First-principles calculations of the structural and electronic properties of the cubic CaZrO3 (001) surfaces

Surface Science 608 (2013) 146–153

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First-principles calculations of the structural and electronic properties of the cubic CaZrO3 (001) surfaces M.G. Brik ⁎, C.-G. Ma, V. Krasnenko Institute of Physics, University of Tartu, Riia 142, Tartu 51014, Estonia

a r t i c l e

i n f o

Article history: Received 23 July 2012 Accepted 3 October 2012 Available online 12 October 2012 Keywords: Ab initio calculations Electronic properties Surface energy Surface rumpling Perovskites

a b s t r a c t The (001) surfaces of cubic perovskite CaZrO3 with two different terminations (CaO and ZrO2) were studied using the first principles density functional theory. The structural, electronic and energetic properties of each surface have been calculated; the differences between the properties of the bulk and slab materials were identified. In particular, changes of the band gap and density of states distributions from atoms located in different layers were revealed. Calculations of the surface rumpling, effective Mulliken charges, and surface energy were compared with data existing for other cubic perovskites. It was also shown that the surface with the CaO-termination has a lower energy than with the ZrO2 termination. © 2012 Elsevier B.V. All rights reserved.

1. Introduction CaZrO3 belongs to a large family of compounds with perovskite structure. It can exist in two structural modifications: the orthorhombic Pbnm phase at low temperature and the cubic Pm3m phase at high temperature, with the temperature of transition from the former to the latter being about 2173 ± 100 K [1]. This material possesses a high melting point (2345 °C [2]), low value of the thermal expansion coefficient (6.5–8.5 × 10 −6 °C −1), and high chemical stability [3], which allows for numerous applications of this ceramic refractory material [4,5]. If doped with In 3+, CaZrO3 is well-known as a proton conducting material [6–8], whose surface states were studied in [9]. There are also some studies of the optical spectra and EPR g-factor of CaZrO3:Mn 4+ [10]. A survey of the scientific publications on CaZrO3 shows that the physical properties of the low-temperature phase are better studied, than those of the cubic phase. Thus, the electronic and structural properties of the orthorhombic CaZrO3 were calculated in [11], its compressibility was studied experimentally in [12] and its vibrational properties were reported in [13]. At the same time, to the best of the authors' knowledge, there is only a single report on the ab initio calculations of the structural, electronic and elastic properties of cubic CaZrO3 [14]. In the present paper the first principles calculations for cubic bulk CaZrO3 are extended to the systematic studies of the (001) surface with different terminations (CaO or ZrO2). The energetic, structural, and electronic properties of these surfaces are calculated and compared to each other. In addition, an

⁎ Corresponding author. Tel.: +372 737 4751; fax: +372 738 3033. E-mail address: brik@fi.tartu.ee (M.G. Brik). 0039-6028/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.susc.2012.10.004

analogy – where it was possible – was found with the surfaces of other cubic perovskites. 2. Computational details All calculations in the present work have been performed in the density functional theory (DFT) framework, as implemented in the CASTEP module [15] of the Materials Studio package developed by Accelrys [16]. The local density approximation (LDA) with the Ceperley–Alder–Perdew–Zunger (CA-PZ) functional [17,18] and the general gradient approximation (GGA) with the Perdew–Burke– Ernzerhof (PBE) functional [19] were used in the calculations. The plane-wave basis energy cutoff was 380 eV. The Monkhorst–Pack scheme k-points grid sampling was set at 7 × 7 × 7 (20 irreducible points) for the Brillouin zone for the bulk calculations and 7 × 7 × 1 (25 irreducible points) for the surface models, which are described below. The convergence parameters were set as follows: total energy – 5 × 10 − 6 eV/atom, maximum force 0.01 eV/Å, maximum stress 0.02 GPa, and maximum atomic displacement 5 × 10 − 4 Å. The electronic configurations were 3s 23p 64s 2 (Ca), 4s 24p 64d 25s 2 (Zr), 2s 22p 4 (O). 3. Bulk and surface models The symmetry of the cubic CaZrO3 crystal lattice is described by the space group Pm3m (No. 221), a = 4.02 Å [20] with one formula unit per unit cell. At first, the structural, electronic and elastic properties were calculated for a perfect bulk CaZrO3 lattice. As the second step, two different surfaces with CaO (type I) and ZrO2 (type II) were built, as shown in Fig. 1. Both surfaces are perpendicular to

M.G. Brik et al. / Surface Science 608 (2013) 146–153

147

(a)

GGA LDA

CaZrO3 bulk 12

Energy, eV

8

4

0

-4

X

R

M

G

R

(b)

Fig. 1. (001) surface models for CaZrO3: CaO (left) and ZrO2 (right) terminations. The Ca, Zr and O atoms are in green, blue, and red, correspondingly. All layers are numbered from 1 to 9.

the c crystallographic axis. Type I model consists of 5 CaO layers and 4 ZrO2 layers, whereas type II model has 4 CaO layers and 5 ZrO2 layers. All atomic positions were fully relaxed to minimize the total energy. Consideration of 7–8 atomic layers was shown to be sufficient for getting converged surface properties [21–23]; therefore, inclusion of nine layers in both models allows performing reliable and well-based analysis of the essential surface properties. Since the CASTEP calculations are essentially periodic in all directions, a vacuum layer with the thickness of 12 Å was used in the surface calculations, in order to avoid interaction between the slabs repeated along the c axis. As seen from Fig. 1, both slab models are symmetric. 4. Calculated results and discussion 4.1. Bulk model The calculated lattice constant was 4.0635 Å (LDA) and 4.1348 Å (GGA), which is very close to the experimental result of 4.02 Å [20]. The calculated “slightly” (in the sense that the maximum of the valence band at the G point is only 0.2 eV below the maxima at the R and M points) indirect band gap (Fig. 2) equals to 3.283 eV (LDA) and 3.315 eV (GGA). The calculated elastic constants (all in GPa): C11 = 379.5, C12 = 74.6, C44 = 63.4, bulk modulus B = 177.7, and Young modulus E = 352.4 for the LDA calculations and C11 = 319.5, C12 = 71.0, C44 = 63.3, bulk modulus B = 153.8, and Young modulus E = 296.7 for the GGA calculations. The results of calculations from [14] (obtained by using the quantum ESPRESSO code) are as follows: indirect band gap 3.30 eV, lattice constant 4.138 Å, elastic parameters (all in GPa) C11 = 322.9, C12 = 70.7, C44 = 62.5, B = 154.8, E = 221.8. The values of the band gap, lattice constant and elastic constants Cij in the present work and in [14] are very close to each other, whereas the values of the Young moduli are somewhat different, which might be due to different computational settings and software used in the calculations. Assignment of the calculated electronic bands can be performed with the help of the density of states (DOS) diagrams in Fig. 2b. The

DOS, electrons/(eV cell)

5

Bulk

s states p states d states

10

Ca

0 15 s states p states d states

10 5

Zr

0 5

s states p states

O 0 -25

-20

-15

-10

-5

0

5

10

15

Energy, eV Fig. 2. Calculated band structure (a) and DOS diagrams (b) for the bulk cubic CaZrO3. The horizontal dashed line in Fig. 2a denotes the Fermi level.

conduction band is wide and stretches from about 4 to 13 eV; it is made basically of the Zr 4d and Ca 3d states, with a small admixture of the oxygen 2p states. The valence band (from − 5 eV to 0 eV) is composed of the oxygen 2p states, and then deep narrow bands follow: 2 s states of O at about − 15 eV, 3p states of Ca at about − 21 eV and 4p states of Zr at about − 25 eV. These bulk electronic properties will be compared below to the electronic properties of both slabs with different surface terminations. 4.2. Surface models: structural relaxation One of the most pronounced differences between the structural properties of the bulk materials and surfaces is that due to the reduced coordination of the atoms in the top layers, the spacing between the adjacent layers is reduced; such a phenomenon is known as the surface relaxation [24]. It can be quantified by calculating the interplanar distances di,i + 1 between neighboring atomic planes (here the index i enumerates the atomic layers in the surface model and runs in our case from 1 to 5). The mean positions of the atomic layers then should be calculated by averaging the z coordinates of the atoms in the corresponding layer; difference of such z coordinates for the adjacent layers gives the di,i + 1 value. In the bulk crystal structure of CaZrO3 the interplanar distance is always equal to the half of the lattice constant a0. To characterize the relative displacements of

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M.G. Brik et al. / Surface Science 608 (2013) 146–153

the atoms in different layers of CaZrO3 one can introduce a nondimensional quantity δi;iþ1 ¼

di;iþ1 −a0 =2  100 %; a0

ð1Þ

where a0 should be taken as the theoretical lattice constant for the bulk model. Table 1 collects the summary of the structural details of the optimized surfaces I and II, with the negative and positive displacements related to the inward (toward the bulk) and outward (toward the vacuum) relaxations. As seen from the Table, the utmost top layer is relaxed inward in both models by about 6.3–6.7%, if the d12 distance is calculated and compared to the unrelaxed interlayer distance. The overall trend in the signs of the di,i + 1 variations (−/+/−/+) is the same for both models and for both LDA/GGA calculations. Analysis of data from Table 1 immediately uncovers an important difference between the models I and II: in the slab with CaO termination the

Ca ions from the top layer relax inward by about 0.342 Å, whereas the O ions in the same top layer relax outward by about 0.118 Å, thus creating considerable surface rumpling of 0.460 Å or 11.32% (in terms of the calculated bulk lattice constant), as follows from the LDA results. In the slab with ZrO2 termination both Zr and O ions in the utmost layer relax inward by 0.027 Å and 0.074 Å, respectively. Thus, the ZrO2-terminated slab has a much “smoother” surface, with the surface rumpling of 1.15%. In both models, the greatest rumpling occurs in the CaO planes (although these planes are from different layers: No. 1 in model I and No. 2 in model II). Such a behavior can be attributed to different character of chemical bonds in the Ca–O and Zr–O pairs. The first one is more ionic (and as such, more easily deformed), whereas the more covalent Zr–O bond located also in the planes parallel to the (001) surface makes such a rumpling (atomic displacements normal to the surface) more difficult. If the results of the GGA calculations are considered (as collected in the lower half of Table 1), the qualitative behavior of both surfaces and individual layers is similar, although the values of the atomic displacements

Table 1 Calculated interplanar distances di,i+1 (Å), relative displacements δi,i+1 (%, in units of the calculated bulk lattice constant), atomic displacements normal to the surface z (Å), layers rumpling s (Å and %, in units of the calculated bulk lattice constant) and Mulliken charges (in units of the proton charge) for the CaO- and ZrO2-terminated (001) CaZrO3 surfaces. LDA calculations Model I CaO termination di,i+1, Å

δi,i+1,%

Atom

z, Å

Rumpling s, Å (%)

Mulliken charge

1

CaO

1.7774

−6.26

ZrO2

2.1482

2.865

3

CaO

1.9575

−1.83

4

ZrO2

2.0448

0.32

5

CaO

−0.3422 0.1178 0.1546 0.0867 −0.0824 0.0473 0.0400 0.0299 0 0

0.460 (11.32)

2

Ca O Zr O Ca O Zr O Ca O

1.37 −0.87 0.87 −0.82 1.43 −0.81 0.93 −0.80 1.44 −0.81

Zr O Ca O Zr O Ca O Zr O

−0.0269 −0.0737 0.3143 0.0831 0.0127 0.0144 0.0758 0.0252 0 0

0.047 (1.15)

Layer

0.068 (1.67) 0.130 (3.19) 0.010 (0.25)

Model II ZrO2 termination 1

ZrO2

1.7610

−6.67

2

CaO

2.1952

4.02

3

ZrO2

1.9730

−1.45

4

CaO

2.0607

0.71

5

ZrO2

0.231 (5.69) 0.002 (0.04) 0.051 (1.25)

1.21 −0.82 1.42 −0.73 0.99 −0.80 1.45 −0.79 0.97 −0.80

GGA calculations Model I CaO termination di,i+1, Å

δi,i+1,%

Atom

z, Å

Rumpling s, Å (%)

Mulliken charge

1

CaO

1.8127

−6.16

ZrO2

2.1976

3.15

3

CaO

2.0081

−1.43

4

ZrO2

2.0845

0.41

5

CaO

−0.1489 0.2841 0.2931 0.2366 0.0194 0.1352 0.0877 0.0708 0 0

0.433 (10.47)

2

Ca O Zr O Ca O Zr O Ca O

1.40 −0.90 0.94 −0.85 1.47 −0.85 1.00 −0.84 1.48 −0.84

Model II ZrO2 termination 1 ZrO2

1.7977

−6.52

CaO

2.2601

4.66

3

ZrO2

2.0142

−1.29

4

CaO

2.0895

0.53

5

ZrO2

−0.1216 −0.1215 0.4623 0.2054 0.0806 0.0870 0.0998 0.0592 0 0

0.0001 (0.002)

2

Zr O Ca O Zr O Ca O Zr O

Layer

0.057 (1.37) 0.116 (2.80) 0.017 (0.41)

0.257 (6.21) 0.006 (0.15) 0.041 (0.98)

1.26 −0.85 1.46 −0.77 1.05 −0.83 1.48 −0.82 1.04 −0.83

M.G. Brik et al. / Surface Science 608 (2013) 146–153

are somewhat different from the LDA data. However, the most pronounced rumpling can be also noticed for the CaO-terminated surface (10.47%), whereas the ZrO2-terminated surface remains practically flat, just relaxing inward by about 6.52% in terms of the GGA-calculated bulk lattice constant. It is also seen that the positions of atoms in the central (fifth) layer coincide with those for the bulk sites due to the mirror symmetry of the considered models. In the present work, the calculated atomic displacements normal to the surface are compared with those for other isostructural perovskites with the general chemical formula ABO3 in Table 2. For all AO-terminated surfaces the A ions in the upper layer relax inward, with the relative displacement varying from −8.8% for Ca in CaTiO3 to −1.99% for heavy Ba ions in BaTiO3 (Table 2). The oxygen ions from the top layer in most cases relax outward, with the largest displacement of about 2.9% in the considered case of CaZrO3. Such an opposite displacement of the A and O ions leads to a well-pronounced surface rumpling, which can be as large as 11.32% (from the calculated lattice constant) in CaZrO3 and 9.50% in CaTiO3. However, in two crystals – BaZrO3 and BaTiO3 – an opposite relaxation (inward) of the oxygen ions can be noted. For all surfaces either with AO or BO2 terminations all ions in the second layer relax outward, and again the CaTiO3 and CaZrO3 perovskites are those compounds (from the considered group) which have the largest ionic displacements. Finally, in the third layers of slabs with the BO2 termination the magnitudes of the ionic displacements are decreased, whereas the same displacements in the third layer of the AO terminated slabs are still noticeable. Finally, Fig. 3 depicts the side views of the optimized CaO and ZrO2 terminated surfaces, as obtained in the LDA calculations. The difference between uppermost layers of both slabs can be seen easily. 4.3. Surface models: electronic properties Asymmetry of the atomic configurations caused by the surface terminations should cause the certain changes in the electronic properties as well. We start with the calculated Mulliken charges [30] of all atoms, which are also collected in Table 1. Decreased coordination of the surface layer's atoms leads to a considerable difference between the “surface” and “bulk” charges (the latter ones are: Ca (1.44); Zr (0.96); O (−0.80)). Thus, in model I the metal ions' charges in the first and second layers are decreased, whereas the charge on the oxygen ions is increased, in comparison to the bulk charges. Only starting from the third

149

Fig. 3. The LDA-calculated CaO (a) and ZrO2 (b) terminated surfaces of CaZrO3. The colors of atoms are those as in Fig. 1.

layer the “surface” and “bulk” charges become practically equal. In model II the charge of the Zr ions in layer 1 is considerably increased, the charge of the O ions in the same layer is only slightly increased. In the second level the charge on the Ca ions is close to its “bulk” value, whereas the oxygen charge is decreased. Then again starting from the third layer the calculated Mulliken charges of all ions reach their “bulk” values. A common trend in the behavior of the Mulliken charges for both models is that the deviation of the Ca charge from the “bulk” value is relatively small, whereas the charges of the Zr and O ions differ from their “bulk” values considerably. This is similar to the results of [27], where an isostructural SrZrO3 crystal was considered and it was shown that the Sr charge (which is analogous to the Ca ions in the present CaZrO3) is close to the bulk value, and the Zr and O charges

Table 2 Comparison of the calculated atomic displacements normal to the surface (in % of the calculated bulk lattice constant) for various ABO3 cubic perovskites with AO and BO2 terminations. Termination

Atom

SrTiO3a

CaTiO3b

SrZrO3c

SrTiO3c

BaHfO3d

BaTiO3e

BaZrO3f

CaZrO3g

AO

A O B O A O B O A O B O

−4.91 0.92 1.20 0.48 – – −2.12 −1.11 2.21 0.07 – –

−8.80 0.70 2.70 1.20 −3.20 −0.01 −2.90 −0.50 7.70 0.80 −0.90 −0.90

−7.30 0.84 1.99 0.65 −1.39 0.14 −2.21 −2.33 3.82 0.60 −0.34 −0.19

−4.73 0.92 1.92 0.10 −0.79 0.23 −2.15 −0.13 3.58 0.51 −0.26 0.05

−3.10 0.24 1.43 0.72 −0.48 0.24 −2.39 −1.19 2.39 0.24 −0.24 0.00

−1.99 −0.63 1.74 1.40 – – −3.08 −0.35 2.51 0.38 – –

−4.30 −1.23 0.47 0.18 −0.01 −0.14 −1.79 −1.70 1.94 0.85 −0.03 0.00

−8.42/−3.60 2.90/6.87 3.80/7.09 2.13/5.72 −2.03/0.47 1.16/3.27 −0.66/−2.94 −1.81/−2.94 7.74/11.18 2.04/4.97 0.31/1.95 0.35/2.10

BO2

a b c d e f g

[25], LDA. [26]. [27]. [28]. [23]. [29]. Present work, LDA/GGA.

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M.G. Brik et al. / Surface Science 608 (2013) 146–153

(a) CaO termination

4

O - layer 1

0 4

O - layer 2

0 2

O - layer 3

s states p states

6

2

DOS, electrons/(eV cell)

Energy, eV

4

GGA LDA

0

-2

-4

G

F

Q

Z G

0 3 0 3

O - layer 4

O - layer 5

0 -25

(b) ZrO2 termination

-20

-15

-10

-5

0

5

Energy, eV

6 Ca - layer 1

10 4

GGA LDA

DOS, electrons/(eV cell)

Energy, eV

5 2

0

-2

-4

G

F

Q

Z

0 s states

10 Ca - layer 3

p states d states

5 0 10 Ca - layer 5

G

5

Fig. 4. Calculated band structure of the slabs with the CaO (a) and ZrO2 (b) terminations.

0 -25

-20

-15

-10

-5

0

5

Energy, eV

Zr - layer 2

8

DOS, electrons/(eV cell)

are different from the bulk due to the well-pronounced covalent interaction between these ions. The calculated band structures for both surface models are given in Fig. 4. It is seen that the width of the conduction band decreases. The calculated band gaps are 2.913 eV (LDA) and 3.106 eV (GGA) for the CaO termination; it is slightly decreased to 2.827 eV (LDA) and 2.967 (GGA) for the ZrO2 termination. It should be noted that the indirect band gap for the bulk material transforms into the direct one for both surface terminations. The conduction band of the ZrO2-terminated slab is a little bit wider than that one of the CaO-terminated one. Fig. 5 presents the atom- and layer-resolved contributions to the DOS diagrams for model I. There is a remarkable difference between the oxygen DOS diagrams for different layers. The oxygen 2s and 2p states in the uppermost layer are sharply peaked, which indicates their high degree of localization. A similar behavior of the oxygen states was observed in [22] for the SrO terminated surface of cubic SrHfO3. A reason for such localization of the oxygen states can be a large surface rumpling, when the oxygen ions are displaced far from the bulk toward vacuum. Moving deeper toward bulk – into the second, third and further layers – is accompanied by broadening of the 2s and 2p states distributions, making them more similar to the oxygen DOS in the bulk (as in Fig. 2). The Zr DOS diagrams are practically layer-independent in this case; however, the conduction band shrinks a little bit, in comparison to the bulk. The same can be said about distribution of the Ca states in the conduction band. A small shift to lower energies of the 3p states peak when moving from the surface to the bulk layers can be noticed for the Ca DOS. Contributions of atoms from different layers to the total DOS of the ZrO2-terminated slab are shown in Fig. 6. It can be noticed immediately

4

0 Zr - layer 4

8

s states p states d states

4

0 -25

-20

-15

-10

-5

0

5

Energy, eV Fig. 5. Calculated DOS diagrams for different layers in the slab with the CaO termination. The layers are numbered as in Fig. 1.

that the oxygen 2p DOS are spread over the whole valence band, even in the uppermost layer. The 2s states are a little bit narrowed in the second layer only. The Zr 4p states shift slowly to the higher energies, when moving from the first to the central layer. The Ca DOS are

DOS, electrons/(eV cell)

M.G. Brik et al. / Surface Science 608 (2013) 146–153

4

O - layer 1

0 4

O - layer 2

0 4

O - layer 3

0 2

O - layer 4

0 4

s states p states

enhanced red color. Asymmetric electron density difference distributions in the top-most layers (not filled chemical bonds) can be noticed, especially in the case of the ZrO2-terminated surface. The Ca electron density is shifted upward (inward) in the CaO- (ZrO2-) terminated slabs. The Zr–O chemical bond, which is the nearest to the surface, becomes stronger comparing to the Zr–O bonds in the bulk, which can be judged from the variation of the electron density difference in the considered cross-sections. 4.4. Surface models: energies

O - layer 5

0 -25

-20

-15

-10

-5

0

5

Energy, eV

Differences in the structures of the surfaces can also manifest themselves in their energetic properties. To find out, which one – either CaO or ZrO2 – termination is energetically favorable, we follow the standard approach to the calculations of the surface energy. Two slabs in Fig. 1, consisting of 9 layers each, have altogether 9 formula units of CaZrO3. If the crystal is cleaved, both surfaces are formed simultaneously, with the cleavage energy distributed equally between all surfaces [25]. The cleavage energy (per surface cell) can be calculated as ðunrelÞ

Zr - layer 1

Es

5

DOS, electrons/(eV cell)

151

0 10

p states

5

ð2Þ

unrel unrel (CaO) and Eslab (ZrO2) are the energies of unrelaxed slabs where Eslab with corresponding termination. Ebulk is the energy of a single unit cell in the bulk. The factor of 4 in the denominator accounts for a creation of four surfaces after two cleavages to make two slabs. The next step is to calculate the negative relaxation energies for each terminations as

s states

Zr - layer 3

  unrel unrel ¼ Eslab ðCaOÞ þ Eslab ðZrO2 Þ−9Ebulk =4;

d states

  unrel Erel ðAÞ ¼ Eslab ðAÞ−Eslab ðAÞ =2;

0 10 Zr - layer 5

ð3Þ

where A denotes CaO or ZrO2 terminations, and Eslab(A) is the corresponding slab energy after relaxation. The last step is to calculate the surface energy as a sum of the two above energies:

5 0 -25

-20

-15

-10

-5

0

5

Energy, eV Ca - layer 2

DOS, electrons/(eV cell)

10

5

0 Ca - layer 4 10 s states p states 5

d states

0 -25

-20

-15

-10

-5

0

5

Energy, eV Fig. 6. Calculated DOS diagrams for different layers in the slab with the ZrO2 termination. The layers are numbered as in Fig. 1.

practically identical in all Ca-containing layers (as was with the Zr DOS in model I). Finally, Fig. 7 shows the distributions of the electron density difference in the space between atoms in both considered slabs. Covalent interaction between the Zr and O ions is well seen. All oxygen ions gain electron density (acquire the negative charge in comparison with the free ions), whereas the Zr and Ca ions lose electron density. Increased charge of the oxygen ions in the surface layers can be seen by their

Es ðAÞ ¼ Es

ðunrelÞ

þ Erel ðAÞ:

ð4Þ

Application of Eqs. (2)–(4) to our system yields the following surface energies: Es(CaO) = 0.558 J/m2 and Es(ZrO2) = 0.829 J/m2 for the LDA calculations, and Es(CaO) = 0.130 J/m 2 and Es(ZrO2) =0.291 J/m2 for the GGA calculations, which indicate that the CaO-terminated surface is more stable. Surface energies for some ABO3 cubic perovskites are collected in Table 3. The AO terminated surface was shown to be energetically favorable in SrTiO3, CaTiO3, SrZrO3, and CaZrO3. It should not be taken, however, that the AO terminated surface is always energetically more stable. Two other examples from Table 3 – PbTiO3 and BaTiO3 – illustrate the opposite case, when the BO2 terminated surface has a lower energy than the AO one. At the moment, it is not completely clear what is the main factor, which can determine the most favorable surface termination, and more studies may be needed to answer this question. In addition, it should be kept in mind that the calculated surface energies depend on the choice of the exchange–correlation functionals [25], so the quantitative comparison of the surface energies for different compounds can be made only if the same calculating settings were used for all compared systems; otherwise, only a careful qualitative discussion can be held. Future studies of the orthorhombic CaZrO3 phase are planned, as was done, for example, in the case of the orthorhombic LaMnO3 perovskite [34], including the thermodynamic stability analysis [33,35]. 5. Conclusions The ab initio calculations of the structural and electronic properties of the CaO- and ZrO2-terminated (001) surfaces of the CaZrO3 cubic perovskite were performed in the present paper. It was shown

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M.G. Brik et al. / Surface Science 608 (2013) 146–153

Fig. 7. The electron density difference in the cross sections perpendicular to the (001) surface in CaZrO3 with CaO (top) and ZrO2 (bottom) terminations.

that the surface rumpling for the slab with the CaO termination is much larger than for the ZrO2 termination (11.3% and 1.15% in terms of the bulk lattice constant). Indirect band gap for the bulk CaZrO3 changes to the direct one for both surface models. Calculated Table 3 Comparison of the calculated (001) surface energies for various ABO3 cubic perovskites with AO and BO2 terminations. SrTiO3a CaTiO3b SrZrO3c SrTiO3c PbTiO3d BaTiO3d BaZrO3e CaZrO3f AO 1.28 BO2 1.32 a b c d e f

1.02 1.22

1.01 1.26

[25], LDA. [31]. [27]. [32]. [29]. Present work, LDA/GGA.

1.20 1.29

0.87 0.77

1.18 1.07

1.16 1.17

0.558/0.130 0.829/0.291

Mulliken charges and electron density distributions highlighted noticeable modifications of the surface slabs electronic properties in comparison with those for the bulk material. Estimations of the surface energy have shown the CaO termination to be more energetically favorable than the ZrO2 termination. The obtained results were compared to those for isostructural perovskites.

Acknowledgements Financial support from the European Social Fund's Doctoral Studies, Internationalization program DoRa, European Union through the European Regional Development Fund (Centre of Excellence “Mesosystems: Theory and Applications”, TK114), European Social Fund (Grant No. GLOFY054MJD) is appreciated. The authors thank Prof. E.A. Kotomin and Dr. D. Gryaznov (Max Planck Institut für Festkörperforschung, Stuttgart, Germany) for valuable discussions.

M.G. Brik et al. / Surface Science 608 (2013) 146–153

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