Ab initio calculations of the CaTiO3 (111) polar surfaces

Solid State Communications 149 (2009) 1871–1876

Contents lists available at ScienceDirect

Solid State Communications journal homepage: www.elsevier.com/locate/ssc

Ab initio calculations of the CaTiO3 (111) polar surfaces Wei Liu a , Chuncheng Wang a , Jie Cui b,∗ , Zhen-Yong Man c a

Energy Engineering Department, Yulin University, Yulin 719000, Shaanxi, PR China

b

School of Materials Science and Engineering, Xi’an University of Technology, Xi’an 710048, Shaanxi, PR China

c

State Key Laboratory of High Performance Ceramics and Superfine Microstructures, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, PR China

article

info

Article history: Received 17 March 2009 Received in revised form 4 August 2009 Accepted 5 August 2009 by P. Sheng Available online 8 August 2009 PACS: 31.15.Ar 68.35.Bs 68.35.Md 73.20.At

abstract The stoichiometric terminations and nonstoichiometric terminations have been constructed for CaTiO3 (111) surface. The cleavage and surface energies, surface grand potential and surface electronic structure have been calculated for the two main classes of terminations using ab initio plane wave ultrasoft pseudopotential method based on Local Density Approximation (LDA). The results show that the stoichiometric terminations are unstable compared with the nonstoichiometric terminations and the polarity compensation achieved through the modification of the surface stoichiometry is more effective than that by the anomalous filling of the surface states. In the O and Ca chemical environments, only CaO2 and TiO terminations can be formed; the CaO3 and Ti terminations cannot be stabilized, even in very O-rich chemical environment. © 2009 Elsevier Ltd. All rights reserved.

Keywords: D. Surface energy D. Surface grand potential D. Surface electronic structure E. Ab initio

1. Introduction ABO3 perovskite ferroelectric films have been used extensively in various technological fields, such as high-capacity memory cells, catalysis, optical waveguides, integrated optics applications, highTc cuprate superconductor growth [1–10]. Compared with the bulk, the thin films have relatively larger surface and interface. Therefore, investigating how the physical properties are affected by the surface or interface is of primary importance. Recently, several ab initio theoretical studies were published for the surfaces of BaTiO3 and SrTiO3 crystals with fairly good agreement with experimental observations [11–16]. Cubic CaTiO3 is widely used in electronic ceramic materials; it is also a key component of Synroc, a synthetic rock form used to immobilize nuclear waste [17]. For the wide applications in cubic phase, we only focus on the cubic CaTiO3 in the present work. The critical transition temperature from the cubic to low temperature phase is 1580 K for CaTiO3 , which is much higher than that for SrTiO3 and BaTiO3 (105 K and 393 K, respectively), resulting in a different dielectricity and phase stability.

∗

Corresponding author. Tel.: +86 29 82312557. E-mail address: [email protected] (J. Cui).

0038-1098/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2009.08.006

In this paper, to make the calculations computationally feasible, we do not explicitly include octahedral rotations in the surface calculations. A similar approximation has been made in earlier studies of ATiO3 perovskites [18], including an earlier DFT study on CaTiO3 (110) surface [19]. For the CaTiO3 (110) nonstoichiometric surfaces, the Ca termination is stable in Oand Ca-rich environments, however, its complementary TiO termination is stable in O- and Ca-poor conditions. The A-type O termination shows a stability domain in moderate O and Ca environments [18]. The surfaces of BaTiO3 and SrTiO3 have been studied extensively by means of low-energy electron-diffraction, reflection highenergy electron-diffraction, medium energy ion scattering, and surface x-ray diffraction measurements. To our knowledge, there are no experimental studies of the CaTiO3 surfaces. Moreover, only the (100) and (110) surfaces of CaTiO3 have been studied from theoretical views [19,18], the (111) terminations are much less known, which is likely due to the polar character of the (111) orientation and the more complicated structures compared with (110) surfaces. In CaTiO3 , the (111) repeat units contain alternating CaO3 and Ti layers, which are undoubtedly charged. If we consider that the ionic charge of O, Ti, and Ca are QO = −2, QTi = +4, and QCa = +2, respectively. Then the CaO3 plane bears a formal charge QCaO3 = −4 and the Ti plane QTi = +4 per two-dimensional unit

1872

W. Liu et al. / Solid State Communications 149 (2009) 1871–1876

of surface states is expected. On the other side, we study the (111)-CaO2 , -TiO terminations, for which the surface structure changes can, in principle, provide the polarity compensation. The nonstoichiometric terminations can be obtained by removing O atoms from CaO3 -terminated surface and add O atoms onto the Titerminated surface, respectively. The periodic boundary condition is used in the repeated slab model calculations. For considered two classes of (111) terminations, the slabs with thirteen atoms’ layer thickness are separated by a 15 Å vacuum region. Tests are performed to see if this vacuum region is adequate and the result shows that this vacuum region is enough for the CaTiO3 (111) surface relaxation calculations. During the surface structure optimization, atoms in all layers are allowed to relax. Fig. 1. Two terminations of the (111) surface: CaO3 and Ti.

cell. The sequence of atomic layers of CaO3 and Ti implies a microscopic electric field, which has to be compensated through either a modification of the surface composition or an anomalous filling of the surface electronic states. According to the criterion for polarity compensation [20], the formal surface charges of the various CaTiO3 (111) surfaces have to be equal to half the bulk value, i.e., Qsurf = ±2. This paper is organized as follows. Some details of the calculation method and the structure of two main classes of (111)terminated surfaces are given in Section 2. The calculated cleavage and surface energies, surface relaxation, surface bond population, surface grand potential and surface electronic structure of CaTiO3 (111) surfaces are given in Section 3. The conclusions of this work are summarized in Section 4. 2. Method All calculations were performed within the framework of density functional theory (DFT) using a basis set consisting of plane waves, as implemented in the CASTEP (Cambridge Serial Total Energy Package) [21]. The electron–ion interactions were described by ultrasoft pseudopotentials and electron exchange and correlation energies were calculated with the CA-PZ formulation of the local density approximation (LDA) [22]. The structure was optimized with the BFGS method [23], and the forces on each ion were converged to less than 0.01 eV/Å. The pseudopotentials used for bulk and slab were constructed by the electron configurations as Ca 3s2 3p6 4s2 states, Ti 3s2 3p6 3d2 4s2 states, and O 2s2 2p4 states. The kinetic energy cutoff (400 eV) of the plane wave basis was used throughout and the Brillouin zone was sampled with special k-points of a 8 × 8 × 8 grid for cubic structure and a 6 × 6 × 1 grid for slab structure respectively, as proposed by Monkhorst and Pack [24]. The convergence with respect to the cutoff energy and the k-points mesh has been tested and the results show that the cutoff energy and the k-points mesh used in this work are enough for the system. The energy tolerance was 5.0 × 10−6 eV/atom, the force tolerance was 0.01 eV/Å, and the displacement tolerance was 5.0 × 10−4 Å. The calculated values were obtained at 0 K. Before the surface calculations, the bulk lattice constant a is calculated firstly and the result of 3.808 Å is slightly smaller than the experimental value of 3.895 Å [25]. The theoretical lattice constant is used in the following surface calculations. Different from the (001) surface which consists of two types of neutral terminations (CaO and TiO2 ), the CaTiO3 (111) surface (displayed in Fig. 1) consists of two charged planes (CaO3 and Ti). In this paper, we consider two main classes of (111) terminations: on one side, called stoichiometric terminations, namely the (111)-CaO3 and Ti ones, for which an anomalous filling

3. Results and discussions 3.1. Cleavage and surface energies It is noted that CaO3 - and Ti-terminated surfaces are complementary mutually, and so are the CaO2 - and TiO-terminated surfaces. The cleavage energy of the complementary surface Ecl (α)(α = CaO3 + Ti or CaO2 + TiO) can be obtained from the total energies computed for the unrelaxed slabs through the following equation:

 1  unrel unrel Eslab (CaO3 ) + Eslab (Ti) − nEbulk , 4  1  unrel unrel Ecl (CaO2 + TiO) = Eslab (CaO2 ) + Eslab (TiO) − nEbulk , 4 Ecl (CaO3 + Ti) =

(1)

unrel where Eslab (α) is the total energy of unrelaxed α -terminated slab, Ebulk is the bulk energy per formula unit in the cubic structure, n is the total number of bulk formula units in the two slabs, and 1/4 means that totally four surfaces are created upon the crystal cleavage. When both sides of the slab are allowed to relax, the relaxation energies for each of the surfaces can be obtained by equation:

Erel (α) =

 1  rel unrel Eslab (α) − Eslab (α) ,

2S

(2)

rel where Eslab (α) is the α -terminated slab energy after relaxation, 1/2 means that two surfaces are created upon the crystal cleavage. Now that the cleavage and relaxation energies are calculated, the surface energy is just a sum of them

Esurf (α) = Ecl (α) + Erel (α).

(3)

Our ab initio calculated results of the cleavage relaxation and surface energies of the two classes of (111) terminations are listed in Table 1. It is noted that the nonstoichiometric terminations correspond the lower cleavage and surface energies comparing with the stoichiometric terminations consistently, which indicates that the stoichiometric termination is unstable compared with the nonstoichiometric termination, in accord with the criterion for polarity compensation [20,26,27]. The CaO2 termination is possessed of the lowest cleavage and surface energies (2.885 J/m2 and 1.236 J/m2 ) among the four (111) terminations. Moreover, the surface energy for the TiO termination is 1.253 eV, slightly higher than that for the CaO2 termination. So we can say that the two nonstoichiometric terminations can coexist with each other. It can be predicted by the values of surface energies that the favorable terminated (111) terminations of the CaTiO3 are CaO2 -, TiO-, Tiand CaO3 -terminated surfaces successively. The cleavage relaxation and surface energies of the CaTiO3 (110) surface are also listed in Table 1. The nonstoichiometric terminations of CaTiO3 (110) surface have been studied by generalized

W. Liu et al. / Solid State Communications 149 (2009) 1871–1876 Table 1 Calculated cleavage, relaxation and surface energies (in J/m2 ) of (111) terminations and six (110) terminations. Esurf indicates the stability of the split crystal in the vacuum. Surface

Termination

Ecl

Erel

Esurf

(111)

CaO3 Ti CaO2 TiO CaTiO O2 TiO Ca A-type O B-type O

4.301 4.301 2.885 2.885 4.117 4.117 3.501 3.501 2.771 3.914

−0.308 −0.890 −1.649 −1.632 −0.813 −0.916 −1.321 −1.830 −1.933 −0.840

3.993 3.411 1.236 1.253 3.304 3.201 2.180 1.671 0.837 3.074

(110)

gradient approximation (GGA) [19]. In order to compare with the former results with facility, we also use GGA in calculating the two stoichiometric terminations. From Table 1, we noted that for the (110) termination, which also consists of charged planes as (111) termination, the four nonstoichiometric terminations (TiO, Ca, asymmetric A-type O-terminated and symmetric B-type Oterminated terminations) have lower cleavage and surface energies than the two stoichiometric ones (CaTiO and O2 terminations). So we can conclude that the polarity compensation that is achieved through the modification of the surface stoichiometry seems to be more effective than that by the anomalous filling of the surface states, as far as the CaTiO3 (110) and (111) polar terminations energetic is concerned. 3.2. Surface relaxation We have computed the geometrical structures of the fully relaxed (111) surfaces of CaTiO3 with the four different terminations (all thirteen layers were allowed to relax to the minimum of the system’s energy), which are presented in Table 2. Ionic displacements of the ith layer from the surface are expressed as 1xi , 1yi and 1zi , which are defined as follows:

1xi = (xi − xbulk,i )/a × 100%,

(4)

1yi = (yi − ybulk,i )/a × 100%,

(5)

1zi = (zi − zbulk,i )/a × 100%.

(6)

Here, the angle of x coordinate with y coordinate is 120◦ , and meet z coordinate at right angles (shown in Fig. 1). xi , yi and zi mean the x, y and z coordinates of Ca, Ti and O in the ith layer from the surface after relaxation, xbulk,i , ybulk,i and zbulk,i are the non-relaxed x, y and z coordinates determined from the theoretical lattice constant, and a is the theoretical lattice constant of cubic CaTiO3 . 1zi < 0 indicates that the direction inwards the surface, on the contrary, 1zi > 0 means the direction outwards the surface. For the stoichiometric terminations, the surface relaxation is only found in the direction perpendicular to the surface. However, the surface relaxation for the nonstoichiometric terminations occurs in all the x, y and z coordinates, which is caused by the modification of the surface composition. Table 2 shows that Ti, Ca, and O ions in the planes close to surface reveal very different displacements from their perfect crystalline sites. In all cases, the surface ions are displaced inwards from the crystal. The displacements of Ca ions in the stoichiometric terminations are largest, whereas it is not the case for nonstoichiometric terminations. The O ions move larger than any other ions in the nonstoichiometric terminations. For the CaO3 -terminated surface, Ca ions in the first layer move 5.59% a inward, and O ions move 2.30% a inward, which lead to a surface rumpling s of 3.29% a. Ti ions in the second layer move 5.37% a outward, Ca ions in the third layer move 8.71% a outward,

1873

and there is a reduction of relative distances between the first four layers. For the Ti-terminated surface, Ti ions in the first layer move inward by 3.57% a; the Ca ions in the second layer also shift inward, whereas the O ions in the same layer move outward. For the nonstoichiometric terminations, all ions move along three directions. As a result of modification of the surface composition, there is an O atom on each CaO3 layer represents different behavior from the other two O atoms. In order to distinguish it, we named it O1 and the other two O atoms named O2 and O3 . For the CaO2 -terminated surface, Ca ions in the first layer move not only inward (4.25% a) but also along the surface (8.25% a and −5.85% a). The O ions in the first layer move inward by 7.68% a, larger than that in CaO3 -terminated surface. On the second layer, Ti ions move 2.92% a and −2.07% a in the x and y directions, also 4.91% a inward the surface. The magnitudes of ionic displacements for O1 ions in the third layer become much larger than all the other ions. For the TiO-terminated surface, the O ions on the first layer move inward by even 14.64% a, and the Ti ions move inward by 8.82% a. The displacements of ions in the firth layer are still large. Table 2 shows that the displacements of the ions in the nonstoichiometric terminations are larger than that in the stoichiometric terminations, which is in agree with that the stoichiometric termination is unstable compared with the nonstoichiometric termination. 3.3. The surface bond length and bond population We calculated the interatomic bond length (R) and bond populations (P) for atoms near the (111) surfaces and the results are given in Table 3. The bond population can be used to assess the covalent or ionic nature of a bond. A high value of the bond population indicates a covalent bond, while a low value indicates an ionic interaction. The bond population of the Ti–O bond is clearly much larger than that of the Ca–O bond consistent with partial Ti–O covalency. The major effect observed here is a moderate increase in the Ti–O chemical bonding near the stoichiometric (CaO2 and TiO) terminated surface as compared to what was found on the and nonstoichiometric (CaO3 and Ti) terminated (111) surfaces, which may result in the former conclusion deduced from the surface energy that the nonstoichiometric is a better mechanism to stabilize the polar surfaces. For the TiO-terminated surface, the Ti(I)–O(I) bond is the only Ti–O bond in the same layer and it is the shortest one among all the Ti–O bonds. The bond population of the Ti(I)–O(I) bond (0.67) is larger than that of the other Ti–O bonds. However, the bond population of the O(I)–Ti(II) bond (0.58) for the CaO2 -terminated surface is large than that of the Ti(I)–O1 (II) bond (0.47) or Ti(I)– O2,3 (II) bond (0.29) for the TiO-terminated surface. 3.4. The surface grand potential Although the values of Esurf are used generally as an indicative of the stability of the split crystal in the vacuum, they give no information about which termination is the most stable in practical environment conditions. In experimental, for example, one of the standard control parameters is the oxygen pressure in the vacuum chamber. In order to compare the relative stability, the surface grand potential, which implies a contact with matter reservoirs, has been calculated for two classes of terminations with equation [28,29]:

Ω (α) =

1  2S

rel Eslab (α) + PV − TS − nCa µCa − nTi µTi − nO µO , (7)



where Ω (α)(α = CaO3 , Ti, CaO2 and TiO) is surface grand potential per unit area of α termination, the µCa , µTi and µO are the chemical potential of the Ca, Ti and O atomic species, and nCa , nTi

1874

W. Liu et al. / Solid State Communications 149 (2009) 1871–1876

Table 2 Relaxation of the uppermost four layers of the CaO3 -, Ti- and CaO2 -, TiO-terminated CaTiO3 (111) surfaces (as a percentage of the bulk crystal lattice parameter a = 3.808 Å). Stoichiometric terminations CaO3 layer 1 2 3 4 Nonstoichiometric terminations CaO2 layer Ion 1

Ca O Ti Ca O1 O2,3 Ti

2 3

4

Ion

1z (%)

Ti layer

Ion

1z (%)

Ca O Ti Ca O Ti

−5.59 −2.30

1 2

−3.57 −8.91

5.37 8.71 −0.54 0.18

3 4

Ti Ca O Ti Ca O

1x (%)

1y (%)

8.27 0.567 2.92 0.90 −4.96 −6.71 0.34

−5.85 0.162 −2.07 −0.63 3.51 6.49 −0.34

1z (%)

−4.25 −7.68 −4.91 3.12 −14.60 6.97 1.02

and nO are the number of Ca, Ti and O atoms in the slab, respectively. For typical pressure P and temperature T , the PV and −TS terms can be neglected with respect to other contributions. Since CaTiO3 is a ternary oxide, the chemical potential µCaTiO3 of the cubic phase is written as a sum of three terms representing the chemical potential of each species within the crystal:

µCaTiO3 = µCa + µTi + 3µO .

(8)

As long as the surface is in equilibrium with the bulk CaTiO3 , we have µCaTiO3 = Ebulk . Substituting Eq. (8) into Eq. (7), we can eliminate the µTi variable in the surface grand potential:

Ω (α) =



1

rel Eslab (α) − nTi Ebulk

2S

TiO layer

Ion

1x (%)

1y (%)

1z (%)

1

O Ti Ca O1 O 2 ,3 Ti Ca O1 O2,3

0.68 −0.73 1.11 5.50 6.334 −0.98 1.19 −3.71 −3.85

−0.68

−14.64 −8.82 −2.42

2

3 4

(9)

Atom (A) CaO3 termination O(I) Ti(II) O(III)

Ti termination Ti(I) O(II)

CaO2 termination O(I) Ti(II)

If the minimum and maximum values of the O and Ca chemical potentials are known, we can deduce the range of the accessible values of Ω (α) for each termination according to Eq. (9). Introducing the variations of the chemical potentials with respect to the reference phases (1µO = µO − EOmol /2 and 1µCa = 2 bulk µCa − ECa ), we can obtain from Eq. (9):

Ω i = φi −

φ(α) =

1 2S



1 2S

−

[1µO (NO − 3NTi ) + 1µA (NA − NTi )], rel Eslab (α) − nTi Ebulk −

bulk ECa

 (nCa − nTi ) .

1 2

(10)

O2,3 (III) O1 (III) TiO termination O(I) Ti(I) O1 (II) O2,3 (II) Ti(III)

EOmol (nO − 3nTi ) 2 (11)

φ(α) expresses the stability of the surface with respect to bulk CaTiO3 , molecular oxygen, and metallic Ca, while (nO − 3nTi ) represents the excess (if positive) or the deficiency (if negative) number of oxygen atoms of the terminations. In order to estimate the surface grand potential Ω (α), we plot Ω (α) as a function of 1µO = µO − EOmol /2. 2 First of all, according to Fig. 2, our calculations predict that in the O and Ca chemical environments only CaO2 and TiO terminations can be formed. Indeed, the CaO3 and Ti terminations cannot be stabilized, even in very O-rich chemical environment. The surface grand potentials are represented as a function of 1µO , for a particular value of the Ca chemical potential 1µCa = 0 eV, shown in Fig. 3. In this figure, we can see clearly that in the range of

0.73 −1.11 −5.50 −7.31 0.98 −1.19 3.71 3.48

10.54

−10.07 0.93

−3.21 −12.03 5.42

Table 3 The interatomic bond length (R) and bond populations (P) for atoms near the four (111) terminations.

Ti(III)

 − µO (nO − 3nTi ) − µCa (nCa − nTi ) .

4.94 1.86 −7.02 2.53

Atom (B)

P

R(Å)

Ca(I) Ti(II) O(III) Ca(III) Ti(IV)

0.12 0.46 0.30 0.04 0.49

2.696 1.809 2.038 2.716 1.892

O(II) Ca (II) Ti(III) O(IV)

0.53 0.06 0.34 0.48

1.754 2.744 1.966 1.891

Ca(I) Ti(II) O1 (III) O2,3 (III) Ca(III) Ti(IV) Ti(IV)

0.17 0.58 0.57 0.29 0.10 0.51 0.33

2.243 1.787 1.796 2.048 2.281 1.919 1.970

Ti(I) O1 (II) O2,3 (II) Ti(III) Ca(II) Ti(III) O1 (IV) O2,3 (IV)

0.67 0.47 0.29 0.65 0.08 0.32 0.35 0.48

1.704 1.804 1.999 1.848 2.381 1.973 2.104 1.899

accessible value of 1µO , only CaO2 termination are likely to be observed. The surface grand potential for CaTiO3 (110) nonstoichiometric terminations have been estimated in our former calculations using generalized gradient approximation (GGA) [19]. However, the stability for (110) stoichiometric terminations in O and Ca chemical environment have not been researched, so here we only refer to the CaTiO3 (110) stoichiometric terminations (CaTiO and O2 ). In order to compare with our former results of CaTiO3 (110) stoichiometric terminations, we calculated the surface grand potential for CaTiO3 (110) nonstoichiometric terminations also using GGA. The difference of formation energy of cubic bulk CaTiO3 , resulted from GGA and LDA, have not an effect on our results. The calculations predict that the two stoichiometric terminations cannot be stabilized. The result is different from the SrTiO3 (110)

W. Liu et al. / Solid State Communications 149 (2009) 1871–1876

1875

0

-7.60 TiO

CaO2

-6.36 Fig. 2. Stability diagram of the CaTiO3 (111) surface. The most stable termination is represented as a function of the excess O and Ca chemical potentials 1µO and 1µCa .

6

CaTiO

4 O(B)

2

O(A)

0 -2

Ca -4

6

TiO

O2

-6

-4 -2 Excess oxygen chemical potential Δμο (eV)

Ti

0

Fig. 4. Surface grand potentials Ω as a function of 1µO for CaTiO3 (110) surfaces using GGA (for a particular value of the Ca chemical potential 1µCa = 0 eV).

4 TiO

bulk

2 CaO3 0 CaO2 -2 -7

-6 -5 -4 -3 -2 -1 Excess Oxygen Chemical Potentials Δμο (eV)

CaO3 0

Fig. 3. Surface grand potentials Ω as a function of 1µO for CaTiO3 (111) surfaces (for a particular value of the Ca chemical potential 1µCa = 0 eV).

surfaces calculated by Bottin et al. and they have shown that the stoichiometric (110)-SrTiO termination can be stabilized in O-poor and Sr-rich environments [20]. From our calculation, however, the stoichiometric (110)-CaTiO termination is not stabilized in O-poor and Ca-rich environments. In order to analyze the stability of stoichiometric (110)-CaTiO termination with respect to the precision of our calculations, the surface grand potentials are represented as a function of 1µO (for a particular value of the Ca chemical potential 1µCa = 0 eV). In Fig. 4, we can see that at the O-poor and simultaneously the Ca-rich zone boundary (1µO = −5.78 eV and 1µCa = 0 eV), the surface grand potential of CaTiO termination is 0.014 eV higher than that of A-type O termination, which means that the stoichiometric (110)CaTiO termination cannot be stabilized. 3.5. Surface electronic structure We calculated the electronic structure for both bulk and two classes of (111) terminations. The Density of States for the two classes of (111) terminations are shown in Fig. 5. The calculated bulk band gap of 1.878 eV is smaller than the experimental value of 3.5 eV, which is caused by the LDA calculations. For the nonstoichiometric (111) terminations, the CaO2 -terminated surface band gap is 2.132 eV and the TiO-terminated surface is 2.377 eV, larger than that of bulk band gap. From Fig. 5, we can see that the DOS of CaO2 - and TiOterminated surfaces are qualitatively similar to the bulk, with the Fermi level on the top of the valence band (the valence band above the Fermi level is caused by the smearing). Therefore, the two nonstoichiometric terminated surfaces are the insulating ones. For the CaO2 -terminated surfaces, however, it seems that the valence band exhibits an upward shift intruding into the lower part of the band gap. The DOS of the Ti-terminated surface is also much different from that of the bulk and the Fermi level is located above the bottom of the conduction band and some conductionlike states are filled.

Density of State (electrons/eV)

Surface Grand Potential Ω (J/m2)

8

Surface grand potential Ω (J/m2)

8 -19.08

Ti

CaO2

TiO

-20

15

-10 -5 Energy (eV)

0

5

Fig. 5. Density of states of CaTiO3 for the bulk and two class (111) terminations (stoichiometric terminations: CaO3 , Ti; nonstoichiometric terminations: CaO2 , TiO). The Fermi level is indicated by the dash line.

4. Conclusions In the present work, two classes of terminations (stoichiometric terminations and nonstoichiometric terminations) have been constructed for CaTiO3 (111) surface. The cleavage and surface energies, surface grand potential, and surface electronic structure have been calculated for these terminations using ab initio plane wave ultrasoft pseudopotential method based on LDA. The following conclusions are obtained 1. For CaTiO3 (111) and (110) polar surfaces, the stoichiometric termination is unstable compared with the nonstoichiometric termination. 2. The polarity compensation that is achieved through the modification of the surface stoichiometry seems to be more effective than that by the anomalous filling of the surface states, as far as the CaTiO3 (110) and (111) polar termination energetic is concerned. 3. In the range of accessible value of O and Ca chemical environments, only CaO2 and TiO terminations are likely to be observed. 4. For the nonstoichiometric (111) terminations, the CaO2 terminated surface band gap is 2.132 eV and the TiO-terminated

1876

W. Liu et al. / Solid State Communications 149 (2009) 1871–1876

surface is 2.377 eV, larger than that of bulk band gap. However, the stoichiometric (111) terminations appear some metallic properties. Acknowledgment The authors would like to acknowledge the Youth Foundation of Yulin University (Grant No. 09YK32) for providing financial support for this research. Appendix. Boundary limits for the chemical potentials In this appendix, the derivation of the range of accessible values for µO and µCa in the stability diagram of the CaTiO3 (111) surfaces is clarified. For that the oxygen, calcium and titanium atoms are assumed to form no condensate on the surface, the chemical potential of each species must be lower than the energy of an atom in the stable phase of the considered species:

1µO = µO −

EOmol 2 2

< 0,

(A.1)

bulk 1µCa = µCa − ECa < 0,

(A.2)

1µTi = µTi − ETibulk < 0.

(A.3)

Eqs. (A.1) and (A.2) define the upper boundaries of the oxygen and calcium chemical potentials. By combining Eq. (A.3), µCaTiO3 = bulk µCa +µTi + 3µO and µCaTiO3 = ECaTiO , we can deduce the following 3 lower boundary: f

1µCa + 31µO > −ECaTiO3 , f

bulk bulk where −ECaTiO3 = ECaTiO . − ECa − ETibulk − 23 EOmol 2 3

(A.4)

References [1] I.A. Kornev, L. Bellaiche, P. Bouvier, P.-E. Janolin, B. Dkhil, J. Kreisel, Phys. Rev. Lett. 95 (2005) 196804. [2] I.I. Naumov, L. Bellaiche, H.X. Fu, Nature (London) 432 (2004) 737. [3] J.H. Haeni, et al., Nature (London) 430 (2004) 758. [4] J. Junquera, Ph. Ghosez, Nature (London) 422 (2003) 506. [5] R.E. Cohen, H. Krakauer, Phys. Rev. B 42 (1990) 6416. [6] R. Cohen, Nature (London) 358 (1992) 136. [7] C. Noguera, Physics and Chemistry at Oxide Surfaces, Cambridge University Press, New York, 1996. [8] M.E. Lines, A.M. Glass, Principles and Applications of Ferroelectrics and Related Materials, Clarendon, Oxford, 1977. [9] O. Auciello, J.F. Scott, R. Ramesh, Phys. Today 22 (July) (1998). [10] Proceedings of the Williamsburg Workshop on Fundamental Physics of Ferroelectrics-99, J. Phys. Chem. Solids 61 (2000) 139–333. [11] J. Padilla, D. Vanderbilit, Surf. Sci. 418 (1998) 64. [12] A. Asthagiri, D.S. Sholl, Surf. Sci. 581 (2005) 66. [13] A. Asthagiri, C. Niederberger, A.J. Francis, L.M. Porter, P.A. Salvador, D.S. Sholl, Surf. Sci. 537 (2003) 134. [14] E. Heifets, W.A. Goddard III, E.A. Kotomin, R.I. Eglitis, G. Borstel, Phys. Rev. B 69 (2004) 035408. [15] C. Cheng, K. Kunc, M.H. Lee, Phys. Rev. B 62 (2000) 10409. [16] L. Fu, E. Yashenko, L. Resca, R. Resta, Phys. Rev. B 60 (1999) 2697. [17] A.E. Ringwood, S.E. Kesson, K.D. Reeve, D.M. Levins, E.J. Ramm, Radioactive Waste Forms for the Future, Elsevier, Amsterdam, 1988. [18] J.-M. Zhang, J. Cui, K.-W. Xu, V. Ji, Z.-Y. Man, Phys. Rev. B 76 (2007) 115426. [19] R.I. Eglitis, David Vanderbilt, Phys. Rev. B 78 (2008) 155420. [20] F. Bottin, F. Finocchi, C. Noguera, Phys. Rev. B 68 (2003) 035418. [21] M.D. Segall, P.L.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717. [22] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048. [23] T.H. Fischer, J. Almlof, J. Phys. Chem. 96 (1992) 9768. [24] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5118. [25] B.J. Kennedy, C.J. Howard, B. Chakoumakos, J. Phys.: Condens. Matter 11 (1999) 1479. [26] C. Noguera, A. Pojani, P. Casek, F. Finocchi, Surf. Sci. 507–510 (2002) 245. [27] C. Noguera, J. Phys.: Condens. Matter 12 (2000) R367. [28] X. Wang, A. Chaka, M. Scheffler, Phys. Rev. Lett. 84 (2000) 3650. [29] A. Pojani, F. Finocchi, C. Noguera, Surf. Sci. 442 (1999) 179.