Ab Initio Calculations of Hydroxyl Impurities in CaF2 - The Journal of

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Ab Initio Calculations of Hydroxyl Impurities in CaF2 H. Shi* and L. Chang Key Laboratory of Cluster Science of Ministry of Education, School of Science, Beijing Institute of Technology, Beijing 100081, People's Republic of China

R. Jia Department of Mathematics and Natural Sciences, Bergische Universität Wuppertal, D-42097 Wuppertal, Germany

R. I. Eglitis Institute of Solid State Physics, University of Latvia, 8 Kengaraga Strasse, Riga LV1067, Latvia ABSTRACT: OH− in CaF2 crystal and the (111) surface have been studied by using density functional theory (DFT) with hybrid exchange potentials, namely, DFTB3PW. Three bulk and 20 surface OH− configurations were investigated, and we found (\) (\) that Configs OH(111) for the bulk case and HO11 and HOfull for the surface case are the energetically most favorable configurations. For the (111) CaF2 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 there is a considerable covalency between the oxygen and hydrogen atoms, and the surface effect strengthens the covalency of surface OH− impurities. The studies on band structures and density of states of the surface OH−-impurity systems demonstrate that there are two defect levels induced by OH− impurities. The O p orbitals form two superposed occupied O bands, located above the valence bands (VBs), and the H s orbitals do the major contribution to an empty H band, located below the conduction bands. Because of the surface effect, the O bands move downward, toward the VBs with respect to the relevant 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. Additionally, the study on the formation of OH− impurities shows that isolated hydroxyls are favorite to substitute fluorine ions and adsorb on the surface energetically in CaF2. On the other hand, the formation of OH− impurities may also be due to the aggregation of separated oxygen and hydrogen impurities in CaF2. The formation of OH− impurities could be avoided in CaF2 crystal if we can control the concentration of the oxygen atoms near the surface, because oxygen does the primary contribution to the formation of OH− impurities in CaF2.

I. 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, CaF2 can be chosen as an optical material also due to its cubic crystal structure with perfect optical isotropy, due to its chemical durability and its mechanical properties which make it applicable for lens fabrication.1−3Also, CaF2 can be used as a material for radiation detection.4 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.5−28 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 © 2012 American Chemical Society

in solids has helped to create a field of technology, namely defect engineering, which is aimed at manipulating the nature and concentration of defects in a material so as to tune its properties in a desired manner or to generate different behaviors. CaF2 could become an important optical material if one could avoid or, at least, control the photoinduced defect formation, which so far in applications degrades its optical quality. Therefore, it is significant to understand the nature of defects in CaF2. Coloration effects in alkaline-earth fluorides are strongly influenced by some impurities. Investigations by Adler et al.29 and Adler and Bontinck30 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 chargecompensating fluorine vacancies, hydrogen impurities dissolved Received: November 17, 2011 Revised: February 3, 2012 Published: February 16, 2012 6392

dx.doi.org/10.1021/jp211075g | J. Phys. Chem. C 2012, 116, 6392−6400

The Journal of Physical Chemistry C

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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.

as Hs− ions in fluorine sites and as Hi0 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 this contamination in the crystals. According to our knowledge, few theoretical investigations on OH− impurities in CaF2 were addressed in the literature. As an extension of our previous studies dealing with oxygen and hydrogen impurities in CaF2, we performed calculations for OH− impurities in CaF2 crystal and surface.

III. RESULTS AND DISCUSSION A. OH− Impurities in the CaF2 Bulk. First, we performed calculations of different configurations for the OH− impurities in CaF bulks. Considering the symmetry of alkaline-earth fluorides, we calculated three simple configurations in which the OH− orients along the (100) or (111) direction. The (100)oriented OH− is labeled OH(100) in this paper. For the (111)oriented case, there are two configurations named OH(111) (see Figure 1) and HO(111). It is clear that the different orders of oxygen

II. 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 CaF2, we applied the first-principles hybrid DFTB3PW 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 exchangecorrelation B3PW functional involves a hybrid of nonlocal Fock exact exchange, local density approximation (LDA) exchange, and Becke’s gradient-corrected exchange functional31 combined with the nonlocal gradient-corrected correlation potential by Perdew and Wang.32−34 All numerical calculations on OH− impurities in CaF2 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 (BSs). In our calculations for CaF2, we applied the basis sets of Ca and F developed by Catti et al.7 For the hydroxyl consisting of an oxygen atom and a hydrogen atom, the BSs of O given in the Basis Sets Library35 and of H developed by Dovesi et al.36 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 integrations were performed by sampling the three-dimensional (3D) and two-dimensional (2D) Brillouin zones of the 96- and 108-atom supercells with 4 × 4 × 4 and 6 × 6 Pack-Monkhorst nets,37 respectively. The thresholds N (i.e., the calculation of integrals with an accuracy of 10−N) 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.38 For the lattice constant (a0) of CaF2, we used our theoretical optimized value of 5.50 Å. To simulate OH− impurities in CaF2, we replaced one fluorine atom with an oxygen atom and inserted a hydrogen atom into an atomic interstitial site near the oxygen. After the fluorine atom is substituted by the OH−, the atomic configuration of surrounding atoms are reoptimized via a search of the total energy minimum as a function of the atomic displacements from the regular lattice sites. To simulate a surface OH−-impurity system, we created a 108-atom (111) slab including four F−Ca−F layers. Each layer unit cell is magnified up to a 3 × 3 2D supercell containing 27 atoms. In our calculations, we set the free relaxation for the upper three layers including 82 atoms (the OH− has two atoms) and fix the bottom layer. The OH− has the same charge as the substituted

Figure 1. View of the (111)-oriented OH− for Config OH(111). The arrows show the directions of the atomic displacements surrounding the OH− impurity. According to the symmetries of the atoms, different labels are defined in spheres.

and hydrogen along the (111) axis correspond to the different OH− configurations in CaF2 crystals, as we can see in Figure 1. According to our calculations, we found that the energetically most favorable configuration of the OH− impurity is Config OH(111), and the total energies of Configs HO(111) and OH(100) are larger than that of Config OH(111) by around 0.47 and 0.21 eV, respectively. We also simulated some other configurations with the orientation slightly diverging the (111) axis, and the results show that those configurations converge to Config OH(111) after geometrical relaxations via a search of the minimum total energy. Therefore, we mainly focus our current discussion on Config OH(111). Next, we computed the geometrical property of the OH− and the relaxation of atoms surrounding the OH− impurity. The distances between the oxygen and hydrogen atoms (or named the length of OH−) are 0.97, 0.95, and 0.96 Å for Configs OH(111), HO(111), and OH(100), respectively. According to our calculations on the H2O molecule and Ca(OH)2 and Ba(OH)2 crystals, the lengths of OH− are all around 0.96−0.97 Å, indicating that the OH− has a steady geometrical structure in different materials. The calculation of the OH− position in CaF2 bulk shows that one fluorine is substituted by an oxygen atom and a hydrogen atom occupies a neighbor interstitial site. For the (111)-oriented OH−, the oxygen atom moves from the regular anion site backward to the neighbor calcium along the (111) direction by 1.93% of a0 for Config OH(111) (see Figure 1). 6393



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The calculated atomic displacements of the OH− and surrounding atoms for Config OH(111) are listed in Table 1. Table 1. Atomic Relaxations (D (% a0), as a Percentage of the Lattice Constant, 5.50 Å) and Effective Charges (Q(e)) of the OH− and Surrounding Atoms in the CaF2 96-Atom Supercell for Config OH(111)a atoms (shell)

no.

D (% a0)

Q (e)

ΔQ (e)

O H Ca1 Ca2 F1 F2 F3 F4 F6

1 1 3 1 3 3 6 3 3

1.93 − 1.10 0.73 0.34 0.32 0.33 0.28 0.18

−0.997 +0.275 +1.772 +1.799 −0.913 −0.915 −0.901 −0.903 −0.900

− − −0.031 −0.004 −0.011 −0.013 +0.001 −0.001 +0.002

Figure 2. Electron density contours in CaF2 with OH− from the (110) side view, being from 0 to 0.4 e/bohr3 with a linear increment of 0.01 e/bohr3.

ΔQ(e) is the charge difference between the defective and perfect crystals (QCa = +1.803 e, QF = −0.902 e in perfect CaF2). The shell labels have been defined in Figure 1.

a

the experimentally observed optical absorption could be due to an electron transition from the ground state to the empty band induced by the OH− impurities. Our calculated band structure regarding the OH−-impurity system of Config OH(111) is shown in Figure 3, and the optical band gaps for Configs OH(111),

The three Ca1 atoms are repulsed from the OH− by around 1.10% of a0, and the one Ca2 moves toward the OH− by around 0.73% of a0. The OH−−Ca1 and OH−−Ca2 distances both increase by around 0.25% and 1.20% of a0, respectively, implicating a repulsion of the OH− impurity to the neighbor calcium atoms. Finally, the relaxations of neighbor fluorine atoms are slight and less than 0.4% of a0. Table 1 also presents the effective charges of the OH− and surrounding atoms for Config OH(111). The total charge of the OH−, i.e., the sum of the O and H charges, is −0.722 e, being much smaller than the charge of the substituted fluorine atom (−0.902 e) by 0.180 e. Around 0.097 and 0.072 e localized on the four nearest Ca and six second-nearest F, respectively, transfer inward to the OH−. For Configs HO(111) and OH(100), the effective charges of OH− are −0.713 and −0.737 e, being close to the corresponding value of Config OH(111). We also calculated the OH− charges in Ca(OH)2 and Ba(OH)2 crystals. The results show that the total effective charges of OH− in Ca(OH)2 and Ba(OH)2 are equal to −0.781 and −0.825 e, respectively. The OH− charge in Ca(OH)2 is larger than OH− as impurities in CaF2 crystal by around 0.4−0.7 e , and this phenomenon can be explained by the fact that fluorine has a stronger oxidative property than that of OH−. It is well-known that the hydroxyl has a considerable covalency between the oxygen and hydrogen, which is also demonstrated by our bond population calculations for the OH−−CaF2 systems. The presence of the covalency of OH− in CaF2 is also clearly shown in the charge density map (see Figure 2). The covalent bonds between the oxygen and hydrogen atoms are 486, 508, and 536 me for Configs OH(111), HO(111), and OH(100), respectively. Compared with the covalent bonds in Ca(OH)2 (458 me) and Ba(OH)2 (434 me) crystals, the covalency of the OH− impurities in CaF2 is stronger than that in the hydroxide crystals. Here, we can conclude that OH− as an atomic group has a steady geometrical structure instead of electronic properties in different materials. Alkaline-earth fluorides with defects degrade their optical quality and exhibit optical absorption. Our calculations on the defect levels induced between the valence bands (VBs) and conduction bands (CBs) suggest a possible mechanism for the optical absorption. In the one-electron approximation scheme,

Figure 3. Calculated B3PW band structure for the 96-atom supercell modeling the OH− impurity in CaF2 for Config OH(111).

HO(111) and OH(100) are collected in Table 2. The optical band gaps between the VBs and CBs for the CaF2 96-atom supercell Table 2. Direct Optical Band Gaps (eV) (Γ → Γ) of the OH−-Impurity Systems for Configs OH(111), HO(111), and OH(100) gaps

OH(111)

HO(111)

OH(100)

O→H O → CB VB → H VB → CB

9.04 9.74 10.47 11.17

8.99 9.78 10.52 11.32

9.04 10.24 10.65 11.85

containing a OH− at the Γ point are 11.17, 11.32, and 11.85 eV for Configs OH(111), HO(111), and OH(100), respectively, being much larger than the relevant gap of the perfect CaF2 crystal (10.96 eV). It is implied that the OH− impurities widen the VB−CB gap, especially for Config OH(100). For Config OH(111), the empty defect level induced by OH− impurities is located 0.70 eV below the bottom of the CB at the Γ point (see Figure 3). The occupied defect levels, containing two superposed bands 6394



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(the gap is less than 0.01 eV), induced by OH− impurities, are located 1.43 eV above the VB top at the Γ point. Since hydroxyl has weaker oxidative property than that of fluorine, the hydroxy binding force to the outer-shell electrons is smaller, leading to the occupied OH− bands shifting upward with respect to the VB top, mainly consisting of F outer p orbitals. From Figure 3 and Table 2, we conclude that the first optical absorption, corresponding to an electron transition from the occupied OH− bands to the empty OH− band, should be centered around 9.04 eV, being much larger than the relevant value of 4.24 eV for CaF2 containing F centers (an electron trapped in the fluorine vacancy).22 It is because the trapped electron in the F center is more delocalized than the valence electron of hydroxyl. Unlike the (111)-oriented configurations, for Config OH(100), the two occupied OH− bands separate slightly and the gap is around 0.05 eV. To further study the electronic structure and electron transitions in a OH−-impurity system, we calculated the density of states (DOS) of the OH(111) system, as we can see in Figure 4.

corresponding to the substitutional OH− impurity located at the No. 1, 3, 4, and 6 fluorine sublayers, respectively, as we can see in Figure 5. As discussed before, hydroxyls orient the (111)

Figure 5. Schematic sketch of the (111) slab containing OH− impurities. The big and small circles denote oxygen and hydrogen atoms, respectively.

direction in CaF2 bulks. However, we could not confirm whether the OH− orients also along the (111) direction for surface OH−-impurity systems. Therefore, we additionally simulated the eight configurations mentioned above, but whose initial guessed orientations are not along the (111) axis accurately, in which some configurations do not converge to the (111) direction after geometrical relaxations via a search of the minimum total energy, indicating that the (111)-oriented OH− is not the most stable configuration for surface OH−impurity systems. We add the superscript (|) or (\) to express the (111)-oriented and (111)-unoriented OH− impurities, (|) (\) and OH11 , etc. Our respectively, such as Configs OH11 calculated results show that the energetically most favorable (\) , in configuration for the surface OH− impurity is Config HO11 − which the angle between the OH axis and the (111) direction is around 3.2°. Table 3 lists the relative energies of Config

Figure 4. Total and partial density of states (DOS) for the OH− impurities (Config OH(111)) in the CaF2 crystal.

According to our calculation, the O p orbitals form the two superposed occupied OH− bands, named O bands, and the H s orbitals do the major contribution to the empty defect band (so-called H band) below the CB bottom. Unlike the occupied O bands with a very sharp peak in the DOS figure, the DOS of the unoccupied H band is diffused and very close to the CB. Additionally, the O p orbitals also make some contribution to the VB top, as we can see Figure 4, which mainly consists of F p orbitals in perfect CaF2 crystal. B. OH− Impurities in the CaF2 Surface. As an extension of previous studies on hydroxyl impurities in CaF2 bulks, we performed calculations for surface OH− impurities. For a (111) slab of CaF2, there are three sublayers in each F−Ca−F layer from the side view, and OH− impurities could be only located at the upper and lower fluorine sublayers. So, a OH− at 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− impurities, named Config OH11, HO11, OH12, HO12, OH21, HO21, OH22, and HO22,

Table 3. Total Energies (eV) of All the Surface OH−(\)a Impurity Configurations with Respect to Config HO11 (\)

(|)

sublayer

HO

OH

HO

OH

11 12 21 22

0.00 +0.62 +0.62 +0.63

+0.62 +0.73 +0.64 +0.76

+0.09 +0.70 +0.95 +0.70

+0.70 +1.06 +0.82 +1.14

a (|) and (\) express the (111)-oriented and (111)-unoriented OH−, respectively.

(\) for other configurations. It implicates a trend of OH− HO11 impurities locating near the surface. From Table 3, we found that most of 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 (111)-unoriented Configs are

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the more energetically favorable configurations with respect to the corresponding (111)-oriented Configs. Additionally, we also calculated the (111) CaF2 slabs full covered by OH− . For the full-covered slabs, hydroxyls can only replace the surface fluorine sublayer, so we may classify the full-covered slabs into (|) (\) (|) (\) four configurations, i.e., HOfull , HOfull , OHfull , and OHfull . Our calculated results demonstrate that the most stable full-covered (\) , in which the deviation angle configuration is Config HOfull (|) , equals around 2.2°, and the total energies of Configs HOfull (|) (\) (\) , and OHfull are larger than that of Config HOfull by 0.06, OHfull 0.63, and 0.58 eV, respectively. So, we can conclude that for the full-covered slabs, hydrogen atoms prefer to locate above (\) oxygen atoms obliquely. Configs HO11(\) and HOfull are more stable than other surface OH− systems; therefore, we mainly focus our current discussion on these two Configs. The geometrical structures of the surface OH− are calculated and depicted in Table 4. According to our studies on bulk Table 4. Geometrical Properties of the Surface OH− Impuritiesa for all Configs (\)

a

(|)

sublayer

HO

OH

HO

OH

11 12 21 22 full

0.96(3.2°) 0.97(5.3°) 0.97(65.0°) 0.97(5.0°) 0.96(2.2°)

0.97(28°) 0.97(58.1°) 0.96(4.8°) 0.96(57.9°) 0.97(2.5°)

0.97 0.97 0.96 0.97 0.97

0.98 0.96 0.97 0.95 0.98

OH− length (Å) and deviation angle shown in brackets. −

Figure 6. Top view of the surface OH−-impurity nearest-neighbor (\) . The geometry with an indication of relaxation shifts for Config HO11 directions of atomic displacements in the XY-plane are shown with arrows. The fluorine and calcium atoms in different shells are labeled. The upper and lower panels denote the first and second layers of the (111) CaF2 slab, respectively.

−

OH -impurity systems, the lengths of OH in CaF2 and BaF2, 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 CaF2 surface OH−impurity lengths for all the configurations are around 0.96−0.98 Å, as we can see in Table 4. It is implied that the surface effect on the length of surface hydroxyls is not remarkable. From Table (\) 4, we found that some Configs, such as OH12(\), HO21 , and (\) OH22 , have very big deviation angles (around 60°), and the orientations of other Configs approach the (111) direction. In an ideal cubic CaF2 bulk, the angle between the (111) and (100) axes is 54.7°, being close to those big obliquities of around 60°. Therefore, we can consider these Configs with big deviation angles as Config OH(100), namely, the (100)-oriented configuration in the bulk case, locating near the (111) surface. It is implied that despite the (111)-oriented OH− being energetically more favorable in CaF2 bulk, hydroxyls located at some specific fluorine sublayers near the surface prefer the (100) orientation. Here, we can classify the eight (111)-unoriented configurations into three OH− types, i.e., OH(111), HO(111), and (\) (\) (\) (\) OH(100) in the bulk case. Configs OH11 , HO12 , OH21 , and HO22 (\) belong to the OH(111) type, Config HO11 belongs to the HO(111) (\) (\) (\) type, and Configs OH12 , HO21 , and OH22 belongs to the OH(100) type. From Tables 3 and 4 and this classification, we can conclude that OH− impurities with HO(111), OH(111), OH(100), and OH(111) configurations prefer to locate at the No.1, 3, 4, and 6 fluorine sublayers, respectively. The relaxations of atoms surrounding the surface OH− impurity are shown in Figure 6 and Table 5. For Config (\) HO11 , all the atoms near the surface shift toward the positive Y-axis from the top view, as we can see Figure 6. 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 0.7% of a0 approximately. Here, we can conclude that the atomic layers containing surface OH− impurities have a remarkable XY-translation. Because of the surface shrinking effect, the atomic coordinates of most of the surface atoms reduce, whereas the oxygen atom shifts outward from the surface by around 2.22% of a0. Table 5 also lists the (\) displacements of atoms at the top two layers 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 surface OH− layer moves upward by around 3.32% of a0, implicating a dilating effect induced by fullcovering hydroxyls. Table 6 presents the effective charges of the surface OH− for all the (111)-unoriented configurations. The OH− charges for most Configs are larger than the OH− charge in the CaF2 bulk (\) (−0.722 e). Especially for Config HO11 , the effective charge of − the surface OH equals −0.746 e and is larger by around 0.024 e. Because of the surface effect, −0.005 e localized on the hydrogen atom transfers inward toward the surface and the oxygen atom attracts −0.028 e from the surrounding atoms. We also calculated the effective charges of atoms surrounding the OH− impurity, as we can see in Table 5. The charge differences of the deeper fluorine and calcium atoms are negligible, whereas the 6396



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Table 5. Atomic Relaxations (as a Percentage of the Lattice Constant, 5.50 Å) and Effective Charges (Q(e)) of the (111) CaF2 (\) (\)a Surfaces Containing OH− for Configs HO11 and HO11 HO11(\)

(\) HOfull

layer

sublayer

atoms (no.)

XY (% a0)

Z (% a0)

Q (e)

ΔQ (e)

atoms

XY (% a0)

Z (% a0)

Q (e)

no. l

1

0 (1) Fl (2) F2 (2) F3 (2) Cal (1) Ca2 (2) F4 (1) F5 (2) F6 (1) F7 (2) Fl (1) F2 (2) F3 (1) F4 (2) Cal (1) Ca2 (2) F5 (l) F6 (2) F7 (2) F8 (2)

1.96 2.37 2.19 2.67 2.46 1.69 1.32 1.66 1.35 1.52 1.74 1.67 1.60 1.66 1.20 1.22 0.76 0.79 0.78 0.69

+2.22 −0.18 −0.15 −0.32 −0.52 −0.31 −0.71 −1.00 −0.54 −0.50 −0.24 −0.18 −0.01 −0.17 −0.35 −0.45 −0.47 −0.35 −0.40 −0.33

−1.025 −0.895 −0.895 −0.895 +1.769 +1.771 −0.918 −0.918 −0.906 −0.907 −0.900 −0.900 −0.901 −0.900 +1.801 +1.801 −0.902 −0.901 −0.901 −0.901

− +0.007 +0.007 +0.007 −0.034 −0.032 −0.016 −0.016 −0.004 −0.005 +0.002 +0.002 +0.001 +0.002 −0.002 −0.002 0 +0.001 +0.001 +0.001

O

0.96

+3.32

−1.010

Ca F

1.01 0.67

−0.31 −0.63

+1.718 −0.945

F

0.78

−0.09

−0.902

Ca

0.58

−0.27

+1.802

F

0.37

−0.33

−0.902

2 3

no. 2

1

2 3

ΔQ (e) −

−0.085 −0.043

0

−0.001 0

a

Positive signs in Z-columns correspond to outward atomic displacements (toward the vacuum). The directions of atomic displacements in the XYplane are indicated in Figure 6. ΔQ(e) labels the change in the effective charge compared to perfect CaF2 crystal (QCa = +1.803 e, QF = −0.902 e). The symbols in atom columns are defined in Figure 6.

60, 58, and 54 me, respectively. The bond populations between oxygen and hydrogen for other Configs are all 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 (458 me) and Ba(OH)2 (434 me) crystals, the covalency of surface OH− impurities is also much (\) stronger. For the OH− full-covered configuration, i.e., Config HOfull , − the surface effect on the strengthening OH -covalency is not quite pronounced, whereas the bond population equals 512 me, still being much larger than that in Ca(OH) 2 (458 me). 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. To investigate the surface effect on the optical band gaps, we studied the band structures of the surface OH−-impurity systems. The theoretical optical band gaps for all the (111)unoriented configurations are collected in Table 7, and the band structure of Config HO11(\) is shown in Figure 7. From Table 7, we can conclude that the surface effect reduces the VB → CB gaps, which are around 11.1−11.5 eV and smaller than that in the bulk cases (11.17, 11.32, and 11.85 eV for Configs OH(111), HO(111), and OH(100) respectively). The O → H gaps, i.e., the first possible optical absorption, for most of the (\) configurations except Config OH11 , are larger than the corresponding gaps in the bulk cases (9.04, 8.99, and 9.04 eV for Configs OH(111), HO(111), and OH(100), respectively). (\) (\) and OH22 , the O → H gaps Especially for Configs HO12 are larger by around 0.3 eV. Further analysis of the band gaps shows that for most of the surface OH−-impurity configurations,

Table 6. Effective Charges (e) and Bond Populations (me) of Surface OH− Impurities for All the (111)-Unoriented Configurations HO(\)

OH(\)

sublayer

O

H

O−H

O

H

O−H

11 12 21 22 full

−1.025 −1.007 −1.004 −1.003 −1.010

+0.280 +0.278 +0.283 +0.280 +0.239

+546 +494 +496 +494 +512

−1.003 −1.032 −1.004 −1.023 −1.017

+0.272 +0.290 +0.280 +0.285 +0.278

+490 +544 +498 +540 +492

electron transfer regarding the first-layer atoms is considerable. Around −0.160 e localized on the fluorine sublayer of the first layer (including the six fluorine atoms and one OH− impurity) is attracted by the three Ca atoms and six F atoms at the second and third sublayers. Tables 6 and 5 also list the results of effective charge calculations for the OH− full-covered configurations. The (\) OH− charge for Config HOfull is −0.771 e, being much larger than that of the bulk case by 0.049 e, and effective charges of −1.010 and +0.239 e are localized on the O and H, respectively. Around −0.085 and −0.043 e localized on the surface OH− transfers downward to the nearest Ca and F, respectively. Additionally, we (\) compared Config HOfull with Ca(OH)2 for the atomic effective charges and geometrical structures. The OH− charge of −0.781 e (\) (−0.771 e). The H− in Ca(OH)2 is close to that of Config HOfull (\) O−Ca angles in Ca(OH)2 (around 118°) and Config HOfull (around 113°) are also closed. Therefore, we can consider the fullcovering OH− as a piece of (CaOH)+ membrane filmed on the CaF2 surface. Table 6 also lists the bond populations for the surface OH−impurity and full-covered systems. We found that the OH− (\) covalencies for Configs HO11(\) (546 me), OH12 (544 me), and (\) OH22 (540 me) are much stronger than that of the bulk case by 6397



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Table 7. Direct Optical Band Gaps (eV) (Γ → Γ) of the Surface OH− for the 10 (111)-Unoriented Configurations gaps

HO11(\)

(\) HO11

(\) HO12

(\) HO12

(\) HO21

(\) HO21

(\) HO22

(\) HO22

(\) HOfull

(\) HOfull

O1 → H O2 → H O1 → CB O2 → CB VB → CB

9.23 9.24 9.79 9.80 11.31

8.97 8.98 9.46 9.47 11.09

9.37 9.38 9.77 9.78 11.0

9.21 9.21 9.86 9.86 11.36

9.19 9.22 9.76 9.79 11.08

9.23 9.24 9.96 9.97 11.16

9.26 9.26 9.88 9.88 11.08

9.32 9.34 10.06 10.08 11.46

7.89 7.89 9.36 9.36 11.10

8.75 8.76 9.83 9.84 11.32

Figure 7. Calculated B3PW band structures for Configs HO11(\) (left) (\) (right). and HOfull Figure 8. Total and projected DOS for Config HO11(\).

the occupied defect levels induced by O atoms move downward around 0.1−0.3 eV (toward VB) with respect to the bulk cases, leading to widening of the O → H gaps. From Figure 7, we also found that the empty defect band induced by H atoms is very close to the CB bottom and there is nearly no separated H band, which almost superposes with the CB. Unlike the surface OH−-impurity systems, the O → H gaps for the OH− fullcovered systems are narrower than that of the bulk case by (\) (\) around 1.1 and 0.3 eV for Configs HOfull and OHfull , respectively. (\) Especially for Config HOfull , the O → H gap reduces to 7.89 eV, being much smaller than the relevant gap of 9.04 eV in the bulk case. It is mainly due to the downward shift of the unoccupied H band, which moves toward the O bands by around 1 eV, as we can see Figure 7. To further study the electronic structure and electron transitions in a surface OH−-impurity system, we calculated the DOS of Config HO11(\), as we can see in Figure 8. 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 (111)-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 cases, 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 (see Figure 8).

C. Formation of OH− Impurities. Finally, we studied the formation of OH− impurities in CaF2. We computed the formation energy of the OH− impurity in CaF2 crystal. In the supercell calculation for an isolated OH−, the formation energy of a neutral (the charge of total supercell is neutral) OH− impurity in CaF2 could be expressed as follows −

(OH ) (iso) − E formation = E F(iso) − + E(OH ) − EOH− − E(perfect) (1) (iso) EF−

(iso) EOH−

where and are the energies for isolated fluorine and hydroxyl ions and E(OH−) and E(perfect) are the total energies of the defective crystal containing a OH− impurity and the perfect crystal, respectively. Our calculated OH−-impurity formation energy equals −1.00 eV, indicating that the total energy of a OH− -impurity system and an isolated F− is lower than the total energy of a perfect CaF2 crystal and an isolated OH−. It implicates that isolated hydroxyls are favorite to substitute fluorine ions in CaF2 crystal. According to our previous (\) discussion, the surface OH− impurities with Config HO11 have the lowest energy, which means that the hydroxyl adsorption on the CaF2 surface is favorable energetically. On the other hand, the formation of OH− impurities in CaF2 crystal may also be due to the aggregation of separated oxygen and hydrogen impurities. To verify this aggregation, we calculated the association energy, defined as the energy difference between the remote oxygen and hydrogen impurities, and the OH− impurity. The corresponding value is +6.12 eV. With this definition, the positive sign indicates stable aggregation. In this formation mode, there should be isolated oxygen and hydrogen impurities in CaF2 crystal. Similar to the calculation on the formation energy of the OH− impurity in CaF2 crystal, we also calculated the formation energies of the oxygen and hydrogen 6398



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induced by OH− impurities. One is two superposed occupied O bands mainly consisting of the O p orbitals, located above the VBs, and the other is an empty H band to which the H s orbitals do the major contribution, almost superposing with the CBs. Because of the surface effect, the O bands move downward, toward the VBs 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. Finally, we investigated the formation of OH− impurities in CaF2. The calculation on the formation energy of the OH− impurity shows that isolated hydroxyls are favorite to substitute fluorine ions and adsorb on the surface energetically. On the other hand, the formation of OH− impurities in CaF2 may also be due to the aggregation of separated oxygen and hydrogen impurities. The formation of oxygen impurities is favorable, whereas that of hydrogen impurities is unfavorable energetically. So, we concluded that oxygen does the primary contribution to the formation of OH− impurities in CaF2, and if we can control the concentration of the oxygen atoms near the surface, the formation of OH− impurities could be avoided in CaF2 crystal.

impurities in CaF2. For the oxygen impurity, the formation energy equals −0.71 eV. The negative sign indicates the stability of oxygen replacing fluorine in CaF2. We also investigated the oxygen impurity located near the (111) CaF2 surface. According to our calculation, the energy of the oxygen located at the surface has the smallest value, indicating a trend of the oxygen impurity located near the surface. The total energies of the oxygen impurity at the second, third, and fourth fluorine sublayers are larger than that for the first fluorine sublayer by 1.14, 1.24, and 1.16 eV, respectively. Additionally, for the hydrogen impurity, the formation energy is +0.33 eV. Unlike the oxygen case, the formation of a hydrogen impurity in CaF2 needs extra energy. Further, according to our calculation regarding a hydrogen atom added on the CaF2 surface, the hydrogen atom has a trend of separating from the surface. Here, we can summarize that oxygen does the primary contribution to the formation of OH− impurities in CaF2. Isolated oxygen atoms surrounding CaF2 adsorb on the surface easily, and then, the oxygen impurities trap the hydrogen atoms near the surface, forming the OH− impurities. So, if we can control the concentration of the oxygen atoms near the surface, the formation of OH− impurities could be avoided in CaF2 crystal.

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AUTHOR INFORMATION

Corresponding Author

IV. CONCLUSIONS We applied the first-principles approach within the hybrid DFT-B3PW scheme to calculations on OH− in CaF2. Three bulk configurations including Configs OH(111), HO(111), and OH(100), and 16 surface configurations including 8 (111)oriented and 8 (111)-unoriented OH− impurities were studied. For the bulk case, Config OH(111), in which the hydroxyl orients along the (111) axis and the oxygen occupies a regular fluorine site, is the energetically most favorable configuration. (\) For the surface case, we found that Config HO11 , in which the − OH is located at the upper fluorine sublayer of the first surface layer, H lies above O obliquely, and the obliquity is around 3.2°, is the most stable configuration for the surface OH−impurity systems. We also performed calculations on the (111) (\) CaF2 surfaces full covered by OH−. Config HOfull has the − lowest total energy among the four OH full-covered configurations, and the deviation angle equals around 2.2°. The lengths of surface OH− impurities for all the configurations are around 0.96−0.98 Å, being close to that in the bulk cases (0.95−0.97 Å), as well as in water molecule and 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. Effective charge analysis shows that the OH− charge equals around −0.722 e, being much smaller than the fluorine (substituted by the OH−) charge (−0.902 e) in perfect CaF2 crystal, and some charges localized on the neighbor atoms (especially for the nearest calcium atoms) transfer inward to the OH−. Because of the surface effect, the charges of the surface OH− impurities are larger than those of the bulk cases for most of the surface OH− configurations. 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 OH−impurity systems demonstrate that there are two defect levels

*E-mail address: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS H.S. was supported by NSFC Grant No. 11004008. R.I.E. was supported by ESF Grant No. 2009/0202/1DP/ 1.1.1.2.0/APIA/VIAA/141.

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Ab Initio Calculations of Hydroxyl Impurities in CaF2 - The Journal of

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