  In this study, we investigate the structure-stability relationship of
hypothetical Nd-Fe-B crystal structures using descriptor-relevance analysis and
the t-SNE dimensionality reduction method. 149 hypothetical Nd-Fe-B crystal
structures are generated from 5967 LA-T-X host structures in Open Quantum
Materials Database by using the elemental substitution method, with LA denoting
lanthanides, T denoting transition metals, and X denoting light elements such
as B, C, N and O. A hypothetical crystal structure is created by substituting
all lanthanide sites with Nd, all transition metal sites with Fe, and all light
element sites with B. High-throughput first-principle calculations are applied
to evaluate the phase stability of these structures. Twenty of them are found
to be potentially formable. The descriptor-relevance analysis on the orbital
field matrix (OFM) materials' descriptor reveals the average atomic
coordination number as the essential factor in determining the structure
stability of these substituted Nd-Fe-B crystal structures. 19 among 20
hypothetical structures that are found potentially formable have an average
coordination number larger than 6.5. In addition, all the local structures
represented by the OFM descriptors are integrated into a visible space to study
the detailed correlation between their characteristics and the stability of the
crystal structure to which they belong. We discover that unstable substituted
structures frequently carry Nd and Fe local structures with two prominent
points: low average coordination numbers and fully occupied B neighboring
atoms. Moreover, there are only three popular forms of B local structures
appearing on all potentially formable substituted structures: cage networks,
planar networks, and interstitial sites. The discovered relationships are
promising to speed up the screening process for the new formable crystal
structures.
