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 the 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. By borrowing the skeletal structure of each of the host materials, 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. As the first investigative result, 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. By applying the t-SNE dimensionality reduction method, 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.

1.
J.
Ma
,
V. I.
Hegde
,
K.
Munira
,
Y.
Xie
,
S.
Keshavarz
,
D. T.
Mildebrath
,
C.
Wolverton
,
A. W.
Ghosh
, and
W. H.
Butler
,
Phys. Rev. B
95
,
024411
(
2017
).
2.
W.
Korner
,
G.
Krugel
, and
C.
Elsasser
,
Sci. Rep.
6
,
2045
2322
(
2016
).
3.
W.
Körner
,
G.
Krugel
,
D. F.
Urban
, and
C.
Elsässer
,
Scr. Mater.
154
,
295
299
(
2018
).
4.
J.
He
,
S. S.
Naghavi
,
V. I.
Hegde
,
M.
Amsler
, and
C.
Wolverton
,
Chem. Mater.
30
,
4978
4985
(
2018
).
5.
J.
Balluff
,
K.
Diekmann
,
G.
Reiss
, and
M.
Meinert
,
Phys. Rev. Mater.
1
,
034404
(
2017
).
6.
A. A.
Emery
,
J. E.
Saal
,
S.
Kirklin
,
V. I.
Hegde
, and
C.
Wolverton
,
Chem. Mater.
28
,
5621
(
2016
).
7.
R.
Michalsky
and
A.
Steinfeld
,
Catal. Today
286
,
124
130
(
2017
), part of special issue on Nitrogen Activation.
8.
K.
Yang
,
W.
Setyawan
,
S.
Wang
,
M.
Buongiorno Nardelli
, and
S.
Curtarolo
,
Nat. Mater.
11
,
614
619
(
2012
).
9.
X.
Li
,
Z.
Zhang
,
Y.
Yao
, and
H.
Zhang
,
2D Mater.
5
,
045023
(
2018
).
10.
A. R.
Oganov
,
C. J.
Pickard
,
Q.
Zhu
, and
R. J.
Needs
,
Nat. Rev. Mater.
4
,
331
348
(
2019
).
11.
M.
Sagawa
,
S.
Fujimura
,
N.
Togawa
,
H.
Yamamoto
, and
Y.
Matsuura
,
J. Appl. Phys.
55
,
2083
2087
(
1984
).
12.
S.
Hirosawa
,
Y.
Matsuura
,
H.
Yamamoto
,
S.
Fujimura
,
M.
Sagawa
, and
H.
Yamauchi
,
J. Appl. Phys.
59
,
873
879
(
1986
).
13.
Y.
Tatetsu
,
Y.
Harashima
,
T.
Miyake
, and
Y.
Gohda
,
Phys. Rev. Mater.
2
,
074410
(
2018
).
14.
J. E.
Saal
,
S.
Kirklin
,
M.
Aykol
,
B.
Meredig
, and
C.
Wolverton
,
JOM
65
,
1501
1509
(
2013
).
15.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
A1138
(
1965
).
16.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
B871
(
1964
).
17.
S.
Kirklin
,
J. E.
Saal
,
B.
Meredig
,
A.
Thompson
,
J. W.
Doak
,
M.
Aykol
,
S.
Rühl
, and
C.
Wolverton
,
npj Comput. Mater.
1
,
15010
(
2015
).
18.
C. B.
Barber
,
D. P.
Dobkin
, and
H.
Huhdanpaa
,
ACM Trans. Math. Software
22
,
469
483
(
1996
).
19.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
47
,
558
561
(
1993
).
20.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
49
,
14251
14269
(
1994
).
21.
G.
Kresse
and
J.
Furthmüller
,
Comput. Mater. Sci.
6
,
15
50
(
1996
).
22.
G.
Kresse
and
J.
Furthmüller
,
Phys. Rev. B
54
,
11169
11186
(
1996
).
23.
P. E.
Blöchl
,
Phys. Rev. B
50
,
17953
17979
(
1994
).
24.
G.
Kresse
and
D.
Joubert
,
Phys. Rev. B
59
,
1758
1775
(
1999
).
25.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
3868
(
1996
).
26.
T.
Lam Pham
,
H.
Kino
,
K.
Terakura
,
T.
Miyake
,
K.
Tsuda
,
I.
Takigawa
, and
H.
Chi Dam
,
Sci. Technol. Adv. Mater.
18
,
756
765
(
2017
).
27.
T.-L.
Pham
,
N.-D.
Nguyen
,
V.-D.
Nguyen
,
H.
Kino
,
T.
Miyake
, and
H.-C.
Dam
,
J. Chem. Phys.
148
,
204106
(
2018
).
28.
D.-N.
Nguyen
,
T.-L.
Pham
,
V.-C.
Nguyen
,
A.-T.
Nguyen
,
H.
Kino
,
T.
Miyake
, and
H.-C.
Dam
,
J. Phys.: Conf. Ser.
1290
,
012009
(
2019
).
29.
L.
Yu
and
H.
Liu
,
J. Mach. Learn. Res.
5
,
1205
1224
(
2004
).
30.
S.
Visalakshi
and
V.
Radha
,
IEEE International Conference on Computational Intelligence and Computing Research
(
IEEE
,
2014
), pp.
1
6
.
31.
H. C.
Dam
,
V. C.
Nguyen
,
T. L.
Pham
,
A. T.
Nguyen
,
K.
Terakura
,
T.
Miyake
, and
H.
Kino
,
J. Phys. Soc. Jpn.
87
,
113801
(
2018
).
32.
T. O.
Kvalseth
,
Am. Stat.
39
,
279
285
(
1985
).
33.
K. P.
Murphy
,
Machine Learning: A Probabilistic Perspective
(
MIT Press
,
2012
).
34.
F.
Pedregosa
,
G.
Varoquaux
,
A.
Gramfort
,
V.
Michel
,
B.
Thirion
,
O.
Grisel
,
M.
Blondel
,
P.
Prettenhofer
,
R.
Weiss
,
V.
Dubourg
,
J.
Vanderplas
,
A.
Passos
,
D.
Cournapeau
,
M.
Brucher
,
M.
Perrot
, and
E.
Duchesnay
,
J. Mach. Learn. Res.
12
,
2825
2830
(
2011
).
35.
K.
Pearson
,
Proc. R. Soc. London
58
,
240
242
(
1895
).
36.
L.
van der Maaten
and
G.
Hinton
,
J. Mach. Learn. Res.
9
,
2579
2605
(
2008
).
37.
M.
Wattenberg
,
F.
Viégas
, and
I.
Johnson
,
Distill
1
,
e2
(
2016
).
38.
P.
Berens
and
D.
Kobak
,
Nat. Commun.
10
(
2041-1723
),
5416
(
2019
).
39.
J.
Venna
and
S.
Kaski
,
Neural Networks
19
,
889
899
(
2006
), part of special issue on Advances in Self Organising Maps - WSOM’05.
40.
J. A.
Lee
and
M.
Verleysen
,
Neurocomputing
72
,
1431
1443
(
2009
), part of special issue on Advances in Machine Learning and Computational Intelligence.

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