Phase transition is one of the most important phenomena in nature and plays a central role in materials design. All phase transitions are characterized by suitable order parameters, including the order–disorder phase transition. However, finding a representative order parameter for complex systems is non-trivial, such as for high-entropy alloys. Given the strength of dimensionality reduction of a variational autoencoder (VAE), we introduce a VAE-based order parameter. We propose that the Manhattan distance in the VAE latent space can serve as a generic order parameter for order–disorder phase transitions. The physical properties of our order parameter are quantitatively interpreted and demonstrated by multiple refractory high-entropy alloys. Using this order parameter, a generally applicable alloy design concept is proposed by mimicking the natural mixing process of elements. Our physically interpretable VAE-based order parameter provides a computational technique for understanding chemical ordering in alloys, which can facilitate the development of rational alloy design strategies.
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The VAE model training and order parameter inference codes are available at https://code.ornl.gov/jqyin/deepthermo. The training code along with sample data can also be found on our Code Ocean capsule50. The figures are plotted with the notebook at https://code.ornl.gov/jqyin/deepthermo/-/blob/master/utils/hea_vae_analysis.ipynb.
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This research was sponsored by and used resources of the Oak Ridge Leadership Computing Facility (OLCF), which is a US Department of Energy (DOE) Office of Science User Facility at the Oak Ridge National Laboratory supported by the US DOE under contract no. DE-AC05-00OR22725. This work was also performed in support of the US DOE’s Fossil Energy Crosscutting Technology Research Program, and in part by an appointment to the US DOE Postgraduate Research Program at the National Energy Technology Laboratory (NETL) administered by the Oak Ridge Institute for Science and Education. Neither the United States Government nor any agency thereof, nor any of its employees, nor the support contractor, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
The authors declare no competing interests.
Peer review information Nature Computational Science thanks Evert van Nieuwenburg, Sebastian Wetzel and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Handling editor: Jie Pan, in collaboration with the Nature Computational Science team.
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VAE embeddings and order parameter, and specific heat data for MoNbTaW.
Second-order moment of the VAE order parameter and VAE embeddings for AlxCoCrFeNi, where x = 1, 1.6, and 2.
Configurations of eight subsystems of TiVNbHf and the VAE order parameter histogram and element distribution for TiVNbHf alloy design, and specific heat for Ti25V25Nb25Hf25, Ti38V15Nb23Hf24, Ti29V15Nb28Hf28 and Ti28V12Nb30Hf30.
SRO, LRO and VAE order parameter, and total order parameter for MoNbTaW.
Training and inference time for up to 96 GPUs on the Summit supercomputer.
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Yin, J., Pei, Z. & Gao, M.C. Neural network-based order parameter for phase transitions and its applications in high-entropy alloys. Nat Comput Sci 1, 686–693 (2021). https://doi.org/10.1038/s43588-021-00139-3