[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-127618-en":3,"doc-seo-127618-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},127618,549768064778,"Finn","https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8",8,"Research & Report","Magnesiothermic Reduction of Silica - A Machine Learning Study","Fundamental experimental and theoretical studies investigate magnesiothermic reduction of silica using Mg/SiO2 molar ratios of 1–4 across 1073–1373 K and reaction times of 10–240 min. Conventional thermochemical equilibrium calculations from FactSage cannot reproduce observed kinetics, including partial persistence of unreacted silica cores and near-complete disappearance in other samples. Quartz fragmentation generates microcracks that provide fracture pathways for Mg infiltration. To capture such complex schemes, a physics-informed Gaussian process machine with a composite kernel is trained on hybrid experimental and equilibrium boundary datasets, achieving a regression score of 0.9665. The model predicts untested effects and validation confirms good interpolative performance.","materials   \nArticle  \nMagnesiothermic Reduction of Silica: A Machine Learning Study  \nKai Tang 1, *, Azam Rasouli 2, Jafar Safarian 2, Xiang Ma 1 and Gabriella Tranell 2  \nCitation: Tang, K.; Rasouli, A.;  \nSafarian, J.; Ma, X.; Tranell, G.  \nMagnesiothermic Reduction of Silica: A Machine Learning Study. Materials 2023, 16, 4098. [https://doi.org/](https://doi.org/)[ ](https://doi.org/)[10.3390/ma16114098](10.3390/ma16114098)  \nAcademic Editors: Mariola Saternusand Ladislav Socha  \nReceived: 23 April 2023  \nRevised: 28 May 2023  \nAccepted: 29 May 2023  \nPublished: 31 May 2023  \nCopyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) .  \n1 SINTEF AS, Industry Institute, N-7465 Trondheim, Norway; [xiang.ma@sintef.no](xiang.ma@sintef.no)  \n2 Department of Materials Science and Engineering, Norwegian University of Science and Technology, N-7034 Trondheim, Norway; [azam.rasouli@ntnu.no](azam.rasouli@ntnu.no) (A.R.); [jafar.safarian@ntnu.no](jafar.safarian@ntnu.no) (J.S.); [gabriella.tranell@ntnu.no](gabriella.tranell@ntnu.no) (G.T.)  \n* Correspondence: [kai.tang@sintef.no](kai.tang@sintef.no)  \nAbstract: Fundamental studies have been carried out experimentally and theoretically on the magnesiothermic reduction of silica with different Mg/SiO 2 molar ratios (1–4) in the temperature range of 1073 to 1373 K with different reaction times (10–240 min) . Due to the kinetic barriers occurring in metallothermic reductions, the equilibrium relations calculated by the well-known thermochemical software FactSage (version 8.2) and its databanks are not adequate to describe the experimental observations. The unreacted silica core encapsulated by the reduction products can be found in some parts of laboratory samples. However, other parts of samples show that the metallothermic reduction disappears almost completely. Some quartz particles are broken into fine pieces and form many tiny cracks. Magnesium reactants are able to infiltrate the core of silica particles via tiny fracture pathways, thereby enabling the reaction to occur almost completely. The traditional unreacted core model is thus inadequate to represent such complicated reaction schemes. In the present work, an attempt is made to apply a machine learning approach using hybrid datasets in order to describe complex magnesiothermic reductions. In addition to the experimental laboratory data, equilibrium relations calculated by the thermochemical database are also introduced as boundary conditions for the magnesiothermic reductions, assuming a sufficiently long reaction time. The physics-informed Gaussian process machine (GPM) is then developed and used to describe hybrid data, given its advantages when describing small datasets. A composite kernel for the GPM is specifically developed to mitigate the overfitting problems commonly encountered when using generic kernels. Training the physics-informed Gaussian process machine (GPM) with the hybrid dataset results in a regression score of 0.9665 . The trained GPM is thus used to predict the effects of Mg-SiO2 mixtures, temperatures, and reaction times on the products of a magnesiothermic reduction, that have not been covered by experiments. Additional experimental validation indicates that the GPM works well for the interpolates of the observations.  \nKeywords: magnesiothermic reduction; silica; kinetic barrier; Gaussian process machine; machine learning  \n1. Introduction  \nTheoretically, silicon is the metal produced by carbothermic reduction at temperatures higher than 1821 􀀎 C [1] . Conventional silicon production has at least two drawbacks: high energy consumption and a negative impact on the environment through CO 2 emissions. It is estimated th","cbCaintlalqL2pbh","https://ap.wps.com/l/cbCaintlalqL2pbh","pdf",2615735,1,12,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"Why do thermochemical equilibrium calculations fail to match experimental observations?\",\"answer\":\"Kinetic barriers in metallothermic reductions make equilibrium relations from FactSage inadequate for describing the experimental behavior.\"},{\"question\":\"What experimental evidence shows that silica reduction can be incomplete or nearly complete?\",\"answer\":\"Some samples retain an unreacted silica core encapsulated by reduction products, while others show the metallothermic reduction nearly disappears, with quartz breaking into fine pieces and forming tiny cracks.\"},{\"question\":\"How does the machine learning approach improve prediction of magnesiothermic reduction outcomes?\",\"answer\":\"A physics-informed Gaussian process machine is trained on a hybrid dataset combining experimental measurements with equilibrium relations as boundary conditions, using a composite kernel to reduce overfitting and enabling accurate regression and predictions beyond the experiments.\"}]","Magnesiothermic Reduction of Silica - 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