First-principles investigation of high pressure effect on structure, mechanical and electronic properties of Mo2ScAlC2

Journal Pre-proof First-principles investigation of high pressure effect on structure, mechanical and electronic properties of Mo2ScAlC2 Yong Tang, Xiangli Zhong, Meiping Liu, Hongjia Song, Jinbin Wang PII:

S0921-4526(20)30185-X

DOI:

https://doi.org/10.1016/j.physb.2020.412171

Reference:

PHYSB 412171

To appear in:

Physica B: Physics of Condensed Matter

Received Date: 11 October 2019 Revised Date:

8 March 2020

Accepted Date: 27 March 2020

Please cite this article as: Y. Tang, X. Zhong, M. Liu, H. Song, J. Wang, First-principles investigation of high pressure effect on structure, mechanical and electronic properties of Mo2ScAlC2, Physica B: Physics of Condensed Matter (2020), doi: https://doi.org/10.1016/j.physb.2020.412171. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

CRediT authorship contribution statement Yong Tang :. Meiping Liu :. Huandong Hu :. data curation, formal analysis, investigation, writing-original draft. Xiangli Zhong:. Hongjia Song:. Jinbin Wang:. conceptualization,

funding

writing-review & editing.

acquisition,

project

administration,

supervision,

1

First-principles investigation of high pressure effect on structure,

2

mechanical and electronic properties of Mo2ScAlC2

3

Yong Tang, Xiangli Zhong, Meiping Liu, Hongjia Song, Jinbin Wang*

4

Corresponding author. School of Materials Science and Engineering, Xiangtan

5

University, Xiangtan, 411105, Hunan, China.

6

E-mail address: [email protected] (Jinbin Wang).

7

Abstract

8

In this work, high pressure effect on the structure, mechanical and electronic

9

properties of Mo2ScAlC2 has been investigated with first-principles method. Results

10

show that Mo2ScAlC2 is much more compressible along a axis than along c axis.

11

Besides, mechanical properties are explored. Elastic constants and moduli creep up

12

with the increasing pressure. Especially, the sharp increment of C33 also predicts a

13

strong resistance to the compression strain along c axis. With the increasing of

14

pressure, Mo2ScAlC2 change from brittle to ductile. Furthermore, the electronic

15

analysis indicates that Mo2ScAlC2 is predicted to be metallic and the metallicity of

16

Mo2ScAlC2 reduces gradually with the increase of pressure. Finally, the deformation

17

charge density distribution indicates that Sc-atom provides more electrons to C-atom

18

obtains with increasing pressure.

19

Keywords: Mo2ScAlC2, mechanical properties, high pressure, first-principles method,

20

deformation charge density distribution

21

1. Introduction

22

The MAX phase material with chemical formula Mn+1AXn(n=1,2,3) expresses a

23

class of layered ternary compound, where M represents the early transition metal

24

element from group 3-6, A is an element from columns 12-16 in the periodic table and

25

X stands for C and/or N[1-4]. The MAX phase exhibits dual characteristics of metal

26

and ceramic, that is, it possesses not only the properties of metal such as conduction,

27

heat conduction, and machinability, but also the features of ceramic, for instance,

28

high-temperature and corrosion resistance[5,6]. In view of the above-mentioned

29

abundant properties, the extensive applications of MAX phase materials in the fields 1

30

of the high-temperature, high-pressure, and chemical-anticorrosion, have proved the

31

MAX phase with significant application prospect and research value[7,8].

32

Researchers have made considerable efforts in the synthesis of new MAX phase

33

materials. To date, about 80 kinds of MAX phase materials[9-12] have been

34

successfully synthesized. Nevertheless, only Mo2GaC of the synthesized MAX phase

35

materials contains Mo as M element. Recently, by alloying on the M-site, the fourth

36

element has been added to MAX phase, providing a new way to form novel type of

37

double transition metal MAX phase materials. There have some new products have

38

been

39

Mo2Ti2AlC3[14], Mo2ScAlC2[16] et al. Thereinto, Mo2ScAlC2 is a very remarkable

40

new MAX phase material, who combines two kinds of uncommon transition metals

41

Mo and Sc as M elements. Relevant studies have been carried out for Mo2ScAlC2.

42

Meshkian et al. have evaluated the phase stability by employing an ab initio

43

calculation based on the Density Functional Theory (DFT), suggesting that the

44

chemical order in the alloy promotes a stable phase. Furthermore, they have

45

successfully synthesized Mo2ScAlC2 by heating the mixture element powder of Mo,

46

Sc, Al, and graphite in 1700°C[16,17]. The experimental results of High-resolution

47

Transmission Electron Microscopy have confirmed that Mo2ScAlC2 possesses a

48

chemically ordered structure, in which one Sc layer is situated in two Mo-C layers,

49

that is in line with the results of theoretical study. Hadi et al. have investigated the

50

mechanical properties, bonding nature and defect behaviors of Mo2ScAlC2 by the

51

first-principles method[18]. Their researches found this compound is a brittle material

52

with higher Debye temperature. For bonding properties, Mo2ScAlC2 mainly exhibits

53

the mixed bonding of strong covalent and metallic, possessing weak ionic

54

characteristics simultaneously. The aforementioned studies indicate that Mo2ScAlC2

55

has the potential to work in the high-pressure environment like other MAX phase

56

materials. However, the absence of relevant researches, including experimental and

57

theoretical, on properties‫ ׳‬evolution of Mo2ScAlC2 under high pressure, such as

58

structure, mechanical and electronic properties, etc. will greatly restrict the practical

59

application of Mo2ScAlC2 in this extreme environment in the future. Therefore, it is

successfully

synthesized,

including

2

Cr2TiAlC2[13],

Mo2TiAlC2[14,15],

60

of great significance to carry out theoretical research on the properties of Mo2ScAlC2

61

under high pressure. With the motivations to reveal this unexplored area, we report

62

detailed theory investigations of structural, mechanical and electronic properties of

63

Mo2ScAlC2 under high pressure within the range of 0 to 100GPa, which is the first

64

time for the study of quaternary MAX phase under high pressure. The reminder of this

65

paper is organized as follows: the computational methods and details are proposed in

66

Section 2; the results are described and discussed in Section 3 and a brief summary of

67

this work is presented in Section 4.

68

2. Computational methods

69

All the calculations, as implemented within the Cambridge Sequential Total

70

Energy Package code ， are carried out by employing DFT with plane wave

71

pseudopotential

72

Perdew-Wang-91(GGA-PW91)[20] is utilized as the exchange-correlation function to

73

treat the exchange-correlation energy. The ultrasoft Vanderbilt-type pseudopotentials

74

with electronic configurations of 4s24p64d55s1, 3s23p63d14s25s2, 3s23p1, and 2s22p2 as

75

the basis sets of the valence electron states for Mo, Sc, Al and C, respectively, have

76

been chosen to treat the electron-ion interactions[21]. A energy cut-off of 600eV is

77

selected as the plane wave basis. A 17×17×3 and a denser 25×25×3 k-meshes

78

sampling Monkhorst-Pack scheme of Brillouin zone are used in the structural

79

optimization and properties calculations, respectively[22]. Structural parameters at

80

different pressure with respect to atomic coordinates and lattice constants have been

81

fully optimized by means of the Broyden-Fletcher-Goldfarb-Shanno(BFGS)

82

algorithm[23].

83

Hellmann-Feynman forces are less than 0.01 eV/ Å and the convergence standard of

84

10-5 eV is adopted.

85

3. Results and discussion

86

3.1. Structural properties

method[19].

Structural

The

generalized

optimization

process

gradient

ceases

approximation

until

the

of

atomic

87

As shown in Fig.1, the structure of Mo2ScAlC2 belongs to the hexagonal crystal

88

system with a space group of P63/mmc. The unit cell contains 2 formula units(Z = 2)

89

of 12 atoms. Mo, Sc, Al, C atoms are located at the 4f (1/3, 2/3, zMo), 2a(0, 0, 0), 2b(0, 3

90

0, 1/4) and 4f (2/3, 1/3, zC) Wyckoff positions, respectively. Here, zMo and zC represent

91

internal coordinates. The lattice constants, internal coordinates and cell volume V of

92

optimized structure under ambient pressure are listed in Table 1. Obviously, our

93

calculations are in good agreement with the previous experimental and theoretical

94

values.

95 96

Fig. 1. Crystal structure of layered Mo2ScAlC2

97

Table 1: Lattice parameters a, c, cell volume V, internal parameter zMo, zC, bulk modulus B0 and its

98

pressure derivative B0’ of Mo2ScAlC under ambient pressure. a/Å

c/Å

V/Å3

zMo

zC

B0

B 0’

ref

3.041

18.986

152.054

0.137

0.072

178.1

4.49

present

3.062

19.072

154.859

3.052

19.065

145.955

3.030

18.770

149.238

3.033

18.775

145.157

16 0.137

0.076

173

18 16

0.136

0.068

18

99

Based on the optimized structure under ambient pressure, we use 10GP as an

100

interval step to exert hydrostatic pressure on the structure in the range of 0 to 100GPa.

101

Pressure makes the difference of structural parameters a and c, internal parameters zMo

102

and zC, and cell volume V. Fig.2 exhibits the dependence of structural parameters on a

103

pressure of optimized structures. As shown in Fig.2(a), the lattice constants a and c

104

decrease with increasing pressure, and the decrease rate a/a0 is more rapidly than c/c0.

105

This result is consistent with the trend that the value of c/a increases gradually with

106

the increase of pressure in Fig. 2(b). The difference between a/a0 and c/c0 indicates 4

107

that Mo2ScAlC2 has a stronger stiffness along c axis than that along a axis. Based on

108

the third order Birch-Murnaghan equation of state[24] described by formula (1), we

109

have fit the curve of pressure P and volume V, as shown in Fig.2(c). The fitting results

110

of the bulk modulus B0, the first derivative of B0 on pressure B0’, and the cell volume

111

V0 under ambient pressure condition are listed in Table 1. What we can obtain from

112

the results is that the fitting value of B0 is very consistent with the value reported in

113

reference.

114

=

/

/

−

/

/

1+

−4

/

/

−1

(1)

115

With regard to internal parameters, it can be seen from Fig. 2(d) that u increases

116

significantly while v decreases with the increase of pressure. This variation tendency

117

of u and v indicates that Mo move toward the Al layer and C move toward the Sc

118

layer respectively in the process of increasing pressure. Generally speaking, all

119

structural parameters shown in Fig.2 are not linearly dependent on a pressure within

120

the range we considered.

121 122 123

Fig. 2. Pressure dependence of structural parameters for Mo2ScAlC

3.2. Mechanical and dynamical properties

124

The mechanical properties of a material reflect the response to an applied load.

125

The mechanical properties of MAX phase materials determine their application 5

126

prospects and a better study of mechanical properties is helpful to the synthesis of

127

MAX phase materials. Calculating the elastic constants can also help us obtain the

128

information of isotropy, anisotropy and crystal structure stability of MAX phase

129

materials.

130

Table 2: Calculated elastic constants Cij, bulk modulus B, share modulus G, Young’s modulus

131

E(GPa),Poisson’s ratio μ and Pugh’s modulus ratio κ for Mo2ScAlC2 under zero pressure C11

C12

C13

C33

C44

BH

GH

E

μ

κ

305

105

132.9

310

134

184.5

108

272

0.255

0.588

293

109

117

290

134

173

105

262

0.250

0.606

Ref

18

132

We firstly evaluated the elastic constants of Mo2ScAlC2 under ambient pressure,

133

which are listed in Table 2. Obviously, the calculation results of five independent

134

elastic constants of hexagonal crystal system compound Mo2ScAlC2 under

135

atmospheric pressure are consistent with previous studies[18]. Within the

136

Voight-Reuss-Hill(VRH) approximation[25-27] for polycrystalline aggregates, the

137

maximum(BV), minimum(BR) and average(BH) values of bulk modulus B for

138

hexagonal crystal system can be obtained from formula (2)-(4). Similarly, the

139

maximum (GV), minimum(GR) and average(GH) values of shear modulus G can be

140

gained from the formula (5)-(7). Furthermore, the Young‫׳‬s modulus E[28] and

141

Poisson‫׳‬s ratio μ[29] can be valued according to formula (8) and (9). Obviously, the

142

ambient mechanical properties of Mo2ScAlC2 are not as good as that of Mo3AlC2[30],

143

attributed to the weaker chemical bond Sc-C than Mo-C bond. Therefore, it is

144

possible to design MAX phase materials with better mechanical properties by adding

145

new elements to form stronger covalent bonds with C.

146

=

(2) (3)

147

!

=

148

"

=

149

& =

150

&! =

#$ #%

(4) '

#% (( ))

'

((

'

))

(5 )

(( ))

((

))

6

(6)

*$ *%

151

&" =

152

E=

153

-=

154

.

155

.44 = .44 −

(7)

#, *,

(8)

#, *, #,

*,

(9)

#, *,

> 0, .'' > |.' |, .'' + .' .

− 2.'

>0

5 = 1,3,4 , .' = .' + , .' = .' +

(10) (11)

156

In addition, the elastic constants must conform to the criteria[31], described in

157

formulas (10) and (11), to maintain mechanical stability of hexagonal crystals under

158

isotropic pressure.

159

Fig.3 reveals the curve of elastic constants and moduli with pressure. It is

160

obvious that all the elastic constants and moduli step up monotonically with the

161

increase of pressure. The detailed results show that the elastic constants under

162

different pressures can meet the requirements of mechanical stability, that is,

163

Mo2ScAlC2 possesses mechanical stability within the range of 0 to 100GPa.

164

Especially noteworthy in Fig.3(a) is that the elastic constants C11, C33, bulk modulus B,

165

and Young‫׳‬s modulus E all enlarge substantially under pressure. Conversely, C66 and

166

shear modulus G increase slowly. Specifically, when the applied hydrostatic pressure

167

increased to 100GPa, C11 and C33 increased by 371.4GPa and 495.1GPa respectively,

168

and C66 increased by just 79.6GPa. The violent increase of C33 and moderate increase

169

of C66 signifies the increasing insensitivity with respect to the compression strain

170

along c axis, not the shear strain. The increment features of bulk modulus B and shear

171

modulus G shown in Fig.3(b) confirms the incompressibility and stiffness properties

172

of Mo2ScAlC2 with the pressure increasing.

173 7

Fig. 3. Pressure dependence of (a) Elastic Constants and (b) Elastic moduli for Mo2ScAlC

174 175

The failure mode of solid (brittle or ductile failure) can be explained by their

176

bulk and shear modulus, which is of great significance to determine the integrity of

177

structures. The Pugh‫׳‬s modulus ratio κ, described by formula (12), is used to

178

characterize the brittleness or ductility of materials[32]. The critical value of κ is 0.57,

179

that is to say, brittle and ductile materials possess the κ values greater than and less

180

than 0.57, respectively. Anisotropy of mechanical properties also plays an important

181

role of materials. The anisotropic factors Aan, AB, AG, and AU, represent by formula

182

(13), are indicators of elastic anisotropy of materials. According to definition, it is

183

known that the elasticity of the material is isotropic when Aan equals to 1 and the

184

greater the difference between Aan and 1 means the stronger elastic anisotropy of

185

material[33]; the value of AU deviates from zero, which corresponds to the anisotropy

186

of material, the value of AU deviating from zero corresponds to the anisotropy level,

187

and for AB and AG, the closer the value of AB and AG to 1, the stronger the elastic

188

anisotropy[34]. Another anisotropic factor kc/ka, exhibited in formula (14), is defined

189

as the ratio between the linear compression coefficient along c axis and a axis[35].

190

7=#

191

89: =

192

*

?@

?A

(12) ;;

8# =

#% #$ #% #$

8* =

*% *$ *% *$

=

8< = 5

*%

*$

+

#%

#$

−6

(13) (14)

193

The results in Table 1 indicate that the calculated values of Poisson's ratio μ at

194

different pressure are in the range of 0.25 to 0.36 and the values increase as pressure

195

increases. The variation tendency of μ indicates that the shear resistance of

196

Mo2ScAlC2 decreases with increasing pressure[36,37]. It is interesting to note that the

197

value of κ is less than the critical value before being pressed, but it exceeds the critical

198

value when pressure is applied to Mo2ScAlC2. The change of κ implies the transform

199

of Mo2ScAlC2 from brittleness to ductility after being pressed and the ductility

200

increases as the pressure rise. For mechanical anisotropy of Mo2ScAlC2, the five

201

anisotropic factors perform uniformly, indicating that the mechanical anisotropy of

202

Mo2ScAlC2 increases with increasing pressure. 8

203

Table 3 Results of Poisson’s ratio μ, Pugh’s modulus ratio κ, anisotropy factors (Aan, AB, AG, AU,

204

and kc/ka) at pressure ranged from 0 to 100 GPa. μ

κ

Aan

AB

AG

AU

kc/ka

0.255

0.588

1.53

0.001

0.018

0.18

0.82

0.25

0.606

1.54

0.19

0.97

10

0.271

0.530

1.55

0.006

0.022

0.22

0.87

20

0.274

0.508

1.61

0.011

0.028

0.28

0.90

30

0.312

0.468

1.67

0.012

0.074

0.61

0.94

40

0.333

0.396

1.69

0.014

0.111

0.74

0.96

50

0.344

0.362

1.70

0.014

0.124

0.87

0.97

60

0.346

0.348

1.72

0.018

0.138

0.93

099

70

0.346

0.321

1.79

0.018

0.141

1.06

1.01

80

0.351

0.318

1.75

0.021

0.156

1.32

1.02

90

0.352

0.299

1.81

0.024

0.181

1.49

1.05

100

0.352

0.291

1.82

0.036

0.196

1.75

1.06

Pressure

Ref

0 18

205

Debye temperature(BC ), defined by formula(15)[38], is an important parameter

206

to determine the thermodynamic property of material. The parameters h, kB, NA, M

207

and n in formula(15) denote the Planck‫׳‬s constant, the Boltzmann‫׳‬s constant, the

208

Avogadro‫׳‬s number, the molecular weight and the number of atoms in the molecule,

209

respectively.

210

BC = ? F

211

D

E

: HI J '/ L G K

F2

J

*

/

+

#

J

*

/

L

'/

(15)

The density ρ and BC of Mo2ScAlC2, shown in Fig.4, increases gradually in the

212

process of increasing pressure. The increasing of BC implies that Mo2ScAlC2

213

becomes thermally more conductive with pressure increasing.

9

214 215

Fig. 4. The density ρ and Debye‫׳‬s temperature BC of Mo2ScAlC2 at pressure ranged from 0 to

216

100GPa.

217

3.2. Electronic properties

218

The electronic structure determines the properties of materials. Over here, we

219

select three structures under pressure of 0, 50, and 100GPa as representatives to

220

explore the electronic structure, obtaining insight into the bonding behavior of

221

Mo2ScAlC2. The electronic structures, total density of states(DOS), and projected

222

density of states(PDOS) of the representatives are investigated, rendered in Fig.5.

223

From Fig.5, we can see that the conduction bands and valence bands are

224

overlaping at the Fermi level, similarly to those of most MAX phase

225

materials[13,15,39-42], indicating the metallicity of Mo2ScAlC2. Moreover, there is a

226

strong anisotropy near the Fermi level. The energy dispersion along c axis, which is

227

represented by G-A, H-K and M-L high symmetry direction, is especially weak.

228

Therefore, the conductivity of Mo2ScAlC2 also exhibits anisotropy, that is to say, the

229

conductivity along the c axis is lower than that of a and b axis. In addition, the

230

number of energy bands near the Fermi level taper with increasing pressure.

231

Corresponding to the Fermi level in the electronic structures, the most of the

232

states at the Fermi level EF comes from the 4d-orbitals of Mo. Moreover, what can be

233

obviously acquired from Fig.5(b), (d), and (f) is that the valence bands of Mo2ScAlC2

234

can be divided into three parts. In the first part, the DOS in the energy range from

235

-12eV to -10ev mainly attributes to the electron contribution of Mo-4d, Sc-3d and

236

C-2s orbitals. Moreover, there exhibits hybridization between C-2s orbitals and 10

237

d-orbitals Mo as well as Sc. In the second part, the energy interval is about -4.1~-2.6

238

eV, which mainly originates from the contribution of the d-orbitals of Mo and Sc and

239

the 2p-orbitals of C. Similarly, the d-orbitals of Mo and Sc overlap with 2p-orbitals of

240

C. The part of valence bands(-2.6 ~ 0 eV) are mainly derived from the contribution of

241

the d-orbitals of Mo and 3p-orbitals of Al and there is also a coincidence of orbital

242

electrons between the d-orbitals of Mo and 3p-orbitals of Al. As the pressure

243

increasing, the energy peak in the DOS diagrams move towards the lower energy

244

level and the orbital hybridization effect is gradually weakening, which may indicate

245

the hardness reduction of Mo2ScAlC2 with the increase of pressure. In addition, the

246

value of DOS N(EF) at the Fermi level decreases with the increase of pressure, leading

247

to a gradual reduction in the metallicity of Mo2ScAlC2. Here we adopt formula

248

(16)[43], where nm and ne are thermally excited the number of electrons and the total

249

number of valence electrons in the unit cell, respectively, to estimate the metallicity of

250

Mo2ScAlC2 at ambient temperature. The outcomes emerged from Fig.6 reflect that the

251

metallicity properties of Mo2ScAlC2 go downhill with increasing pressure.

252

MN =

:O :P

=

?E Q×H ST :P

=

.

V×H ST

(16)

:P

11

253 254

Fig. 5. Electronic structures(a,c,e) and DOS(b,d,f) for Mo2ScAlC2 at 0, 50, and 100 GPa.

255 256

Fig. 6. Pressure dependence of metallicity for Mo2ScAlC2.

257

Furthermore, the charge density difference[44] in 112W0 plane of Mo2ScAlC2

258

under pressure of 0, 50, and 100GPa, are presented in Fig.7(a,b,c) to investigate the

259

charge transfer in the process of applying pressure. From the diagrams, we can see

260

that the charge transfer from Sc to C occurs during the pressure applied. As the

261

pressure increases, more electrons transfer from Sc to C. The charge transfer should 12

262

be should be attributed to the difference in electronegativity of elements. This transfer

263

forms stronger ionic bonds and weakens the covalent bonds, leading to the decrease in

264

the hardness of Mo2ScAlC2. Mulliken overlap population analysis[45] is also

265

performed to describe the ionic/covalent properties qualitatively. The consequences

266

are that the Sc-C bonds populations are 0.52, 0.37, and 0.23 for 0, 50, and 100 GPa.

267

For C-Mo bonds, the value decreases from 1.45 to 1.38 with increasing pressure, and

268

finally to 1.36 at 100GPa. The ratio of bond length(LMo-C and LSc-C) and Millikan

269

population(PMo-C and PSc-C) under pressure to that under zero pressure is shown in the

270

Fig.7(d). It can be seen that all the bond lengths are shortened after compression and

271

the shorten of Sc-C is more serious than that of Mo-C. With the shortening of bond

272

length, the bond population of Sc-C decreases sharply and that of Mo-C decreases

273

slightly. The change of chemical bond population indicates that the covalent bond

274

components of Mo-C and Sc-C decrease, and that the latter changes more

275

dramatically than the former. Naturally, the ionic bond components increase

276

gradually.

277 278

Fig.7. The charge density difference in 112W0 plane of Mo2ScAlC2 under the pressure of (a)0GP,

279

(b)50GPa and (c)100GPa

280

4. Summary

281

In conclusion, for the purpose of revealing behaviors of Mo2ScAlC2 at high

282

pressure, we have employed a detailed theory study to investigate the structural,

283

mechanical and electronic properties of Mo2ScAlC2 within the pressure range of 0 to

284

100GPa. Results illustrate that, under the hydrostatic pressure, Mo2ScAlC2 behaves an

285

obvious uniaxial compression anisotropy, and it’s easier to compress a axis than c axis. 13

286

The studies of mechanical properties demonstrate that the elastic constants, moduli

287

and anisotropy increase gradually with the increase of pressure, and Mo2ScAlC2

288

possesses mechanical stability in the range of 0-100GPa. After being applied high

289

pressure, Mo2ScAlC2 transforms from brittleness to ductility gradually. Finally, the

290

electronic properties of Mo2ScAlC2 dependent on pressure are investigated. The

291

reason for the decrease of metallicity has been explored by analyzing the changes in

292

electronic properties such as electronic structures, DOS, and charge transfer during

293

pressure application. We believe that our research is helpful in understanding the

294

changes and improvements in the properties of quaternary MAX phase compounds

295

with double M elements under high pressure.

296 297

Acknowledgements

298

This work was financially supported by the National Natural Science Foundation

299

of China (Nos. 61574121, 51872251, and 11847106). The work was carried out at

300

LvLiang Cloud Computing Center of China, and the calculations were performed on

301

TianHe-2.

302 303

Conflicts of interest:

304

There are no conflicts to declare.

305

Reference： ：

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Conflicts of interest: There are no conflicts to declare.