The understanding of the precipitation of topological close packed (TCP) [1] phases in single-crystal superalloys is of central importance for the design of these materials for high-temperature applications. However, the structural complexity of many intermetallic compounds and the chemical complexity of the superalloys hampers the exhaustive sampling of chemical space by density-functional theory (DFT) calculations. For example, the computation of the convex hull of the R phase with 11 inequivalent lattice sites would require N¹¹ DFT calculations in an N-component system.
  We overcome these computational barrier by combining machine learning (ML) techniques with descriptors of the local atomic environment of the TCP phases. The descriptors are derived from bond order potential (BOP) [2,3] theory and  retain domain knowledge of the interatomic interaction from the underlying tight-binding Hamiltonians. We demonstrate the use of the BOP descriptors to train simple regression algorithms to predict the formation energies obtained from DFT for a heterogeneous dataset containing various TCP crystal structures. We apply this methodology to several binary and ternary intermetallic systems with experimental evidence of R phase formation.

References
[1] A.K. Shinha, Met Soc of AIME - trans, 1969, 5, 81-185.
[4] J. Jenke et.al., J. Jenke et.al. Physical Review B, 2018, 98, 144102.
[3] T. Hammerschmidt et. al., Computer Physics Communications, 235, 2019, 221-233.