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A Mathematical Computer Model for Estimating Phase Weight/Atomic Fractions for Iron Slags’ System (SiO2-Al203-CaO-MgO) at Subsolidus Temperatures

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Abstract

In this study, the 3 dimensional description of the quaternary subsolidus slag system aluminasilicacalcia-magnesia is evaluated using Mathematica programming based on previous experimental research data. The lever rule in the tetrahedra is then applied for a given arbitrary liquid composition %A + %B + %C + %D = 100 in order to calculate the solid phases present (neglecting solid solutions) with their relative proportions after the solidification is completed. A novel transformation and algorithm are then developed using simple geometry and Matlab programming which can also be used for other subsolidus systems in case appropriate data are provided.

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Acknowledgment

We are grateful and respectful to the honor of Professor Mathematician Tahsin Çizenel deceised, author of Geometry books in 2D and 3D for his help in the derivation of transformations based on 3D Geometry.

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Authors and Affiliations

  1. Turkish-German University, Faculty of Engineering, 34820, Istanbul, Turkey

    Tanju Yelkenci

  2. Marmara University, Faculty of Engineering, 34854, Istanbul, Turkey

    Z. Engin Erkmen

Authors
  1. Tanju Yelkenci
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  2. Z. Engin Erkmen
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Correspondence to Tanju Yelkenci.

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Yelkenci, T., Engin Erkmen, Z. A Mathematical Computer Model for Estimating Phase Weight/Atomic Fractions for Iron Slags’ System (SiO2-Al203-CaO-MgO) at Subsolidus Temperatures. J. Phase Equilib. Diffus. 44, 200–207 (2023). https://doi.org/10.1007/s11669-023-01033-3

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