First-principles calculations on surface hydroxyl impurities in BaF2

Computational Materials Science 53 (2012) 220–225

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First-principles calculations on surface hydroxyl impurities in BaF2 H. Shi a,⇑, R. Jia b, R.I. Eglitis c a

School of Science, Beijing Institute of Technology, 100081 Beijing, PR China Department of Mathematics and Natural Sciences, Bergische Universität Wuppertal, D-42097 Wuppertal, Germany c Institute of Solid State Physics, University of Latvia, 8 Kengaraga Str., Riga LV1067, Latvia b

a r t i c l e

i n f o

Article history: Received 19 June 2011 Received in revised form 7 September 2011 Accepted 8 September 2011 Available online 22 October 2011 Keywords: DFT BaF2 Electronic structure Surface hydroxyl impurities Band structures

a b s t r a c t OH impurities located near the (1 1 1) BaF2 surface have been studied by using density functional theory (DFT) with hybrid exchange potentials, namely DFT-B3PW. Twenty surface OH configurations were studied, and the hydroxyls located on the first surface layer are the energetically most favorable configurations. For the (1 1 1) BaF2 surface atomic layers, the surface hydroxyls lead to a remarkable XY-translation and a dilating effect in the Z-direction, overcoming the surface shrinking effect in the perfect slab. Bond population analysis shows that the surface effect strengthens the covalency of surface OH impurities. The studies on band structures and density of states (DOS) of the surface OH-impurity systems demonstrate that there are two defect levels induced by OH impurities. The O px and py orbitals form two superposed occupied O bands, located above the valence bands (VB), and the H s orbitals do the major contribution to an empty H band, located below the conduction bands (CB). Because of the surface effect, the O bands move downward, toward the VB with respect to these bands in the bulk case, and this leads to narrowing of the VB ? O gap and widening of the O ? H gap which corresponds to the first optical absorption. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction Alkaline-earth fluorides such as CaF2 and BaF2, whose band gaps are larger than 10 eV, are very important for many optical applications. As an example, a recent demand for lens materials available in short wavelength lithography is a typical application. The currently targeted wavelength is 157 nm (about 8 eV) from an F2-excimer laser. This wavelength is far shorter than the transparent region of quartz that is the most popular optical material in the ultraviolet (UV) region. Additionally, for BaF2, it is the fastest luminescent material that has been found to date [1]. Recently, BaF2 has also been found to exhibit superionic conductivity by dissolving appropriate impurities into the lattice or by introducing an interface that causes the redistribution of ions in the space charge region, and is therefore considered as a candidate material for high-temperature batteries, fuel cells, chemical filters and sensors [2]. Considering the high technological importance of alkaline-fluorides, it is not surprising that during the last years, they have been the subject of many experimental and theoretical studies [3–27]. It is well known that optical and mechanical properties of crystals are strongly affected by defects and impurities unavoidably present in any real material. Contemporary knowledge of defects in solids has helped to create a field of technology, namely defect engineering, which is aimed at manipulating the nature and ⇑ Corresponding author. E-mail address: [email protected] (H. Shi). 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2011.09.014

concentration of defects in a material so as to tune its properties in a desired manner or to generate different behaviors. BaF2 could become important optical materials if one could avoid or, at least, control the photoinduced defect formation, which so far in applications degrades its optical quality. Therefore, it is significative to understand the nature of defects in BaF2. Coloration effects in alkaline-earth fluorides are strongly influenced by some impurities. Investigations by Adler et al. [28] and Bontinck [29] show that alkaline-earth fluorides reacts readily with water vapor at high temperatures and suggest that the resulting hydrolysis gives rise to a variety of defects which includes O2 ions in fluorine sites and charge-compensating fluorine vacancies, hydrogen impurities dissolved as H s ions in fluorine sites and as H0i in interstitial sites, as well as OH impurities. One of the big unsolved problems in the context of the application of alkaline-earth fluorides as optical materials is these contamination in the crystals. According to our knowledge, few theoretical investigations on OH impurities in BaF2 were addressed in literatures [30]. As an extension of our previous studies dealing with oxygen, hydrogen and hydroxyl impurities in BaF2 crystals, we performed calculations for surface OH impurities in BaF2. 2. Calculation method It is well known that the HF method considerably overestimates the optical band gap and density functional theory (DFT) underestimates it. To study the hydroxyl (OH) impurities in BaF2, we

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applied the first-principles hybrid DFT-B3PW method, according to our previous studies dealing with CaF2, BaF2 and SrF2 perfect crystals, which gave the best agreement with experiments for the lattice constants, bulk modulus and optical band gaps. The hybrid exchange–correlation B3PW functional involves a hybrid of nonlocal Fock exact exchange, local density approximation (LDA) exchange, and Becke’s gradient-corrected exchange functional [31] combined with the nonlocal gradient-corrected correlation potential by Perdew and Wang [32–34]. All numerical calculations on surface OH impurities in BaF2 were performed by the CRYSTAL2006 computer code [35]. The CRYSTAL-2006 code employs Gaussian-type functions (GTF) localized at atoms as the basis for an expansion of the crystalline orbitals. In order to employ the LCAO-GTF (linear combination of atomic orbitals) method, it is desirable to have optimized basis sets (BS). In our calculations for fluorine atoms, we applied the basis set developed by Catti et al. [5]. For Ba, the BS optimization for BaTiO3 perovskite was developed and discussed in [36,37]. The Hay–Wadt small-core effective core pseudopotential (ECP) was adopted for the Ba atom [38]. The small-core ECP replaces only inner core orbitals, but orbitals for subvalence electrons as well as for valence electrons are calculated self-consistently. In this paper, we used this BS for Ba. The hydroxyl consists of an oxygen atom and a hydrogen atom. In our calculations, the BS for O given in the Basis Sets Library [35] and for H developed by Dovesi et al. [39] were adopted. The basis sets are believed to be transferable, so that, once determined for some chemical constituents, they may be applied successfully in calculations for a variety of chemical substances where the latter participates. The reciprocal space integration was performed by sampling the two-dimensional (2D) Brillouin zone of the 108-atom supercell with 6  6 Pack–Monkhorst net [40]. The thresholds N (i.e., the calculation of integrals with an accuracy of 10N) in our calculations were chosen as a compromise between the accuracy of calculations and the large computational time for large supercells. They are 7, 7, 7, 7 and 14 for the Coulomb overlap, Coulomb penetration, exchange overlap, the first-exchange pseudo-overlap and the second-exchange pseudo-overlap, respectively [41]. For the lattice constant (a0) of BaF2, we used our theoretical optimized value of 6.26 Å. To simulate a surface OH-impurity system, we created a 108atom (1 1 1) slab including four F–Ba–F layers. Each layer unit cell is magnified up to a 3  3 2D supercell containing 27 atoms. After a fluorine atom located near the surface is substituted by a OH, becoming a 109-atom supercell, the atomic configuration of surrounding atoms are re-optimized via a search of the total energy minimum as a function of the atomic displacements from the regular lattice sites. In our calculations, we set the free relaxation for the upper three layers (including 82 atoms) and fix the bottom layer. The OH has the same charge as the substituted F in the ideal ionic case, so the supercell is neutral in our calculations and the electrostatic potential interactions between the neighboring defect supercells are eliminable.

(111)

11

12

21

22

OH -

Ba

F

Fig. 1. Schematic sketch of the (1 1 1) slab containing OH impurities. The big and small circles denote oxygen and hydrogen atoms, respectively.

cated at nos. 1, 3, 4 and 6 fluorine sublayer, respectively, as we can see Fig. 1. According to our calculations on OH impurities in BaF2 crystal, hydroxyls orient the (1 1 1) direction. However, we could not confirm whether the OH orients also the (1 1 1) direction for surface OH-impurity systems. Therefore, we additionally simulated the eight configurations mentioned above, but whose initial guessed orientations are not along the (1 1 1) axis accurately, in which some configurations do not converge to the (1 1 1) direction after geometrical relaxations via a search of the minimum total energy, indicating that the (1 1 1)-oriented OH is not the most stable configuration for surface OH-impurity systems. We add the superscript (j) or (n) to express the OH oriented or unoriented the (1 1 1) ðjÞ ðnÞ axis respectively, such as OH11 and OH11 . Our calculated results show that the energetically most favorable configuration for the ðnÞ surface OH impurity is Config HO11 , in which the angle between  the OH axis and (1 1 1) direction is around 3.4°. Table 1 lists the relðnÞ ative energies of Config HO11 for other configurations. It implicates a trend of OH impurities locating near the surface. This is similar to what has been obtained for our previous work regarding surface F centers in BaF2 and is due to the reduced coordination at the surface [21]. From Table 1, we found that almost all Configs HO have lower energies with respect to the corresponding Configs OH, indicating a preference of the hydrogen atom locating above the oxygen atom for the surface OH-impurity systems, and the (1 1 1)-unoriented Configs are the more energetically favorable configurations with respect to the corresponding (1 1 1)-oriented Configs. Additionally, we also calculated the (1 1 1) BaF2 slabs full covered by OH impurities. For the full-covered slabs, hydroxyls can only replace the surface fluorine sublayer, so we may classify the full-covered slabs into ðjÞ ðnÞ ðjÞ ðnÞ four configurations, i.e., HOfull , HOfull , OHfull and OHfull . Our calculated results demonstrate that the most stable full-covered configuration ðnÞ is Config HOfull , in which the deviation angle equals to around 2.7°,

3. Results and discussions 3.1. Geometrical properties For a (1 1 1) slab of BaF2, there are three sublayers in each F–Ba–F layer from the side view and OH impurities could be only located on the upper and lower fluorine sublayers. So, a OH on one fluorine sublayer has two configurations corresponding to the cases of O above H and H above O, labeled OH and HO respectively in this paper. We calculated eight different configurations of the surface OH impurity, named Config OH11, HO11, OH12, HO12, OH21, HO21, OH22 and HO22, corresponding to the substitutional OH impurity lo-

Table 1 Total energies (eV) of all the surface OH-impurity configurations with respect to ðnÞ Config HO11 . (j) and (n) express the (1 1 1)-oriented and (1 1 1)-unoriented OH, respectively. Sublayer

11 12 21 22

(n)

(j)

HO

OH

HO

OH

0.00 +0.39 +0.36 +0.40

+0.38 +0.46 +0.40 +0.49

+0.07 +0.45 +0.68 +0.47

+0.47 +0.80 +0.54 +0.81

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Table 2 Geometrical properties of the surface OH impurities (OH length (Å) and deviation angle shown in brackets) for all Configs. Sublayer

(n)

(j)

HO

OH

11 12 21 22

0.97 0.96 0.97 0.97

(3.4°) (1.0°) (66.4°) (1.2°)

Full

0.97 (2.7°)

0.97 0.97 0.96 0.97

(2.6°) (59.9°) (0.6°) (58.3°)

0.97 (2.2°)

ðjÞ

ðjÞ

HO

OH

0.97 0.97 0.96 0.97

0.98 0.96 0.97 0.96

0.97

0.98

ðnÞ

and the total energies of Configs HOfull , OHfull and OHfull are larger ðnÞ than that of Config HOfull by 0.04 eV, 0.41 eV and 0.39 eV, respectively. So, we can conclude that for the full-covered slabs, hydrogen ðnÞ atoms prefer to locate above oxygen atoms obliquely. Configs HO11 ðnÞ and HOfull are more stable than other surface OH-impurity sys-

tems, therefore, we mainly focus our current paper on the investigation of these two Configs. The geometrical structures of the surface OH are calculated and depicted in Table 2. According to our previous work regarding the bulk OH-impurity system, the lengths of OH, i.e., the distance between O and H, in BaF2 and CaF2, as well as in H2O, Ca (OH)2 and Ba (OH)2, are all around 0.96  0.97 Å, indicating that the OH as a diatomic group has a steady geometrical structure. Our calculated BaF2 surface OH-impurity lengths for all the configurations are around 0.96  0.98 Å, as we can see Table 2. It is implied that the surface effect on the length of surface hydroxyls is not remarkable. From Table 2, we can see that some Configs, such ðnÞ ðnÞ ðnÞ as OH12 , HO21 and OH22 , have very big deviation angles (around 60°), and the orientations of other Configs approach to the (1 1 1) direction. The relaxations of atoms surrounding the surface OH impurity ðnÞ are shown in Fig. 2 and Table 3. For Config HO11 , all the atoms near the surface shift towards the positive Y axis from the top view, as we can see Fig. 2. The oxygen and the six nearest fluorine atoms, i.e., F1, F2 and F3, on the upper sublayer of the first layer have considerable XY-shifts over 2% of a0, the XY-displacements of fluorine atoms located at the lower sublayer of the first layer and the upper sublayer of the second layer are around 1–2% of a0, and the XYtranslations of the fluorine atoms on the lower sublayer of the second layer equal to 0.6% of a0 approximately. Here, we can conclude that the atomic layers containing surface OH impurities have an remarkable XY-translation. Further analysis of atomic relaxations demonstrates that the OH impurity has a pulling force on the atoms at deeper sublayers along the Z direction. Despite the surface shrinking effect leading to the atomic coordinate reduction of surface atoms in the perfect (1 1 1) BaF2 slab, most atoms at the top two layers overcome the surface shrinking effect and move upwards (toward the vacuum), being due to this pulling force. For the upper sublayer of the first layer, the oxygen atom shifts outward the surface by around 1.30% of a0, whereas the surface shrinking effect on the fluorine atoms at this sublayer is still available. Table 3 also lists the displacements of atoms at top two layers ðnÞ ðnÞ for Config HOfull , i.e., the full-covered case. Similar to Config HO11 , the top layers have an obvious XY-translation with respect to the deeper layers and the pulling force on the deeper sublayers in the Z axis due to the hydroxyls still exists, overcoming the surface shrinking effect. Further, for the full-covered case, the oxygens on the surface move upward by around 2.38% of a0, implicating a dilating effect induced by full-covering hydroxyls. 3.2. Electronic properties

Fig. 2. A top view of the surface OH-impurity nearest-neighbor geometry with a ðnÞ indication of relaxation shifts for Config HO11 . The directions of atomic displacements in the XY-plane are shown with arrows. The fluorine and barium atoms in different shells are labeled. The upper and lower panels denote the first and second layers of the (1 1 1) BaF2 slab, respectively.

Table 4 presents the effective charges of the surface OH for all the (n) configurations. We define the effective OH charge as the sum of O and H effective charges. Our former work demonstrated that the bulk effective OH-impurity charge (0.792e) is smaller than the fluorine charge in BaF2 perfect crystal (0.923e) by 0.131e and the O and H charges are 1.033e and +0.241e, respecðnÞ tively. The OH charge for Config HO11 equals to 0.803e and is larger than the OH charge in the BaF2 bulk by 0.011e, whereas, ðnÞ the OH charge for Config OH11 (0.770e) is smaller by 0.022e. The effective charges of OH in other configurations corresponding to the OH located deeper are closed to the value of the bulk OH-impurity case. We also calculated the effective charges of atoms surrounding the OH impurity, as we can see Table 5. The charge differences of the fluorine and deeper barium atoms are negligible, whereas the electron transfer regarding the three nearest Ba atoms is considerable. 0.092e localized on the OH is attracted by these Ba atoms. Compared with the bulk case, the ability of attracting electrons of Ba atoms surrounding the OH is stronger, being due to the surface effect. Tables 4 and 5 also

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Table 3 ðnÞ ðnÞ Atomic relaxations of the (1 1 1) BaF2 surfaces containing OH (as a percentage of the lattice constant: 6.26 Å) for Configs HO11 and HOfull . Positive signs correspond to outward atomic displacements (toward the vacuum). The directions of atomic displacements in the XY-plane are indicated in Fig. 2. Layer

Sublayer

No. 1

1

2 3

No. 2

1

2 3

ðnÞ

ðnÞ

HO11

HOfull

Atoms (number)

XY (% a0)

Z (% a0)

Atoms

XY (% a0)

Z (% a0)

O (1) F1 (2) F2 (2) F3 (2) Ba1 (1) Ba2 (2) F4 (1) F5 (2) F6 (1) F7 (2)

2.04 2.23 2.15 2.54 2.33 1.59 1.21 1.48 1.13 1.55

+1.30 0.11 0.10 0.28 +0.31 +0.62 +0.05 0.16 +0.09 +0.10

O

0.99

+2.38

Ba

0.84

+0.49

F

0.61

+0.12

F1 (1) F2 (2) F3 (1) F4 (2) Ba1 (1) Ba2 (2) F5 (1) F6 (2) F7 (2) F8 (2)

1.77 1.57 1.56 1.63 1.12 1.15 0.65 0.61 0.66 0.58

+0.71 +0.89 +0.96 +0.84 +0.34 +0.21 +0.02 +0.12 +0.06 +0.11

F

0.74

+0.87

Ba

0.52

+0.39

F

0.29

+0.14

Table 4 Effective charges (e) and bond populations (me) of surface OH impurities for all the (n) configurations. Sublayer

11 12 21 22 Full

HO(n)

OH(n)

charges and geometrical structure of Ba (OH)2. The OH charge of Ba(OH)2 equals 0.825e, being the same as that of Config ðnÞ HOfull , and the charges of O and H are 1.044e and +0.211e, respecðnÞ

tively, closed to the corresponding values of Config HOfull . The

O

H

O–H

O

H

O–H

H–O–Ba angles in Ba (OH)2 (around 116°) and Config HOfull (around

1.055 1.033 1.040 1.037 1.048

+0.252 +0.240 +0.253 +0.244 +0.223

+522 +476 +486 +480 +498

1.028 1.068 1.036 1.063 1.033

+0.258 +0.272 +0.244 +0.264 +0.240

+498 +546 +482 +540 +472

110°) are closed. Therefore, we can consider the full-covered OH as a piece of (BaOH)+ membrane filmed on the BaF2 surface. It is well known that the hydroxyl has a considerable covalency between the oxygen and hydrogen atoms, which is demonstrated by our bond population calculations for the bulk OH-BaF2 systems. The covalent bond between oxygen and hydrogen for the bulk system is 472me. Table 4 also lists the bond populations for the surface OH-impurity and full-covered systems. We found that ðnÞ ðnÞ the OH covalencies for Configs HO11 (522me), OH12 (546me) and ðnÞ OH22 (540me) are much stronger than that of the bulk case by

list the results of effective charge calculations for the OH full-covðnÞ ered configurations. The OH charge for Config HOfull is 0.825e, being much larger than that of the bulk case by 0.033e, and effective charges of 1.048e and +0.223e are localized on the O and H, respectively. Additionally, we also calculated the atomic effective

ðnÞ

Table 5 ðnÞ ðnÞ Effective charges (Q (e)) of the (1 1 1) BaF2 surfaces containing OH for Configs HO11 and HOfull . DQ (e) labels the change in the effective charge compared to perfect BaF2 crystal (QBa = +1.845e, QF = 0.923e). The symbols in atom columns are defined in Fig. 2. Layer

Sublayer

No. 1

1

2 3

No. 2

1

2 3

ðnÞ

ðnÞ

HO11

HOfull

Atoms (number)

Q (e)

DQ (e)

Atoms

Q (e)

DQ (e)

O (1) F1 (2) F2 (2) F3 (2) Ba1 (1) Ba2 (2) F4 (1) F5 (2) F6 (1) F7 (2)

1.055 0.921 0.921 0.921 +1.813 +1.815 0.928 0.927 0.923 0.924

– +0.002 +0.002 +0.002 0.032 0.030 0.005 0.004 0 0.001

O

1.048

–

Ba

+1.768

0.077

F

0.944

0.021

F1 (1) F2 (2) F3 (1) F4 (2) Ba1 (1) Ba2 (2) F5 (1) F6 (2) F7 (2) F8 (2)

0.922 0.922 0.922 0.921 +1.846 +1.846 0.924 0.924 0.924 0.924

+0.001 +0.001 +0.001 +0.002 +0.001 +0.001 0.001 0.001 0.001 0.001

F

0.923

Ba

+1.847

+0.002

F

0.924

0.001

0

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Table 6 Direct optical band gaps (eV) (C ? C) of the surface OH for the ten (n) configurations. Gaps

HO11

OH11

HO12

OH12

HO21

OH21

HO22

OH22

HOfull

OHfull

O1 ? H O2 ? H O1 ? CB O2 ? CB VB ? CB

9.15 9.15 9.47 9.48 11.11

8.59 8.60 9.23 9.24 10.87

8.90 8.90 9.39 9.40 10.83

9.04 9.10 9.37 9.43 11.05

8.70 8.75 9.51 9.56 10.89

8.71 8.72 9.64 9.65 10.91

8.68 8.68 9.57 9.57 10.89

9.15 9.19 9.62 9.65 11.15

8.38 8.39 9.28 9.29 10.95

8.48 8.49 9.63 9.64 11.10

ðnÞ

ðnÞ

ðnÞ

50me, 74me and 68me, respectively. The bond population between ðnÞ oxygen and hydrogen for Config OH11 , the other configuration of OH impurities located on the surface, equals to 498me, also being larger than that of the bulk OH impurity. We can conclude here that the surface effect strengthens the covalency of OH impurities located near the surface. Compared with the covalent bonds of hydroxyls in Ca (OH)2 (458me) and Ba (OH)2 (434me) crystals, the covalency of surface OH impurities is also much stronger. ðnÞ For the OH full-covered configuration, i.e., Config HOfull , the sur face effect on the strengthening OH -covalency is not pronounced, whereas the bond population equals to 498me, still being much larger than that in Ba (OH)2. Combining the previous discussion about the geometrical structures of OH impurities, we indicate that the OH as an atomic group has a steady geometrical structure instead of electronic properties in different materials. Also the main surface effect on the OH impurities is on the electronic structures instead of the geometrical structures.

ðnÞ

ðnÞ

ðnÞ

ðnÞ

ðnÞ

ðnÞ

H [s]

DOS [arb. units]

ðnÞ

O [px + py]

Total

-2

0

2

4

6

8

10

12

14

Energy [eV] 3.3. Band structure and density of states for surface OH impurities Alkaline-earth fluorides with defects degrade their optical quality and exhibit optical absorption. Our calculations on the defect levels induced between the valence bands (VB) and conduction bands (CB) suggest a possible mechanism for the optical absorption. In the one-electron approximation scheme, the experimentally observed optical absorption could be due to an electron transition from the OH-impurity ground state to the empty band induced by the OH. According to our previous work dealing with OH impurities in BaF2 bulk, the optical band gap between VB and CB at C point is 11.34 eV, the empty defect level induced by H atoms is located 0.78 eV below the bottom of the CB at C point, and the occupied defect levels, containing two superposed bands induced by the O atoms, are located 1.95 eV above the VB top at C point. Therefore, we imply that the first optical absorption should be centered around 8.61 eV for the bulk BaF2 containing OH impurities. The calculated optical band gaps for all the (n) configurations are collected in Table 6 and the band structure of Config ðnÞ HO11 is shown in Fig. 3. From Table 6, we can conclude that the

10

Energy [eV]

8 6 4 2 0 -2 Γ

M

K

Γ

Fig. 3. Calculated B3PW band structure for the 109-atom supercell modeling the ðnÞ surface OH impurities for Config HO11 .

ðnÞ

Fig. 4. Total and projected density of states (DOS) for Config HO11 .

surface effect reduces the VB ? CB gaps, which are around 10.9  11.1 eV and smaller than that in the bulk case (11.34 eV). The O ? H gaps, i.e., the first possible optical absorption, for most ðnÞ of the configurations except Config OH11 , are larger than the correðnÞ sponding gap in the bulk case (8.61 eV). Especially for Configs HO11 ðnÞ and OH22 , the O ? H gaps are larger by over 0.5 eV. Unlike the surface OH-impurity systems, the O ? H gaps for the OH full-covered systems are narrower than that of the bulk case by around 0.1–0.2 eV. Further analysis of the band gaps shows that the occupied defect levels induced by O atoms move downward around 0.3–0.6 eV (toward VB) with respect to the bulk case. On the other hand, the defect band induced by H atoms is very close to the CB bottom and the relevant gap is only 0.32 eV at C point for Config ðnÞ HO11 . Thereby, there is no separated H band almost superposing with the CB, as we can see Fig. 3. However, according to our study on the bulk OH-impurity systems, there is a clear defect band induced by H atoms located between the VB and CB. To further study the electronic structure and electron transitions in a surface OH-impurity system, we calculated the density ðnÞ of states (DOS) of Config HO11 , as we can see Fig. 4. Our previous  bulk OH -impurity study demonstrated that the O p orbitals form the two superposed occupied O bands, i.e., so-called O bands, and the H s orbitals do the major contribution to the empty defect band, named H band in the bulk case, below the CB bottom. In the 2D cases, the symmetry of px, py and pz states is broken by the (1 1 1)-terminated surface, therefore the p-state electrons are not equivalent in the three directions. Our DOS calculations show that the two superposed occupied O bands mainly consist of O px and py orbitals. Because of the surface effect, the O px and py orbitals move downward, toward the VB top, with respect to the O p orbitals in the bulk case, and this leads to narrowing of the VB ? O gaps and widening of the O ? H gaps. As discussion above, there is no remarkably separated defect band induced by H atoms located below the CB bottom, being in agreement with our DOS calculation on H atoms.

H. Shi et al. / Computational Materials Science 53 (2012) 220–225

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4. Conclusions

References

We applied the first-principles approach within the hybrid DFTB3PW scheme to calculations on OH impurities located near the (1 1 1) BaF2 surface. Sixteen surface OH configurations including eight (1 1 1)-oriented and eight (1 1 1)-unoriented OH impurities ðnÞ were studied and we found that the configuration named HO11 , in which the OH located at the upper fluorine sublayer of the first surface layer, H lies above O obliquely and the obliquity is around 3.4°, is the energetically most favorable configuration for the surface OH-impurity systems. We also performed calculations on ðnÞ the (1 1 1) BaF2 slabs full covered by OH. Config HOfull is the most  stable one among the four OH full-covered configurations and the deviation angle equals to around 2.7°. The lengths of surface OH impurities for all the configurations are around 0.96–0.98 Å, being close to that in the bulk case, as well as in water molecule, Ca (OH)2 and Ba (OH)2 crystals, indicating that The surface effect on the length of surface hydroxyls is not remarkable and the OH as a diatomic group has a steady geometrical structure. The calculations on the relaxations of atoms surrounding the surface OH impurity demonstrated that the atomic layers containing surface OH impurities have a remarkable XY-translation, and the presence of surface OH impurities or layer (the full-covered case) leads to a dilating effect in the Z-direction, overcoming the surface shrinking effect in the perfect slab. Effective charge analysis shows that the surface OH-impurity ðnÞ charge (0.803e for Config HO11 ) is much smaller than the fluorine  (substituted by the OH ) charge (0.923e) in BaF2 perfect crystal. Because of the surface effect, the charge of OH impurity for Config ðnÞ HO11 is larger than that of the bulk case, some electrons localized on the hydrogen atoms transfer inward the surface, and the oxygen atoms attract some electrons from the surrounding atoms. Bond population calculations indicate that the surface effect strengthens the covalency of OH impurities located near the surface. The main surface effect on the OH impurities is on the electronic structures instead of the geometrical structures. The studies on band structures and DOS of the surface OH-impurity systems demonstrate that there are two defect levels induced by OH impurities. One is two superposed occupied O bands mainly consisting of the O px and py orbitals, located above the VB, the other is an empty H band to which the H s orbitals do the major contribution, almost superposing with the CB. Because of the surface effect, the O bands move downward, toward the VB with respect to these bands in the bulk case, and this leads to narrowing of the VB ? O gap and widening of the O ? H gap which corresponds to the first optical absorption.

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