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The electronic structure and phase diagram of chlorine adsorption on Mg (0 0 0 1) surface
Computational Materials Science 84 (2014) 108–114
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The electronic structure and phase diagram of chlorine adsorption on Mg (0 0 0 1) surface Y.H. Duan a,b,⇑, S.G. Zhou a, Y. Sun a, M.J. Peng a a b
School of Material Science and Engineering, Kunming University of Science and Technology, Kunming 650093, China Key Lab of Advance Materials in Rare & Precious and Nonferrous Metals, Ministry of Education, Kunming 650093, China
a r t i c l e
i n f o
Article history: Received 15 April 2013 Received in revised form 21 November 2013 Accepted 23 November 2013 Available online 25 December 2013 Keywords: First-principles Chlorine Mg (0 0 0 1) surface Adsorption energy Phase diagram
a b s t r a c t First-principles methods are applied to investigate the adsorption energy and electronic structure of p(2 2) configuration of chlorine atoms adsorbed in variety of sites of Mg (0 0 0 1) surface. It is found that the fcc-hollow site is the energetically most favorable for the whole coverage range considered. The adsorption energy decreases with the increasing coverage h. It can be concluded from the charge densities and density of states that the charges transfer between substrate Mg atoms and Cl atoms leads to the appearance of dipole moment. It has been also found from the electronic structure that the repulsion between Cl atoms becomes stronger and the charge distribution is localized getting closer to the Cl atoms with the increasing coverage. The chlorine adatom reduces the surface energy rapidly and leads to form the stable bulk MgCl2 and in the fcc-hollow site adsorption the 1/4 ML Cl–Mg structure is stable while the higher 1/2 ML, 3/4ML and 1/1ML Cl–Mg structures are unstable from the phase diagram of Cl–Mg structures. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Adsorption of chlorine atom on simple metal surfaces is commonly considered as a model for understanding more complicated systems. The investigations of chlorine adsorption on metal surfaces have showed a variety of phenomena. Chlorine adsorption at the fcc hollow site is slightly preferred over that at the hcp hollow for the Cl/Cu (1 1 1) system [1]. For Cl adsorption on Cu (0 0 1) surface, the subsurface adsorption of Cl atoms dramatically increases the stability of the 1 ML and 2 ML adsorption configurations providing a possible pathway for the formation of the bulk-chloride surface phases in the kinetic regime [2]. Chlorine adsorbs at the fcc hollow site on Au (1 1 1) surface with a vertical distance of 1.94 Å and a Cl–Au bond length is 2.56 Å [3]. In our previous investigation on F atom adsorption on Mg (0 0 0 1) surface, it is found that the hollow site is the energetically most favorable [4]. Many surface investigations have been devoted to halogen adsorption on metal (mainly for transition metal) surfaces in the past thirty years [5,6], but only a few adsorption geometries have been determined quantitatively so far [7–9,3], and to our knowledge, no atomistic first-principles calculations for chloride-magnesium system have been performed so far.
⇑ Corresponding author at: School of Material Science and Engineering, Kunming University of Science and Technology, Kunming 650093, China. Tel./fax: +86 871 65136698. E-mail address: [email protected] (Y.H. Duan). 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.11.064
In the present work we present the first-principles density functional calculations on adsorption properties of four different coverages of Cl atoms on p(2 2) Mg (0 0 0 1) surface. Subsequently we have also investigated the most favorable adsorption position, the reconstructed Mg (0 0 0 1) surface and the interaction between Cl atoms and Mg atoms by adsorbed Cl atoms at different coverages.
2. Calculation methods We applied first-principles methods based on the density functional theory, ultrasoft pseudo-potentials, and the plane wave basis set as implemented in the CASTEP code [10]. The exchangecorrelation energy functional was treated in generalized gradient approximation (GGA) using the Perdew–Burke–Ernzerhof functional (PBE) [11]. For Mg unit cell, after convergence tests, k-points and cutoff energy were 11 11 1 and 400.0 eV, respectively. The optimized lattice parameter of Mg is a = 0.3212 nm, c/a = 1.621 which are agreed well with the experimental values (a = 0.321 nm, c/a = 1.624) [12]. Based on the optimized Mg unit cell, the (0 0 0 1) surface of Mg was represented by a slab consisting of seven Mg atomic layers and vacuum region of 1.5 nm after surface energies and stability calculations. After convergence tests, a mesh of 7 7 1 k-points and the maximum cutoff energy of 400.0 eV were applied for Mg (0001) surface unit cell. The calculated relaxations for the three topmost atomic layers are agreed well with the
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three topmost layers experiment [13]. In order to examine the effect of coverage, the surface unit cell of 2 2 symmetry was used. Cl atoms were adsorbed on one side of the slab. Adatoms and atoms of three uppermost Mg atomic layers were allowed relaxed while the other four Mg atomic layers were fixed. We provided four possible adsorption sites for atomic chlorine on p (2 2) Mg (0 0 0 1) surface as shown in Fig. 1. Four different coverages of chlorine atoms corresponding to h = 1/4, 1/2, 3/4 and 1/1 monolayer (ML) occupying a variety of sites: fcc-hollow, hcp-hollow, bridge, and on-top, were considered in search for the most stable configurations. In our calculation, we also examined the effects of spin polarization. The energy of spin-polarized Cl atom is different from that of non-spin polarized Cl atom. However, the effects of spin polarization on the structures and energies of clean and adsorption surfaces are not significant. Therefore, the spin polarization on the surfaces did not consider in the present work. The convergence threshold for the maximum energy change, force and displacement were assigned as 1.0 105 eV/atom, 0.01 eV/Å and 0.001 Å, respectively. The adsorption energies of different on-surface atoms sites are calculated from the following difference of total energies as follow:
Eads ¼
1 ðECl=Mgð0001Þ EMgð0001Þ NCl ECl Þ; NCl
ð1Þ
where Eads is the adsorption energy of Cl atom adsorbed on Mg (0 0 0 1) surface, NCl is the number of adsorbed Cl atom, ECl/Mg(0001) and EMg(0001) are the total energies of the relaxed adsorbate covered Mg (0 0 0 1) slab and a relaxed clean Mg (0 0 0 1) slab, respectively. ECl is the total energy of a free Cl atom. A positive adsorption energy of absorption system corresponds to an exothermic process and more stable than the clean Mg (0 0 0 1) surface, a greater adsorption energy means a stronger adsorption action of chlorine atoms-surface and a more stable adsorption structure. The work function is the important property of the metal surface which changes in the work function (DU) can be well described the charge transfer caused by the adsorption. Based on Helmholtz equation, the relationship between dipole moment lD and DU is [14]:
lD ¼ ð12pÞ1 ADU=h;
ð2Þ
where A is the surface area of the (2 2) Mg (0 0 0 1) with the units of Å2. h is the coverage and h = 1/4 ML, 1/2 ML, 3/4 ML, and 1/1 ML in this work. The effective radius of the adsorbate is calculated as follow:
r ad ¼ dnn r Mg ;
ð3Þ
where dnn is the adsorbate bond length and rMg (1.56 Å) [15] is the metallic radius of bulk Mg. Charge density differences are calculated according to
DqðrÞ ¼ qCl=Mgð0001Þ ðrÞ qMgð0001Þ ðrÞ qCl ðrÞ
ð4Þ
Fig. 1. Adsorption sites of the Mg (0 0 0 1) surface with a 2 2 surface unit cell. The adsorption sites marked by black dots and appear from the left to the right in the following order: hcp-hollow, fcc-hollow, on-top and bridge.
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Fig. 2. Two possible positions named fcc1 and fcc2 in fcc-hollow site on Mg (0 0 0 1) surface.
qCl/Mg(0001)(r) corresponds to the charge density of a Mg (0 0 0 1) slab with Cl atoms adsorbed, whereas qMg(0001)(r) corresponds to the charge density of the Mg slab without Cl atoms. qCl(r) denotes the charge density of Cl atoms in the Cl/Mg (0 0 0 1) slab. Charge density difference plots represent the characterizations of the chemical bond between the Cl adsorbate layer and the uppermost Mg layers. 3. Results and discussion 3.1. Adsorption energy For the coverage of 1/2 ML, there are two possible positions for every adsorption site which are the nearest neighbor position and the farthest position. We take fcc-hollow site as an example in Fig. 2. From Fig. 2, two possible positions are named fcc1 and fcc2 which the distances between the first adsorbed Cl atom and the second adsorbate are 5.591 Å and 3.328 Å, respectively. The adsorption energy of fcc1 is 0.003 eV larger than that of fcc2 and fcc1 is slightly stable than fcc2. Similarly, for Cl atoms adsorption in hcp-hollow, bridge and on-top sites with the coverage of 1/2 ML, the longer distance between two adsorption positions is, the greater adsorption energy is. Therefore, in this work we only consider the adsorption position with a longer distance in the coverage of 1/2 ML. The calculated adsorption energies of Cl atoms in different adsorption sites are shown in Fig. 3. For the coverage of 1/4 ML, as it can be seen from Fig. 3, the two more favored positions for Cl atom adsorption, which are fcc-hollow and hcp-hollow, are equivalent with the adsorption energy of 4.18 eV. It is interesting that the adsorption energies decreases with the Cl coordination number CCl in the order: fcc-hollow (CCl = 3), hcp-hollow (CCl = 3), bridge (CCl = 2), and on-top (CCl = 1). For the hollows-sites adsorption of Cl atom, the Cl atom will interact with three Mg atoms and the adsorption energy is the sum of the interactions of one Cl atom and three Mg atoms. The interaction atom number of Mg is reduced to 2 and 1 when Cl atom adsorbs in bridge and on-top sites, indicating that the adsorption energy decreases due to the reduced interacted atom number. With the coverage increasing, the adsorption energy of Cl atom adsorption in fcc-hollow site possesses the highest while that in the on-top site is the lowest, indicating that Cl atom adsorption in fcc-hollow site is the most favorable and the least favored adsorption position is the on-top site. With the increase of coverage, the numbers of Cl atoms increase from 1 to 4 and the distance of Cl atoms on Mg (0 0 0 1) surface become shorter; thereby the electrostatic energy between the adsorbed Cl atoms increases, resulting in the adsorption energy reduces. Moreover, as for Cl atoms adsorption in bridge and on-top sites, the adsorption energies increase when the coverage increases from 1/4 ML to 1/2 ML and decrease when the coverage increases from 1/2 ML to 1/1 ML, indicating the adsorptions of Cl atoms in these sites are unstable and will move to the most stable adsorption
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Fig. 3. The adsorption energy versus coverage in different adsorption sites for Cl on Mg (0 0 0 1) surface.
position (fcc-hollow). It is similar to Na and K atoms adsorption in Mg (0 0 0 1) surface adsorption which the bridge and on-top sites are unstable adsorption positions for alkali adatoms [16]. Obviously, the larger radius of Cl and less electronegativity compared to F can be attributed to the difference of Mg–Cl and Mg–F bonds. Compared with the adsorption of F [4], the adsorption energies of Cl atom in corresponding adsorption sites with the increasing coverage are smaller than that of F atom, indicating that the interaction between Cl and Mg atoms is weaker than the interaction between F and Mg atoms. It also reveals that the binding between F atom and Mg (0 0 0 1) surface is stronger than Cl atom. It suggests that MgF2 protective film is easier to form than MgCl2 on Mg surface, further conclude that the corrosion velocity of Mg alloy in F-containing solution is smaller than in Cl-containing solution. It is agreement with the corrosion behaviors of Mg–Li alloy [17] and AZ91D magnesium alloy [18] in F, Cl, Br and I halide solutions which the corrosion velocity increases in the order: F < I < Br < Cl. 3.2. Geometric structure The adsorption height zads which is defined as a vertical distance between the adsorbate and the average position of the top Mg atomic layer, decreases followed by the order: hollow, bridge and
on-top structures in the coverage of 1/4 ML from Table 1. The calculated adsorption energy of Cl in fcc-hollow site is similar to hcphollow site, which mean their vertical distances of the adsorbate to the surface (Zad) should be close to each other. The difference in adsorbate heights of Cl atom in fcc and hcp-hollow site is no more than 0.02 Å with the increasing coverage. In the low-coverage of 1/4 ML, both the bond lengths of Cl adsorbed in the fcc-hollow site and hcp-hollow site on Mg (0 0 0 1) surface are 2.59 Å. The bond lengths of H adsorbed in the fcc-hollow site and hcp-hollow site are 2.01 Å and 2.00 Å [19] while those of Na or K atom are 3.17 Å and 3.16 Å or 3.64 Å and 3.64 Å [16], respectively. It is reveals that the interaction of Cl atom and Mg atom is less than that of H atom, but larger than that of Na or K atom. The adsorption height and bond length of Cl atoms adsorption in fcc- and hcp hollows sites decrease with the increasing coverage. As for Cl atoms adsorption in bridge and on-top sites, the trends of adsorption height and bond length with the coverage are similar to the adsorption energies. It also indicates the adsorptions of Cl atoms in bridge and on-top sites will move to the most stable adsorption position. Cl atoms adsorption in the different positions leads to offsets occur in vertical direction of the substrate layer. For Cl adsorption in hollow sites, the distance of uppermost and secondary upper Mg layers (d12) contracts by greatest degree and increases with the coverage due to the larger attraction interaction between Cl and Mg atoms. The degrees of contraction of distances of d23 and d34 are less than that of d12, Dd23 increases while Dd34 decreases with the increase coverage. There is a smallest contraction of d23, which is due to the larger degree of contraction of d12 and d34. For Cl atom adsorption in bridge and on-top sites, due to movement of Cl atoms to the more stable adsorption position with the increasing coverage, the attraction interaction between Cl and Mg atoms becomes larger, causing the difference of d12 to increase dramatically. The binding between Cl and Mg atoms obviously shortens the effective atomic radius. The atomic radius of Cl atom is 1.07 Å [20] while the effective radius of Cl atom is no more than 1.03 Å for Cl adsorption on Mg (0 0 0 1) surface in Table 1. Since a strong ionic bond is formed between Mg atom and Cl atom, the two atoms close to each other under the binding force, resulting in the effective atomic radius of Cl atom decrease. The values of effective radius reported for K/Mg (0 0 0 1) and Na/Mg (0 0 0 1) [16] are bigger than that of Cl/Mg (0 0 0 1) with the coverage of 1/4 ML. This is due to the larger atomic radiuses of K and Na compared to Cl.
Table 1 The adsorption height zads, bond length dnn, effective radius rad, and relative change Ddij = (dij d)/d in the distance between average position of the upper Mg layers at the Mg (0 0 0 1) surface. dij is the distance of between layer i and j after relaxation, d is the distance between the bulk Mg layers, the negative Ddij means a contraction. The positions of layers were calculated as average values of vertical coordinates of Mg atoms in a relaxed layer. Site
h (ML)
Zads (Å)
dnn (Å)
Dd12 (%)
Dd23 (%)
Dd34 (%)
rad (Å)
fcc
1/4 1/2 3/4 1/1
1.76 1.69 1.63 1.58
2.59 2.54 2.49 2.44
1.56 1.75 2.09 2.24
0.90 0.92 1.00 1.07
1.24 1.19 1.14 1.12
1.03 0.98 0.93 0.88
hcp
1/4 1/2 3/4 1/1
1.75 1.67 1.62 1.56
2.59 2.53 2.47 2.43
1.03 1.72 2.07 2.22
0.89 0.92 0.93 1.04
1.23 1.11 1.03 0.80
1.03 0.97 0.91 0.87
Bridge
1/4 1/2 3/4 1/1
1.63 1.68 1.65 1.60
2.42 2.50 2.44 2.38
1.49 1.74 2.02 2.18
0.87 0.90 0.95 1.06
0.98 1.16 1.21 1.26
0.86 0.94 0.88 0.82
Ontop
1/4 1/2 3/4 1/1
1.59 1.67 1.61 1.54
2.39 2.46 2.40 2.33
1.61 1.79 2.04 2.21
1.00 1.04 1.08 1.12
1.05 1.18 1.25 1.30
0.83 0.90 0.84 0.77
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3.3. Work function Fig. 4 shows the work function changes and dipole moment versus coverage in different adsorption sites for Cl on Mg (0 0 0 1) surface. The calculated work function of the clean Mg (0 0 0 1) surface is 3.33 eV which is slightly smaller than the experimental result of 3.66 eV [21]. Generally, the work function calculated by GGA method is slightly smaller than the LDA method and experimental values [22]. With adsorption of Cl atom in the coverage of 1/4 ML, the work functions of adsorption sites considered are larger than 3.33 eV and the dipole moment arises. The reason for the increase of the work function with adsorption of Cl atom is that, when the Cl atom adsorbed in the Mg (0 0 0 1) surface, electrons will transfer from the Mg surface atoms to Cl atom, leading to the Cl adatom has negative charges and Mg (0 0 0 1) surface possesses positive charges, thereby forming a surface dipole moment. Comparing the work function of the clean Mg (0 0 0 1) surface and the Cl–Mg (0 0 0 1) surface, one can be concluded that the increase of work function should be mainly related to the transfer of Mg 3s electrons to the lower levels of Cl 3p though the dipole moment also contributes to the increase of work function. The results of work function in Fig. 4 show that, for the Cl atoms adsorption on Mg (0 0 0 1) surface, the work function changes increase almost linearly with increasing coverage. It is similar to the K/Mg (0 0 0 1) system in fcc- and hcp-hollow sites, which the work function change in fcc-hollow site increases from 1.62 eV to 1.39 eV and that in hcp-hollow site increases from 1.79 eV to 1.71 eV [23]. The work function change is associated with the difference in electronegativity. The differences in electronegativity of Cl–Mg, H–Mg and K–Mg systems are 1.85 eV, 0.89 eV and -0.49 eV, respectively. The greater the difference in electronegativity is, the larger the work function change is. The reported work function changes in fcc-hollow site of H/Mg (0 0 0 1) and K/Mg (0 0 0 1) systems with the coverage of 1/4 ML were 0.027 eV [19] and 1.71 eV [23], respectively. Actually, the present calculated work function change in fcc-hollow site of Cl/Mg (0 0 0 1) system with the coverage of 1/4 ML is 0.19 eV, which is larger that of H/Mg (0 0 0 1) and K/Mg (0 0 0 1) systems. The relationship of dipole moment versus coverage is shown in Fig. 4(b). The dipole moment decreases with the increasing coverage, which is related to the transfer of charges between Mg atom and Cl atom. With the coverage increasing from 1/4 ML to 1/1
111
ML (The numbers of Cl atoms on Mg (0 0 0 1) surface unit cell increase from 1 to 4), it becomes increasingly difficult to transfer electrons between Mg atoms and Cl atoms, resulting in the charges of each Cl atom decreases, thus the dipole moment goes down accordingly and then causes depolarization effect. 3.4. Electronic structures The partial density of states (PDOS) for the clean Mg (0 0 0 1) surface and Cl atoms adsorption in the most favorable site (fcchollow) on Mg (0 0 0 1) surface are shown in Fig. 5(a). For the clean Mg (0 0 0 1) surface, the PDOS is composed of one evident band ranging from 7 eV to Fermi level which is dominated by Mg 3s and 2p orbitals. In case Cl adsorption on Mg (0 0 0 1) surface with the coverage of 1/4 ML, the hybridization arise between Cl 3p orbital and Mg 3s orbital from 6 eV to 4 eV. The Mg 3s orbital is full-filled with electrons while the Cl 3p orbital is unfilled, which lead to electrons transfer from Mg 3s orbital to Cl 3p orbital and final form adsorption bonds. The hybridization between Cl 3p orbital and Mg 3s orbital cause the band of isolated Cl atom broaden, further form bonding state and anti-bonding state from 7 eV to Fermi level, as shown in Fig. 5(b), the difference between the DOS of the clean and the adsorbate-covered surfaces (DN, which DN > 0 means bonding states) mentioned by Todorova et al. [24] clearly reveal the Cl–Mg bonding and anti-bonding states. The bonding state is mostly occupied by electrons, indicating that the interaction between Cl and Mg atoms is stronger and the adsorption energy of Cl adsorption in fcc-hollow is 4.18 eV. With the coverage increasing to 1/2 ML, the peak intensity of bonding state is weakening, revealing that the interaction between Cl and Mg atoms is weaker than that in coverage of 1/4 ML. The adsorption energy of Cl adsorption reduces to 4.15 eV. The adsorption of Cl with the coverages of 3/4 ML and 1/1 ML leads to an obvious change in Fig. 5(b) which the peak intensity of bonding state weakens very evident. It indicates that the repulsion between Cl and Mg atoms becomes strong with the adsorption energies dropped to 4.12 eV and 4.08 eV with the coverages of 3/4 ML and 1/1 ML, respectively. To further analyze the electronic structure of the Cl adsorption on Mg (0 0 0 1) surface (the most favorable fcc-hollow site), the electron charge density Dq(r) of the Cl/ Mg (0 0 0 1) system with the considered coverage (h = 1/4, 1/2, 3/4 and 1/1 ML) are shown in Fig. 6. In Fig. 6 the absorption position is fcc-hollow site. Electron
Fig. 4. Work function changes (a) and dipole moment (b) versus coverage in different adsorption sites for Cl on Mg (0 0 0 1) surface.
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Fig. 5. Partial density of states of the clean Mg (0 0 0 1) surface and Cl adsorption on Mg (0 0 0 1) surface in different adsorption sites (a) and corresponding differences of the DOS (b).
Fig. 6. Charge density difference of Cl atoms adsorption on Mg (0 0 0 1) surface in fcc-hollow site with the coverages of 1/4 ML (a), 1/2 ML (b), 3/4 ML (c), and 1/1 ML (d). Electron excess is drawn in red and electron deficiency in blue. The side views show the planes cut by the white line in the structure overview while the top views show a plane parallel to the surface that passes through the nuclei of the Cl atoms.
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excess is drawn in red and electron deficiency in blue in units of number of electrons per Å3. The electron density difference displays the polarization due to Cl–Mg and Cl–Cl bond formation. The side views show the planes indicated by the white line in the structure overview while the top views show a plane parallel to the surface that passes through the nuclei of the Cl atoms. As can be seen from Fig. 6(a), electron accumulation is observed at the Cl atom and electron depletion at the attached Mg atoms at h = 1/4 ML. The observation is consistent with a charge transfer from the Mg atoms (Mg 3s orbital) towards to the attached Cl atom (Cl 3p orbital). The electrons transfer to the Cl atom leads to an internal polarization due to screening, which is represented by the electron depletion below the Cl atom. This phenomenon of electrons transfer in Cl/Mg (0 0 0 1) system is similar to the Cl/Ru (0 0 0 1) [6]. The three petals in the top view of the electron density difference in Fig. 6(a) represent three equal Mg-Cl bonds. At a coverage of h = 1/2 ML, the charge distribution is localized closer to the Cl atoms compared to 1/4 ML in Fig. 6(b). Due to the larger Cl–Cl separation of 5.59 Å, there is only little lateral repulsion between these two Cl atoms. However, the coverage of 1/2 ML is a little unfavorable compared to 1/4 ML. At h = 3/4 ML in Fig. 6(c), which corresponds to 3 Cl atoms on Mg (0 0 0 1) surface unit cell, the Cl–Cl distance between nearest neighbor is rather small (3.33 Å) which leads to stronger lateral repulsion than 1/2 ML. When the coverage increases to 1/1 ML, the strongest repulsion becomes apparent and the charge distribution is localized very close to the Cl atoms in the top view in Fig. 6(d). It indicates that the coverage of 1/1 ML is very unfavorable in contrast to 1/4 ML and also to the 1/2 ML or 3/4 ML structures. 3.5. Thermodynamic stability of Mg (0 0 0 1) surface The relative stability of the various Cl–Mg phases with varying Cl coverage depends on the chemical potential of chlorine above the surface, as determined by the partial Cl-pressure, P, and temperature, T. The thermodynamically most stable system minimizes the surface free energy, c(T, P), defined as [25,26]
cðT; PÞ ¼
i 1 h slab G ðT; P; NMg ; NCi Þ NMg lMg ðT; PÞ NCl lCl ðT; PÞ ; 2A ð5Þ
where lMg and lCl represent the chemical potentials of Mg and Cl atoms, respectively. NMg and NCl are the numbers of Mg and Cl atoms in the surface, while A is the surface area of the unit cell. The chemical potential of Mg is fixed by the condition that the surface is in equilibrium with bulk Mg crystal. lMg is equal to the cohesive energy of hcp Mg. G(T, P, NMg, NCl) is the Gibbs free energy. An upper limit to the chemical potential is set by the value beyond which the formation of bulk MgCl2 is energetically favored:
1 bulk GMgCl2 Gbulk 6 lCl 6 0; Mg 2
ð6Þ
where Gbulk MgCl2 can be approximated by the cohesive energies of bulk MgCl2 which is 3.66 eV/atom. lMg can be approximated by the cohesive energies of bulk Mg (1.47 eV/atom) which is in good agreement with the calculated 1.43 eV/atom [27] and experimental 1.51 eV/atom [28]. G (T, P, NMg, NCl) is replaced by the total energy of the slab by using a approximation which neglected the vibrational contributions to the enthalpy and entropy [26]. To obtain a stability of the Mg (0 0 0 1) surface in Cl atmosphere, the surface energy calculated for different Cl–Mg structures is plotted against the Cl chemical potential. The considered structures with the coverage are represented by the lines. The structure with the lowest energy at a given chemical potential is most stable at this Cl partial pressure.
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Fig. 7. Surface energy of the Mg (0 0 0 1) surface as a function of chlorine chemical potential for different chlorine coverages. The solid arrows with sold lines indicate the change tendencies of surface configuration (The gray solid arrows with gray sold lines represent the unstable 1/2 ML, 3/4ML, and 1/1ML Cl–Mg structures). The solid arrows with dot lines represent the values of chlorine chemical potential while the Cl–Mg adsorption structures changed. Mg and Cl atoms are drawn as white and black spheres, respectively.
Fig. 7 shows phase diagrams calculated for the most stable adsorption structure (fcc-hollow site). The calculated surface energy of the clean Mg (0 0 0 1) surface in this work is 0.796 J/m2, which agrees well with the results calculated by the FCD (full charge density) method in the GGA (0.792 J/m2) [29] and obtained by experiment (0.785 J/m2) [30]. At a low chemical potential of chlorine, the clean Mg (0 0 0 1) surface is thermodynamically most stable. With increasing concentration of chlorine, the chemical potential lCl increases to 1.42 eV, the 1/4 ML Cl–Mg structure is stabilized. For the Mg (0 0 0 1) surface, already at lCl P 1.10 eV, formation of bulk MgCl2 is energetically favored. Although the surface energy of 1/2 ML, 3/4ML, and 1/1ML covered Mg (0 0 0 1) surface are smaller that of clean surface, these Cl–Mg structures are unstable and 1/1ML covered surface is most unfavorable. With the increase of chlorine chemical potential, the surface energy of the p (2 2)-Cl/Mg phase decreases rapidly, the change tendency of surface energy is clean surface firstly, followed by 1/4 ML, 1/2 ML, 3/4ML, and 1/1ML covered surface at 1.42 eV < lCl < 0 eV. The clean Mg (0 0 0 1) surface is stable only at lCl < 1.42 eV. Although the 1/4 ML Cl–Mg structure at 1.42 eV < lCl < 1.10 eV and 1/2 ML Cl–Mg structure at 1.20 eV < lCl < 1.10 eV are stable, the surface energy of 1/4 ML Cl–Mg adsorption structure is lower than that of 1/2 ML Cl–Mg adsorption structure at 1.20 eV < lCl < 1.10 eV. It indicates that chlorine atom is easily adsorbed on Mg (0 0 0 1) surface to forms a stable 1/4 ML Cl–Mg adsorption structure, and eventually forms the bulk MgCl2 at lCl above 1.10 eV. It can be concluded that the clean surface is stable at a low chlorine chemical potential and becomes unstable at a slightly high chlorine chemical potential which led to chlorine adsorb on the surface. The chlorine adatom reduces the surface energy rapidly and a stable structure, i.e. the bulk MgCl2, is formed. However, we have to emphasize that the limiting values of the chlorine chemical potential, calculated in terms of the bulk cohesive energy, ignore the surface- and interface-energies of the growing chloride. 4. Conclusion In conclusion, we calculated the adsorption of different coverage chlorine on the Mg (0 0 0 1) surface in different adsorption
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sites considered by first-principles. The results for adsorption energy calculations show that the fcc-hollow site is the energetically most favorable for the Cl adatom. It can be concluded from analysis of the charge density and density of states that the charges transfer from the substrate Mg atoms to the Cl atoms leads to the appearance of a dipole moment. With the increasing coverage, the repulsion between Cl atoms becomes stronger and the charge distribution is localized getting closer to the Cl atoms. It indicates that the coverage of 1/1 ML is very unfavorable in contrast to 1/4 ML, 1/2 ML, and 3/4 ML structures. In the basis of chlorine chemical potential results, chlorine atom is easily adsorbed on Mg (0 0 0 1) surface and eventually forms the bulk MgCl2. Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant No. 51201079 and the Scientific Research Fund of Department of Education of Yunnan Province under Grant No. 2012Z099. References [1] K. Doll, N.M. Harrison, Chem. Phys. Lett. 317 (2000) 282. [2] I.A. Suleiman, M.W. Radny, M.J. Gladys, P.V. Smith, J.C. Mackie, E.M. Kennedy, B.Z. Dlugogorski, Phys. Chem. Chem. Phys. 13 (2011) 10306. [3] Z.V. Zheleva, V.R. Dhanak, G. Held, Phys. Chem. Chem. Phys. 12 (2010) 10754. [4] Y.H. Duan, Y. Sun, S.G. Zhou, Comput. Mater. Sci. 72 (2013) 81. [5] O.M. Magnussen, Chem. Rev. 102 (2002) 679.
[6] J.P. Hofmann, S.F. Rohrlack, F. Heß, J.C. Goritzka, P.P.T. Krause, A.P. Seitsonen, W. Moritz, H. Over, Surf. Sci. 606 (2012) 297. [7] G.M. Lamble, R.S. Brooks, S. Ferrer, D.A. King, S. Norman, Phys. Rev. B 34 (1986) 2975. [8] A. Shard, V. Dhanak, A. Santoni, Surf. Sci. 429 (1999) 279. [9] A.G. Shard, C. Ton-That, P.A. Campbell, V.R. Dhank, Phys. Rev. B 70 (2004) 155409. [10] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717. [11] M. Marlo, V. Milman, Phys. Rev. B 62 (2000) 2899. [12] V.M. Amonenko, V.Y. Ivanov, G.F. Tikhinskij, Phys. Met. Metall. 14 (1962) 47. [13] P.T. Sprunger, K. Pohl, H.L. Davis, E.W. Plummer, Surf. Sci. 297 (1993) L48. [14] W.X. Li, C. Stampfl, M. Scheffler, Phys. Rev. B 65 (2002) 075407. [15] G.S. Song, M. Staiger, M. Kral, Mater. Sci. Eng., A 371 (2004) 371. [16] A. Kiejna, T. Ossowski, E. Wachowicz, Surf. Sci. 548 (2004) 22. [17] Y.B. Ma, N. Li, D.Y. Li, M.L. Zhang, X.M. Huang, Corros. Sci. Prot. Technol. 23 (2011) 467. [18] F.E.T. Heakal, A.M. Fekry, M.Z. Fatayerji, Electrochim. Acta 54 (2009) 1545. [19] G.X. Wu, J.Y. Zhang, Y.Q. Wu, Q. Li, J. Liu, K.C. Chou, China J. Nonferr. Met. 17 (2007) 280. [20] J.P. Schaffer, A. Saxena, S.D. Antolovich, T.H. Sanders Jr, S.B. Warner, The Science and Design of Engineering Materials, second ed., McGraw-Hill Companies Inc., USA, 1999. [21] H.B. Michaelson, J. Appl. Phys. 48 (1977) 4719. [22] T.C. Leung, C.L. Kao, W.S. Su, Y.J. Feng, C.T. Chan, Phys. Rev. B 68 (2003) 195408. [23] T. Ossowski, A. Kiejna, Surf. Sci. 566–568 (2004) 983. [24] M. Todorova, K. Reuter, M. Scheffler, J. Phys. Chem. B 108 (2004) 14477. [25] K. Reuter, M. Scheffler, Phys. Rev. B 65 (2002) 35406. [26] P. Blon´ski, A. Kiejna, J. Hafner, Surf. Sci. 590 (2005) 88. [27] H.J. Tao, J. Yin, Z.M. Yin, C.F. Zhang, J. Li, B.Y. Huang, China J. Nonferr. Met. 18 (2008) 2224. [28] W. Köster, H. Franz, Met. Rev. 6 (1961) 1. [29] L. Vitos, A.V. Ruban, H.L. Skriver, J. Kollár, Surf. Sci. 411 (1998) 186. [30] W.R. Tyson, W.A. Miller, Surf. Sci. 62 (1977) 267.
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
The electronic structure and phase diagram of chlorine adsorption on Mg (0 0 0 1) surface Y.H. Duan a,b,⇑, S.G. Zhou a, Y. Sun a, M.J. Peng a a b
School of Material Science and Engineering, Kunming University of Science and Technology, Kunming 650093, China Key Lab of Advance Materials in Rare & Precious and Nonferrous Metals, Ministry of Education, Kunming 650093, China
a r t i c l e
i n f o
Article history: Received 15 April 2013 Received in revised form 21 November 2013 Accepted 23 November 2013 Available online 25 December 2013 Keywords: First-principles Chlorine Mg (0 0 0 1) surface Adsorption energy Phase diagram
a b s t r a c t First-principles methods are applied to investigate the adsorption energy and electronic structure of p(2 2) configuration of chlorine atoms adsorbed in variety of sites of Mg (0 0 0 1) surface. It is found that the fcc-hollow site is the energetically most favorable for the whole coverage range considered. The adsorption energy decreases with the increasing coverage h. It can be concluded from the charge densities and density of states that the charges transfer between substrate Mg atoms and Cl atoms leads to the appearance of dipole moment. It has been also found from the electronic structure that the repulsion between Cl atoms becomes stronger and the charge distribution is localized getting closer to the Cl atoms with the increasing coverage. The chlorine adatom reduces the surface energy rapidly and leads to form the stable bulk MgCl2 and in the fcc-hollow site adsorption the 1/4 ML Cl–Mg structure is stable while the higher 1/2 ML, 3/4ML and 1/1ML Cl–Mg structures are unstable from the phase diagram of Cl–Mg structures. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Adsorption of chlorine atom on simple metal surfaces is commonly considered as a model for understanding more complicated systems. The investigations of chlorine adsorption on metal surfaces have showed a variety of phenomena. Chlorine adsorption at the fcc hollow site is slightly preferred over that at the hcp hollow for the Cl/Cu (1 1 1) system [1]. For Cl adsorption on Cu (0 0 1) surface, the subsurface adsorption of Cl atoms dramatically increases the stability of the 1 ML and 2 ML adsorption configurations providing a possible pathway for the formation of the bulk-chloride surface phases in the kinetic regime [2]. Chlorine adsorbs at the fcc hollow site on Au (1 1 1) surface with a vertical distance of 1.94 Å and a Cl–Au bond length is 2.56 Å [3]. In our previous investigation on F atom adsorption on Mg (0 0 0 1) surface, it is found that the hollow site is the energetically most favorable [4]. Many surface investigations have been devoted to halogen adsorption on metal (mainly for transition metal) surfaces in the past thirty years [5,6], but only a few adsorption geometries have been determined quantitatively so far [7–9,3], and to our knowledge, no atomistic first-principles calculations for chloride-magnesium system have been performed so far.
⇑ Corresponding author at: School of Material Science and Engineering, Kunming University of Science and Technology, Kunming 650093, China. Tel./fax: +86 871 65136698. E-mail address: [email protected] (Y.H. Duan). 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.11.064
In the present work we present the first-principles density functional calculations on adsorption properties of four different coverages of Cl atoms on p(2 2) Mg (0 0 0 1) surface. Subsequently we have also investigated the most favorable adsorption position, the reconstructed Mg (0 0 0 1) surface and the interaction between Cl atoms and Mg atoms by adsorbed Cl atoms at different coverages.
2. Calculation methods We applied first-principles methods based on the density functional theory, ultrasoft pseudo-potentials, and the plane wave basis set as implemented in the CASTEP code [10]. The exchangecorrelation energy functional was treated in generalized gradient approximation (GGA) using the Perdew–Burke–Ernzerhof functional (PBE) [11]. For Mg unit cell, after convergence tests, k-points and cutoff energy were 11 11 1 and 400.0 eV, respectively. The optimized lattice parameter of Mg is a = 0.3212 nm, c/a = 1.621 which are agreed well with the experimental values (a = 0.321 nm, c/a = 1.624) [12]. Based on the optimized Mg unit cell, the (0 0 0 1) surface of Mg was represented by a slab consisting of seven Mg atomic layers and vacuum region of 1.5 nm after surface energies and stability calculations. After convergence tests, a mesh of 7 7 1 k-points and the maximum cutoff energy of 400.0 eV were applied for Mg (0001) surface unit cell. The calculated relaxations for the three topmost atomic layers are agreed well with the
Y.H. Duan et al. / Computational Materials Science 84 (2014) 108–114
three topmost layers experiment [13]. In order to examine the effect of coverage, the surface unit cell of 2 2 symmetry was used. Cl atoms were adsorbed on one side of the slab. Adatoms and atoms of three uppermost Mg atomic layers were allowed relaxed while the other four Mg atomic layers were fixed. We provided four possible adsorption sites for atomic chlorine on p (2 2) Mg (0 0 0 1) surface as shown in Fig. 1. Four different coverages of chlorine atoms corresponding to h = 1/4, 1/2, 3/4 and 1/1 monolayer (ML) occupying a variety of sites: fcc-hollow, hcp-hollow, bridge, and on-top, were considered in search for the most stable configurations. In our calculation, we also examined the effects of spin polarization. The energy of spin-polarized Cl atom is different from that of non-spin polarized Cl atom. However, the effects of spin polarization on the structures and energies of clean and adsorption surfaces are not significant. Therefore, the spin polarization on the surfaces did not consider in the present work. The convergence threshold for the maximum energy change, force and displacement were assigned as 1.0 105 eV/atom, 0.01 eV/Å and 0.001 Å, respectively. The adsorption energies of different on-surface atoms sites are calculated from the following difference of total energies as follow:
Eads ¼
1 ðECl=Mgð0001Þ EMgð0001Þ NCl ECl Þ; NCl
ð1Þ
where Eads is the adsorption energy of Cl atom adsorbed on Mg (0 0 0 1) surface, NCl is the number of adsorbed Cl atom, ECl/Mg(0001) and EMg(0001) are the total energies of the relaxed adsorbate covered Mg (0 0 0 1) slab and a relaxed clean Mg (0 0 0 1) slab, respectively. ECl is the total energy of a free Cl atom. A positive adsorption energy of absorption system corresponds to an exothermic process and more stable than the clean Mg (0 0 0 1) surface, a greater adsorption energy means a stronger adsorption action of chlorine atoms-surface and a more stable adsorption structure. The work function is the important property of the metal surface which changes in the work function (DU) can be well described the charge transfer caused by the adsorption. Based on Helmholtz equation, the relationship between dipole moment lD and DU is [14]:
lD ¼ ð12pÞ1 ADU=h;
ð2Þ
where A is the surface area of the (2 2) Mg (0 0 0 1) with the units of Å2. h is the coverage and h = 1/4 ML, 1/2 ML, 3/4 ML, and 1/1 ML in this work. The effective radius of the adsorbate is calculated as follow:
r ad ¼ dnn r Mg ;
ð3Þ
where dnn is the adsorbate bond length and rMg (1.56 Å) [15] is the metallic radius of bulk Mg. Charge density differences are calculated according to
DqðrÞ ¼ qCl=Mgð0001Þ ðrÞ qMgð0001Þ ðrÞ qCl ðrÞ
ð4Þ
Fig. 1. Adsorption sites of the Mg (0 0 0 1) surface with a 2 2 surface unit cell. The adsorption sites marked by black dots and appear from the left to the right in the following order: hcp-hollow, fcc-hollow, on-top and bridge.
109
Fig. 2. Two possible positions named fcc1 and fcc2 in fcc-hollow site on Mg (0 0 0 1) surface.
qCl/Mg(0001)(r) corresponds to the charge density of a Mg (0 0 0 1) slab with Cl atoms adsorbed, whereas qMg(0001)(r) corresponds to the charge density of the Mg slab without Cl atoms. qCl(r) denotes the charge density of Cl atoms in the Cl/Mg (0 0 0 1) slab. Charge density difference plots represent the characterizations of the chemical bond between the Cl adsorbate layer and the uppermost Mg layers. 3. Results and discussion 3.1. Adsorption energy For the coverage of 1/2 ML, there are two possible positions for every adsorption site which are the nearest neighbor position and the farthest position. We take fcc-hollow site as an example in Fig. 2. From Fig. 2, two possible positions are named fcc1 and fcc2 which the distances between the first adsorbed Cl atom and the second adsorbate are 5.591 Å and 3.328 Å, respectively. The adsorption energy of fcc1 is 0.003 eV larger than that of fcc2 and fcc1 is slightly stable than fcc2. Similarly, for Cl atoms adsorption in hcp-hollow, bridge and on-top sites with the coverage of 1/2 ML, the longer distance between two adsorption positions is, the greater adsorption energy is. Therefore, in this work we only consider the adsorption position with a longer distance in the coverage of 1/2 ML. The calculated adsorption energies of Cl atoms in different adsorption sites are shown in Fig. 3. For the coverage of 1/4 ML, as it can be seen from Fig. 3, the two more favored positions for Cl atom adsorption, which are fcc-hollow and hcp-hollow, are equivalent with the adsorption energy of 4.18 eV. It is interesting that the adsorption energies decreases with the Cl coordination number CCl in the order: fcc-hollow (CCl = 3), hcp-hollow (CCl = 3), bridge (CCl = 2), and on-top (CCl = 1). For the hollows-sites adsorption of Cl atom, the Cl atom will interact with three Mg atoms and the adsorption energy is the sum of the interactions of one Cl atom and three Mg atoms. The interaction atom number of Mg is reduced to 2 and 1 when Cl atom adsorbs in bridge and on-top sites, indicating that the adsorption energy decreases due to the reduced interacted atom number. With the coverage increasing, the adsorption energy of Cl atom adsorption in fcc-hollow site possesses the highest while that in the on-top site is the lowest, indicating that Cl atom adsorption in fcc-hollow site is the most favorable and the least favored adsorption position is the on-top site. With the increase of coverage, the numbers of Cl atoms increase from 1 to 4 and the distance of Cl atoms on Mg (0 0 0 1) surface become shorter; thereby the electrostatic energy between the adsorbed Cl atoms increases, resulting in the adsorption energy reduces. Moreover, as for Cl atoms adsorption in bridge and on-top sites, the adsorption energies increase when the coverage increases from 1/4 ML to 1/2 ML and decrease when the coverage increases from 1/2 ML to 1/1 ML, indicating the adsorptions of Cl atoms in these sites are unstable and will move to the most stable adsorption
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Fig. 3. The adsorption energy versus coverage in different adsorption sites for Cl on Mg (0 0 0 1) surface.
position (fcc-hollow). It is similar to Na and K atoms adsorption in Mg (0 0 0 1) surface adsorption which the bridge and on-top sites are unstable adsorption positions for alkali adatoms [16]. Obviously, the larger radius of Cl and less electronegativity compared to F can be attributed to the difference of Mg–Cl and Mg–F bonds. Compared with the adsorption of F [4], the adsorption energies of Cl atom in corresponding adsorption sites with the increasing coverage are smaller than that of F atom, indicating that the interaction between Cl and Mg atoms is weaker than the interaction between F and Mg atoms. It also reveals that the binding between F atom and Mg (0 0 0 1) surface is stronger than Cl atom. It suggests that MgF2 protective film is easier to form than MgCl2 on Mg surface, further conclude that the corrosion velocity of Mg alloy in F-containing solution is smaller than in Cl-containing solution. It is agreement with the corrosion behaviors of Mg–Li alloy [17] and AZ91D magnesium alloy [18] in F, Cl, Br and I halide solutions which the corrosion velocity increases in the order: F < I < Br < Cl. 3.2. Geometric structure The adsorption height zads which is defined as a vertical distance between the adsorbate and the average position of the top Mg atomic layer, decreases followed by the order: hollow, bridge and
on-top structures in the coverage of 1/4 ML from Table 1. The calculated adsorption energy of Cl in fcc-hollow site is similar to hcphollow site, which mean their vertical distances of the adsorbate to the surface (Zad) should be close to each other. The difference in adsorbate heights of Cl atom in fcc and hcp-hollow site is no more than 0.02 Å with the increasing coverage. In the low-coverage of 1/4 ML, both the bond lengths of Cl adsorbed in the fcc-hollow site and hcp-hollow site on Mg (0 0 0 1) surface are 2.59 Å. The bond lengths of H adsorbed in the fcc-hollow site and hcp-hollow site are 2.01 Å and 2.00 Å [19] while those of Na or K atom are 3.17 Å and 3.16 Å or 3.64 Å and 3.64 Å [16], respectively. It is reveals that the interaction of Cl atom and Mg atom is less than that of H atom, but larger than that of Na or K atom. The adsorption height and bond length of Cl atoms adsorption in fcc- and hcp hollows sites decrease with the increasing coverage. As for Cl atoms adsorption in bridge and on-top sites, the trends of adsorption height and bond length with the coverage are similar to the adsorption energies. It also indicates the adsorptions of Cl atoms in bridge and on-top sites will move to the most stable adsorption position. Cl atoms adsorption in the different positions leads to offsets occur in vertical direction of the substrate layer. For Cl adsorption in hollow sites, the distance of uppermost and secondary upper Mg layers (d12) contracts by greatest degree and increases with the coverage due to the larger attraction interaction between Cl and Mg atoms. The degrees of contraction of distances of d23 and d34 are less than that of d12, Dd23 increases while Dd34 decreases with the increase coverage. There is a smallest contraction of d23, which is due to the larger degree of contraction of d12 and d34. For Cl atom adsorption in bridge and on-top sites, due to movement of Cl atoms to the more stable adsorption position with the increasing coverage, the attraction interaction between Cl and Mg atoms becomes larger, causing the difference of d12 to increase dramatically. The binding between Cl and Mg atoms obviously shortens the effective atomic radius. The atomic radius of Cl atom is 1.07 Å [20] while the effective radius of Cl atom is no more than 1.03 Å for Cl adsorption on Mg (0 0 0 1) surface in Table 1. Since a strong ionic bond is formed between Mg atom and Cl atom, the two atoms close to each other under the binding force, resulting in the effective atomic radius of Cl atom decrease. The values of effective radius reported for K/Mg (0 0 0 1) and Na/Mg (0 0 0 1) [16] are bigger than that of Cl/Mg (0 0 0 1) with the coverage of 1/4 ML. This is due to the larger atomic radiuses of K and Na compared to Cl.
Table 1 The adsorption height zads, bond length dnn, effective radius rad, and relative change Ddij = (dij d)/d in the distance between average position of the upper Mg layers at the Mg (0 0 0 1) surface. dij is the distance of between layer i and j after relaxation, d is the distance between the bulk Mg layers, the negative Ddij means a contraction. The positions of layers were calculated as average values of vertical coordinates of Mg atoms in a relaxed layer. Site
h (ML)
Zads (Å)
dnn (Å)
Dd12 (%)
Dd23 (%)
Dd34 (%)
rad (Å)
fcc
1/4 1/2 3/4 1/1
1.76 1.69 1.63 1.58
2.59 2.54 2.49 2.44
1.56 1.75 2.09 2.24
0.90 0.92 1.00 1.07
1.24 1.19 1.14 1.12
1.03 0.98 0.93 0.88
hcp
1/4 1/2 3/4 1/1
1.75 1.67 1.62 1.56
2.59 2.53 2.47 2.43
1.03 1.72 2.07 2.22
0.89 0.92 0.93 1.04
1.23 1.11 1.03 0.80
1.03 0.97 0.91 0.87
Bridge
1/4 1/2 3/4 1/1
1.63 1.68 1.65 1.60
2.42 2.50 2.44 2.38
1.49 1.74 2.02 2.18
0.87 0.90 0.95 1.06
0.98 1.16 1.21 1.26
0.86 0.94 0.88 0.82
Ontop
1/4 1/2 3/4 1/1
1.59 1.67 1.61 1.54
2.39 2.46 2.40 2.33
1.61 1.79 2.04 2.21
1.00 1.04 1.08 1.12
1.05 1.18 1.25 1.30
0.83 0.90 0.84 0.77
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3.3. Work function Fig. 4 shows the work function changes and dipole moment versus coverage in different adsorption sites for Cl on Mg (0 0 0 1) surface. The calculated work function of the clean Mg (0 0 0 1) surface is 3.33 eV which is slightly smaller than the experimental result of 3.66 eV [21]. Generally, the work function calculated by GGA method is slightly smaller than the LDA method and experimental values [22]. With adsorption of Cl atom in the coverage of 1/4 ML, the work functions of adsorption sites considered are larger than 3.33 eV and the dipole moment arises. The reason for the increase of the work function with adsorption of Cl atom is that, when the Cl atom adsorbed in the Mg (0 0 0 1) surface, electrons will transfer from the Mg surface atoms to Cl atom, leading to the Cl adatom has negative charges and Mg (0 0 0 1) surface possesses positive charges, thereby forming a surface dipole moment. Comparing the work function of the clean Mg (0 0 0 1) surface and the Cl–Mg (0 0 0 1) surface, one can be concluded that the increase of work function should be mainly related to the transfer of Mg 3s electrons to the lower levels of Cl 3p though the dipole moment also contributes to the increase of work function. The results of work function in Fig. 4 show that, for the Cl atoms adsorption on Mg (0 0 0 1) surface, the work function changes increase almost linearly with increasing coverage. It is similar to the K/Mg (0 0 0 1) system in fcc- and hcp-hollow sites, which the work function change in fcc-hollow site increases from 1.62 eV to 1.39 eV and that in hcp-hollow site increases from 1.79 eV to 1.71 eV [23]. The work function change is associated with the difference in electronegativity. The differences in electronegativity of Cl–Mg, H–Mg and K–Mg systems are 1.85 eV, 0.89 eV and -0.49 eV, respectively. The greater the difference in electronegativity is, the larger the work function change is. The reported work function changes in fcc-hollow site of H/Mg (0 0 0 1) and K/Mg (0 0 0 1) systems with the coverage of 1/4 ML were 0.027 eV [19] and 1.71 eV [23], respectively. Actually, the present calculated work function change in fcc-hollow site of Cl/Mg (0 0 0 1) system with the coverage of 1/4 ML is 0.19 eV, which is larger that of H/Mg (0 0 0 1) and K/Mg (0 0 0 1) systems. The relationship of dipole moment versus coverage is shown in Fig. 4(b). The dipole moment decreases with the increasing coverage, which is related to the transfer of charges between Mg atom and Cl atom. With the coverage increasing from 1/4 ML to 1/1
111
ML (The numbers of Cl atoms on Mg (0 0 0 1) surface unit cell increase from 1 to 4), it becomes increasingly difficult to transfer electrons between Mg atoms and Cl atoms, resulting in the charges of each Cl atom decreases, thus the dipole moment goes down accordingly and then causes depolarization effect. 3.4. Electronic structures The partial density of states (PDOS) for the clean Mg (0 0 0 1) surface and Cl atoms adsorption in the most favorable site (fcchollow) on Mg (0 0 0 1) surface are shown in Fig. 5(a). For the clean Mg (0 0 0 1) surface, the PDOS is composed of one evident band ranging from 7 eV to Fermi level which is dominated by Mg 3s and 2p orbitals. In case Cl adsorption on Mg (0 0 0 1) surface with the coverage of 1/4 ML, the hybridization arise between Cl 3p orbital and Mg 3s orbital from 6 eV to 4 eV. The Mg 3s orbital is full-filled with electrons while the Cl 3p orbital is unfilled, which lead to electrons transfer from Mg 3s orbital to Cl 3p orbital and final form adsorption bonds. The hybridization between Cl 3p orbital and Mg 3s orbital cause the band of isolated Cl atom broaden, further form bonding state and anti-bonding state from 7 eV to Fermi level, as shown in Fig. 5(b), the difference between the DOS of the clean and the adsorbate-covered surfaces (DN, which DN > 0 means bonding states) mentioned by Todorova et al. [24] clearly reveal the Cl–Mg bonding and anti-bonding states. The bonding state is mostly occupied by electrons, indicating that the interaction between Cl and Mg atoms is stronger and the adsorption energy of Cl adsorption in fcc-hollow is 4.18 eV. With the coverage increasing to 1/2 ML, the peak intensity of bonding state is weakening, revealing that the interaction between Cl and Mg atoms is weaker than that in coverage of 1/4 ML. The adsorption energy of Cl adsorption reduces to 4.15 eV. The adsorption of Cl with the coverages of 3/4 ML and 1/1 ML leads to an obvious change in Fig. 5(b) which the peak intensity of bonding state weakens very evident. It indicates that the repulsion between Cl and Mg atoms becomes strong with the adsorption energies dropped to 4.12 eV and 4.08 eV with the coverages of 3/4 ML and 1/1 ML, respectively. To further analyze the electronic structure of the Cl adsorption on Mg (0 0 0 1) surface (the most favorable fcc-hollow site), the electron charge density Dq(r) of the Cl/ Mg (0 0 0 1) system with the considered coverage (h = 1/4, 1/2, 3/4 and 1/1 ML) are shown in Fig. 6. In Fig. 6 the absorption position is fcc-hollow site. Electron
Fig. 4. Work function changes (a) and dipole moment (b) versus coverage in different adsorption sites for Cl on Mg (0 0 0 1) surface.
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Fig. 5. Partial density of states of the clean Mg (0 0 0 1) surface and Cl adsorption on Mg (0 0 0 1) surface in different adsorption sites (a) and corresponding differences of the DOS (b).
Fig. 6. Charge density difference of Cl atoms adsorption on Mg (0 0 0 1) surface in fcc-hollow site with the coverages of 1/4 ML (a), 1/2 ML (b), 3/4 ML (c), and 1/1 ML (d). Electron excess is drawn in red and electron deficiency in blue. The side views show the planes cut by the white line in the structure overview while the top views show a plane parallel to the surface that passes through the nuclei of the Cl atoms.
Y.H. Duan et al. / Computational Materials Science 84 (2014) 108–114
excess is drawn in red and electron deficiency in blue in units of number of electrons per Å3. The electron density difference displays the polarization due to Cl–Mg and Cl–Cl bond formation. The side views show the planes indicated by the white line in the structure overview while the top views show a plane parallel to the surface that passes through the nuclei of the Cl atoms. As can be seen from Fig. 6(a), electron accumulation is observed at the Cl atom and electron depletion at the attached Mg atoms at h = 1/4 ML. The observation is consistent with a charge transfer from the Mg atoms (Mg 3s orbital) towards to the attached Cl atom (Cl 3p orbital). The electrons transfer to the Cl atom leads to an internal polarization due to screening, which is represented by the electron depletion below the Cl atom. This phenomenon of electrons transfer in Cl/Mg (0 0 0 1) system is similar to the Cl/Ru (0 0 0 1) [6]. The three petals in the top view of the electron density difference in Fig. 6(a) represent three equal Mg-Cl bonds. At a coverage of h = 1/2 ML, the charge distribution is localized closer to the Cl atoms compared to 1/4 ML in Fig. 6(b). Due to the larger Cl–Cl separation of 5.59 Å, there is only little lateral repulsion between these two Cl atoms. However, the coverage of 1/2 ML is a little unfavorable compared to 1/4 ML. At h = 3/4 ML in Fig. 6(c), which corresponds to 3 Cl atoms on Mg (0 0 0 1) surface unit cell, the Cl–Cl distance between nearest neighbor is rather small (3.33 Å) which leads to stronger lateral repulsion than 1/2 ML. When the coverage increases to 1/1 ML, the strongest repulsion becomes apparent and the charge distribution is localized very close to the Cl atoms in the top view in Fig. 6(d). It indicates that the coverage of 1/1 ML is very unfavorable in contrast to 1/4 ML and also to the 1/2 ML or 3/4 ML structures. 3.5. Thermodynamic stability of Mg (0 0 0 1) surface The relative stability of the various Cl–Mg phases with varying Cl coverage depends on the chemical potential of chlorine above the surface, as determined by the partial Cl-pressure, P, and temperature, T. The thermodynamically most stable system minimizes the surface free energy, c(T, P), defined as [25,26]
cðT; PÞ ¼
i 1 h slab G ðT; P; NMg ; NCi Þ NMg lMg ðT; PÞ NCl lCl ðT; PÞ ; 2A ð5Þ
where lMg and lCl represent the chemical potentials of Mg and Cl atoms, respectively. NMg and NCl are the numbers of Mg and Cl atoms in the surface, while A is the surface area of the unit cell. The chemical potential of Mg is fixed by the condition that the surface is in equilibrium with bulk Mg crystal. lMg is equal to the cohesive energy of hcp Mg. G(T, P, NMg, NCl) is the Gibbs free energy. An upper limit to the chemical potential is set by the value beyond which the formation of bulk MgCl2 is energetically favored:
1 bulk GMgCl2 Gbulk 6 lCl 6 0; Mg 2
ð6Þ
where Gbulk MgCl2 can be approximated by the cohesive energies of bulk MgCl2 which is 3.66 eV/atom. lMg can be approximated by the cohesive energies of bulk Mg (1.47 eV/atom) which is in good agreement with the calculated 1.43 eV/atom [27] and experimental 1.51 eV/atom [28]. G (T, P, NMg, NCl) is replaced by the total energy of the slab by using a approximation which neglected the vibrational contributions to the enthalpy and entropy [26]. To obtain a stability of the Mg (0 0 0 1) surface in Cl atmosphere, the surface energy calculated for different Cl–Mg structures is plotted against the Cl chemical potential. The considered structures with the coverage are represented by the lines. The structure with the lowest energy at a given chemical potential is most stable at this Cl partial pressure.
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Fig. 7. Surface energy of the Mg (0 0 0 1) surface as a function of chlorine chemical potential for different chlorine coverages. The solid arrows with sold lines indicate the change tendencies of surface configuration (The gray solid arrows with gray sold lines represent the unstable 1/2 ML, 3/4ML, and 1/1ML Cl–Mg structures). The solid arrows with dot lines represent the values of chlorine chemical potential while the Cl–Mg adsorption structures changed. Mg and Cl atoms are drawn as white and black spheres, respectively.
Fig. 7 shows phase diagrams calculated for the most stable adsorption structure (fcc-hollow site). The calculated surface energy of the clean Mg (0 0 0 1) surface in this work is 0.796 J/m2, which agrees well with the results calculated by the FCD (full charge density) method in the GGA (0.792 J/m2) [29] and obtained by experiment (0.785 J/m2) [30]. At a low chemical potential of chlorine, the clean Mg (0 0 0 1) surface is thermodynamically most stable. With increasing concentration of chlorine, the chemical potential lCl increases to 1.42 eV, the 1/4 ML Cl–Mg structure is stabilized. For the Mg (0 0 0 1) surface, already at lCl P 1.10 eV, formation of bulk MgCl2 is energetically favored. Although the surface energy of 1/2 ML, 3/4ML, and 1/1ML covered Mg (0 0 0 1) surface are smaller that of clean surface, these Cl–Mg structures are unstable and 1/1ML covered surface is most unfavorable. With the increase of chlorine chemical potential, the surface energy of the p (2 2)-Cl/Mg phase decreases rapidly, the change tendency of surface energy is clean surface firstly, followed by 1/4 ML, 1/2 ML, 3/4ML, and 1/1ML covered surface at 1.42 eV < lCl < 0 eV. The clean Mg (0 0 0 1) surface is stable only at lCl < 1.42 eV. Although the 1/4 ML Cl–Mg structure at 1.42 eV < lCl < 1.10 eV and 1/2 ML Cl–Mg structure at 1.20 eV < lCl < 1.10 eV are stable, the surface energy of 1/4 ML Cl–Mg adsorption structure is lower than that of 1/2 ML Cl–Mg adsorption structure at 1.20 eV < lCl < 1.10 eV. It indicates that chlorine atom is easily adsorbed on Mg (0 0 0 1) surface to forms a stable 1/4 ML Cl–Mg adsorption structure, and eventually forms the bulk MgCl2 at lCl above 1.10 eV. It can be concluded that the clean surface is stable at a low chlorine chemical potential and becomes unstable at a slightly high chlorine chemical potential which led to chlorine adsorb on the surface. The chlorine adatom reduces the surface energy rapidly and a stable structure, i.e. the bulk MgCl2, is formed. However, we have to emphasize that the limiting values of the chlorine chemical potential, calculated in terms of the bulk cohesive energy, ignore the surface- and interface-energies of the growing chloride. 4. Conclusion In conclusion, we calculated the adsorption of different coverage chlorine on the Mg (0 0 0 1) surface in different adsorption
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sites considered by first-principles. The results for adsorption energy calculations show that the fcc-hollow site is the energetically most favorable for the Cl adatom. It can be concluded from analysis of the charge density and density of states that the charges transfer from the substrate Mg atoms to the Cl atoms leads to the appearance of a dipole moment. With the increasing coverage, the repulsion between Cl atoms becomes stronger and the charge distribution is localized getting closer to the Cl atoms. It indicates that the coverage of 1/1 ML is very unfavorable in contrast to 1/4 ML, 1/2 ML, and 3/4 ML structures. In the basis of chlorine chemical potential results, chlorine atom is easily adsorbed on Mg (0 0 0 1) surface and eventually forms the bulk MgCl2. Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant No. 51201079 and the Scientific Research Fund of Department of Education of Yunnan Province under Grant No. 2012Z099. References [1] K. Doll, N.M. Harrison, Chem. Phys. Lett. 317 (2000) 282. [2] I.A. Suleiman, M.W. Radny, M.J. Gladys, P.V. Smith, J.C. Mackie, E.M. Kennedy, B.Z. Dlugogorski, Phys. Chem. Chem. Phys. 13 (2011) 10306. [3] Z.V. Zheleva, V.R. Dhanak, G. Held, Phys. Chem. Chem. Phys. 12 (2010) 10754. [4] Y.H. Duan, Y. Sun, S.G. Zhou, Comput. Mater. Sci. 72 (2013) 81. [5] O.M. Magnussen, Chem. Rev. 102 (2002) 679.
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