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Surface Tension of Molten Al–Si Alloys Measured by Electromagnetic Levitation and Evaluated Using the Butler Equation

This study utilizes electromagnetic levitation to demonstrate that the surface tension of molten Al–Si alloys decreases linearly with both temperature and silicon concentration, a behavior that contradicts previous reports of nonlinearity and is accurately modeled by the Butler equation under an ideal-solution approximation, suggesting minimal thermodynamic nonideality.

Original authors: Yusaku SEIMIYA, Haruto YONEYAMA, Shumpei OZAWA

Published 2026-08-20

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CC BY 4.0

Original authors: Yusaku SEIMIYA, Haruto YONEYAMA, Shumpei OZAWA

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a drop of liquid metal floating in mid-air, held there not by a container, but by invisible magnetic forces. This is the setting for a quiet but crucial investigation into the nature of molten aluminum and silicon, two metals that form the backbone of modern casting and manufacturing. When these metals are melted together, they create alloys used in everything from car engines to aircraft parts. To understand how these materials flow, fill molds, and bond together, scientists need to know a specific property called surface tension. Think of surface tension as the skin of a liquid, a force that tries to pull the surface tight, much like a stretched rubber sheet. If this skin is too strong or too weak, or if it changes unpredictably as the mixture of metals shifts, the final product can end up with hidden flaws or defects. For decades, measurements of this property in aluminum-silicon mixtures have been confusing, with different studies reporting wildly different behaviors depending on how much silicon was added. Some researchers claimed the surface tension would rise sharply in certain mixtures, while others saw it fall steadily.

A team of researchers at the Chiba Institute of Technology and Gakushuin University set out to resolve this confusion by measuring the surface tension of pure liquid aluminum, pure liquid silicon, and various mixtures of the two. They used a technique called electromagnetic levitation, which allows them to melt the metals without touching any container walls, thereby avoiding contamination that could skew the results. By heating the floating droplets and watching them vibrate, they could calculate the strength of the liquid's surface skin. Their measurements covered a wide range of silicon content, from a tiny amount up to eighty percent, and spanned temperatures from just above the melting point of aluminum to well over two thousand Kelvin. The researchers were particularly careful to ensure their samples were free of oxide films, which are thin layers of rust that can form on hot metals and distort the measurements. They only used data from moments when the droplet surface was perfectly clean, a rigorous standard that required discarding many heating curves where even a hint of oxidation appeared.

The results painted a clear and surprisingly simple picture. For every mixture they tested, the surface tension dropped in a straight, steady line as the temperature rose. More importantly, as they added more silicon to the aluminum, the surface tension decreased in a smooth, nearly straight line from start to finish. There were no sudden jumps, no unexpected spikes in the middle, and no strange increases at the silicon-rich end. This finding directly contradicts several previous studies that had reported a complex, curved relationship where the surface tension would rise again as the mixture became richer in silicon. The new data suggests that those earlier reports of a rise in surface tension were likely caused by experimental errors, such as the presence of oxide films or contamination, rather than a true property of the metal itself. The researchers confirmed that their own measurements were precise enough that this straight-line trend was not just a fluke of uncertainty, but a real physical behavior.

To understand why the surface tension behaved so simply, the team turned to a mathematical model known as the Butler equation, which predicts how the surface of a liquid should behave based on the properties of its ingredients. They ran two different calculations: one that assumed the aluminum and silicon atoms interacted in a complex, non-ideal way, and another that assumed they mixed perfectly like an ideal solution. The complex calculation predicted a slight curve in the results, but the simple, ideal calculation matched the experimental data almost perfectly. This suggests that the atoms in the molten mixture do not form strong, unusual bonds with each other that would change the surface tension in a complicated way. Instead, the behavior of the surface is largely determined by the basic properties of the pure metals and their temperature. The study concludes that the confusing, nonlinear patterns seen in older literature were likely artifacts of the experimental conditions rather than the true nature of the alloy. By establishing this clear, linear relationship, the researchers have provided a reliable foundation for engineers who need to model how these metals flow and solidify, ensuring that the next generation of cast parts can be designed with greater confidence and fewer defects.

Technical Summary: Surface Tension of Molten Al–Si Alloys Measured by Electromagnetic Levitation and Evaluated Using the Butler Equation

Problem Statement
Reliable surface tension data for molten Al–Si alloys are essential for the quantitative modeling of high-temperature melt-processing phenomena, such as casting, brazing, and mold filling. However, existing literature exhibits significant scatter regarding the composition dependence of surface tension. Some studies report a nearly monotonic decrease with increasing silicon (Si) concentration, while others suggest relatively high values in the aluminum (Al)-rich region and an increase toward the Si-rich side. These discrepancies may stem from experimental variables including sample purity, contamination from supporting materials, and, critically, oxygen-related effects at the melt surface. Furthermore, the role of thermodynamic nonideality in the surface tension behavior of these alloys remains unelucidated.

Methodology
This study employed the oscillating drop method using electromagnetic levitation (EML) to measure surface tensions without container contact, thereby minimizing contamination.

Samples: High-purity aluminum (>99.99 mass%) and silicon were used to create alloys with Si concentrations ranging from 5 to 80 at.%.
Experimental Conditions: Measurements were conducted in a high-purity Ar–He atmosphere with an oxygen partial pressure of $10^{-2}$ Pa.
Data Selection Criteria: To ensure data integrity, the researchers strictly excluded heating curves where oxide films were observed within the pyrometer measurement spot. Similarly, only oscillation data from droplets with no detectable oxide films on their surfaces were analyzed.
Temperature Calibration: Emissivity was calibrated by solidifying the droplet and identifying the inflection point corresponding to the equilibrium liquidus temperature ( $T_L$ ) during reheating.
Analysis: Surface tension ( $\sigma$ ) was calculated from surface oscillation frequencies using the Rayleigh equation with Cummings and Blackburn corrections. Density was estimated assuming ideal mixing of molar volumes.
Theoretical Evaluation: The measured data were compared against Butler equation calculations. Two thermodynamic models were tested: a subregular-solution model using evaluated excess Gibbs energies and an ideal-solution approximation ( $G^{ex} = 0$ ).

Key Results

Pure Components: The surface tension of pure liquid Al and pure liquid Si decreased linearly with increasing temperature. The measured values for pure Al and Si were consistent with specific prior studies (e.g., Kobatake et al., Rhim et al.).
Alloy Composition Dependence: For all examined compositions (5–80 at.% Si), surface tension decreased linearly with increasing temperature. At a fixed temperature (near 1700 K), surface tension decreased monotonically and nearly linearly with increasing Si concentration.
Absence of Nonlinearity: Within the expanded uncertainty of the measurements (approximately 2%), the study observed no evidence of the nonlinear behaviors reported in some previous literature, specifically the "relatively high values in the Al-rich region" or the "increase toward the Si-rich side."
Uncertainty Analysis: A rigorous uncertainty budget based on the Guide to the Expression of Uncertainty in Measurement (GUM) confirmed that the observed linear trend was a robust feature of the measurements and not an artifact of experimental error. The maximum expanded uncertainty was $\pm 14.3 \times 10^{-3}$ N·m $^{-1}$ .
Thermodynamic Modeling: Butler equation calculations revealed that the ideal-solution approximation reproduced the measured composition dependence and temperature coefficients more consistently than the subregular-solution calculation. The subregular model predicted a slight positive curvature that was not observed in the experimental data.

Significance and Claims
The authors conclude that under the present experimental conditions, thermodynamic nonideality makes only a limited contribution to the surface tension behavior of molten Al–Si alloys. The study posits that the ideal-solution approximation is sufficient to describe the system's surface tension characteristics.

Consequently, the paper argues that the nonlinear composition dependences and specific trends (high Al-rich values, Si-rich increases) reported in previous works are unlikely to arise solely from the intrinsic thermodynamic composition dependence of the alloys. Instead, the authors suggest these discrepancies likely reflect differences in experimental conditions, data analysis procedures, sample purity, oxide-related effects, or contamination from supporting materials. The study provides a refined, linear baseline for surface tension data in the Al–Si system, free from the scatter attributed to oxide contamination in prior measurements.

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