29Si NMR in Cement: A Theoretical Study on Calcium SilicateHydratesPawel Rejmak,†,* Jorge S. Dolado,‡ Malcolm J. Stott,§ and Andres Ayuela†,∥
†Donostia International Physics Center (DIPC), p. Manuel de Lardizabal 4, p. Manuel de Lardizabal 4, Donostia-San Sebastian, Spain‡Tecnalia Research and Innovation, Geldo Edificio 700, 48160 Derio, Spain§Queen's University, Kingston, ON K7L 3N6, Canada∥Centro de Física de Materiales CFM-MPC, Centro Mixto CSIC-UPV/EHU, p. Manuel de Lardizabal 5, Donostia-San Sebastian,Spain
*S Supporting Information
ABSTRACT: The NMR spectra of 29Si in cement-based materials are studied throughcalculations of the isotropic shielding of silicon atoms within the density functionaltheory. We focus on the main component of cement, the calcium-silicate-hydrate gel,using widely accepted models based on the observed structures of jennite andtobermorite minerals. The results show that the 29Si chemical shifts are dependent notonly on the degree of condensation of the (SiO4) units, as commonly assumed, but alsoon the local arrangement of the charge compensating H and Ca cations. We find that theNMR spectra for models of the calcium-silicate-hydrate gel based on tobermorite are in better agreement with experiment thanthose for jennite-based models.
■ INTRODUCTIONDespite the ubiquitous application of cement-based materials,our knowledge of these construction materials, particularly onthe atomic scale, is still lacking. The product resulting from thehydration of common Portland cement clinker is a porousmatrix consisting of several crystallites embedded in a poorlycrystallized phase, the so-called calcium−silicate−hydrate (C−S−H) gel.1 This C−S−H gel is the most important hydrationproduct. It constitutes about 50−70% of the fully hydratedcement paste and is responsible for most of the engineeringproperties of cement-based materials. The structure of C−S−Hgel is complex and not fully understood. Various atomisticmodels of the gel have been proposed, which have Ca−O layersribbed with silicate chains.2 The most accepted models arebased on the crystal structures of jennite3 and tobermorite 14Å4 minerals, as seen in Figure 1. The silicate chains in theseminerals follow the so-called dreierkette structure, wherein eachpair of silica pairing tetrahedra sharing O−O edges with CaOoctahedra, is followed by a silica bridging tetrahedron, the lattersharing only O vertices with CaO octahedra. The Ca−O layersin tobermorite have bare Ca cations, whereas in jennite they aremonohydroxylated. In addition, the bridging tetrahedra intobermorite are protonated forming silanol groups.Much information on the atomic characteristics of
cementitious materials is provided by nuclear magneticresonance spectroscopy (NMR) of 29Si (ref 5 for a recentreview and references). The assignment of observed NMRpeaks is based on the assumption that 29Si chemical shiftsdecrease with the degree of condensation of (SiO4) units,structures which range from isolated monomers to tetrahedrallycoordinated networks. This assignment led to the conclusion
that the C−S−H gel contains silicate chains with finite lengthsof (3n − 1) tetrahedra, n = 1, 2, ..., and the C−S−H structuremay be seen as jennite or tobermorite with a number ofbridging tetrahedra removed as shown in Figure 2.6 This finitechain model was also supported by the chromatographicanalysis of trimethylsilyl derivatives of C−S−H gel.1 Thetheoretical justification of this model came recently fromcalculations within the DFT.7 Atomistic simulations of C−S−H
Received: March 7, 2012Published: April 5, 2012
Figure 1. Structures of (a) jennite and (b) tobermorite 14 Å minerals.The pairing Si tetrahedra are denoted as Q2; bridging ones, as Q2b(jennite), or Q2bOH (tobermorite) when having a SiOH group. Notethat there are two types of charge compensating Ca cations, given withlight blue balls, in the layered (L) and interlayer (I) positions.
gel are still quite scarce,7−12 in particular quantum calculationsof the NMR spectra are still missing. The aim of this work is tofulfill this need through the DFT investigation of the 29Si NMRspectra of models of C−S−H gels derived from jennite andtobermorite 14 Å.
■ MODELS AND METHODSGeometric models. Our models for C−S−H gel, like those
used previously,10 are based on the observed structures ofjennite and tobermorite 14 Å. Apart from the mineral structureswith infinite silicate chains, we focused on models consisting ofdimeric and pentameric silicate species, proposed for C−S−Hgel. In agreement with previous suggestions from experimentalwork,2 we found in preliminary calculations that the structureswith pairing tetrahedra removed are less stable than the oneswith bridging sites removed (by at least 100 kJ/mol); thereforeonly the latter are discussed below. The dimeric/pentamericmodels were obtained by removing each/every second bridgingtetrahedra from the infinite chains in the initial unit cell of themineral doubled along the b direction. The finite chains wereobtained by removing either neutral SiO2 units from jennitestructure or charged SiO(OH)+ units from tobermoritestructure (Figure 2). The excess negative charge can beneutralized with protons, Ca2+ or Ca(OH)+ ions. All of thesecharge compensating schemes were applied with severalpossible distributions of cations. The detailed descriptions ofthe models used along with their structures are attached in the
Supporting Information. We will refer to a particular model asAn−Bm, where (i) A is T or J denoting tobermorite- or jennite-based models, (ii) n is the length of silicate chains, namely ∞for minerals and 5 or 2 for C−S−H gel models, (iii) B denotesthe charge compensation scheme, either H for protons or Cafor Ca2+/Ca(OH)+ ions, and (iv) m is the serial number of thegiven model.We also looked at β-belite and α-quartz, as reference systems,
with input structures taken from the experimental data.13,14 Inaddition to the periodic lattice models, we performed someauxiliary calculations on finite cluster models extracted from theoptimized periodic structures of β-belite and α-quartz. Theclusters for belite and quartz host 21 and 29 Si atoms,respectively (Figure S2 of the Supporting Information). TheVESTA code was used for the processing of structures andfigures.15
For the description of various types of silica units, we used acommon NMR notation, according to which Qn denotes Siatoms in a (SiO4) tetrahedron coordinated to n othertetrahedra. The Si atoms in the tetrahedra terminating dimersor pentamers will be referred to as the Q1 sites. In doublycoordinated tetrahedra, they will be denoted as Q2 and Q2b forthe pairing and bridging positions, respectively (see Figure 2).If a Q1 or Q2b tetrahedron hosts a hydroxyl group, it would bedenoted by an additional OH index. We will discuss five typesof distinguishable Si sites in our models, namely Q1, Q1OH,Q2b, Q2bOH, and Q2. Note that higher coordinated sites Q3
and Q4 are not normally present in C−S−H gels.Computational Methods. For all the periodic models,
both the atomic positions and the parameters of the unit cellswere optimized using interatomic potentials of the polarizablecore−shell type,16 as implemented in the GULP code.17 Weemployed a potential parametrization slightly refined withrespect to ref 10 (Figure S3 of the Supporting Information fordetails).18 The electronic calculations for these structures weresubsequently performed within DFT with the QuantumEspresso code.19 The gradient corrected exchange-correlationfunctional of Perdew-Burke-Ernzerhof (PBE)20 and the normconserving pseudopotentials of Troullier−Martins21 wereemployed. Because of the large size of our models, particularlythe ones based on the structure of tobermorite, structuraloptimization was performed with GULP. The reference modelsbased on β-belite and α-quartz were treated in the same way forinternal consistency.The isotropic magnetic shieldings were obtained with the
Gauge Including Projector Augmented Waves (GIPAW)method.22 Within this approach, the induced magnetic fieldand the shielding tensor are calculated from the electric currentinduced by the external magnetic field using the first orderlinear response. The all-electron wave functions are used for thecalculations of isotropic shielding. These are obtained from theself-consistent pseudowave functions using a linear operatordependent on the field, which ensures the translationalinvariance of wave functions in the external magnetic field.The GIPAW method has been successfully applied to study43Ca and 17O NMR in several Ca silicates, including jennite andtobermorite.23 The plane wave basis had an energy cutoff of 80Ry. The k-points sampling for tobermorite models was 2 × 1 ×1 (i.e., 2 points along the shortest a lattice constant, being about6.7 Å). Because jennite lattice constants (about 10 Å) arelonger than the shortest dimensions of the tobermorite unitcell, we found that Γ point calculations were sufficient for thejennite based models. A k-point mesh of 4 × 4 × 4 was applied
Figure 2. Optimized structures of the selected models of C−S−H gel:(a) tobermorite-based dimeric model (T2−H1), (b) tobermorite-based pentameric model (T5−H2), and (c) jennite-based pentamericmodel (J5−1). According to the different local environment of Sitetrahedra, five types of Si atoms are distinguished, namely Q1, Q1OH,Q2, Q2b, and Q2bOH. The charge compensating Ca cations are givenas in the previous figure.
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for belite and quartz models. Checks of the convergence ofthese computational details are reported in Figure S5 of theSupporting Information.We also performed DFT/PBE calculations for the cluster
models with the Amsterdam Density Functional (ADF)program.24 These calculations employed Slater type triple-ζbasis sets augmented with polarization functions.25 The 29Sishieldings were calculated within the Gauge Including AtomicOrbitals approach26 using the NMR package,27 distributed withthe ADF code.Computation of 29Si Chemical Shifts. We wish to
compare our calculated values with observed NMR chemicalshifts. The dispersion of all the computed isotropic shieldings isshown in Figure 3. The quantities measured experimentally are
not the magnetic shieldings themselves, but the chemical shifts,taken with respect to the signal of a suitable reference system,typically tetramethylsilane for 29Si. The accurate reproductionof experimental chemical shifts at the DFT level can be difficultbecause the common functionals account differently forexchange and correlation in the reference and studied systems.This is the case for the reference tetramethylsilane withcovalent Si−C bonds and our silicates in which the Si−O bondshave more ionic character. In order to compute chemical shiftswith experimental accuracy, it is recommended to use somesecondary reference compounds or interpolation procedure.28
We calibrated our results with respect to two silicates with awell-defined single NMR signal, namely β-belite and α-quartz.The observed values of chemical shifts for these species are−71.3 ppm for Q0 in belite29 and −107.4 ppm for Q4 inquartz,30 with a difference of 36.3 ppm. The GIPAW differencebetween Q0 and Q4 shieldings is only 25.9 ppm, and in theADF/GIAO cluster calculations, a similar value of 23.4 ppmwas obtained. This indicates that the possible inaccuracies inour calculations stem rather from the exchange-correlationfunctional, not from the particular way of computing NMRshieldings.The chemical shift of i-th 29Si nuclei in M model (δGIPAW
i,M )was calculated according to the formula
δ δδ δ
σ σ
σ σ
= +−
−
× −
( )
( )
( )
i M pp q
p q
p i M
GIPAW,
expref, exp
ref,expref,
GIPAWref,
GIPAWref,
GIPAWref,
GIPAW,
(1)
where δ and σ denote chemical shifts and isotropic shieldings,respectively, and the p and q letters denote the belite and quartz
reference systems. Because the observed chemical shifts ofatoms in a given chemical environment are averaged due tomotional effects, we also calculated average values of chemicalshifts for a given type of Qn site in M model, replacing theδGIPAWi,M in formula 1 by the arithmetic average of Qn shieldings.More sophisticated methods to include atomic motions withinfirst principles are beyond our current computational facilities,due to the large size of our cells (about 200 atoms).
■ RESULTSStructural and Elastic Properties. For selected mineral
silicates, the structural and elastic properties from GULPcomputations were compared with observed values (Figure S6of the Supporting Information). In all of the cases, thecomparison between the theoretical and available experimentaldata of the minerals is very good.The structural data and elastic constants of C−S−H gel
models, with finite chains, are summarized in Table 1. These
calculated elastic quantities have larger values than theexperimental ones for C−S−H gel31 because of the effects ofporosity in the cement materials. The elastic propertiesdepended strongly on the model, although, not surprisingly,they usually increased with density. The biggest discrepancybetween our calculated elastic properties and those presented inref 10 is for the bulk modulus predicted for the T2−Ca modeland especially the T2−H1 one. It should be noted that, in thepresent work, a wider systematic search of structures was made.In these cases, the bulk moduli and densities are even higherthan for tobermorite. As a consequence of the optimization,these T2 models have a densely packed structure due to thesignificant shrinkage of the unit cell in the c direction by about3 Å after removing the Q2b tetrahedra. The pentameric modelsof tobermorite, T5−Ca2 and T5−Ca3, also show higherdensities and elastic constants than in the basic T∞ structure,because the selected protons were replaced with Ca(OH)+ ions.
Figure 3. Dispersion of 29Si GIPAW isotropic magnetic shieldings (inppm) for various types of Si sites in the finite chain models based onjennite (green) and 14 Å tobermorite (red) structures.
Table 1. GULP Calculated Properties of C−S−H GelModels: Density (ρ), Elastic Properties (K − Bulk Modulus,G − Shear Modulus, Y − Young’s Modulus), and the EnergyDifference Calculated between Models with the SameComposition in the Unit Cell
model ρ (g/cm3) K (GPa) G (GPa) Y (GPa)a ΔEb (kJ/mol)
aK and G according to the Hill definition; Y = (9G)/(3 + (G/K)). bInparentheses, the DFT/PBE values calculated with the code QuantumEspresso for the GULP relaxed structures.
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The densities of jennite based models are slightly smaller incomparison to that of the J∞ structure because the removal ofSiO2 units does not lead to much contraction of the unit cell.We calculated the relative energy stability of the models with
the same unit cell composition in Table 1. The trends are thesame for both J and T5−H models, but the GULP values aresignificantly larger than the DFT ones. The opposite is foundfor the T2−H models, though, in these cases, the energydifferences are small.
29Si Chemical Shifts for Minerals. Table 2 shows thechemical shifts calculated according to the formula 1. The Q2
values predicted for T∞ and J∞ models agree well with theexperimental data for tobermorite 14 Å and jennite.32−34 Ourcalculations predict Q2b units less shielded than the Q2 ones.Some contradictions exist in the experimental literature. Congand Kirkpatrick reported a single peak around −85 ppm forsynthetic tobermorite and jennite.32 Maeshima et al. reportedanother deshielded peak for natural tobermorite,33 assigned toQ2b or Q2 sites connected to Al substituted bridging tetrahedral(i.e., Q2(1Al)). Komarneni et al. observed a strong signal at−81 ppm, which they assigned to Q1 sites in the defectivestructure of jennite.34 It was observed that the Q2b sites wereless shielded than the Q2 sites in C−S−H gel,35 thus one couldexpect a similar trend in all the dreierekette minerals. In ouropinion, these discrepancies can be settled only if the 29Si NMRexperiments can be performed on a well characterized mineralsample with resolved crystal structure. The simulated spectra ofT∞ and J∞ models are attached in Figure S8 of theSupporting Information.
29Si Chemical Shifts for C−S−H Gel Models. Thechemical shifts computed for C−S−H gel models are also
presented in Table 2. Although the predicted values for varioustypes of 29Si sites lie in partially overlapping ranges (Table 2),some general trends are clear: (i) the Q1OH sites are usuallyless shielded than the Q1 sites saturated only by Ca because ofthe smaller electron transfer from hydrogens than from Cacations, (ii) the Q1 sites in tobermorite models are morestrongly shielded than those in jennite models, due to thebonding of additional Ca cations in the interlayer position, (iii)the Q2 sites are more strongly shielded than the Q1 sites, (iv)the chemical shifts of the Q2 sites show a smaller dispersionthan those of Q1 and Q2b sites.The small dispersion of the Q2 signals is due to the similarity
of the neighborhoods of Q2 tetrahedra consisting of two otherSiO4 units and four Ca cations in all the models. The mean 29Sichemical shifts of Q2 species lie typically in the range from −82to −85 ppm, in good agreement with the experimental data.Among the Q2b sites, the ones in the J5 models are the leastshielded. This is attributed to the lack of coordination betweenQ2b tetrahedra and interlayer Ca ions in J models. Thetetrahedra in tobermorite models are linked to one (T5−H3)or two (T5−Ca3) interlayer Ca cations and are thus stronglyshielded. The Q2bOH sites in tobermorite models are slightlyless shielded than the Q2b ones though the effect is not asprominent as in the case of the Q1 and Q1OH species.We next simulated the NMR spectra by broadening and
summing the chemical shifts calculated for each 29Si atom.However, the chemical shifts were calculated for staticstructures at 0 K, and their dispersion is much larger thanthe experimental ones because atomic motions are neglected. Amagnetic nucleus changing its chemical environments suffi-ciently fast contributes to a single NMR signal at the meanvalue of the chemical shifts for the various configurations.Because the thermal motions are the fastest for the light nuclei,these dynamical effects should be indeed important at roomtemperature for our systems due to the presence of mobilehydroxyl groups and water molecules. To average dynamicallythe NMR spectra, we then assumed that all 29Si nuclei within acertain Qn site for a given model contribute to an average signal(also Table 2). The spectra following both assumptions arepresented in Figure 4. Dotted lines are obtained by summingthe chemical shifts from individual Si atoms; solid lines, bysumming the average chemical shifts for Qn sites in a particularmodel. Each plot includes one dimeric and three pentamericmodels, corresponding to a sample of C−S−H gel with a meanchain length of 4.25 tetrahedra. The dotted lines sum 76 and 38peaks for the T and J models, respectively. For solid curves,there are 10 (T5−Ca plot) or 11 (T5−H and J plots) peaks.The spectra with both dotted and solid lines present a fewmaxima at similar values. Since solid lines take some account ofdynamical effects we will focus on these lines in the discussionwhich follows.
■ DISCUSSION29Si NMR experimental results for C−S−H gel show twodistinct peaks: the first about −79 ppm assigned to Q1 sites,and the second about −85 ppm assigned to Q2 sites. The thirdpeak, about −82 ppm, is often resolved and assigned toQ2(1Al) sites.5 However, cross-polarization and 2D NMRexperiments showed the presence of middle peaks in pure silicaC−S−H gels, which were assigned to Q2b sites.35 The observedQ2/Q1 ratio evolves with the age of the C−S−H sampleindicating that the mean chain length of silicate chains increaseswith the age of C−S−H gel, with dimers prevailing in fresh
Table 2. Mean Values of Scaled 29Si Chemical Shifts,Obtained from the GIPAW Isotropic Shieldings Accordingto Formula 1
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samples, whereas pentameric and longer species are mostabundant in aged pastes.1 When discussing the models ofmature C−S−H gel, we shall therefore focus on the resultsobtained for the structures with large pentameric chains.The experimental spectrum closely resembles those simu-
lated for the tobermorite models saturated by Ca ions (part a ofFigure 4), with two dominant peaks visible, Q1 and Q2, and theQ2b sites contributing partially to both main peaks.5,35
However, the spectrum obtained for H saturated tobermoritemodels has three peaks, with the least shielded peak due to theQ1OH sites. For jennite model (part b of Figure 4), there is aspectrum with multiple peaks, shifted too much toward highervalues, and quite different from the data reported for C−S−Hgel. Although the Q2 signals agree with measured values, the Q1
chemical shifts computed for jennite models are higher thanexperimental ones. In conclusion, the good agreement of 29Sichemical shifts between experiments and calculations for the T5
models supports the presence of tobermorite-like phases in C−S−H gel.The calculated NMR spectra of both tobermorite- and
jennite-based models are affected by the charge compensationscheme. Most of the Q1OH peaks lie in the range usuallyassigned to Q0 sites. Weak Q0 signals are observed in somework on mature cement pastes, and are attributed largely tounreacted orthosilicates. Our results indicate that those Q0
peaks can be partially ascribed to Q1OH sites. Note that at highCa/Si ratio, the Q1OH sites should be scarce, if present at all.We also suggest that the Q2b sites, less shielded than the Q2
ones, may partially contribute to the NMR signals traditionallyassigned to the Q2(1Al) or even the Q1 sites. The exact positionof Q2b peak may depend on the local Ca concentration and thepresence or lack of hydroxyl groups. The assignment of thepeak between the Q1 and Q2 signals to the Q2b sites is inqualitative agreement with experimental results obtained withcorrelated NMR techniques.35
To further differentiate between the jennite and tobermoritemodels of C−S−H gels it is useful to assess other properties aswell as the NMR spectra. First of all, we discuss thestoichiometry. The typical composition of C−S−H gel is(CaO)1.7·(SiO2)·(H2O)1.2−1.8. This measured value for the Ca/Si ratio is fully realized by the pentameric jennite models.Although the Ca load in tobermorite models is lower, thecorrect Ca content is attained because Ca(OH)2 domains areknown to grow in solid solution with the silicate phase.36
Further experimental studies showed that Ca(OH)2 leachingdecreases the Ca/Si ratio of C−S−H gels from 1.7 to about1.137 If our jennite-like structures model C−S−H gel, the Ca/Siratio should remain near the initial value of 1.7, as giventypically for J5 models. Whereas the Ca/Si ratio after Ca(OH)2leaching is in the perfect agreement with the correspondingvalue in our T5 models.Recently, neutron scattering experiments showed that once
porosity is excluded, the density of C−S−H gel particles is inthe range 2.5−2.9 g/cm3.38 Both jennite and tobermoritemodels have lower densities than this observed range (seeTable 1), although the density of T5-Ca2 models (2.4 g/cm3) isclose to the values observed for C−S−H gel. Moreover, higherdensities are obtained in tobermorite models by includingdensely packed water molecules in the interlayer space or at thesilicate grain boundaries.11,12 The issue of low density cannotbe solved in jennite models by increasing the water contentbecause the degree of hydration in the jennite models regularlyexceeds the observed value for C−S−H gel.It is noteworthy that neutron scattering experiments also
show the presence of Ca−OH bonds,37 which was attributed tojennite-like species. However, the tobermorite-like structureswith finite chains can host Ca(OH)+ ions in the interlayerpositions. The latter was suggested by Taylor1 and was realizedin our T5−Ca2 and T5−Ca3 models. These tobermoritederived models with interlayer Ca(OH)+ ions could beconsidered as intermediate structures between normaltobermorite and jennite. C−S−H structure combiningtobermorite and jennite features was already suggested inmolecular dynamics study.9 Therefore, the models based ontobermorite explain not only the stoichiometry and massdensity of C−S−H gel but also its 29Si NMR spectra.
■ CONCLUSIONSSimulations of various periodic C−S−H gel models have beenperformed in order to calculate the 29Si chemical shifts. The
Figure 4. Simulated 29Si NMR spectra of C−S−H gel. The NMRsignals correspond to the following models: (a) tobermorite-basedwith the charge compensation of Ca (T5−Ca and T2−Ca, top) and ofprotons (T5−H and T2−H2, bottom), and (b) jennite-based (J5 andJ2). The spectra show the chemical shifts of individual Si atoms(dotted line) and the average on the site types of Table 2 (solid line).The peaks are broadened with gaussians with a half-maximum width of2.0 ppm. Vertical solid lines indicate the experimental positions of Q1
(−79 ppm) and Q2 peaks (−85 ppm).
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models were derived from observed structures of tobermorite14 Å and jennite minerals, which are regarded in cementscience as canonical models of C−S−H gel. The calculated Q2
chemical shifts were found to be almost model independent,and the Q1 and Q2b signals showed large dispersions. Typically,the shielding of these sites was weaker for hydroxylated speciesand increased with the number of Ca cations in its nearestneighborhood. We found good agreement between thecalculated and experimental chemical shifts for models basedon tobermorite 14 Å structure, while jennite-like modelsshowed too high Q1 values. Our calculations support thepresence of tobermorite-like domains in C−S−H gel, wherethey frequently coexist with domains of Ca(OH)2 and watermolecules in pore volumes. Note that tobermorite models withinterlayer Ca(OH)+ ions agree well with experiment. Thepoorer agreement between the computed chemical shifts andexperiment, along with other structural considerations seem toexclude jennite-like phases as the main components of C−S−Hgel.
■ ASSOCIATED CONTENT*S Supporting InformationThe detailed description of the models and their geometries,GULP parametrization, complete ref 19, structural and elasticproperties computed for mineral phases, the convergence oftest SCF results, simulated 29Si NMR spectra of T∞ and J∞models. This material is available free of charge via the Internetat http://pubs.acs.org.
■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected], [email protected] ContributionsThe manuscript was written through contributions of allauthors. All authors have given approval to the final version ofthe manuscript.NotesThe authors declare no competing financial interest.
■ ACKNOWLEDGMENTSWe acknowledge the support of the Basque Departamento deEducacion and the UPV/EHU (Grant No. IT-366-07), theSpanish Ministerio de Innovacion, Ciencia y Tecnologia (GrantNos. TEC2007-68065-C03-03 and FIS2010-19609-C02-02),and the ETORTEK research program (NANO-IKER GrantNo. IE11-304) funded by the Basque Departamento deIndustria and the Diputacion Foral de Guipuzcoa. P.R. andM. S. gratefully acknowledge a grant and the hospitality of theDonostia International Physics Center, respectively.
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