Mechanism of Al Coordination Change in Alkaline-earth Aluminosilicate Glasses: An Application of Bond Valence Model

Abstract

Aluminum cations are generally present in four-fold (^[4]Al³⁺) or five-fold coordination (^[5]Al³⁺) in aluminosilicate slags, where the concentration of ^[5]Al³⁺ varies depending on the type of charge compensator, for example, Mg²⁺ and Ca²⁺. Although it has been reported that the amount of ^[5]Al³⁺ species increases with the replacement of CaO with MgO in the CaO–MgO–SiO₂–Al₂O₃ system, the detailed mechanism underlying the change in the local structure near the aluminum cations remains unclear. Because the residual negative charge on the bridging oxygen between ^[4]Si⁴⁺ and ^[5]Al³⁺ (^[4]Si⁴⁺–O_BO–^[5]Al³⁺) is larger than that of ^[4]Si⁴⁺–O_BO–^[4]Al³⁺, it is essential to understand the positive charge contributions of alkaline-earth cations to compensate for these negative charges on the bridging oxygens. In the present study, the valence of a single chemical bond near Mg²⁺ and Ca²⁺ cations in the chosen aluminosilicate glasses was determined using a simple empirical model, which enabled calculation of the bond valence from the observed interatomic distance of near alkaline-earth cations by synchrotron X-ray total scattering. Magnesium cations had a larger average bond valence (+0.39) than calcium cations (+0.31). The difference in the positive charge contribution from Mg²⁺ and Ca²⁺ should explain the variation in the coordination number of aluminum cations.

1. Introduction

Alkaline-earth oxides play an important role in controlling the physical properties of aluminosilicate melts, which have been used as slags and fluxes in metallurgical processes at elevated temperatures. For example, the additive effects of alkaline-earth oxides on the viscosity strongly depend on the type of alkaline-earth elements, having different ionic radii.^1,2,3,4) Viscosity measurements⁴⁾ undertaken in our previous study show that the viscosity of the 30 mol%CaO–15 mol%Al₂O₃–55 mol%SiO₂ (CAS) melt is higher than that of the 30 mol%MgO–15 mol%Al₂O₃–55 mol%SiO₂ (MAS) melt, which can be explained by the difference in the coordination number of the aluminum cations: aluminum cations in four-fold (^[4]Al³⁺) and five-fold coordination (^[5]Al³⁺) are present in both CAS and MAS glasses, whereas the fraction of ^[5]Al³⁺ in the MAS glass was higher than that of the CAS glass (see Table 1). However, it is unclear why the fraction of ^[5]Al³⁺ species increases when CaO is replaced with MgO in the aluminosilicate system. A previous ¹⁷O nuclear magnetic resonance study of calcium aluminosilicate glass with a similar composition verified that most aluminum cations share a bridging oxygen with silicon cations and do not tend to bond with non-bridging oxygens.⁵⁾ To understand the mechanism underlying the variation in the Al coordination, it is essential to consider the charge balance near bridging oxygens (BO) between silicon and aluminum cations (i.e., Si–O_BO–Al).

Table 1. Nominal composition, coordination number of aluminum, and density of chosen samples. The coordination number of aluminum cations was determined ²⁷Al MAS NMR spectroscopy in the previous study.⁴⁾

Sample	Nominal composition (mol%)				Fraction		Density [kg m−3]
	CaO	MgO	Al2O3	SiO2	[4]Al	[5]Al
CAS	30	–	15	55	97.3	2.7	2710
MAS	–	30	15	55	89.1	10.9	2650

According to the classical valence sum rule,⁶⁾ the valence of atom i (Z_i) is the total amount of charge used for bonding. When the coordination number of atom i is N_i, the average valence of a single chemical bond is represented by Z_i/N_i. Stebbins et al.⁷⁾ applied this concept to estimate the residual negative charge of bridging oxygen depending on the variations in the coordination number of aluminum cations in silicate glasses. When aluminum cations are in four-fold coordination, the residual charge on the Si–O_BO–Al bridging oxygen should be −1/4 because oxygen ions have a formal charge of −2 and the contributions from ^[4]Si⁴⁺ and ^[4]Al³⁺ are +4/4 and +3/4, respectively. In contrast, the Si–O_BO–Al bridging oxygen has a larger residual negative charge of −2/5 when the coordination number of the aluminum cation is five. This concept is schematically illustrated in Fig. 1. This estimation indicates that to maintain charge neutrality, BOs near ^[5]Al³⁺ require more positive charges from charge compensators (e.g., alkaline-earth cations) than those near ^[4]Al³⁺. The single bond valence near alkaline-earth cations should differ depending on the type of alkaline-earth cations, and thus, will influence the coordination number of aluminum cations. Local structures near alkaline-earth cations have been reported for oxide melts and glasses.^{8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)} These reports indicate that the coordination number of alkaline-earth cations varies depending on the parent glass compositions to which the alkaline-earth oxides are added. To estimate the bond valence near alkaline-earth cations, it is necessary to investigate the local structure near magnesium and calcium cations in the chosen aluminosilicate glasses. However, it has been reported that alkaline-earth cations are located in highly distorted sites,^12,21) and the direct determination of their coordination number in glasses is still a difficult challenge. Brown⁶⁾ proposed a “bond valence” calculation model that predicts the bond valence from the interatomic distance without using the coordination number of the cations. This model has been successfully used to understand the structure of inorganic compounds. In the present study, the ”bond valence” calculation model is applied to determine the bond valence near alkaline-earth cations in aluminosilicate glasses. Synchrotron X-ray total scattering is used to determine the interatomic distance between the alkaline-earth cations and oxygen.

Fig. 1.

Schematic of local structure near (a) ^[4]Si⁴⁺–O_BO–^[4]Al³⁺ and (b) ^[4]Si⁴⁺–O_BO–^[5]Al³⁺species. Numbers near O indicate residual negative charge on bridging oxygens.

2. Experimental

To investigate the interaction between the local structure near the alkaline-earth cations and negative charge on the Si–O_BO–Al bridging oxygen, it is essential to choose an appropriate sample composition. The molar content of alkaline-earth oxides should be sufficiently high to detect correlations between the alkaline-earth elements and oxygen atoms using synchrotron X-ray total scattering. Guignard and Cormier²⁰⁾ have characterized the Mg–O correlations in magnesium aluminosilicate glass using X-ray scattering. Their differential distribution functions indicated that the molar content of MgO should be higher than 25 mol% to facilitate characterization of the Mg–O correlation. In parallel, a high Al₂O₃ content is preferable for maximizing the fraction of Si–O_BO–Al bridging oxygen, whereas the formation of Al–O_BO–Al should be minimized. Theoretical and experimental studies^30,31,32,33) have indicated the formation of Al–O_BO–Al, which has a larger negative charge than Si–O_BO–Al in aluminosilicate glasses with a high Al/Si ratio. Allu et al.³⁴⁾ have proposed an aluminum avoidance parameter (AAP), described as follows:   

$$\mathrm{A}\mathrm{A}\mathrm{P}=\frac{4X_{{\text{Al}}_2{\text{O}}_3}}{2X_{{\text{SiO}}_2}-X_{\text{RO}}+X_{{\text{Al}}_2{\text{O}}_3}},$$(1)

where $X_{{\text{Al}}_2{\text{O}}_3}$, $X_{{\text{SiO}}_2}$, and X_RO are the molar fractions of Al₂O₃, SiO₂, and RO (R: Mg or Ca), respectively. When the AAP is less than 1, there are sufficient Si–O_BO– linkages to prevent the formation of Al–O_BO–Al bridges. The AAP model indicates that the molar content of Al₂O₃ should be lower than 22 mol% when the RO concentration is 30 mol%. Finally, the present study selected the 30 mol%RO–15 mol%Al₂O₃–55 mol%SiO₂ (R: Mg or Ca) composition as samples, as listed in Table 1. The CaO–Al₂O₃–SiO₂ and MgO–Al₂O₃–SiO₂ glass samples were labeled as CAS and MAS, respectively. These glasses were prepared using a conventional melt-quench method presented in a previous study⁴⁾ and were used for synchrotron X-ray total scattering experiments. Synchrotron X-ray total scattering measurement was performed at the BL04B2 beamline in SPring-8 (Japan) to determine the total correlation function T(r), which provides the interatomic distance. The glass samples in powder form were packed into a polyimide capillary tube with a diameter of 3 mm, and the scattering patterns of the glasses were measured using a horizontal two-axis diffractometer under a vacuum with an incident X-ray energy of 61.37 keV at room temperature. This high-energy X-ray enables measurement of the scattering patterns with a wave vector (q) as high as 260 nm⁻¹, which is sufficient for determining the interatomic distance in the glass samples accurately. To determine the Faber-Ziman structure factor (S(q)), scattering patterns were handled according to a previously established procedure.^35,36) In a scattering experiment on samples containing n chemical components, the total structure factor S(q) is represented by Eqs. (2), (3), (4):   

$$\begin{array}{l}S(q)=\\ 1+{\displaystyle \frac{1}{{\left|⟨\omega (q)⟩\right|}^2}}{\sum }_{\alpha =1}^n{\sum }_{\beta =1}^n{c}_{\alpha }{c}_{\beta }{\omega }_{\alpha }(q){\omega }_{\beta }(q)\left[S_{\alpha \beta }(q)-1\right],\end{array}$$(2)

  

$$⟨\omega (q)⟩={\sum }_i{c}_i{\omega }_i(q),$$(3)

  

$$q=\frac{4\pi sin\theta }{\lambda },$$(4)

where c_α and c_β are the atomic fractions of the chemical components α and β, respectively. ω_α(q) is a q-independent atomic form structure factor, λ is the X-ray wavelength, and 2θ is the scattering angle. To determine the interatomic distance between the two atoms, the total correlation function T(r) was obtained from Fourier-transform of the relations corresponding to Eqs. (5) and (6):   

$$T(r)=4\pi r{\rho }_{0}g(r)$$(5)

  

$$g(r)=1+\frac{1}{2{\pi }^2{\rho }_{0}r}{\int }_{q_{\text{min}}}^{q_{\text{max}}}q\left[S(q)-1\right]sin(qr)\mathrm{\hspace{0.17em} }dq,$$(6)

where ρ₀ [m⁻³] is the atomic number density calculated from the measured density [kg·m⁻³] of the glass samples, and g(r) represents the weighted sum of the partial functions. To determine the density of the samples, bubble-free bulk glass was synthesized using the conventional melt-quench method in the present study. The densities of these glass samples were measured using the Archimedean method with ethanol fluid at room temperature. The densities of these glasses are listed in Table 1.

3. Results and Discussion

Figure 2(a) shows the S(q) values of the MAS and CAS glasses. The T(r) values of the glasses were derived from S(q) using Eqs. (4) and (5), as shown in Fig. 2(b). The first four correlations for the MAS glass were assigned to (Si, Al)–O, Mg–O, O–O, and (Si, Al)–(Si, Al), respectively.⁹⁾ To investigate the interatomic distance between Mg and oxygen, the T(r) of the MAS glass was fitted to a Gaussian distribution (see Fig. 2(c)). The obtained interatomic distance of Mg–O has a broad distribution with an average value of 0.204 nm, which is in the range of previously reported values for magnesium silicate glasses and melts (0.198–0.221 nm).^17,20,24,28) In the T(r) of the CAS glass, precise determination of the Ca–O peak position was difficult because of its overlap with the O–O correlation. The linewidth of the O–O correlation for the MAS glass was 0.018 nm, which is in the range of the reported line width for the O–O correlation in calcium aluminosilicate glasses determined by reverse Monte Carlo (RMC) simulation.¹²⁾ Assuming that the line width of the O–O correlation for CAS glass is the same as that for MAS glass, the Gaussian fit of the T(r) of the CAS glass gives an average interatomic distance of Ca–O of 0.240 nm (see Fig. 2(d)). This value is close to the reported interatomic distance for calcium-containing silicate glasses (0.232–0.243 nm).^{9,12,18,26,37)} The compositions of the MAS and CAS glasses are in the peralkaline region, where the molar content of RO is higher than that of Al₂O₃. Hence, the positive charges of alkaline-earth cations are used to compensate for the negative charges of the Si–O_BO–Al bridging and non-bridging oxygen atoms (Si–O_NBO). Although it was difficult to extract the interatomic distance between alkaline-earth cations and Si–O_BO–Al BO (i.e., the lengths of Mg–O_BO and Ca–O_BO), an RMC study based on MAS glasses reported that the difference in lengths of Mg–O_NBO and Mg–O_BO is approximately 0.002 nm.²⁰⁾ This is much smaller than the difference between the average lengths of Mg–O and Ca–O (> 0.03 nm). It is reasonable to use the average interatomic distances of Mg–O and Ca–O to determine the bond valences of the alkaline-earth cations in the chosen glasses. Equation (7) shows the well-known empirical model⁶⁾ used to estimate the single bond valence:   

$$s_{i-j}=exp\left(\frac{r_0-10r}{0.37}\right),$$(7)

where s_i–j and r [nm] are the bond valence and length between atoms i and j, respectively. r₀ is the empirical bond valence parameter. Using the reported values for r₀ (Mg–O:1.693, Ca–O:1.967),³⁸⁾ the derived average bond valence of Mg²⁺ (s_Mg–O = 0.39) was larger than that of Ca²⁺ (s_Ca–O = 0.31). Although this is a rough estimate of the average bond valence near the alkaline-earth cations, it is clear that the magnesium cations have a larger bond valence, the value of which is close to the residual negative charge near the ^[4]Si⁴⁺–O_BO–^[5]Al³⁺ species (i.e., −2/5), as shown in Fig. 1. Ca²⁺ provides a smaller positive charge contribution, which is relatively close to the residual negative charge on the ^[4]Si⁴⁺–O_BO–^[4]Al³⁺ species (i.e., −1/4). The differences in the bond valences between the calcium and magnesium cations should explain the mechanism underlying the differences in the local structure near the aluminum cations when CaO is replaced with MgO in aluminosilicate glasses: MgO-containing systems tend to have a higher concentration of ^[5]Al³⁺ species than CaO-containing systems.

Fig. 2.

(a) S(q) and (b) T(r) of the MAS and CAS glasses. Results of Gaussian fit for (c) MAS and (d) CAS glasses. (Online version in color.)

4. Conclusions

A simple empirical model was applied to estimate the valence of a single chemical bond near alkaline-earth cations. Because this model requires the interatomic distance for the target chemical bond, the interatomic distance between alkaline-earth cations and oxygen is characterized using the synchrotron X-ray total scattering of the chosen aluminosilicate glasses. The observed average bond lengths of Mg–O and Ca–O are 0.204 and 0.240 nm, respectively. The empirical bond valence model indicates that magnesium cations have a higher bond valence than calcium cations. The coordination number of aluminum cations should be a variable parameter to maintain the charge neutrality near Si–O_BO–Al. When CaO is replaced with MgO in aluminosilicate glasses, the coordination number of aluminum cations should increase to increase the residual negative charge on Si–O_BO–Al. The variation in Al coordination plays an essential role in accommodating non-framework cations with a high bond valence (e.g., Mg²⁺) in aluminosilicate glasses.

Acknowledgments

The synchrotron X-ray total scattering experiments were performed at the BL04B2 beamline at SPring-8 with the approval of JASRI (Proposal No. 2017B1400). This work was supported in part by Institute of Multidisciplinary Research for Advanced Materials (IMRAM) Project (2022–2023), and the Dynamic Alliance for Open Innovation Bridging of Human, Environment, and Materials from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (MEXT). We appreciate Dr. Kyung-Ho Kim for the sample synthesis. We would also like to thank the two anonymous reviewers and the managing editor for their constructive comments that improved this manuscript.

References

• 1)   G.  Urbain,  Y.  Bottinga and  P.  Richet: Geochim. Cosmochim. Acta, 46 (1982), 1061. https://doi.org/10.1016/0016-7037(82)90059-X
• 2)   S.  Sukenaga,  N.  Saito,  K.  Kawakami and  K.  Nakashima: ISIJ Int., 46 (2006), 352. https://doi.org/10.2355/isijinternational.46.352
• 3)   Z.  Wang and  I.  Sohn: J. Am. Ceram. Soc., 101 (2018), 4285. https://doi.org/10.1111/jace.15559
• 4)   K.-H.  Kim,  S.  Sukenaga,  M.  Tashiro,  K.  Kanehashi,  S.  Yoshida and  H.  Shibata: J. Non-Cryst. Solids, 587 (2022), 121600. https://doi.org/10.1016/j.jnoncrysol.2022.121600
• 5)   S.  Sukenaga,  P.  Florian,  K.  Kanehashi,  H.  Shibata,  N.  Saito,  K.  Nakashima and  D.  Massiot: J. Phys. Chem. Lett., 8 (2017), 2274. https://doi.org/10.1021/acs.jpclett.7b00465
• 6)   I. D.  Brown: The Chemical Bond in Inorganic Chemistry: The Bond Valence Model, Oxford University Press, Oxford, UK, (2016), 41.
• 7)   J. F.  Stebbins,  J.  Wu and  L. M.  Thompson: Chem. Geol., 346 (2013), 34. https://doi.org/10.1016/j.chemgeo.2012.09.021
• 8)   Y.  Waseda and  J. M.  Toguri: Metall. Trans. B, 8 (1977), 563. https://doi.org/10.1007/BF02669331
• 9)   M.  Okuno and  F.  Marumo: Mineral. J., 16 (1993), 407. https://doi.org/10.2465/minerj.16.407
• 10)   P. S.  Fiske and  J. F.  Stebbins: Am. Mineral., 79 (1994), 848.
• 11)   A. M.  George and  J. F.  Stebbins: Am. Mineral., 83 (1998), 1022. https://doi.org/10.2138/am-1998-9-1010
• 12)   L.  Cormier,  D. R.  Neuville and  G.  Calas: J. Non-Cryst. Solids, 274 (2000), 110. https://doi.org/10.1016/S0022-3093(00)00209-X
• 13)   S.  Kroeker and  J. F.  Stebbins: Am. Mineral., 85 (2000), 1459. https://doi.org/10.2138/am-2000-1015
• 14)   L.  Cormier and  D. R.  Neuville: Chem. Geol., 213 (2004), 103. https://doi.org/10.1016/j.chemgeo.2004.08.049
• 15)   S.  Kohara,  K.  Suzuya,  K.  Takeuchi,  C.-K.  Loong,  M.  Grimsditch,  J. K. R.  Weber,  J. A.  Tangeman and  T. S.  Key: Science, 303 (2004), 1649. https://doi.org/10.1126/science.1095047
• 16)   D. R.  Neuville,  L.  Cormier,  A.-M.  Flank,  V.  Briois and  D.  Massiot: Chem. Geol., 213 (2004), 153. https://doi.org/10.1016/j.chemgeo.2004.08.039
• 17)   M. C.  Wilding,  C. J.  Benmore,  J. A.  Tangeman and  S.  Sampath: Europhys. Lett., 67 (2004), 212. https://doi.org/10.1209/epl/i2003-10286-8
• 18)   K.  Shimoda and  K.  Saito: ISIJ Int., 47 (2007), 1275. https://doi.org/10.2355/isijinternational.47.1275
• 19)   K.  Shimoda,  Y.  Tobu,  M.  Hatakeyama,  T.  Nemoto and  K.  Saito: Am. Mineral., 92 (2007), 695. https://doi.org/10.2138/am.2007.2535
• 20)   M.  Guignard and  L.  Cormier: Chem. Geol., 256 (2008), 111. https://doi.org/10.1016/j.chemgeo.2008.06.008
• 21)   K.  Shimoda,  T.  Nemoto and  K.  Saito: J. Phys. Chem. B, 112 (2008), 6747. https://doi.org/10.1021/jp711417t
• 22)   K.  Shimoda,  Y.  Tobu,  K.  Kanehashi,  T.  Nemoto and  K.  Saito: J. Non-Cryst. Solids, 354 (2008), 1036. https://doi.org/10.1016/j.jnoncrysol.2007.08.010
• 23)   N.  Trcera,  D.  Cabaret,  S.  Rossano,  F.  Farges,  A.-M.  Flank and  P.  Lagarde: Phys. Chem. Miner., 36 (2009), 241. https://doi.org/10.1007/s00269-008-0273-z
• 24)   L.  Cormier and  G. J.  Cuello: Phys. Rev. B, 83 (2011), 224204. https://doi.org/10.1103/PhysRevB.83.224204
• 25)   S.  Kohara,  J.  Akola,  H.  Morita,  K.  Suzuya,  J. K. R.  Weber,  M. C.  Wilding and  C. J.  Benmore: Proc. Natl. Acad. Sci. U.S.A., 108 (2011), 14780. https://doi.org/10.1073/pnas.1104692108
• 26)   L.  Hennet,  J. W. E.  Drewitt,  D. R.  Neuville,  V.  Cristiglio,  J.  Kozaily,  S.  Brassamin,  D.  Zanghi and  H. E.  Fischer: J. Non-Cryst. Solids, 451 (2016), 89. https://doi.org/10.1016/j.jnoncrysol.2016.05.018
• 27)   N.  Bisbrouck,  M.  Bertani,  F.  Angeli,  T.  Charpentier,  D.  de Ligny,  J.-M.  Delaye,  S.  Gin and  M.  Micoulaut: J. Am. Ceram. Soc., 104 (2021), 4518. https://doi.org/10.1111/jace.17876
• 28)   K.  Gong,  V. O.  Özçelik,  K.  Yang and  C. E.  White: Phys. Rev. Mater., 5 (2021), 015603. https://doi.org/10.1103/PhysRevMaterials.5.015603
• 29)   M. I.  Tuheen and  J.  Du: Int. J. Appl. Glass Sci., 13 (2022), 554. https://doi.org/10.1111/ijag.16599
• 30)   S.  Siwadamrongpong,  M.  Koide and  K.  Matusita: J. Ceram. Soc. Jpn., 112 (2004), 590. https://doi.org/10.2109/jcersj.112.590
• 31)   S. K.  Lee and  J. F.  Stebbins: Am. Mineral., 84 (1999), 937. https://doi.org/10.2138/am-1999-5-631
• 32)   B.  Mysen: ISIJ Int., 61 (2021), 2866. https://doi.org/10.2355/isijinternational.ISIJINT-2021-100
• 33)   P.  Florian,  A.  Novikov,  J. W. E.  Drewitt,  L.  Hennet,  V.  Sarou-Kanian,  D.  Massiot,  H. E.  Fischer and  D. R.  Neuville: Phys. Chem. Chem. Phys., 20 (2018), 27865. https://doi.org/10.1039/C8CP04908D
• 34)   A. R.  Allu,  A.  Gaddam,  S.  Ganisetti,  S.  Balaji,  R.  Siegel,  G. C.  Mather,  M.  Fabian,  M. J.  Pascual,  N.  Ditaranto,  W.  Milius,  J.  Senker,  D. A.  Agarkov,  V. V.  Kharton and  J. M. F.  Ferreira: J. Phys. Chem. B, 122 (2018), 4737. https://doi.org/10.1021/acs.jpcb.8b01811
• 35)   K.  Ohara,  Y.  Onodera,  M.  Murakami and  S.  Kohara: J. Phys. Condens. Matter, 33 (2021), 383001. https://doi.org/10.1088/1361-648X/ac0193
• 36)   S.  Sukenaga,  T.  Endo,  T.  Nishi,  H.  Yamada,  K.  Ohara,  T.  Wakihara,  K.  Inoue,  S.  Kawanishi,  H.  Ohta and  H.  Shibata: Front. Mater., 8 (2021), 753746. https://doi.org/10.3389/fmats.2021.753746
• 37)   C. D.  Yin,  M.  Okuno,  H.  Morikawa,  F.  Marumo and  T.  Yamanaka: J. Non-Cryst. Solids, 80 (1986), 167. https://doi.org/10.1016/0022-3093(86)90391-1
• 38)   I. D.  Brown and  D.  Altermatt: Acta Crystallogr. B, 41 (1985), 244. https://doi.org/10.1107/S0108768185002063