Modeling the Structure of Complex Aluminosilicate Glasses: The Effect

Article pubs.acs.org/JPCB

Modeling the Structure of Complex Aluminosilicate Glasses: The Effect of Zinc Addition Andrea Bernasconi,*,† Monica Dapiaggi,‡ Alessandro Pavese,‡ Giovanni Agostini,† Maurizio Bernasconi,§ and Daniel T. Bowron∥ †

ESRF The European Synchrotron, 71 Rue Des Martyrs, Grenoble, France 38000 Dipartimento di Scienze della Terra, Università degli Studi di Milano, Milano, Italy ∥ ISIS Pulsed Neutron and Muon Source, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Harwell Oxford Didcot, OX11 0QX, United Kingdom ‡

ABSTRACT: An empirical potential structure refinement of neutron and Xray diffraction data combined with extended absorption fine structure evidence has been applied to the investigation of two distinct sets of complex aluminosilicate glasses containing different quantities of zinc. Data come from (i) neutron and X-ray total scattering experiments, which have been performed at the ISIS neutron spallation source (SANDALS beamline) and at the European Synchrotron Radiation Facility (ID11 beamline), and (ii) EXAFS experiments which have been performed at the European Synchrotron Radiation Facility (BM23 beamline). By careful examination of the modeled ensemble of atoms, a wide range of structural information has been extracted: coordination numbers, bond distances, cluster sizes, type of oxygen sharing, and the preference of large cations to adopt a chargecompensating role. The first series of glasses, which is characterized by a fixed network modifier element content (i.e., Na), shows how the introduction of Zn at the expense of Si and Al network forming elements does not significantly alter the polymerization degree, as a result of its dominant 4-fold coordination. In the case of the second series, which is characterized by fixed network forming element content (i.e., Si and Al), it is shown how the replacement of a network modifier element (i.e., Ca) with the introduction of Zn does not change the propensity of Zn to be mainly 4-fold coordinated by promoting the network. Where appropriate the experimental results have been compared with classical theoretical approaches such as stoichiometric models based on Zachariasen’s rules and computational routines.

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INTRODUCTION Complex aluminosilicate glasses are frequently found in nature in materials such as volcanic magmas1 and impact meteorites,2 as well as having important roles in materials manufacturing such as the production of vitreous ceramics3 and optical fibers.4 For these materials, structural investigation with conventional crystallography is limited due to the lack of long-range periodic arrangements between the atoms that constitute the glasses. In spite of this lack crystalline order, structural motifs are equally present in the materials, as highlighted by the many different theories and experimental studies of disordered materials that have been undertaken over the last century. From the large number of glass structure theories, random network theory by W. H. Zachariasen5 is particularly useful when looking at silicabased glasses. This theory establishes the chemical composition as the most important factor controlling the structure of the glasses and, in turn, the final properties of the materials. Most of this theory is based on the distinction between species that are able to occur as glasses by themselves, polymerizing the network (i.e., network forming element) like silicon and boron, and species that are not able to occur as glasses by themselves and that, when present in a glass environment, interrupt its © 2016 American Chemical Society

polymerization (i.e., network modifier element) like alkali and alkaline earth metals. Aside from these two principal species, there is an additional group of elements whose structural role in glass is not unique (i.e., intermediate element), for example, Al, Zn, and Be. For these elements, whose role cannot be unequivocally assigned by different theories, such as, for example, Dietzel field strength,6 which considers V/a2, where V is the cation valence and a is the cation−oxygen bond distance, a more accurate characterization is required to clarify if, in the investigated compositional range, they act as network forming or as network modifier elements. Because of this, using a range of materials characterization techniques is essential when investigating complex silica-based glasses. In the present paper, we aim to unravel the structure of six complex aluminosilicate glasses with different zinc amounts, paying particular attention to the role of this element. These glasses have different applications, in particular, in some ceramic materials like glazes,3 where glass is the dominant phase (about Received: November 6, 2015 Revised: January 8, 2016 Published: February 5, 2016 2526

DOI: 10.1021/acs.jpcb.5b10886 J. Phys. Chem. B 2016, 120, 2526−2537

Article

The Journal of Physical Chemistry B

Si, Al, Na, Zn, and O, is designed to investigate the role of zinc when it is introduced in the bulk composition at the expense of network forming elements like silicon and, for these compositional range, aluminum.20 In this series, zinc content increases from A1 to A3. Series B, which also includes calcium, is designed to investigate the role of zinc when it is introduced into the bulk composition at the expense of a network modifier element like calcium. In this series, zinc content increases from B1 to B3. Samples have been prepared by first weighing out appropriate amounts of quartz SiO2 from Sigma-Aldrich (purum ≥ %95), alumina Al2O3 from Sigma Aldrich (99.7%), Na2CO3 from Analar (≥99%), ZnCO3 from Analar (99.5%), and CaCO3 from Analar (99%). Each raw mixture was then heated at 1350 °C, for 30 min, in a vertical furnace and then rapidly quenched to avoid crystallization. Density measurements have been performed with a Quantachrome micropychnometer. Full experimental compositions, expressed as molar fractions, and densities are shown in Table 1.

90 wt %), affecting in turn the technological properties of the whole material, due to the increased chemical durability and mechanical processing ability as zinc is introduced in the structure.7,8 Moreover, similar compositions have also recently found interest in the immobilization of nuclear waste.9 The nonspecific structural role of zinc in silica-based glasses is confirmed by the literature. Cassingham et al.,10 in 2011, revealed the presence of (ZnO4)6− tetrahedra participating in network formation by combining XANES and EXAFS zinc Kedge measurements on Na2O−CaO−ZnO−SiO2 glasses. A similar behavior has been observed by Lusvardi et al.11 using Raman and molecular dynamics simulations on a series of Na2O−CaO−ZnO−SiO2 glasses, where in particular zinc maintained its weak tetrahedral network forming role, independently from the sodium content. For similar composition, the effect of zinc introduction into soda-silicabased glasses resulted in (ZnO4)6− tetrahedra incorporation into the polymerized (SiO4)4− matrix, where in consequence there is a lowering of the tendency for accumulation of alkali species into large clusters, improving the glass durability.12 These network forming capabilities of zinc have been observed also in the presence of borosilicate glasses, showing a 4-fold coordination of zinc, which is invariant with composition.13 However, other authors observed a loss in network polymerization when zinc content increases, attributing to the element a network modifier role, and this is, for example, the case of Minser et al.14 and Goswami et al.15 A relevant aspect related to silica-based glasses including zinc has been highlighted by Rosenthal and Garofalini16 by means of EXAFS experiments, showing the presence of edge-sharing oxygen phenomena, instead of the typical corner-sharing, 3-fold-coordinated oxygen, which implies the presence of the so-called “tricluster”, and overcoordinated silicon. More recently, the study proposed by Xiang et al.17 on ZnO−SrO−CaO−Na2O−SiO2 bioglasses, combining high-energy X-ray diffraction and molecular dynamics simulations, discriminated high-coordinated zinc ions from the majority of 4-fold coordinated, finally considering zinc as an intermediate element in the investigated compositional range. In this paper, a structural model of two distinct series of complex aluminosilicate glasses with different zinc amounts has been built by combining neutron and X-ray total scattering experiments, whose data have been modeled with an empirical potential structure refinement approach18 and finally processed to give a comprehensive picture of each composition. The reliability of this kind of EPSR approach has already been shown by Bernasconi et al.,19 where a good structural model has been achieved for glasses belonging to the Si−Al−Ca−Na− O series; the present work represents a continuation of this study to somewhat more complex glass compositions. To help check the suitability of the method based on structure refinement of diffraction data to these increasingly complex materials, complementary Zn-edge extended X-ray absorption fine structure spectroscopy (EXAFS) measurements have been used to fix some additional constraints on the total scattering model and also to validate its output. The results have been compared with additional information derived from independent computational calculations and stoichiometric models.

Table 1. Chemical Experimental Composition, Expressed as Molar Fraction, and Density of the Six Different Investigated Samples sample

SiO2

Al2O3

ZnO

Na2O

CaO

density (g/ cm3)

A1 A2 A3 B1 B2 B3

0.7597 0.7197 0.6802 0.7196 0.7197 0.7198

0.0761 0.0722 0.0679 0.0722 0.0720 0.0720

0.0241 0.0680 0.1120 0.0102 0.0302 0.0500

0.1401 0.1401 0.1399 0.0597 0.0598 0.0597

0.000 0.000 0.000 0.1383 0.1183 0.0985

2.38 2.50 2.63 2.55 2.53 2.54

Zn K-Edge Extended Absorption Fine Structure Spectroscopy. Zn K-edge absorption spectroscopy measurements have been performed at the BM23 beamline at the European Synchrotron Radiation Facility.21 Each sample was powdered and mixed with BN, homogenized, and then pressed into 13 mm diameter pellets. After a preliminary Zn K-edge calibration using a Zn foil, the six samples have been measured in transmission geometry at room temperature. Additionally, standard samples including 4-fold-coordinated Zn (ZnO) and 6-fold-coordinated Zn (ZnCO3) were measured to discriminate the different Zn−O distances for the two different coordinations. Data have been measured up to a k wavevector of 14 Å−1, allowing one to get the total EXAFS signal χ, which corresponds to eq 1 J

χ (k ) =

S02

∑

Fe , i(k)Ni

i=1

e

kR i2

2 2

sin(2kR i + 2δl(k) + θi(k))e−2k σi

−2R i / λi(k)

(1)

S00

where is the average amplitude reduction factor, Fe,i is the scattering amplitude, Ni is the number of back-scattering atoms i at a distance Ri from the absorber, δl(k) is the absorbing atom phase shift, θi(k) is the scattering atom phase shift, 2σ2i reflects the structural disorder in the atomic positions captured in the Debye−Waller factor, and λi(k) is the finite elastic mean free path of photoelectrons. This χ(k) function is finally Fourier transformed to get the real space function χ(r) following eq 2

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EXPERIMENTAL PROCEDURE Samples. Two series of complex aluminosilicate glasses (three samples per series) have been prepared, approaching the composition of sanitary-glaze glasses.3 Series A, which includes

∞

χ (r ) = 2527

∫−∞ W (k)χ(k)kne2iπkR dk

(2)


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The Journal of Physical Chemistry B where W(k) is the applied Fourier transform window function and kn is a multiplicative factor to amplify signal at high k. For each sample, 3 scans have been performed to improve the signal/noise ratio. Data are shown in Figure 1.

was loaded into a kapton capillary (diameter of 1.5 mm), and then 20 images with a 20 s exposure time were collected using a CCD area detector (Frelon camera25) with a resultant Qmax of 28 Å−1. Dark current, empty instrument, and empty capillary measurements have also been performed. After azimuthal integration with Fit2D software, an incident angle correction has been applied26 and data finally normalized and corrected using GudrunX23 to get the X-ray total scattering structure function S(Q), which is the same as that given in eq 3 with neutron scattering length b replaced by Q-dependent X-ray scattering factors f. Neutron and X-ray total scattering functions S(Q)s are then Fourier transformed to the pair distribution function g(r) that represents distance correlations between atoms involved in the sample, as expressed by eq 4 G(r ) = 4πρ0 r(g (r ) − 1) ∞ 2 = Q [Sα , β(Q ) − 1]sin(Qr ) dQ π 0

∫

where G(r) is the total pair distribution function and ρ is the average number density of the material. A more detailed description of pair distribution function theory can be found in the study by Warren.27 All neutron and X-ray F(Q)s (where the quantity, e.g., F(Q) = Q[S(Q) − 1] is the reduced structure function28) and g(r)s, resulting from GudrunN and GudrunX data processing, are displayed in Figure 2. The effect of the introduction of Zn is clearly visible in the g(r) in the 1.9−2 Å region, where a shoulder appears in the right side of the first peak centered at 1.62 Å, as marked by black arrows. To process the diffraction data to a three-dimensional atomistic model, an empirical potential structure refinement approach has been used, where atomic interaction potentials based on a reference Lennard−Jones 12-6 plus Coulomb charge model are refined under the condition that the simulated data should converge to agreement with the experimental data. 18 The perturbation potential which ultimately drives the evolution of the atomistic model into agreement with the information contained within the experimental diffraction data is calculated from the difference between the experimental and the model structure factors at each iteration of the refinement process. At the end of the modeling process, a wide range of structural information can be accessed, such as coordination numbers, bond angles, interatomic distances and clustering phenomena. In this study we also investigated the glass network structure in terms of types of oxygen sharing and the Pn distribution (different from the more common Qn),29 which give information about the polymerization degree. For types of oxygen sharing we have paid particular attention to (i) NBO (i.e., not-bridging oxygen), defined as an oxygen that is shared only by a low-coordination polyhedron, (ii) BO (i.e., bridging oxygen), defined as an oxygen that is shared by two lowcoordination polyhedra, and (iii) TBO (i.e., tricluster), defined as an oxygen that is shared by three low-coordination polyhedra, where by “low-coordination polyhedron” we are referring to a polyhedron centered on a cation surrounded by 3 or 4 oxygens, while by “high-coordination polyhedron” we are referring to a polyhedron centered by a cation surrounded by 5 or more oxygens. As far as the notation Pn, n refers to the number of lowcoordinated polyhedra connected to a low-coordinated polyhedron. The value n ranges from 0 and 4 in a network

Figure 1. k2χ and FT (corresponding to χ(r) in eq 2) of samples belonging to series A and series B. In series A, black lines are referred to sample A1, red lines are referred to sample A2, and blue lines are referred to sample A3. In series B, black lines are referred to sample B1, red lines are referred to sample B2, and blue lines are referred to sample B3.

Data have been first processed with the Athena program for data reduction, normalization, and EXAFS data extraction and then with IFEFFIT for the fitting procedure.22 Total Scattering Experiment and Data Refinement. Neutron and X-ray total scattering measurements have been performed at the ISIS neutron spallation source and at the European Synchrotron Radiation Facility, respectively. Neutron data have been collected using the small angle neutron diffractometer for amorphous and liquid sample (SANDALS) over a wide range of neutron wavelengths (i.e., 0.05−4.95 Å), allowing measurement of the material’s structure factor to a Qmax of 50 Å−1. Each powdered sample was contained in flat null-scattering TiZr sample holders of 2 mm thickness. Data were collected for 9 h to obtain a good signal/ noise ratio. Additional measurements required for data processing were made for a vanadium reference sample, empty instrument, and empty containers over 6, 3, and 6 h, respectively. Finally, data have been normalized and corrected using the GudrunN program23 to obtain the neutron total scattering structure function S(Q), which is given in eq 3 S(Q ) =

∑∑ α

β

cαcβbαbβ ⟨b⟩2

(4)

Sα , β (3)

where cα and cβ are the atomic fractions of species α and β in the sample, respectively, bα and bβ are the Q-independent neutron scattering lengths of the species α and β, and Sα,β are the partial structure factors corresponding to the correlations between the pairs of atoms of type α and β. X-ray diffraction data have been collected at the ID11 Materials Science beamline using a wavelength of 0.15986 Å and a sample−detector distance of 92.104 mm, resulting from CeO2 standard calibration using Fit2D software.24 Each sample 2528


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Stoichiometric Calculations. The glass structural features can be calculated for each starting composition, based on simple stoichiometric assumptions. In this approach a structural role has to be attributed to each chemical species, as shown in the Zachariasen random network theory rules.5 In an example of a soda−silicate glass, assumptions are limited because the glass is characterized by silicon as the network forming element and sodium as the network modifier elements. It is then reasonably simple to establish structural parameters, like fraction of not-bridging oxygen, or Qn species (which depends on the number of oxygens and number of modifier species), simply taking into account the nominal chemical composition. If an additional atomic species is introduced the complexity of the structural characterizing parameters increases as further assumptions need to be made. If, for example, one considers a soda−lime−silicate glass, calcium is now also a network modifier species. Once again it is possible to establish the not-bridging oxygen fraction. See the work by Shelby29 for a detailed explanation. Things inevitably become more complicated still if further species are added that may act as network formers as well as network modifiers. For example, dealing with aluminum (part of the aluminum can have a network forming role) requires part of Na and Ca ions present to act as chargecompensating elements (and not as network modifier elements), as aluminum-centered tetrahedra have one additional negative ionic charge to be balanced with respect to silicon-centered tetrahedra (i.e., (AlO4)5− vs (SiO4)4−). When calculating not-bridging oxygen, this increased number of variables leads to a nonunique fraction of not-bridging oxygen and also to the need to evaluate the preference of a species for a charge-compensating role rather than for a network modifier one. In the case of both series investigated in this paper, most of the complexity is given by the presence of zinc, which is an intermediate element, i.e., it does not have a preference for its structural role. Moreover, the presence of aluminum, which acts as network forming element if the concentration of Al2O3 does not exceed that of Na2O, or other network modifier species30 generates a negative charge for each aluminum-centered tetrahedron that needs to be compensated. In series A, this charge compensation can be provided by sodium and (eventually) zinc while in series B by sodium, calcium, and (eventually) zinc. Because of this complexity stoichiometric calculations cannot provide a unique structural role for each element present in the starting composition, and as a result we have performed not-bridging oxygen stoichiometric calculations using two hypotheses: (i) all zinc is a network former, (ii) all zinc acts as a not-network-forming species (network modifier or charge-compensating element). Additionally, when using the latter hypothesis, there are two possibilities: (i) all zinc will be used as a charge compensator for aluminum-centered tetrahedra before using any sodium or (ii) all sodium will be used to charge compensate before using any zinc. In series B, the contribution of calcium will be considered in the same way of the sodium one, due to their similar field strength. Thus, NBO (stoichiometric not-bridging oxygen fraction) and CCPi (stoichiometric charge-compensating preference of the ith species) have been calculated by the equations

Figure 2. Neutron and X-ray F(Q)s and g(r)s of samples belonging to series A and series B. In series A, black lines are referred to sample A1, red lines are referred to sample A2, and blue lines are referred to sample A3. In series B, black lines are referred to sample B1, red lines are referred to sample B2, and blue lines are referred to sample B3.

including only NBO and BO, but if also triclusters are present, it also implies that a low-coordinated polyhedron can be connected to 5 or more low-coordinated polyhedra. Thus, for example, the fraction of P0 represents the fraction of lowcoordinated polyhedra which are connected to any lowcoordinated polyhedron (in a certain shell), the fraction of P1 represents the fraction of low-coordinated polyhedra which are connected to one low-coordinated polyhedron (in a certain shell), and so on. Furthermore, attention was also paid to the low-coordinated cation distances like Si−Si, Si−Al, and so on, which can provide information about the type of connection between polyhedra (i.e., corner or edge sharing). Finally, the preferences of highcoordinated cations for a charge compensation role rather than for a network modifier role was also explored as well as clustering phenomena. It is important to bear in mind that when determining all these parameters one has to define the atomic shell of interest, fixing some rmin and rmax values which for consistency of comparison have to be maintained the same across all samples.

NBO = 2529

∑i VM i i N0

(5) DOI: 10.1021/acs.jpcb.5b10886 J. Phys. Chem. B 2016, 120, 2526−2537

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CCPi =

VC i i ∑i Ci

Table 2. EXAFS Measurement Resultsa (6)

where Vi is the valence of the ith species, Mi is the number of network modifier atoms of the ith species, N0 is the total number of oxygen in the sample, and Ci is the total number of charge-compensating atoms of the ith species. GULP Simulations. Lattice energy calculation is another approach to obtain information about an ensemble of atoms.31 As previously mentioned, in glasses the main difficulties lie in the presence of intermediate elements whose role in the structure can vary as a function of the composition. Therefore, we investigated the role of such intermediate cations by distributing them differently in low-coordinated sites, which means assigning them a network forming role, and/or in highcoordinated sites, which means assigning them a chargecompensating/network modifier role, to evaluate lattice energy changes. To do this study, for each of the investigated samples, a grid was previously defined by distributing a Xi fraction of the ith intermediate species in the low-coordinated site and, consequently, a 1 − Xi fraction of the same ith species to the high-coordinated site, for a total of FI distributions, where F is the number of distribution fractions per intermediate species and I is the number of intermediate species involved in the grid. When creating the box of atoms, such fractions are added to the other low-coordinated (i.e., silicon) and high-coordinated (i.e., sodium and calcium) species, and for each distribution, one gets L and H, which are the number of low-coordinated and highcoordinated sites, respectively, in the box. As an example, for a sample including a, b, c, d, and e atoms of Si, Al, Zn, Na, and O, respectively, in order to generate the configuration with XAl and XZn both equal to 0.5, a resultant box made of (i) (a + 0.5b + 0.5c) low-coordinated sites, (ii) (0.5b + 0.5c + d) highcoordinated sites, and (iii) e oxygen atoms will be created. After some thousands of Monte Carlo cycles, for each of the FI distributions, chemical species are reassigned to L and H sites, following the grid, and finally lattice energy is calculated, after relaxation, with the GULP program.31 For each sample, the comparison between the different FI energies leads one to evaluate the most stable configuration for the investigated composition as a function of the adopted potentials.

sample

average Zn−O distance (Å)

σN (Å−2)

σX (Å−2)

A1 A2 A3 B1 B2 B3

1.957(6) 1.96(1) 1.95(2) 1.95(2) 1.950(6) 1.95(1)

0.004(1) 0.006(2) 0.007(3) 0.007(3) 0.006(1) 0.008(2)

0.004 (1) 0.006(3) 0.007(4) 0.005(4) 0.006(1) 0.007(2)

a For each sample, the average Zn−O distance is referred to a single peak fit of its FT, while σN and σX are the Debye Waller factors refined by the IFEFFIT program22 with a three Zn−O paths model using as input zinc coordination fractions coming from EPSR neutron and Xray results, respectively.

Figure 3. Imaginary part of FT of sample A3 (black line) compared with the imaginary part of FTs of samples ZnO and ZnCO3 (red and blue lines, respectively).

as those of Bernasconi et al,.19 while in the case of Ca and Na σLJ values were slightly changed from Bernasconi et al.19 and tuned using a separate series of 12 SiO2−Al2O3−CaO−Na2O glasses. Adopted Lennard−Jones 12-6 potential input parameters (i.e., the well-depth parameter ϵLJ and the range parameter σLJ) are summarized in Table 3; regarding the Coulomb part, integer ionic charges have been selected.

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Table 3. Adopted Lennard−Jones 12-6 Potential Parameters for the Six Different Chemical Speciesa

RESULTS AND DISCUSSION The starting point for modeling the complex composition of the materials was the Zn-edge EXAFS investigation. For all six investigated samples, a single peak fit of the first Zn−O shell has been performed in the 0.9−2 Å range, leading to a peak at about 1.95 Å, which corresponds to a 4-fold-coordinated zinc.32 This is in agreement with many previous studies.10,33,34 The second column in Table 2 summarizes the results for both series, while a graphical example is also displayed in Figure 3 where the comparison between the imaginary part of FT of sample A3 (black line) and the selected standards (i.e., blue line for ZnO and red line for ZnCO3) clearly shows that the average Zn−O distance matches with ZnO, which is the standard where zinc is coordinated by four oxygen atoms, at a distance of about 1.95 Å. As the next step considerable attention was then paid to neutron and X-ray total scattering modeling by using the empirical potential structure refinement approach, tuning Zn Lennard−Jones potential parameters in order to have a Zn−O distance in agreement with the results coming from EXAFS experiment. In the case of Al, Si, and O the values are the same

chemical species

ϵLJ (kJ/mol)

σLJ (Å)

Al Ca Na O Si Zn

1.2 2.35 2.15 3.69 0.76 1.47

0.8 0.8 0.8 0.65 0.8 0.8

ϵLJ (kJ/mol) is the well-depth parameter, while σLJ (Å) is the range parameter.

a

Separate neutron and X-ray refinements have been performed for each sample in order to avoid results that are an average between the neutron and the X-ray data; the Q range was from 0 to 22 Å−1. In agreement with the chemical composition of Table 1, for each sample a box of 2700 atoms has been created, with an atomic density, expressed as atoms/ Å3 of 0.070092, 0.071536, and 0.072917 for samples A1, A2, and A3, respectively, and of 0.07305, 0.07199, and 0.07170 for samples B1, B2, and B3, respectively. The corresponding cubic 2530


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widespread distribution (between 5.5 and 6.5 coordination number) for Na and Ca. Figure 6 is an example (for sample A3) of the neutron and Xray cation−oxygen coordination number distributions observed, while Table 4 summarizes bond distances and coordination numbers of all investigated samples. Oxygen− cation−oxygen bond angle distributions have been also evaluated in Figure 7, showing for Si and Al values that are centered on the typical tetrahedral angle (i.e., 109.5 °C), with sharper distributions for Si, suggesting that (SiO4)4− tetrahedra are less distorted than (AlO4)5− tetrahedra. In the case of Zn, differently from Lusvardi et al.,33 bond angle distributions are more dispersed, due to the presence of even 3-fold-, 5-fold-, and 6-fold-coordinated zinc. A similar O−Zn−O distribution has been observed in Xiang et al.17 Finally, in the case of Na and Ca, bond angles distributions are much broader, reflecting the high disorder associated to these cations. According to the random network theory, low-coordinated cations (i.e., 3-fold and 4-fold coordinated) can be considered as network forming species while high-coordinated cations (i.e., 5-fold, 6-fold) can be considered either as network modifier cations or as charge compensating, because ionic charge deficits are present in (AlO4)5− and (ZnO4)6− tetrahedra. Because of this, for each sample, the high-coordinated fraction of Zn (i.e., Zn[5] and Zn[6]) has been separated from the low-coordinated fraction (i.e., Zn[3] and Zn[4]) and taken into account when calculating the structural parameters like types of oxygen sharing and Pn distribution. The results are summarized in Table 5. Zn[5] and Zn[6] fractions belonging to series A range between 0.05 and 0.1, with no trend when moving from sample A1 to sample A3, while Zn[5] and Zn[6] fractions belonging to series B are higher, ranging between 0.15 and 0.25, again with no trend when moving from sample B1 to sample B3. Although most of zinc is 4-coordinated, an unequivocal structural arrangement has not emerged from the models. In fact, when comparing, for example, the experimental notbridging oxygen fraction from Table 5 with the stoichiometric calculation (using eq 5, see section Stoichiometric Calculation for details), one can observe differences. For series A (upper part in Figure 8) zinc addition at the expense of network forming species like silicon and aluminum does not affect the NBO fraction, which stays fixed at about 0.09 value (for both neutron and X-ray models) rather than (i) falling to zero if all zinc is assigned to a network forming role or (ii) increasing up to more than 0.2 if all zinc is assigned to a network modifier/ charge-compensating role. For series B (lower part in Figure 8), zinc addition at the expense of a network modifier like calcium decreases the fraction of NBO from about 0.16 to 0.10 rather than (i) fall to about 0.03 if all zinc is assigned to network forming role or (ii) stay fixed at about 0.15 if all zinc is assigned to network modifier/charge-compensating role. Although one should expect a trend similar to the case in which all zinc is a network forming element (i.e., red squares in Figure 8), due to its dominant 4-fold coordination in both series, these discrepancies can be addressed to the small fraction of high-coordinated zinc (i.e., Zn[5] and Zn[6]), which range from 0.05 to 0.1 in series A and from 0.15 to 0.25 in series B and also, as displayed in Table 5, by relevant fractions of triple bonded oxygen (i.e., triclusters). Triclusters, which are a typical way to balance negative ionic charge in network structural units,35 are related to negative ionic charge in (ZnO4)6− and (AlO4)5−. As a consequence, the observed

length size, expressed in Angstroms, was 33.77, 33.54, 33.33 for samples A1, A2 and A3, respectively, and 33.32, 33.48, and 33.53 for samples B1, B2, and B3, respectively. Figure 4 shows

Figure 4. F(Q) and g(r) fits of neutron (top) and X-ray (bottom) data in sample A3. Continuous lines represent the data, dotted lines with black squares represent the empirical potential structure refinement fit, and dashed lines represent the difference between the data and the fit.

the F(Q) and g(r) fits achieved for sample A3 in neutron and X-ray refinements. This sample was selected because it includes the highest zinc content, enabling one to evaluate the goodness of the fit, especially in the g(r), where Zn contribution is most evident in the sample. Very good F(Q) and g(r) fits have been achieved. At this point, when extracting the structural parameters of each sample, the first coordination shell of each cation was considered. To do this we looked at the simulated partial cation−oxygen pair distribution functions (Figure 5 is an example), selecting proper r ranges for the different cation− oxygen pairs. The selected ranges were 1−2.5 Å for Si−O, Al− O, and Zn−O pairs and 1−3.3 Å for Na−O and Ca−O pairs. Cation−oxygen coordination numbers have been extracted, showing a dominant 4-fold coordination for Si and Al in all samples, an average almost 4-fold coordination for Zn, and a

Figure 5. Total scattering model partial cation−oxygen pair distribution functions for sample A3 . Continuous lines are referred to neutron pairs, while dashed lines are referred to X-ray pairs. 2531


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Figure 6. Cation−oxygen coordination distributions in sample A3 using neutron (black bar) and X-ray (gray bar) data.

Table 4. Summary of Coordination Numbers and Average Bond Distances Resulting from EPSR Refinements Using Neutron and X-ray Data neutron sample

Si−O

A1 A2 A3 B1 B2 B3

3.99 3.96 3.98 3.99 3.98 3.99

A1 A2 A3 B1 B2 B3

1.59 1.59 1.59 1.59 1.59 1.59

sample

Si−O

A1 A2 A3 B1 B2 B3

4.01 3.97 3.96 4.03 4.03 4.05

A1 A2 A3 B1 B2 B3

1.6 1.59 1.59 1.59 1.59 1.59

Al−O

Zn−O

coordination number 3.94 3.87 3.94 3.86 3.94 3.93 3.95 3.97 3.94 4.03 3.96 3.90 average bond distance (Å) 1.76 1.94 1.76 1.93 1.76 1.94 1.76 1.94 1.76 1.93 1.76 1.94 X-ray Al−O

Zn−O

coordination number 3.99 3.78 3.95 3.89 3.96 3.85 3.98 4.00 3.98 4.05 4.01 4.11 average bond distance (Å) 1.77 1.94 1.76 1.94 1.77 1.94 1.75 1.94 1.76 1.95 1.76 1.94

Na−O

Ca−O

5.80 5.95 6.04 6.55 6.46 6.31

n.p. n.p. n.p. 6.21 6.11 6.16

2.37 2.37 2.41 2.41 2.43 2.45

n.p. n.p. n.p. 2.36 2.35 2.36

Na−O

Ca−O

Figure 7. Oxygen−cation−oxygen bond angle distributions in sample A3 using neutron (continuous lines) and X-ray (dashed lines) data.

Table 5. Network Parameters Obtained from EPSR Refinements Performed with Neutron and X-raya type of oxygen sharing

5.82 6.02 6.38 6.37 6.37 6.24

n.p. n.p. n.p. 6.06 6.08 6.02

2.38 2.38 2.38 2.42 2.43 2.44

n.p. n.p. n.p. 2.36 2.34 2.35

P5 + P6 distribution

[5]

sample

tricluster increasing trends from sample A1 to A3 and from sample B1 to B3 are consistent with composition: if the added zinc is in 4-fold coordination, as it is mainly resulting from pair distribution modeling, the ratio between 4-fold-coordinated polyhedra and the total number of available oxygen increases and triclustering is the answer of the structure to that. A relevant presence of triclusters has already been highlighted in previous zinc-containing silica-based glasses.16,17 Moreover, the presence of triclusters cannot be predicted by a stoichiometric model because in all compositions, except for sample A3, sodium (and calcium) content are enough to stoichiometrically compensate (ZnO4)6− and (AlO4)5− ionic deficits. Complementary information is also provided by Pn distributions using a cutoff value of 3.6 Å. This cutoff value has been considered as the limit of the first coordination shell of low-coordinated

Zn and Zn[6]

NBO

A1 A2 A3 B1 B2 B3

0.05 0.1 0.087 0.22 0.15 0.17

0.098 0.1 0.088 0.17 0.149 0.113

A1 A2 A3 B1 B2 B3

0.05 0.08 0.09 0.25 0.19 0.2

0.104 0.096 0.097 0.154 0.142 0.111

BO neutron 0.861 0.844 0.828 0.803 0.819 0.834 X-ray 0.842 0.849 0.823 0.819 0.814 0.826

TBO

Si

Al

Zn

0.04 0.056 0.084 0.027 0.032 0.051

0.09 0.09 0.15 0.06 0.06 0.09

0.17 0.23 0.31 0.23 0.19 0.29

0.4 0.35 0.42 0.45 0.46 0.35

0.053 0.056 0.080 0.028 0.045 0.063

0.09 0.08 0.12 0.06 0.08 0.13

0.21 0.26 0.37 0.19 0.2 0.32

0.55 0.36 0.38 0.37 0.38 0.45

a Both highly coordinated zincs (i.e., Zn[5] and Zn[6]), type of oxygen sharing, and Pn distributions are expressed as fraction.

cations. Attention was paid to the P5 and P6 fraction, looking at the chemical nature of the low-coordinated cations in the lowcoordinated polyhedra, which allows one to evaluate the species which are mainly involved in triclustering phenomena. In series A, moving from sample A1 to sample A3, the (P5 + P6) fraction related to Si increases from 0.08 to 0.12, (P5 + P6) fraction related to Al is bigger and increases from 0.17 to 0.37, and the (P5 + P6) fraction related to Zn is constant, with values always bigger than 0.35. In series B, moving from sample B1 to sample B3, similar trends are observed: (P5 + P6) fraction related to Si 2532


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modeling results with the theoretical corner-sharing and edgesharing distances, assuming a tetrahedron as a principal polyhedral unit and assuming that neighboring polyhedra are aligned (in the case of corner sharing) and with inverted apex. Deviations from these conditions will provide smaller distances in corner-sharing geometry than in edge-sharing geometry. These theoretical distances have been calculated using Si−O, Al−O, and Zn−O distances of 1.59, 1.76, and 1.94 Å, respectively, in agreement with partial pair distribution functions resulting from EPSR modeling (see Table 4). It was observed that the average low-coordinated cation−cation distances coming from total scattering models are compatible with the theoretical corner-sharing distances, and also, when looking at the different partials, no distances attributable to edge-sharing phenomena have been observed. The only exception is given by the left tail in the Zn−Zn pair for sample A3 (X-ray model), which is close to the 2.24 Å value, suggesting the presence of a minority of edge-sharing related to Zn lowcoordinated polyhedra, which has been quantified to be 0.4%. Figure 9 is an example of this, related to sample A3 and B3, where the presence of edge-sharing phenomena due to zinc addition, if any, should be more evident than in the other samples. The full results are shown in Table 7. Clustering phenomena have been also taken into account, because some technical properties of the glass may be influenced by inhomogeneity in cationic distributions, especially in the case of alkali/alkaline earth species and zinc, whose clustering may generate regions more prone to dissolution phenomena and, in turn, cracking. To evaluate the presence of clustering trends in both series, Na clusters and Zn clusters have been considered using a threshold value of 4.5 Å, which means that, for example, if two Na atoms are closer to each other than this value they are considered as belonging to the same clusters. Using this criterium, the fraction of Na atoms included into clusters bigger than 100 atoms (defined as ϕNa) and the fraction of Zn atoms included into clusters made of at least 2 atoms (defined as ϕZn) have been considered. In the case of series B, where also calcium is present, Ca atoms have been considered as Na atoms due to their similar dissolution proclivity; therefore the results are expressed as ϕNa & Ca. Figure

Figure 8. Not-bridging oxygen evolution in the two investigated series as a function of the different ZnO molar content (series A and series B). Black and white squares represent the NBO fraction resulting from neutron and X-ray total scattering modeling, respectively, while blue and red squares represent the stoichiometric NBO fractions when considering all zinc as network modifier and network forming element, respectively.

increases from 0.06 to 0.13, (P5 + P6) fraction related to Al is bigger and increases from 0.19 to 0.32, and (P5 + P6) fraction related to Zn is again constant, with values always bigger than 0.36. The last three columns in Table 5 provide all the (P5 + P6) results. (P5 + P6) fraction results are a confirmation that triclustering is mainly associated to Zn-centered low-coordinated polyhedra rather than Al/Si-centered polyhedra. By looking at Pn distributions, it is also clear that zinccentered low-coordinated polyhedra are well connected into the network. In fact, the fraction of P0 was lower than 0.01 in all investigated samples, while the fraction of Pn with n ≥ 2 is dominating, as summarized in Table 6. Moreover, it was observed that Zn−O−Al bonds are favored with respect to Zn−O−Si bonds, although the number of silicon atoms is larger. The type of connection occurring between coordination polyhedra has also been evaluated, comparing the average lowcoordinated cation−cation distances coming from EPSR

Table 6. Full Pn Distributions Related to Low-Coordinated Zinc Atoms and Their Relative Connectivity for Al- or Si-Centered Polyhedraa Pn distribution sample

P0

P1

P2

P3

connectivity preference P4

P5

P6

Si

Al

0.32 0.42 0.25 0.34 0.31 0.37

0.33 0.25 0.24 0.45 0.31 0.26

0.06 0.11 0.19 0.09 0.15 0.09

0.13 0.11 0.12 0.25 0.19 0.12

0.87 0.89 0.88 0.75 0.81 0.88

0.25 0.36 0.32 0.13 0.16 0.17

0.31 0.25 0.23 0.12 0.20 0.36

0.14 0.10 0.14 0.25 0.18 0.1

0.14 0.16 0.14 0.18 0.16 0.15

0.86 0.84 0.86 0.82 0.84 0.85

neutron A1 A2 A3 B1 B2 B3

0 0 0 0 0 0

0.04 0.02 0.02 0 0.04 0.02

0.11 0.04 0.13 0.01 0.08 0.09

0.15 0.18 0.18 0.10 0.12 0.16

A1 A2 A3 B1 B2 B3

0 0 0.01 0 0 0.01

0.04 0.04 0.03 0.01 0.08 0.08

0.02 0.09 0.12 0.24 0.21 0.05

0.10 0.16 0.14 0.26 0.17 0.24

X-ray

a

Both Pn distributions and connectivity preferences are expressed as fraction. 2533


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Figure 9. Total scattering model partial cation−cation pair distribution functions related to sample A3 (left) and sample B3 (right). Neutron curves are a solid line, while X-ray curves are dashed lines. Black is related to Al−Al pair, red to Al−Si pair, green to Al−Zn pair, blue to Si−Si pair, gray to Si−Zn pair, and orange to Zn−Zn pair. Large black vertical line at 2.24 Å indicates the Zn−Zn theoretical edge-sharing distance.

Figure 10. Cluster fraction evolution in series A and series B, expressed as ϕNa (i.e., fractions of Na clusters with the number of Na atoms per cluster bigger than 100), ϕZn (i.e., fractions of Zn clusters with the number of Zn atoms per cluster bigger than 1), and ϕNa & Ca (i.e., fractions of Na and Ca clusters with the number of Na or Ca atoms per cluster bigger than 100). Neutron data results are in black, while X-ray data results are in red.

Table 7. Summary of Theoretical and Refined LowCoordinated Polyhedra Distances for All Possible Pairs: Neutron and X-ray Results low-coordinated polyhedra distances Al− Al

theoretical corner sharing theoretical edge sharing A1 A2 A3 B1 B2 B3

3.24 3.24 3.22 3.22 3.17 3.18

A1 A2 A3 B1 B2 B3

3.29 3.31 3.22 3.21 3.18 3.21

sample

Si−Si

Zn− Zn

Al−Si

Al− Zn

Si− Zn

3.52

3.16

3.88

3.34

3.7

3.52

2.03

1.83 neutron 3.18 3.17 3.17 3.17 3.16 3.17 X-ray 3.18 3.15 3.16 3.15 3.15 3.16

2.24

1.93

2.14

2.03

n.p. 3.05 3.07 n.p. 2.96 3.02

3.21 3.22 3.22 3.21 3.2 3.21

3.29 3.48 3.57 3.37 3.33 3.46

3.52 3.54 3.54 3.49 3.59 3.5

n.p. 3.16 3.02 n.p. 2.95 2.97

3.24 3.21 3.21 3.19 3.18 3.22

3.43 3.5 3.56 3.48 3.54 3.34

3.66 3.52 3.44 3.38 3.54 3.58

70% of it that charge compensates the ionic charge in ZnO46− and AlO45−. This preference can be addressed to the smaller valence of sodium rather than calcium and zinc. In the case of zinc and calcium, it is harder to discriminate the preference for a charge-compensating role rather than for network modifier one. All of the charge-compensating preference results are displayed in Table 8. Table 8. Charge-Compensating Preferences Resulting from EPSR Refinements Performed with Neutron and X-ray Expressed as Percentage neutron

10 summarizes the clustering results which have been calculated using rmin and rmax values of 1 and 4.5 Å, respectively. The results of clustering phenomena highlighted a prominent decrease of clusters formed by more than 100 Na and Na & Ca species if Zn is introduced in the structure, favoring a more even distribution of these heterogeneities, as predicted by Stechert et al.12 with molecular dynamics simulations. On the other hand, looking at Figure 10 (right side) zinc clustering is promoted when moving from sample A1 to A3 and from B1 to B3, but over 95% of Zn are concentrated in clusters smaller than or equals to 7 members for series A and smaller than or equal to 3 for series B, suggesting a quite homogeneous distribution of zinc in the structure. When looking at high-coordinated cations preferences (i.e., Zn[5−6], Na, and, when present, Ca) for charge-compensating or network modifier role, a clear preference emerges for Na, with

sample

Na

Zn

A1 A2 A3 B1 B2 B3

73.78 75.44 79.48 78.05 72.22 73.01

20.11 21.43 41.67 66.23 31.32 57.14

X-ray Ca

Na

Zn

Ca

62.90 50.10 60.65

69.25 74.55 76.90 69.34 71.78 78.69

13.76 54.94 60.03 51.14 58.33 44.70

51.16 57.53 63.76

Again, if one considers for each sample how the negative ionic charge in the structural polyhedral units is balanced by Na, Zn[5], Zn[6], and, when present, Ca, the distribution is displayed in Figure 11 and is influenced by the composition. In fact, for series A, sodium contributing to balance the negative ionic charge is dominant (blue area), but the zinc chargecompensating species increases as zinc content increases (red area). A similar trend is also present in series B, where more charge-compensating zinc species have been observed as zinc is introduced in the glass structure, at the expense of calcium (black area). When calculating the stoichiometric preferences by eq 6, if charge to be balanced is preferentially balanced by zinc and after, if necessary, by sodium and, if present, by calcium, the red areas in Figure 11 would be extended from the top up to the white square trends, indicating a behavior that is 2534


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Figure 12. Three paths fit for sample A3 using as input the zinc coordination fraction coming from neutron (color) total scattering modeling. Fit has been performed in the 0.9−2 Å range (Zn−O first shell), as shown by the two vertical lines.

in the future, possibly with low-temperature measurements to minimize the thermal disorder effect on the EXAFS signal. The last part of this section is dedicated to the results coming out from GULP simulations, evaluating the role of zinc and aluminum, following criteria expressed in section GULP Simulations, with an F value equal to 5, for a total of 25 explored distributions. Moreover, GULP simulations run with two distinct kinds of interactions: a two body short-range Buckingham potential31 and a Lennard−Jones 12-6 potential plus effective Coulomb charge potential.18 Table 9 summarizes the adopted Bucking-

Figure 11. Charge-compensating preferences of zinc (considering Zn[5] and Zn[6]), sodium, and calcium in series A (top) and series B (bottom). Colored area referred to total scattering modeling results averaging neutron and X-ray results. Blue, red, and black fields are referred to sodium, zinc, and calcium, respectively, while white squares represent stoichiometric preferences assuming that charge to be compensated is preferentially balanced by zinc.

Table 9. List of Buckingham Potential Parameters Adopted for Lattice Energy Calculations type of potential 36

Al core O core Ca core O core36 Si core O core36 O core O core36 Na core Na core36 Zn core O core36

dissimilar from EPSR modeling results. Therefore, zinc is playing a low charge-compensating role. The implications of such variety of structural features are important when comprehending some technological properties of glasses. As an example, NBO fractions that provide information related to polymerization degree of the network and, in turn, to properties like the glass transition temperature Tg suggest a similar behavior for the three sample of series A, while in the case of series B, an increased Tg can be expected when moving from sample B1 to sample B3. Furthermore, in consideration of the evolution of Na and Na/Ca cluster size, a better chemical durability of sample A3 in series A and of sample B3 in series B is expected. The suitability of this EPSR modeling approach is also evident when performing a three-path fit model for Zn−O distances (one for 3-fold-, one for 4-fold-, and one for 5- and 6fold-coordinated Zn) of the EXAFS data using the IFEFFIT software. For doing that the Zn[3], Zn[4], and Zn[5−6] fractions resulting from EPSR results have been kept fixed, while the Debye−Waller σ term was refined. The results are summarized in the third and fourth columns of Table 2, while Figure 12 displays the graphical fit obtained in the case of sample A3. The results clearly show that the EPSR models are compatible with the EXAFS data, underlining, in both investigated series, an increase in static disorder if zinc content increases (see σN and σX in Table 2). This effect will be clarified

A (eV)

ρ

1142.678 1227.7 983.557 22 764.000 1788.189 700.3

0.29912 0.3372 0.32052 0.14900 0.1586 0.3372

ham core−shell potentials, while Lennard−Jones 12-6 potential parameters are the same as those adopted in EPSR modeling, which are displayed in Table 3. In all samples, calculations based on Buckingham potentials reached the lowest lattice energy values when all Al was assigned to low-coordinated sites and all Zn was assigned to high-coordinated sites, attributing to these two intermediate elements a network forming role and a network modifier/ charge-compensating role, respectively. On the other side, calculation based on Lennard−Jones 12-6 potential plus effective Coulomb charge provided lowest lattice energy values when all Al and Zn were assigned to low-coordinated sites, in agreement with experimental results. Additionally, for each sample, F(Q) and g(r) of the resulting Buckingham and Lennard−Jones 12-6 potentials ensemble of atoms have been compared with the neutron and X-ray total scattering data. Figure 13 is an example related to sample A3: it clearly shows a reasonable fit in the case of the Lennard−Jones 12-6 potential model, while in the case of the Buckingham model the fit is not satisfactory, exhibiting discrepancies in the Zn−O distance region, as indicated by the arrow. 2535


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12-6 and Buckingham potentials. With the former, a reasonable fit is obtained (see blue g(r) in Figure 13), but this was possible only after experimental evidence obtained from EXAFS spectroscopy, which enabled us to properly tune the zinc potentials. Moreover, a more accurate structural model is obtained only after introduction of an empirical potential to the reference Lennard−Jones 12-6 potential, as highlighted by EPSR results. With the latter, a problem in the g(r) fit is evident, due to the Zn−O distance peak located at 2.15 Å instead of the correct values of 1.95 Å (see red g(r) in Figure 13), resulting from EXAFS investigation, leading also to much higher NBO fractions when comparing the results from Tables 5 and 10. This evidence underlines the necessity of tuning zinc potential to improve the results, instead of using the reference values.36

■

CONCLUSIONS The structure of two series of complex aluminosilicate glasses with different zinc additions has been investigated combining neutron and X-ray total scattering data with Zn-edge extended absorption fine structure spectroscopy. EXAFS measurements have proved to be important to unravel the Zn−O distance in all samples, acting as a constraint for the emprical potential structure refinement. An evident network forming role was assigned to silicon and aluminum, as shown by coordination numbers and bond angles, and an evident charge-compensating/network modifier role was assigned to sodium and, if present, calcium. Zinc, which is a well-known intermediate element, is mainly in 4-fold coordination, but also some 3-fold-, 5-fold-, and 6-fold-coordinated species were observed. Therefore, a network forming role was assigned to zinc atoms in 3- or 4-fold coordination, and a charge-compensating/network modifier role was assigned to zinc atoms in 5- or 6-fold coordination. In series A, zinc occurrence at the expense of silicon and aluminum does not modify the polymerization degree, without increasing the NBO fraction but generating a significant fraction of triclusters, which are a way to better compensate for the negative charge of ZnO46− polyhedra. In series B, zinc occurrence at the expense of calcium improves the connectivity as shown by the lowering in NBO fraction. Fourfold- and three-fold-coordinated zinc atoms were also well connected with aluminum and silicon species into the cornersharing network. Good agreement in the results was observed comparing the neutron and X-ray structural parameters. The consistency of the EPSR modeling is enhanced by EXAFS data fit.

Figure 13. F(Q) and g(r) fit of neutron (top) and X-ray (bottom) data (black line) in sample A3 using a Buckingham potential (red line) and Lennard−Jones 12-6 potential (blue line). Red dashed lines represent the difference between the data and the Buckingham fit; blue dashed lines represent the difference between the data and the Lennard−Jones 12-6 potential fit.

Moreover, as for the total scattering modeling results, the type of oxygen-sharing and high-coordinated cations preferences results have been extracted. After graphical inspection of partial site−site g(r)s, in the case of the Lennard−Jones 12-6 potential the selected cutoff values were exactly the same (i.e., 1−2.5 Å for Si−O, Al−O, and Zn−O and 1−3.3 Å for Na−O and Ca−O), while in the case of the Buckingham potential it was necessary to extend the rmax of Zn−O to 2.9 Å, due to the fact that this site−site distribution has its peak at about 2.15 Å, even bigger than typical octahedral Zn−O distances.32 The results are summarized in Table 10. The importance of the experimental approach for investigating these complex aluminosilicate glasses clearly emerges by looking at the GULP simulation results using Lennard−Jones Table 10. Type of Oxygen Sharing and High-Coordinated Preferences Resulting from GULP Simulations Performed with Buckingham and Lennard−Jones 12-6 Potentialsa polymerization sample

NBO

A1 A2 A3 B1 B2 B3

16.04 15.71 15.53 21.13 19.31 17.86

A1 A2 A3 B1 B2 B3

12.47 10.72 8.74 19.10 16.12 13.52

BO

charge-compensating preference TBO

Na

Buckingham potential 82.19 1.77 62.65 80.55 3.74 62.99 79.69 4.78 65.80 78.38 0.49 52.22 79.35 1.34 56.38 79.34 2.80 54.35 Lennard−Jones 12-6 potential 85.23 2.30 70.06 85.23 4.05 72.36 84.34 6.92 77.81 78.91 1.99 67.77 82.00 1.88 67.41 82.99 3.48 74.01

Zn

Ca

74.07 55.71 61.87 42.31 56.25 57.69

53.07 52.19 55.69

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +33-476882116 Notes

40.11 60.23 40.65 5.43 4.76 32.99

The authors declare no competing financial interest. § The late Maurizio Bernasconi was a consultant that contributed actively to this work.

■

48.86 51.96 53.91

ACKNOWLEDGMENTS We thank the Earth Science Department of the University of Pavia for the use of their Carbolite tube furnace in sample preparation, Dr Silvia Imberti for being the local contact at SANDALS beamline, and Professor Marcello Merli (University of Palermo) for help with GULP simulations.

a

Note that for high-coordinated preferences, numbers are expressed as fraction of the cationic species that has a charge-compensating role preference. Network modifier role preference can be directly calculated as the complementary percentage. 2536


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