Ab initio calculation and Boltzmann transport equation have been integrated to find the fundamental influences of trigonal transformation on band structures and thermoelectric performances of antimony. Calculations reveal that antimony could keep its semimetal feature within the c/a range of 2.27–2.82 and that two transitions of band structures of antimony under trigonal transformation are revealed for the first time. Moreover, trigonal transformation has a significant influence on the thermoelectric performances of antimony, and the Seebeck coefficients for the electrons and holes of antimony reach the peaks at the c/a points of 2.72 and 2.57, respectively. The calculated results are in good agreement with the values from experiments in the literature and could deepen the comprehension of the intrinsic relationship between trigonal transformation, band structures, and Seebeck coefficients of antimony.

1.
Y.
Liu
and
R. E.
Allen
,
Phys. Rev. B
52
,
1566
(
1995
).
2.
P. J.
Lin
and
J. C.
Phillips
,
Phys. Rev.
147
,
469
(
1966
).
3.
X.
Gonze
,
J. P.
Michenaud
, and
J. P.
Vigneron
,
Phys. Rev. B
41
,
11827
(
1990
).
4.
L. M.
Falicov
and
P. J.
Lin
,
Phys. Rev.
141
,
562
(
1966
).
5.
J.
Rose
and
R.
Schuchardt
,
Phys. Status Solidi B
139
,
499
(
1987
).
6.
X.
Gonze
,
R.
Sporken
,
J. P.
Vigneron
,
R.
Caudano
,
J.
Ghijsen
,
R. L.
Johnson
,
L.
Ley
, and
H. W.
Richter
,
Phys. Rev. B
44
,
11023
(
1991
).
7.
J.-P.
Issi
,
Aust. J. Phys.
32
,
585
(
1979
).
8.
L.
Ley
,
R. A.
Pollak
,
S. P.
Kowalczyk
,
R.
McFeely
, and
D. A.
Shirley
,
Phys. Rev. B
8
,
641
(
1973
).
9.
G. A.
Saunders
and
Ö.
Öktü
,
J. Phys. Chem. Solids
29
,
327
(
1967
).
10.
G. A.
Saunders
,
C.
Miziumski
,
G. S.
Cooper
, and
A.
Lawson
,
J. Phys. Chem. Solids
26
,
1299
(
1965
).
11.
J.
Mao
,
Z.
Liu
,
J.
Zhou
,
H.
Zhu
,
Q.
Zhang
,
G.
Chen
, and
Z.
Ren
,
Adv. Phys.
67
,
69
(
2018
).
12.
J.
He
and
T. M.
Tritt
,
Science
357
,
eaak9997
(
2017
).
13.
C. S.
Barrett
,
P.
Cucka
, and
K.
Haefner
,
Acta Crystallogr.
16
,
451
(
1963
).
14.
H.
Iwasaki
and
T.
Kikegawa
,
Acta Crystallogr. B
53
,
353
(
1997
).
15.
X.
Wang
,
K.
Kunc
,
I.
Loa
,
U.
Schwarz
, and
K.
Syassen
,
Phys. Rev. B
74
,
134305
(
2006
).
16.
K. J.
Chang
and
M. L.
Cohen
,
Phys. Rev. B
33
,
7371
(
1986
).
17.
J.
Rose
and
R.
Schuchardt
,
Phys. Status Solidi B
117
,
213
(
1983
).
18.
M.
Zouhar
and
M.
Šob
,
Phys. Rev. B
94
,
184110
(
2016
).
19.
C. Y.
Wu
,
J.
Han
,
L.
Sun
,
H. R.
Gong
, and
C. P.
Liang
,
J. Phys. Condens. Matter
30
,
429501
(
2018
).
20.
C. Y.
Wu
,
L.
Sun
,
H. R.
Gong
, and
S. F.
Zhou
,
J. Mater. Sci.
54
,
6347
(
2019
).
21.
G.
Kresse
and
J.
Furthmüller
,
Phys. Rev. B
54
,
11169
(
1996
).
22.
G.
Kresse
and
J.
Furthmüller
,
Comput. Mater. Sci.
6
,
15
(
1996
).
23.
G.
Kresse
and
D.
Joubert
,
Phys. Rev. B
59
,
1758
(
1999
).
24.
D. M.
Ceperley
and
B. J.
Alder
,
Phys. Rev. Lett.
45
,
566
(
1980
).
25.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
26.
J. P.
Perdew
,
J. A.
Chevary
,
S. H.
Vosko
,
K. A.
Jackson
,
M. R.
Pederson
,
D. J.
Singh
, and
C.
Fiolhais
,
Phys. Rev. B
46
,
6671
(
1992
).
27.
L.
Chen
,
Q.
Wang
,
L.
Xiong
, and
H. R.
Gong
,
Int. J. Hydrog. Energy
43
,
16180
(
2018
).
28.
J.
Qian
,
C. Y.
Wu
,
H. R.
Gong
, and
S. F.
Zhou
,
J. Alloys Comp.
768
,
387
(
2018
).
29.
G. K. H.
Madsen
and
D. J.
Singh
,
Comput. Phys. Commun.
175
,
67
(
2006
).
30.
L. C.
Liu
,
J. W.
Wang
,
J.
Qian
,
Y. H.
He
,
H. R.
Gong
,
C. P.
Liang
, and
S. F.
Zhou
,
J. Membr. Sci.
550
,
230
(
2018
).
31.
J.
Qian
,
C. Y.
Wu
,
J. L.
Fan
, and
H. R.
Gong
,
J. Alloys Comp.
737
,
372
(
2018
).
32.
H.
Peng
,
N.
Kioussis
, and
G. J.
Snyder
,
Phys. Rev. B
89
,
195206
(
2014
).
33.
J. X.
Yang
,
H. L.
Zhao
,
H. R.
Gong
,
M.
Song
, and
Q. Q.
Ren
,
Sci. Rep.
8
,
1992
(
2018
).
34.
J. X.
Yang
,
L. C.
Liu
,
H. R.
Gong
, and
M.
Song
,
Solid State Commun.
284–286
,
40
(
2018
).
35.
W.
Kramer
and
J.
Noelting
,
Acta Metall.
20
,
1353
(
1972
).
36.
E.
Gruneisen
and
H. D.
Erfling
,
Ann. Phys-Berlin
36
,
357
(
1939
).
37.
K.
Rausch
,
Ann. Phys-Berlin
1
,
190
(
1947
).
38.
G. J.
Snyder
and
E. S.
Toberer
,
Nat. Mater.
7
,
105
(
2008
).
39.
J. P.
Heremans
,
V.
Jovovic
,
E. S.
Toberer
,
A.
Saramat
,
K.
Kurosaki
,
A.
Charoenphakdee
,
S.
Yamanaka
, and
G. J.
Snyder
,
Science
321
,
554
(
2008
).
You do not currently have access to this content.