Experimental Investigation and Molecular Dynamics Modeling of the Effects of K₂O on the Structure and Viscosity of SiO₂-CaO-Al₂O₃-MgO-K₂O Slags at High Temperatures

Abstract

Variations in slag properties critically influence smelting operations and product quality. The effects of K₂O on the CaO-SiO₂-MgO-Al₂O₃-K₂O slag system at 1823 K were systematically analyzed through an integrated approach combining viscosity measurements, FTIR spectroscopy, and molecular dynamics simulations. The results revealed a rapid 52% decrease in slag viscosity and an 18.32 kJ/mol reduction in activation energy as K₂O content increased from 0% to 3%. K₂O releases O²⁻ ions that depolymerize Si-O network structures. Within the 3% to 5% range, structural network formation is promoted by the K₂O-SiO₂ reaction, resulting in increased slag viscosity and elevated activation energy. Molecular dynamics simulations elucidate the depolymerization of complex Si-O networks, accompanied by a proliferation of smaller [AlO₄] tetrahedral fragments. The diminished Si-O-Si bridging oxygen (BO) bonds contrast with the enhanced increase in Si-O-K non-bridging oxygen (NBO) linkages. When K₂O exceeds 3%, the diffusion capacity of K atoms becomes constrained as K₂O participates in structural network assembly, a phenomenon validated by FTIR spectroscopic analysis. Elevated K₂O concentrations enhance slag network polymerization, leading to increased viscosity. Therefore, the precise control of K₂O content is critical during smelting operations and by-product manufacturing (e.g., glass or mineral wool) to optimize material performance. These findings provide theoretical support for controlling the alkali metal content during the actual metallurgical process and thus further optimizing blast furnace operation.

1. Introduction

Slag is a critical component in ironmaking composed primarily of ore gangue, fuel ash, flux, and reaction products. Its major chemical constituents include SiO₂ (35–45%), CaO (33–45%), Al₂O₃ (8–17%), MgO (5–10%), and alkali metals (K₂O, Na₂O). Although typically present in trace amounts, alkali metals accumulate under high-temperature conditions in blast furnaces, converters, and gasifiers, altering slag viscosity, reactivity, and structure [1]. Slag also functions as a secondary resource for manufacturing mineral wool, glass, cement, and floor tiles, driving substantial research interest in slag systems [2]. Slag consists predominantly of silicates, with compositional variations exerting pronounced effects on both smelting operations and glass/cement production, particularly in the presence of Na₂O and K₂O. The effects of Na₂O presence on slag, mineral wool, glass, and other molten systems have been systematically established, with physicochemical property modification enhancing smelting efficiency and product quality. In mineral wool and glass production systems, Na₂O functions as both a fluxing agent and modifier, demonstrating measurable enhancements in material performance and industrial applicability [3,4,5,6,7,8,9]. The presence of K₂O in silicate systems remains controversial. Some studies suggest that K₂O reduces viscosity and fluidity by forming low-melting phases, whereas others argue it increases viscosity and the slag network polymerization degree, thereby enhancing system stability [10,11]. These variations are not only related to changes in the composition of the molten slag system but also associated with K₂O content and temperature [12,13,14,15]. Current investigations on K₂O in silicate systems remain predominantly conducted as either experimental investigations or computational modeling approaches, with notably limited studies implementing combined methodologies with cross-verification mechanisms [16,17,18]. Therefore, integrating modeling and experimental approaches to investigate K₂O effects on molten slag systems enables the microstructural elucidation of network modifications while providing experimentally validated findings with enhanced technical credibility and industrial applicability.

Microstructural transformations directly govern macroscopic property alterations in slag systems. Viscosity, as a critical parameter of molten slag, exhibits acute sensitivity to compositional and structural variations, as such constituting a primary research focus. K₂O demonstrates multifaceted influence on viscosity and flow characteristics within silicate-based slag systems. Higo et al. revealed that silicate slag viscosity increases with K₂O content at K₂O/Al₂O₃ molar ratios below 0.7, attributed to K₂O-induced [AlO₄] tetrahedral formation and elevated oxygen ion concentrations [19]. Conversely, viscosity decreases with further K₂O additions beyond this threshold due to network structure depolymerization by excess K₂O, enhancing flowability. Kim et al. demonstrated that at elevated temperatures (e.g., 1773 K), K₂O additions increase silicate slag viscosity, whereas Na₂O typically induces viscosity reduction, exhibiting contrasting effects [20]. Liu et al. reported that Na₂O exhibits a more pronounced effect in reducing the viscosity of silicate slags compared to K₂O, with further reduction in slag viscosity occurring upon the substitution of K₂O with Na₂O [21]. He et al. proposed that SiO₂ reacts with Na₂O to reduce the activity of potassium and calcium, thereby increasing slag viscosity—an effect particularly evident in slags with high silicon content [22]. Xing et al. established that precise K₂O regulation is critical for optimizing slag fluidity and viscosity. Reducing K₂O content lowers slag viscosity, thereby improving operational efficiency [23]. K₂O supplies free oxygen ions, which disrupt Si-O-Si bonds in silicate networks, effectively reducing flow activation energy. As an alkaline oxide, K₂O disrupts silicate network structures in slag systems. Within Mg-Al-Si-Ca containing slags, K₂O reacts with SiO₂ to generate non-bridging oxygen (NBO), reducing the polymerization degree through structural loosening, consequently decreasing viscosity [15,24,25,26,27]. Adjusting K₂O content can effectively regulate slag fluidity and reactivity, enhancing smelting efficiency and product quality. K₂O exerts dual effects on the viscosity and fluidity of silicate slag systems, with the specific outcomes depending on its concentration, temperature, and interactions with other components. The composition of coke, a key raw material in the smelting process, influences slag composition through the direct input of ash oxides. Coke ash (typically 10–20 wt.%) is rich in acidic oxides (SiO₂, Al₂O₃) and minor basic oxides (CaO, MgO, K₂O/Na₂O), serving as a primary slag source. Ash from low-rank coal or low-quality coke may contain 1–5 wt.% K₂O/Na₂O. The entry of these alkali metals into the slag may affect its composition and properties [28]. These ash-derived components collectively impact slag composition, influencing properties such as viscosity and reactivity. This study aims to investigate the single-variable effect of K₂O (0–5 wt.%) on slag by controlling the use of external high-alkali metal coke in the smelting process.

In metallurgy, metallurgical slags play a critical role in ironmaking and steelmaking processes, including desulfurization, dephosphorization, the protection of metal melts, and the regulation of heat and mass transfer. These functions are closely linked to slag properties such as viscosity and fluidity. Additionally, slag fluidity influences blast furnace operation and refractory erosion. K₂O accumulates in blast furnaces, affecting slag properties, thus underscoring the necessity of studying K₂O’s effects on slag properties [1]. This study employs rotational viscometry to investigate the viscosity of CaO-SiO₂-MgO-Al₂O₃-K₂O slag systems with a controlled CaO/SiO₂ mass ratio of 1.32. Molecular dynamics simulations employing SCIGRESS software (Version Number: FJ 2.8.1) systematically characterized the network structures, polymerization degrees, atomic diffusivity, and bridging/non-bridging oxygen (BO/NBO) evolution within the slag system with controlled thermal gradients. FTIR spectroscopy was employed to perform qualitative analysis of the structural evolution in quenched slag at 1823 K, aiming to investigate the effects of K₂O on Si and Al structural units. This study not only validated the consistency between the simulation and experimental results, thereby enhancing persuasiveness, but also deepened the understanding of K₂O’s effects on slag viscosity and structure. It provides theoretical and technical support for applications of K₂O-containing slag systems. This study integrates interdisciplinary methods to overcome the limitations of single approaches in understanding the complex mechanisms of K₂O action, providing direct technical parameters for metallurgical slag process optimization (e.g., changes in slag viscosity due to changes in K₂O content) and new analytical dimensions for fundamental research on multicomponent silicate systems. It advances precision regulation research linking microstructural features to macroscale properties to new heights.

2. Experimental Part

2.1. Slag Sample Preparation

The selected slag system for the experiment was CaO-SiO₂-MgO-Al₂O₃-K₂O. Slag samples were prepared using analytical-grade reagents (purity ≥ 99 wt%) of CaO, SiO₂, Al₂O₃, MgO, and K₂O at a fixed basicity CaO/SiO₂ = 1.32 (Shanghai Macklin Biochemical Technology Co., Ltd., Shanghai, China). The compositional variations are summarized in

Table 1. Chemical composition design of slag (wt/%).

No.	CaO	SiO2	MgO	Al2O3	K2O	R
1	42.63	32.29	10	15	0	1.32
2	41.79	31.66	10	15	1	1.32
3	41.53	31.46	10	15	2	1.32
4	40.68	30.99	10	15	3	1.32
5	39.79	30.14	10	15	5	1.32

. This study employs a binary basicity definition, calculated as the mass fraction ratio of the basic oxide (CaO) to the acidic oxide (SiO₂): R = w(CaO)/w(SiO₂). Although the slag system contains MgO (basic oxide) and Al₂O₃ (amphoteric oxide), a simplified binary basicity was chosen to highlight the fundamental properties of the CaO-SiO₂-based slag. MgO content was fixed at 10 wt.% as a background parameter (not included in the basicity formula), while Al₂O₃ (15 wt.%, fixed) served as a supplementary acidic component to control variables and focus on the structural effects of K₂O. A 200 g sample was weighed and thoroughly ground/mixed in an agate mortar. An 80 g portion of the homogenized sample was placed into a graphite crucible and heated to 1823 K in a high-temperature furnace under argon gas protection. After 2 h of isothermal holding, the crucible was rapidly removed and quenched in cold water. The quenched samples were subjected to tests such as XRD and FTIR spectroscopy for the qualitative analysis of the slag structure. The remaining 120 g of the samples was used for viscosity tests.

2.2. Molecular Dynamics Simulation

Molecular dynamics simulation is commonly used for simulating the network structures of metallurgical slag and silicate systems, based on the Born–Mayer–Huggins (BMH) potential function as shown in Equation (1) [29,30,31,32,33,34]:

E = Aij*exp(−Bij*r) − Cij/r**6 − Dij/r**8

(1)

In Equation (1), E represents the interatomic pair potential between atomic types i and j at distance r. The first term denotes the repulsive interaction, while the second and third terms correspond to van der Waals forces, with potential parameters tabulated in

Table 2. Numerical value of BMH potential function parameters.

Ionic	Ionic	Aij	Bij	Cij	Dij
K	K	5.0665 × 10−20	6.25	1.5632 × 10−25	0
K	Ca	1.6346 × 10−20	6.25	1.0421 × 10−25	0
Ca	Ca	5.2737 × 10−22	6.25	6.9467 × 10−26	0
Mg	K	3.3626 × 10−21	6.25	2.0843 × 10−26	0
Mg	Ca	1.0849 × 10−21	6.25	1.3895 × 10−26	0
Si	K	1.3251 × 10−21	6.25	0	0
Mg	Mg	2.2318 × 10−22	6.25	2.7791 × 10−27	0
Si	Ca	4.2751 × 10−22	6.25	0	0
Al	K	1.8339 × 10−21	6.25	0	0
Mg	Si	8.7947 × 10−23	6.25	0	0
Al	Ca	5.9169 × 10−20	6.25	0	0
Si	Si	3.4656 × 10−23	6.25	0	0
O	K	3.4457 × 10−20	6.06	2.0843 × 10−25	0
Mg	Al	1.2172 × 10−22	6.25	0	0
O	Ca	1.1505 × 10−20	6.06	1.38950 × 10−25	0
Al	Si	4.7966 × 10−23	6.25	0	0
O	Mg	2.4829 × 10−21	6.06	2.7791 × 10−26	0
Al	Al	6.3869 × 10−23	6.25	0	0
O	Si	1.0064 × 10−21	6.06	0	0
O	Al	1.3792 × 10−21	6.06	0	0
O	O	2.3993 × 10−20	5.88	2.7791 × 10−21	0

. The simulation system was set up as a cubic box with three-dimensional periodic boundary conditions. A total of 6000 particles were included in the simulation, with the number of particles for each element calculated based on their molar ratios.

Table 3. Simulated particle number and box side length.

No.	Particle Count						Box Side Length/A	Density
	Si	Al	Ca	K	Mg	O
1	802	464	1074	0	287	3374	42.291	3.052
2	793	465	1061	34	288	3360	42.353	3.047
3	783	465	1049	67	288	3347	42.416	3.041
4	774	466	1036	101	289	3334	42.484	3.035
5	754	467	1010	172	291	3306	42.614	3.024

lists the atomic numbers, box edge length, and density of the simulation system. The calculations were performed using the SCIGRESS FJ 2.8.1 (Large-scale Atomic/Molecular Massively Parallel Simulator) package, with the BMH potential function implemented via user-defined pair coefficients (Table 2). The simulation employed the NVT ensemble with the Gear algorithm for trajectory integration [35]. The temperature profile over time is shown in Figure 1. It is a temperature control curve that varies with the time step. First, a random model was generated at 5000 K over 10,000 fs. Then, it was cooled to the target temperature of 1823 K in the next 10,000 fs. Finally, the slag structure at 1823 K was obtained after another 10,000 fs. The radial distribution function and coordination number were calculated using the last 1000 fs trajectory for analyzing the slag network structure. The simulation employed a time step of 1 fs for trajectory integration in the NVT ensemble, maintaining constant temperature using a Nosé–Hoover thermostat. Post-simulation analysis for radial distribution functions and coordination numbers utilized in-house Python (version number 2.7) scripts leveraging the MD Analysis library to process trajectory data from the final equilibrium state.

2.3. Viscosity Test

The slag viscosity was measured via the rotational method, with the experimental setup illustrated in Figure 2. First, 120 g of pre-melted slag was placed into crucible and positioned in the constant temperature zone of a resistance furnace. The sample was heated to 1823 K in an argon atmosphere and held for 30 min. A molybdenum rotor was then immersed into the slag, with its lower end positioned approximately 10 mm above the crucible bottom and suspended within the crucible. The graphite crucible dimensions were Φ30 × 75 mm (inner diameter × height), and the molybdenum rotor dimensions were Φ15 × 20 mm (outer diameter × height). Viscosity measurements commenced once stable temperature and viscosity values were achieved. Three replicate measurements were taken per test group and averaged. Prior to each measurement, calibration was performed using standard castor oil.

2.4. Slag Structural Analysis

XRD measurements were performed using a Bruker D8 Advance diffractometer (Bruker, Billerica, MA, USA) with Cu Kα radiation (40 kV, 40 mA), a scanning range of 10–90° (2θ), and a step size of 0.02°. XRD was used to verify the amorphous state of all samples. Analysis using the PDF-5+ database and high-precision algorithms in JADE (version number 6.5) software ensured result reliability. FTIR spectroscopy was applied to analyze the structural characteristics of molten slags by identifying the vibration modes of functional groups (e.g., Si-O and Al-O bonds), enabling insights into the degree of polymerization and network connectivity in slag systems. FTIR spectroscopy was employed to analyze the structural evolution of the slag and corroborate the results of molecular dynamics simulations. Infrared spectroscopy (model: Thermo Fisher iS50, Waltham, MA, USA) was performed by homogenously grinding 2.0 mg of sample with 200 mg KBr in an agate mortar, followed by compressing the mixture into flakes. A wavenumber range of 400–4000 cm⁻¹ was selected (with analysis focused on 400–1200 cm⁻¹) with the aim of qualitatively analyzing structural changes in [SiO₄] and [AlO₄] groups [36].

3. Results and Discussion

3.1. XRD Analysis

Figure 3 shows the XRD patterns of the samples. Broad diffuse peaks (2θ ≈ 20°–35°) are a characteristic feature of the “short-range order, long-range disorder” structure in silicates, directly confirming that the bulk of the sample is an amorphous phase with minor crystalline phases of MgAl₂O₄ and SiC. Minor amounts of carbon (C) may be present due to the use of a graphite crucible during testing.

3.2. FTIR Spectroscopic Analysis

Figure 4 presents the FTIR spectra of samples with varying K₂O contents. This technique enables the qualitative analysis of structural modifications in [SiO₄] and [AlO₄] tetrahedral units, as well as alterations in Si-O-Al bridging. The FTIR spectra analysis in Figure 4 indicates three distinct regions: 400–600 cm⁻¹ [37] corresponding to Si-O-Al bending vibrations, 630–750 cm⁻¹ [38] associated with asymmetric stretching vibrations of [AlO₄], and 750–1200 cm⁻¹ reflecting symmetric band variations of [SiO₄] [39]. The spectral region between 750 and 1200 cm⁻¹ can be further resolved into four silicon-associated structural units: Q⁰ (monomeric units), Q¹ (dimeric structures), Q² (chain-like configurations), and Q³ (layered network architectures) [36,40]. As evident from Figure 4, the characteristic bands associated with [SiO₄] tetrahedra and the peak height h of Si-O-Al linkages exhibit a marked reduction as the K₂O content increases from 1% to 3%. This trend signifies that free oxygen dissociates silicon-centered network structures, simplifying molecular complexity and lowering the polymerization degree of the slag system. Figure 4 reveals that at 5% K₂O content, the observed spectral changes reverse previous trends, indicating that excessive K₂O enhances the degree of polymerization. This leads to silicate structural complexity and strengthens linkages between [SiO₄] and [AlO₄] tetrahedra. Additionally, the [AlO₄] tetrahedral peaks become slightly sharper with the increase in K₂O content, indicating the enhanced structural ordering of these units. This observation aligns with the simulated reduction in Al-O coordination numbers, suggesting a proliferation of Al-associated molecular clusters within the system. However, compared to Si-O bonds, Al-O bonds exhibit greater bond lengths and reduced stability, rendering them more susceptible to O²⁻-induced depolymerization. This mechanism ultimately contributes to the observed viscosity reduction. In addition, when the K₂O content exceeds 3%, the curves of Q₀, Q₁, and Q₃ change from being flat to slightly convex [38]. This indicates that the number of chainlike and sheet-like structures increases, and the degree of polymerization rises. As a result, the viscosity increases when the K₂O content exceeds 3%.

3.3. Viscosity Change

Figure 5 shows the viscosity and activation energy changes caused by varying K₂O content at 1823 K, with experimental data and modeled viscosity values displaying aligned trends. The simulated viscosity values represent shear viscosities calculated using the SCIGRESS molecular dynamics software. To calculate the activation energy, shear viscosities at 1853 K, 1823 K, and 1793 K were first computed using kinetic software (SCIGRESS FJ 2.8.1), and the activation energy was then determined via the Arrhenius equation. Namely, for each condition, shear viscosities at 1853 K, 1823 K, and 1793 K temperatures were calculated, and then one activation energy was derived using the Arrhenius equation, resulting in five activation energy values for five conditions. The Arrhenius-type equation (Equation (2)) is transformed into a linear form by taking the natural logarithm: lnη = lnη₀ + (E_η/R)·(1/T), where lnη is the ordinate and 1/T is the abscissa [2]. By performing linear fitting, the slope k = E_η/R is obtained, and thus the activation energy E_η = k·R is calculated. The activation energy (E_η) for viscous flow in slag is directly related to its viscosity: a higher E_η indicates greater energy required for atomic/molecular movement, leading to higher resistance to flow (i.e., higher viscosity). The activation energy was calculated to characterize the kinetic barriers governing key processes in the slag system, such as viscous flow or ionic diffusion, which are critical for understanding temperature-dependent properties like viscosity. These data provide mechanistic insights into how structural modifications (e.g., network depolymerization/polymerization induced by K₂O) influence atomic mobility, directly linking microstructural changes to macroscale thermophysical behavior.

$$\mathsf{\eta }={\mathsf{\eta }}_0\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{E_{\mathsf{\eta }}}{RT}}\right)$$

(2)

where η₀ is the exponential factor; E_η denotes the activation energy for viscous flow; R represents the universal gas constant; and T is the absolute temperature.

Figure 5 results show that in the CaO-SiO₂-MgO-Al₂O₃-K₂O slag system, K₂O at low concentrations (≤3%) significantly reduces slag viscosity by 52% and activation energy by 18.32 kJ/mol, indicating that K₂O acts as a network modifier causing depolymerization of [SiO₄] and [AlO₄] tetrahedral structures. Additionally, the provision of O²⁻ ions by K₂O induces depolymerization of macromolecular structures, increasing the concentration of smaller molecular species and consequently reducing viscosity. K⁺ ions exhibit lower ionic potential and higher mobility compared to Ca²⁺ ions, enhancing O²⁻ activity, which loosens the structural network, reduces the overall slag system dissociation energy, and lowers activation energy. When K₂O exceeds 3%, the slag system exhibits increased viscosity and elevated activation energy. This phenomenon may be attributed to the K₂O-SiO₂ reaction [16], which generates high-melting-point phases that abruptly enhance the melting point. The resulting structural complexity drives concurrent rises in both viscosity and activation energy. The simulated values being higher than experimental ones in Figure 5 may stem from multiple factors. Simulations often rely on idealized models that might disregard impurities present in experiments that can reduce viscosity. Additionally, theoretical models may oversimplify molecular interactions or structural complexities (e.g., the actual dynamic behavior of the silicate network in slag), overestimating viscosity. We also measured the softening (T_s), melting (T_m), and flow temperatures (T_p) of the samples using an ash fusion tester, as shown in Figure 6. We observed that these temperatures decreased with the increase in K₂O content but increased slightly when K₂O reached 5 wt.%. As a network modifier, K₂O reduces slag viscosity and melting difficulty by breaking siloxane bonds (disrupting [SiO₄] tetrahedron polymerization), thus causing Ts, Tm, and Tp to decline with the rise in K₂O—consistent with trends from viscosity and activation energy experiments, which validates the experimental accuracy.

3.4. Radial Distribution Functions (RDFs) and Coordination Numbers (CNs)

The radial distribution function (RDF) is typically employed to analyze structural evolution in slag systems, including ordering, bond lengths, and the polymerization degree. It establishes critical correlations between microscopic atomic arrangements and macroscopic properties. When the particle count within a radial shell from r to r + δr is defined as n(r), the RDF g(r) can be mathematically expressed by Equation (3) [41].

$$g(r)={\displaystyle \frac{1}{{\rho }_0}}{\displaystyle \frac{n(r)}{V}}={\displaystyle \frac{1}{{\rho }_0}}{\displaystyle \frac{n(r)}{4\pi r^2\delta r}}$$

(3)

Figure 7 presents the variations in radial distribution functions (RDFs) and coordination numbers (CNs) for Si-O, Al-O, Mg-O, Ca-O, and K-O pairs in slag systems with and without K₂O. The average bond lengths of these atomic pairs correspond to first peak positions at 1.6 Å, 1.75 Å, 1.95 Å, 2.35 Å, and 2.65 Å, respectively. These values remain invariant across K₂O concentrations, consistent with prior literature findings [2]. The K-O bonds exhibit the longest bond length with relatively weak bond strength, predisposing them to ionic character formation at elevated temperatures. This consequently disaggregates the macromolecular network of the slag structure into smaller molecular clusters. Longer bond lengths correlate with sharper radial distribution peaks, indicating enhanced atomic pair stability. Consequently, the bond stability hierarchy is as follows: Si-O > Al-O > Mg-O > Ca-O > K-O. Furthermore, the coordination number curves in Figure 7b,d reveal stable plateaus at 4.0 for Si-O and 4.2 for Al-O, demonstrating the predominance of tetrahedral structural units centered on silicon and aluminum within the slag matrix. The coordination curves of Mg-O, Ca-O, and K-O do not have stable plateaus. Therefore, they do not participate in the formation of the slag network and serve to provide charge balance. A wider plateau indicates a more stable structure. These findings are consistent with previous studies [27].

Figure 8 depicts the variations in radial distribution functions (RDFs) and coordination numbers (CNs) for Si-O, Al-O, Si-Si, and Si-K atomic pairs. As shown in Figure 8a, the first peak intensity of Si-O bonds decreases with the increase in K₂O content, while the coordination number N rises from 3.95 to 4.05 (Figure 8b). This trend indicates that the silicon-associated network transitions from a compact to a more open configuration, with a reduced degree of polymerization. The stable [SiO₄] tetrahedra undergo progressive depolymerization as the K₂O concentration increases. When the K₂O content reaches 5%, the Si-O peak intensity exhibits a subsequent increase. This suggests that structural reorganization in K⁺-Si interactions enhances Si-O bond stability, consistent with the viscosity experimental results. In contrast to the Si-O structure, the Al-O peak intensity also decreases (Figure 8c), while its coordination number (CN) diminishes (Figure 8d). This phenomenon indicates that cations generated during K₂O-induced network depolymerization provide charge compensation to [AlO₄] tetrahedra, causing the dissociation of larger Al-associated molecular aggregates into smaller, stabilized [AlO₄] tetrahedral units. However, Al-O bonds exhibit greater bond lengths and lower stability compared to Si-O bonds, ultimately reducing slag system viscosity and activation energy. Furthermore, when K₂O exceeds 3%, the coordination number (CN) of Al-O stabilizes, indicating that excessive K₂O concentrations can trigger the reaggregation of free ionic species into high-melting-point phases. This structural reorganization compromises flow properties by reducing melt fluidity. Figure 8e,f demonstrate a concurrent reduction in the Si-Si peak intensity and coordination number with the decrease in K₂O content. This trend correlates with the diminished bridging oxygen (BO) content within Si-O-Si linkages, further evidencing the declining polymerization degree of silicon-associated network structures. Figure 8g,h reveal the increased Si-K peak intensity and coordination number, indicating a rise in non-bridging oxygen (NBO) within Si-O-K configurations. This structural evolution drives the disaggregation of lamellar network architectures into smaller molecular chains or monomeric units. Notably, even during subsequent reconfiguration into larger aggregates, K₂O remains integral to the polymerization process.

3.5. Mean Square Displacements (MSDs) and [SiO₄] Tetrahedral Population Variations

Figure 9 compares the diffusion capacities of K, Ca, Mg, Si, and Al. Within the same system in 3% K₂O (Figure 9a), K exhibits the highest mobility, followed by Ca and Mg, while Si and Al demonstrate negligible displacement due to structural confinement within the network. This hierarchy confirms that K atoms predominantly exist as ionic species, providing charge compensation to the system, while the accompanying O²⁻ ions facilitate network depolymerization. Figure 9b reveals that the diffusion capacity of K initially increases but subsequently declines with the increase in K₂O content, exhibiting constrained mobility. The data indicate maximal K diffusion at 3% K₂O. At 5% K₂O, the aggregation of molecular clusters likely occurs, where K participates in structural network formation as a network-forming species. This integration restricts K atomic diffusion and displacement. Macroscopically, these structural modifications manifest as increased viscosity, altered flow properties, and the generation of high-melting-point phases.

In Figure 10, the variation in the number of Si-centered [SiO₄] tetrahedra, statistically analyzed using MATLAB (version number R2016a), reveals a decrease from 592 to 560 followed by an increase to 572. These results demonstrate that K₂O initially depolymerizes the Si-O network, but beyond 3% content, K₂O participates in network formation, leading to a rebound in the tetrahedral population. This finding corroborates the previous simulation results, validating the consistency of the research outcomes.

4. Conclusions

The integrated analysis of the experimental and computational results demonstrates the dual role of K₂O in the specific CaO-SiO₂-MgO-Al₂O₃-K₂O slag system investigated. K₂O simultaneously acts as a network modifier and charge compensator, exhibiting concentration-dependent structural modulation behavior. During the initial stages of K₂O addition, structural depolymerization is promoted, reducing network connectivity. This process increases the population of low-molecular-weight species, driving a significant viscosity reduction. However, beyond a critical threshold (3% in this study), K₂O actively participates in the slag network architecture, inducing structural complexity through increased chain-like and layered configurations. This elevates the polymerization degree and viscosity, as evidenced by radial distribution function analyses and coordination number variations. The analysis of atomic mobility reveals constrained K diffusion in 5% K₂O systems. Thus, the proper control of the K₂O concentration changes plays a crucial role in regulating slag structure. During slag operations, the K₂O concentration can be maintained within specified thresholds to minimize its impact on the slag structure. From an application perspective, while K₂O exhibits its dual role in the specific CaO-SiO₂-MgO-Al₂O₃-K₂O slag system investigated here, analogous slag systems suggest this work offers guidance for precise K₂O concentration control in industries reliant on slag viscosity regulation. In metallurgical processes, controlling K₂O content (e.g., 2–4%) to regulate slag viscosity and fluidity can optimize blast furnace operations. Leveraging K₂O’s dual roles (network modification and charge compensation) modulates slag–metal interfacial reaction kinetics. In addition, higher K₂O levels (4–5%) can stabilize slag films and prevent nozzle clogging. In the manufacturing of specialty glasses or glazes, they enable precise control over melt flow during forming and cooling. In emerging applications like molten salt batteries and thermal energy storage, 2–4% K₂O-containing slags may enhance heat transfer efficiency. In SiO₂-Al₂O₃-based slag systems, K₂O typically demonstrates consistent structural effects: high concentrations may induce structural crosslinking with SiO₂, influencing overall slag properties. By establishing the K₂O concentration–viscosity–structure relationship, this study provides a scientific basis for the multipurpose utilization of slags. Furthermore, this study provides actionable insights for optimizing metallurgical processes through the targeted control of alkali oxides by establishing a structure–property–metallurgical application relationship.