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Unraveling the nano-structure of a glassy CaO-FeO-SiO2 slag by molecular dynamics simulations
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Unraveling the nano-structure of a glassy CaO-FeO-SiO2slag by molecular dynamics simulations ⁎
Christina Siakatia, , Roberto Macchieraldob, Barbara Kirchnerb, Frederik Tielensc, Arne Peysa, David Sevenoa, Yiannis Pontikesa a
KU Leuven Department of Materials Engineering, Kasteelpark Arenberg 44, Leuven, 3001, Belgium Mulliken Center for Theoretical Chemistry, University of Bonn, Beringstr. 4+6, Bonn, D-53115, Germany c General Chemistry (ALGC – Materials Modeling Group), Vrije Universiteit Brussel (Free University Brussels, VUB), Pleinlaan 2, Brussels, 1050, Belgium b
A R T I C LE I N FO
A B S T R A C T
Keywords: Non-ferrous metallurgy slags Molecular dynamics Pair distribution function Ferrous silicate glass Nano-structure
Non-ferrous metallurgy slags are gaining significant interest as a resource in the production of alternative lowenergy cementitious materials. Their atomistic structures, however, are still not fully understood due to their glassy nature. In the work presented herein, a comprehensive description of the nano-structure of a CaO-FeOSiO2 slag was obtained by using molecular dynamic simulations in conjunction with previously obtained experimental data from X-ray and neutron pair distribution function studies. Iron was predominately 4- and 5-fold coordinated with oxygen, forming polyhedra in tetrahedral and pyramidal/triangular bipyramidal configuration. The [FeOx] polyhedra were corner-shared to the silica tetrahedra, while the higher coordinated fractions (x = 5 or 6) seemed to prefer to be next to each other, sharing edges. Ca was mostly surrounded by 6 or 7 oxygens in polyhedra that are predominantly edge-sharing with other units. The obtained results fit the experimental data well and as such provide an accurate and realistic picture of the iron-rich slag structure.
1. Introduction The substantial CO2 emissions associated with the production of ordinary Portland cement (OPC) led to the need for partial or total clinker substitution with industrial by-products and other resources that possess a lower carbon footprint [1]. One such option is slags, an industrial by-product originating from ferrous and non-ferrous pyrometallurgy [1]. Slags have been used in blended cements for decades and are standardized as CEM III (EN197) or type IS (ASTM C595) cements. In new binders, slags can be used in higher volumes, for instance, when used as precursor materials in the production of inorganic polymers (IPs) and alkali activated materials (AAM); those are types of alternative cementitious materials that display similar or even better performance than OPC [2, 3]. The final properties are largely controlled by the intrinsic characteristics of the slags (e.g. chemical composition, mineralogy and nano-structure) [4–8], which are determined by the production process [9, 10]. Consequently, an accurate knowledge of the nano-structure of the slags is of paramount importance as this information can be linked to the reactivity of the slag during alkali activation and the final performance of the resulting IPs. Understanding the slag structure and its relation to reactivity would allow the design of optimal slags, created to fulfill the needs of the alkali-activated ⁎
materials. This knowledge has a crucial strategic importance for metallurgical companies wanting to optimize the quality (i.e. value) of their slags, with a substantial and direct positive impact to the environment and society. To exhibit sufficient reactivity for the synthesis of inorganic polymers, the slag from the non-ferrous metallurgy has to be glassy. The challenge of characterizing the nano-structure of slags is also mainly being discussed in the context of their glassy nature [11]. The complexity becomes even greater for the non-ferrous metallurgy slags in particular, where, due to the presence of Fe as major component, fundamental questions remain. In pure silica glass, the atomic network consists of silica tetrahedra ([SiO4]) that are interconnected through their corners to four other [SiO4] by bridging oxygen (BO) atoms [12]. The introduction of network modifier cations affects the degree of polymerization. The modifier cation disrupts the connectivity of the silica network, forming non-bridging oxygen (NBO) atoms. Thus, the depolymerized silica network has different proportions of BOs and NBOs [12]. The silica tetrahedra are arranged in two dimensional rings, surrounding the network modifying cations [13, 14]. The size of these rings is an alternative way to express the connectivity of the glass network. Multicomponent glasses consist of a variety of former and modifier
Corresponding author. E-mail address: [email protected] (C. Siakati).
https://doi.org/10.1016/j.jnoncrysol.2019.119771 Received 26 August 2019; Received in revised form 12 October 2019; Accepted 8 November 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Christina Siakati, et al., Journal of Non-Crystalline Solids, https://doi.org/10.1016/j.jnoncrysol.2019.119771
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direct validation with the MD simulation results. A short description of the experimental procedure outlined in this reference is presented in the supplementary material to provide background details and some of the instrument parameters that were used for the generation of the simulated X-ray and neutron pair distribution functions (PDFs) (supplementary material, sections S.1 and S.2). In this work, the two body Born-Mayer-Huggins (BMH) potential function was selected as it has been successfully used to study oxide systems [23, 24, 27, 31]. It consists of long-range Coulomb interactions, short-range repulsion interactions and Van der Waals forces. The interatomic force field reads:
cations. For non-ferrous metallurgy slags in particular, the high proportion of iron cations affects significantly the glass network, as iron can be both former and modifier due to its multivalence nature and coordination. Apart from the possibility of having different valence and coordination states in different samples, a variety of species occurs within one glass, increasing the complexity of the experimental analysis. Fe3+ is observed to be mainly in 4-fold coordination with oxygen having the role of network former if sufficient charge balancing elements are present [12]. The presence of small amounts of higher coordination numbered Fe3+ has also been suggested, acting as network modifier [15–18]. In this instance, it is mostly assumed to be in 5-fold coordination [15, 16], however the presence of a minor portion of 6fold [17] cannot be decisively rebutted. In any case, it has been found that the average coordination number of Fe3+ is lower than that of Fe2+ when they coexist in one glass [19]. For Fe2+, a range of 4- to 6fold coordination with oxygen has been suggested for various compositions and it is usually considered as a network modifier [12, 18, 20]. The specific coordination number, or distribution of coordination numbers, is dependent on the presence of other elements. Recent studies on synthetic (CaO)-FeOx-SiO2 slags by means of X-ray absorption near-edge structure (XANES) spectroscopy showed that the presence of Ca and increased Si contents leads to lower coordination numbers for Fe [21]. Further analysis on the same slags using X-ray and neutron pair distribution function and Mössbauer spectroscopy revealed that Fe is mainly present as Fe2+in 4- and 5-fold coordination with minor amount of Fe3+ in 5-fold coordination [11, 22]. The experimental uncertainties together with the need to acquire detailed knowledge of the nano-structure of the non-ferrous metallurgy slags led to the use of atomistic scale simulations in conjunction with experimental data. Among several simulation techniques, classical molecular dynamics (MD) simulations have been widely applied to explore the structure of glassy materials and melts, providing quantitatively accurate results [23–29]. Previous studies with MD simulations revealed information concerning the viscosity behavior of slags and how this is affected by the depolymerization of the silicate network [25]. Similarly, structural characteristics such as pair distribution function and oxygen bond types as well as thermodynamic properties have also been calculated by MD simulations with great success [27, 30, 31]. However, many of these studies focused on the molten state of the material at high temperatures, where direct experimental validation is hard. A dedicated study that elucidates the structure of glassy Fe-rich slags at room temperature, where advanced experimental and molecular simulation methods are combined, has not yet been done, to the best of our knowledge. In the present investigation, a synergistic combination of experimental X-ray and neutron pair distribution function (PDF) and MD simulations is used to determine the nano-structure of CaO-FeO-SiO2 slag. The experimental data were obtained from Peys et al. [11]. By using X-ray and neutron PDFs the authors were able to extract useful information about the molecular structure of Fe-rich slags. However, the complexity of the system hinders the determination of a quantitative structural representation of the slag, which is needed before this structure can be linked to the reactivity and performance of the slag in the target application. From the results of MD simulations, the partial Xray and neutron PDFs, the distributions of coordination numbers (CNs) and the bond angles are obtained, revealing new information regarding the local structure.
Vij (r ) =
qi qj rij
+ Bij exp (−rij / ρij ) −
Cij r6
(1)
where rij is the distance between atoms i and j, qi the effective partial charge of atom i, and Bij, ρij and Cij are the energy parameters of atoms (i,j), corresponding to the Coulombic interactions, short-range electronic repulsion and Van der Waals interactions, respectively. In view of both accuracy and computational efficiency, the empirical values introduced by Guillot and Sator [32] were applied in this study. This potential has been proven to show good transferability over a wide compositional range of silicate minerals and glasses retaining constant parameters [32–34]. The full set of parameters is listed in Table 1. The MD simulations were performed with LAMMPS software package [35], using an integration time-step of 1 fs. For both shortrange and Coulombic interactions, a cutoff of 11 Å was used. The longrange Coulombic interactions were evaluated using the Ewald summation method [36] with an accuracy of 10−5. The total number of atoms used is 2835, calculated in accordance with the experimental chemical composition and density (see Table S.1 in the supplementary material) as well as the size of the box (cubic box of 3.3 nm) [11], while maintaining the system neutral charged. Initially, all atoms were randomly placed within a cubic box using PACKMOL software [37], ensuring the absence of overlapping and applying periodic boundary conditions in all directions. The glass structure was generated following a “melt-quench” methodology as follows [24–26, 31, 34]. The system was first relaxed at 300 K in microcanonical (NVE) ensemble for 0.3 ns to reach thermodynamic equilibrium. The temperature was then increased to 5000 K in an isothermal-isobaric (NPT) ensemble to attain a melt. It was maintained at that temperature for 1 ns to assure the complete mixing of the system and loss of memory of the initial configuration. The system was subsequently quenched linearly to 300 K with a cooling rate of 1 K/ps. Once the glass was formed, the system was relaxed for 1 ns in NPT ensemble and this was followed by a canonical (NVT) run for 3 ns to provide better statistical averaging. For the above ensembles, the NoséHoover thermostat and barostat algorithms were adopted [38, 39]. All the following results are averaged over 3000 configurations extracted from the last run with an interval of 1 ps. The X-ray and neutron PDFs were generated by processing the produced atomic trajectories from MD with PDFgui software [40]. To enable an accurate comparison, the same instrumental contributions to X-ray and neutron PDF data that were used experimentally were employed in PDFgui. Specifically, the PDFs, G(r), were obtained according to Eq. (2), where Q is the momentum transfer given in Eq. (3) [41]. In Eq. (3), 2θ is the scattering Table 1 Parameters of interatomic potential by Guillot et al. [32].
2. Materials and simulation details An Fe-rich slag of the ternary CaO-FeO-SiO2 system has been investigated as a simplified representation of more complex systems that occur as by-products in the non-ferrous metallurgy. The chemical composition of the slag is equivalent to the one used in previous experimental work [11] (approximate molar composition of 0.33CaO0.67FeO-SiO2 with molar ratio of (CaO+FeO)/SiO2 = 1) to enable for a 2
Atom type
q (e)
B (kcal/mol)
ρ (Å)
C (Å6 kcal/mol)
Ca Fe2+ O Si
0.945 1.20 −1.20 2.40
3589,789 346,785.4 212,695 1410,261
0.178 0.19 0.265 0.161
974.534 0 1962.278 1067.655
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angle and λ is the wavelength of the measured radiation.
G (r ) =
Q=
2 π
Q = Qmax
∫
Q [S (Q) − 1] sin (Qr ) dQ
Q = Qmin
4πsinθ λ
(2) (3)
For X-ray PDFs the Q-dependent instrument resolution (Qdamp) was 0.028 Å−1 and the Q-dependent instrumental peak broadening (Qbroad) was 0.011 Å−1. For neutron PDFs, the Qdamp was 0.018 Å−1 and the Qbroad was 0.019 Å−1. The maximum scattering vector (Qmax) for both X-ray and neutron PDFs was 21.5 Å−1. A detailed description of the instrument-dependent parameters as well as the generation of the simulated X-ray and neutron PDFs is provided in the supplementary material at sections S.1 and S.2. The graphic representation of the final structure was made by using VESTA software [42]. 3. Results and discussion 3.1. Comparison of MD model with X-ray and neutron pair distribution function X-ray and neutron PDFs have been widely used for probing the local atomic structure of amorphous materials, providing information about the atom-atom correlations [11, 43–45]. However, discerning the local structure correlations can often be challenging if solely based on experimental results, for example, due to peak overlapping. On the other hand, from MD simulations, the X-ray and neutron PDFs for each atomatom correlation as well as for the total PDF can be obtained by processing the produced atomic trajectories with PDFgui software [40] (see supplementary material, section S.2). To validate the simulation results of the present study, the experimental and simulated X-ray and neutron PDFs of the CaO-FeO-SiO2 slag structure are compared, as shown in Fig. 1. Overall, a good agreement is observed between the computed and the experimental data, especially for the neutron data, which further confirms the reliability of the selected potential as well as the “melt-quench” procedure that was followed for the generation of the slag structure. Specifically, the positions and the intensities of the peaks are well predicted and the level of agreement yields a χ2 factor (defined as Rw in PDFgui [40]) of 0.38 and 0.31 for X-ray and neutron PDF, respectively. Smaller Rw value indicates a better agreement (see supplementary material, section S.2). It should be noted that the intensity of the peak located at around r = 2.3 Å in experiments is not well reproduced. However, this appears to be a general limitation of two body empirical potentials, as analogous discrepancies are also observed in Ca containing silicate glasses [24, 33]. These discrepancies being caused by Ca provide a reason for neutron PDFs to fit better than their X-ray equivalents. As Ca has a significantly higher scattering cross-section for X-ray than neutrons, errors in the location of Ca in the structure will be exposed more clearly in the X-ray PDFs.
Fig. 1. X-ray (a) and neutron (b) pair distribution functions derived from molecular dynamics simulations and compared with experimental data from Peys et al. [11]. The identification of the atom-atom correlations is based on the experimental data. The horizontal and vertical lines are provided for visual guidance.
2.04 Å. The position of the peak is also in accordance with previously reported experimental and computational data [15, 16, 25, 32, 46]. The Fe-O distance observed here in combination with the asymmetry of the peak on high r side, suggests the presence of a different environment for Fe species, more specifically in 4- and 5-fold configuration [46]. The intensity of the peak is slightly higher for the neutrons compared to Xrays due to the higher scattering cross-section. For the Ca-O correlation (Fig. 2c), the position of the peak is observed at 2.4 Å. The intensity of the peak is quite low (for both X-rays and neutrons) with respect to the other atom-atom correlations, explaining the absence of this contribution in the total X-ray and neutron PDFs in Fig. 1. Concerning the O-O correlation (Fig. 2d), a broad peak with a bimodal distribution is observed. The first peak located at lower r distance, is centered around 2.6 Å and is within the range commonly found for O-O correlation in [SiO4] tetrahedra [15, 16, 46]. The second smaller peak is present at around 3 Å. For regular [FeOx] polyhedra, where x equals to 4 or 5, the O-O contribution is expected to be within the range of 2.85 to 3.1 Å [15, 16, 46]. To this end, this second peak can be attributed to the contribution of O-O correlations in [FeO4] tetrahedra or [FeO5] pyramids/ triangular bipyramids. The difference in intensity between X-rays and neutrons is due to the different scattering cross-section. The simulated partial cation-cation correlations are shown in Fig. 3. The Fe-Si correlation (Fig. 3a) is observed at 3.31 Å, which can be attributed to [SiO4] tetrahedra that are connected to [FeOx] polyhedra by
3.2. Partial X-rays and neutron pair distribution function To elucidate in detail the environment of each element, the partial X-ray and neutron PDFs were computed using PDFgui on the molecular dynamics final averaged structure (see supplementary material, section S.2) [40]. Note that this information cannot be derived from the experimental data. Fig. 2 shows the partial Si-O, Fe-O, Ca-O and O-O Xray and neutron PDFs while Fig. 3 shows the partial cation-cation Fe-Si, Fe-Fe, Fe-Ca, Si-Si, Ca-Si and Ca-Ca X-ray and neutron PDFs. The first peak of each atom-atom correlation corresponds to the most probable distance in the first coordination shell. As shown in Fig. 2a, the Si-O correlation has a main contribution centered at 1.62 Å. This is in good agreement with the experimental value and aligns with the characteristic Si-O distance expected for [SiO4] [11, 12, 16, 46]. The Fe-O correlation (Fig. 2b) is found at 3
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Fig. 2. (a) Si-O, (b) Fe-O, (c) Ca-O and (d) O-O partial X-ray and neutron pair distribution functions of the simulated CaO-FeO-SiO2 slag.
intensity of the Ca-Ca peak. For the low intensity partial PDF peaks, the reader is referred to the re-scaled figures at section S.3 of the supplementary material (Fig. S.1). Overall, the investigation of the partial pair distribution functions shows that the first cation-cation correlation peak in Fig. 1 is even more complex than assumed when investigated experimentally [11], because of the significant contribution of Si-Si and Ca-Si and the breadth of the Fe-Fe and Fe-Ca correlations. On the other hand, Fig. 3 confirms that Fe-Si is the correlation with the largest relative contribution of all cation-cation correlations in the PDFs. Additionally, the graphs in Fig. 3 confirm that the high r part of the cation-cation peak (Fig. 1) is caused by correlations involving Ca (Fe-Ca and Ca-Si), as these are the only ones with a significant intensity beyond 3.3 Å. The low r part of the cation-cation peak (Fig. 1) should be associated with both Si-Si and FeFe correlations rather than exclusively with the Fe-Fe, as was the case in previous work [11].
sharing corners [46]. In addition, the asymmetric shape of the peak (small shoulder located at around 3 Å) confirms the presence of different Fe species, i.e. 4- and 5-fold coordinated Fe2+ [46]. The peak of Fe-Fe correlation (Fig. 3b) is broader compared to the Fe-Si correlation, within a range of 2.5–4.28 Å. The breadth of the peak can be attributed to the connectivity of the [FeOx] polyhedra, that is predominantly edgesharing [FeO5] polyhedra and corner-sharing [FeO4] tetrahedra, which will be directly derived and more elaborately discussed later in this paper, in the section on bond angle distributions. Likewise, the first peak of Fe-Ca correlation (Fig. 3c) is broad, compromised by two contributions observed at 3.06 and 3.26 Å that can be assigned to edge and corner-sharing [FeOx] and [CaOx] units, respectively. A significant contribution of Si-Si correlation is shown in Fig. 3d, which is not completely in line with the interpretation of the cation-cation correlations by Peys et al. [11]. Based on the relative scattering cross-sections of Si and the other elements, the authors assumed that a Si-Si correlation would not contribute significantly to the cation-cation correlations. However, according to the intensities observed in Fig. 3, the Si-Si correlation can be considered as an acceptable approximation, taking into account the area underneath the peaks. The Si-Si peak is narrow and sharp with a main contribution observed at 3.14 Å, which corresponds well to what is expected for corner-sharing [SiO4] tetrahedra. A much broader peak, with respect to the Si-Si correlation peak, can be observed for the Ca-Si and Ca-Ca correlation (Fig. 3e and 3 f, respectively). As Ca is the least abundant element in our system, there are not many [CaOx] units neighboring each other, as evidenced by the low
3.3. Coordination number, CN To acquire more accurate structural information, the distribution of CNs is evaluated (Fig. 4).This is of paramount importance as they significantly affect the rigidity of the structural network. The distribution of CNs is obtained by counting the O atoms around Si, Fe and Ca atoms within the first coordination shell (Fig. 4). The latter is specified by the cut-off distance between the pairs determined by the first minimum position of the first partial PDF peak (1.85, 2.56 and 2.90 Å for Si-O, Fe4
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Fig. 3. (a) Fe-Si, (b) Fe-Fe, (c) Fe-Ca, (d) Si-Si, (e) Ca-Si and (f) Ca-Ca partial X-ray and neutron pair distribution functions of the simulated CaO-FeO-SiO2 slag.
found for the presence of both 4- and 5-fold coordinated ferrous iron species [21, 22]. The presence of these different iron species also explains the asymmetry of the partial Fe-O PDF in Fig. 2b. A more detailed description of the local configuration, based on the bond angle distributions, is presented in the next section. A small portion of 3-fold and 6-fold coordination (2% and 10%, respectively) is also present. It should be noted that the low amount of 6-fold coordination observed here for Fe is not often observed in minerals, where Fe mainly occurs in 6-fold configuration [12]. However, in several glasses lower
O and Ca-O, respectively). As shown in Fig. 4, the Si-O distribution of CN indicates a mainly 4fold environment with a percentage of 97%. A small percent of 5-fold coordinated Si is also detected, implying a small distortion of the [SiO4] tetrahedra [47]. The distribution of CN for Fe atoms appears to be broader, compared to the Si atoms, consisting mainly of 4-fold and 5fold coordination with a percentage of 41% and 47%, respectively. This is in agreement with previous studies on similar (CaO)-FeOx-SiO2 slag systems by means of Mössbauer and XANES, where indications were 5
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Fig. 5. Average CN of X-X’ pair (where X, X’= Si, Fe or Ca) in correlation with the total amount of each X’ cation used in the simulation box (total amount of X’ cations: 202 for Ca, 394 for Fe, 549 for Si).
Fig. 4. Distribution of coordination numbers of Si-O, Fe-O, and Ca-O atom pairs.
coordinated species are often present [12]. In fact, the presence of a high amount of 5-fold coordinated Fe is important for the reactivity of the slag, as it is well-known that for Al the 5-fold coordinated species are the cause of the high reactivity of metakaolin [48–50]. In the case of Ca, the distribution is quite broad exhibiting a wide range of CN around the most probable value. The higher proportion is observed for 6- and 7-fold coordination (40% and 37%, respectively), while a smaller amount of 4-fold, 5-fold and 8-fold coordination is also present (3%, 13% and 7%, respectively). Valuable information about the nano-structure can also be derived from the distribution of CNs of cation-cation pairs. This can be obtained by counting the amount of Si, Fe or Ca atoms after the nearest oxygen atom around the Si, Fe or Ca atoms (see Fig. S.2 in the supplementary material). The information derived from the distribution of CNs of cation-cation pairs (X-X’ where X, X’= Si, Fe or Ca), can be used as a measure of the probability of having an X’ next to X. This can be achieved by relating the average CN of each X-X’ pair (Table 2) to the total amount of each X’ cation (202 for Ca, 394 for Fe, 549 for Si) used in the simulation box (Fig. 5). A random distribution of the polyhedra would result in a linear relation between the average CN of X-X’ to the total amount of X’ atoms. Here, a linear correlation is observed for the Ca-X’ and Fe-X’ correlation, with R2 of 0.999 and 0.998, respectively. The [CaOx] and [FeOx] polyhedra are thus randomly distributed, meaning that there is no preference of Ca or Fe towards another neighboring cation. On the other hand, the Si atoms show a non-linear Si-X’ correlation. As in this study Si is the only network forming element, the distribution of the Si-Si CNs can provide directly the Qn speciation, where Qn refers to the connectivity of the network in Engelhardt notation [51] and indicates the polymerization degree of the
Fig. 6. Distribution of Qn species of the simulated CaO-FeO-SiO2 slag.
slag. The distribution of Qn is shown in Fig. 6 and the average 〈Qn〉 equals to 2.08 ( ± 0.6). This average can be used to calculate the amount of non-bridging oxygens, using the formula NBO/T = 4 〈Qn〉 = 1.92. This number differs from the molar ratio (CaO+FeO)x2/ SiO2 = 2.17. This difference could arise from imprecisions in the calculations or the partial network forming action of the Fe2+. This possible partial network forming behavior of Fe2+ and high 〈Qn〉 has repercussions on the reactivity of the glass, which will be lower than what is expected from the chemical composition and the (CaO+FeO)x2/SiO2 molar ratio.
Table 2 Average coordination numbers of cation-cation pairs and standard deviation characterizing the breadth of the distribution. Atom pairs
Average CN
Standard deviation
Si-Si Si-Fe Si-Ca Fe-Si Fe-Fe Fe-Ca Ca-Si Ca-Fe Ca-Ca
2.08 3.33 2.23 4.64 3.57 2.02 6.07 3.94 1.44
0.31 0.27 0.73 0.34 0.36 0.28 0.77 0.43 0.22
3.4. Bond angle distributions The bond angle distributions of intra-polyhedral O-X-O and interpolyhedral X-O-X’, with X, X’ = Si, Fe, or Ca, are depicted in Fig. 7. The intra-polyhedral O-X-O bond angle distribution is a measure of the distortion of the polyhedral network while the inter-polyhedral angle distributions provide information about the arrangements of the structural units relative to each other. The O-Si-O bond angle distribution (Fig. 7a) shows a very sharp peak centered at around 108° which is similar to those expected for a [SiO4] unit (~ 109.5°). Additionally, the Si-O-Si bond angle distribution (Fig. 7b), which is related to the connectivity of [SiO4] tetrahedra, 6
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Fig. 7. (a) O-X-O, (b) Si-O-X, (c) Fe-O-X and (d) Ca-O-X bond angle distributions, where X=Si, Fe, Ca. Note that Si-O-Fe and Fe-O-Si, Fe-O-Ca and Ca-O-Fe, Si-O-Ca and Ca-O-Si are the same, as the calculation of the bond angle is reversible. They are repeated in the different graphs in this figure for comparison purposes.
appears to have a broad band centered around 147° This value is close to that expected for corner-sharing [SiO4] tetrahedra (~144°) and the distribution of the bond angles is broad, as often observed in silicate glasses, which indicates the disorder in the tetrahedral connectivity. The O-Fe-O distribution (Fig. 7a) is broad with the most abundant bond angle centered around a lower value (90°) compared to O-Si-O, while a smaller peak at around 65° is also present. The breadth of this bond angle distribution in combination with the asymmetry observed for the partial Fe-O PDF (Fig. 2b), further confirms the presence of different Fe species (4- and 5-fold coordinated) as well as the distortion of [FeOx] polyhedra [46]. Moreover, the position of the bond angles observed here are consistent with previous work of Rossano et al. [27, 52] on CaO-FeO-2SiO2 glass system. The authors showed the presence of a continuous distribution of 4- and 5-fold coordination associated with distorted tetrahedra and triangular bipyramids, respectively [52]. Likewise, the Fe-O-Fe bond angle distribution (Fig. 7c) appears in lower values compared with Si-O-Si, with a maximum at 87° As mentioned in the previous sections for Fe-Fe correlation, the [FeOx] polyhedra are connected in two ways: by edge-sharing [FeO5] polyhedra and by corner-sharing [FeO4] tetrahedra. Having the major fraction at 90°, the type of connection is predominantly edge-sharing, although a significant fraction of tetrahedrally coordinated Fe was observed ( see Fig. 4). This was already suggested from the partial pair distribution functions in Fig. 3 and indicates that only the higher coordinated Fe species are adjacent to each other, while [FeO4] tetrahedra are neighboring [SiO4] tetrahedra. This is qualitatively illustrated by observing the graphic representation of the structure in Fig. 8. This knowledge of the preferred aggregation of higher coordinated [FeOx] species,
together with the seemingly random distribution of the Fe atoms on average, which was shown in Fig. 5, delivers additional information about the glass structure. It shows that the Fe atoms get randomly distributed throughout the network and will then obtain a coordination with O dependent on the neighboring cations. With more Si around, the coordination number is mostly 4 and with more Fe or Ca around, the coordination number is rather 5 or 6. The Si-O-Fe bond angles (Fig. 7b or Fig. 7c) present a broad distribution with two bands centered at approximately 93° and 123° which further confirms the assumption that the [SiO4] tetrahedra are connected to [FeOx] polyhedra by sharing corners (Fig. 8). The O-Ca-O distribution (Fig. 7a) exhibits a bimodal distribution with average bond angles around 63° and 78° This might arise from the wide distribution of the local environment of Ca atoms, as shown in the previous sections. Similarly, the inter-polyhedral Ca-O-Ca bond angle distribution (Fig. 7d) shows two bands at around 80° and 93° suggesting that the neighboring [CaOx] units are connected in different ways. However, the amount of [CaOx] units neighboring with each other is quite low due to the low amount of Ca present, as was observed in Fig. 3f. The bond angular distributions of Ca-O-Fe (Fig. 7c or 7 d) and Ca-O-Si (Fig. 7b or 7 d) are quite broad with higher distribution at lower angles (around 82° and 93°, respectively). This indicates that the [FeOx] and [SiO4] polyhedra are connected to [CaOx] units mostly by edge-sharing. The low distribution at higher angles (118°) suggests that there is also a small proportion of corner-sharing polyhedra, which is observed particularly for Ca-O-Si.
7
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Fig. 8. Graphic representation of the simulated CaO-FeO-SiO2 slag structure. The colors for the structural representation are: yellow for [FeOx] polyhedra, blue for [SiO4] tetrahedra, red for O atoms and light blue for Ca atoms.
4. Conclusion
References
The combination of previously obtained experimental X-ray and neutron pair distribution functions with molecular dynamics simulations provided a more detailed description of the glassy structure of a synthetic non-ferrous metallurgy (CaO-FeO-SiO2) slag. The results from MD simulations are well consistent with the experimental PDF data. The analysis of the partial X-ray and neutron PDFs, CNs and bond angular distribution revealed structural characteristics that were impossible to discern experimentally. Fe is present mainly in 4- and 5-fold coordination in tetrahedral and pyramidal/triangular bipyramidal configuration, respectively. The [FeO4] units are predominantly connected by sharing corners while the [FeO5] polyhedra mostly share edges. The higher coordinated [FeOx] polyhedra (x = 5 or 6) are more prone to neighboring each other by sharing edges while [FeO4] tetrahedra are predominantly neighboring [SiO4] tetrahedra by sharing corners. The silicate network is polymerized with average=2.08 while the modifier elements (Fe and Ca) seem to be randomly distributed throughout it. This suggests that Ca and Fe atoms do not show a tendency to neighbor any specific polyhedron. The importance of complementing experimental X-ray and neutron PDFs with MD simulations is evident in this investigation, which has allowed for a detailed understanding of the nano-structure of the synthetic non-ferrous metallurgy slag.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments This work has been implemented within MSCA-ETN SOCRATES project that has received funding from the European Union's EU Framework Programme for Research and Innovation Horizon 2020, under Grant Agreement No 721385. Project website: http://etnsocrates.eu/. A. Peys is thankful to the Research Foundation – Flanders (FWO) for the FWO-SB scholarship.
Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jnoncrysol.2019.119771. 8
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Unraveling the nano-structure of a glassy CaO-FeO-SiO2slag by molecular dynamics simulations ⁎
Christina Siakatia, , Roberto Macchieraldob, Barbara Kirchnerb, Frederik Tielensc, Arne Peysa, David Sevenoa, Yiannis Pontikesa a
KU Leuven Department of Materials Engineering, Kasteelpark Arenberg 44, Leuven, 3001, Belgium Mulliken Center for Theoretical Chemistry, University of Bonn, Beringstr. 4+6, Bonn, D-53115, Germany c General Chemistry (ALGC – Materials Modeling Group), Vrije Universiteit Brussel (Free University Brussels, VUB), Pleinlaan 2, Brussels, 1050, Belgium b
A R T I C LE I N FO
A B S T R A C T
Keywords: Non-ferrous metallurgy slags Molecular dynamics Pair distribution function Ferrous silicate glass Nano-structure
Non-ferrous metallurgy slags are gaining significant interest as a resource in the production of alternative lowenergy cementitious materials. Their atomistic structures, however, are still not fully understood due to their glassy nature. In the work presented herein, a comprehensive description of the nano-structure of a CaO-FeOSiO2 slag was obtained by using molecular dynamic simulations in conjunction with previously obtained experimental data from X-ray and neutron pair distribution function studies. Iron was predominately 4- and 5-fold coordinated with oxygen, forming polyhedra in tetrahedral and pyramidal/triangular bipyramidal configuration. The [FeOx] polyhedra were corner-shared to the silica tetrahedra, while the higher coordinated fractions (x = 5 or 6) seemed to prefer to be next to each other, sharing edges. Ca was mostly surrounded by 6 or 7 oxygens in polyhedra that are predominantly edge-sharing with other units. The obtained results fit the experimental data well and as such provide an accurate and realistic picture of the iron-rich slag structure.
1. Introduction The substantial CO2 emissions associated with the production of ordinary Portland cement (OPC) led to the need for partial or total clinker substitution with industrial by-products and other resources that possess a lower carbon footprint [1]. One such option is slags, an industrial by-product originating from ferrous and non-ferrous pyrometallurgy [1]. Slags have been used in blended cements for decades and are standardized as CEM III (EN197) or type IS (ASTM C595) cements. In new binders, slags can be used in higher volumes, for instance, when used as precursor materials in the production of inorganic polymers (IPs) and alkali activated materials (AAM); those are types of alternative cementitious materials that display similar or even better performance than OPC [2, 3]. The final properties are largely controlled by the intrinsic characteristics of the slags (e.g. chemical composition, mineralogy and nano-structure) [4–8], which are determined by the production process [9, 10]. Consequently, an accurate knowledge of the nano-structure of the slags is of paramount importance as this information can be linked to the reactivity of the slag during alkali activation and the final performance of the resulting IPs. Understanding the slag structure and its relation to reactivity would allow the design of optimal slags, created to fulfill the needs of the alkali-activated ⁎
materials. This knowledge has a crucial strategic importance for metallurgical companies wanting to optimize the quality (i.e. value) of their slags, with a substantial and direct positive impact to the environment and society. To exhibit sufficient reactivity for the synthesis of inorganic polymers, the slag from the non-ferrous metallurgy has to be glassy. The challenge of characterizing the nano-structure of slags is also mainly being discussed in the context of their glassy nature [11]. The complexity becomes even greater for the non-ferrous metallurgy slags in particular, where, due to the presence of Fe as major component, fundamental questions remain. In pure silica glass, the atomic network consists of silica tetrahedra ([SiO4]) that are interconnected through their corners to four other [SiO4] by bridging oxygen (BO) atoms [12]. The introduction of network modifier cations affects the degree of polymerization. The modifier cation disrupts the connectivity of the silica network, forming non-bridging oxygen (NBO) atoms. Thus, the depolymerized silica network has different proportions of BOs and NBOs [12]. The silica tetrahedra are arranged in two dimensional rings, surrounding the network modifying cations [13, 14]. The size of these rings is an alternative way to express the connectivity of the glass network. Multicomponent glasses consist of a variety of former and modifier
Corresponding author. E-mail address: [email protected] (C. Siakati).
https://doi.org/10.1016/j.jnoncrysol.2019.119771 Received 26 August 2019; Received in revised form 12 October 2019; Accepted 8 November 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Christina Siakati, et al., Journal of Non-Crystalline Solids, https://doi.org/10.1016/j.jnoncrysol.2019.119771
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direct validation with the MD simulation results. A short description of the experimental procedure outlined in this reference is presented in the supplementary material to provide background details and some of the instrument parameters that were used for the generation of the simulated X-ray and neutron pair distribution functions (PDFs) (supplementary material, sections S.1 and S.2). In this work, the two body Born-Mayer-Huggins (BMH) potential function was selected as it has been successfully used to study oxide systems [23, 24, 27, 31]. It consists of long-range Coulomb interactions, short-range repulsion interactions and Van der Waals forces. The interatomic force field reads:
cations. For non-ferrous metallurgy slags in particular, the high proportion of iron cations affects significantly the glass network, as iron can be both former and modifier due to its multivalence nature and coordination. Apart from the possibility of having different valence and coordination states in different samples, a variety of species occurs within one glass, increasing the complexity of the experimental analysis. Fe3+ is observed to be mainly in 4-fold coordination with oxygen having the role of network former if sufficient charge balancing elements are present [12]. The presence of small amounts of higher coordination numbered Fe3+ has also been suggested, acting as network modifier [15–18]. In this instance, it is mostly assumed to be in 5-fold coordination [15, 16], however the presence of a minor portion of 6fold [17] cannot be decisively rebutted. In any case, it has been found that the average coordination number of Fe3+ is lower than that of Fe2+ when they coexist in one glass [19]. For Fe2+, a range of 4- to 6fold coordination with oxygen has been suggested for various compositions and it is usually considered as a network modifier [12, 18, 20]. The specific coordination number, or distribution of coordination numbers, is dependent on the presence of other elements. Recent studies on synthetic (CaO)-FeOx-SiO2 slags by means of X-ray absorption near-edge structure (XANES) spectroscopy showed that the presence of Ca and increased Si contents leads to lower coordination numbers for Fe [21]. Further analysis on the same slags using X-ray and neutron pair distribution function and Mössbauer spectroscopy revealed that Fe is mainly present as Fe2+in 4- and 5-fold coordination with minor amount of Fe3+ in 5-fold coordination [11, 22]. The experimental uncertainties together with the need to acquire detailed knowledge of the nano-structure of the non-ferrous metallurgy slags led to the use of atomistic scale simulations in conjunction with experimental data. Among several simulation techniques, classical molecular dynamics (MD) simulations have been widely applied to explore the structure of glassy materials and melts, providing quantitatively accurate results [23–29]. Previous studies with MD simulations revealed information concerning the viscosity behavior of slags and how this is affected by the depolymerization of the silicate network [25]. Similarly, structural characteristics such as pair distribution function and oxygen bond types as well as thermodynamic properties have also been calculated by MD simulations with great success [27, 30, 31]. However, many of these studies focused on the molten state of the material at high temperatures, where direct experimental validation is hard. A dedicated study that elucidates the structure of glassy Fe-rich slags at room temperature, where advanced experimental and molecular simulation methods are combined, has not yet been done, to the best of our knowledge. In the present investigation, a synergistic combination of experimental X-ray and neutron pair distribution function (PDF) and MD simulations is used to determine the nano-structure of CaO-FeO-SiO2 slag. The experimental data were obtained from Peys et al. [11]. By using X-ray and neutron PDFs the authors were able to extract useful information about the molecular structure of Fe-rich slags. However, the complexity of the system hinders the determination of a quantitative structural representation of the slag, which is needed before this structure can be linked to the reactivity and performance of the slag in the target application. From the results of MD simulations, the partial Xray and neutron PDFs, the distributions of coordination numbers (CNs) and the bond angles are obtained, revealing new information regarding the local structure.
Vij (r ) =
qi qj rij
+ Bij exp (−rij / ρij ) −
Cij r6
(1)
where rij is the distance between atoms i and j, qi the effective partial charge of atom i, and Bij, ρij and Cij are the energy parameters of atoms (i,j), corresponding to the Coulombic interactions, short-range electronic repulsion and Van der Waals interactions, respectively. In view of both accuracy and computational efficiency, the empirical values introduced by Guillot and Sator [32] were applied in this study. This potential has been proven to show good transferability over a wide compositional range of silicate minerals and glasses retaining constant parameters [32–34]. The full set of parameters is listed in Table 1. The MD simulations were performed with LAMMPS software package [35], using an integration time-step of 1 fs. For both shortrange and Coulombic interactions, a cutoff of 11 Å was used. The longrange Coulombic interactions were evaluated using the Ewald summation method [36] with an accuracy of 10−5. The total number of atoms used is 2835, calculated in accordance with the experimental chemical composition and density (see Table S.1 in the supplementary material) as well as the size of the box (cubic box of 3.3 nm) [11], while maintaining the system neutral charged. Initially, all atoms were randomly placed within a cubic box using PACKMOL software [37], ensuring the absence of overlapping and applying periodic boundary conditions in all directions. The glass structure was generated following a “melt-quench” methodology as follows [24–26, 31, 34]. The system was first relaxed at 300 K in microcanonical (NVE) ensemble for 0.3 ns to reach thermodynamic equilibrium. The temperature was then increased to 5000 K in an isothermal-isobaric (NPT) ensemble to attain a melt. It was maintained at that temperature for 1 ns to assure the complete mixing of the system and loss of memory of the initial configuration. The system was subsequently quenched linearly to 300 K with a cooling rate of 1 K/ps. Once the glass was formed, the system was relaxed for 1 ns in NPT ensemble and this was followed by a canonical (NVT) run for 3 ns to provide better statistical averaging. For the above ensembles, the NoséHoover thermostat and barostat algorithms were adopted [38, 39]. All the following results are averaged over 3000 configurations extracted from the last run with an interval of 1 ps. The X-ray and neutron PDFs were generated by processing the produced atomic trajectories from MD with PDFgui software [40]. To enable an accurate comparison, the same instrumental contributions to X-ray and neutron PDF data that were used experimentally were employed in PDFgui. Specifically, the PDFs, G(r), were obtained according to Eq. (2), where Q is the momentum transfer given in Eq. (3) [41]. In Eq. (3), 2θ is the scattering Table 1 Parameters of interatomic potential by Guillot et al. [32].
2. Materials and simulation details An Fe-rich slag of the ternary CaO-FeO-SiO2 system has been investigated as a simplified representation of more complex systems that occur as by-products in the non-ferrous metallurgy. The chemical composition of the slag is equivalent to the one used in previous experimental work [11] (approximate molar composition of 0.33CaO0.67FeO-SiO2 with molar ratio of (CaO+FeO)/SiO2 = 1) to enable for a 2
Atom type
q (e)
B (kcal/mol)
ρ (Å)
C (Å6 kcal/mol)
Ca Fe2+ O Si
0.945 1.20 −1.20 2.40
3589,789 346,785.4 212,695 1410,261
0.178 0.19 0.265 0.161
974.534 0 1962.278 1067.655
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angle and λ is the wavelength of the measured radiation.
G (r ) =
Q=
2 π
Q = Qmax
∫
Q [S (Q) − 1] sin (Qr ) dQ
Q = Qmin
4πsinθ λ
(2) (3)
For X-ray PDFs the Q-dependent instrument resolution (Qdamp) was 0.028 Å−1 and the Q-dependent instrumental peak broadening (Qbroad) was 0.011 Å−1. For neutron PDFs, the Qdamp was 0.018 Å−1 and the Qbroad was 0.019 Å−1. The maximum scattering vector (Qmax) for both X-ray and neutron PDFs was 21.5 Å−1. A detailed description of the instrument-dependent parameters as well as the generation of the simulated X-ray and neutron PDFs is provided in the supplementary material at sections S.1 and S.2. The graphic representation of the final structure was made by using VESTA software [42]. 3. Results and discussion 3.1. Comparison of MD model with X-ray and neutron pair distribution function X-ray and neutron PDFs have been widely used for probing the local atomic structure of amorphous materials, providing information about the atom-atom correlations [11, 43–45]. However, discerning the local structure correlations can often be challenging if solely based on experimental results, for example, due to peak overlapping. On the other hand, from MD simulations, the X-ray and neutron PDFs for each atomatom correlation as well as for the total PDF can be obtained by processing the produced atomic trajectories with PDFgui software [40] (see supplementary material, section S.2). To validate the simulation results of the present study, the experimental and simulated X-ray and neutron PDFs of the CaO-FeO-SiO2 slag structure are compared, as shown in Fig. 1. Overall, a good agreement is observed between the computed and the experimental data, especially for the neutron data, which further confirms the reliability of the selected potential as well as the “melt-quench” procedure that was followed for the generation of the slag structure. Specifically, the positions and the intensities of the peaks are well predicted and the level of agreement yields a χ2 factor (defined as Rw in PDFgui [40]) of 0.38 and 0.31 for X-ray and neutron PDF, respectively. Smaller Rw value indicates a better agreement (see supplementary material, section S.2). It should be noted that the intensity of the peak located at around r = 2.3 Å in experiments is not well reproduced. However, this appears to be a general limitation of two body empirical potentials, as analogous discrepancies are also observed in Ca containing silicate glasses [24, 33]. These discrepancies being caused by Ca provide a reason for neutron PDFs to fit better than their X-ray equivalents. As Ca has a significantly higher scattering cross-section for X-ray than neutrons, errors in the location of Ca in the structure will be exposed more clearly in the X-ray PDFs.
Fig. 1. X-ray (a) and neutron (b) pair distribution functions derived from molecular dynamics simulations and compared with experimental data from Peys et al. [11]. The identification of the atom-atom correlations is based on the experimental data. The horizontal and vertical lines are provided for visual guidance.
2.04 Å. The position of the peak is also in accordance with previously reported experimental and computational data [15, 16, 25, 32, 46]. The Fe-O distance observed here in combination with the asymmetry of the peak on high r side, suggests the presence of a different environment for Fe species, more specifically in 4- and 5-fold configuration [46]. The intensity of the peak is slightly higher for the neutrons compared to Xrays due to the higher scattering cross-section. For the Ca-O correlation (Fig. 2c), the position of the peak is observed at 2.4 Å. The intensity of the peak is quite low (for both X-rays and neutrons) with respect to the other atom-atom correlations, explaining the absence of this contribution in the total X-ray and neutron PDFs in Fig. 1. Concerning the O-O correlation (Fig. 2d), a broad peak with a bimodal distribution is observed. The first peak located at lower r distance, is centered around 2.6 Å and is within the range commonly found for O-O correlation in [SiO4] tetrahedra [15, 16, 46]. The second smaller peak is present at around 3 Å. For regular [FeOx] polyhedra, where x equals to 4 or 5, the O-O contribution is expected to be within the range of 2.85 to 3.1 Å [15, 16, 46]. To this end, this second peak can be attributed to the contribution of O-O correlations in [FeO4] tetrahedra or [FeO5] pyramids/ triangular bipyramids. The difference in intensity between X-rays and neutrons is due to the different scattering cross-section. The simulated partial cation-cation correlations are shown in Fig. 3. The Fe-Si correlation (Fig. 3a) is observed at 3.31 Å, which can be attributed to [SiO4] tetrahedra that are connected to [FeOx] polyhedra by
3.2. Partial X-rays and neutron pair distribution function To elucidate in detail the environment of each element, the partial X-ray and neutron PDFs were computed using PDFgui on the molecular dynamics final averaged structure (see supplementary material, section S.2) [40]. Note that this information cannot be derived from the experimental data. Fig. 2 shows the partial Si-O, Fe-O, Ca-O and O-O Xray and neutron PDFs while Fig. 3 shows the partial cation-cation Fe-Si, Fe-Fe, Fe-Ca, Si-Si, Ca-Si and Ca-Ca X-ray and neutron PDFs. The first peak of each atom-atom correlation corresponds to the most probable distance in the first coordination shell. As shown in Fig. 2a, the Si-O correlation has a main contribution centered at 1.62 Å. This is in good agreement with the experimental value and aligns with the characteristic Si-O distance expected for [SiO4] [11, 12, 16, 46]. The Fe-O correlation (Fig. 2b) is found at 3
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Fig. 2. (a) Si-O, (b) Fe-O, (c) Ca-O and (d) O-O partial X-ray and neutron pair distribution functions of the simulated CaO-FeO-SiO2 slag.
intensity of the Ca-Ca peak. For the low intensity partial PDF peaks, the reader is referred to the re-scaled figures at section S.3 of the supplementary material (Fig. S.1). Overall, the investigation of the partial pair distribution functions shows that the first cation-cation correlation peak in Fig. 1 is even more complex than assumed when investigated experimentally [11], because of the significant contribution of Si-Si and Ca-Si and the breadth of the Fe-Fe and Fe-Ca correlations. On the other hand, Fig. 3 confirms that Fe-Si is the correlation with the largest relative contribution of all cation-cation correlations in the PDFs. Additionally, the graphs in Fig. 3 confirm that the high r part of the cation-cation peak (Fig. 1) is caused by correlations involving Ca (Fe-Ca and Ca-Si), as these are the only ones with a significant intensity beyond 3.3 Å. The low r part of the cation-cation peak (Fig. 1) should be associated with both Si-Si and FeFe correlations rather than exclusively with the Fe-Fe, as was the case in previous work [11].
sharing corners [46]. In addition, the asymmetric shape of the peak (small shoulder located at around 3 Å) confirms the presence of different Fe species, i.e. 4- and 5-fold coordinated Fe2+ [46]. The peak of Fe-Fe correlation (Fig. 3b) is broader compared to the Fe-Si correlation, within a range of 2.5–4.28 Å. The breadth of the peak can be attributed to the connectivity of the [FeOx] polyhedra, that is predominantly edgesharing [FeO5] polyhedra and corner-sharing [FeO4] tetrahedra, which will be directly derived and more elaborately discussed later in this paper, in the section on bond angle distributions. Likewise, the first peak of Fe-Ca correlation (Fig. 3c) is broad, compromised by two contributions observed at 3.06 and 3.26 Å that can be assigned to edge and corner-sharing [FeOx] and [CaOx] units, respectively. A significant contribution of Si-Si correlation is shown in Fig. 3d, which is not completely in line with the interpretation of the cation-cation correlations by Peys et al. [11]. Based on the relative scattering cross-sections of Si and the other elements, the authors assumed that a Si-Si correlation would not contribute significantly to the cation-cation correlations. However, according to the intensities observed in Fig. 3, the Si-Si correlation can be considered as an acceptable approximation, taking into account the area underneath the peaks. The Si-Si peak is narrow and sharp with a main contribution observed at 3.14 Å, which corresponds well to what is expected for corner-sharing [SiO4] tetrahedra. A much broader peak, with respect to the Si-Si correlation peak, can be observed for the Ca-Si and Ca-Ca correlation (Fig. 3e and 3 f, respectively). As Ca is the least abundant element in our system, there are not many [CaOx] units neighboring each other, as evidenced by the low
3.3. Coordination number, CN To acquire more accurate structural information, the distribution of CNs is evaluated (Fig. 4).This is of paramount importance as they significantly affect the rigidity of the structural network. The distribution of CNs is obtained by counting the O atoms around Si, Fe and Ca atoms within the first coordination shell (Fig. 4). The latter is specified by the cut-off distance between the pairs determined by the first minimum position of the first partial PDF peak (1.85, 2.56 and 2.90 Å for Si-O, Fe4
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Fig. 3. (a) Fe-Si, (b) Fe-Fe, (c) Fe-Ca, (d) Si-Si, (e) Ca-Si and (f) Ca-Ca partial X-ray and neutron pair distribution functions of the simulated CaO-FeO-SiO2 slag.
found for the presence of both 4- and 5-fold coordinated ferrous iron species [21, 22]. The presence of these different iron species also explains the asymmetry of the partial Fe-O PDF in Fig. 2b. A more detailed description of the local configuration, based on the bond angle distributions, is presented in the next section. A small portion of 3-fold and 6-fold coordination (2% and 10%, respectively) is also present. It should be noted that the low amount of 6-fold coordination observed here for Fe is not often observed in minerals, where Fe mainly occurs in 6-fold configuration [12]. However, in several glasses lower
O and Ca-O, respectively). As shown in Fig. 4, the Si-O distribution of CN indicates a mainly 4fold environment with a percentage of 97%. A small percent of 5-fold coordinated Si is also detected, implying a small distortion of the [SiO4] tetrahedra [47]. The distribution of CN for Fe atoms appears to be broader, compared to the Si atoms, consisting mainly of 4-fold and 5fold coordination with a percentage of 41% and 47%, respectively. This is in agreement with previous studies on similar (CaO)-FeOx-SiO2 slag systems by means of Mössbauer and XANES, where indications were 5
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Fig. 5. Average CN of X-X’ pair (where X, X’= Si, Fe or Ca) in correlation with the total amount of each X’ cation used in the simulation box (total amount of X’ cations: 202 for Ca, 394 for Fe, 549 for Si).
Fig. 4. Distribution of coordination numbers of Si-O, Fe-O, and Ca-O atom pairs.
coordinated species are often present [12]. In fact, the presence of a high amount of 5-fold coordinated Fe is important for the reactivity of the slag, as it is well-known that for Al the 5-fold coordinated species are the cause of the high reactivity of metakaolin [48–50]. In the case of Ca, the distribution is quite broad exhibiting a wide range of CN around the most probable value. The higher proportion is observed for 6- and 7-fold coordination (40% and 37%, respectively), while a smaller amount of 4-fold, 5-fold and 8-fold coordination is also present (3%, 13% and 7%, respectively). Valuable information about the nano-structure can also be derived from the distribution of CNs of cation-cation pairs. This can be obtained by counting the amount of Si, Fe or Ca atoms after the nearest oxygen atom around the Si, Fe or Ca atoms (see Fig. S.2 in the supplementary material). The information derived from the distribution of CNs of cation-cation pairs (X-X’ where X, X’= Si, Fe or Ca), can be used as a measure of the probability of having an X’ next to X. This can be achieved by relating the average CN of each X-X’ pair (Table 2) to the total amount of each X’ cation (202 for Ca, 394 for Fe, 549 for Si) used in the simulation box (Fig. 5). A random distribution of the polyhedra would result in a linear relation between the average CN of X-X’ to the total amount of X’ atoms. Here, a linear correlation is observed for the Ca-X’ and Fe-X’ correlation, with R2 of 0.999 and 0.998, respectively. The [CaOx] and [FeOx] polyhedra are thus randomly distributed, meaning that there is no preference of Ca or Fe towards another neighboring cation. On the other hand, the Si atoms show a non-linear Si-X’ correlation. As in this study Si is the only network forming element, the distribution of the Si-Si CNs can provide directly the Qn speciation, where Qn refers to the connectivity of the network in Engelhardt notation [51] and indicates the polymerization degree of the
Fig. 6. Distribution of Qn species of the simulated CaO-FeO-SiO2 slag.
slag. The distribution of Qn is shown in Fig. 6 and the average 〈Qn〉 equals to 2.08 ( ± 0.6). This average can be used to calculate the amount of non-bridging oxygens, using the formula NBO/T = 4 〈Qn〉 = 1.92. This number differs from the molar ratio (CaO+FeO)x2/ SiO2 = 2.17. This difference could arise from imprecisions in the calculations or the partial network forming action of the Fe2+. This possible partial network forming behavior of Fe2+ and high 〈Qn〉 has repercussions on the reactivity of the glass, which will be lower than what is expected from the chemical composition and the (CaO+FeO)x2/SiO2 molar ratio.
Table 2 Average coordination numbers of cation-cation pairs and standard deviation characterizing the breadth of the distribution. Atom pairs
Average CN
Standard deviation
Si-Si Si-Fe Si-Ca Fe-Si Fe-Fe Fe-Ca Ca-Si Ca-Fe Ca-Ca
2.08 3.33 2.23 4.64 3.57 2.02 6.07 3.94 1.44
0.31 0.27 0.73 0.34 0.36 0.28 0.77 0.43 0.22
3.4. Bond angle distributions The bond angle distributions of intra-polyhedral O-X-O and interpolyhedral X-O-X’, with X, X’ = Si, Fe, or Ca, are depicted in Fig. 7. The intra-polyhedral O-X-O bond angle distribution is a measure of the distortion of the polyhedral network while the inter-polyhedral angle distributions provide information about the arrangements of the structural units relative to each other. The O-Si-O bond angle distribution (Fig. 7a) shows a very sharp peak centered at around 108° which is similar to those expected for a [SiO4] unit (~ 109.5°). Additionally, the Si-O-Si bond angle distribution (Fig. 7b), which is related to the connectivity of [SiO4] tetrahedra, 6
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Fig. 7. (a) O-X-O, (b) Si-O-X, (c) Fe-O-X and (d) Ca-O-X bond angle distributions, where X=Si, Fe, Ca. Note that Si-O-Fe and Fe-O-Si, Fe-O-Ca and Ca-O-Fe, Si-O-Ca and Ca-O-Si are the same, as the calculation of the bond angle is reversible. They are repeated in the different graphs in this figure for comparison purposes.
appears to have a broad band centered around 147° This value is close to that expected for corner-sharing [SiO4] tetrahedra (~144°) and the distribution of the bond angles is broad, as often observed in silicate glasses, which indicates the disorder in the tetrahedral connectivity. The O-Fe-O distribution (Fig. 7a) is broad with the most abundant bond angle centered around a lower value (90°) compared to O-Si-O, while a smaller peak at around 65° is also present. The breadth of this bond angle distribution in combination with the asymmetry observed for the partial Fe-O PDF (Fig. 2b), further confirms the presence of different Fe species (4- and 5-fold coordinated) as well as the distortion of [FeOx] polyhedra [46]. Moreover, the position of the bond angles observed here are consistent with previous work of Rossano et al. [27, 52] on CaO-FeO-2SiO2 glass system. The authors showed the presence of a continuous distribution of 4- and 5-fold coordination associated with distorted tetrahedra and triangular bipyramids, respectively [52]. Likewise, the Fe-O-Fe bond angle distribution (Fig. 7c) appears in lower values compared with Si-O-Si, with a maximum at 87° As mentioned in the previous sections for Fe-Fe correlation, the [FeOx] polyhedra are connected in two ways: by edge-sharing [FeO5] polyhedra and by corner-sharing [FeO4] tetrahedra. Having the major fraction at 90°, the type of connection is predominantly edge-sharing, although a significant fraction of tetrahedrally coordinated Fe was observed ( see Fig. 4). This was already suggested from the partial pair distribution functions in Fig. 3 and indicates that only the higher coordinated Fe species are adjacent to each other, while [FeO4] tetrahedra are neighboring [SiO4] tetrahedra. This is qualitatively illustrated by observing the graphic representation of the structure in Fig. 8. This knowledge of the preferred aggregation of higher coordinated [FeOx] species,
together with the seemingly random distribution of the Fe atoms on average, which was shown in Fig. 5, delivers additional information about the glass structure. It shows that the Fe atoms get randomly distributed throughout the network and will then obtain a coordination with O dependent on the neighboring cations. With more Si around, the coordination number is mostly 4 and with more Fe or Ca around, the coordination number is rather 5 or 6. The Si-O-Fe bond angles (Fig. 7b or Fig. 7c) present a broad distribution with two bands centered at approximately 93° and 123° which further confirms the assumption that the [SiO4] tetrahedra are connected to [FeOx] polyhedra by sharing corners (Fig. 8). The O-Ca-O distribution (Fig. 7a) exhibits a bimodal distribution with average bond angles around 63° and 78° This might arise from the wide distribution of the local environment of Ca atoms, as shown in the previous sections. Similarly, the inter-polyhedral Ca-O-Ca bond angle distribution (Fig. 7d) shows two bands at around 80° and 93° suggesting that the neighboring [CaOx] units are connected in different ways. However, the amount of [CaOx] units neighboring with each other is quite low due to the low amount of Ca present, as was observed in Fig. 3f. The bond angular distributions of Ca-O-Fe (Fig. 7c or 7 d) and Ca-O-Si (Fig. 7b or 7 d) are quite broad with higher distribution at lower angles (around 82° and 93°, respectively). This indicates that the [FeOx] and [SiO4] polyhedra are connected to [CaOx] units mostly by edge-sharing. The low distribution at higher angles (118°) suggests that there is also a small proportion of corner-sharing polyhedra, which is observed particularly for Ca-O-Si.
7
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Fig. 8. Graphic representation of the simulated CaO-FeO-SiO2 slag structure. The colors for the structural representation are: yellow for [FeOx] polyhedra, blue for [SiO4] tetrahedra, red for O atoms and light blue for Ca atoms.
4. Conclusion
References
The combination of previously obtained experimental X-ray and neutron pair distribution functions with molecular dynamics simulations provided a more detailed description of the glassy structure of a synthetic non-ferrous metallurgy (CaO-FeO-SiO2) slag. The results from MD simulations are well consistent with the experimental PDF data. The analysis of the partial X-ray and neutron PDFs, CNs and bond angular distribution revealed structural characteristics that were impossible to discern experimentally. Fe is present mainly in 4- and 5-fold coordination in tetrahedral and pyramidal/triangular bipyramidal configuration, respectively. The [FeO4] units are predominantly connected by sharing corners while the [FeO5] polyhedra mostly share edges. The higher coordinated [FeOx] polyhedra (x = 5 or 6) are more prone to neighboring each other by sharing edges while [FeO4] tetrahedra are predominantly neighboring [SiO4] tetrahedra by sharing corners. The silicate network is polymerized with average
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments This work has been implemented within MSCA-ETN SOCRATES project that has received funding from the European Union's EU Framework Programme for Research and Innovation Horizon 2020, under Grant Agreement No 721385. Project website: http://etnsocrates.eu/. A. Peys is thankful to the Research Foundation – Flanders (FWO) for the FWO-SB scholarship.
Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jnoncrysol.2019.119771. 8
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