Relationship between Structure and Thermodynamic Properties in the CaO–SiO₂–BO_1.5 Slag System

Abstract

To understand the relationship between thermodynamic properties and structures in the CaO–SiO₂–BO_1.5 slag system, the thermodynamic properties of BO_1.5 and SiO₂ were measured by a chemical equilibrium technique and the local structures of boron(B) and silicon(Si) were investigated by ¹¹B and ²⁹Si magic angle spinning–nuclear magnetic resonance (MAS–NMR) measurements.Activity coefficients of BO_1.5 increased with an increase in the BO_1.5 content of the slag system. Activity coefficients of SiO₂ increased with increasing BO_1.5 content and decreased with increasing CaO/SiO₂ ratio.By using ¹¹B MAS–NMR, the existence of two types of B sites was confirmed—three- and four-coordinated B sites. The relative fraction of four-coordinated B increased with an increase in the BO_1.5 content and decreased with an increase in the CaO/SiO₂ ratio. ²⁹Si MAS–NMR results revealed that bridging oxygen bonding to Si atoms increased with an increase in the BO_1.5 content and decreased with decreasing CaO/SiO₂ ratio. The number of non-bridging oxygen atoms bonded to the tetrahedrally coordinated Si atom (NBO/T) was calculated using ²⁹Si and ¹¹B MAS–NMR under specific assumptions. By comparing NBO/Ts calculated from these two methods, the number of non-bridging oxygen atoms bonded to three-coordinated B in the studied composition region was estimated to be one.Finally, by comparing the thermodynamic properties with the results of MAS–NMR measurements, it was found that the composition dependences on BO_1.5 and SiO₂ activity coefficients were dependent on changes in the local structure of B and Si with composition.

1. Introduction

In the continuous casting of steel, mold flux plays important roles in producing lubrication between the mold and solidifying steel, and in controlling the heat transfer from the steel to mold. These functions of the mold flux are related to the defects on the surface of the products, such as oscillation marks and longitudinal cracks. Therefore, the composition of mold flux has been optimized to control its physical properties such as viscosity, thermal conductivity, and transmission. Boric oxide (B₂O₃) is an additive for controlling the physical properties of mold flux. It is used to decrease the viscosity and liquidus or crystallization temperature of mold flux. However, B₂O₃ in mold flux is reduced during reactions between the flux and molten steels by strong dioxide elements such as Al and Ti; moreover, the change in the flux composition is also significant. Because of such composition changes, mold flux cannot maintain its physical properties during continuous casting. To prevent this problem, fundamental information about the thermodynamic properties of mold flux, such as activity, activity coefficients, and their dependence on composition, is essential.

In the past, several researches have measured the thermodynamic properties of BO_1.5 in the CaO–SiO–BO_1.5 slag system. Teixeira et al.^1,2) investigated the thermodynamic properties of BO_1.5 at 1823 K in the CaO–SiO₂–BO_1.5 system in the low BO_1.5 content region (<0.25 mass% BO_1.5). Their results showed a strong dependence of CaO/SiO₂ ratio on the activity coefficient of BO_1.5 in the slag system. Sunkar et al.³⁾ also measured the thermodynamic properties of BO_1.5 in the CaO–SiO₂–BO_1.5 slag system in the high BO_1.5 content region (molar fraction of BO_1.5, X_BO1.5 > 0.2). Their results showed that the activity coefficient of BO_1.5 increased with increasing BO_1.5 content and was independent of the CaO/SiO₂ ratio in more acidic regions. They elucidated the thermodynamic behavior of BO_1.5 and its composition dependency in both low and high BO_1.5 content regions. However, the thermodynamic properties of BO_1.5 and its composition dependency in the low BO_1.5 content region (0.05 < X_BO1.5 < 0.2), which are required for designing mold flux composition, have not been clarified yet.

On the other hand, the composition dependency of the thermodynamic and physical properties of a slag system has an intensive relationship with the structure of molten slags. In particular, the local structure of boron(B) in molten slags changes so drastically with composition that these structural changes significantly affect the thermodynamic and physical properties. For example, the coordination number of oxygen atoms bonded to B in molten slags varies with chemical composition and this phenomenon influences the viscosity behavior of mold flux.⁴⁾ Teixeira et al. also explained the relationship between the thermodynamic properties and local structure of B on the basis of ¹¹B MAS–NMR measurements. They showed that a strong CaO/SiO₂ ratio dependency on the activity coefficient of BO_1.5 was related to changes in the local structure around B. However, such a relationship has not been understood in regions with a high BO_1.5 content.

In this study, the thermodynamic properties of BO_1.5 and SiO₂ in the low BO_1.5 content region have been measured by the chemical equilibration technique using a molten Cu–Si alloy. In addition, the local structures of B and silicon(Si) have been investigated by ¹¹B and ²⁹Si MAS–NMR measurements to understand the relationship between the thermodynamic properties and structure in the CaO–SiO₂–BO_1.5 slag system.

2. Experimental

2.1. Measurement of Thermodynamic Properties

The chemical equilibrium technique with the Cu–Si alloy as the reference metal was employed to measure the thermodynamic properties of BO_1.5 and SiO₂.

A MoSi₂ heating resistance furnace was used for this experiment. The temperature of this furnace was maintained at 1823 ± 1 K by using a Pt-6%Rh/Pt-30%Rh thermocouple. Slag samples were prepared from reagent-grade SiO₂, B₂O₃, and CaO, calcined from CaCO₃ in air. Two grams of mixed slag samples and 2.4 g of Cu-5 mass%Si (Cu-10.6 mol%Si) were inserted in a graphite crucible. Cu-5 mass% Si was preliminarily prepared by homogeneous melting in a graphite crucible under an Ar atmosphere at 1823 K for 30 min. The graphite crucible containing the slag and alloy was placed in the furnace hot zone for 18 h under CO atmosphere (P_CO = 1 atm). This equilibrated time of 18 h is referenced to the experiments of Sunkar et al.^3,5) The crucible was taken out from the furnace and was then quenched by flushing Ar gas on the Cu plate.

The BO_1.5 and CaO contents of the slag and the B content of the alloy were analyzed by inductively coupled plasma atomic emission spectroscopy (ICP-AES). The SiO₂ content of the slag and the Si content of the alloy were determined by the means of a gravimetric method.

The compositions of the slag and alloy after the experiments are listed in Table 1, along with the activities and activity coefficients of each component. The method of calculating the activities and activity coefficients is discussed in the Results section.

Table 1. Molar fraction of each component in the slag and metal after experiments, and the activities and activity coefficients of BO_1.5 and SiO₂ in the CaO–SiO₂–BO_1.5 slag system at 1823 K.

Number	Slag sample				Metal		Activity		Activity coefficient
	XBO1.5	XCaO	XSiO2	XCaO/XSiO2	XB	XSi	aBO1.5	aSiO2	aBO1.5	aSiO2
101	0.056	0.461	0.483	0.96	1.14 × 10–4	0.133	0.0025	0.485	0.044	1.01
102	0.108	0.445	0.446	1.00	2.38 × 10–4	0.137	0.0051	0.512	0.047	1.15
103	0.174	0.420	0.406	1.04	4.15 × 10–4	0.143	0.0086	0.552	0.050	1.36
104	0.225	0.394	0.381	1.03	6.41 × 10–4	0.152	0.0128	0.615	0.057	1.61
105	0.062	0.488	0.450	1.08	1.06 × 10–4	0.123	0.0024	0.425	0.039	0.94
106	0.104	0.475	0.421	1.13	2.30 × 10–4	0.127	0.0052	0.452	0.049	1.07
107	0.143	0.463	0.394	1.18	3.78 × 10–4	0.133	0.0082	0.486	0.058	1.24
108	0.196	0.455	0.349	1.30	6.08 × 10–4	0.142	0.0127	0.547	0.065	1.57
109	0.058	0.502	0.441	1.14	1.18 × 10–4	0.122	0.0027	0.421	0.047	0.95
110	0.103	0.488	0.409	1.19	2.29 × 10–4	0.127	0.0051	0.448	0.050	1.10
111	0.155	0.475	0.369	1.29	3.56 × 10–4	0.133	0.0077	0.490	0.050	1.33
112	0.192	0.467	0.341	1.37	5.13 × 10–4	0.137	0.0109	0.517	0.057	1.51
113	0.065	0.541	0.393	1.38	0.99 × 10–4	0.105	0.0024	0.329	0.037	0.84
114	0.108	0.532	0.360	1.48	2.02 × 10–4	0.118	0.0047	0.397	0.043	1.10
115	0.158	0.509	0.333	1.53	3.32 × 10–4	0.122	0.0076	0.419	0.048	1.26
116	0.201	0.492	0.307	1.60	5.54 × 10–4	0.130	0.0122	0.467	0.061	1.52
117	0.101	0.542	0.357	1.52	1.60 × 10–4	0.109	0.0039	0.347	0.038	0.97
118	0.165	0.511	0.324	1.58	4.31 × 10–4	0.111	0.0103	0.357	0.063	1.10
119	0.229	0.494	0.277	1.79	7.31 × 10–4	0.118	0.0107	0.398	0.074	1.44
120	0.302	0.464	0.234	1.98	1.17 × 10–3	0.134	0.0254	0.492	0.084	2.10

2.2. Structural Analysis

2.2.1. Sample Preparation

For ¹¹B MAS–NMR samples, reagent-grade SiO₂, B₂O₃, and CaO, calcined from CaCO₃ for 24 h at 1273 K in air, were used as raw materials. They were mixed and placed in a platinum crucible. The crucible was put in the MoSi₂ electrical furnace at 1823–1873 K (this temperature depended on the liquidus temperature of the samples.) for 1 h. To obtain a vitrified sample that can maintain its structure in the molten state, the samples were quenched by pouring into water. The composition of the samples used for ¹¹B MAS–NMR measurements is listed in Table 2.

Table 2. Composition of samples for structural analysis. Numbers in the parentheses indicate the number of the sample with a similar composition.

Sample number	Target nuclei for MAS–NMR	Composition (mol%)				CaO/SiO2 ratio	Optical basicity
		CaO	SiO2	BO1.5	FeO1.5
201	11B	38.7	56.2	5.1	–	0.69	0.604
202		45.5	49.5	5.0	–	0.92	0.633
203		43.1	46.9	10.1	–	0.92	0.621
204		40.7	44.3	15.1	–	0.92	0.610
205		38.2	41.7	20.1	–	0.92	0.599
206		35.9	39.0	25.1	–	0.92	0.588
207		50.7	44.3	5.0	–	1.15	0.657
208		48.1	41.9	10.0	–	1.15	0.644
209		45.5	39.6	14.9	–	1.15	0.632
210		42.8	37.3	20.0	–	1.15	0.619
211		40.1	35.0	24.9	–	1.15	0.606
212		55.0	40.0	5.0	–	1.38	0.678
213		53.3	37.0	9.7	–	1.44	0.669
214		49.3	35.8	14.9	–	1.38	0.650
215		46.4	33.7	19.9	–	1.38	0.636
216		43.6	31.6	24.9	–	1.38	0.622
217(202)	29Si	45.5	49.4	5.0	0.2	0.92	0.633
218(204)		40.6	44.1	15.1	0.2	0.92	0.611
219(206)		35.9	39.0	25.0	0.2	0.92	0.589
220(207)		50.7	44.1	5.0	0.2	1.15	0.658
221(209)		45.4	39.5	15.0	0.2	1.15	0.632
222(211)		40.1	34.8	25.0	0.2	1.15	0.607
223(212)		54.9	39.9	5.0	0.2	1.38	0.678
224(214)		49.3	35.7	14.9	0.2	1.38	0.650
225(216)		43.4	31.5	25.0	0.2	1.38	0.622

When ²⁹Si MAS–MAS measurements were performed for the samples described above, the spin-lattice relaxation time (T₁) was found to be extremely long (over 5 min). Therefore, for preparing samples for ²⁹Si MAS–NMR measurements, 0.2 mol% Fe₂O₃ was added to the samples to accelerate spin-lattice relaxation.⁶⁾ The procedure for sample preparation was the same as that for the ¹¹B MAS–NMR samples. The composition of the samples for ²⁹Si MAS–NMR measurements is also listed in Table 2. No appreciable change in the ²⁹Si MAS–NMR spectra was observed upon adding 0.2 mol% Fe₂O_3.

2.2.2. NMR Measurements

MAS–NMR spectra for ¹¹B and ²⁹Si were recorded on a JEOL ECA-500 (11.4 T) spectrometer. The Larmor frequencies for ¹¹B and ²⁹Si nuclei under the applied magnetic field were 160.4 and 99.4 MHz, respectively. The samples were inserted into a 4-mm ZrO₂ sample holder and were spun at 16 kHz. For the standards of ¹¹B and ²⁹Si MAS-NMR, a saturated H₃BO₃ solution (19.69 ppm) and 2,2,3,3-d(4)-3-(trimethylsilyl)propionic acid sodium salt (98%D) (1.445 ppm), respectively, were used. For ¹¹B MAS–NMR measurements, an RF pulse with less than one-third of the π/2 pulse length was employed to obtain more quantitative spectra.⁷⁾ More details on the conditions used in the NMR measurements are listed in Table 3.

Table 3. Conditions for MAS–NMR measurements.

Nuclear property	11B	29Si
Nuclear spin	3/2	1/2
Larmor frequency [MHz]	160.4	99.4
RF pulse intensity [kHz]	142	51
Reputation times	64–1024	1000–2000
Flip angle [rad]	π/6	π/2
Delay time [s]	5	10
Spinning rate [kHz]	16	16

3. Results and Discussion

3.1. Activities and Activity Coefficients of BO_1.5

The activities and activity coefficients of BO_1.5 have been calculated from the composition of the slag and metal phases in accordance with reactions (1)–(3) given below:   

$$\text{B(s)}+3/\text{2}\text{CO}(\text{g})={\text{BO}}_{\text{1}\text{.5}}(\text{l)}+3/\text{2}\text{C(s)}$$(1)

  

$$\mathrm{\Delta }{G}_{\text{1}}^{\text{0}}=-441\mathrm{\hspace{0.17em} }165+233.3\hspace{0.17em}T\hspace{0.17em}{(\text{J}/\text{mol})}^{}$$⁸⁾ (2)

  

$$K_1=\frac{a_{{\text{BO}}_{\text{1}\text{.5}}}\cdot a_{\text{C}}^{3/2}}{a_{\text{B}}\cdot P_{\text{CO}}^{3/2}}=\frac{{\gamma }_{{\text{BO}}_{\text{1}\text{.5}}}\cdot X_{{\text{BO}}_{\text{1}\text{.5}}}\cdot a_{\text{C}}^{3/2}}{{\gamma }_{\text{B}}\cdot X_{\text{B}}\cdot P_{\text{CO}}^{3/2}}$$(3)

Here, ΔG₁ and K₁ are Gibbs free energy change and the equilibrium constant for reaction(1), respectively; a_BO1.5 and γ_BO1.5 are the activity and activity coefficient of BO_1.5 in the slag phase in reference to the pure liquid state, respectively; a_B and γ_B are the activity and activity coefficient of B in the alloy in reference to the pure solid state, respectively. a_c is the activity of carbon in reference to the pure solid state and is unity in this experiment because of the presence of the carbon crucible. The value of γ_B at 1823 K was calculated from the reported values at 1873 K by assuming a regular solution model, as shown by Eq. (4).³⁾ The calculated activities and activity coefficients are listed in Table 2.   

$$ln{\gamma }_{\text{B}}=2.38-0.626X_{\text{Si}}-14.93X_{\text{Si}}^{\text{2}}\mathrm{\hspace{0.17em} }\text{(at 1 823 K)}$$(4)

The relationship between BO_1.5 activity and BO_1.5 content in the slag is shown in Fig. 1. The value of a_BO1.5 increases with an increase in the BO_1.5 content and negatively deviates from ideality.

Fig. 1.

Relationship between activities of BO_1.5 in the CaO–SiO₂–BO_1.5 slag system and molar fraction of BO_1.5 at 1823 K. The dotted line is for aid in understanding.

Figure 2 shows the relationship between the molar fraction of BO_1.5 and activity coefficients of BO_1.5 for the present experimental composition. The activity coefficients of BO_1.5 increase with an increase in the BO_1.5 content and are independent of the CaO/SiO₂ ratio. Increase in the BO_1.5 activity coefficients with an increase in the BO_1.5 content is attributed to increasing basicity because B₂O₃ is an acidic oxide. In addition, as mentioned in the Introduction, an increase in the BO_1.5 activity coefficient seems to be influenced by changes in the local structure around B. Therefore, the local structure of B in the same composition region was investigated by ¹¹B MAS–NMR measurements, and the relationship between the activity coefficients of BO_1.5 and the local structure of B was discussed.

Fig. 2.

Relationship between activity coefficients of BO_1.5 in the CaO–SiO₂–BO_1.5 slag system and molar fraction of BO_1.5 at 1823 K.

3.2. Activity and Activity Coefficients of SiO₂

The activities and activity coefficients of SiO₂ are calculated according to reaction(5) given below:   

$$\text{Si(l)}+2\hspace{0.17em}\text{CO}(\text{g})={\text{SiO}}_{\text{2}}(\text{s)}+2\text{C(s)}$$(5)

  

$$\mathrm{\Delta }{G}^0=-706\mathrm{\hspace{0.17em} }990+364.4T\hspace{0.17em}(\text{J}/\text{mol})$$⁸⁾ (6)

  

$$K_4=\frac{a_{{\text{SiO}}_{\text{2}}}\cdot a_{\text{C}}^2}{a_{\text{Si}}\cdot P_{\text{CO}}^2}=\frac{{\gamma }_{{\text{SiO}}_{\text{2}}}\cdot X_{{\text{SiO}}_{\text{2}}}\cdot a_{\text{C}}^2}{{\gamma }_{\text{Si}}\cdot X_{\text{Si}}\cdot P_{\text{CO}}^2}$$(7)

Here, a_SiO2 and γ_SiO2 are the activity and activity coefficient of SiO₂ in reference to the pure solid state, respectively. a_Si and γ_Si are the activity and activity coefficient of Si in reference to the pure liquid state, respectively. γ_Si at 1823 K was calculated from the excess Gibbs energy change of the binary Cu–Si melt, ΔG^ex, reported by Miki et al., as shown in Eq. (7).⁹⁾ To calculate γ_Si, the influence of B on γ_Si was ignored because the B content in Cu–Si was extremely low (below 0.001 in terms of molar fraction).   

$$\mathrm{\Delta }{G}^{\text{ex}}=X_{\text{Cu}}{X}_{\text{Si}}\left\{{}^{0}L+{}^{1}L(X_{\text{Cu}}-X_{\text{Si}})+{}^{2}L{(X_{\text{Cu}}-X_{\text{Si}})}^2\right\}$$(8)

  

$$\begin{array}{l}{}^{0}L=-38\mathrm{\hspace{0.17em} }463.5+5.63362T\\ {}^{1}L=-52\mathrm{\hspace{0.17em} }431.2+25.2386T\\ {}^{2}L=-29\mathrm{\hspace{0.17em} }426.5+14.6938T\end{array}$$⁹⁾ (9)

  

$$ln{\gamma }_{\text{Si}}=\frac{1}{RT}\left\{\mathrm{\Delta }{G}^{\text{ex}}+(1-X_{\text{Si}})\frac{\partial \mathrm{\Delta }{G}^{\text{ex}}}{\partial X_{\text{Si}}}\right\}$$(10)

The relationship between the activities of SiO₂ and molar fraction of BO_1.5 is shown in Fig. 3. The activities of SiO₂ were found to increase with increasing BO_1.5 content in the slag system, and found to decrease with increasing CaO/SiO₂ ratio. Because activities are influenced by the SiO₂ content, it is better to focus attention on the activity coefficients of SiO₂ to understand the effect of BO_1.5 addition on the thermodynamic properties of SiO₂. Figures 4 and 5 show the relationship between the activity coefficients of SiO₂ and the BO_1.5 content and the relationship between the activity coefficients of SiO₂ and the CaO/SiO₂ ratio, respectively. The activity coefficients of SiO₂ increased with an increase in the BO_1.5 content and decreased with an increase in the CaO/SiO₂ ratio.

Fig. 3.

Relationship between activities of SiO₂ in the CaO–SiO₂–BO_1.5 slag system and molar fraction of BO_1.5 at 1823 K.

Fig. 4.

Relationship between activity coefficients of SiO₂ in the CaO–SiO₂–BO_1.5 slag system and molar fraction of BO_1.5 at 1823 K.

Fig. 5.

Relationship between activity coefficients of SiO₂ in the CaO–SiO₂–BO_1.5 slag system and CaO/SiO₂ ratio at 1823 K.

3.3. Composition Dependence on Local Structure of B

Figure 6 shows the ¹¹B MAS–NMR spectra for samples with a CaO/SiO₂ ratio of 1.15. In all spectra, including those for samples with a CaO/SiO₂ ratio of 0.92 and 1.34, two peaks around 10 and 0 ppm were observed. According to the ¹¹B MAS–NMR results for the Na₂O–B₂O₃–SiO₂ system reported by Stebbins et al.,¹⁰⁾ the peaks at 10 and 0 ppm correspond to signals from ^[3]B and ^[4]B, respectively.

Fig. 6.

¹¹B MAS–NMR spectra for samples with a CaO/SiO₂ ratio of 1.15.

By deconvoluting the peaks and by comparing the peak areas, the relative fraction of each B species can be calculated. Figure 7 shows the relationship between the relative fraction of ^[4]B, N₄, and BO_1.5 content. N₄ increased with an increase in the BO_1.5 content at a constant CaO/SiO₂ ratio. On the other hand, N₄ decreased with an increase in the CaO/SiO₂ ratio.

Fig. 7.

Relationship between the relative fraction of ^[4]B and BO_1.5 content of samples.

3.4. Composition Dependence on Local Structure of Si

The ²⁹Si MAS–NMR spectra for samples no. 217–225 are shown in Fig. 8. In all spectra, the chemical shift of main peaks ranged from –60 to –100 ppm. Figure 9 shows the relationship between the peak position of ²⁹Si MAS–NMR spectra and the BO_1.5 content of the samples. The peaks shifted toward higher magnetic fields with increasing BO_1.5 content at a constant CaO/SiO₂ ratio. In addition, the peaks shifted to lower magnetic fields with increasing CaO/SiO₂ ratio at a constant BO_1.5 content.

Fig. 8.

²⁹Si MAS–NMR spectra for samples.

Fig. 9.

Relationship between chemical shifts of peaks in ²⁹Si MAS–NMR spectra and BO_1.5 content in the slag.

Table 4 lists the ²⁹Si MAS–NMR chemical shifts of Qⁿ (n: 1–3) in sodium, potassium, and calcium silicate binary glasses.^11,12) In these systems, the value of chemical shifts varies toward higher magnetic fields with an increase in the number of bridging oxygen atoms bonded to the Si atom. Therefore, in the studied CaO–SiO₂–BO_1.5 system, the number of bridging oxygen atoms bonded to the Si atom increases with increasing BO_1.5 content and decreases with increasing CaO/SiO₂ ratio.

Table 4. ²⁹Si MAS–NMR chemical shifts of Qⁿ (n: 1–3) in sodium, potassium, and calcium silicate binary glasses.^10,11)

	Na2O–SiO2	K2O–SiO2	CaO–SiO2
Q1	–69	–72	–74.6
Q2	–76	–80	–81.7
Q3	–89	–88	–90.4

4. Discussion

The local structures of B and Si will be first discussed in more detail. At the end of the discussion, the relationship between the local structure and thermodynamic properties for the studied slag system will be discussed.

4.1. Basicity Dependence of Local Structure of B

To comprehensively understand the BO_1.5 content dependence and CaO/SiO₂ ratio dependence on the local structure of B, the basicity dependence on the local structure of B was investigated. As a criterion for basicity, the theoretical optical basicity suggested by Duffy and Ingram was chosen.¹³⁾ The theoretical basicity can be calculated using Eq. (11).¹⁴⁾   

$${\text{Λ}}_{\text{th}}=\frac{\sum _i{X}_{\text{i}}\cdot {\text{n}}_{\text{i}}\cdot {\text{Λ}}_{\text{th},\text{i}}}{\sum _{\text{i}}{X}_{\text{i}}\cdot {\text{n}}_{\text{i}}}$$(11)

where Λ_th,i is the theoretical optical basicity of a pure subtance (CaO: 1, SiO₂: 0.48, and BO_1.5: 0.42).¹⁴⁾ The variable n_i represents the number of oxygen atoms in the molecule; for the present system, n_i is 1 for CaO, 2 for SiO₂, and 1.5 for BO_1.5.

Figure 10 shows the relationship between Λ_th and the fraction of ^[4]B, N₄. The reported N₄ values by Tanaka et al. for the CaO–SiO₂–B₂O₃ glass system are shown in Fig. 10.¹⁵⁾ N₄ values in the present study are in good agreement with the reported values. N₄ decreased with increasing Λ_th. The dependence of Λ_th on N₄ was independent of the CaO/SiO₂ ratio.

Fig. 10.

Relationship between the relative fraction of ^[4]B and theoretical optical basicity of samples.

In terms of the local structure of ^[4]B in borosilicate glass or a slag system, Dell et al.¹⁶⁾ suggested a structural model, in which the ^[4]B atoms are bonded to four bridging oxygen atoms connected to Si atoms. In addition, Duffy and Ingram showed the stability of the local structure of ^[3]B and ^[4]B at various optical basicities. On the basis of their results, the local structure of B changes with an increase in basicity as follows: ^[3]B with three, ^[4]B with four, ^[3]B with two, and ^[3]B with one bridging oxygen atom, and ^[3]B with three non-bridging oxygen atoms.

For the studied composition, N₄ decreases with an increase in basicity. From this result, an increase in basicity seems to result in the destruction of the ^[4]B structure; moreover, ^[3]B with two or one bridging oxygen atom is also created with an increase in basicity.

4.2. Influence of BO_1.5 on Local Structure of Si

At a constant CaO/SiO₂ ratio, as discussed in section 3.4, the number of bridging oxygen atoms increases with an increase in the BO_1.5 content. This phenomenon can be explained as follows. From the optical basicity of pure substances, BO_1.5 is more acidic than SiO₂ (optical basicities of pure BO_1.5 and SiO₂ are 0.42 and 0.48, respectively¹⁴⁾). This means that the B cation (B³⁺) attracts the O^2– ion more than the Si cation (Si⁴⁺) does. With increasing BO_1.5 content in the slag system, the non-bridging oxygen atom bonded to the Si atom is extracted by BO_1.5 and the number of bridging oxygen atoms bonded to the Si atom increases. In this case, two reactions can occur, depending on the number of oxygen atoms coordinated to the B atoms. In the case when B exists as ^[3]B, reaction(12) occurs upon increasing BO_1.5 content.   

$$\text{2}\hspace{0.17em}\text{(Si}-{\text{O}}^{-}\text{)}\hspace{0.17em}+{(}^{[3]}\text{B}-\text{O}-{}^{[3]}\text{B}\text{)}=\text{(Si}-\text{O}-\text{Si)}+2\hspace{0.17em}({}^{[3]}\text{B}-{\text{O}}^{-})$$(12)

In the case when B exists as ^[4]B, the non-bridging oxygen atom directly bonded to the Si atom coordinates to ^[3]B and makes it ^[4]B, as shown by Eq. (13).   

$$\text{(Si}-{\text{O}}^{-}\text{)}\hspace{0.17em}+( {}^{[3]}\text{B}\text{)}=\text{(Si}-\text{O}-{}^{[4]}\text{B}{}^{-}\text{)}$$(13)

On the other hand, as discussed in section 3.4, the number of bridging oxygen atoms bonded to the Si atom decreases with an increase in the CaO/SiO₂ ratio. This implies that the silicate network is broken with an increase in the CaO/SiO₂ ratio. This happens because with an increase in the CaO content, the modifying oxide of CaO breaks the silicate network, as shown by Eq. (14). This phenomenon is identical to that observed in a binary alkali or alkali silicate slag system.¹⁷⁾   

$$\text{(Si}-\text{O}-\text{Si)}+{\text{O}}^{2-}=\text{2}\hspace{0.17em}\text{(Si}-{\text{O}}^{-}\text{)}\hspace{0.17em}$$(14)

4.3. Basicity Dependence on Local Structure of Si

The optical basicity dependence on the local structure of Si was also investigated. The relative ratio of Qⁿ was calculated by deconvoluting the ²⁹Si MAS–NMR spectra. On the basis of the chemical shift values of CaSiO₃ glass reported by Zhang et al. (Table 4¹²⁾), the ²⁹Si MAS–NMR spectra for the samples have been deconvoluted using a Gaussian function. According to Martin et al., in the alkali borosilicate glasses system, the possible effect of Si–O–B bonds on the chemical shifts values of Qⁿ is negligible and affects those values by a few ppm at most.^18,19,20) Therefore, in this deconvolution of the ²⁹Si MAS–NMR spectra, the chemical shifts values of Qⁿ were assumed to be independent of the slag composition such as BO_1.5 content and CaO/SiO₂ ratio. The obtained relative ratios of Qⁿ from each peak area are listed in Table 5. The relationship between the optical basicity and relative ratio of Qⁿ is shown in Fig. 11. In the studied composition, Q¹ increases with an increase in the optical basicity. In the low basicity region, Q² increases with the optical basicity but then decreases when the optical basicity exceeds 0.63. Q³ and Q⁴ decrease with an increase in the optical basicity.

Table 5. Relative fraction of Qⁿ component and NBO/T (NBO/T_Si) values obtained from ²⁹Si MAS–NMR results for each sample.

Number	Relative fraction of Qn					NBO/TSi
	Q0	Q1	Q2	Q3	Q4
217	0.00	0.13	0.82	0.05	0.00	2.07
218	0.00	0.05	0.49	0.40	0.06	1.53
219	0.00	0.08	0.24	0.59	0.09	1.30
220	0.00	0.15	0.68	0.18	0.00	1.97
221	0.00	0.12	0.67	0.20	0.00	1.92
222	0.00	0.07	0.52	0.37	0.04	1.62
223	0.03	0.45	0.44	0.08	0.00	2.44
224	0.00	0.24	0.62	0.13	0.00	2.11
225	0.00	0.08	0.74	0.18	0.00	1.89

Fig. 11.

Relationship between the relative fraction of Qⁿ and theoretical optical basicity.

At the optical basicity of 0.63, the relative ratio of Q² becomes maximum. This optical basicity of 0.63 is close to the optical basicity of CaSiO₃ glass (Λ_th = 0.65). The local structure of Si in CaSiO₃ glass is thought to be Q². Therefore, in Fig. 11, it is quite reasonable that the relative ratio of Q² reaches the maximum value at around the optical basicity of 0.65.

4.4. Estimation of Number of Non-bridging Oxygen Atoms Bonded to Three-coordinated B, ^[3]B

On the basis of ¹¹B and ²⁹Si MAS–NMR results, the local structure of B will be discussed in more detail. The number of non-bridging oxygen atoms bonded to three-coordinated B, ^[3]B, can be estimated from ¹¹B and ²⁹Si MAS–NMR results.

By using the relative fraction of Qⁿ calculated from ²⁹Si MAS–NMR results, the number of non-bridging oxygen atoms bonded to the tetrahedrally coordinated Si atom (denoted here as NBO/T_Si) was calculated according to Eq. (15). The calculated NBO/T_Si values are listed in Table 5.   

$$\begin{array}{c}{\text{NBO}/\text{T}}_{\text{Si}}=\hfill \\ \text{4}-{\text{(}[\text{Q}}^{\text{0}}]\times \text{0}+[{\text{Q}}^{\text{1}}]\times \text{1}+[{\text{Q}}^{\text{2}}]\times \text{2}+[{\text{Q}}^{\text{3}}]\times \text{3}+[{\text{Q}}^{\text{4}}]\times \text{4)}\end{array}$$(15)

There is another method of calculating the NBO/T values by using ¹¹B MAS–NMR results. For this, some assumptions are needed. The first assumption is that in the slag system, CaO is completely ionized and O^2– ions are bonded to Si⁴⁺ and B³⁺. The second is that ^[4]B bonds only to the bridging oxygen atoms. The third assumption is that the non-bridging oxygen atoms are bonded to the ^[3]B or Si atom. Under these assumptions, NBO/T (denoted here as NBO/T_B) can be calculated from the ¹¹B MAS–NMR results by using Eq. (16).   

$${\text{NBO}/\text{T}}_{\text{B}}=\frac{\text{CaO}-\text{0}\text{.5}\cdot N_{\text{4}}\cdot {\text{BO}}_{\text{1}\text{.5}}-0.5\cdot i\cdot (1-N_4)\cdot {\text{BO}}_{\text{1}\text{.5}}}{{\text{SiO}}_{\text{2}}}$$(16)

where N₄ is the relative fraction of ^[4]B calculated from the ¹¹B MAS–NMR results; and i is the number of non-bridging oxygen atoms bonded to ^[3]B (i = 0–3). The calculated NBO/T_B values for each i value are listed in Table 6.

Table 6. NBO/T values calculated from ¹¹B MAS–NMR results. i denotes the number of non-bridging oxygen atoms bonded to three-coordinated B. Numbers in parentheses denote the sample number with a similar composition.

Number	NBO/TB
	i = 0	i = 1	i = 2	i = 3
217(202)	1.82	1.74	1.66	1.58
218(204)	1.74	1.50	1.26	1.03
219(206)	1.60	1.20	0.80	0.40
220(207)	2.29	2.19	2.09	1.99
221(209)	2.21	1.92	1.63	1.34
222(211)	2.06	1.58	1.11	0.63
223(212)	2.75	2.63	2.52	2.40
224(214)	2.70	2.34	1.98	1.62
225(216)	2.54	1.97	1.40	0.83

Figure 12 shows the relationship between the NBO/T_B and NBO/T_Si values for each sample according to i. In this figure, NBO/T_Si and NBO/T_B values should be the same because both of them denote the number of the non-bridging oxygen atoms bonded to the Si atom. Therefore, each plot should move along the dashed line, which implies that NBO/T_B is equal to NBO/T_Si. Among the four figures, the one in which the plot is almost near to or on the dotted line is the figure within which i is equal to one. Therefore, in the studied composition, a maximum of three coordinated B atoms were estimated to bond to one non-bridging oxygen atom and two bridging oxygen atoms.

Fig. 12.

Relationship between NBO/T values obtained from ¹¹B MAS–NMR results (NBO/T_B) and NBO/T values calculated from ²⁹Si MAS–NMR results (NBO/T_Si).

This estimated local structure of B is in good agreement with that discussed previously, i.e., ^[3]B with a non-bridging oxygen atom is created from the destruction of ^[3]B upon an increase in the basicity. The method for estimating the local structure of ^[3]B can be performed under several assumptions. Therefore, the possibility that the local structure of ^[3]B will change with composition cannot be denied. To understand the local structure of oxygen in more detail, other structural analysis methods such as ¹⁷O NMR would be needed.

4.5. Relationship between Activity Coefficient of BO_1.5 and Local Structure of B

Finally, the relationship between the local structure of B and thermodynamic properties of the studied slag system are discussed. The relationship between the activity coefficients of BO_1.5 and the relative fraction of ^[4]B was estimated as shown in Fig. 13. It was found that at similar CaO/SiO₂ ratios, the activity coefficients of BO_1.5 increase with an increase in the fraction of ^[4]B. The activity coefficient of BO_1.5 indicates the stability of B in the slag. An increase in the activity coefficients with an increase in the fraction of ^[4]B implies that B in the molten slag becomes more unstable. ^[4]B is more unstable than ^[3]B in this composition region. Dell suggested a structural model for B in the borosilicate glass system, in which ^[4]B atoms were coordinated to four bridging oxygen atoms.¹⁶⁾ On the other hand, as discussed in Section 4.4, ^[3]B mainly exists as ^[3]B bonded to two bridging oxygen atoms in the studied composition. By changing the structure from ^[3]B coordinated to two bridging oxygen atoms to ^[4]B, B becomes more unstable, resulting in an increase in the activity coefficients of BO_1.5.

Fig. 13.

Relationship between the fraction of four-coordinated B atoms to total B atoms, N₄ , and the BO_1.5 activity coefficients of samples.

4.6. Relationship between Thermodynamic Properties and Local Structure of Si

As shown in Fig. 4, the activity coefficients of SiO₂ increase with the BO_1.5 content. This composition dependence on the activity coefficients of SiO₂ can be explained as follows. As shown by ²⁹Si MAS–NMR results, the number of the bridging oxygen atoms bonded to the Si atom increases and the polymerization of the silicate network is promoted with an increase in the BO_1.5 content. This polymerization of the silicate network seems increase the energy level; thus, the addition of BO_1.5 increases the activity coefficient of SiO₂.

On the other hand, as shown in Fig. 5, the activity coefficients of SiO₂ decrease with an increase in the CaO/SiO₂ ratio. The ²⁹Si MAS–NMR results revealed that increasing CaO/SiO₂ ratio breaks down the silicate network and decreases the number of bridging oxygen atoms bonded to the Si atom. This structural change makes the Si atom more stable, so that the activity coefficients of SiO₂ decrease with an increase in the CaO/SiO₂ ratio.

In the studied slag system, the thermodynamic properties of SiO₂ are strongly dependent on the local structure of Si.

5. Conclusions

To understand the relationship between the thermodynamics properties and local structures in the CaO–SiO₂–BO_1.5 slag system, activities and activity coefficients of BO_1.5 and SiO₂ were measured by the chemical equilibrium technique. Moreover, the local structures of B and Si were estimated by MAS–NMR. The following conclusions were obtained.

The activity coefficients of BO_1.5 increase with an increase in the BO_1.5 content and are independent of the CaO/SiO₂ ratio. The activity coefficients of SiO₂ increase with an increase in the BO_1.5 content and decreases with an increase in the CaO/SiO₂ content.

The local structures of B and Si in the CaO–SiO₂–BO_1.5 slag system were estimated by ¹¹B and ²⁹Si MAS–NMR. The relative fraction of ^[4]B N₄, increased with an increase in the BO_1.5 content and decreased with an increase in the CaO/SiO₂ ratio. Moreover, N₄ decreased with an increase in the theoretical optical basicity. In the case of ²⁹Si MAS–NMR, it was found that the number of bridging oxygen atoms around the Si atom increased with an increase in the BO_1.5 content and decreased with decreasing CaO/SiO₂ ratio. From these results, it was found that depending on the coordination number of the oxygen ion, the reactions listed below occurred upon increasing the BO_1.5 content.

  

$$\text{2}\hspace{0.17em}\text{(Si}-{\text{O}}^{-}\text{)}\hspace{0.17em}+{(}^{[3]}\text{B}-\text{O}-{}^{[3]}\text{B}\text{)}=\text{(Si}-\text{O}-\text{Si)}+2\hspace{0.17em}({}^{[3]}\text{B}-{\text{O}}^{-})$$

  

$$\text{(Si}-{\text{O}}^{-}\text{)}\hspace{0.17em}+({}^{[3]}\text{B}\text{)}=\text{(Si}-\text{O}-{}^{[4]}\text{B}{}^{-}\text{)}$$

The number of the non-bridging oxygen atoms bonded to the tetrahedrally coordinated Si atom (NBO/T) was calculated by two methods—using ²⁹Si and ¹¹B MAS–NMR under specific assumptions. By comparing the NBO/T values calculated from these methods, the number of the non-bridging oxygen atoms around three-coordinated B in the studied composition region was estimated to be one.

Finally, the activity coefficients of BO_1.5 decreased with an increase in the fraction of four-coordinated B in the slag system. This implies that the thermodynamic properties of the slag system are dependent on the local structure of B in the system. The composition dependences on the activity coefficients of SiO₂ can be explained by changes in the local structure of Si, such as the number of the bridging oxygen atoms around Si.

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