The structure and stability of the low-index surfaces of D8m-Mo5Si3 by first-principles calculations

Ceramics International xxx (xxxx) xxx–xxx

Contents lists available at ScienceDirect

Ceramics International journal homepage: www.elsevier.com/locate/ceramint

The structure and stability of the low-index surfaces of D8m-Mo5Si3 by firstprinciples calculations S. Gua, S.P. Suna,∗, X.P. Lia, W.N. Leia, M. Rashadb, L. Yinb,∗∗∗, Y.X. Wangb,∗∗, L.Y. Chenc, Y. Jiangd a School of Materials Engineering, Jiangsu Key Laboratory of Advanced Materials Design and Additive Manufacturing, Jiangsu University of Technology, Changzhou, 213001, China b School of Materials Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212003, China c Faculty of Materials Metallurgy and Chemistry, Jiangxi University of Science and Technology, Ganzhou, 341000, China d School of Materials Science and Engineering, Central South University, Changsha, 410083, China

A R T I C LE I N FO

A B S T R A C T

Keywords: D8m-Mo5Si3 First-principles Surfaces Electronic structure Stability

Atomic relaxations, surface energies and electronic structures of the (100), (001) and (110) surfaces for D8mMo5Si3 are investigated to analyze the surface stability by DFT (Density Functional Theory) based first-principles plane-wave pseudo-potential calculations. The atomic relaxation and surface energy results reflect minimum relaxations of the (ns-8Mo4Si)-terminated (001), (ns-4Si)-terminated (110) and (ns-2Si-2)-terminated (100) surfaces. Moreover, the (ns-8Mo4Si)-terminated (001) and (ns-4Si)-terminated (110) surfaces are most stable under Si-poor and Si-rich conditions, respectively. The density of states indicates that the surface electronic structures are mainly influenced by the atomic relaxations. The calculated charge densities show dependence of the surface relaxation mainly on dangling bonds. According to the calculated surface energies, the predicted crystal shapes show the octagonal prism and a structure which is close to cuboid in the μSislab − μSibulk range from −1.077 eV to −0.546 eV and −0.546 eV–0 eV, respectively. These calculation results are compared with the previous reports.

1. Introduction Recently, refractory metal silicides have attracted wide attention for various applications as a potential high-temperature structure, due to their outstanding properties such as high melting point, good creep behavior, and high strength at the elevated temperatures [1–4]. As an important compound in the molybdenum silicides (Mo–Si) system, Mo5Si3 has a promising application in severe conditions [5] owing to the high melting point (2180 °C), superior conductivity and excellent resistance to creep strength, etc. [6–10]. Nevertheless, Mo5Si3 exhibits poor oxidation resistance at 600 °C, which severely limits its wide range application [11,12]. T. Lizuka et al. [13] reported that the poor oxidation resistance of the Mo5Si3 is due to the appearance of non-continuous SiO2 [14] and the vaporization of the MoO3 particles, which is known as the ‘pesting’ phenomenon. In order to effectively overcome the pesting oxidation, some experiments have been performed for improving the oxidation resistance of the Mo5Si3 via alloying (Cr, Ti, Co, Ni, B [15], Nb, V [16]) or composting approaches (Al2O3 [17], MoSi2

[18], Si3N4 [13]). Damage to materials often begins from the surface [19], such as wear, corrosion, fatigue fracture, and high temperature oxidation, etc. The initial period of high temperature oxidation is the adsorption of oxygen on the material surfaces. Surface bond is the main reason of affecting the chemical displacement and geometric structure of the adsorption layer. Moreover, different terminating surfaces have different adsorption energies, adsorption sites, adsorption heights and bond lengths [20–23]. It is clear that the oxidation resistance of the Mo5Si3 has a close relationship with the surface properties [24]. Unfortunately, up to now, there are few investigations about the surface properties of the Mo5Si3 because of the experimental difficulty in preparation of high-quality clean surfaces. At present, the first-principles method has been widely used to research surface properties [25–30]. In addition, our previous studies focused on the oxygen adsorption behaviors on the (110) surface for the MoSi2 [28], and the equilibrium morphology and surface stability of the MoO3 [29]. Furthermore, no surface research of the Mo5Si3 has been reported by using the first-

∗

Corresponding author. Corresponding author. ∗∗∗ Corresponding author. E-mail addresses: [email protected] (S.P. Sun), [email protected] (L. Yin), [email protected] (Y.X. Wang). ∗∗

https://doi.org/10.1016/j.ceramint.2019.09.045 Received 28 July 2019; Received in revised form 4 September 2019; Accepted 4 September 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Please cite this article as: S. Gu, et al., Ceramics International, https://doi.org/10.1016/j.ceramint.2019.09.045

Ceramics International xxx (xxxx) xxx–xxx

S. Gu, et al.

distance between ith and jth layers before and after relaxations, respectively. From Eq. (1), a negative Δdij represents an interlayer contraction between these two layers, while a positive value implies interlayer expansion. The ‘rumpling’ phenomenon appears after the surface relaxation, when one layer is composed of Mo and Si atoms. The surface rumpling influences the surface stability [42]. The occurrence of ‘rumpling’ phenomenon is attributed to the movement of atoms toward different directions induced by different forces on Mo and Si atoms of the same layer [43]. The ‘rumpling’ phenomenon can be elaborated using rumpling value ri as:

principles calculation. In this research, the calculation on the D8m-Mo5Si3 is performed using first-principles methods. The paper content arranges as follows: the calculation methodology is introduced in Section 2. The surface relaxations, surface energies and electronic properties of low-index surfaces are investigated in Section 3.1, 3.2 and 3.3, respectively. Following this, the Wulff sharp of the D8m-Mo5Si3 is calculated and presented in Section 3.4. Final conclusions are exhibited in Section 4. 2. Calculation methodology 2.1. Computational detail

ri =

The present calculations in our study were done using first-principles approach based on DFT [31,32], as implemented in the Vienna Ab initio Simulation Package (VASP) [33–35]. These present calculations were employed by plane-wave pseudopotential methods [36]. The exchange-correction function was implemented by the PAW (Projector Augmented Wave) approach with the PBE (Perdew-Burke-Ernzerhof) [37] approach. The Mo-4p64d55s1 and Si-3s23p2 were considered as the valence electron, while the remaining inner electrons were used as core states. The plane-wave cutoff energy was 340 eV. In order to integrate the Brillouin zone (BZ), the Monkhorst-Pack [38] k-point grids of 18 × 18 × 10 was employed for the bulk Mo5Si3.

As is well known, tetragonal crystal D8m-Mo5Si3 is the space group I4/mcm structure, where Mo atoms locate at the 16k (0.0786, 0.0225, 0) and 4b (0, 0.5, 0.25) Wyckoff sites, and Si atoms are on the 8h (0.171, 0.671, 0) and 4a (0, 0, 0.25) Wyckoff sites. In order to optimize the surface structure, the bulk calculation of D8m-Mo5Si3 should be discussed firstly. Through optimization of the crystal structure, the lattice parameter of a = 9.681 Å and c = 4.903 Å for bulk Mo5Si3 was obtained, which was reasonably consistent with the experimental result (a = 9.687 Å, c = 4.881 Å) [39] and the previous theoretical data (a = 9.648 Å, c = 4.903 Å) [40]. The periodic boundary conditions were employed to investigate the low-index surfaces. The symmetric slab model was separated by a 16 Å vacuum region. (9 × 9 × 1), (5 × 13 × 1), and (9 × 5 × 1) k-points mesh for the low-index surfaces (001), (110) and (100) were performed to integrate the Brillouin zone (BZ), respectively. During the process of optimizing all atomic positions, the convergence on the total energy was set to 5 × 10−6 eV/atom, and the convergence on the force allowed by every atom was 0.1 eV/nm. 3. Results and discussion 3.1. Surface relaxation Since the forces exerted on the nearest neighbor atoms at the outermost layer have a large difference from those applied on the atoms in the bulk, the surface layer atoms move to a new position to reduce the total system energy. Therefore, the main feature of the surface structure is surface relaxation [41]. After the complete relaxation of each atom, the atomic displacements cause changes of space between atomic layers along the z direction. According to the slabs mentioned above, the relative deviation Δdij of the interlayer relaxations is employed and calculated as [25]:

dij′ − dij0(bulk ) dij0(bulk )

(2)

where ZiSi and ZiMo denote the average position of Si and Mo atoms around the ith layer in z axis, respectively. The calculated values of dij0(bulk ) and dij′ parameters are shown in Tables 1–3. A clear observation is that there are no surface reconstructions after complete relaxation. The calculated ri is shown in Table 4 that also illustrates the relative deviation. It is clear from Table 4 that the outermost three atomic layers exhibit significant expansion/contraction effect. The outermost interlayer spacing (Δd12) of (ns-8Mo4Si)-terminated (001) and (ns-2Mo2Si)-terminated (001) surfaces experiences contraction. The inter-layer distance d23 of the (ns8Mo4Si)-terminated (001) surface reduces after relaxation, while that of the (ns-2Mo2Si)-terminated (001) surface increases. Moreover, the (001) surface with (ns-8Mo4Si)-terminated reveals that the relaxation in 1st and 2nd layers is smaller in comparison to the (ns-2Mo2Si)-terminated structure. These findings suggest that the stability of the (ns8Mo4Si)-terminated (001) surface is probably more excellent. Mostly for eight structures of (110) surface, the interlayer spacing Δd12 and Δd34 experience contraction and the inter-planar distances d23 and d45 increase after relaxation. Meanwhile, the 1st-layer atoms experience the maximum relaxation compared to the inner three layers for one surface in general. The outermost interlayer spacing (Δd12) of the (ns-4Mo-3)-terminated (110) surface is contracted by over 50%, suggesting cleavage of the bonds between Si atoms of 2nd-layer and Mo atoms of 3rd-layer. This is because the interaction between Mo atoms of the 1st layer and Si atoms of the 2nd layer is strong. The (ns-4Si)-terminated (110) surface shows the smallest expansion/contraction effect, indicating that it is the most stable. Conversely, the (ns-4Mo-3)-terminated (110) surface shows the largest expansion/contraction effect, implying that it is likely to be the most unstable. For seven structures of (100) surface, the interlayer spacing Δd23 of the (ns-2Mo-3)-terminated (100) surface contracts by the greatest degree (−71.119%). Similar to the (ns-4Mo-3)-terminated (110) surface, it is also attributed to the strong interaction between 2nd-layer Mo atoms and 3rd-layer Si atoms. The maximum relaxation suggests that the (ns-2Mo-3)-terminated (100) surface is probably the most unstable surface. By contrast, the (ns-2Si-2)-terminated (100) surface shows the smallest relaxation, reflecting more stability than the other (100) surfaces. According to the above structure relaxations, the (ns-8Mo4Si)terminated (001), (ns-4Si)-terminated (110) and (ns-2Si-2)-terminated (100) surfaces may be relatively stable. From Table 4, it can be observed that the strong rumpling appears in first/second layer, and the value of ri continually reduces from surface to bulk. Due to the stronger scattering intensity of metal atoms relative to non-metal atoms [44], their relaxation degree is even larger in the same layer for any surface structure. These surfaces with the positive r1 suggest that Mo atoms move inward compared to Si atoms in the 1st layer. For these surfaces with the outermost layer simultaneously containing both Mo and Si atoms, the interlayer distances d12 decrease, indicating that the 1st layer moves toward inner layer. It is clear that the degree of relaxation on Mo atoms is larger than that on Si atoms, which agrees well with the previous reports [44].

2.2. Surface model

Δdij =

ZiSi − ZiMo × 100% dij (bulk )

× 100% (1)

where dij = Zj-Zi (Zi is the average position of all atoms around the ith layer). With the (ns-8Mo4Si)-terminated (001) surface as an example, it is obvious from Fig. 1 that dij0(bulk ) and dij′ represents the interlayer 2

Ceramics International xxx (xxxx) xxx–xxx

S. Gu, et al.

Fig. 1. The sketch map of slab models for the (ns-8Mo4Si)-terminated (001) surface before and after relaxations. Table 1 Changes of the space between atomic layers of (001) surface before and after relaxations.

of bulk Mo5Si3 is in correlated with the heat of formation (ΔH) at T = 0 K [47,48], therefore

3.2. Surface energy In order to describe the stability of surfaces with different terminations for Mo5Si3, Esurf (surface energy) is calculated by the following equation [45,46].

Esurf =

1 slab (Eslab − NMo × μMo − NSi × μSislab ) 2A

bulk bulk 5μMo + 3μSibulk + ΔH = μMo . 5 Si3

bulk μMo

where and denote the total energies of bulk bcc-Mo and fccSi, respectively. Using Eq. (7), the calculated heat of formation (ΔH) is −3.23 eV, which is in good agreement with the reported value of −3.07 eV [9]. Combined with Eqs. (4) and (7), thus

(3)

where A and Eslab represent the surface area and total energy of the investigated surface, respectively. Ni refers to the total number of Mo or Si atoms, and μislab denotes the surface chemical potential of the Mo or Si atom. It is difficult to calculate the atomic surface chemical potential accurately. However, the surface chemical potential is equal to the system bulk energy of bulk Mo5Si3 ( μMo ). Therefore, 5 Si3 bulk μMo 5 Si3

=

slab 5μMo

+

3μSislab

bulk slab 5μMo + 3μSibulk + ΔH = 5μMo + 3μSislab .

5 bulk 1 slab (μ − μMo ) + ΔH = μSislab − μSibulk 3 Mo 3

(4)

1 ⎛ 1 3 bulk Eslab − NMo × μMo + ⎛ NMo − NSi ⎞ μSislab ⎞ 5 Si3 2A ⎝ 5 ⎠ ⎝5 ⎠

1 1 bulk ⎞ ⎛Eslab − NMo × μMo , 5 Si3 2A ⎝ 5 ⎠

(9)

As far as we know, the atomic chemical potential in slabs should be smaller than that in bulk phases, so bulk slab μMo − μMo ≥ 0, μSislab − μSibulk ≤ 0

(5)

(10)

Moreover, the range of the Si chemical potential can be derived as follows:

For the stoichiometric surfaces (3NMo = 5NSi), Esurf is calculated as

Esurf =

(8)

Namely,

Combined with Eq. (3) and Eq. (4), the surface energy is written as follows:

Esurf =

(7)

μSibulk

1 ΔH ≤ μSislab − μSibulk ≤ 0 3

(6)

in the slab For the non-stoichiometric surfaces (3NMo≠5NSi), should be considered. It is generally known that the chemical potential

μSislab

(11)

For the non-stoichiometric surfaces, Eq. (5) can be converted into a function of the surface energy and μSislab − μSibulk : 3

Ceramics International xxx (xxxx) xxx–xxx

S. Gu, et al.

Table 2 Changes of the space between atomic layers of (110) surface before and after relaxations.

Table 3 Changes of the space between atomic layers of (100) surface before and after relaxations.

4

Ceramics International xxx (xxxx) xxx–xxx

S. Gu, et al.

Table 4 Relaxation results of the low-index surfaces for Mo5Si3. Surfaces (001) (110)

(100)

ns-8Mo4Si ns-2Mo2Si ns-4Mo4Si ns-4Mo-1 ns-4Mo2Si-1 ns-4Mo-2 ns-4Si ns-4Mo2Si-2 ns-2Si ns-4Mo-3 stoi-2Mo ns-2Mo2Si ns-2Mo-1 ns-2Si-1 ns-2Mo-2 ns-2Mo-3 ns-2Si-2

Δd12(%)

Δd23(%)

Δd34(%)

Δd45(%)

r1(%)

r2(%)

r3(%)

r4(%)

−8.238 −22.431 −14.937 −44.109 −24.090 −33.996 −5.136 −8.777 15.970 −50.346 −30.144 −6.586 −43.010 35.379 −55.479 −22.967 −0.228

−0.979 17.374 15.206 26.050 19.234 2.649 5.035 −3.900 −26.343 18.207 −0.457 −21.095 −2.016 −19.106 42.419 −71.119 −32.392

−3.752 −4.649 −10.924 −11.578 −5.438 8.963 −1.545 −3.091 2.355 −0.201 −4.167 36.347 13.584 −25.812 −36.382 13.584 25.672

3.507 6.036 5.602 1.007 0.515 −1.961 0.589 4.028 8.157 −1.987 7.796 −5.691 −12.094 7.314 39.170 14.785 −2.169

7.259 24.551 10.375

11.256 −15.987

−6.851 1.468 −3.268

3.181 −6.117

1 ⎧ 1 3 bulk Eslab − NMo × μMo + ⎛ NMo − NSi ⎞ [μSibulk + (μSislab − μSibulk )] 5 Si3 2A ⎨ 5 ⎝5 ⎠ ⎩ ⎫ ⎬ ⎭

−14.703 −23.162 −1.325

22.256 34.642

2.502 36.130 −10.924 −11.828

34.069 15.591

22.581 30.780

(001) surface is much less relative to (ns-2Mo2Si)-terminated (001) surface in the investigated Si chemical potential, implying the relative higher stability of (ns-8Mo4Si)-terminated (001) surface. Conversely, for (110) and (100) surface (Fig. 2b and c), the Esurf of the (ns-4Si)terminated (110) and (ns-2Si-2)-terminated (100) surfaces are lower compared to their other corresponding surfaces, indicating these two structures are the most stable. These calculations are consistent with the above surface relaxation results. Table 5 shows the surface energies of Mo5Si3 and other A5B3-type compounds at the boundary conditions. Si-poor and Si-rich conditions 1 correspond to the boundaries μSislab − μSibulk = 3 ΔH and μSislab − μSibulk = 0 for the D8m-Mo5Si3, respectively. The date in bold represents the most stable terminating surfaces of (001), (110) and (100) Mo5Si3 surfaces under Si-poor and Si-rich conditions, respectively. For above-mentioned three surfaces of the Mo5Si3 under Si-poor conditions, the order of the stability is: (ns-8Mo4Si)-(001) > (ns-4Si)-(110) > (ns-2Si-2)-(100),

Esurf =

−16.012

39.122 22.689

(12)

The stoichiometric and non-stoichiometric (including Mo-rich structure and Si-rich structure) surface energies of the (100), (001) and (110) surfaces for D8m-Mo5Si3 are shown in Fig. 2. The stoichiometric surface energy is independent of the Si chemical potential, so the surface energy of (stoi-2Mo)-terminated (100) surface is a constant (2.806 J/m2). Except the (stoi-2Mo)-terminated (100) surface, all others are non-stoichiometric surfaces. The surface energy of Mo-rich structure increases with μSislab − μSibulk , while that of Si-rich structure decreases with μSislab − μSibulk . For (001) surface (Fig. 2a), the Esurf of the (ns-8Mo4Si)-terminated

Fig. 2. Surface energies for different terminations of Mo5Si3 (001), (110) and (100) facets as functions of μSislab − μSibulk . 5

Ceramics International xxx (xxxx) xxx–xxx

S. Gu, et al.

Table 5 Calculated surface energies Esurf (J/m2) at the boundary condition for μSislab − μSibulk . Compound

D8m-Mo5Si3

Ref.

Present work

Surfaces

001 110

100

C11b-MoSi2

Ref. [28]

D81-Nb5SiB2

Ref. [49]

001 100 110 101 013 001

D81-Nb5Si3

Ref. [50,51]

001

D8m-V5Si3 D8m-Cr5Si3

Ref. [52] Ref. [52]

– –

Surface energy

ns-8Mo4Si ns-2Mo2Si ns-4Mo4Si ns-4Mo-1 ns-4Mo2Si-1 ns-4Mo-2 ns-4Mo-3 ns-2Si ns-4Mo2Si-2 ns-4Si ns-2Mo2Si ns-2Mo-1 ns-2Si-1 ns-2Mo-2 stoi-2Mo ns-2Si-2 ns-2Mo-3 – – – – – Nb(Si) Nb(NbB) NbB(Nb) Si(Nb) NbSi Nb1 Si Nb2 – –

Si-poor

Si-rich

2.124 2.412 2.507 2.974 2.760 2.765 3.450 2.956 2.554 2.219 2.992 2.742 2.454 2.872

2.198 2.339 2.301 3.179 2.349 3.175 3.553 2.853 3.067 1.706 2.847 3.033 2.164 3.017

2.375 2.881

1.939 3.316

Stoichiometric

2.806

2.31 2.62 2.16 2.17 2.24 ~3.75 ~1.20 ~2.85 ~3.75 ~2.92 ~2.77 ~2.34 ~2.63

~3.35 ~3.30 ~3.20 ~1.65 ~2.04 ~3.43 ~1.75 ~3.60 1.11 1.098

Fig. 3. The calculated total and partial density of states for (001) surface. The Fermi level (EF) represented as a dashed line is at zero.

stability. D.L. Anton [55] and M.K. Meyer [56] study the oxidation products of Mo5Si3 at different temperatures and find that the Mo5Si3 surface forms MoO3 and SiO2 during the oxidation process from room temperature to 750 °C. When the temperature exceeds 750 °C, MoO3 can gradually volatilize, which leads to ‘Pesting’ pulverization phenomenon. Moreover, Mo5Si3 exhibits the best oxidation resistance at 900 °C, because the dense SiO2 protective film on the Mo5Si3 surface improves the surface stability. In our work, compared with the other terminating surfaces, the (ns-8Mo4Si)-terminated (001), (ns-4Si)-terminated (110) and (ns-2Si-2)-terminated (100) surfaces have higher Si content, and it is easier to form the protective SiO2 film [3,57]. Therefore, these three terminating surfaces have the better surface stability according to the analysis of surface composition.

while under Si-rich conditions it changes to: (ns-4Si)-(110) > (ns-2Si2)-(100) > (ns-8Mo4Si)-(001). Unfortunately, due to few investigations about the Mo5Si3 surface energies, the exact value is not found. K.S. Chan [53] assumes that the surface energy of D8m-Mo5Si3 is 2 J/ m2, which agrees well with our results of the calculation. Furthermore, the calculated (001) surface energies of the D8m-Mo5Si3 are very close to that of the C11b-MoSi2, D81-Nb5SiB2 and D81-Nb5Si3. However, there is a little difference between the D8m-Mo5Si3 and D8m-V5Si3, D8mCr5Si3 surface energies. This is probably because the first-principles density functional method is different from the Popel’-Pavlov approach [54] which is employed to calculate the D8m-V5Si3 and D8m-Cr5Si3 surface energies. It is well known that the Mo5Si3 surface stability not only depends on the surface structure, but also is associated with the surface composition. Therefore, it is very necessary to discuss the effect of surface composition on the surface stability. The D8m-Mo5Si3 surface involves the reaction of Mo and Si with oxygen and produces the surface phase of MoO3 and SiO2, which has an important influence on the surface

3.3. Electronic structure The calculated TDOS (total density of states) and PDOS (partial density of states) are employed to illustrate the electronic structure of 6

Ceramics International xxx (xxxx) xxx–xxx

S. Gu, et al.

Fig. 4. The calculated total and partial density of states for (110) surface. The Fermi level (EF) represented as a dashed line is at zero.

differences from that of bulk structure. For (ns-4Mo-2)-terminated (110) surface, it is clear from Fig. 4d that the orbital hybridization between Mo atoms of the 1st layer and Si atoms of the 2nd layer ranging from −9 eV to −3 eV implies the formation of the strong bonding interaction, which is consistent with the above relaxation discussion. For (ns-2Mo-3)-terminated (100) surface (Fig. 5f), the orbital hybridization similarly occurs between Mo atoms of the 2nd layer and Si atoms of the 3rd layer within the range from −6 eV to −3 eV. For (ns-4Si)-terminated (110) surface and (ns-2Si-1)-, (ns-2Si-2)terminated (100) surfaces (Figs. 4e, 5d and g), it is observed that the peak between −9 eV and −7 eV of the 1st-layer Si atoms move to EF relative to the inner layer. This suggests the decrease in metallic property and increased stability. Thus, the calculated Esurf of these surface structures are relatively small, which is consist with the previous analysis in Fig. 2b and c. The charge density is studied to gain insights into the electronic properties of the (001), (110) and (100) surfaces. The deformation charge density Δρ is evaluated via the equation:

D8m-Mo5Si3 surfaces, as shown in Figs. 3–5. For a better comparison, the TDOS and PDOS of bulk Mo5Si3 are also calculated and shown in Fig. 6. The TDOS contours of surface structures show an obvious change compared to the bulk Mo5Si3 because of using slab model calculations. Fig. 6 depicts that the DOS contour at EF (Fermi level) implies the existence of metallic bonds in Mo5Si3 structure. Moreover, a pseudogap near EF indicates the strong covalent bonds, which are induced by the orbital hybridization between Mo-4d and Si-3p. It is clear from Fig. 3a and b that the electronic structure of (001) surface is similar to that of the bulk D8m-Mo5Si3. This is because the coexistence of Mo and Si atoms in the outermost layer compensates the dangling bonds caused by cleaving the crystal, which reduces the impact of external environment and stabilizes the surfaces. For (ns-4Mo4Si)-, (ns-4Mo2Si-1)-, and (ns-4Mo2Si-2)-terminated (110) surfaces (Fig. 4a, c and f), the PDOS of atoms in the 1st layer has a difference from that in the 3rd and 5th layers, which implies that Mo and Si atoms of the outermost layer form the surface state. The same phenomenon occurs in (ns-4Mo-1)-, (ns-4Mo-2)-, and (ns-4Mo-3)-terminated (110) surfaces (Fig. 4b, d and h). In these surface structures, the 1st-layer Mo atoms also form the surface states, and the behaviors of Mo atoms in the inner layers are quite similar to that in bulk Mo5Si3. Differentiating from Fig. 4b, d and h, the (stoi-2Mo)-, (ns-2Mo-1)-, (ns2Mo-2)- and (ns-2Mo-3)-terminated (100) surfaces (Fig. 5a, c, e and f) show the high peaks at EF, which is attributed to truncation of the chemical bonds in the surface layer. It leads to the disruption of potential field, the destruction of periodic arrangement for crystals and the occurrence of distortion. Thus, their electronic states have obvious

Δρ = ρsc − ρnsc

(13)

where ρnsc and ρsc denote non-self-consistent and self-consistent charge density, respectively. The calculated charge density and deformation charge density for the most stable terminations of each surface, including (ns-8Mo4Si)(001), (ns-4Si)-(110) and (ns-2Si-2)-(100) surfaces, are shown in Fig. 7 and Fig. 8, respectively. The atomic charge density contours in the 1st 7

Ceramics International xxx (xxxx) xxx–xxx

S. Gu, et al.

Fig. 5. The calculated total and partial density of states for (100) surface. The Fermi level (EF) represented as a dashed line is at zero.

electrons of surface atoms shift from the broken bonds to the unbroken bonds. And the electron transfer can reduce the bond length, strengthen unbroken bonds, and lead to the contraction of outermost interlayer spacing (Δd12). The degree of the electron transfer decreases with the layer depth, so the surface relaxations become small rapidly from surface to bulk. The main reason is that the outermost layer atoms are influenced sensitively by external environments [58]. It is concluded that the surface relaxation mainly depends on dangling bonds. 3.4. Wulff shape We can predict the ideal equilibrium shape of the nano-particles by Wulff principles [59], which is widely applied in previous studies [29,60,61]. The minimum (001), (110) and (100) surface energies are used to form the terminal geometrical shape of nano-particles in Wulff principles. Wulff shape minimizes the total surface energy, and provides (hkl) a simple relationship between the (hkl) surface energy (Esurf ) and the normal distance (D(hkl)) away from the crystallite center [62], which can be calculated using:

Fig. 6. The calculated density of states of bulk Mo5Si3. The Fermi level (EF) represented as a dashed line is at zero. (a) total density of states of D8m-Mo5Si3 (b) partial density of states of Mo atoms (c) partial density of states of Mo atoms.

(hkl) Esurf

layer is closer to round shapes compared with that in the inner layer (Fig. 7). However, the atomic deformation charge density contours in the 1st layer deviate from the circle, and show a large difference from that in the inner layer, as depicted in Fig. 8. Moreover, the deformation charge density shifts significantly to the vacuum direction, which is referred to as surface feature. It is clear that the original bonding

D (hkl) = constant

(14)

The surface energies listed in Table 5 are used to calculate the equilibrium morphology of D8m-Mo5Si3, as shown in Fig. 9a. Over the investigated range of Si chemical potential, it can be seen that the crystal shape is an octagonal prism consisting of ten faces. The top and bottom faces denote the {001} plane, and the sides represent {110} and 8

Ceramics International xxx (xxxx) xxx–xxx

S. Gu, et al.

Fig. 7. The charge density of low-index surface structures of D8m-Mo5Si3 crystal. (a) (ns-8Mo4Si)-terminated (001) surface (b) (ns-4Si)-terminated (110) surface (c) (ns-2Si-2)-terminated (100) surface.

Fig. 8. The deformation charge density of low-index surface structures of D8m-Mo5Si3 crystal. (a) (ns-8Mo4Si)-terminated (001) surface (b) (ns-4Si)-terminated (110) surface (c) (ns-2Si-2)-terminated (100) surface. Fig. 9. The equilibrium morphology, minimum surface energies and preferential growth direction of D8m-Mo5Si3 surface structures. (a) The predicted equilibrium morphology over all range of Si chemical potential. (b) The correspondent relationship between the preferential growth direction and Si chemical potential. The critical potential is Δ1 μSi∗ = −0.546 eV. (001)-min, (110)-min and (100)-min denote the (ns-8Mo4Si)-terminated (001) surface, (ns-4Si)-terminated (110) surface and (ns-2Si-2)-terminated (100) surface, respectively.

4. Conclusions

{100} plane, respectively. In Fig. 9b, the Si chemical potential is divided into two parts by the critical potential ΔμSi∗ = −0.546eV, which is the horizontal coordinate of joint point of surface energy curves for (100) and (001) surfaces. As reported previously [63], the surfaces with relatively high surface energy have high driving force of preferential growth. According to the surface energies of Mo5Si3, it is observed that the single crystal Mo5Si3 grows preferentially along < 100 > directions from −1.077 eV to −0.546 eV. The predicted crystal shape remains an octagonal prism, which is very similar to the topmost surface of columnar grain in a TEM image of Ref. [64]. On the other hand, the Mo5Si3 crystal grows preferentially along < 001 > direction ranging from −0.546 eV to 0 eV. The predicted equilibrium morphology is close to a cuboid, which is well consistent with the Ref. [65]. Since the elemental chemical potential can cause rapid changes in relative surface areas of different surfaces [66], it can be concluded that the equilibrium shape of nano-particle Mo5Si3 depends on the Si chemical potential.

The atomic relaxations, surface energies and electronic structures of the (100), (001) and (110) low-index surfaces for the D8m-Mo5Si3 are investigated to explore the surface stability by first-principles planewave pseudo-potential calculations based on DFT (Density Functional Theory). The obtained conclusions as follows: (1) The (ns-8Mo4Si)-terminated (001), the (ns-4Si)-terminated (110), and the (ns-2Si-2)-terminated (100) surfaces have minimum relaxations, suggesting that they are relatively stable. Conversely, the (ns-4Mo-3)-terminated (110) and (ns-2Mo-3)-terminated (100) surfaces show maximum relaxations reflecting their instability. (2) The surface energy results show that the (ns-8Mo4Si)-terminated (001) and (ns-4Si)-terminated (110) surfaces are quite stable under the Si-poor and Si-rich conditions, respectively. (3) The density of states show that the electronic structures of the (100), (001) and (110) low-index surfaces are mainly affected by the atomic relaxations, while the charge density results 9

Ceramics International xxx (xxxx) xxx–xxx

S. Gu, et al.

demonstrate the dependence of the surface relaxation on dangling bonds. (4) Within the μSislab − μSibulk range from −1.077 eV to −0.546 eV and −0.546 eV–0 eV, the predicted crystal shape appears like octagonal prism and is close to cuboid, respectively.

[25]

[26] [27]

Acknowledgements

[28]

This work is supported by the Natural Science Foundation of China (51401093), and the Educational Commission of Jiangsu Province of China (17KJA430006).

[29]

[30]

References [31] [32]

[1] C.J. Volders, E. Monazami, G. Ramalingam, P. Reinke, Alternative route to silicene synthesis via surface reconstruction on h-MoSi2 crystallites, Nano Lett. 17 (2017) 299–307. [2] J. Sun, Q.G. Fu, T. Li, G.P. Zhang, R.M. Yuan, Oxidation behavior of thermally sprayed Mo-Si based composite: effect of metastable phase, porosity and residual stress, J. Alloy. Comp. 776 (2019) 712–721. [3] Y.Y. Zhang, Y.G. Li, C.G. Bai, Microstructure and oxidation behavior of Si-MoSi2 functionally graded coating on Mo substrate, Ceram. Int. 43 (2017) 6250–6256. [4] H. Matsunoshita, K. Fujiwara, Y. Sasai, K. Kishida, H. Inui, Orientation relationships, interface structures, and mechanical properties of directionally solidified MoSi2/Mo5Si3/Mo5Si3C composites, Intermetallics 73 (2016) 12–20. [5] C.C. Dharmawardhana, R. Sakidja, S. Aryal, W.Y. Ching, In search of zero thermal expansion anisotropy in Mo5Si3 by strategic alloying, J. Alloy. Comp. 620 (2015) 427–433. [6] H. Chen, Q. Ma, X. Shao, J. Ma, B.X. Huang, Corrosion and microstructure of the metal silicide (Mo1-xNbx)5Si3, Corros. Sci. 70 (2013) 152–160. [7] J. Xu, W. Hu, Y. Yan, X. Lu, P. Munroe, Z.H. Xie, Microstructure and mechanical properties of a Mo-toughened Mo3Si-based in situ nanocomposite, Vacuum 109 (2014) 112–119. [8] J. Arreguín-Zavala, S. Turenne, A. Martel, A. Benaissa, Microwave sintering of MoSi2-Mo5Si3 to promote a final nanometer-scale microstructure and suppressing of pesting phenomenon, Mater. Char. 68 (2012) 117–122. [9] Y. Pan, P. Wang, C.M. Zhang, Structure, mechanical, electronic and thermodynamic properties of Mo5Si3 from first-principles calculations, Ceram. Int. 4 (2018) 12357–12362. [10] C.L. Fu, X.D. Wang, Y.Y. Ye, K.M. Ho, Phase stability, bonding mechanism, and elastic constants of Mo5Si3 by first-principles calculation, Intermetallics 7 (1999) 179–184. [11] H.A. Zhang, S.W. Tang, J.H. Yan, C.J. Zhang, Fabrication and wear characteristics of MoSi2 matrix composites reinforced by La2O3 and Mo5Si3, Int. J. Refract. Met. H. 26 (2008) 115–119. [12] H. Chen, Q. Ma, X. Shao, J. Ma, C.Z. Wang, B.X. Huang, Microstructure, mechanical properties and oxidation resistance of Mo5Si3-Al2O3 composite, Mater. Sci. Eng. A 592 (2014) 12–18. [13] T. Lizuka, H. Kita, Oxidation mechanism of Mo5Si3 particle in Si3N4 matrix composite at 750 °C, Mater. Sci. Eng. A 366 (2004) 10–16. [14] C. Liang, Y. Chen, H.H. Xu, Y. Xia, X.H. Hou, Y.P. Gan, X.C. Ma, X.Y. Tao, H. Huang, J. Zhang, W.Q. Han, W.K. Zhang, Embedding submicron SiO2 into porous carbon as advanced lithium-ion batteries anode with ultralong cycle life and excellent rate capability, J. Taiwan Inst. Chem. E 95 (2019) 227–233. [15] E. Ström, J. Zhang, S. Eriksson, C.H. Li, D. Feng, The influence of alloying elements on phase constitution and microstructure of Mo3M2Si3 (M=Cr, Ti, Nb, Ni, or Co), Mater. Sci. Eng. A 329–331 (2002) 289–294. [16] C.L. Fu, J.H. Schneibel, Reducing the thermal expansion anisotropy in Mo5Si3 by Nb and V additions: theory and experiment, Acta Mater. 51 (2003) 5083–5092. [17] C.L. Yeh, J.A. Peng, Effects of oxide precursors on fabrication of Mo5Si3-Al2O3 composites via thermite-based combustion synthesis, Intermetallics 83 (2017) 87–91. [18] J.A. Vega Farje, H. Matsunoshita, K. Kishida, H. Inui, Microstructure and mechanical properties of a MoSi2-Mo5Si3 eutectic composite processed by laser surface melting, Mater. Char. 148 (2019) 162–170. [19] W.D. Gao, D. Cao, Y.X. Jin, X.W. Zhou, G. Cheng, Y.X. Wang, Microstructure and properties of Cu-Sn-Zn-TiO2 nano-composite coatings on mild steel, Surf. Coat. Tech. 350 (2018) 801–806. [20] X.J. Liu, Y.J. Yin, Y. Ren, H. Wei, Adsorption and evolution behavior of 4C1Si island configurations on diamond (001) surface: a first principle study, J. Alloy. Comp. 618 (2015) 516–521. [21] V.V. Ilyasov, K.D. Pham, O.M. Holodova, I.V. Ershov, Adsorption of atomic oxygen, electron structure and elastic moduli of TiC (001) surface during its laser reconstruction: ab initio study, Appl. Surf. Sci. 351 (2015) 433–444. [22] A. Mohajeri, M. Sotudeh, Adsorption of sulfur containing molecules on monoatomic Au, Ag, and binary Au-Ag nanowires: size and composition dependence, J. Alloy. Comp. 780 (2019) 888–896. [23] H.M. Ding, Q. Liu, J.C. Jie, W.L. Kang, Y. Yue, X.C. Zhang, Influence of carbon vacancies on the adsorption of Au on TiC (001): a first-principles study, J. Mat. Sci. 51 (2016) 2902–2910. [24] Y.X. Wang, S.L. Tay, X.W. Zhou, C.Z. Yao, W. Gao, G. Cheng, Influence of Bi

[33] [34]

[35]

[36] [37] [38] [39]

[40] [41]

[42] [43] [44] [45]

[46]

[47] [48] [49] [50]

[51]

[52]

[53] [54] [55] [56] [57] [58]

[59]

[60]

10

addition on the property of Ag-Bi nano-composite coatings, Surf. Coat. Tech. 349 (2018) 217–223. Z. Jiao, Q.J. Liu, F.S. Liu, B. Tang, Structural and electronic properties of low-index surfaces of NbAl3 intermetallic with first-principles calculations, Appl. Surf. Sci. 419 (2017) 811–816. J.Q. Dai, J.W. Xu, J.H. Zhu, First-principles study on the multiferroic BiFeO3 (0001) polar surfaces, Appl. Surf. Sci. 392 (2017) 135–143. K.X. Gu, M.J. Pang, Y.Z. Zhan, Insight into interfacial structure and bonding nature of diamond(001)/Cr3C2(001) interface, J. Alloy. Comp. 770 (2019) 82–89. S.P. Sun, X.P. Li, H.J. Wang, Y. Jiang, D.Q. Yi, Adsorption of oxygen atom on MoSi2 (110) surface, Appl. Surf. Sci. 382 (2016) 239–248. S.P. Sun, J.L. Zhu, S. Gu, X.P. Li, W.N. Lei, Y. Jiang, D.Q. Yi, G.H. Chen, First principles investigation of the surface stability and equilibrium morphology of MoO3, Appl. Surf. Sci. 467–468 (2019) 753–759. Y. Ren, X.J. Liu, C. Zhang, X. Tan, S.Y. Sun, Surface modification of reconstruction by evolution process of the B/P_C dimer on diamond (001) surface, J. Alloy. Comp. 737 (2018) 456–463. P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Phys. Rev. B 136 (1964) 864. W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. A 140 (1965) 1133. G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169–11186. G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6 (1996) 15–50. G. Kresse, J. Hafner, Ab initio molecular-dynamics simulation of the liquid-metalamorphous-semiconductor transition in germanium, Phys. Rev. B 49 (1994) 14251–14269. D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B 41 (1990) 7892–7895. J.P. Perdew, Y. Wang, Accurate and simple analytic representation of the electrongas correlation energy, Phys. Rev. B 45 (1992) 13244–13249. H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13 (1976) 5188–5192. H. Liang, F. Peng, C. Fan, Q. Zhang, J. Liu, S.X. Guan, Structural stability of ultrahigh temperature refractory material MoSi2 and Mo5Si3 under high pressure, Chin. Phys. B 26 (2017) 053101. J.P. Lothe, J.P. Hirth, Theory of Dislocations, Wiley, New York, 1982. X.G. Ma, C.Q. Tang, J.Q. Huang, L.F. Hu, X. Xue, W.B. Zhou, First-principle calculations on the geometry and relaxation structure of anatase TiO2 (101) surface, Acta Phys. Sin. 55 (2006) 4208–4213. K.X. Gu, M.J. Pang, Y.Z. Zhan, Insight into the structural and electronic properties of orthorhombic Cr3C2 (001) surface, J. Phys. Chem. Solids 118 (2018) 68–72. N. Wang, L. Dong, M.S. Li, D.J. Li, Comparison and stability of the low-index surfaces of c-BN by first-principles, Vacuum 104 (2014) 92–96. N.W. Ashcroft, N.D. Mermin, Solid State Physics, Cengage Learning, London, 1976. Y. Duan, Electronic properties and stabilities of bulk and low-index surfaces of SnO in comparison with SnO2: a first-principles density functional approach with an empirical correction of van der Waals interactions, Phys. Rew. B 77 (2008) 045332. C.H. Xu, Y. Jiang, D.Q. Yi, S.P. Sun, Z.M. Yu, Environment-dependent surface structures and stabilities of SnO2 from the first principles, J. Appl. Phys. 111 (2012) 063504. G.H. Chen, Z.F. Hou, X.G. Gong, Structural and electronic properties of cubic HfO2 surfaces, Comput. Mat. Sci. 44 (2008) 46–52. W. Zhang, J.R. Smith, Stoichiometry and adhesion of Nb/Al2O3, Phys. Rev. B 61 (2000) 16883. J.Z. Xuyu, J.X. Shang, F.H. Wang, First-principles study of electronic properties and stability of Nb5SiB2 (001) surface, Chin. Phys. B 20 (2011) 037101. J.X. Shang, K. Guan, F.H. Wang, Atomic structure and adhesion of the Nb(001)/αNb5Si3(001) interface: a first-principles study, J. Phys. Condens. Matter 22 (8) (2010) 085004. S.Y. Liu, J.X. Shang, F.H. Wang, S.Y. Liu, Y. Zhang, H.B. Xu, Ab initio atomistic thermodynamics study on the selective oxidation mechanism of the surfaces of intermetallic compounds, Phys. Rev. B 80 (2009) 085414. V.I. Nizhenko, Free surface energy as a criterion for the sequence of intermetallic layer formation in reaction couples, Powder Metall. Met. Ceram. 43 (2004) 273–279. K.S. Chan, Relationships of fracture toughness and dislocation mobility in intermetallics, Metall. Mater. Trans. A 34 (2003) 2315–2328. S.I. Popel’, V.V. Pavlov, The Physical Chemistry of Surface Phenomena at High Temperatures, Metallurgiya, Moscow, 1977. D.L. Anton, D.M. Shah, Ternary alloying of refractory in termetallics, Mater. Res. Soc. Symp. Proc. 213 (1991) 733–737. M.K. Meyer, M. Akinc, Oxidation behavior of boron-modified Mo5Si3 at 800°C ~ 1300°C, J. Am. Ceram. Soc. 79 (1996) 938–944. W.L. Daloz, Developing a High Temperature, Oxidation Resistant MolybdenumSilica Composite, Georgia Institute of Technology, America, 2015. C. Liang, S. Liang, Y. Xia, Y.P. Gan, L.B. Fang, Y.Z. Jiang, X.Y. Tao, H. Huang, J. Zhang, W.K. Zhang, Synthesis of hierarchical porous carbon from metal carbonates towards high-performance lithium storage, Green Chem. 20 (2018) 1484–1490. Y. Meng, X.W. Liu, M.M. Bai, W.P. Guo, D.B. Cao, Y. Yang, Y.W. Li, X.D. Wen, Prediction on morphologies and phase equilibrium diagram of iron oxides nanoparticles, Appl. Surf. Sci. 480 (2019) 478–486. L.M. Molina, S. Lee, K. Sell, G. Barcaro, A. Fortunelli, B. Lee, S. Seifert, R.E. Winans, J.W. Elam, M.J. Pellin, et al., Size-dependent selectivity and activity of silver

Ceramics International xxx (xxxx) xxx–xxx

S. Gu, et al.

[64] J. Xu, L.L. Liu, Z.Y. Li, P. Munroe, Z.H. Xie, Effect of Al addition upon mechanical robustness and corrosion resistance of Mo5Si3/MoSi2 gradient nanocomposite coatings, Surf. Coat. Tech. 223 (2013) 115–125. [65] Z.I. Zaki, N.Y. Mostafa, M.M. Rashad, High pressure synthesis of magnesium aluminate composites with MoSi2 and Mo5Si3 in a self-sustaining manner, Ceram. Int. 38 (2012) 5231–5237. [66] Q.F. Zhou, X.T. Liu, T. Maxwell, B. Vancil, T.J. Balk, M.J. Beck, BaxScyOz on W (001), (110), and (112) in scandate cathodes: connecting to experiment via μO and equilibrium crystal shape, Appl. Surf. Sci. 458 (2018) 827–838.

nanoclusters in the partial oxidation of propylene to propylene oxide and acrolein: a joint experimental and theoretical study, Catal. Today 160 (2011) 116–130. [61] M.C. Oliveira, L. Gracia, I.C. Nogueira, M.F. do Carmo Gurgel, J.M.R. Mercury, E. Longo, J. Andrés, Synthesis and morphological transformation of BaWO4 crystals: experimental and theoretical insights, Ceram. Int. 42 (2016) 10913–10921. [62] I.V. Markov, Crystal growth for beginners: fundamentals of nucleation, crystal growth and epitaxy, World Sci. (1995). [63] E. Ringe, R.P. Van Duyne, L.D. Marks, Wulff construction for alloy nanoparticles, Nano Lett. 11 (2011) 3399–3403.

11