We propose a hybrid scheme that smoothly interpolates the Ziegler-Biersack-Littmark (ZBL) screened nuclear repulsion potential with a deep learning potential energy model. The resulting deep potential-ZBL model can not only provide overall good performance on the predictions of near-equilibrium material properties but also capture the right physics when atoms are extremely close to each other, an event that frequently happens in computational simulations of irradiation damage events. We applied this scheme to the simulation of the irradiation damage processes in the face-centered-cubic aluminum system and found better descriptions in terms of the defect formation energy, evolution of collision cascades, displacement threshold energy, and residual point defects than the widely adopted ZBL modified embedded atom method potentials and their variants. Our work provides a reliable and feasible scheme to accurately simulate the irradiation damage processes and opens up extra opportunities to solve the predicament of lacking accurate potentials for enormous recently discovered materials in the irradiation effect field.

1.
W. L.
Jorgensen
,
D. S.
Maxwell
, and
J.
Tirado-Rives
,
J. Am. Chem. Soc.
118
,
11225
(
1996
).
2.
S.
Dumpala
,
S. R.
Broderick
,
U.
Khalilov
,
E. C.
Neyts
,
A. C. T.
van Duin
,
J.
Provine
,
R. T.
Howe
, and
K.
Rajan
,
Appl. Phys. Lett.
106
,
011602
(
2015
).
3.
S.
Hooda
,
S. A.
Khan
,
B.
Satpati
,
D.
Kanjilal
, and
D.
Kabiraj
,
Appl. Phys. Lett.
108
,
201603
(
2016
).
4.
R.
Car
and
M.
Parrinello
,
Phys. Rev. Lett.
55
,
2471
(
1985
).
5.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
6.
L.
Zhang
,
J.
Han
,
H.
Wang
,
R.
Car
, and
E.
Weinan
,
Phys. Rev. Lett.
120
,
143001
(
2018
).
7.
K.
Yao
,
J. E.
Herr
,
S. N.
Brown
, and
J.
Parkhill
,
J. Phys. Chem. Lett.
8
,
2689
(
2017
).
8.
J.
Han
,
L.
Zhang
,
R.
Car
, and
E.
Weinan
,
Commun. Comput. Phys.
23
,
629
(
2018
).
9.
S.
Chmiela
,
A.
Tkatchenko
,
H. E.
Sauceda
,
I.
Poltavsky
,
K. T.
Schütt
, and
K.-R.
Müller
,
Sci. Adv.
3
,
e1603015
(
2017
).
10.
J.
Behler
and
M.
Parrinello
,
Phys. Rev. Lett.
98
,
146401
(
2007
).
11.
A. P.
Bartók
,
M. C.
Payne
,
R.
Kondor
, and
G.
Csányi
,
Phys. Rev. Lett.
104
,
136403
(
2010
).
12.
K. T.
Schütt
,
F.
Arbabzadah
,
S.
Chmiela
,
K. R.
Müller
, and
A.
Tkatchenko
,
Nat. Commun.
8
,
13890
(
2017
).
13.
A. P.
Bartók
,
R.
Kondor
, and
G.
Csányi
,
Phys. Rev. B
87
,
184115
(
2013
).
14.
L.
Zhang
,
H.
Wang
, and
E.
Weinan
,
J. Chem. Phys.
149
,
154107
(
2018
).
15.
A. P.
Thompson
,
L. P.
Swiler
,
C. R.
Trott
,
S. M.
Foiles
, and
G. J.
Tucker
,
J. Comput. Phys.
285
,
316
(
2015
).
16.
M. A.
Wood
and
A. P.
Thompson
,
J. Chem. Phys.
148
,
241721
(
2018
).
17.
J. F.
Ziegler
and
J. P.
Biersack
, “
The stopping and range of ions in matter
,” in
Treatise on Heavy-Ion Science
(
Springer
,
1985
), pp.
93
129
.
18.
B.
Jelinek
,
S.
Groh
,
M. F.
Horstemeyer
,
J.
Houze
,
S. G.
Kim
,
G. J.
Wagner
,
A.
Moitra
, and
M. I.
Baskes
,
Phys. Rev. B
85
,
245102
(
2012
).
19.
S. S.
Gupta
,
M. A.
van Huis
,
M.
Dijkstra
, and
M. H. F.
Sluiter
,
Phys. Rev. B
93
,
085432
(
2016
).
20.
R.
Qiu
,
H.
Lu
,
B.
Ao
,
L.
Huang
,
T.
Tang
, and
P.
Chen
,
Philos. Mag.
97
,
2164
(
2017
).
21.
N. T. H.
Trung
,
H. S. M.
Phuong
,
M. D.
Starostenkov
,
V. V.
Romanenko
, and
V. A.
Popov
,
IOP Conf. Ser.: Mater. Sci. Eng.
447
,
012004
(
2018
).
22.
M. I.
Mendelev
,
M. J.
Kramer
,
C. A.
Becker
, and
M.
Asta
,
Philos. Mag.
88
,
1723
(
2008
).
23.
V.
Botu
and
R.
Ramprasad
,
Phys. Rev. B
92
,
094306
(
2015
).
24.
V.
Botu
,
R.
Batra
,
J.
Chapman
, and
R.
Ramprasad
,
J. Phys. Chem. C
121
,
511
(
2017
).
25.
L.
Zhang
,
J.
Han
,
H.
Wang
,
W.
Saidi
,
R.
Car
, and
W.
E
, in
Advances in Neural Information Processing Systems
(NIPS,
2018
), pp.
4441
4451
.
26.
L.
Zhang
,
D.-Y.
Lin
,
H.
Wang
,
R.
Car
, and
E.
Weinan
,
Phys. Rev. Mater.
3
,
023804
(
2019
).
27.
V. A.
Medvedev
,
J. D.
Cox
, and
D. D.
Wagman
, CODATA Key Values for Thermodynamics (Hemisphere Publishing Corporation,
1990
), Vol. 94, p.
93
.
28.
A.
Cooper
,
Acta Crystallogr.
15
,
578
(
1962
).
29.
W.
Triftshäuser
,
Phys. Rev. B
12
,
4634
(
1975
).
30.
M. J.
Fluss
,
L. C.
Smedskjaer
,
M. K.
Chason
,
D. G.
Legnini
, and
R. W.
Siegel
,
Phys. Rev. B
17
,
3444
(
1978
).
31.
R. Q.
Hood
,
P. R. C.
Kent
, and
F. A.
Reboredo
,
Phys. Rev. B
85
,
134109
(
2012
).
32.
G. N.
Kamm
and
G. A.
Alers
,
J. Appl. Phys.
35
,
327
(
1964
).
33.
V. C.
Kannan
and
G.
Thomas
,
J. Appl. Phys.
37
,
2363
(
1966
).
34.
P. S.
Dobson
,
P. J.
Goodhew
, and
R. E.
Smallman
,
Philos. Mag.
16
,
9
(
1967
).
35.
J.-P.
Tartour
and
J.
Washburn
,
Philos. Mag. A
18
,
1257
(
1968
).
36.
M. J.
Mills
and
P.
Stadelmann
,
Philos. Mag. A
60
,
355
(
1989
).
37.
D.
Zhao
,
O. M.
Løvvik
,
K.
Marthinsen
, and
Y.
Li
,
J. Mater. Sci.
51
,
6552
(
2016
).
38.
M.
Ross
,
L. H.
Yang
, and
R.
Boehler
,
Phys. Rev. B
70
,
184112
(
2004
).
39.
J.
Bouchet
,
F.
Bottin
,
G.
Jomard
, and
G.
Zérah
,
Phys. Rev. B
80
,
094102
(
2009
).
40.
R. A.
McDonald
,
J. Chem. Eng. Data
12
,
115
(
1967
).
41.
42.
B.
Settles
,
Active Learning (Synthesis Lectures on Artificial Intelligence and Machine Learning)
(
Morgan & Claypool Publishers
,
2012
), Vol.
6
, pp.
1
114
.
43.
L.
Zhang
,
H.
Wang
, and
E.
Weinan
,
J. Chem. Phys.
148
,
124113
(
2018
).
44.
K. W.
Jacobsen
,
J. K.
Norskov
, and
M. J.
Puska
,
Phys. Rev. B
35
,
7423
(
1987
).
45.
M. I.
Pascuet
and
J. R.
Fernández
,
J. Nucl. Mater.
467
,
229
(
2015
).
46.
V. N.
Popok
,
S.
Vučković
,
J.
Samela
,
T. T.
Järvi
,
K.
Nordlund
, and
E. E.
Campbell
,
Phys. Rev. B
80
,
205419
(
2009
).
47.
H. M.
Urbassek
,
Nucl. Instrum. Methods Phys. Res., Sect. B
122
,
427
(
1997
).
48.
S.
Lu
,
D.
Li
, and
D. W.
Brenner
,
Handbook of Damage Mechanics: Nano to Macro Scale for Materials and Structures
(Springer, New York,
2015
), p.
453
.
49.
H.
Wang
,
L.
Zhang
,
J.
Han
, and
E.
Weinan
,
Comput. Phys. Commun.
228
,
178
(
2018
).
50.
S.
Plimpton
,
J. Comput. Phys.
117
,
1
(
1995
).
51.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
47
,
558
(
1993
).
52.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
49
,
14251
(
1994
).
53.
G.
Kresse
and
D.
Joubert
,
Phys. Rev. B
59
,
1758
(
1999
).
54.
A.
Stukowski
,
Modell. Simul. Mater. Sci. Eng.
18
,
015012
(
2009
).
55.
J.
Wallace
,
L. B. B.
Aji
,
L.
Shao
, and
S. O.
Kucheyev
,
Phys. Rev. Lett.
120
,
216101
(
2018
).
56.
H.
Wang
,
J.-T.
Tian
,
W.
Zhou
,
X.-F.
Chen
,
B.
Bai
, and
J.-M.
Xue
,
RSC Adv.
8
,
14017
(
2018
).
57.
W.
Zhou
,
J.
Tian
,
Q.
Feng
,
J.
Zheng
,
X.
Liu
,
J.
Xue
,
D.
Qian
, and
S.
Peng
,
J. Nucl. Mater.
508
,
540
(
2018
).
58.
A.
Meldrum
,
S. J.
Zinkle
,
L. A.
Boatner
, and
R. C.
Ewing
,
Nature
395
,
56
(
1998
).
59.
K.
Nordlund
,
J.
Keinonen
,
M.
Ghaly
, and
R. S.
Averback
,
Nature
398
,
49
(
1999
).
60.
M. T.
Robinson
and
I. M.
Torrens
,
Phys. Rev. B
9
,
5008
(
1974
).
61.
M. J.
Norgett
,
M. T.
Robinson
, and
I. M.
Torrens
,
Nucl. Eng. Des.
33
,
50
(
1975
).
62.
R. S.
Averback
,
R.
Benedek
, and
K. L.
Merkle
,
Phys. Rev. B
18
,
4156
(
1978
).
63.
S. J.
Zinkle
and
B. N.
Singh
,
J. Nucl. Mater.
199
,
173
(
1993
).
64.
R.
Konings
,
Comprehensive Nuclear Materials
(
Elsevier
,
Amsterdam
,
2011
), Vol.
1
.
65.
G. S.
Was
,
Fundamentals of Radiation Materials Science: Metals and Alloys
(
Springer
,
2016
).
66.
G. H.
Kinchin
and
R. S.
Pease
,
Rep. Prog. Phys.
18
,
1
(
1955
).
67.
K.
Nordlund
,
S. J.
Zinkle
,
A. E.
Sand
,
F.
Granberg
,
R. S.
Averback
,
R.
Stoller
,
T.
Suzudo
,
L.
Malerba
,
F.
Banhart
,
W. J.
Weber
,
F.
Willaime
,
S. L.
Dudarev
, and
D.
Simeone
,
Nat. Commun.
9
,
1084
(
2018
).
68.
M. J.
Norgett
,
M. T.
Robinson
, and
I. M.
Torrens
,
Annual Book of ASTM Standards
(ASTM,
1975
).

Supplementary Material

You do not currently have access to this content.