Detailed first-principles studies on surface energy and work function of hexagonal metals

Surface Science 651 (2016) 137–146

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Detailed first-principles studies on surface energy and work function of hexagonal metals De-Peng Ji ⁎, Quanxi Zhu, Shao-Qing Wang Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, PR China

a r t i c l e

i n f o

Article history: Received 3 December 2015 Received in revised form 18 April 2016 Accepted 18 April 2016 Available online 20 April 2016 Keywords: Work function Surface energy Hexagonal metals First-principles

a b s t r a c t The surface energies and work functions for ten kinds of Miller-indices surfaces of hexagonal metals, Be, Mg, Tc, Re, Ru, and Os are calculated by means of the density functional theory (DFT) method. The results show that the metals belonging to the same group have a very similar rule in work functions and surface energies. The work functions of (0001), ð0111Þ, and ð1010Þ surfaces are generally larger than the work functions of ð1121Þ, ð1122Þ, ð1123Þ, and ð3140Þ surfaces. In contrast to work functions, there is more regularity in the crystallographic orientation dependence of surface energies. However, for the metals belonging to different groups, there are always some differences in the exact order of orientation dependence. It is also shown that the work functions and surface energies of the main group metals decrease as they go from top to the bottom in the same group of periodic table, while for the transition metals, they do not always obey this rule. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Surface energy and work function are very important parameters that can determine various properties of materials, such as the Young's modulus for mechanical behaviors [1–3], the surface morphology of metals and alloys [4], and the zero charge potential of electrode surface [5]. These parameters can also help to understand many surface phenomena, for example, underpotential deposition (UPD) [6], surface segregation [7,8] and dealloying [9], metal dissolution or corrosion [10], and the formation of grain boundaries [11]. Surface energy, defined as the amount of energy required to divide an infinite crystal into two parts, is a very fundamental parameter of materials surface. Work function is defined as the minimum energy needed to remove an electron from the bulk of a material through surface to a point outside the material. Research works on surface energy and work function have been reported in many publications [5,12,13]. These studies have deeply promoted the development of materials science. In experimental aspect, there have been numerous reports about the surface energies and work functions of metals, especially in the mid of last century. Since the end of the last century, theoretical calculations based on density functional theory (DFT) [14–22] have become a very widely accepted and useful tool to understand the surface energy and work function properties of materials. A roughly inverse proportional relationship between surface energy and work function was found by Wang et al. [23] through the analysis of their DFT results. Singh et al. [24] studied some BCC and FCC metals, ⁎ Corresponding author. Tel.: +86 02423971846. E-mail address: [email protected] (D.-P. Ji).

http://dx.doi.org/10.1016/j.susc.2016.04.007 0039-6028/© 2016 Elsevier B.V. All rights reserved.

as well as Ti(0001), by first-principles calculation. Kokko et al. [19] reported their first-principles results on the (100), (110) and (111) surfaces of lithium. Although the surface energies and work functions for most of the cubic metals have been calculated and reported so far, the situation for hexagonal metals is still far from satisfactory. Tang et al. [25] reported a detailed first-principles study on the surface energy of magnesium. Vitos et al. [26] calculated the surface energies of two kinds of low-index surfaces for a few hexagonal metals. In addition to a bit of data for ð101 0Þ surface, the work function calculations of hexagonal metals were mostly done for (0001) surface only [18,27–30], reports on the other hexagonal surfaces are hardly touched yet. In this work, we focus on calculation of the surface energies and work functions of six typical hexagonal metals for their (0001), ð1010Þ, ð0111Þ, ð0112Þ, ð0113Þ, ð1121Þ, ð1122Þ, ð1123Þ, ð2130Þ, and ð3140Þ surfaces. In some experimental work, some scientists [31–34] have reported the existence of (0001), ð1010Þ, ð0111Þ, ð0112Þ, and ð112kÞ surface in hexagonal crystals. But their work functions and surface energies are seldom studied theoretically. All the calculations are made with firstprinciples method within the framework of density-functional theory. The calculated surfaces are represented by periodic slab models, separated by 1.6 nm vacuum space to avoid successive repeat slab interactions. The results obtained by the present study are expected to provide a valuable database reference for the surface science.

2. Calculation method The calculations are performed via the Vienna Ab initio Simulation Package (VASP) [35] with periodic boundary condition using the

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projector augmented wave (PAW) method [36,37]. The local density approximation (LDA) and Perdew–Burke–Ernzerh (PBE) [38] generalized gradient approximation (GGA) are both adopted for comparison.

Table 2 The comparison of the calculated crystal lattices with experimental values. Potential

Metal

The surfaces are modeled by 12 layer slabs for (0001) and ð1010Þ surfaces, 16 layer slabs for ð0111Þ, ð0112Þ, and ð0113Þ surfaces, 22 layers for ð1121Þ, ð1122Þ, and ð1123Þ, and 30 layers for ð2130Þ and ð3140Þ surfaces to obtain the converged results, which is similar to the work of Wang et al. [23], Tang et al. [25], Skriver et al. [25] and Perdew et al. [38]. The Gamma centered grids are used for k-space integration, and the k-point meshes are adjusted depending on the size of the surface models. The energy cutoff is set to be 400 eV. For the structural relaxation, the convergence criterion of self-consistent calculations is 10− 6 eV and a force criterion of 0.03 eV/Å between two consecutive steps is adopted for ionic relaxations. The surface unit cells are p(1 × 1) with the vacuum thickness set to be 1.6 nm. Spin polarization is taken into account through all the calculations to decrease some unexpected errors. The electron occupancies with a smearing width of 0.1 eV is taken. During relaxation, all the atoms in the slab models are allowed to relax. The details of our calculations are listed in Table 1. It gives almost all of the information about the calculations of Mg calculated with PBE functional. As for the other metals' calculations, the parameter settings are very similar. The calculated lattice constants are listed in Table 2, compared with experimental values [39]. The results calculated with PBE functional show very good agreement with the experimental results. The results calculated with LDA approximation are a little bad, but still show good agreement with the experimental results. The calculated values of c/a ratio are similar for two approximations. 2.1. Slab models Six hexagonal elemental metals are studied, including Be, Mg, Tc, Re, Ru, and Os. For each metal, the slab models of (0001), ð1010Þ, ð0111Þ, ð0112Þ, ð0113Þ, ð1121Þ, ð1122Þ, ð1123Þ, ð2130Þ, and ð3140Þ crystal orientations are built and calculated. Our created slab models are presented in Fig. 1. Although the surface models used in this work are the p(1 × 1) slab structure, Fig. 1 shows the p(3 × 2) models of the slabs in order to illustrate the periodic structures of these models. In view of the surface configurations in this study there are rarely seen in other works, some more detailed explanations of these model buildings are supplied in Figs. 2 to 5. Fig. 2 takes the model of Mg ð0111Þ as an example to illustrate the structural periodicity of these models. Fig. 2(a) is a configuration of (3 × 2) super cell of the ð0111Þ slab model used in this calculation, Fig. 2(b) is a slab structure cut directly from the metal bulk. It is seen that the atomic arrangements in Fig. 2(a) and (b) by the two different methods are the same, which confirms that the models used in this work are strict for their periodicity. Fig. 3 gives a simple explanation of the ð0111Þ surface slab model, which is very similar to the slab models of ð0112Þ and ð0113Þ surfaces.

PAW-PBE

PAW-LDA

Experiment [39]

Be Mg Tc Re Ru Os Be Mg Tc Re Ru Os Be Mg Tc Re Ru Os

Lattice constant

Error to experiment value [39]

a (Å)

c (Å)

c/a

Δa (%)

Δc (%)

Δc =a (%)

2.264 3.191 2.746 2.774 2.715 2.759 2.232 3.124 2.707 2.741 2.673 2.725 2.286 3.209 2.735 2.761 2.706 2.734

3.567 5.187 4.395 4.481 4.279 4.355 3.524 5.078 4.327 4.422 4.216 4.304 3.584 5.211 4.388 4.456 4.282 4.317

1.575 1.626 1.601 1.615 1.576 1.578 1.579 1.625 1.598 1.613 1.577 1.579 1.568 1.624 1.604 1.614 1.582 1.579

−0.96 −0.56 0.40 0.47 0.33 0.91 −2.36 −2.65 −1.02 −0.72 −1.21 −0.33 0

−0.47 0.46 0.15 0.56 −0.07 0.88 −1.67 −2.55 −1.39 −0.76 −1.54 −0.30

0.45 0.12 −0.19 0.06 −0.38 −0.06 0.70 0.06 −0.37 −0.06 −0.31 0

Fig. 3(a) is a perspective view of 2 × 2 × 1 Mg cell. Where, the four index coordinate system of hexagonal close-packed crystals is indicated by the blue lines, the ð0111Þ plane and the ½2110 direction are also labeled in this figure. Fig. 3(b) is the projective view of Fig. 3(a) along the ½ 2110 direction; the two oblique lines indicate the ð0111Þ plane. Fig. 3(c) is the 2 × 2 view of Fig. 3(b) in order to give a better view of the atomic arrangement along the vertical direction of ð0111Þ plane. Fig. 3(d) rotates an anticlockwise angle from Fig. 3(c). Fig. 3(e) is the slab model of ð0111Þ surface built in this work. It is seen that the atomic positions in Fig. 3(e) are in strict conformity with the labeled area in Fig. 3(d). Figs. 4 and 5 are very similar to Fig. 3. Fig. 4 presents a simple explanation of the slab model of ð1121Þ surface, which is very similar to the ones of ð1122Þ and ð1123Þ surfaces. Fig. 5 is for the slab model of ð2130Þ surface, it is very similar to ð3140Þ surface. As for the slab models of (0001) and ð1010Þ surfaces, they are very easy to build. There is no need to give too many explanations for them. 2.2. Surface energy and work function The surface energy is the work required to form a unit area of surface. It is defined as follows: σ¼

 1  N Eslab  N  Ebulk 2S

ð1Þ

where EN slab is the total energy of the slab, Ebulk is the per atom energy of the bulk metal, N is the total number of atoms in the slab, S is the surface

Table 1 The calculation details of Mg. Surface orientation

Atom layers

Slab thickness (Å)

K mesh

K points

Energy cutoff (eV)

Vacuum thickness (Å)

Energy convergence criteria (eV)

Force convergence criteria (eV/Å)

(0001)

12 12

44.48 30.75

14*14*1 10*6*1

57 24

400

16

10−6

0.03

ð1010Þ ð0111Þ

16

33.49

10*6*1

32

ð0112Þ

16

30.49

10*4*1

18

ð0113Þ

16

26.49

8*3*1

13

ð1121Þ

22

32.02

6*5*1

16

ð1122Þ

22

29.59

6*5*1

12

ð1123Þ

22

28.31

5*4*1

11

ð2130Þ

30

29.93

5*3*1

6

ð3140Þ

30

26.99

5*2*1

6

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139

Fig. 1. Slab models used in this work. Here it gives the (3 × 2) super cell models of the models used in this work.

area, 12 is denoted because there are two equal surfaces in the slab model. Thus, it should be noted that the upper and bottom surfaces must be equivalent when creating the slab model; otherwise it will be wrong to use this equation for the surface energy calculation. From this equation, it is also clearly shown that the smaller the surface energy is, the easier the surface will form.

For the purpose of theoretical calculations, one can define the work function as the energy required to remove an electron from the Fermi level to the potential of vacuum at 0 K. From that point of view, there are two methods commonly applied to calculate the surface work function of pure metals [24,40–45]. The first one stems from the initial definition of work function by Kohn et al. [46], the formula is written as: Φ ¼ Vvacuum  Efermi

ð2Þ

where Vvacuum is calculated as electrostatic potential in the middle of the vacuum region, and Efermi denotes the Fermi energy of the slab. One thing needs to be noticed is that the data are derived from one slab calculation. The second used method is based on macroscopic averages [47], by means of which work function is calculated as:     ð sÞ ðbÞ sÞ bÞ  V b  Eðvac  Vb Φ ¼ V ðvac

Fig. 2. The slab models of Mgð0111Þ, in order to get a better understanding of models' periodicity. (a), the (3 × 2) super slab model of Fig. 2(c); (b), the super slab model built from the metal bulk directly; (c), the slab model.

ð3Þ

(s) where V (s) vac and V b are the macroscopically averaged electrostatic potential in the vacuum and bulk region, respectively, for the slab model (b) calculations; and E(b) vac and V b are the Fermi energy and the averaged electrostatic potential, respectively, obtained from the calculation of the corresponding bulk system. Remember that all the potentials discussed here refer to the Hartree part of the total Kohn–Sham potential. Comparing Eqs. (2) and (3), it can be seen that the major source of difference comes from the potential reference point, for which the

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Fig. 3. Schematic diagrams showing the ð0111Þ slab model in HCP cell, (a) perspective view; (b) the ½2110 projective view of panel (a); (c) the ½2110 projective view of more atoms; (d) a rotation of panel (c); (e) the slab model of ð0111Þ surface.

point is in vacuum and in material bulk, respectively. Because of this, the first method, corresponding to the one slab calculation, suffers from quantum size effect; while the later one, corresponding to the bulk, does not. Therefore, generally speaking, the second method can achieve a more converged and accurate results, and it is used widely in the work

function calculations [24,44,45]. On the other side, several authors [24, 44] have also pointed out that this method is particularly high accuracy and computational efficiency for unrelaxed surfaces; however, when taking relaxation of all layers into account, the method of macroscopic averaging converges much more slowly. Singh et al. [24] gave a

Fig. 4. Schematic diagrams showing the ð1121Þ slab model in HCP cell, (a) perspective view; (b) ½1100 projective view; (c) 2 × 2 of panel (b); (d) a rotation of panel (c); (e) the slab model of ð1121Þ surface.

D.-P. Ji et al. / Surface Science 651 (2016) 137–146

Fig. 5. Schematic diagrams showing the ð2130Þ slab model in HCP cell, (a) ½0001 projective view; (b) a rotation of panel (a); (c) the slab model of ð2130Þ surface.

comparison of the two methods for Pd (100) slabs calculations, and demonstrated the slow convergence as the fact that the averaging window for the reference potential and the layer spacing of the interior of the slab are not equivalent. Given about the focus of this paper is to systematically investigate the work functions of various Millar-indices facets for Hexagonal metals, it is more convenient to adopt the first method through a large number of calculations. What's more, Roman et al. [4] used the same strategy to investigate the work function properties for halide adsorption on a series of close-packed metal electrodes. Besides, in order to guarantee the data reliability (usually include the convergence and accuracy), all the atoms in the slab models are allowed to relax, and we test the slab thickness for the typical metal surfaces of Be upper bound to 32 atom layers. The preliminary results confirmed that the used number of atomic layers for all the slab models gives converged values of work functions and minimizes quantum size effects to below 0.04 eV, which is within the limit of accuracy achievable by DFT calculations.

3. Results The full calculated results of the surface energies and work functions in this work are listed in Table 3, as well as some comparisons with other available theoretical and experimental results. The converged results for the work function and surface energy of Ru ð1122Þ surface can still not be obtained, as they are not stable in the course of geometry optimization. From Table 3, it is seen that even for the same metal the surface energies and work functions may have large differences as the surface orientation changes. The range of this variation can reach 1.0 eV for work function and 1.0 J/m2 for surface energy. Though many published articles are checked, there are little direct experimental determinations except a few on the poly-crystals of these hexagonal metals. Publications on the dependence of the surface energy and work function on the surface orientations are even less, thus only some theoretical reports of these metals are listed in the table. For some special crystal orientations, there are only published surface energies or work functions available. What's more, most of the experiment data are based on the poly-crystals of these metals, especially for the surface energy.

141

It is seen from Table 3 that both of the theoretical and experimental results show some degree of fluctuation. This can be caused by the different measuring methods and conditions, and various methods adopted through the theoretical calculations (LDA or GGA approximations, PW91 or PBE exchange-correlation functional, ultra-soft or PAW pseudopotentials), as well as the different model sizes. Results show that the work functions calculated with LDA are a little larger than the other ones; on the other side, the surface energies calculated with GGA are a little smaller than the other results. This is consistent with the traditional consensus, i.e. the GGA approximation is usually more accurate than the LDA one for the majority of cases. However, in the calculation of surface energy, LDA approximation tends to be much better [48]. By comparing our calculated results with those of the other ones, it can be seen that most of the work functions are in accordance with each other very well. But the results obtained with LDA approximation tend to have larger differences compared with the experimental ones. For the surface energies, the results calculated with GGA approximation tend to be smaller than those calculated with LDA approximation, with differences about 0.4–1.0 J/m2. The results calculated with LDA approximation are more similar with the other results. Of course, there are still some differences. It can be easily explained. This study is based on VASP, and all the energies are calculated at 0 K, but the other theoretical results are based on different software or approximations and the experimental data can only be obtained under finite temperature. Except this difference of temperature, most of the experimental results were done in the period between 1960s to 1980s, significant discrepancies exist even among different experimental results. 3.1. Be and Mg In the periodic table, Be and Mg belong to the alkaline-earth metals (IIA) and they have only two outermost valence electrons that occupied the s-orbital. The calculated results are listed in Table 3. Fig. 6 shows the variations of the surface energy and work function of Be and Mg with surface orientations. The work functions and surface energies vary a lot as the surface orientations. This might be caused by the differences of the distribution about the surface atoms and electrons. The (0001),ð0111Þ andð1010Þ surfaces have more concentrated atoms in the outmost surfaces. And the ð1122Þ, ð1123Þ and ð3140Þ have less concentrated atoms in the outmost surfaces. The atoms' distributions influence the surface electronic structure and then result in the huge differences of the surface properties. According to Table 3 and Fig. 6, it is seen that the calculated work functions for the (0001) surfaces of Be and Mg exhibit a small difference about 10% with the other theoretical results, and a little large difference with the experimental results. The results calculated with GGA seem to be more reliable than those calculated with LDA approximation for the calculation of work function, which is consistent with the DFT features. Considering that most of the experimental results are based on the polycrystal and the Φ(0001) usually is the largest one, calculated results in this work may be considered as a proper reflection of the reality. The two metals share the similar variation tendency in both of surface energy and work function, especially for the surface energy. However, there is some kind of disorder for the work functions of Be, which might be caused by the material anisotropy. Generally speaking, the surface energy can be used to judge the stability of the crystal surface. The smaller the surface energy, the more stable the surface tends to be, and the easier the surface to be formed. Hence, the surface energy calculated in this work is directly related to the forming ability of the surface. The present study shows that exchange-correlation functional has a significant influence on the results. The surface energies calculated with GGA approximation are smaller than those with LDA approximation. The latter tends to be more accurate for surface energy calculation as Wang et al. suggested [11].

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Table 3 The calculated results and the comparison with other results. Surface

σ (J/m2)

Φ (eV)

Present

Theory

LDA

GGA

Be (0001)

2.162

1.750

 ð101 0Þ  ð011 1Þ  ð011 2Þ  ð011 3Þ  ð112 1Þ  ð112 2Þ  ð112 3Þ  ð213 0Þ  ð314 0Þ Mg (0001)

2.144 2.197 2.581 2.627 2.769 2.779 2.923 2.377 2.655 0.641

1.871 1.879 2.239 2.522 2.443 2.470 2.635 2.104 2.343 0.528

 ð101 0Þ

0.756

0.643

ð0113Þ

0.811 0.841 0.845

0.744 0.616 0.704

 ð011 1Þ  ð011 2Þ

Exp.

1.834a 2.122b 1.657c 1.945d 1.924e 2.126a

1.628m 2.700n

0.792a 0.642b 0.634c 0.641f 0.624g 0.977k 0.782g 0.737g 0.864g 0.785g

0.785m 0.760n

Present LDA

GGA

5.45

5.29

4.71 5.23 5.04 4.73 4.82 4.94 4.42 4.38 4.55 3.89

4.52 5.03 4.81 4.46 4.58 4.81 4.25 4.17 4.23 3.76

3.76

3.64

3.88 3.74 3.66

3.70 3.63 3.58

ð1121Þ

0.903

0.765

3.68

3.56

ð1122Þ

0.886

0.776

3.80

3.67

ð1123Þ

0.911

0.681

3.68

3.53

ð2130Þ

0.792

0.746

3.72

3.49

ð3140Þ Tc (0001)

0.875

0.711

3.68

3.48

ð1010Þ

2.882 3.196

2.190 2.551

4.95 4.83

4.69 4.50

3.691a 3.897a

3.150n

ð0111Þ

3.451

2.761

5.05

4.70

ð0112Þ

3.489

2.856

4.67

4.31

ð0113Þ

3.347

2.747

4.60

4.25

ð1121Þ

3.529

2.843

4.44

4.09

ð1122Þ

3.551

2.906

4.63

4.28

ð1123Þ

3.553

2.937

4.56

4.23

ð2130Þ

3.337

2.725

4.58

4.26

ð3140Þ Re (0001)

3.495

2.862

4.64

4.32

ð1010Þ

3.192 3.511

2.581 2.923

5.17 4.93

4.88 4.62

4.214a,1.682j 3.192a

2.625t 3.626m 3.600n

ð0111Þ

3.920

3.321

5.25

4.94

ð0112Þ

3.938

3.389

4.86

4.55

ð0113Þ

3.762

3.241

4.73

4.44

ð1121Þ

3.962

3.361

4.62

4.33

ð1122Þ

4.017

3.441

4.79

4.48

ð1123Þ

3.999

3.469

4.72

4.41

ð2130Þ

3.688

3.136

4.77

4.49

ð3140Þ Ru (0001)

3.855

3.292

4.80

4.55

ð1010Þ

3.413 3.710

2.603 2.994

5.31 5.13

4.97 4.79

3.928a 4.236a

3.04m 3.05n

ð0111Þ

3.638

2.899

5.26

4.91

ð0112Þ

3.890

3.141

4.85

4.50

ð0113Þ

3.793

3.061

4.82

4.45

ð1121Þ

4.083

3.292

4.76

4.39

ð1122Þ

–

–

–

–

ð1123Þ

3.983

3.235

4.80

4.43

ð2130Þ

4.021

3.282

4.86

4.47

ð3140Þ Os (0001)

3.935

3.221

4.96

4.37

ð1010Þ

3.701 4.114

2.975 3.473

5.64 5.45

5.32 5.17

4.566a 5.02a

3.450n

ð0111Þ

4.097

3.436

5.53

5.23

ð0112Þ

4.439

3.768

5.15

4.85

ð0113Þ

4.293

3.640

4.98

4.67

ð1121Þ

4.645

3.941

4.98

4.67

ð1122Þ

4.436

3.770

5.22

4.90

Theory

Exp.

5.62b 5.36c 5.57d

4.98o 5.10p

3.86b 3.76c 3.88d 3.69h

3.66q 3.84r

5.36a,4.72i

4.81s 4.70s

5.22u 4.99–5.08v 5.05 ± 0.04w

5.84k,5.03l

4.71x

6.42k

4.83y 6.05z 5.78z

D.-P. Ji et al. / Surface Science 651 (2016) 137–146

143

Table 3 (continued) Surface

σ (J/m2)

Φ (eV)

Present  ð112 3Þ  ð213 0Þ  ð314 0Þ

Theory

Exp.

Present

Theory

LDA

GGA

LDA

GGA

4.574 4.491 4.505

3.907 3.891 3.849

5.09 5.20 5.09

4.77 4.87 4.77

a

FCD-LMTO, Ref. [16]. Green's function TB-LMTO, Ref. [18]. GGA(PW), Ref. [51]. d LDA(PZ), Ref. [51]. e LDA potential LAPW, Ref. [54]. f LDA(PZ) potential, Ref. [56]. g PBEsol potential, Ref. [25]. h LDA potential, Ref. [59]. i FP-LMTO, Ref. [60]. j AMEAM many-body potentials, Ref. [62]. k Green's function TB-LMTO, Ref. [18]. l FP-LMTO, Ref. [64]. m Experimental, Ref. [66]. n Experimental, Ref. [49]. o Experimental, Ref. [50]. p Experimental, Ref. [52]. q Experimental, Ref. [53]. r Experimental, Ref. [55]. s Experimental, Ref. [57]. t Experimental, Ref. [58]. u Experimental, Ref. [29]. v Experimental, Ref. [61]. w Experimental, Ref. [63]. x Experimental, Ref. [19]. y Experimental, Ref. [65]. z Experimental, Ref. [67]. b c

Fig. 6. Surface energy and work function of Be and Mg as a function of surface orientations.

Exp.

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D.-P. Ji et al. / Surface Science 651 (2016) 137–146

Fig. 7. Surface energy and work function of Tc and Re as a function of surface orientations.

The (0001) surface has the largest work function with the smallest surface energy, which means that this surface is the easiest one to form for Be and Mg. The ð0111Þ and ð1010Þ surfaces also have larger work functions and smaller surface energies, which indicates that they tend to be more stable than the rest of other surfaces. For the other Miller-index facets shown in Fig. 6, such as ð1121Þ, ð1122Þ, ð1123Þ and ð3140Þ, they present small work functions and high surface energies, which is a symbol of instability. This information can be very useful: if one wants to use these metals in stable state, he should try to decrease the existence of ð1121Þ, ð1122Þ, ð1123Þ, ð3140Þ planes; on the contrary, if one wants to utilize these metals for chemical applications, such as catalysis and electrochemical cells, focusing on (0001), ð0 111Þ, ð1010Þ surfaces may suppress the chemical reactions and focusing on ð1121Þ, ð1122Þ, ð1123Þ, ð3140Þ surfaces may accelerate the reactions.

Similar to Be and Mg, Tc and Re (0001) surfaces show the smallest surface energies. The work functions of (0001) and ð0111Þ surfaces are apparently larger than the other ones, correspondingly, their surface energies are smaller than the other surfaces. However, the surface energy of ð0111Þ is unlike the others, which occupies the middle position in the order but has very small difference with the surface energy of ð1123Þ. The ð1121Þ, ð1122Þ, ð1123Þ, and ð3140Þ surfaces present small work functions and high surface energies, which is very similar to Be and Mg. Unlike Be and Mg, the work functions of Re are always larger than the work functions of Tc for the same crystal orientation. The surface energies of Re are also always larger than the work functions of Tc for the same crystal orientation. However, the atomic number of Re is larger than Tc. This is very different to the situation of Be and Mg, even to some other main group metals [23,24]. 3.3. Ru and Os

3.2. Tc and Re As the VIIB rare earth elements, Tc and Re have two electrons that occupied the outermost s-orbit and five electrons on the outermost dorbit. The electronic structure details are more complex than the main group metals like Be and Mg. The calculated results of surface energies and work functions are presented in Table 3 and Fig. 7. From Fig. 7, it can be easily found that Tc and Re share a very similar variation tendency in work functions and surface energies. Compared with the tendencies of Be and Mg, the tendencies of Tc and Re are much more orderly, which may infer that the two metals are quite similar in physical and chemical properties.

Ru and Os belonging to rare earth elements (VIII), and they have only one electron on the outermost s-orbit and seven electrons on the outermost d-orbit. The details of their calculated outcomes are shown in Table 3 and Fig. 8. Similar to Tc and Re, the work functions and surface energies of Os are always larger than the work functions of Ru for the same crystal orientation. However the atomic number of Os is larger than Ru. It's also similar to above four metals, the (0001), ð0111Þ, ð1010Þ surfaces have large work functions and small surface energies, and ð1121Þ, ð1123Þ, ð3140Þ surfaces have small work functions and large surface energies.

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Fig. 8. Surface energy and work function of Ru and Os as a function of surface indices.

4. Discussion From the results of this work, it can be found that the surface energies calculated with LDA approximation tend to be more accurate than the results with GGA approximation, while the work functions calculated with GGA tend to be more accurate than the results with LDA. The work functions and surface energies present obvious differences for different crystal orientations of the same metal. For different metals, these differences of work functions and surface energies are varied. It infers that different crystal orientations of the same metal may present very different physical and chemical properties and the influences of crystal orientations should be seriously considered in some research fields. Looking at these six metals, Be, Mg, Tc, Re, Ru and Os, the (0001), ð0111Þ, ð1010Þ surfaces are relatively stable compared with the other ones. All of them have relatively larger work functions and smaller surface energies. The ð1121Þ, ð11 22Þ,ð1123Þ, andð3140Þ surfaces are relatively unstable compared with the other surfaces, which have small work functions and large surface energies. This information can be very useful, especially in crystallography and catalytic surface science, and may help researchers understanding crystal growth and catalytic processes.

share the similar trend in surface energies across the ten kinds of Miller-index facets. (2) For the work functions of different Miller-index facets, metals in the same group share a roughly reverse regularity as it is found in the surface energies, i.e. (0001) and ð0111Þ surfaces have relatively larger work functions and the surfaces of ð1121Þ, ð1123Þ, and ð3140Þ have quite smaller work functions. (3) Comparison of the results of almost 60 different metal surfaces reveals that the surface energies calculated with LDA approximation are larger than the results with GGA approximation, the differences are about 0.4–1.0 J/m2, on the contrary, the work functions calculated with GGA are larger than the results obtained with LDA, the differences are about 0.3–0.5 eV. (4) With regard to the main group metals, the surface energies and work functions in the same group decrease with the atomic number increase; however, for the same group transition metals, those who have larger atomic numbers don't always have smaller work functions and larger surface energies. Thus, there is not an inevitable relationship for all the metals in a same group between the surface energy and work function with their atomic numbers.

5. Conclusions (1) In terms of the surface energies, there is some regularity for different Miller-index facets of the six hexagonal metals (Be, Mg, Tc, Re, Ru, Os), i.e. the (0001) surface is always the smallest one, ð0111Þ and ð1010Þ surfaces have the intermediate surface energies, while ð1121Þ, ð1122Þ, ð1123Þ, and ð3140Þ surfaces have relatively higher surface energies. For the metals in the same group, they

Acknowledgment This work was funded by the National Basic Research Program of China (973) (No. 2011CB606403) and the National Natural Science Foundation of China (No. 51471164). The computational support from the Informalization Construction Project of Chinese Academy of

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Sciences during the 11th Five-Year Plan Period (No. INFO-115-B01) and Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase) are also highly acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]

H. Lu, G. Hua, D. Li, Appl. Phys. Lett. 103 (2013) 261902. G. Hua, D. Li, Appl. Phys. Lett. 99 (2011) 041907. M.K. Niranjan, U.V. Waghmare, J. Appl. Phys. 112 (2012) 093702. M. Xue, W. Wang, F. Wang, J. Ou, C. Li, W. Li, J. Alloys Compd. 577 (2013) 1. S. Trasatti, J. Electroanal. Chem. 33 (1971) 351 (-&). D.M. Kolb, M. Przasnyski, H. Gerischer, J. Electroanal. Chem. Interfacial Electrochem. 54 (1974) 25. A.V. Ruban, H.L. Skriver, J.K. Nørskov, Phys. Rev. B 59 (1999) 15990. A.U. Nilekar, A.V. Ruban, M. Mavrikakis, Surf. Sci. 603 (2009) 91. J. Erlebacher, J. Electrochem. Soc. 151 (2004) C614. A. Maljusch, J.B. Henry, J. Tymoczko, A.S. Bandarenka, W. Schuhmann, RSC Adv. 4 (2014) 1532. J. Wang, S.-Q. Wang, Surf. Sci. 630 (2014) 216. S. Trasatti, Surf. Sci. 32 (1972) 735. B.E. Conway, J. Liu, S.Y. Qian, J. Electroanal. Chem. 329 (1992) 201. G.N. Luo, K. Yamaguchi, T. Terai, M. Yamawaki, Surf. Sci. 505 (2002) 14. C.M. Horowitz, C.R. Proetto, J.M. Pitarke, Phys. Rev. B 78 (2008) 085126. S.V. Shevkunov, J. Exp. Theor. Phys. 107 (2009) 965. P.S. Bagus, C. Wőll, A. Wieckowski, Surf. Sci. 603 (2009) 273. H.L. Skriver, N.M. Rosengaard, Phys. Rev. B Condens. Matter 46 (1992) 7157. K. Kokko, P.T. Salo, R. Laihia, K. Mansikka, Surf. Sci. 348 (1996) 168. H. Kawano, Prog. Surf. Sci. 83 (2008) 1. A. Kiejna, V.V. Pogosov, Phys. Rev. B 62 (2000) 10445. V.A. Sozaev, R.A. Chernyshova, Tech. Phys. Lett. 29 (2003) 69. J. Wang, S.-q. Wang, Appl. Surf. Sci. 357 (Part A) (2015) 1046. N.E. Singh-Miller, N. Marzari, Phys. Rev. B 80 (2009). T. Jia-Jun, Y. Xiao-Bao, O. LiuZhang, Z. Min, Z. Yu-Jun, J. Phys. D. Appl. Phys. 47 (2014) 115305. L. Vitos, A.V. Ruban, H.L. Skriver, J. Kollár, Surf. Sci. 411 (1998) 186. H. Stanislaw, D. Tomasz, J. Phys. Condens. Matter 10 (1998) 10815. W. Mannstadt, A.J. Freeman, Phys. Rev. B 57 (1998) 13289. S. Tatarenko, M. Alnot, R. Ducros, Surf. Sci. 163 (1985) 249. M. Alnot, V. Gorodetskii, A. Cassuto, J.J. Ehrhardt, Thin Solid Films 151 (1987) 251. X. Zhou, Z.-X. Xie, Z.-Y. Jiang, Q. Kuang, S.-H. Zhang, T. Xu, R.-B. Huang, L.-S. Zheng, Chem. Commun. (2005) 5572.

[32] J. Hu, Z. Chen, N. Wang, Y. Song, H. Jiang, Y. Sun, Chem. Commun. (2009) 4503. [33] L. Zhang, X. Liu, C. Geng, H. Fang, Z. Lian, X. Wang, D. Shen, Q. Yan, Inorg. Chem. 52 (2013) 10167. [34] S. Jiang, Mater. Trans. 55 (2014) 907. [35] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [36] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [37] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953. [38] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [39] http://www.periodictable.com/Properties/A/LatticeConstants.htm. [40] T. Roman, F. Gossenberger, K. Forster-Tonigold, A. Gross, Phys. Chem. Chem. Phys. 16 (2014) 13630. [41] F. Gossenberger, T. Roman, K. Forster-Tonigold, A. Gross, Beilstein J. Nanotechnol. 5 (2014) 152. [42] I.A. Pašti, S.V. Mentus, Electrochim. Acta 55 (2010) 1995. [43] I. Pašti, S. Mentus, J. Alloys Compd. 497 (2010) 38. [44] I. Pašti, S. Mentus, Mater. Chem. Phys. 116 (2009) 94. [45] Z.-B. Ding, F. Wu, Y.-C. Wang, H. Jiang, J. Chem. Phys. 142 (2015) 214706. [46] N.D. Lang, W. Kohn, Phys. Rev. B 3 (1971) 1215. [47] C.J. Fall, N. Binggeli, A. Baldereschi, J. Phys. Condens. Matter 11 (1999) 2689. [48] D. Alfè, M.J. Gillan, J. Phys. Condens. Matter 18 (2006) L435. [49] F. De Boer, R. Boom, W. Mattens, A. Miedema, A.K. Niessen, Cohesion in Metals, Transition Metal Alloys, North-Holland, Amsterdam, 1988. [50] T. Gustafsson, G. Broden, P.O. Nilsson, J. Phys. F: Met. Phys. 4 (1974) 2351. [51] E. Wachowicz, A. Kiejna, J. Phys. Condens. Matter 13 (2001) 10767. [52] A.K. Green, E. Bauer, Surf. Sci. 74 (1978) 676. [53] R. Garron, C. R. Hebd. Seances Acad. Sci. 258 (1964) 1458 (-&). [54] P.J. Feibelman, Phys. Rev. B 46 (1992) 2532. [55] H.B. Michaelson, J. Appl. Phys. 48 (1977) 4729. [56] A.F. Wright, P.J. Feibelman, S.R. Atlas, Surf. Sci. 302 (1994) 215. [57] A. Rose, Solid State Commun. 45 (1983) 859. [58] Y. Dai, J.H. Li, B.X. Liu, J. Phys. Condens. Matter 21 (2009) 385402. [59] E.V. Chulkov, V.M. Silkin, Solid State Commun. 58 (1986) 273. [60] H.W. Hugosson, O. Eriksson, U. Jansson, A.V. Ruban, P. Souvatzis, I.A. Abrikosov, Surf. Sci. 557 (2004) 243. [61] D.R. Bosch, D.L. Jacobson, The high-temperature effective work function of chemically vapor deposited rhenium on a polycrystalline molybdenum substrate, J. Mater. Eng. Perform. 2 (1993) 97. [62] H. Wangyu, Z. Bangwei, H. Baiyun, G. Fei, J.B. David, J. Phys. Condens. Matter 13 (2001) 1193. [63] A. Kashetov, N. Gorbaty, Sov. Phys. Solid State 11 (1969) 389. [64] M. Methfessel, D. Hennig, M. Scheffler, Phys. Rev. B 46 (1992) 4816. [65] R.G. Wilson, J. Appl. Phys. 37 (1966) 3170. [66] W.R. Tyson, W.A. Miller, Surf. Sci. 62 (1977) 267. [67] Y.I. Kostikov, V. Dvoryankin, Russ. J. Phys. Chem. 66 (1992) 277.