oxide interfaces

Available online at www.sciencedirect.com

Computational Materials Science 42 (2008) 426–433 www.elsevier.com/locate/commatsci

Atomistic simulation of misfit dislocation in metal/oxide interfaces Y. Long b

a,*

, N.X. Chen

a,b

a Department of Physics, Tsinghua University, Beijing 100084, China Institute for Applied Physics, University of Science and Technology, Beijing 100083, China

Received 14 May 2007; received in revised form 5 July 2007; accepted 11 August 2007 Available online 1 November 2007

Abstract In this work, we use a Chen–Mo¨bius inversion method to get the interatomic potentials for metal/oxide interfaces, and then study the misfit dislocation in a series of interfaces, including Au/MgO, Rh/MgO and Ni/MgO. The calculation shows that dislocation line always prefers at the first monolayer of metal side, with metal on top of Mg at the dislocation core, and metal on top of O at the interface coherent area. Also, the Burgers vector for these interfaces is determined at two cases. For Rh/MgO and Ni/MgO, it keeps the value of a2 ½1 1 0. But for Au/MgO, it changes from a2 ½1 1 0 to a[1 0 0] as the number of monolayers in metal side increases. This work shows a theoretical understanding of misfit dislocations in metal/oxide interfaces, from dislocation structure, density to Burgers vector orderly, and gives some hints to experiments. Ó 2007 Elsevier B.V. All rights reserved. PACS: 61.72.Lk; 68.35.p Keywords: Misfit dislocation; Metal/oxide interface; Chen–Mo¨bius inversion method

1. Introduction Nowadays, metal/oxide interface has attracted a large amount of theoretical and experimental studies for its important role in technology, such as catalytic converters, field effect transistors and anticorrosion coatings, etc. Among the various theoretical techniques, ab initio method has been widely used on this topic [1–7], with an electronic determination of charge distribution, interfacial distance and adhesive energy, etc. However, it is difficult to study some more complex problems by this method, such as the misfit dislocation, metastable structure and epitaxy. People call for atomistic simulation based on model potentials. In order to get a reasonable potential model for interfaces, many methods have been put forward in the past years, for example, the discrete classical model (DCM) [8–12], the series expansion method [13], and the fitting *

Corresponding author. Fax: +86 010 62772783. E-mail address: [email protected] (Y. Long).

0927-0256/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2007.08.007

method [14–19], etc. They have provided us a basic understanding of the metal/oxide interfaces, including the challenges and difficulties in using model potentials to interface systems. Now, considering their experiences, we use a Chen–Mo¨bius inversion method to study the metal/ oxide interfaces, try to get an improved understanding of this important problem in material science. About the Chen–Mo¨bius inversion method, it provides a concise and general inversion formula, which is used to extract the interatomic potentials from ab initio cohesive or adhesive energies without any prerequisite of their functional forms [20–22]. Besides, it is a pair potential approach for the target system. This seems a very simple approximation for the bulk materials and interfaces, but it is quite practical and usually gives a reasonable description on some complex systems, such as ionic crystals [23], rare earth compounds [24], semiconductors [25] and metal/ oxide interfaces [21,22,26]. In this work, we perform an atomistic simulation of misfit dislocations in Au/MgO, Rh/MgO and Ni/MgO interfaces, as an extension of our previous work on Pd/MgO

Y. Long, N.X. Chen / Computational Materials Science 42 (2008) 426–433

[26], and go deep into the energetic determination of Burgers vector. Note that the three kinds of interfaces are chosen for their remarkable difference on the interfacial adhesive energies (see Fig. 2a), which may give quite different pictures in the dislocation morphologies. Also, the (Au, Rh, Ni)/MgO interfaces have attracted a large amount of experiments, for their epitaxial films on MgO substrate can be obtained by the current techniques. Here we give a brief introduction of the experimental results. For Au/MgO, the works of Pauwels, Wang, and Yulikov et al. show that Au clusters on MgO(0 0 1) surface have a polyhedron shape covered by (1 0 0) and (1 1 1) faces, its interface orientation is Au(0 0 1) MgO(0 0 1) and Au[1 1 0] MgO[1 1 0], accompanied with Au on top of O site [27,28,30,31,29]. And for Rh/MgO, Kato et al.’s work [32] reports a Rh film on MgO(0 0 1) with the orientation relationship of Rh(0 0 1)kMgO(0 0 1) and Rh[1 1 0]kMgO[1 1 0], which is the same with AukMgO. Furthermore, for Ni/ MgO, Barbier and Sao-Joao et al.’s works show the Ni films and particles grow on MgO substrate. They also have an interface orientation of Ni(0 0 1)kMgO(0 0 1) and Ni[1 1 0]kMgO[1 1 0], accompanied with the interfacial dis˚ [33,34]. tance of 1.82 ± 0.02 A The following work consists of five parts. First, the potentials used in this work are introduced in Section 2, including the atom–atom, atom–ion and ion–ion potentials. Next, Section 3 shows the method to construct a misfit dislocation atomically. Note that there are two kinds of interface models used in this work: the two-dimension model and three-dimension model. Third, in Section 4, we proceed the atomistic study for the misfit dislocations in Au/MgO, Rh/MgO and Ni/MgO interfaces. This is the main part of the present work, in which the dislocation structure, density and Burgers vector are energetically determined. Fourth, the dislocation network on a concrete interface is studied in Section 5. It is demonstrated by plotting the distribution of metal–O distance on the interface plane. At last, Section 6 shows the discussion and conclusion. 2. Interatomic potential model For a M/MgO interface system (M = Au, Rh and Ni), there are two kinds of atom–ion interactions across the interface (UM–O and UM–Mg), three kinds of ion–ion interactions inside bulk MgO (UO–O, UMg–Mg and UMg–O), accompanied with the atom–atom interaction UM–M inside metal. All the three types of potentials are obtained by the Chen–Mo¨bius inversion method. First, the atom–ion potentials UM–O and UM–Mg (M = Au, Rh and Ni) are obtained by using an inversion formula for fcc/rocksalt type interface, where the inversion formula is a special concept in the Chen–Mo¨bius method, and has been presented carefully in our previous work [21,26], so without say more here. Table 1 shows the resultant potential parameters, on the functional form of Rahman–Stillinger–Lemberg (RSL2) potential:

427

Table 1 Potential parameters of atom–ion interactions

D0 (eV) ˚) R0 (A y a1 (eV) ˚ 1) b1 (A ˚) c1 (A a2 (eV) ˚ 1) b2 (A ˚ c2 (A) a3 (eV) ˚ 1) b3 (A ˚) c3 (A

U ¼ D0 e

UAu–O

UAu–Mg

URh–O

URh–Mg

UNi–O

UNi–Mg

290.30 1.00 2.61 157.34 3.78 1.16 89.80 2.31 1.31 0.10 2.17 3.93

170.34 1.00 2.36 753.00 2.21 0.07 6.53 4.46 1.71 0.88 3.66 2.46

404.98 1.00 2.18 489.61 2.92 0.90 175.30 1.90 1.18 4.28 1.12 0.79

173.60 1.00 3.06 3.21 1.71 2.72 69.03 4.02 1.28 5.54 1.45 1.70

51.05 1.00 2.12 54.78 2.50 1.63 11.26 3.69 1.85 4.83 3.07 2.25

25.42 1.00 1.84 5.27 1.85 0.60 17.63 1.58 0.67 12.11 3.86 1.08

yð1Rr Þ 0

þ

a1 a2 a3 þ þ b ðrc Þ b ðrc Þ 1 1 2 2 1þe 1þe 1 þ eb3 ðrc3 Þ ð1Þ

Second, the ion–ion potentials UO–O, UMg–Mg and UO–Mg comprise two parts, the short-range and long-range parts (U = USR + UCoul), that the latter is Coulomb interaction. According to the previous work of our group [35], the Coulomb part is determined by an effective charge Qeff of 2e in this case: Coul Coul UCoul Mg-Mg ¼ UO–O ¼ UMg–O ¼

Q2eff 4p0 r

ð2Þ

And for the short-range part, there are two cases, of SR USR Mg–Mg and UO–O in Morse potentials:   ! U ¼ D0 e

r R0 1

y

 2e

2y ðRr 1Þ

ð3Þ

0

and USR Mg–O in ‘‘Exp-Repulsive’’ potential:   U ¼ D0 e

y 1Rr

ð4Þ

0

Table 2 shows the related potential parameters. Third, the atom–atom potentials (UM–M, M = Au, Rh, Ni) are a simple case, that they are just short-range Morse potentials, with the parameters also listed in Table 2. Before the atomistic simulation, we need to check the validity of these pair potentials in studying misfit dislocation. Fur this purpose, we consider the experimental and ab initio results on some basic structure and energy properties of the metal/oxide interfaces. First, for the atom–atom and ion–ion interactions, we study the cell constants and elastic constants of bulk materials, as shown in Table 3. The theoretical values are obtained by the pair potentials, and the experimental valTable 2 Potential parameters of atom–atom and ion–ion interactions

D0 (eV) ˚) R0 (A y

UAu–Au

URh–Rh

UNi–Ni

USR Mg–Mg

USR O–O

USR Mg–O

0.53 3.01 11.71

0.78 2.91 10.29

0.57 2.70 8.92

0.86 2.42 9.96

0.87 2.36 9.45

1.09 2.45 5.98

428

Y. Long, N.X. Chen / Computational Materials Science 42 (2008) 426–433

Table 3 The cell constant (a) and elastic constants (C11, C12 and C44) for Au, Rh, Ni and MgO ˚) a (A C11 (GPa) C12 (GPa) C44 (GPa) Au This work Expt.

4.17 4.08

184.8 192.9

118.4 163.8

118.4 41.5

Rh This work Expt.

3.85 3.80

375.7 413

235.5 194

235.5 184

Ni This work Expt.

3.52 3.52

266.0 248.1

165.2 154.9

165.2 124.2

MgO This work Expt.

4.32 4.22

319.2 294

89.9 93

89.9 155

Here we compare our theoretical results with the experimental values [36].

ues are from Ref. [36]. As a result, we see that the cell constant a and elastic constants C11 and C12 are in agreement with experiments. However, C44 is not so good in this comparison. This is the limitation of our pair potentials due to the Cauchy relation C12 = C44. Fortunately, C11 and C12 play a more important role than C44 in describing the misfit dislocation in metal/MgO(0 0 1) interfaces, for the lattice distortion is limited in tensile strain, without any transformation of the crystal angles. So these pair potentials are credible for this problem. Also, we need to make an effort

to improve the potential model, result in a precise description of the elastic constants. This is our future work. Second, for checking the metal–ion interactions, we need to invoke some results in the latter part of this work, as shown in Fig. 5a. It demonstrates that the dislocation core is of metal on Mg site, and the interface coherent area is of metal on O site, accompanied with metal on hollow site (H site) in the transition part. The three kinds of interface structures are presented in Fig. 1 for an intuitive view. For the validity checking, we use the atom–ion potentials to recalculate their ab initio adhesive energies. The ab initio calculation is performed by the CASTEP code [37,38] with a generalized gradient approximation (GGA). About the parameter setting, the plane-wave cut˚ 1, genoff energy is 340 eV, and k-point spacing is 0.05 A erated by Monkhorst–Pack scheme [39,40]. Fig. 2 shows the resultant adhesive energies for the O site, H site and Mg site structures both by ab initio calculation and pair potentials. We see that the pair potentials can precisely reproduce the ab initio adhesive energies for the structures in dislocation core, transition part and interface coherent area, so they are credible in describing the metal/MgO interface structure. By the way, from Fig. 2 see that the O site structure is the low energy state, and Mg site structure is the high energy state. So the minimum value in the O site energy curve is equal to the adhesive energy of a certain interface, which is used in the following discussion. Fig. 2a shows

Fig. 1. The O site, H site and Mg site structures of metal/MgO interface. (a) The vertical view, (b) the O site structure, (c) the H site structure, (d) the Mg site structure.

Fig. 2. The adhesive energies of O site, H site and Mg site structures. Scatter symbols indicate ab initio results, and lines indicate pair potential results. (a) Adhesive energies for O site structures, (b) for H site structures, (c) for Mg site structures.

Y. Long, N.X. Chen / Computational Materials Science 42 (2008) 426–433

429

that this value is largest for Ni/MgO, middle for Rh/MgO and smallest for Au/MgO. 3. Methodology Usually, a concrete interface is accompanied with misfit dislocation network. In the case of metal/MgO, it is made by a series of mutually perpendicular dislocation lines. Along the dislocation lines, the atomic arrangement remains unchanged except at their intersection points. So a one layer cross-section model is a good representation for studying the dislocation structure, as shown in Fig. 3. This two-dimension (2D) interface model helps us to reduce the computational time significantly. However, for studying the dislocation network, a three-dimension (3D) interface model includes intersected dislocation lines is necessary (see Fig. 4). This 3D model shows more detailed structure properties than 2D model, also, it needs much more computational time. The misfit dislocation is obtained by inserting an extra metal layer into the coherent interface model, as shown in Fig. 3. Its equilibrium structure is achieved by an energy minimization calculation using the Cerius2 software [37]. About the dislocation structure, there are two possible Burgers vectors (B), of a2 ½1 1 0 and a[1 0 0], respectively (a denotes the cell constant). In this work, the Burgers vector is determined by the Miller indices of the extra layer, which is B ¼ a2 ½1 1 0 for (1 1 1) plane and B = a[1 0 0] for (1 0 0) plane. Also, the edge of the extra layer determines the dislocation position (P) in the energy minimized model. For example, in Fig. 3, it is in the first monolayer (ML) of metal side, so P = 1 ML in this case. Further more, misfit dislocation is located at the metal side, for MgO has an ionic lattice, which is more rigid than metals.

Fig. 3. The 2D interface model which contains an extra metal layer.

Fig. 4. The 3D interface model which contains dislocation network. The intersection point of dislocation lines is in the center of this model with metal on Mg site, while the coherent area is in the edge of this model with metal on O site.

By the way, from Fig. 3, we see that the stacking fault appears as the extra metal layer is inserted. Fortunately, it is just in the unrelaxed model, but disappears after the energy minimization calculation, as shown in Fig. 5. So

Fig. 5. The metastable dislocation structures of Au/MgO with B ¼ a2 ½1 1 0. (a) P = 1 ML, (b) P = 2 ML, (c) P = 3 ML, (d) P = 4 ML, (e) P = 5 ML. The P = 1 ML structure is drawn in a wide range for a detailed description, because it is the most stable dislocation structure.

430

Y. Long, N.X. Chen / Computational Materials Science 42 (2008) 426–433

Table 4 The lattice, surface and interface energies of M/MgO interfaces (M = Au, Rh, Ni) e (eV)M

rM (J/m2)

rM/MgO (J/m2)

Au Rh Ni

2.97 5.74 4.79

2.29 4.19 4.67

3.84 4.33 4.60

eMgO rMgO

37.88 eV 1.73 J/m2

we need not consider the stacking fault in the main part of this work, just pay attention to the edge dislocation. In this work, the dislocation structure, density and Burgers vector are obtained by an energy consideration. So it is necessary to get a reasonable expression for the dislocation energy Edis. Note that the total energy of metal/oxide interface contains various contributions not only from dislocation, but also from surface, interface and bulk, respectively. In order to evaluate the contribution of dislocation, we must subtract all the other parts from the total energy: Edis ¼

Etotal  nMgO eMgO  nmetal emetal  ðrMgO þ rmetal S þ rinterface Þ

ð5Þ

where Etotal denotes the total energy, eMgO and emetal denote the lattice energy per atom, rMgO and rmetal denote the unit-area surface energy, rinterface denotes the unit-area interface energy, nMgO and nmetal denote the atom numbers of MgO and metal sides, and S denotes the area of interface plane. These parameters are obtained by the energy minimization calculation of some ideal surface and interface models, as shown in Table 4. In fact, this energy formula has already been used in our previous work for Pd/ MgO interface [26]. 4. Dislocation properties in cross-section

P = 1–5 ML, to see the evolution of dislocation structure when it rises in the metal side. Fig. 5 shows the resultant dislocation structures of Au/ MgO with B ¼ a2 ½1 1 0 as the examples. From the figure, we see that the incoherent area on interface caused by misfit dislocation expands as the parameter P increases, and vacancies appear after P P 2 ML. According to Fig. 2a, the adhesive energy of Au/MgO is much smaller than the ones of Rh/MgO and Ni/MgO. As a result, it brings different pictures of misfit dislocation for these interfaces: the distortion of the first MgO ML caused by dislocation is much larger in Rh/MgO and Ni/MgO than the one in Au/MgO, and the vacancy formed on Au/MgO is bigger than those on Rh/MgO and Ni/MgO. In particular, for Ni/MgO, the energy minimization calculation by assuming B = a[1 0 0] results in a totally mixedup Ni lattice. It means that the B = a[1 0 0] misfit dislocation of Ni/MgO interface can not be obtained in this way. This is why only the case of B ¼ a2 ½1 1 0 is mentioned for Ni/MgO in the following work. And then, we study the dislocation energy Edis for these dislocation structures. The Edis consists of two parts, first is the dislocation core energy, which is positive and independent of the thickness of metal side (Lmetal), and second is the reduction of strain energy, which is negative and proportional to Lmetal. Note that the strain energy is brought by the misfit between MgO and metal lattices. As a result, Edis decreases with Lmetal, with a positive value when Lmetal is small, and a negative value when Lmetal is large, see Fig. 6 of Au/MgO as the example. The calculation shows that the lowest Edis is achieved at P = 1 ML, for all the three (Au, Pd, Rh)/MgO interfaces no matter B ¼ a2 ½1 1 0 or a[1 0 0]. About the lowest energy structure, the dislocation line is in the first ML of metal side, with metal on top of Mg in dislocation core and on top of O in the interface coherent area, see Fig. 5a as an example. This interface coherent area structure is consistent with experiments [29,33].

The misfit dislocations in (Ag, Pd, Cu)/MgO interfaces have been widely studied in experiments [41–44], and the Burgers vector for them is experimentally determined as a ½1 1 0. But for the cases of (Au, Rh, Ni)/MgO, there are 2 no such kinds of experimental values. The atomistic simulation for determining Burgers vector is desired. For the computational details, we use the MINIMIZER module of Cerius2 software [37] for energy minimization calculation. A periodic boundary condition is used to avoid the unexpected boundary effect. About the interface model, the MgO side has 6 MLs. This is because MgO is an ionic crystal, 6 MLs are enough to support the metal film. For the metal side, it is from 1 to 15 MLs, in order to show the evolution of dislocation density and Burgers vector. 4.1. Dislocation position and structure Now, we pay attention to the structures of dislocation line located at the first to fifth ML of metal side, for which

Fig. 6. Edis of a series of dislocation structures for Au/MgO with B ¼ a2 ½1 1 0. The lines are just to guide eyes.

Y. Long, N.X. Chen / Computational Materials Science 42 (2008) 426–433

431

4.2. Determination of Burgers vector When a concrete periodic interface model with arbitrary Burgers vector is established, it must associate with a certain cell length Lcell. This cell length is equal to the number of unit cells between two parallel dislocation lines, for example, in Fig. 3, Lcell = 6. As a result, pffiffi the dislocation 2 density is automatically determined as aLcell for B ¼ a2 ½1 1 0 1 and aLcell for B = a[1 0 0]. Now, let us consider how to get the dislocation density. In principle, we have to go through all the possible cell lengths, for each case the dislocation energy Edis is calculated carefully. The preferable dislocation density corresponds to the minimum dislocation energy min{Edis}. Also, this min{Edis} (or briefly, Edis) is used in determining the Burgers vector. Fig. 7 shows the curves of Edis against the possible dislocation densities of Au/MgO interface with B ¼ a2 ½1 1 0 as an example. Note that there is no minimum point in the Edis curves when Lmetal is less than 5 MLs. So the misfit dislocation appears in Au/MgO only if the thickness of metal side is greater than 5 MLs. The starting Lmetal of dislocation appear in other interfaces are presented in Table 6. Based on the above idea, we study Au/MgO, Rh/MgO and Ni/MgO interfaces one by one in a self-consistent way. The resultant dislocation density with certain Burgers vector is increasing with Lmetal and coming to a saturation value, as shown in Fig. 8. Also, we can get an estimated value of the dislocation density in another way, just by considering the lattice misfit between the metal side and MgO side. For this purpose, the misfit d is derived from the cell constants firstly: d¼2

aMgO  ametal aMgO þ ametal

Fig. 8. Dislocation density against Lmetal of (Au, Rh, Ni)/MgO interfaces. The lines are just to guide eyes. pffiffi 2d d for B ¼ a2 ½1 1 0 and aMgO for B = a[1 0 0] the formula aMgO cases. All these results are listed in Table 5. Comparing Fig. 8 and Table 5, we see that the dislocation densities obtained by energy consideration are lower than the ones derived from lattice misfit. Factually, the latter can be treat as the theoretical boundary of the dislocation density, which is achieved when Lmetal is large enough. As a result, the dislocation density increases with Lmetal, and reaches the value in Table 5 at last.

Table 5 The dislocation densities derived from the lattice misfit d for (Au, Rh, Ni)/ ˚ 1) MgO interfaces (A

ð6Þ

where aMgO and ametal denote the cell constants of MgO and metal sides, respectively, as shown in Table 3. And then, the estimated dislocation density is obtained by using

Fig. 7. The curves of Edis against the possible dislocation densities for Au/ MgO interface with B ¼ a2 ½1 1 0.

Au Rh Ni

d (%)

a 2 ½1 1 0

a[1 0 0]

3.5 11.5 20.4

0.012 0.038 0.067

0.008 0.027 0.047

Fig. 9. Dislocation energies of (Au, Rh, Ni)/MgO interfaces at the preferable dislocation densities, for B ¼ a2 ½1 1 0 and a[1 0 0], respectively. The lines are just to guide eyes.

432

Y. Long, N.X. Chen / Computational Materials Science 42 (2008) 426–433

Table 6 Burgers vector of misfit dislocations in (Au, Rh, Ni)/MgO interfaces Burgers vector

Au/MgO

Rh/MgO

Ni/MgO

No dislocation a 2 ½1 1 0 a[1 0 0]

Lmetal < 5 MLs 5 MLs 6 Lmetal 6 7 MLs Lmetal > 7 MLs

Lmetal < 3 MLs Lmetal P 3 MLs –

Lmetal < 5 MLs Lmetal P 5 MLs –

Finally, the Burgers vector is determined from a2 ½1 1 0 and a[1 0 0] by comparing Edis at the preferable dislocation densities, as shown in Fig. 9. For Au/MgO, when Lmea tal 6 7 MLs, B ¼ 2 ½1 1 0 has the lower Edis, otherwise, it is B = a[1 0 0]. It means that the Burgers vector in Au/MgO changes from a2 ½1 1 0 to a[1 0 0] as Lmetal increases. But for Rh/MgO, Edis of B ¼ a2 ½1 1 0 is always lower than the one of B = a[1 0 0], so the Burgers vector is a2 ½1 1 0 unchanged. However, for Ni/MgO, there is not any stable B = a[1 0 0] dislocation structure, as we have mentioned in the previous subsection. Its Burgers vector only can be a2 ½1 1 0. A summarization of these results is presented in Table 6.

5. Dislocation network In the previous sections, 2D interface models are used for studying dislocation structures, densities, and Burgers vectors, etc. Now, we pay attention to the dislocation network and intersection points of dislocation lines. The 3D model is taken into account. Factually, the investigation of dislocation network is built on the results of previous sections. Here we consider the interface models of Lmetal = 15 MLs and B ¼ a2 ½1 1 0, use the dislocation structure extracted from Fig. 5a, and dislocation density extracted from Fig. 8. In order to demonstrate the dislocation network, we plot the distribution of metal–O distance on the interface plane, as shown in Fig. 10 for Rh/MgO case. Note that at the dislocation core area metal atom is just on top of Mg site, thus the distance between metal and O is larger than the one at the coherent area. In the figure, the deep blue color corresponds to the coherent area, the light blue color corresponds to the dislocation core area, and the red color corresponds the intersection area between dislocation lines. It shows that the metal–O distance reaches minimum on the interface coherent area, becomes large at the dislo-

Table 7 ˚) Interfacial distance for (Au, Rh, Ni)/MgO (A

This work Experiment

Au/MgO

Rh/MgO

Ni/MgO

2.65 2.081 ± 0.033 [27]

2.10 –

1.90 1.82 ± 0.02 [33]

cation lines, and reaches maximum on the intersection points of these lines. And then, we consider the interfacial distance, which is the vertical distance between the last ML of MgO side and first ML of metal side. Obviously, it is equal to the metal–O distance on the interface coherent area. Table 7 presents the resultant interfacial distances for (Au, Rh, Ni)/MgO as well as the available experimental values. It shows that the theoretical results are in fair agreement with experiments. 6. Discussion and conclusion In this work, an ab initio based pair potential model is introduced by the Chen–Mo¨bius inversion method for metal/oxide interface. Based on the potentials, we proceed an atomistic study of misfit dislocations in (Au, Rh, Ni)/ MgO interfaces, resulted in a theoretical understanding of their structure and energy properties. First, the most stable dislocation structures in these interfaces are obtained. Their dislocation lines are located at the first ML of metal side, with metal on top of Mg in the dislocation core, and metal on top of O in the interface coherent area. Also, the interfacial distances are extracted from the equilibrium interface models. They are in agreement with the available experimental values, indicating a possibility for predicting interfacial distance theoretically. Second, the Burgers vector for the misfit dislocation is determined from a2 ½1 1 0 and a[1 0 0] by an energy consideration. For Rh/MgO and Ni/MgO interfaces, it is a2 ½1 1 0. But for Au/MgO interface, it changes from a2 ½1 1 0 to a[1 0 0] as Lmetal increases. However, this is different from the dislocation in bulk material with fcc structure, in which the Burgers vector is a2 ½1 1 0 for the (1 1 1) sliding plane. As a result, this work shows a possibility of Burgers vector being a[1 0 0] for fcc-metal/MgO interface. Acknowledgements

Fig. 10. Distribution of metal–O distance on Rh/MgO interface plane.

This work is supported by the Nature Science Foundation of China (NSFC), No. 50531050 and 973 project,

Y. Long, N.X. Chen / Computational Materials Science 42 (2008) 426–433

No. 2006CB605100. And we also express our thanks to H.Y. Zhao for helpful discussion. References [1] M.W. Finnis, C. Kruse, U. Schonberger, Nanostruct. Mater. 6 (1995) 145. [2] J. Goniakowski, Phys. Rev. B 59 (1999) 11047. [3] K.M. Neyman, C. Inntam, V.A. Nasluzov, R. Kosarev, N. Ro¨sch, Appl. Phys. A 78 (2004) 823. [4] J.R. Smith, T. Hong, D.J. Srolovitz, Phys. Rev. Lett. 72 (1994) 4021. [5] J.A. Snyder, J.E. Jaffe, M. Gutowski, Z.J. Lin, A.C. Hess, J. Chem. Phys. 112 (2000) 3014. [6] L. Giordano, C. Valentin, G. Pacchioni, J. Goniakowski, Chem. Phys. 309 (2005) 41. [7] S.G. Wang, Y.W. Li, H. Jiao, J.X. Liu, M.Y. He, J. Phys. Chem. B 108 (2004) 8359. [8] D.M. Duffy, J.H. Harding, A.M. Stoneham, Acta Metall. Mater. 40 (1992) S11. [9] D.M. Duffy, J.H. Harding, A.M. Stoneham, Philos. Mag. A 67 (1993) 865. [10] M.W. Finnis, Acta Metall. Mater. 40 (1992) S25. [11] J. Purton, S.C. Parker, D.W. Bullett, J. Phys.: Condens. Matter 9 (1997) 5709. [12] J.A. Purton, D.M. Bird, S.C. Parker, D.W. Bullett, J. Chem. Phys. 110 (1999) 8090. [13] Y.G. Yao, Y. Zhang, Phys. Lett. A 256 (1999) 391. [14] A. Endou, K. Teraishi, K.Y.K. Yajima, N. Ohashi, S. Takami, M. Kubo, A. Miyamoto, E. Broclawik, Jpn. J. Appl. Phys. 39 (2000) 4255. [15] W. Vervisch, C. Mottet, J. Goniakowski, Eur. Phys. J. D 24 (2003) 311. [16] S.V. Dmitriev, N. Yoshikawa, Y. Kagawa, M. Kohyama, Surf. Sci. 542 (2003) 45. [17] S. Dmitriev, N. Yoshikawa, Y. Kagawa, Comp. Mater. Sci. 29 (2004) 95. [18] S.V. Dmitriev, N. Yoshikawa, M. Kohyama, S. Tanaka, R. Yang, Y. Kagawa, Acta Mater. 52 (2004) 1959.

433

[19] S.V. Dmitriev, N. Yoshikawa, M. Kohyama, S. Tanaka, R. Yang, Y. Tanaka, Y. Kagawa, Comp. Mater. Sci. 36 (2006) 281. [20] N.X. Chen, Phys. Rev. Lett. 64 (1990) 1193. [21] Y. Long, N.X. Chen, W.Q. Zhang, J. Phys.: Condens. Matter 17 (2005) 2045. [22] Y. Long, N.X. Chen, J. Phys.: Condens. Matter 19 (2007) 196216. [23] S. Zhang, N.X. Chen, Philos. Mag. 83 (2003) 1451. [24] S.Q. Hao, N.X. Chen, J. Shen, Phys. Status Solidi B 234 (2002) 487. [25] J. Cai, X.Y. Hu, N.X. Chen, J. Phys. Chem. Solids 66 (2005) 1256. [26] Y. Long, N.X. Chen, H.Y. Wang, J. Phys.: Condens. Matter 17 (2005) 6149. [27] B. Pauwels, G. Tendeloo, W. Bouwen, L.T. Kuhn, P. Lievens, H. Lei, M. Hou, Phys. Rev. B 62 (2000) 10383. [28] C.M. Wang, V. Shutthanandan, Y. Zhang, S. Thevuthasan, J. Am. Ceram. Soc. 88 (2005) 3184. [29] M. Yulikov, M. Sterrer, M. Heyde, H.-P. Rust, T. Risse, H.-J. Freund, G. Pacchioni, A. Scagnelli, Phys. Rev. Lett. 96 (2006) 146804. [30] J. Xu, J. Moxom, B. Somieski, et al., Phys. Rev. B 64 (2001) 113404. [31] M.A. Huis, A.V. Fedorov, et al., Nucl. Instrum. Methods B 191 (2002) 442. [32] K. Kato, Y. Abe, K. Sasaki, Jpn. J. Appl. Phys. 44 (2005) 7605. [33] A. Barbier, G. Renaud, O. Robach, J. Appl. Phys. 84 (1998) 4259. [34] S. Sao-Joao, S. Giorgio, C. Mottet, J. Goniakowski, C.R. Henry, Surf. Sci. 600 (2006) L86. [35] S. Zhang, Ph.D. thesis, Tsinghua University, 2002. [36] M. Levy, H.E. Bass, R.R. Stern (Eds.), Handbook of Elastic Properties of Solids, Liquids and Gases, vol. 2. [37] A. Inc., Cerius2 Users Guide. [38] V. Milman, B. Winkler, J.A. White, C.J. Pickard, M.C. Payne, E.V. Akhmatskaya, R.H. Nobes, Int. J. Quantum Chem. 77 (2000) 895. [39] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [40] A.H. Macdonald, Phys. Rev. B 18 (1978) 5897. [41] G. Renaud, P. Guenard, A. Barbier, Phys. Rev. B 58 (1998) 7310. [42] G. Renaud, A. Barbier, Appl. Surf. Sci. 142 (1999) 14. [43] P. Lu, F. Cosandey, Acta Metall. Mater. 40 (1992) S259. [44] F.R. Chen, S.K. Chiou, L. Chang, C.S. Hong, Ultramicroscopy 54 (1994) 179.