Resolving Thermodynamic Inaccuracies in the CaO–Al₂O₃–SiO₂ System Through Solid Solution Modeling and CALPHAD Reassessment

The thermodynamic behavior of oxide systems is important in optimizing a wide range of applications—everything from ceramics and glasses to cement and metallurgical slags. Within this broad domain, the CaO–Al₂O₃–SiO₂ system is especially important. Its relevance spans not just industrial processes, but also geological environments, showing up in natural formations like volcanic rocks and magmatic systems. And yet, for all its significance, this ternary system remains surprisingly difficult to model accurately across its full composition and temperature ranges. The reasons are both subtle and complex: calcium, aluminum, and silicon oxides interact to form numerous solid and liquid phases, each with its own stability limits and solubility behaviors. Capturing all of this in a coherent thermodynamic framework is highly complex. One major shortcoming in existing thermodynamic databases is their treatment of calcium aluminate phases—especially CA₂ (CaO·2Al₂O₃). Many previous models underestimate the heat of formation for this compound, resulting in that CA. This kind of inaccuracy has real consequences. In cement science, for instance, phase formation pathways determine how the material sets and hardens, affecting not just its strength but also its long-term durability. If your model gets the thermodynamics wrong, the entire materials design process risks being built on shaky ground. Another key issue has to do with how models have traditionally treated silicate phases like anorthite and cristobalite which are assumed to behave as stoichiometric compounds, with fixed, idealized compositions. however, studies have shown consistently that both phases can accommodate significant solid solubility. Anorthite, for example, is known to dissolve extra silicon, while cristobalite can include small amounts of aluminum and calcium through a mechanism often referred to as “stuffing.” These substitutions might seem minor, but they shift phase boundaries and influence crystallization behavior—factors that are critically important in ceramic and glass manufacturing. Ignoring them leads to thermodynamic models that fall out of sync with real-world materials processing. In response to these unresolved gaps, a recent study published in the Journal of the American Ceramic Society presents a thorough reassessment of both the CaO–Al₂O₃ and CaO–Al₂O₃–SiO₂ systems. The work of PhD candidate Jing Tan, Chenying Shi, Associate Professor Yuling Liu, Qing Wu, and Professor Yong Du from Central South University, together with Tengfei Deng from Wuhan University of Technology, they introduced advanced sublattice models to account for solid solutions, and applied the CALPHAD method to construct a thermodynamically consistent picture that spans the entire composition and temperature range with the goal to eliminate long-standing inaccuracies and provide a model that not only reflects reality more closely but also offers practical value for scientists and engineers working with aluminosilicate materials.

The research team began by re-examining the CaO–Al₂O₃ binary system, a crucial foundation for modeling more complex oxide systems and to do this, the researchers turned to experimental data derived from oxide melt solution calorimetry, particularly the reliable measurements from Geiger et al. These values indicated that earlier models had significantly underestimated the enthalpies of formation for these compounds. When they incorporated these more accurate experimental results into their recalculations, the team was able to correct the thermodynamic landscape of the system and resolved the previously reported instability of CA₂ and ensured that their model aligned with known phase stability under typical processing conditions. The authors also tested CaO–Al₂O₃–SiO₂ ternary system, where phases like anorthite and cristobalite had been simplistically modeled as fixed, stoichiometric compounds. However, experimental work—including phase diagram analyses, X-ray diffraction, and microprobe measurements—has shown that these phases accommodate small but significant substitutions. For example, Longhi and Hays demonstrated that anorthite can dissolve excess silicon, while cristobalite can host calcium and aluminum through what’s known as the “stuffing” mechanism, originally proposed by Buerger. Acknowledging these findings, the researchers introduced more flexible sublattice models. In the case of anorthite, they constructed a four-endmember model that allowed for simultaneous substitution of Ca²⁺ and Al³⁺ by vacancies and Si⁴⁺. This model respected the electroneutrality of the structure and captured the way in which the phase boundary of anorthite expands with increasing silica content. Their model wasn’t just more accurate—it was more reflective of how these materials behave in the lab and in practice.

Modeling the liquid phase posed another set of challenges. To better represent melt behavior near the silica-rich corner of the ternary system, the team chose an ionic two-sublattice model incorporating AlO₂⁻ species. This model addressed persistent issues with other models, which often produced unrealistic miscibility gaps or failed to account for the evolving coordination environments of Al and Si as compositions shifted. The inclusion of AlO₂⁻ helped the model more accurately reflect the role of aluminum in forming network structures, which is especially important in systems where silicate chains and rings play a role in melt viscosity and phase separation. When tested against experimental activity data—measured through mass spectrometry and equilibrium analysis—the model performed remarkably well. Deviations that had plagued previous assessments were largely eliminated, with only a few high-temperature outliers remaining, most likely due to inherent experimental limitations rather than shortcomings in the model itself. To test how their refined thermodynamic database would perform under realistic processing conditions, the team ran Scheil solidification simulations. These simulations allowed them to track how phases evolve and crystallize during the cooling of cement clinker compositions—a scenario highly relevant to industry. Their results matched the expected sequence of phase formation and liquid evolution with impressive accuracy. This wasn’t just a theoretical validation; it demonstrated that their work could be directly applied to improve material processing strategies. By aligning simulated predictions with what practitioners actually observe, the researchers effectively built a bridge between abstract thermodynamic data and tangible industrial outcomes. Their work shows how detailed, careful modeling—anchored in reliable experimental evidence—can lead to practical tools that enhance everything from ceramic sintering to cement formulation. It’s a clear example of how rigorous science, grounded in the lab and informed by real-world needs, can make a lasting impact on both research and application.

In conclusion, the authors successfully refined the thermodynamic parameters and addressed inconsistencies in previous models which significantly improved the reliability of phase predictions. This is important because accurate thermodynamic data enable better control over material behavior during manufacturing processes, such as how clinker phases crystallize during cement production or how silicate melts evolve under high-temperature conditions. Moreover, there is vital applications in cement technology. Engineers now have a much stronger foundation for simulating the crystallization and cooling of clinker materials, where even slight shifts in composition or temperature can lead to changes in performance. The improved ability to model phases like anorthite means it’s now easier to avoid forming unwanted or unstable phases that could compromise the mechanical integrity or longevity of the final product. That kind of predictive power is essential for optimizing not just performance, but also energy efficiency and environmental sustainability in large-scale production. Furthermore, in glass and ceramic manufacturing, the study’s incorporation of solid solution behavior—particularly in cristobalite and anorthite—represents a key breakthrough. These materials don’t always behave as clean, stoichiometric compounds; instead, they can accommodate varying amounts of Si, Al, and Ca in their structures. This variability affects how they form and transform during cooling, which in turn influences material properties like thermal shock resistance, transparency, and overall strength. Being able to model these subtle shifts more accurately allows for greater control in both industrial design and laboratory experimentation. Importantly, the team also tackled a long-standing artifact in previous models: the appearance of a high-temperature miscibility gap that didn’t align with experimental evidence. In high-temperature applications—such as glass refining, metallurgy, or advanced ceramics—even a small error in predicting phase separation can lead to costly mistakes. By eliminating this fictitious gap, the researchers have opened the door for more trustworthy simulations in extreme conditions, providing a more dependable basis for process planning and alloy development.