Structural and spectroscopic characterization of ettringite mineral –combined DFT and experimental study

Journal of Molecular Structure 1100 (2015) 215e224

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Journal of Molecular Structure journal homepage: http://www.elsevier.com/locate/molstruc

Structural and spectroscopic characterization of ettringite mineral ecombined DFT and experimental study
a, *, Lenka Kuckova
b, Jozef Ko Eva Scholtzova zísek b, Daniel Tunega a, c
cesta 9, 845 36 Bratislava, Slovakia Institute of Inorganic Chemistry of Slovak Academy of Sciences, Dúbravska Department of Physical Chemistry, Institute of Physical Chemistry and Chemical Physics, Faculty of Chemical and Food Technology, Slovak University of Technology in Bratislava, Radlinsk
eho 9, 812 37 Bratislava, Slovakia c Institute for Soil Science, University of Natural Resources and Life Sciences, Peter-Jordanstrasse 82, A-1190 Wien, Austria a

b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 April 2015 Received in revised form 24 June 2015 Accepted 24 June 2015 Available online 23 July 2015

The structure of the ettringite mineral was studied by means of FTIR spectroscopy and single crystal Xray diffraction method. The experimental study was combined with the first principle calculations based on density functional theory (DFT) method. Predicted structural parameters (unit cell vectors and positions of heavy atoms) are in a very good agreement with the experimental data. Moreover, calculations also enabled to refine the positions of the hydrogen atoms not determined precisely by the single crystal X-ray measurement. The detailed analysis of the hydrogen bonds in the ettringite structure was performed and several groups of the hydrogen bonds were classified. It was found that the water molecules from the coordination sphere of Ca2þ cations act as proton donors in moderate OeH$$$O hydrogen bonds with SO2 3 anions. Further, multiple OeH$$$O hydrogen bonds were identified among water molecules themselves. In addition, also hydroxyl groups from the [Al(OH)6]3 octahedral units are involved in the weak OeH$$$O hydrogen bonding with the water molecules. The calculated vibrational spectrum showed all typical features observed in the experimental FTIR spectrum. Moreover, performing the analysis of the calculated spectrum, all vibrational modes were distinguished and assigned. Such a complete analysis of the measured IR and/or Raman spectra is not fully possible, specifically for the region below 1500 cm1, which is characterized by a complex curve with many overlapped bands. A comparison of the vibrational spectra of ettringite and thaumasite (mineral structurally similar to ettringite) revealed the origin of the most important differences between them. © 2015 Elsevier B.V. All rights reserved.

Keywords: Ettringite IR DFT Crystal structure Hydrogen bonds Thaumasite

1. Introduction Portland cement is one of the most frequently used building materials around the world. In reaction with water, hydration phases are formed representing main binders in concrete material. Detailed study of the hydration mechanisms and also of the structure of the hydration products is important for the use of cementitious pastes and concrete in the building industry. Several natural calcium-alumino-silicate (CAS) minerals, direct analogs of cement counterparts, offer good opportunity for in-depth understanding of the structural and chemical features of cement and concrete. Ettringite, boro-ettringite and thaumasite are typical CAS compounds constituting an ettringite group of minerals. Ettringite

* Corresponding author.
). E-mail address: [email protected] (E. Scholtzova http://dx.doi.org/10.1016/j.molstruc.2015.06.075 0022-2860/© 2015 Elsevier B.V. All rights reserved.

is a hexacalcium aluminate trisulfate hydrate mineral (ideal formula Ca6[Al(OH)6]2(SO4)3.~26H2O) formed during Portland cement hydration. Its formation in the early cement hydration stage plays an important role in controlling the setting rate of the highly reactive aluminate phases and its formation results in a volume increase in the fresh, plastic concrete, which has also been associated spatially with severe cracking in cured hardened concrete during what is referred to as delayed ettringite formation (DEF) and during cement degradation via sulfate attacks [1]. The sulfate ions react with ionic species of the pore solution to precipitate gypsum, ettringite, thaumasite or mixtures of these phases [2]. Sulfate attack from external sources is described, including processes resulting in the formation of ettringite and thaumasite, in the work by Glasser et al. [3]. Although thaumasite and ettringite are from the same family of minerals, several differences exist between their structures. Apart from the hexagonal structure of thaumasite (space group P63), the

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et al. / Journal of Molecular Structure 1100 (2015) 215e224 E. Scholtzova

ettringite structure is trigonal (space group P31c). Further, ettringite contains Al atoms instead of Si, and three SO2 4 anions and two 2 H2O molecules replace two SO2 4 and two CO3 ions. The structural columns, a typical feature for both minerals, are essentially similar and a difference in the c parameter and symmetry arises from the ordering of the sulfate anions in ettringite [4]. The ordered arrangement of the intercolumn material leads to the halving of the c-dimension of the unit cell in thaumasite [5]. The structures of thaumasite and ettringite were reported first time by Edge and Taylor [6], followed by the work of Moore and Taylor [7]. Both structures have been refined later [8e11], with the reported structures agreeing with the earlier works except fine structural details. Selected area electron diffraction (SAED) patterns were obtained in the study of the structure of ettringite, carbonate ettringite, and thaumasite [4] and it was revealed that the presence of carbonate in ettringite hinders water loss preventing the movement of the columns along the a axis and also reducing the shrinkage along the c direction. Vibrational spectroscopy, specifically the Fourier Transform infrared spectroscopy (FTIR), was used to obtain a local symmetry and structural information of reactive groups such as OH and H2O presented in the ettringite structure [12]. FTIR analysis together with the XRD and EDX (Energy Dispersive X-ray) methods was used in the analysis of the structure of ettringite [13], synthetized ettringite [14], solid solutions of thaumasite and ettringite [5], and hydrated Portland cement [15]. These studies reported an assignment of several well-distinguished bands to vibrational modes of the basic functional groups (e.g. stretching and bending of 2 2 3 eOH, CO2 groups) later com3 , SO4 , [Si(OH)6] , and [Al(OH)6] plemented by the interpretation of Raman spectra [12,16]. However, a complete analysis of both IR and Raman spectra is not possible because both spectra are complicated with many overlapping unresolved bands; thus, their identification can be problematic. Computational chemistry represents very useful tool for description and analyzing the structure and properties of compounds. For example, calculated frequencies can be unambiguously assigned to particular vibrational modes and types of vibrations can be determined from the corresponding eigenvectors. In our recent paper this type of analysis was performed on the measured IR spectrum of thaumasite by means of the DFTcalculated vibrational modes [17]. The DFT method was also used in earlier study by Dr
abik et al. [18] for a characterization of specific structural features of thaumasite including hydrogen bonding. The present work reports combined experimental (single crystal X-ray and FTIR) and theoretical studies of the ettringite structure with the aim to provide complete structural and spectroscopic data of the natural ettringite crystal sample. DFT-based geometry relaxation of the all atomic positions is performed to complete the structural information on the position of hydrogen atoms followed by the hydrogen bond analysis. Further, vibrational spectrum, first time calculated at ab initio level, is used in a complete assignment of frequencies helping to understand all features of experimental IR and Raman spectra. Finally, the main differences between the IR spectra of thaumasite and ettringite are explained with respect to structural and compositional differences of both minerals. 2. Experimental details A natural, yellow crystal sample of the ettringite mineral (Fig. 1) was obtained from Wessels Mine, Nothern Cape Province, South Africa. The structural data were derived by single crystal X-ray diffraction and FTIR spectrum was measured in a range of

Fig. 1. Ettringite sample.

400e4000 cm1. The single crystal X-ray data were collected at 298.0 (1) K on an Oxford Diffraction Kappa geometry GEMINI R diffractometer equipped with Ruby CCD area detector using graphite monochromated MoKa radiation (l ¼ 0.71073 Å) at 30 kV and 30 mA. Distance from crystal to detector was 53 mm. The crystallographic data of ettringite together with the conditions of the X-ray diffraction measurement are given in Table 1. Infrared spectra were collected by a Nicolet 6700 Fourier Transform Infrared spectrometer from Thermo Scientific. The KBr pressed disk technique (1 mg of sample and 200 mg KBr) was used to measure spectrum in the middle infrared region. Spectra were obtained by co-addition of 64 scans at a resolution of 4 cm1. Spectra manipulations were performed using the Thermo Scientific OMNIC™ software package.

3. Computational details All calculations were performed using the Vienna Ab Initio Simulation Package, VASP [19,20], built on DFT method. In the used PBE functional, the exchange-correlation energy is described according Perdew, Burke, and Ernzerhof [21] approach, based on the generalized gradient approximation (GGA). The KohneSham equations are solved variationally using plane-wave (PW) basis set and projector-augmented-wave (PAW) method [22,23]. All calculations were performed by applying an energy cut-off of 500 eV. The Brillouin-zone sampling was restricted to the gamma-point only because of a large computational cell. The initial structural model for calculations was taken from our single crystal X-ray data collected in Tables 1e3. The all atomic positions and lattice parameters were fully relaxed with no symmetry restriction (P1 symmetry). The relaxation criteria were 107 eV/atom for the total energy change and 0.005 eV/Å for the maximal allowed forces acting on each atom. Normal modes of vibrations were calculated within the frame of harmonic approximation using a finite difference method and fixed parameters of the computational cell. The Hessian was constructed from the single point energy calculations on the 6n structures generated from the completely optimized structure by displacing each of the n atoms in the cell in positive and negative senses along the Cartesian directions x, y, and z. Each pair of single point calculations was used to calculate the individual force constants [24]. No scaling factor was used in the comparison with experimental data.


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Table 1 Crystal data of ettringite and X-ray experimental details. Chemical formula Formula weight Temperature, wavelength Crystal system, space group Unit cell dimensions

Ca6[Al(OH)6]2(SO4)3.24H2O 1219.10 g mol1 293 (2) K, 0.71073 Å trigonal, P31 c a ¼ 11.203 (2) Å c ¼ 21.467 (4) Å g ¼ 120.0 2 1.735 g cm3 0.977 mm1 1276 0.606  0.518  0.434 mm 4.10 e26.37 14  h<¼14 14  k<¼14 26  l<¼26 0.559 and 0.655 91380 3177 (R(int) ¼ 0.0527) 99.5% 3177/37/275 1.053 R1 ¼ 0.0583, wR2 ¼ 0.1673 R1 ¼ 0.0637, wR2 ¼ 0.1763 1.273 and 0.822 (e.Å3)

Formula units per unit cell Calculated density Absorption coefficient F (000) Crystal size q range for data collection Index ranges

Max. and min. transmission Reflections collected Independent reflections Completeness to 2q ¼ 25.00 Data/restraints/parameters Goodness-of-fit on F^2 1.041 Final R indices [I>s(I)] R indices (all data) Largest diff. peak and hole 0.349 and 0.404 (eÅ-3)

Table 2 Atomic coordinates and equivalent isotropic displacement parameters, U(eq), for heavy atoms in the ettringite structure. U(eq) is defined as one third of the trace of the orthogonalized Uij tensor. Atom type

Wyckoff position

x

y

z

Occ.

U(eq) [Å2]

Al1 Al2 Ca1 Ca2 O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 O11 O12 O13 O14 O15 O16 O18 O19 O20 O21 O22 S1 S2 S3 S4 O24 O17

2a 2a 6c 6c 6c 6c 6c 6c 6c 6c 6c 6c 6c 6c 6c 2b 6c 6c 6c 6c 2b 6c 2b 6c 2b 2b 2b 2b 2b 6c 2b

0.0 0.0 0.1878(1) 0.0004(1) 0.4003(6) 0.3358(7) 0.3366(9) 0.0036(3) 0.1341(5) 0.1320(5) 0.1323(5) 0.0025(4) 0.2555(6) 0.1479(5) 0.4049(5) 0.6667 0.5703(9) 0.0045(6) 0.6183(17) 0.5715(16) 0.3333 0.1932(6) 0.3333 0.1919(15) 0.3333 0.6667 0.6667 0.3333 0.3333 0.1936(9) 0.6667

0.0 0.0 0.1943(1) 0.1923(1) 0.1597(5) 0.3401(7) 0.3434(8) 0.1314(5) 0.0035(3) 0.1335(5) 0.1338(5) 0.3408(8) 0.4045(5) 0.4061(5) 0.2567(6) 0.3333 0.3762(10) 0.3438(9) 0.1911(14) 0.1906(15) 0.6667 0.5706(7) 0.6667 0.6170(20) 0.6667 0.3333 0.3333 0.6667 0.6667 0.5681(10) 0.3333

0.1245(2) 0.3757(2) 0.2495(1) 0.4995(1) 0.2495(3) 0.1674(4) 0.3299(4) 0.1795(2) 0.3192(2) 0.0694(2) 0.4296(2) 0.4160(4) 0.5029(3) 0.2494(3) 0.4969(3) 0.2998(10) 0.3908(5) 0.0823(4) 0.1142(9) 0.1466(8) 0.0520(8) 0.1455(4) 0.3090(13) 0.3972(7) 0.4445(10) 0.1323(3) 0.3681(3) 0.3787(3) 0.1220(3) 0.3558(7) 0.2004(11)

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.5 0.6 1 0.3167 0.3167 0.9 1 0.4 0.3 0.6 0.5 0.5 1 1 0.5 0.5

0.014(1) 0.014(1) 0.023(1) 0.025(1) 0.048(1) 0.038(2) 0.053(2) 0.021(1) 0.021(1) 0.025(1) 0.024(1) 0.038(2) 0.048(2) 0.042(1) 0.046(1) 0.036(4) 0.041(2) 0.059(2) 0.033(3) 0.035(4) 0.068(3) 0.059(2) 0.060(7) 0.034(4) 0.056(5) 0.031(2) 0.027(2) 0.031(1) 0.031(1) 0.041(2) 0.049(5)

4. Results and discussion 4.1. Structure of ettringite The structure was solved by direct methods and refined by leastsquares procedures on F2 (SHELXL-2013) [25]. Least-squares refinements were performed by minimizing the function P wðF02  Fc2 Þ2 ; where F0 and Fc are the observed and calculated

structure factors. The weighting scheme used in the last refinement cycle was w ¼ 1=½s2 F02 þ ð0:1192PÞ2 þ 2:2218P; where P ¼ ðF02 þ 2Fc2 Þ=3. The final fractional coordinates of heavy atoms are given in Table 2. The geometry optimization by DFT led only to minimal changes of the positions of the heavy atoms with a mean difference of 0.005 (x), 0.009 (y), and 0.003 (z). The positions of hydrogen atoms from the single-crystal X-ray diffraction were determined using a following procedure. The H atoms (all visible in


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Table 3 Comparison between DFT calculated and experimental positions of H atoms from single X-ray measurement (this work) and from neutron diffraction (Expn) [11]. H Atoms

x Calc

y Exp

Expn

0.3847 0.4933 0.3498 0.4283 0.3946 0.3147 0.0046 0.2153 0.2035 0.2026 0.0863 0.0703 0.3375 0.2447 0.1867 0.1538 0.4348 0.4468 0.0804 0.0744 0.089 14.1

0.3545 0.5078 0.3738 0.4334 0.4138 0.357 0.9987 0.214 0.2089 0.1927 0.9115 0.0658 0.3183 0.2829 0.1745 0.1665 0.7163 0.7085 0.0724 0.0747

Calc

This work H1A H1B H2B H2A H3A H3B H4 H5A H6 H7 H8A H8B H9A H9B H10A H10B H11A H11B H14A H14B MADa MRDb a b

0.3943 0.4865 0.3723 0.4244 0.4005 0.3581 0.9718 0.2123 0.2175 0.2098 0.9222 0.0803 0.3102 0.2933 0.1689 0.1979 0.5957 0.5667 0.0939 0.0883 0.026 8.7

z Exp

Expn

Calc

0.0754 0.2047 0.4333 0.3588 0.3187 0.4056 0.1926 0.0055 0.2045 0.1986 0.3415 0.4292 0.4068 0.4577 0.4764 0.4465 0.2389 0.2878 0.3557 0.4275 0.024 17.0

0.0603 0.1925 0.4343 0.3474 0.3323 0.4409 0.2077 0.0115 0.2059 0.2123 0.3544 0.4125 0.3736 0.4955 0.4677 0.4643 0.1893 0.1723 0.359 0.4004

0.2870 0.2370 0.1560 0.1620 0.3441 0.3440 0.1490 0.3000 0.0390 0.4040 0.4500 0.3920 0.5160 0.4589 0.2210 0.2860 0.5140 0.4528 0.0560 0.0990 0.016 7.7

This work 0.0661 0.1671 0.4174 0.3351 0.3499 0.4248 0.1954 0.005 0.1997 0.2066 0.3533 0.4423 0.387 0.4656 0.4625 0.4879 0.2869 0.2059 0.3514 0.4094 0.019 10.3

Exp

Expn

0.2703 0.2343 0.1644 0.1574 0.3532 0.3503 0.1483 0.3224 0.0443 0.4023 0.4234 0.4064 0.4923 0.4692 0.2192 0.2895 0.5362 0.4642 0.0905 0.0975 0.020 9.2

0.2524 0.2309 0.1588 0.1585 0.3426 0.3375 0.1599 0.3383 0.0939 0.4062 0.412 0.3983 0.5046 0.4806 0.2127 0.2834 0.5259 0.4532 0.1647 0.1483

This work

MAD e Mean Absolute Deviation. MRD e Mean Relative Deviation (%).

the difference maps) were fixed geometrically and then treated as riding atoms with an OeH distance of 0.96 Å. The positions of H atoms were refined using isotropic displacement parameters setting to 1.2 times of the Ueq of the parent atom. Table 3 collects experimentally determined fractional coordinates of the all H atoms together with the values obtained from the full geometry optimization. In addition, Table 3 also contains the coordinates obtained from the neutron diffraction measurements presented in the work by Hartman and Berlinger [11]. DFT-optimized values are in a good agreement with that data with a mean absolute deviation (MAD) for each fractional coordinate of 0.026(x), 0.019(y), and 0.016(z), and corresponding overall mean relative deviations (MRD) of 8.7% (x), 10.3% (y), and 7.7% (z). Our experimentally determined hydrogen atoms positions are a bit improved by using constrained OeH distances to 0.96 Å in the final refinement but the deviations from the referenced neutron diffraction data [11] are still relatively large (see corresponding MAD and MRD in Table 3). Our single crystal X-ray data of lattice parameters and average main atomic distances of the natural ettringite sample are collected in Table 4 showing a very good agreement with the previously published result [11]. The DFT optimized structural parameters of the ettringite (unit cell parameters and averaged interatomic

Table 4 Comparison of the experimental and calculated structural data of ettringite. Exp

Calc

Exp [11]

11.223 21.867 120.0 2385.401 2.5076 1.9229 1.5025(x3) 1.4937 1.5003

11.166881(82) 21.35366(22) 120.0 2306.04(3) 2.414 1.8898 1.475(5) (x3) 1.435(10) 1.479

This work a/Å c/Å g/ V/Å3 SeO SeO

11.2023(16) 21.467(4) 120.0 2333.0(8) 2.4829 1.9015 1.4680(11) (x3) 1.4544(5) 1.4587

distances in the basic structural units (½AlðOHÞ6 3 , SO2 4 ) are also collected in Table 4 as well. The structural relaxation resulted in cell parameters of 11.223 Å (a) and 21.867 Å (c), respectively, meaning only 2.2% larger unit cell volume in comparison to our experimental value (2333.0(8) cm3). The PBE calculated interatomic distances (CaeO and AleO) are only slightly longer (~0.02 Å) than those from the experiment (Table 4). Similarly, for the SO2 4 anions the calculations provided little longer bonds. The same trends were observed for the calculated and experimental structural parameters of thaumasite [17]. 4.2. Hydrogen bonds The ettringite structure, similarly to thaumasite, contains a lot of crystalline water and forms a rich network of hydrogen bonds with other structural components. The main structural units are columns of the {Ca6[Al(OH)6]2  24H2O}6þ composition with intercolumn channels occupied by SO2 anions and additional H2O 4 molecules [12]. These columns are parallel to the c axis (Fig. 2a, b). The anions are involved in a network of hydrogen bonds as proton acceptors with water molecules (Fig. 3) holding the columns together. The scheme of the hydrogen bonds is visible in Fig. 3 (black dashed lines) and important parameters (distances and angles) are collected in Table 5. In the structure, the moderate OeH$$$O hydrogen bonds were detected, in which the water molecules from the coordination sphere of the Ca2þ cations and oxygen atoms from the SO2 4 anions participate. Multiple, stronger OeH$$$O hydrogen bonds were identified among water molecules themselves. Our experimental and calculated average D···A values (2.8085 and 2.8111 Å) are in good agreement with an average value of 2.8093 Å from the work by Hartman and Berlinger [11]. In the ettringite structure also weak hydrogen bonds were classified, which are formed between hydroxyl groups of [Al(OH)6]3 units and water molecules (Table 5). For these hydrogen bonds, experimental (3.0835 Å) and calculated (3.0361 Å) average D···A distances also fit well.


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2þ Fig. 2. Structure of ettringite: octahedra ½AlðOHÞ6 3 (cyan), tetrahedral SO2 (dark blue) a) c view; b) b view. (For interpretation of the references 4 (yellow), eight coordinated Ca to colour in this figure legend, the reader is referred to the web version of this article.)

In general, all DFT-calculated donoracceptor distances are in very good agreement with the experimental data (both our measured and from literature [11]). For example, the mean relative deviation for the optimized structure, MRDo, for D$$$A distances is below 3.5% and for DeH$$$A angles is about 6%. Our experimental values deviate from the neutron diffraction data [11] a little more (MRDe ¼ 3.7% for D$$$A distances and 7.7% for DeH$$$A angles). The formed hydrogen bonds are also responsible for the structural deformations of the SO2 4 units. Whereas the isolated anion has a perfect tetrahedral symmetry, in the ettringite structure the SO2 4 anions have three SeO distances equivalent and the fourth one is significantly shortened (see calculated and measured SeO distances in Table 4). Water molecules involved in the hydrogen bonding are also slightly deformed with varying OeH bond lengths between 0.965 and 0.991 Å.

Fig. 3. Hydrogen bond scheme for ettringite structure in c view. Color code for atoms: Al e gray, Ca e gray blue, S e yellow, O e red, H e dark gray. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

4.3. Infrared spectrum The further characterization of ettringite was done by means of FTIR spectroscopy and calculated vibrational modes. The interpretation and the assignment of the bands in the experimental IR spectrum were performed on the base of the calculated harmonic vibrational modes. The characterization of the bands depicted in Table 6 was achieved from the analysis of the eigenvectors of the calculated vibrational modes. Experimental data published previously [12,16] were only partially described due to a complex character of the ettringite spectra (they are also collected in Table 6). The red lines in Fig. 4 represent our calculated (a) and measured (b) spectra of ettringite compared to thaumasite (black line). 4.3.1. OH groups vibrations In the structure of ettringite, the OH groups with a different structural environment are present, e.g. OH groups from [Al(OH)6]3 octahedra ((OH)Al) and from water molecules ((OH)w). This contributes to a broadening of the corresponding bands in the measured spectrum. Although the calculated bands are without anharmonic corrections (this effect can acquire ~50-100 cm1 for the OH stretching modes [23]), the theoretical spectrum reflects main features of the measured IR spectrum. Two typical regions can be detected in the spectra. The first, high-frequency region (4000e2500 cm1), represents exclusively the OH stretching vibrations. The band with the highest energy in the experimental spectrum (3637 cm1) is a complex band, in which asymmetric and symmetric OeH stretching vibrations of the Al(OH)6 unit are mixed. These vibrations are easily distinguished in the calculated spectrum  the band at 3713 cm1 is assigned to the asymmetric mode whereas the band at 3672 cm1 corresponds to symmetric mode. Previous experiments [12,16] interpreted only one wavenumber value for both vibrations (Table 6). The calculated spectrum also allowed us to distinguish the mixed asymmetric OeH stretching vibrations of water molecules (OHw) and OeH stretching vibrations coming from the [Al(OH)6]3 unit (OHAl) appearing at 3617 cm1 (shoulder). The calculated asymmetric OeH stretching vibrations of the water


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Table 5 Hydrogen bonds scheme in ettringite structure (distances in Å, angles in  ). Symmetry codes: i) ex þ y,ex,z; ii) y,x,1/2 þ z; iii) ey þ 1,xey þ 1,z; iv) ex þ y,ex þ 1,z; Experimental data from our single crystal Xeray measurement (Times new roman) experimental data from HartmaneBerliner [11] (italic) and optimized data (arial bold). Labels of atoms are according to Tables 2 and 3. Type Water molecules: O1CaeH1A / O10iCa

O9CaeH9A / O11Ca

O8CaeH8A / O12iCa

O9CaeH9A / O3Ca

O14CaeH14A / O9iiCa

O2CaeH2B / O19iii S

O3CaeH3A / O13S

O3CaeH3B / O21iii S

O8CaeH8B / O13iv S

O8CaeH8B / O21S

O9CaeH9B / O21iii S

O10CaeH10A / O19S

O11CaeH11A / O18iiS

O11CaeH11B / O13S

O14CaeH14B / O19S

Hydroxyls: O6Al eH6A / O9

Ca

O7Al eH7A / O3

Ca

O4Al eH4A / O12

O5Al eH5A / O1Ca

MADoa MRDob MADea MRDeb

Ca

DeH

H/A

D/A

DeH/A

0.961 (5) 1.049 0.985 0.960 (5) 0.998 0.991 0.960(5) 0.990 0.976 0.96(3) 0.991 0.930 0.960 (5) 0.943 0.965 0.960 (5) 0.976 0.987 0.959 (5) 0.962 0.987 0.959 (5) 0.954 0.988 0.959 (5) 0.979 0.985 0.960 (5) 0.979 0.990 0.960 (5) 0.994 0.986 0.960 (5) 1.027 0.988 0.960 (5) 0.930 0.965 0.960 (5) 1.067 0.986 0.960 (5) 0.962 0.984

2.19 (6) 2.078 2.051 2.18 (5) 1.863 1.864 2.17(7)) 1.775 1.752 2.25(3) 1.864 1.708 1.94 (7) 1.562 1.723 1.87 (3) 1.752 1.810 1.92 (4) 1.813 1.791 1.93 (4) 1.769 1.797 2.06 (4) 1.824 1.857 1.91 (2) 1.894 1.774 2.10 (5) 1.906 1.904 1.88 (3) 1.890 1.818 2.30 (7) 1.708 1.892 2.21 (7) 1.764 1.843 1.80 (3) 2.019 1.810

2.940 (10) 3.116 3.017 2.939 (10) 2.846 2.850 2.78(2) 2.7533 2.5143 2.8862(16) 2.8502 2.4403 2.750(10) 2.3686 2.4286 2.792 (10) 2.640 2.7933 2.764 (10) 2.699 2.7449 2.779 (15) 2.701 2.7679 2.880 (12) 2.788 2.8090 2.86 (2) 2.848 2.753 2.823 (19) 2.896 2.850 2.789 (10) 2.872 2.7984 2.854 (9) 2.551 2.860 2.802 (12) 2.808 2.8244 2.737 (10) 2.947 2.7742

134 (6) 170.2 168.1 135 (6) 168.1 173.1 120(5) 126.3 149.6 123(3) 173.1 149.1 141 (8) 141.1 150.6 159 (7) 149.6 173.2 146 (6) 151.9 160.9 146 (5) 164.6 166.3 142 (5) 167.3 161.6 168 (5) 164.3 169.3 131 (5) 173.1 161.3 156 (6) 173.3 171.5 116 (5) 149.1 166.6 119 (6) 164.9 172.8 164 (9) 161.6 165.7

0.964 (4) 0.978 0.976 0.960 (5) 0.913 0.976 0.960 (5) 0.972 0.973 0.960 (5) 0.986 0.974 0.031 2.4 e e

2.17 (4) 2.130 2.181 2.21 (2) 2.235 2.102 2.209 (14) 2.347 2.36 2.26 (4) 2.241 2.197 0.065 3.3 e e

3.008 (7) 3.103 3.059 3.154 (13) 2.824 3.0521 3.167 (12) 3.096 2.892 3.005 (9) 2.696 3.1413 0.103 3.5 0.111 3.6

144 (5) 173.0 148.9 167 (7) 151.0 164.1 177 (5) 153.9 103.9 134 (5) 156.9 162.8 9.7 6.1 21.4 7.5

o e DFT optimized, e  our experiment. a MAD e Mean Absolute Deviation. b MRD e Mean Relative Deviation (%).

molecules appear also at 3577, 3485, 3443, 3391, and 3285 cm1 respectively, whereas corresponding symmetric OeH vibrations can be found at 2897 cm1 with a distinguishable shoulder at 2957 cm1. In the experimental spectrum, it is possible to see only one broad complex band at 3432 cm1 (Fig. 4) and bands with a very low intensity for symmetric OeHw vibrations at 2922 and 2832 cm1, respectively. The both calculated and experimental bands agree well also with the measured IR and Raman spectra by Myneni et al. [12] and Frost et al. [16] (Table 6). For example, the FTIR spectrum by Myneni exhibits the broad bands around 3500 and 3300 cm1. In that work the OeHw asymmetric vibrations were assigned at 3560 cm1 and symmetric ones at 3356 cm1. Frost et al. [16] assigned the band at 3629 cm1 to the OeHAl stretching vibrations and the broad band, centred at 3398 cm1, to OeHw vibrations. The latter band was deconvoluted into component bands at 3398, 3241, and 3116 cm1 in the FTIR spectrum, and 3487, 3386, and 3260 cm1 in the Raman spectrum, respectively. A specific feature of the OeH stretching modes is their distribution over a broad range of frequencies (2800e3800 cm1) as a consequence of the different strengths of the hydrogen bonds collected in Table 5. A relation between the calculated wavenumbers of the stretching modes of the OH groups involved in the hydrogen bonds and donoreacceptor distances is presented in Fig. 5. The categorization of the hydrogen bonds onto three groups is evident. The plot shown in Fig. 5 demonstrates a typical relation between OeH stretching frequencies and hydrogen bond distances known for the conventional hydrogen bonds [26]. The second, lowfrequency region of the spectrum, lies below 2000 cm1 and the interpretation of the experimental spectrum is more complicated because many overlaps of the vibrational bands exist in this region. Thus, the support from the calculated spectrum is inevitable. The OeH bending vibrations of the water molecules are clearly assigned to the bands at the 1667 cm1 and 1633 cm1 in the calculated spectrum having corresponding bands in the experimental IR spectrum (1678 cm1 with a shoulder at 1631 cm1). These vibrations were assigned to 1655 and 1645 cm1 by Myneni et al. [12] whereas Frost et al. [16] identified them at 1676 and 1636 cm1. The splitting of the HeOeH bending mode can be explained by the presence of the ‘non-equivalent’ water molecules in the crystal structure related to the different hydrogen bond strength and the different structural environment. 4.3.2. SO2 4 anions SO2 4 is oxyanion with a typical tetrahedral structure (Td symmetry) in aqueous solution having Raman active bands at 981 cm1 (n1, symmetric stretching), the in-plane bending (n2) at 451 cm1, the asymmetric stretching mode (n3) at 1104 cm1, and out-ofplane bending mode (n4) at 613 cm1 [12] (Table 7). These assignments correspond very well with those by Nakamoto et al. [27] 1 for the SO2 for n1, 450 cm1 for n2, 1105 cm1 4 solution (983 cm for n3, and 611 cm1 for n4, respectively). The SO2 4 anions in the ettringite structure are completely hydrated and can found in three crystallographically different sites in the unit cell [7,12]. Those works suggested the reduction of the tetrahedral symmetry of the SO2 4 anions to C3v or, according site-symmetry calculations and local coordination of anions, even lower the C1 symmetry was suggested [28]. Another study showed a correlation between the site-symmetry of the SO2 anion in three different ettringite 4 structures and corresponding proposed models assumed the C3 site symmetry [29]. The X-ray and Raman results by Renaudin et al. [29] were in a good accordance with the results by Hartman and Berlinger [11], and Myneni et al. [12], respectively. In this work, based on the calculated and measured SO2 4 structural parameters (Table 4) we suppose the reduction from Td to C3v symmetry (calculated SeO bond lengths are 1.4937 Å (x1)


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221

Table 6 Types of the vibrational modes and corresponding calculated wavenumbers [cm1] in comparison with experiment. (OeH)Al e hydroxyl groups from ½AlðOHÞ6 3 octahedral; (OeH)w e hydroxyl groups from water molecules.

nas (OeH)Al ns (OeH)Al ns (OeH)Al, nas (OeH)w nas (OeH)w ns (OeH)w ns (OeH)w d HeOeH d HeOeH nas SeO ns SeO nas AleO d AleOeH d AleOeH, d Ale(OeH) d CaeOeH d Ale(OeH) d OeSeO d CaeOeH n SeO d AleOeH d CaeOeH dscis HeOeH d AleOeH d HeOeH) d OeSeO nasCaeO drock OeAleO dwagg OeAleO drock OeAleO ns CaeO Whole structure rocking

This work,calculated

This work, IR (KBr)

Exp.12, IR/Raman

3713 3672 3617 3577, 3485, 3443, 3391, 3285, 2957 2897 1667 1633 1143 1011

3637

3560/

Exp.16, IR/Raman 3626/3629

3432 2922 2832 1678 1631 1113 989

3400-3235/

3398,3241,3116/3487,3386,3260

1655/ 1645/ 1136/1170-1129 989/990

1676/ 1636/ 1109,1078,1109/1136 /1016,1008,989

957 915, 885, 839 786, 737

942 863 750

872/871-837

877,851/ /762

704, 645

616

639-610/668-607

/651,625,602,

582

542

547/555-542

/582,546

550, 424

418

/450-430

/455,430

346,317/373,344, 317

/359

385 305 277,248

/237,211

190, 99

/180,115

ns CaeO Whole structure rocking

and 1.5025 Å (x3), and corresponding OeSeO bond angles are 109.0 (x3) and 110.1 (x3), respectively). The reduced site symmetry of the SO24 anion in the ettringite structure has a consequence in the splitting of the triply degenerate vibrations (n3 and n4) to A and E modes (Table 7) and the reconsideration of the band assignments of the experimental spectra. The band at 1113 cm1 in the FTIR spectrum of ettringite (Tables 6 and 7, Fig. 6) can be assigned to the n3 vibration of the SO2 4 anions agreeing well with the peak at 1136 cm1 identified in the work by Myneni et al. [12] (Table 6). In that work this band was deconvoluted into four peaks at 1190, 1165, 1141, and 1098 cm1 (Table 7), which likely correspond to the degenerate and nondegenerate modes of the SO2 4 units occupying the three crystallographically different sites [7]. The broad band observed at 1113 cm1 in this work can be clearly identified with the four calculated peaks at 1143, 1098, 1078 and 1044 cm1 (Table 7, Fig. 6) supporting the discussion about the deconvoluted bands in Ref. [12]. The symmetric stretching vibration (n1) of the SO2 4 anion occurs as low intense band at 989 cm1 in the experimental FTIR spectrum. In the calculated spectrum the bands at 1011, 959 and 917 cm1 were identified as symmetric stretching vibrations and correspond to the crystallographically different SO2 units. The 4 assignment of these bands agrees well with the previously published data [12,16]. Myneni at al [12] interpreted bands at 1016, 1008 and 989 cm1 (FTIR) and 1011, 996, and 982 cm1 (Raman), whereas Frost et al. [16] found three peaks at 998, 991 and 982 cm1 in the Raman spectrum (Table 7). The symmetric n2 and asymmetric n4 bending vibrations are difficult to distinguish in the FTIR spectrum because of their overlap with the Ca/AleOH bending modes. However, the calculated spectrum offered a clear

identification of the n4 modes at 704, 645, 582, and 550 cm1 that correspond to broad peaks at 616 and 542 cm1 in the FTIR spectrum (Table 7, Fig. 7). This interpretation is in a good correlation with assignment by Myneni et al. [12] for peaks 669, 627 and 606 cm1. The symmetric n2 bending vibration is identified at 424 cm1 (calculated) perfectly corresponding with the band at 418 cm1 found in the experimental spectrum) and agreeing well with the other experimental values at 489 and 451 sh cm1 [12], and 455 and 430 cm1 [16], respectively. 4.3.3. Other modes below 1000 cm1 Towards the lower energies below 1000 cm1 more complex bands appear in the FTIR and calculated vibrational spectra. For example, the six-fold coordination of the aluminum cation is reflected in the absorption band of the nas (AleO) vibration at 989 cm1 (experimental) that corresponds to the calculated mode at 1011 cm1 together with ns(SeO). The analysis of the calculated spectrum distinguishes also the bending vibrations d(AleOeH), d(OeAleO), and d(HeOeH) and the calculated band at 786 cm1 is a complex band consisting of the d(AleOeH), and d(CaeOeH) bending modes (Table 6). The nas(CaeO) vibration was distinguished at 424 cm1 together with the d(AleOeH), d(OeSeO), and d(HeOeH) bending modes. The calculated spectrum also allows interpretation of the bands below 400 cm1 what is not possible by using a conventional midIR spectroscopy (e.g. the ns(CaeO) vibrations at 305, 277 and 248 cm1). Generally, in the low energy region, vibrations of skeletal and rocking types dominate. The low-wavenumber lattice modes detected below the 300 cm1 in the calculated spectrum were not assigned by Myneni et al. [12] but agree well with the

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Raman spectrum by Frost et al. [16].

Fig. 4. Calculated (a) and experimental (IR) (b) vibrational spectra for ettringite (red lines) and thaumasite (black lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5. Dependence of calculated eOH stretching modes on donor e acceptor distances in hydrogen bonds. Red line represents an exponential asymptotic fit to the data points.

4.3.4. Comparison with thaumasite Ettringite and thaumasite have a similar structure as it was discussed in Introduction. Thus, a certain resemblance between their spectra is expected. Fig. 4a and b displays calculated vibrational and measured IR spectra for both minerals. Three main differences are easily distinguishable as it is depicted by rectangles in Fig. 4. These differences correspond directly to the differences in the structure and composition. The first distinction is observed for the high-frequency edge. In the calculated spectrum of ettringite two bands with the highest energy (at 3712 and 3672 cm1) are assigned to the stretching vibrations of OeH groups from the [Al(OH)6]3 units having corresponding distinguishable band in the experimental spectrum. However, such band is not visible in the IR spectrum of thaumasite and also in the calculated spectrum no separate bands are observed. This difference can be explained by the presence of the [Si(OH)6]2unit in thaumasite in contrast to the [(Al(OH)6]3 in ettringite. The OeH bond is weakened by the stronger binding to Si and, consequently, OeH stretching modes are shifted to lower frequencies where they are overlapped with the stretching vibrations of the OeH groups from water molecules. The second difference is observed in the spectral window between 3200 and 2800 cm1. In the calculated spectrum of thaumasite, two main bands are clearly distinguishable whereas only one main band is observed in the calculated spectrum of ettringite. This difference can be explained by a more complicated structure of thaumasite, which contains, in addition to sulfate anions, also carbonate anions in the structure. This has a direct impact on the more complicated hydrogen bond scheme in comparison to ettringite where only sulfate anions are present. The low frequency band at 2900 cm1 in both calculated spectra is assigned to the symmetric stretching OeH vibrations of water molecules involved in relatively strong hydrogen bonds (O$$$H distances of about 1.80 Å) among water molecules themselves. Moreover, in thaumasite, also the vibrations of the water OH groups from the hydrogen bonds with CO2 3 anion contribute. Bands at 3183 and 3141 cm1 (doublet in the calculated spectrum of thaumasite) represent symmetric stretching OeH vibrations of the water molecules involved in weaker hydrogen bonds with O$$$H distances of about 1.85 Å, which are not present in the ettringite structure. Even weaker hydrogen bonds of the water molecules (e.g. formed with the sulfate anion e see Table 5) have a smaller effect on the red shift of the OH stretching modes and corresponding stretching vibrations are in a region above 3300 cm1. The bands in the experimental IR spectra of both minerals, which correspond to low frequency OH stretching modes, are distinguishable only with a difficulty because of their low intensity and a convolution with broad intensive band starting at 2800 cm1. The third main difference between ettringite and thaumasite is a band at ~1400 cm1, which is very intensive in the thaumasite IR spectrum. This band corresponds to the asymmetric stretching CeO vibration of the CO2 3 anion. In the IR spectrum of ettringite, a small band at 1410 cm1 is observed. It can indicate a carbonate impurity in the natural sample of the ettringite crystal. Our computational model of ettringite does not contain CO2 3 anions; thus, there is no calculated band at ~1400 cm1. In the calculated spectrum of thaumasite, this band is easily recognized. From other differences between the spectra of thaumasite and ettringite, which are not so pronounced, it is worthy to mention the vibrations of the sulfate anions. From the comparison of the IR spectra it is evident that the asymmetric stretching mode is shifted to the higher frequency for ettringite (an intensive band at ~1100 cm1) in comparison to thaumasite. The same trend is also observed for the calculated asymmetric stretching modes


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Table 7 Correlation diagram for internal vibrations of SO2 4 anion in the ettringite structure. Fundamental modes

n1 n2 n3 n4

Site symmetry Free ion (Td) [12]

Ettringite (C3v) [this work] FTIR/CALC

Ettringite [12] FTIR/Raman

Ettringite [16] FTIR/Raman

A1 E T1 T2

A E AþE AþE

1016,1008,989/1011,996,982 /489, 451 sh 1190,1165,1141, 1098/ /669,627,606

/998,991,982 /455,430 /1118,1206 /651,625,602,586,546

981 451 1104 613

989/1011,959,917 418/424 1113/1143,1098,1078,1044 616,542/704, 645, 582, 550

Moreover, in thaumasite, this vibration overlaps with the symmetric stretching vibration of CO2 3 . These differences are not so well distinguishable in the experimental IR spectra because of the low intensity of the stretching modes. 5. Conclusions

Fig. 6. Calculated (CALC) and experimental (EXP) stretching vibrations of SO2 4 anion in the ettringite structure.

(1143 cm1 for ettringite, Table 6, cf. 1095 cm1 for thaumasite). A difference of the symmetric stretching vibration of the SO2 4 unit is a bit larger (1011 cm1 for ettringite cf. 951 cm1 for thaumasite).

The crystal structure of the natural sample of ettringite was solved on the base of single crystal X-ray measurement and DFT calculations. The full structural relaxation performed by using PBE functional completed the determination of the positions of hydrogen atoms and corresponding hydrogen bonds what was not possible with a required accuracy from the single crystal X-ray data. Further, the complete geometrical analysis of the complex network of the hydrogen bonds was performed on the base of the DFT relaxed structure leading to the determination of the several groups of the hydrogen bonds. The moderate OeH$$$O hydrogen bonds exist between water molecules, slightly stronger are found between water molecules and SO2 ions, and, finally, the weak 4 OeH$$$O hydrogen bonds are detected for the hydroxyl groups from the [Al(OH)6]3 units and water molecules. The IR spectrum collected by FTIR spectroscopy in the mid-IR region showed a good correspondence with the calculated spectrum by using finite difference method. The analysis of the eigenvectors of the all calculated frequencies allowed full and unambiguous assignment of the all modes to the particular types of the vibrations what was not possible so far from the measured IR/ Raman spectra. This analysis helped in the interpretation of the measured spectra, for which complex structure with a lot of broad and overlapping bands is typical, especially in the spectral range below 1500 cm1. Finally, the comparison between the spectra (both calculated and experimental) of thaumasite and ettringite was performed and the most relevant differences for these structurally similar minerals were explained. From detailed analysis and comparison of the both measured and calculated spectra of ettringite is evident that the calculated spectrum is very useful and reliable tool at the analysis of the problematic parts of measured IR spectrum. Acknowledgment The financial support for this research by the Scientific Grant Agency VEGA (projects No. 2/0083/12, 1/0679/11) is gratefully acknowledged. Authors wish to express their thanks to Dr. H.
lkova
for IR spectra measurements. Pa References

Fig. 7. Calculated (CALC) and experimental (EXP) bending vibrations of SO2 4 anion in the ettringite structure.

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