ca polyhedra, whereas J3 is mainly due to the deformation of Si tetrahedra. As shown by the OH\Cax projection, the deformations of Ca polyhedra are responsible for the peak J2 falling in between J1

and J3. In J1, the O\Si2 and the O8 components are found at a slightly lower frequency than the O\SiCax one. Since there is only one O atom of the latter type in Si1, this can explain the apparent shift of J1 to lower frequencies for Si1, compared to Si2 and Si3, which have two of such O atoms. In J3, the O8 contribution is at a slightly lower frequency than O\Si2 and \SiCax configurations, which explains the splitting in J3 for Si1. In the Si\O stretching modes (800–1200 cm−1), the shoulder J8 is mainly due to O atoms of the O\SiCax type. The peak J10 comes mainly from O atoms with two Si neighbors, while the peak J9 contains components from all O atoms attached to at least one Si atom. The Si1 component of J9 is smaller than that of Si2 and Si3 as O8 contributes less than O\Cax at this frequency. The feature J11 pertaining to the Si1 tetrahedron is not found in the projections of Fig. 5b. Therefore, we must consider projections onto O atoms in the interlayer to understand its origin. In Fig. 5c, we show the v-DOS projected onto water molecules and OH groups, including H atoms. We find that J11 is due to the interaction between the Si1\O8 stretching mode with the vibrational modes of water molecules surrounding the deprotonated O8 oxygen atom (cf. Section 3.1). Among all the other peaks that can be seen in Fig. 5c, we point our attention to the three peaks, J5–7, between 600 and 800 cm−1. They are due to librations of water and hindered translations of water and OH groups. These vibrations are used in the next section to interpret some spectral features in the infrared absorption. As said above, the isolated peak J12 at ~1600 cm−1 is entirely due to the bending modes of water molecules.

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4.2. Tobermorite 14 Å The v-DOS of tobermorite 14 Å is analyzed in Fig. 6. The principal features are denoted P1–12, after plombierite, an alternative name for this mineral. From the projections onto the Si tetrahedra (Fig. 6a), we recognize that the spectrum roughly decomposes in the same three vibrational bands found in jennite. Up to 550 cm−1, we mainly find deformations of Si tetrahedra (P1–3), partly coupled to deformations of Ca polyhedra. The Si\O\Si bending modes are represented here by a single peak P5 centered at 650 cm−1 instead of a group of peaks as in jennite, while the Si\O stretching modes are represented by P7–11 and span the frequency range between 750 and 1200 cm− 1. As seen in jennite, the SiO4-projections of the two paired tetrahedra (S1 and S3) are quite similar to each other, but show noticeable differences compared to those of the bridging tetrahedron (Si2) for which P1 is more pronounced and P2 shifted to higher frequency. The intensity of P3 is larger for the two paired tetrahedra, but they both lack peak P7, which only occurs for the bridging tetrahedron. Next, we consider the projections onto O atoms (Fig. 6b). There are no OH groups attached to the main Ca\O layer of tobermorite 14 Å (cf. Section 3.2). therefore the OH\Cax configuration does not occur. As in jennite, the two paired tetrahedra have two O\SiCax and two O\Si2 oxygen atoms each. The bridging tetrahedron has two O atoms of the O\Si2 type, which connect Si2 to Si1 and Si3 in the silicate chain. Its other two O atoms establish a link with the interlayer Ca2 ion (O\SiCa) and a Ca ion in the main layer (OH\SiCa, the O being

a

b

c

Fig. 6. Vibrational density of states (v-DOS) of tobermorite 14 Å projected onto (a) SiO4 tetrahedra, (b) O atoms in the silicate chains, and (c) OH groups and water molecules. In (a), we distinguish the three inequivalent tetrahedra (Si1, Si2, and Si3) and include projections on all the atoms belonging to these structural units. In (b), the O atoms are distinguished according to their nearest neighbor configuration (see text), but the projection is only performed onto the O atoms. The peaks are named after plombierite, an alternative name for tobermorite 14 Å.

part of an OH group). The main differences between the projections on bridging and paired tetrahedra can be explained by these two O configurations in the bridging tetrahedron, which are absent in the paired tetrahedra. The reduced intensity of P3 and, to some extent, the shift of P2 are instead related to the missing O\SiCax component in the decomposition of the bridging tetrahedron. The origin of the peak P7 is assigned to a Si\O stretching mode involving the O atom of Si2 which forms an OH group (OH\SiCa) (cf. Fig. 6c). The decomposition on O atoms also allows us to characterize the differences between the projections on the Si tetrahedra in the frequency range of P8–10. The peak P8 results from the paired tetrahedra with a dominant contribution from O\SiCax configurations, but also with a sizeable contribution from the O\Si2 configurations. The peak P9 is mainly due to the bridging tetrahedron, with contributions from both O\Si2 and O\SiCa configurations. The shoulder P10 results from stretching vibrations involving the O atom which connects the Si2 and Si3 tetrahedra. The remaining features in Fig. 6a can be understood from the projection onto water molecules shown in Fig. 6c. The small shoulder P11 for Si2 in Fig. 6a appears as a broad peak in Fig. 6c. Indeed, it is related to the interaction between water molecules and the Si\O stretching modes within a O\SiCa configuration of the bridging tetrahedron, as confirmed by visual inspection. Finally, we note the appearance of two extra peaks P4 and P6 at 500 cm−1 and 700 cm−1, respectively, which are due to water librations and are useful for the interpretation of the infrared spectra. 4.3. Tobermorite 11 Å The v-DOS of anomalous tobermorite 11 Å is studied through its projections in Fig. 7. In the SiO4 projections (Fig. 7a), we recognize the same three ranges of frequency identified for the two previous minerals. The features T1–3, reaching up to 550 cm−1, are due to deformations of Ca polyhedra and Si tetrahedra and closely correspond to the peaks P1–3 in tobermorite 14 Å. The group of peaks T5 centered around 650 cm−1 are due to the Si\O\Si bending modes, while the peaks T7–11 ranging from 750 to 1200 cm−1 are Si\O stretching modes. As seen for the other minerals, the projections on the paired tetrahedra (Si1 and Si3) are rather similar, whereas significant differences appear when comparing to the projection on the bridging tetrahedron (Si2). In the lowest frequency range, the main difference is the shift and the lower intensity of T3 for Si2 compared to those for Si1 and Si3. At larger frequencies, the main differences between the projections on Si2 vs. those on Si1 and Si3 occur in the Si\O stretching region. In Fig. 7b, we show the projections onto O atoms distinguished by their local environment. In tobermorite 11 Å, the O\SiCa3 configuration is the only one of the O\SiCax type. A new class of oxygen configurations occurs (Si2\O\Si2) and corresponds to O atoms linking two bridging tetrahedra of adjacent chains. From the O projections, we infer that the differences between bridging and paired tetrahedra in the frequency range up to 550 cm−1 have the same origin as in tobermorite 14 Å, namely an extra component (only OH\SiCa in this case) and a missing one (O\SiCa3) in Si2 compared to Si1 and Si3. It is in the Si\O stretching region where we can see the largest differences between Si2 and Si1/Si3. The peaks T7 at 860 cm−1 and T10 at about 1200 cm− 1 result entirely from the bridging tetrahedron Si2, but have different origins. T7 is due to the presence of an O belonging to an OH group (OH\SiCa), as for peak P7 in tobermorite 14 Å, while T10 results from O atoms in the Si2\O\Si2 configuration which is peculiar to tobermorite 11 Å. T8 originates from O atoms in the paired tetrahedra, with a dominant contribution from O\SiCa3 configurations and a smaller contribution from O\Si2 configurations. All Si tetrahedra are found to contribute to T9 which is composed solely of Si\O stretching modes in O\Si2 configurations. In the projections onto water molecules (Fig. 7c), we find three peaks (T4–6) coming from water librations. We remark that water

A. Vidmer et al. / Cement and Concrete Research 60 (2014) 11–23

a

a

19

b

b Fig. 8. Vibrational density of states in the Si\O stretching region projected onto (a) the bridging tetrahedron Si2 and (b) onto the O atoms linking different silicate chains (Si2\O\Si2), for anomalous (dashed) and normal (solid) tobermorite 11 Å.

c

Fig. 7. Vibrational density of states (v-DOS) of anomalous tobermorite 11 Å projected onto (a) SiO4 tetrahedra, (b) O atoms in the silicate chains, and (c) OH groups and water molecules. In (a), we distinguish the three inequivalent tetrahedra (Si1, Si2, and Si3) and include projections on all the atoms belonging to these structural units. In (b), the O atoms are distinguished according to their nearest neighbor configuration (see text), but the projection is only performed onto the O atoms.

librations at 650 cm− 1 fall at the same frequency as the Si\O\Si bending modes in Fig. 7a, and thus contribute both to the feature T5. However, this degeneracy is accidental and these modes are not related to each other, as we verified visually. T11 corresponds to the water bending mode at about 1600 cm−1. The vibrational properties of normal tobermorite are very close to those of anomalous tobermorite as the two structures are very similar to each other (cf. Section 3.3). The main differences occur in the frequency range between 800 cm−1 and 1200 cm−1. A detailed investigation of the projections of the v-DOS reveals that these differences originate from the bridging tetrahedra, as inferred from the comparison in Fig. 8. The projection onto the bridging tetrahedra in normal tobermorite 11 Å shows a single broad feature (Fig. 8a), as opposed to the four features in anomalous tobermorite 11 Å (T7–10). The projection onto the O atoms linking different silicate chains (Fig. 8b) shows that in normal tobermorite 11 Å the associated Si\O stretching modes are slightly more spread and at lower frequencies than in its anomalous counterpart. 5. Infrared spectra The simulation of infrared spectra from first principles requires the calculation of Born effective charges and high-frequency dielectric constants (cf. Section 2), in addition to the vibrational properties given in the previous section. The Born effective charges, which describe the coupling between the electric field and the vibrational modes, are obtained in the form of 3 × 3 tensors for each atom in the unit cell.

We find the isotropic components of these tensors to vary between −0.8 and −2 for O, between 0.2 and 0.9 for H, around 2.3 for Ca, and between 2.8 and 3.4 for Si, in agreement with typical values found for similar materials [27,39]. The detailed distributions of these isotropic charges are given in the Supplemental material [30]. The calculated high-frequency (ϵ∞) and static dielectric (ϵ0) tensors are found to be almost diagonal and nearly isotropic, and can thus be well represented by their isotropic component. The values used in the calculation of the infrared spectra of the four minerals studied in this work are reported in Table 7. For completeness, full tensors of ϵ∞ together with the real part of the dielectric functions are given in the Supplemental material [30]. In the following section, we first identify the origin of the main absorption peaks in the simulated spectra in terms of the underlying vibrational modes (cf. Table 6). When a single feature arises from multiple underlying vibrations of different nature, we evaluate their relative contributions. For this purpose, we selectively switch off the coupling of a chosen set of vibrations by setting the Born effective charges to zero prior to the calculation of the IR absorption spectrum. Next, we assign the features in the experimental infrared spectra [16] by comparison with our simulated spectra (last column in Table 6). 5.1. Jennite The simulated IR absorption spectrum of jennite is displayed in Fig. 9a, superimposed to the experimental intensity taken from Ref. [16]. In order to make a direct comparison possible, the intensities were rescaled such that the areas underlying the principal absorption peaks at about 1000 cm−1 coincide for the two curves. The main features of the experimental spectrum are generally well reproduced by the theoretical one, especially when we consider the well-known tendency of the GGA of slightly underestimating the vibrational frequencies [41]. The vibrational features J1–3, due to deformations of Ca polyhedra and Si tetrahedra are all visible also in the simulated IR absorption spectrum. We find a good correspondence between J3 and the experimental peak near 450 cm−1, which is therefore attributed to deformations of Si tetrahedra. However, we could not compare J1 and J2 with experimental data, since they have not been obtained below 400 cm−1. Between 500 and 700 cm−1, the theoretical spectrum presents a single peak at 600 cm−1 (J5) due to water librations, while the Si\O\Si bending modes do not contribute appreciably. The experimental spectrum has two peaks in this range, one at 630 cm− 1, which can be assigned to J5, and a second one at about 550 cm−1, which is not present in our simulated spectrum. The plateau between 700 and 800 cm−1 arises from librations of water (J6) and vibrations of OH groups (J7). It could be identified with a plateau at slightly lower frequencies in the experimental spectrum, although this assignment would be at odds with the general tendency of the GGA.

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Table 6 Origin of the features in the calculated vibrational densities of states of jennite, tobermorite 14 Å, and tobermorite 11 Å, together with the identification of the corresponding features in the experimental infrared spectra. Peaks

ω (cm−1)

Interpretation

ωexpt (cm−1)

J1 J2 J3 – J4 J5 J6 J7 J8 J9 J10 J11 J12 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11

80–270 270–360 370–520 – 610, 680 600 750 790 860 920 1020 1120 1610 100–200 200–350 370–520 510 650 705 815 930 985 1060 1155 1610 100–200 200–350 360–520 510 640 735 860 940 1030–1060 1185 1595

Deformations of Si and Ca polyhedra Deformations of Ca polyhedra Deformations of Si tetrahedra Not reproduced by simulations O\Si\O bending (very low IR activity) H2O librations OH librations H2O librations Si\O stretching (O\SiCax) Si\O stretching (O\SiCax, O\Si2) Si\O stretching (O\Si2) Water interacting with Si1\O8 stretching Water bending Deformations of Si and Ca polyhedra Deformations of Ca polyhedra Deformations of Si tetrahedra H2O librations O\Si\O bending, H2O librations H2O librations Si\O stretching (OH\SiCa in bridging tetr.) Si\O stretching (O\SiCax, O\Si2) Si\O stretching (O\Si2, O\SiCa) Si\O stretching (O\Si2) Water interacting with O\Si2 neighbor Water bending Deformations of Si and Ca polyhedra Deformations of Ca polyhedra Deformations of Si tetrahedra H2O librations O\Si\O bending, H2O librations H2O librations Si\O stretching (OH\SiCa in bridging tetr.) Si\O stretching (O\SiCax, O\Si2) Si\O stretching (O\Si2) Si\O stretching (O-links bet. bridging tetr.) Water bending

Not avail. Not avail. 448 545 – 630 696 744 902 964, 984 1081 – 1640 250 300 445 530 670 – 830 969 1050 1120 1200 1640 240 285 450 540 670 – 900 980 1060 1200 1630

In the Si\O stretching region, the theoretical spectrum has four peaks J8–11, which correspond to O atoms vibrating in four different local environments, as discussed in Section 4.1. Each of these four peaks can be related to a feature in the experimental spectrum. The experimental peak at 900 cm−1 is assigned to J8 and originates from O atoms with only one Si neighbor (O\SiCax). The double peak between 950 and 1000 cm−1 can be identified with J9, which appears as a single peak in the theoretical spectrum as the chosen broadening prevents a more detailed resolution. The two components of J9 can be associated to Si\O stretching modes in O\Si2 and in O\SiCax configurations, respectively. The experimental peak at about 1080 cm−1 can be assigned to J10 and is thus due to Si\O stretching in O\Si2 configurations. The shoulder slightly above 1100 cm−1 in the experimental spectrum can be assigned to J11 in the simulated spectrum, which is due to the water molecules interacting with the Si\O stretching modes involving the O8 atom. In the experimental spectrum, the features between 1300 and 1600 cm−1, as well as the shoulder above 800 cm−1, are due to CO2 incorporation in the sample [16]. Hence, these features do not occur in the

Table 7 High-frequency (ϵ∞) and static (ϵ0) dielectric constants for jennite and tobermorite minerals.

Jennite Tobermorite 14 Å Anomalous tobermorite 11 Å Normal tobermorite 11 Å

ϵ∞

ϵ0

2.57 2.48 2.58 2.64

7.80 7.03 8.37 9.39

a

b

c

Fig. 9. Infrared (IR) absorption spectra of (a) jennite, (b) tobermorite 14 Å, and (c) anomalous tobermorite 11 Å. Theoretical spectra from simulations (thick red lines) are compared to experimental data from Ref. [16] (thin green lines). The low-frequency data from the experiment (dashed) were obtained from a different dataset [16]. Lorentzian and Gaussian broadenings of 14 cm−1 are used to smooth the simulated spectra [40].

theoretical spectrum of pure jennite. At variance, the peak at 1640 cm−1 is represented by J12 and can be assigned straightforwardly to the bending modes of water. 5.2. Tobermorite 14 Å Fig. 9b shows the experimental and simulated spectra for tobermorite 14 Å. As in jennite, the simulated spectrum reproduces well the main features of the experimental one, if we account for the usual shift in frequency ascribed to the GGA [41]. The experimental data covers also the far IR range in this case. The three vibrational peaks, P1–3, related to deformations, result in two absorption peaks in the theoretical spectrum, since P1 and P2 are very close in frequency and merge together to form a single feature. Also the experimental spectrum shows two peaks in this frequency range, one at 300 cm−1 and another at 445 cm−1. They can be assigned to coupled deformations of Ca polyhedra and Si tetrahedra (P1 and P2) and to deformations of Si tetrahedra alone (P3), respectively. Between 500 and 800 cm−1, the theoretical spectrum is dominated by water librations, which give rise to three peaks, P4–6. The Si\O\Si bending modes fall in the same frequency range and account for about half of the intensity of P5. In the experimental spectrum, we find a shoulder slightly above 500 cm−1, which we assign to water librations (P4), and a peak at 670 cm− 1 which we attribute to Si\O\Si bending modes and water librations (P5). The experimental absorption spectrum shows an enhanced intensity for P4 and the absence of P6. These

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discrepancies could result from thermal effects and from different water contents in the real mineral compared to our model. For instance, as P6 is exclusively due to water librations, it could be spread over a larger region and not appear as a clear peak in the experimental spectrum. In the theoretical spectrum five distinct peaks (P7–11) can be resolved in the frequency range between 800 and 1200 cm−1 corresponding to Si\O stretching modes. At variance, the experimental spectrum shows a single broad feature composed of a main peak just below 1000 cm− 1 and several shoulders on either side. The broadening of this region of the spectrum points to some degree of structural disorder, such as missing or displaced Si tetrahedra in the silicate chains of the sample used for the experiment. The main peak in the experimental spectrum can be associated to Si\O stretching modes in O\SiCax configurations (P8). The shoulder on the low-frequency side of the main experimental peak might result from CO2 infiltration, which is expected to contribute at 850 cm−1, as in jennite. However, this shoulder could also be interpreted as due to Si\O stretching modes within OH\SiCa configurations in the bridging tetrahedron (P7), which give a sizeable intensity in the simulated spectrum. The remaining theoretical peaks can explain various shoulders above 1000 cm−1 in the experimental spectrum. The two intense shoulders between 1000 and 1150 cm−1 can be attributed to P9 and P10 which both mainly arise from Si\O stretching modes in O\Si2 configurations. The weak feature at about 1200 cm−1 might relate with the interaction of water molecules with the Si\O stretching modes (P11). The frequency range above 1300 cm−1 can be interpreted as in jennite. 5.3. Tobermorite 11 Å The IR absorption of tobermorite 11 Å is presented in Fig. 9(c). The experimental absorption spectrum shown in Fig. 9(c) results from a sample containing both anomalous and normal forms of tobermorite 11 Å [16]. We first compare this spectrum with the theoretical one obtained for anomalous tobermorite. The spectrum of our model of normal tobermorite is discussed subsequently, insofar as differences are confined to a limited frequency range. The experimental spectrum of tobermorite 11 Å is similar to that of tobermorite 14 Å up to frequencies of 800 cm−1. The same can be said for the theoretical spectrum. This is not unexpected, since the two minerals share the same geometry of the Ca\O layer, the main differences being in the interlayer region and in the water content. In the frequency range of Si\O stretching, the principal peak falls at the same frequency as in tobermorite 14 Å, both in the experiment and in the theory (T8). The small peak associated to Si\O stretching in OH\SiCa configurations (T7) is shifted to higher frequencies with respect to the analogous peak of tobermorite 14 Å (P7), but this cannot easily be assessed in the experimental spectrum. On the high-frequency side of the principal peak, we notice a shoulder just below 1100 cm−1 and a small bump just above 1200 cm−1. The former can be associated to T9 and involves stretching modes within the chains, similarly to P9 and P10 in tobermorite 14 Å. In contrast, the latter is specific to tobermorite 11 Å and signals the existence of double silicate chains (cf. Section 3.3). Indeed, in Section 4.3 it is shown that the stretching of the Si2\O\Si2 bonds, which constitute the link between two bridging tetrahedra in the double silicate chain, gives rise to an additional peak T10 at about 1200 cm−1. The experimental feature at ~1650 cm−1 results from water bending modes (T11). The most significant differences between the IR absorption spectra of normal and anomalous tobermorite 11 Å take place in the Si\O stretching region (Fig. 10). Despite the noticeable difference in the density of stretching modes (Fig. 8), the calculated infrared spectrum of normal tobermorite shows features which are similar to T7 and T8 of anomalous tobermorite. Differences are only observed in the frequency range pertaining to T9 and T10. In particular, the intensity of the characteristic peak T10 of anomalous tobermorite 11 Å spreads out, making it less discernible in the normal form. The experimental observation

21

of the bump around 1200 cm− 1 therefore points to the occurrence of anomalous tobermorite in the investigated sample. As far as the normal form is concerned, a similar characteristic signature cannot be identified. 6. Discussion and conclusion In this work, we considered three minerals which present structural similarities with C–S–H, namely jennite, tobermorite 14 Å, and tobermorite 11 Å, and studied their structural and vibrational properties within density functional theory. The calculated cell parameters and bond-lengths are overall in good agreement with previous experimental and theoretical data. The vibrational frequencies and eigenmodes were calculated through a finite difference method and used to provide a detailed analysis of the vibrational density of states. The dielectric properties and Born effective charges were obtained within densityfunctional perturbation theory and used, together with the vibrational frequencies and eigenmodes, to calculate the IR absorption spectra of the considered minerals. For each mineral, we compared the simulated IR spectrum with its experimental counterpart (Fig. 9) and provided an interpretation of the experimental features (Table 6). It is important to address the question to what extent the present analysis is helpful in the interpretation of IR absorption spectra of C–S–H materials [16]. Our calculations show that all the minerals considered show vibrational densities of states which are basically similar. It is therefore important to identify distinct infrared features which would arise from specific structural arrangements. We focus first on the frequency range extending from 550 to 800 cm−1. In jennite, Si\O\Si bending modes are spread over the 500–700 cm−1 range and do not result in a sharp peak. The peak J5 in jennite is thus almost entirely due to water. The plateau J6–J7 is a specific feature of jennite which mainly results from water and OH modes. At variance, the tobermorite peaks at ~ 610 cm−1 (P5 and T5) can clearly be identified as a mixture of Si\O\Si bending modes and water librations. OH librations do not contribute significantly to the tobermorite spectra. Distinctive features can also be identified in the frequency range above 800 cm− 1 pertaining to the Si\O stretching modes. The peak J11 in jennite is specific since it relates to the water molecules around the special atom O8. Similarly, tobermorite 14 Å has a specific peak P10 corresponding to Si\O\Si configurations. Anomalous tobermorite shows a distinct peak T10 at about 1200 cm−1 signaling the occurrence of double silicate chains which are absent in tobermorite 14 Å. However, the broadening caused by the structural disorder likely prevents any of these specific features to appear as a strong or distinct signature in the infrared spectra of C–S–H. Infrared spectra for C–S–H samples having different C/S ratios show significant differences in the low-frequency region [16]. In Fig. 11, we compare the experimental spectra of C–S–H samples in the far-IR region

Fig. 10. Calculated infrared spectra of anomalous (solid, red) and normal (dashed, red) tobermorite 11 Å in the frequency range of Si\O stretching modes, compared to the experimental IR spectrum of a sample containing both forms of tobermorite 11 Å [16].

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a

b

Fig. 11. Comparison between the low-frequency part of (a) the experimental infrared spectra of C–S–H (from Ref. [16]) and of (b) the simulated infrared spectra of the minerals studied in this work (from Fig. 9), ordered according to their C/S ratio.

with the simulated spectra of jennite, tobermorite 14 Å, and anomalous tobermorite 11 Å. In this range of frequencies, the experimental spectra (Fig. 11a) show two well spaced peaks. The peak at higher frequencies dominates at low C/S ratio, but the peak intensities become more similar as the peak at lower frequencies acquires additional weight at around 300 cm−1 with increasing Ca content. The simulated spectra of the three minerals (Fig. 11b) also show two peaks in this lowfrequency part of the spectrum. The peak at higher frequencies (~ 420 cm− 1) is similar for the three considered minerals. This peak mainly originates from deformation of Si tetrahedra (cf. Table 6) and does not appear to be sensitive to the C/S ratio. At variance, the peak at lower frequency is found to be more sensitive to the increasing C/S ratio showing a significant shift of its intensity towards higher frequencies. In particular, for jennite, which has a C/S ratio of 1.5, the two peaks at lowest frequencies show a similar intensity. One can recognize the appearance of additional weight at 300 cm−1, in accord with the experimental C–S–H spectrum at the high C/S ratio of 1.70. Analysis of the IR intensities clearly allows us to associate the extra weight at 300 cm−1 to the deformation of the calcium polyhedra in the corrugated Ca\O layers present in jennite (cf. Fig. 5). The comparison of the simulated spectra of the two forms of tobermorite also shows a shift of the peak at lower frequencies despite the rather small difference in C/S ratios (0.67 for anomalous tobermorite 11 Å vs. 0.83 for tobermorite 14 Å). We searched for a connection between this behavior and the C/S ratio, but concluded that the observed shift results from a series of specific features which are apparently not directly related to the C/S ratio. In conclusion, we theoretically determined in this work the IR absorption spectra of jennite, tobermorite 14 Å, and tobermorite 11 Å from first principles. An extensive analysis of their vibrational properties allowed us to assign specific vibrational modes to the principal peaks in the experimental IR spectra of these minerals. We identified features in the low-frequency region which depend on the C/S ratio of the mineral and could thus be instrumental in the interpretation of infrared spectra of C–S–H. Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.cemconres.2014.03.004.

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