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Journal of Alloys and Compounds 681 (2016) 412e420

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Journal of Alloys and Compounds

journal homepage: http: / /www.elsevier .com/locate/ ja lcom

Theoretical study of structural characteristics, mechanical propertiesand electronic structure of metal (TM¼V, Nb and Ta) silicides

Biao Wan a, b, Furen Xiao a, Yunkun Zhang a, Yan Zhao a, Lailei Wu a, *, Jingwu Zhang a,Huiyang Gou b, **

a Key Laboratory of Metastable Materials Science and Technology, College of Material Science and Engineering, Yanshan University, Qinhuangdao 066004,Chinab Center for High Pressure Science and Technology Advanced Research, Shanghai 201203, China

a r t i c l e i n f o

Article history:Received 24 December 2015Received in revised form22 April 2016Accepted 24 April 2016Available online 26 April 2016

Keywords:First-principles calculationsTransition metal silicidesStabilityMechanical propertyElectronic structure

* Corresponding author.** Corresponding author.

E-mail addresses: wll@ysu.edu.cn (L. Wu), huiyang

http://dx.doi.org/10.1016/j.jallcom.2016.04.2530925-8388/© 2016 Elsevier B.V. All rights reserved.

a b s t r a c t

Using first-principles calculations, the crystal structure, mechanical property and electronic structurewere investigated systematically for TM-Si (TM ¼ V, Nb and Ta) systems. Pm3 n-V3Si, I4/mcm-V5Si3 andP6222-VSi2 for V-Si system, I4/mcm-Nb5Si3, P6222-NbSi2 for Nb-Si system, and P42/n-Ta3Si, I4/mcm-Ta2Si,I4/mcm-Ta5Si3, P6222-TaSi2 for Ta-Si system, are identified as thermodynamically stable structures, wellconsistent with previous theoretical and experimental reports. Stable P4/mbm-Nb3Si2, P41212-Nb5Si4,Ibam-Nb6Si5, Pnma-NbSi and P4/mbm-Ta3Si2 are proposed to be more likely realized in experimentbecause their formation enthalpies are close to convex-hull. The general order of bulk modulus is foundto be Ta-Si > Nb-Si > V-Si at each stoichiometry. P6222-TMSi2 in each system shows the better me-chanical properties. Both covalent bonding between Si-Si and Si-TM in TMSi2 are responsible for thestructural stability and good mechanical property. The present study may shed light on better under-standing of the phase relations in these transition metal silicides.

© 2016 Elsevier B.V. All rights reserved.

1. Introduction

Transition metal silicides possess excellent physical and chem-ical properties, e.g. high melting points, low densities, resistance tooxidation and good creep to tolerance, endowing them with mul-tiple applications in high-temperature device, catalysis and verylarge scale integrated (VLSI) circuit technology [1e3]. For example,as an early transition metal silicides with 5:3 stoichiometry, Ti5Si3is an excellent candidate for coating materials in wear resistantcomposite material due to the high melting point (2130 K) [4].Zr3Si2 satisfies the requirements for gas fast reactors due to its goodthermal conductivity [5]. MoSi2 and WSi2 are promising materialsfor high temperature device [6e8]. Among these silicides, VBtransition metal silicides (TMSix, TM ¼ V, Nb, Ta) exhibit variousstoichiometries, and thus received continual attentions due to theirintriguing electronic and thermodynamic characteristics. The A15type V3Si, Nb3Si and Ta3Si were well studied as high-Tc

.gou@gmail.com (H. Gou).

superconductors with transition temperatures, 17 K, 18 K and 9.3 K,respectively [9e12]. Au2Cu type Ta2Si can be used to be SiC field-effect transistors, with prolonged the stable operation at 500 �C[13]. Three different structure types, D8l (Cr5B3 prototype), D8m(W5Si3 prototype) and D88 (Mn5Si3 prototype) with 5:3 ratio havebeen observed in experiment. The low-temperature phase is D8mfor V5Si3, and D8l for Nb5Si3 and Ta5Si3, all of them possess perfectthermal stability, good mechanical property, high hardness andcompatibility with complementary metal-oxide-semiconductor(CMOS) devices [14e17]. P6222-TMSi2 is found to be widelyapplied in thin films for microelectronics, due to their high elec-trical conductivity, corrosion resistance, and good ability to contactwith silicon.

Theoretically, elastic properties and electronic structure of va-nadium silicides, V:Si ¼ 3:1, 5:3, 6:5 and 1:2, were calculated byThieme and Gemming using the projector augmented wavemethod [18]. The thermal and physical properties of Nb3Si (Ti3Ptype), a-Nb5Si3 (Cr5B3 type), b-Nb5Si3 (W5Si3 type) and NbSi2 in Nb-Si systemwere evaluated by Papadimitriou [19] and Chen et al. [20].The structural stability of TM5Si3 (TM ¼ V, Nb, Ta) were studied indetail by Chen et al. [17]. and Tao et al. [21]. Unfortunately, a sys-tematical investigation on the structural features,

Table

1Calcu

latedcrystallatticeparam

eters,a,

b,an

dc(inÅ),an

dform

ationen

thalpy

DHf(ineV

per

atom

)of

V-Si,Nb-Si

andTa

-Sic

ompou

nds,co

mpared

withtheav

ailableex

perim

entala

ndtheo

reticalworks.

Phase

Prototyp

eSG

ab

cDHf

Phase

Prototyp

eSG

ab

cDHf

Phase

Prototyp

eSG

ab

cDHf

V3Si

Cr 3Si

Pm3n

4.71

1�0

.477

Nb 3Si

PTi 3

P42/n

10.209

5.25

0�0

.463

Ta3Si

PTi 3

P42/n

10.277

5.31

1�0

.449

Exp.

4.72

5[30]

Exp.

10.224

5.18

9[30]

Exp.

10.193

5.17

5[30]

Theo

.4.71

8[10]

AuCu3

Pm3m

4.06

7�0

.232

Ta2Si

Au2Cu

I4/m

cm6.24

75.13

1�0

.577

V2Si

Au2Cu

I4/m

cm5.74

64.84

6�0

.474

Exp.

4.21

1[30]

Exp.

6.16

05.05

6[30]

V5Si

3W

5Si

3I4/m

cm9.42

44.71

4�0

.632

Cr 3Si

Pm3n

5.11

2�0

.378

a-Ta 5Si

3Cr 5B3

I4/m

cm6.63

311

.982

�0.637

Exp.

9.43

04.71

0[30]

Exp.

5.12

0[30]

Exp.

6.51

611

.873

[30]

Theo

.9.39

54.72

7�0

.587

[33]

Nb 2Si

Au2Cu

I4/m

cm6.19

65.11

9�0

.461

Theo

.6.56

011

.917

[21]

Mn5Si

3P6

3/m

cm7.14

34.82

6�0

.570

a-N

b 5Si

3Cr 5B 3

I4/m

cm6.60

811

.872

�0.706

b-Ta 5Si

3W

5Si

3I4/m

cm10

.105

5.15

0�0

.611

Exp.

7.13

54.84

2[30]

Exp.

6.57

011

.884

[30]

�0.666

[34]

Exp.

9.88

5.06

[30]

Theo

.7.11

384.83

30�0

.532

6[33]

Theo

.6.59

911

.917

[19]

�0.652

[20]

Theo

.10

.01

5.10

63[21]

V3Si

2U3Si

2P4

/mbm

6.36

93.26

4�0

.535

b-N

b 5Si

3W

5Si

3I4/m

cm10

.075

5.06

3�0

.694

Ta5Si

3Mn5Si

3P6

3/m

cm7.61

75.30

4�0

.525

V5Si

4Zr

5Si

4P4

12 1

26.40

711

.744

�0.524

Exp.

10.026

5.07

2[30]

Exp.

7.47

45.22

6[30]

V6Si

5Ti

6Ge 5

Ibam

15.931

7.48

94.84

1�0

.590

Theo

.10

.02

5.06

9[35]

Theo

.7.53

25.25

8[21]

Exp.

15.966

7.50

14.85

8[30]

Nb 5Si

3Mn5Si

3P6

3/m

cm7.58

35.24

9�0

.625

Ta3Si

2U3Si

2P4

/mbm

6.77

63.53

6�0

.610

Ti6Sn

5Im

mm

14.891

8.05

94.93

5�0

.506

Exp.

7.53

65.24

9[30]

Ta5Si

4Zr

5Si

4P4

12 1

26.82

412

.549

�0.538

Exp.

15.966

7.50

14.85

8[30]

Nb 3Si

2U3Si

2P4

/mbm

6.74

43.51

2�0

.690

Ta6Si

5Ge 5Ti

6Ibam

16.894

7.95

25.28

7�0

.527

VSi

FeSi

P213

4.74

14.74

14.74

1�0

.495

Exp.

9.97

5.08

[30]

TaSi

FeSi

P213

5.07

6�0

.480

Theo

4.72

4.72

4.72

[36]

Nb 5Si

4Zr

5Si

4P4

12 1

26.78

712

.467

�0.650

Ta2Si

3Hf 2Al 3

Fdd2

9.03

912

.337

5.27

0�0

.290

V2Si

3Hf 2Al 3

Fdd2

7.83

712

.098

5.66

4�0

.314

Nb 6Si

5Ti

6Ge 5

Ibam

16.825

7.93

05.21

9�0

.642

TaSi

2CrSi 2

P6222

4.82

16.63

7�0

.542

VSi

2CrSi 2

P6222

4.54

76.41

2�0

.563

NbS

iFe

BPn

ma

6.53

43.78

15.02

3�0

.607

Exp.

4.77

36.55

2[30]

Exp.

4.56

26.35

9[30]

Nb 2Si

3Hf 2Al 3

Fdd2

8.95

012

.476

5.30

2�0

.423

TaSi

3Ni 3P

I/4

9.81

35.03

8�0

.077

Theo

.4.57

6.37

[37]

NbS

i 2CrSi 2

P6222

4.81

06.61

8�0

.598

VSi

3Ni 3P

I/4

9.52

14.83

8�0

.091

NbS

i 3Ni 3P

I/4

9.78

75.00

8�0

.153

B. Wan et al. / Journal of Alloys and Compounds 681 (2016) 412e420 413

thermodynamical stability, mechanical properties and electronicstructures for various stoichiometries of TM-Si (TM ¼ V, Nb andTa) is still rare. In this work, we perform first-principles calcula-tions on VB transition metal silicides, over a wide stoichiometryrange, (TM:Si ¼ 3:1, 2:1, 5:3, 3:2, 5:4, 6:5, 1:1, 1:2 and 1:3), whichaims to provide a fundamental understanding of the structuralcharacteristics, mechanical properties and electronic structure ofstudied silicides.

2. Computational method

The structural optimization, electronic structure have beenperformed within CASTEP [22] code based on density functionaltheory (DFT). The exchange and correlation functional wereconsidered by generalized gradient approximation of Perdew-Burke-Ernzerhof (GGA-PBE) [23]. The valence electrons of theelements are treated as, 3s23p2 for Si:, 3d34s2 for V, 4d35s2 for Nband 5d36s2 for Ta, respectively. A cutoff energy of 500 eV anddense Monkhorst-Pack kmeshes were selected to ensure the totalenergy converged within 1 meV per formula unit. The pin polar-ized was included for metal-rich phases. The magnetism wasfound to be neglected. To construct the convex hull, extensivestructures (stoichiometric ratio, TM:Si ranging from 3:1 to 1:3)were considered here, namely experimental phases (Pm3 n-V3Si,P63/mcm-V5Si3, I4/mcm-V5Si3, Ibam-V6Si5, Immm-V6Si5 andP6222-VSi2 in V-Si system, Pm3 n-Nb3Si, P42/n-Nb3Si, P4/mbm-Nb3Si2, a-Nb5Si3, b-Nb5Si3, P63/mcm-Nb5Si3 and P6222-NbSi2 inNb-Si system, P42/n-Ta3Si, I4/mcm-Ta2Si, a-Ta5Si3, b-Ta5Si3, P63/mcm-Ta5Si3 and P6222-TaSi2 in Ta-Si system), and chemicallyrelated compounds of Ⅲ-Ⅶ B transition metal borides, carbides,silicides, nitrides, phosphide, and arsenides. All of the structureswere fully relaxed without any symmetry and stress constraint.The elastic constants were calculated from evaluation of stresstensor generated small strains. The elastic modulus and Poisson’sratio were derived from Voigt-Reuss-Hill approximations[24e26]. Phonon spectra of new proposed phases were calculatedthrough finite displacement methods [27,28]. Structure figureswere obtained by using VESTA package [29].

3. Results and discussion

3.1. Thermodynamic stability

The calculated lattice parameters, and formation enthalpiesDHf (eV/atom) of TM-Si systems are listed in Table 1, Fig. 1 andFig. S1 in the Supporting Information. In general, the obtainedlattice parameters are well consistent with previous experimentaland theoretical results within the error of 3.5%, except for Nb3Si2[30], which was proved to be Nb5Si3 in experiment [15]. DHf forTMxSiy were determined by the following equation:

DHf�TMxSiy

� ¼ �ETMxSiy exETM � yESi�.

ðxþ yÞ: (1)

where E is the total energy of a compound or a constituentelement, here cubic V, Nb, Ta (Space group Im3m) and diamond Siwere selected as the reference structures. In V-Si system, as shownin Fig. 1a, Pm3 n-V3Si, I4/mcm-V5Si3 and P6222-VSi2 are just lyingon the convex-hull, perfectly explaining the observations at lowtemperature in experiment [31]. Similar results can also be ob-tained for I4/mcm-Nb5Si3, P6222-NbSi2 in Nb-Si system, and P42/n-Ta3Si, I4/mcm-Ta2Si, I4/mcm-Ta5Si3 and P6222-TaSi2 in Ta-Sisystem. Especially, W5Si3-type V5Si3, Cr5B3-type Nb5Si3 andTa5Si3 show the lowest the formation enthalpies (�0.632, �0.706and�0.637 eV/atom) in V-Si, Nb-Si and Ta-Si system, respectively,

Fig. 1. Formation enthalpies of V-Si (a), Nb-Si (b) and Ta-Si (c) compounds, calculated at zero temperature and zero pressure. Each red solid circle represents an individualexperimental phase and each blue solid square represents an individual theoretical phase. The brown tie line is convex hull. Experimental phases V3Si, V5Si3 and VSi2 of V-Si system,Nb5Si3 and Nb2Si of Nb-Si system and Ta3Si Ta2Si Ta5Si3 and TaSi2 of Ta-Si system are located at convex hull indicating they are ground state phases, and marked by solid green circle.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

B. Wan et al. / Journal of Alloys and Compounds 681 (2016) 412e420414

suggesting that they are more easily to be synthesized. It should benoted that, in the Nb-Si system, the formation enthalpy of U3Si2-type Nb3Si2 is very close to the convex-hull line, reasonable inter-preting that it has been proposed by different researchers [15,32].Meanwhile, the formation enthalpies of the high temperaturephases in experiment, P63/mcm-V5Si3, Ibam-V6Si5, and Immm-V6Si5in V-Si system, P42/n-Nb3Si, Pm/3n-Nb3Si, Pm/3m-Nb3Si, b-Nb5Si3and P63/mcm-Nb5Si3 in Nb-Si system, b-Nb5Si3 and P63/mcm-Ta5Si3in Ta-system, are also negative, but above the convex-hull. There-fore, their stability under high temperature should ascribe to thegreat contribution of entropy. On the other hand, formation en-thalpies of all the new proposed phases (e.g., V2Si, V3Si2, V5Si4, VSi,V2Si3 and VSi3 in V-Si system, Nb2Si,Nb5Si4, Nb6Si5, NbSi, Nb2Si3and NbSi3 in Nb-Si system, Ta3Si2, Ta5Si4, Ta6Si5, TaSi, Ta2Si3 andTaSi3 in Ta-Si system, as shown in Fig. 1) show negative values.Therefore, they may be synthesized under some unequilibriumconditions, e.g. high temperature or high pressure, as the hightemperature phases verified by experiment. Peculiarly, the forma-tion enthalpy of the proposed Nb3Si2, Nb5Si4, Nb6Si5, NbSi andTa3Si2 are very close to the convex hull, indicating their goodthermodynamic stability and may be more likely to be realized inexperiment. Dynamic stability of the new predicted phases werefurther checked by calculating their phonon spectra. As shown inFig. S2, except VSi3, no imaginative frequency can be observed forthe phonon dispersion curves in the whole Brillouin zone, implyingthat they are dynamic stable at zero temperature and zero pressure.

3.2. Structure property

The crystal structure of the experimental and hypothetic phasesin TM-Si system present in Fig. S2, representative phases TM3Si2,P63/mcm-TM5Si3 Ibam-TM6Si5 and TMSi2 are listed in Fig. 2 Opti-mized atomic positions of TM-Si newly predicted phases aretabulated in Table. S1. As shown in Fig. 2 and Fig. S2, the patterns ofSi atoms in the crystal can be classified into four different types, i.e.isolated atoms, Si2 pairs, chains (linear or zigzag) and threedimensional network. In TM3Si, HT phase P63/mcm-TM5Si3 (Fig. 2a),proposed P213-VSi and P213-TaSi, the Si atoms are isolated fromeach other with the Si-Si distance larger than 3 Å. Si2 pairsappeared in a-Nb5Si3 and a-Ta5Si3, TM3Si2 (Fig. 2b), TM5Si4, and theSi-Si bond length is 2.403 and 2.432 Å, for a-Nb5Si3 and a-Ta5Si3;2.355, 2.434 and 2.437 Å for V3Si2, Nb3Si2 and Ta3Si2; 2.408, 2.485,2.511 Å for V5Si4, Nb5Si4 and Ta5Si4, respectively. Linear siliconchains can be observed in TM2Si, I4/mcm-V5Si3 b-Nb5Si3 and b-Ta5Si3, Immm-V6Si5. The chains run along [001] direction with a

unique bond length of 2.432, 2.560 and 2.565 Å for V2Si, Nb2Si andTa2Si; 2.357, 2.531 and 2.575 Å for I4/mcm-V5Si3, b-Nb5Si3, b-Ta5Si3and alternative bond lengths 2.391 and 2.544 Å for Immm-V6Si5,respectively. A general feature can be found that the Si-Si bondlength is monotonously increased from vanadium silicides totantalum silicides, due to the increasing atomic radius from V to Ta.V6Si5, Nb6Si5 and Ta6Si5 (Fig. 2c) with Ibam symmetry have themixing Si atomic motifs of isolated atoms, linear chains and zigzagchains. Both linear and zigzag chains run along [001] direction. TheSi-Si bond lengths in linear/zigzag chains are 2.769/2.421 Å, 2.610/2.517 Å and 2.644/2.514 Å, for Ibam-V6Si5, Nb6Si5 and Ta6Si5respectively. Infinite zigzag Si chains along [010] direction can alsobe found in Pnma-NbSi with unique bond length, 2.429 Å. In thehypothetical TM2Si3 and TMSi3, Si atoms adopt three dimensionalnetwork with Si-Si bond lengths varying from 2.424 to 3.068 Å.Intriguing, the Si atoms in TMSi2 (Fig. 2d) adopt DNA-like doublehelix chains, the Si-Si bond lengths in helix chain are 2.492 (VSi2),2.573 (NbSi2) and 2.579 Å (TaSi2), and a couple of helix chains areconnected together by Si-Si bond length of 2.657 (VSi2), 2.651(NbSi2) and 2.852 Å(TaSi2). The unique structural feature shouldplay important role for the stability of TMSi2.

3.3. Mechanical property

The calculated elastic constants (Cij) of considered phases at zerotemperature and zero pressure are shown in Tables 2e4, togetherwith available theoretical and experimental results. According toBorn-Huang stability criterion [38,39], the mechanical stabilitywere firstly judged by Cij. As shown in Tables 2e4, Cij of all the newpredicted phases satisfy Born-Huang stability criterion, indicatingtheir mechanical stability. However, HT phases P63/mcm-V5Si3 andTa5Si3, Pm3 m-Nb3Si are mechanical unstable (negative C44 for P63/mcm-V5Si3 and P63/mcm-Ta5Si3, and C11< C12 for Pm3 m-Nb3Si),implying they are hardly recoverable at ambient conditions,consistent with previous reports [20,33]. Besides of C33 value ofV2Si3 (133 GPa), generally, C11 C22 and C33 values of TMxSiy aregreater than that of element Si, and close or higher than that ofmetal V, Nb and Ta, indicating a relatively strong interaction be-tween TM and Si. The largest individual elastic constant among V-Si, Nb-Si and Ta-Si system, C33 of VSi2, NbSi2 and TaSi2 is 404 GPa,456 GPa and 461 GPa, respectively, indicating the most compres-sion resistance along [001] direction, which should contribute totheir unique double helix chains running along c axis.

To better understand the mechanical properties of those com-pounds, the bulk modulus (B), shear modulus (G) derived from the

Fig. 2. The optimized crystal structure of (a) P63/mcm -TM5Si3, (b) TM3Si2, (c) Ibam-TM6Si5 and (d) TMSi2.

Table 2Calculated elastic constants (Cij in GPa) Bulk Modulus (B in GPa), Shear Modulus (G in GPa), Young’s Modulus (E in GPa), Poisson’s ratio (n) and Debye temperature (QD in K) ofVxSiy, compared with available results.

C11 C22 C33 C44 C55 C66 C12 C13 C23 B G E G/B n QD Ref.

V 295 92 123 180 90 231 0.5 0.286 e

V3Si 248 42 151 183 45 125 0.246 0.386 400Theo. 252.87 44.26 155.55 187.99 46.02 e e 0.3809 e [40]V2Si 272 291 82 104 133 122 177 83 215 0.469 0.297 550I4/mcm-V5Si3 386 331 107 128 101 100 189 121 299 0.640 0.236 665Theo. 401.7 351.1 103.1 127.8 106.7 99.6 195.8 122.1 303.1 0.24 658.5 [33]P63/mcm-V5Si3 313 359 �146 84 146 73 e e e e e e

Theo. 306.3 359.6 �121.9 60.0 186.4 84.1 e e e e e e

V3Si2 286 286 130 131 185 118 188 101 257 0.537 0.272 615V5Si4 289 348 65 117 143 94 176 85 220 0.483 0.292 574Ibam-V6Si5 360 326 343 131 92 114 124 75 83 177 116 286 0.655 0.231 665Immm-V6Si5 283 312 346 91 115 112 120 92 87 171 106 264 0.620 0.243 639VSi 287 62 118 175 70 185 0.400 0.324 530V2Si3 329 307 133 68 130 84 91 121 86 138 79 199 0.572 0.260 577VSi2 383 404 136 54 38 159 156 353 0.981 0.130 810Exp. 357.8 422.3 135.7 153.6 50.6 68.1 167.2 147.9 342.6 791 [41]VSi3 231 273 36 15 62 51 118 42 113 0.356 0.341 447Si 147 67 52 84 58 141 0.690 0.219

B. Wan et al. / Journal of Alloys and Compounds 681 (2016) 412e420 415

Voigt-Reuss-Hill (VRH) [42] approximation and Poisson’s ratio n areshown in Table 3 and Fig. 3, the Young’s modulus (E) and Poisson’sratio n estimated by the following relations are also listed.

E ¼ 9BG3Bþ G

(2)

n ¼ 3B� 2G2ð3Bþ GÞ (3)

Our results are excellent agreement with previous studies,further verifying the reliability of our calculations. As shown inFig. 3(a)e(c), a general trend of the bulk modulus of TMxSiy is V-Si < Nb-Si < Ta-Si. Moreover, the bulk modulus firstly increase

slowly with the increasing concentration of silicon, varying from180 GPa (metal V) to 189 GPa (I4/mcm-V5Si3) for V-Si system,174 GPa (metal Nb) to 193 GPa (a-Nb5Si3) for Nb-Si system and190 GPa (metal Ta) to 207 GPa (Ta2Si) for Ta-Si system, thendecrease to the lowest value, 84 GPa for diamond-like silicon.However, there is no general tendency for G values. First highervalue appears at TM5Si3 (121 GPa for I4/mcm-V5Si3, 129 GPa a-Nb5Si3 and 129 GPa a-Ta5Si3), and the highest G value is for TMSi2(156 GPa for VSi2; 132 GPa for NbSi2 and 137 GPa for TaSi2). Similartendency can also be found for the Young’s modulus. HT Ibam-V6Si5and newly predicted Ibam- Nb6Si5 and Ta6Si5 phases also possesshigh shear modulus and Young’s modulus, 116 GPa (G) and286 GPa (E) for Ibam-V6Si5, 107 GPa (G) and 269 GPa (E) for Ibam-Nb6Si5 and 103 GPa (G) and 263 GPa (E) for Ta6Si5, respectively.

Table 3Calculated elastic constants (Cij in GPa) Bulk Modulus (B in GPa), Shear Modulus (G in GPa), Young’s Modulus (E in GPa), Poisson’s ratio (n) and Debye temperature (QD in K) ofNbxSiy, compared with available results.

C11 C22 C33 C44 C55 C66 C12 C13 C23 B G E G/B n QD Ref.

Nb 246 36 138 174 43 119 0.247 0.386P42/n-Nb3Si 260 289 80 80 182 124 185 68 182 0.367 0.336 392Theo. 290.2 306.0 89.2 119.4 150.5 117.6 [30]Pm3 n-Nb3Si 353 78 99 184 94 241 0.511 0.282 456

Pm3 m-Nb3Si 32 73 252Nb2Si 283 269 89 108 144 153 192 81 213 0.422 0.315 439a-Nb5Si3 376 323 140 120 100 115 193 129 316 0.668 0.227 558Theo. 372.9 338.1 133.5 122.1 96.0 115.5 193.1 127.9 555 [20]b-Nb5Si3 377 331 90 129 115 104 192 111 279 0.578 0.258 519Theo. 378.3 338.1 89.2 132.7 119.3 107.9 193.1 109.8 515 [20]P63/mcm-Nb5Si3 326 378 17 145 89 186 54 148 0.290 0.368 368Nb3Si2 286 299 134 125 200 113 190 99 253 0.521 0.278 497Nb5Si4 300 336 66 119 145 103 182 86 223 0.473 0.296 474Nb6Si5 368 342 311 116 80 113 126 92 111 186 107 269 0.575 0.259 528NbSi 258 227 374 97 90 138 160 103 141 184 87 225 0.473 0.296 488Nb2Si3 178 292 249 60 88 110 171 135 107 168 61 163 0.363 0.338 432NbSi2 344 456 115 85 69 176 132 317 0.75 0.200 651Exp. 380.2 468.0 145.3 152.2 75.9 88.3 191.5 153.2 362.8 688 [41]NbSi3 251 296 45 37 68 56 129 60 156 0.465 0.299 472

Table 4Calculated elastic constants (Cij in GPa) Bulk Modulus (B in GPa), Shear Modulus (G in GPa), Young’s Modulus (E in GPa), Poisson’s ratio (n) and Debye temperature (QD in K) ofTaxSiy, compared with available results.

C11 C22 C33 C44 C55 C66 C12 C13 C23 B G E G/B n QD Ref.

Ta 238 36 165 190 36 102 0.189 0.411Ta3Si 289 291 86 84 141 200 73 195 0.365 0.337 299Ta2Si 300 305 85 115 167 155 207 84 222 0.406 0.321 333a-Ta5Si3 386 331 138 130 109 133 206 129 320 0.626 0.241 418Theo. 412.65 361.91 135.95 123.61 116.65 114.81 200.11 130.57 327.53 0.254 414 [21]b-Ta5Si3 391 350 91 192 135 114 206 112 284 0.543 0.270 390Theo. 410.19 338.89 92.94 132.91 145.66 125.45 215.7 113.0 288.6 0.28 388 [21]P63/mcm-Ta5Si3 329 387 �953 187 103Ta3Si2 372 299 127 114 130 135 204 115 290 0.564 0.263 400Ta5Si4 295 334 27 118 161 115 190 59 160 0.311 0.259 299Ta6Si5 362 350 347 108 73 111 142 96 118 196 103 263 0.526 0.276 393TaSi 361 79 128 206 92 240 0.447 0.306 381Ta2Si3 199 330 294 38 89 121 193 141 136 189 63 170 0.333 0.350 342TaSi2 351 461 123 84 73 179 137 327 0.765 0.195 526Exp. 375.3 468.0 143.7 148.5 78.4 90.1 192.5 151.0 359.0 552 [41]TaSi3 251 287 35 31 67 57 128 53 140 0.414 0.318 364

B. Wan et al. / Journal of Alloys and Compounds 681 (2016) 412e420416

To provide a straightforward way to describe the elasticanisotropy of TM5Si3, TM6Si5 and TMSi2, the Young’s moduli inthree dimensions (3D) and corresponding 2D projections of I4/mcm-V5Si3, a-Nb5Si3, Nb6Si5 and NbSi2 are calculated as a functionof the crystallographic directions [43] (as shown in Fig 3(e)e(h)).For isotropic materials, the shape of 3D curved surface is sphere,and the corresponding 2D projections are circle. The deformationextent of 3D curved surface from sphere defines the extent of singlecrystal anisotropy. As shown in Fig 3cef, I4/mcm-V5Si3 and a-Nb5Si3are close to isotropy, with small separation between Emax and Emin67 GPa for I4/mcm-V5Si3 and 70 GPa for a-Nb5Si3. Nb6Si5 and NbSi2show obvious anisotropy with separation between Emax and Emin94 GPa for Nb6Si5 and 142 GPa for NbSi2. The extremely largeYoung’s Modulus is following along [001] direction (434 GPa) ofNbSi2, further implying the significant increasing mechanicalproperties by double helix silicon chains.

The Poisson’s ratio n is connected with the rate of expansion orshrink when the material being stretched or compressed, and itprovides a valuable information about covalent bonding characterof materials [44]. The metal rich phases TM3Si and TM2Si possesshigh values of n (large than 0.282), due to metallic characteristic.Contrarily, TMSi2 have the smallest value of n, 0.130 for VSi2, 0.200for NbSi2 and 0.195 for TaSi2, respectively, indicating relatively

strong covalent interactions exiting in these phases. Additionally,Pugh ratio (G/B) [45] was also calculated to distinguish the brittle orductile materials, the critical value is 0.571. Thus Ibam-V6Si5,Immm-V6Si5 and VSi2 in V-Si system, a-Nb5Si3, b-Nb5Si3 and NbSi2in Nb-Si system, a-Ta5Si3 and TaSi2 of Ta-Si system are brittle, all theothers are ductile.

Debye temperature QD is an important fundamental parameterrelated to many physical properties (e.g. Heat capacity and stiff-ness). Which can be estimated by using the following equation[46]:

QD ¼ hK

�3n4p

�NAr

M

��1=3

nm (4)

where h is Plank constant, K is Boltzmann’s constant, NA is theAvogadro’s number, r is the density, M is the molecular weight. nmis average sound velocity in a polycrystalline system and can beevaluated by Ref. [46]:

Fig. 3. Bulk Modulus (a), Shear Modulus (b), Young’s Modulus (c) and Debye Temperature (d) as a function of Si content, the tie line connecting the phases which possess lowestenergy in each stoichiometric ratio. Young’s moduli in three dimensions (3D) and corresponding 2D projections of I4/mcm-V5Si3 (e), a-Nb5Si3 (f), Nb6Si5 (g) and NbSi2 (h), thenegative sign denotes the negative direction corresponding to the positive one.

B. Wan et al. / Journal of Alloys and Compounds 681 (2016) 412e420 417

nm ¼"13

2n3t

þ 1n3l

!#�1=3

(5)

where nt and nl are the mean transverse and longitudinal soundvelocities, which can be related to the shear and bulk moduli by theNabier’s equations [47]:

nl ¼�3Bþ 4G

3r

�1=2

And nt ¼�Gr

�1=2

(6)

As shown in Table 3, the calculated Debye temperature is wellconsistent with experimental results [14,32]. From Fig. 3d, thecalculated Debye temperatures are following the sequence of V-Si > Nb-Si > Ta-Si, probably caused by the density of TM-Si systemsis V-Si < Nb-Si < Ta-Si in corresponding stoichiometric ratio.Further, TMSi2 exhibit the largest values, 810 K for VSi2, 651 K forNbSi2 and 526 K for TaSi2, respectively.

3.4. Electronic structure

To elucidate the bonding nature of TMxSiy, the total and partial

B. Wan et al. / Journal of Alloys and Compounds 681 (2016) 412e420418

density of states (TDOS and PDOS) are calculated and plotted inFig. S4e6. As shown in Fig. S4e6, all the phases considered hereshow metallic characters, due to the finite values of DOS at Femilevel (EF). From TM3Si to TMSi (Figs. S4aeh, 5aej and 6aej), ageneral feature is that the valence band is dominated by Si-3s statesin the vicinity of �9 eV, Si-3p states in the middle zone(�6 eV � �3.5 eV), and TM-d states at the higher energy. To get agood view of the influence of silicon concentration on electronicstructures, the DOS profile of TM3Si, TM2Si, TM5Si3 and TMSi2 arepresented in Fig. 4. From Fig. 4, for TM3Si (Fig. 4a, e and i), due to thelow silicon concentration, each Si atom is separated by TM atoms,introducing highly localization of Si-s band. On the other hand, arelativelyweaker hybridization between Si-3p and TM-d orbital canbe observedwith a narrow overlapping, about 1.6 eV for V3Si, 2.3 eVfor P42/n-Nb3Si, and 3.0 eV for Ta3Si. Furthermore, the Fermi levelin TM3Si catches the edge of TM-d peak, resulting extremely high EFvalues, which should contribute to their outstanding super-conducting characters in A15 type superconductors [48, 49].

Different from TM3Si, there is a small band gap of Si-s orbital,around �9 eV for V2Si (Fig. 4b) and Nb2Si (Fig. 4f), �9.8 eV for Ta2Si(Fig. 4j), formed by the hybridization between the Si-s and Si-porbital, resulting from the infinite Si-Si chains configuration. As forTM5Si3 (Fig. 4c, g and k), the hybridization between Si-3p and TM-d orbital is relatively strong with overlapping range about 4.5 eV.Especially, there is a deep pseudogap around Fermi level for a-Nb5Si3 (�0.41 eV) and a-Ta5Si3 (�0.43 eV), caused a special stabilityfor these phases. We focus on another ground state structure TMSi2(Fig. 4d, h and l), significantly strong hybridization in the wholevalence band can be observed, (�13eV ~ �6 eV) adopted by s-phybridization of Si atoms and (�6eV ~ 0 eV) dominated by p-d hy-bridization between Si and TM atoms, respectively. As a result,strong Si-Si s bond in the double helix chains and Si-TM covalent

Fig. 4. Calculated total and partial density of states (DOS) of TM3Si (a, e and i), TM2Si (b, f anby a black solid line.

bond are formed, which plays a crucial role for their perfect me-chanical property and structural stability. As for the new proposedTMSi3, the s-p-d hybridization can also be found, however, which ismuch less than that in TMSi2, introducing much lower elasticmodulus.

To get further visualization of the bonding characters in I4/mcm-V5Si3, a-Ta5Si3 and TaSi2, the valence electron charge density dis-tributions are shown in Fig. 5. For I4/mcm-V5Si3, there are signifi-cant electronic accumulations in the linear Si chain, implyingstrong nonpolar Si-Si s bonding. Additionally, higher charge den-sity between V and Si atoms is also visible, indicating the covalentV-Si interactions. On the other hand, in a-Ta5Si3 and TaSi2, lesselectronic accumulation between the Si2 pairs (for a-Ta5Si3) and inthe double helix silicon chains can be found, along with increasingelectronic accumulation between Ta-Si atoms, indicating relativelyweaker Si-Si and enhanced Ta-Si covalent bonding. Interesting, arather strong Ta-Ta bond can be found in a-Ta5Si3, as shown inFig. 5c, the relative bond strength is also evaluated by calculatingMulliken overlap populations (MOP). For I4/mcm-V5Si3, the calcu-lated Si-Si MOP value in the linear chain is 0.74 and MOP for V-Sihas the maximum value of 0.39. For a-Ta5Si3, MOP values for Si-Sibond in Si2 pairs (for a-Ta5Si3) and in the double helix siliconchains (for TaSi2) are 0.28 and 0.31, respectively, smaller than thatin I4/mcm-V5Si3. The MOP value of Ta-Si bond in a-Ta5Si3 and TaSi2is comparable to that of V-Si bond with maximum value 0.38 (a-Ta5Si3) and 0.39 (TaSi2). Analogous results can also be acquired fora-Nb5Si3, VSi2 and NbSi2 (not shown here), because of their similaratomic arrangement.

4. Conclusions

In conclusion, the crystal structure, stability, mechanical

d j), TM5Si3 (c, g and k) and TMSi2 (d, h and l). The Fermi level is set at 0 eV and marked

Fig. 5. Electron charge densities of I4/mcm-V5Si3 (a), a-Ta5Si3 (b) and NbSi2 (c). Theisovalue line was set 0.317 eV for I4/mcm-V5Si3, 0.2514 eV for a-Ta5Si3 and 0.2842 eVfor TaSi2 respectively.

B. Wan et al. / Journal of Alloys and Compounds 681 (2016) 412e420 419

property and electronic structure of TMxSiy (1:3 � x:y � 3:1) weresystematically studied by using the first-principles calculations.Although V, Nb and Ta belong to the same VB group, the V-Si, Nb-Siand Ta-Si systems display very different phase equilibriumbehavior. The ground state structures are Pm3 n-V3Si, I4/mcm-V5Si3and P6222-VSi2 for V-Si system, a-Nb5Si3, P6222-NbSi2 for Nb-Sisystem, and P42/nTa3Si, P6222-Ta2Si, a-Ta5Si3, P6222-TaSi2 for Ta-Sisystem, respectively. Except for the experimental phases, manyothers with different stoichiometry are also predicted to be ener-getically, dynamically and mechanically stable at zero temperatureand zero pressure, they should be recoverable at room conditions.Importantly, the hypothetical phases, P4/mbm-Nb3Si2 P41212-Nb5Si4, Ibam-Nb6Si5, Pnma-NbSi and P4/mbm-Ta3Si2 are mechani-cal and dynamic stable, and close to the convex-hull, they should bemore likely to be realized in experiment. For the most energeticphases at corresponding stoichiometric ratio, bulk modulus show ageneral tendency Ta-Si > Nb-Si > V-Si, while shear modulus,

Young’s modulus and Debye temperature at TM5Si3 and P6222-TMSi2 are greater than others. Further electronic analysis identifiedthat both Si-Si and TM-Si covalent interactions plays crucial rolesfor the good structural stability and mechanical property forground state structure of TM-Si systems. We expected that presentwork can provide a better understanding of group VB silicides.

Acknowledgements

This work was supported by National Natural Science Founda-tion of China (NSFC) under Grants No. 51201148 and U1530402. L.Wu thanks the foundation of Hebei Province Education Departmentunder Grant No. QN2014114 and the Autonomic Research Project ofYanshan University under Grant No. 13LGB007.

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.jallcom.2016.04.253.

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