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Ab initio lattice relaxation and electronic structures of LiYF4 crystals containing VF color center
ARTICLE IN PRESS Physica B 404 (2009) 1053–1057
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Ab initio lattice relaxation and electronic structures of LiYF4 crystals containing VF color center Jigang Yin, Qiren Zhang , Tingyu Liu, Xiaofeng guo, Min Song, Xien Wang, Haiyan Zhang College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
a r t i c l e in fo
abstract
Article history: Received 29 June 2008 Received in revised form 27 September 2008 Accepted 31 October 2008
The electronic structures of perfect LiYF4 and the LiYF4 containing lithium vacancy V Li with the lattice structure optimized are studied within the framework of the density functional theory. By analyzing the lattice relaxation and electronic structure of the LiYF4 containing V Li we can reasonably believe that once V Li is formed in LiYF4 crystal, its compensating hole will turn out to be shared by two F nearest to VLi forming a diatomic fluoride molecular ion (F2 ) perturbed by VLi, or to say VF color center. According to the molecular-orbital linear combination of atomic orbital (MO-LCAOs) theory, compared to the alkali halides, e.g. LiF, the F 2 in VF center in LiYF4 peaks at about 337 nm, which is in agreement with the experimental results. & 2008 Elsevier B.V. All rights reserved.
PACS: 61.72.Ji 61.72.Bb 71.15.Mb Keywords: LiYF4 crystal Absorption band Lattice relaxation VF color center ABINIT
1. Introduction Considering the high technological importance of LiYF4 (YLF), it is not surprising, that during the last years, it has been the subject of many experimental and theoretical studies [1–5]. Certain aspects of this research recently gained large interest in the context of the use of YLF as an optical material for the deep ultraviolet (DUV) and vacuum ultraviolet (VUV) spectral regions. Many alkali halides and fluorides provide an attractive medium for color center research because of the ease with which they can be grown in reasonably pure single-crystal form and because they may be colored by ionizing radiations. 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 concentration of defects in a material so as to tune its properties in a desired manner to generate different behavior. YLF could become an important optical material if one could avoid or, at least, control the photo-induced defect formation, which so far in applications degrades its optical quality. Therefore, it is important to understand the nature of defects in YLF.
The experiment of pure YLF single crystal under gamma ray irradiation has been performed by Louis et al. [6]. The irradiated crystal exhibits five absorption spectrum peaks at 268, 337, 420, 530 and 640 nm. Two kinds of intrinsic color center have been observed in YLF by electron spin-resonance techniques. One is an X2-like center, whose resonance has been reported by Renfro et al. [7]. The other is the F center, an electron trapped in an anion vacancy, whose resonance has been found by Deshpande et al. [8]. As in the case of other fluorides for example in LiF [9,10], gamma ray irradiation-induced absorption spectrum of YLF supports the idea that several kinds of color centers are related to the lithium vacancy (V Li), however, which has seldom been discussed yet. This work reports our study on the electronic structure of perfect YLF and the YLF containing V Li with the lattice structure optimized are studied within the framework of the density functional theory (DFT). In this paper, the ab initio calculation (ABINIT package) is employed.
2. Computational model and method 2.1. Computational model
Corresponding author. Tel.: +86 021 55274943; fax: +86 021 55274057.
E-mail address: [email protected] (Q. Zhang). 0921-4526/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2008.10.052
The tetragonal cell belongs to the space group I4I/a with four formula units per cell [11,12]. The crystal is birefringent since it
ARTICLE IN PRESS 1054
J. Yin et al. / Physica B 404 (2009) 1053–1057
Table 1 The distances between ions before and after optimization.
Y
System
VLiLi (A˚)
VLiF (A˚)
VLiY (A˚)
Pre-optimized
3.7252
1.897
3.6514 3.7252
Optimized
3.5643
1.905 1.907 1.574 1.576
3.6414 3.7187
Li F Table 2 Calculated properties of perfect YLF crystal. Property
z
Calculated
Experimental Ref. [15]
Ref. [16]
5.171 10.748
5.16 10.74
Lattice energy (Ha/formula) LiYF4 98.1348 Lattice parameters (A˚) a¼b c
5.164 10.741
x
y Fig. 1. Structure of the LiYF4.
has a scheelite structure as shown in Fig. 1. The as-grown crystal contains a significant amount of rare-earth impurities so the structure for a pure YLF may be slightly different. The Li ion has four and the Y ion has eight nearest-neighbor (NN) F ions. The two Y–F NN distances of 2.244 and 2.297 A˚ are much larger than the single Li–F NN distance of 1.897 A˚ [13].
Density (g cm3)
3.957
3.98
4.00
Interatomic distance (A˚) Li–F Y–F Y–F F–F F–F F–F F–F Li–F F–F
1.8975 2.2437 2.3043 2.6142 2.7815 2.7820 2.8523 2.9334 3.0516
1.89 2.24 2.29 2.60 2.75 2.76 2.82 2.90 2.95
1.89 2.24 2.29 2.59 2.74 2.76 2.83 2.89 2.95
2.2. Computational method All ab initio calculations were performed within the framework of the DFT. We use the ABINIT package [14], based on pseudopotentials and plane waves. It relies on an efficient fast Fourier transform algorithm for the conversion of wave functions between real and its reciprocal space, on the adaptation to a fixed potential of the band-by-band conjugate-gradient method and on a potential-based conjugate-gradient algorithm for the determination of the self-consistent potential. In order to access to the real gap, we combine the new generated pseudopotentials and the pseudopotentials of the Troullier–Martins type in the local density approximation (LDA). The equilibrium parameters were computed using 8 8 8 K-point mesh in Brillouin zone, and plane-wave cut-off kinetic energy was 40 Hartree (about 1088.44 eV). It is necessary to optimize the lattice structure before calculating the electronic structures of the crystal since the existence of fluorine vacancy V Li would cause lattice distortion. For geometry relaxation we combine the minimizations of conjugate-gradient energy and the force acting on ions were less than 1.0 104 eV/A˚ and the energy difference between two consecutive cycles was less than 1.0 1010 Hartree. The maximal permitted scaling of the lattice parameters is 1.05 when the cell shape and dimension is varied. Once the defect is created in cluster, it would change the total energy of the cluster. Since there are many ions in cluster, the total energy of the cluster would be different, depending on which kind of the defect forms. The most probable defect that might appear
Table 3 The total energy of cluster containing the different defects. Kinds of defect
Energy (Ha)
Kinds of defect
Energy (Ha)
Perfect V3+ Y
392.53923618 101.97249965
V Li V+F
400.76925129 395.34679243
should correspond to the lowest total energy of the cluster. Therefore, the conjugate gradient energy minimization method is used to optimize lattice, in the procedure of the lattice relaxation, to keep the total energy of the cluster low. Comparing with the calculated results, it is found that the total energy is the lowest when the V Li is appearing. The calculated results are listed in Table 1.
3. Results and discussion 3.1. Structure optimization The calculated results of lattice parameters and interatomic distances are listed in Table 2. They are seen to match fairly, with the experimentally observed values, justifying the viability of our model to correctly account for the further calculations. The results of the optimized lattice structure are listed in Table 3. Compared with the perfect YLF structure, the optimized
ARTICLE IN PRESS J. Yin et al. / Physica B 404 (2009) 1053–1057
1055
1200
1
Total
800 EF
400
4 0 450
Y
4d
300 PDOS
150
4p
0 150
3
Li 2s
100 2s
50 0
2
750
VLi-
F
hole
F
2s
2p
500 250
Fig. 2. Scheme of the F ions around the V Li, the small hollow circle is a hole shared by two F3,4 ions forming a diatomic molecular ion F 2.
lattice structures containing V Li exhibit the following characteristics: (1) the cations (Li+ and Y3+) nearest to the V Li slightly shift + towards the V Li and the displacement of the Li is larger than that of the Y3+; (2) each V Li is surrounded by four neighboring F . The lattice relaxation results show that two F ions shifted towards the V Li, while other F ions shifted outwards from the VLi. In order to be distinguished, they are labeled from 1 to 4, as shown in Fig. 2. The distortion of the structure of the YLF is obvious. This distortion will significantly affect the electronic structures of the YLF crystal with lithium vacancy. Once the lithium vacancy V Li is created in YLF, there would be two types of potentials caused by the fluorine vacancy V Li: one is the electrical potential caused V Li, the other is the mechanical potential originated from the structure deficiency of the Li ion. The latter attracts all the ions towards the V Li, while the former only attracts the cations Li+ and Y3+ nearest to the V Li and simultaneously repulses the anions F nearest to the V Li. Since the electrical forces are larger than the mechanical ones, the cations Li+ and Y3+ shift towards the V Li. This coincides with the calculated results. The anions F should have been repulsed by the V Li and shifted outwards. However, two F3,4 ions were attracted and shifted towards V Li, while F1,2 ions are repulsed and shifted outwards. This seems to be contradicted with the physical analyses. In order to explain this abnormal phenomenon, the electronic structure of the perfect YLF and the YLF containing V Li should be calculated in detail. The densities of states are calculating by Tetrahedron method. The Gaussian smearing parameter is chosen as 0.01 Hartree in calculating the total densities of states.
3.2. Electronic structure The electronic structures are calculated in the region from 30 to 30 eV. The total density of states (TDOS) and partial densities of states (PDOS) of the perfect YLF crystal are given in Fig. 3. Comparing the TDOS and PDOS, it is easy to find that the ionic nature of YLF is very obvious. First, the gap is much larger and there are very little PDOS components from Li and Y ions in the
2p
0 -30
-20
-10
0 Energy(eV)
10
20
30
Fig. 3. Total densities of states and partial densities of states for the perfect LiYF4 crystal.
upper valence band. Most of the Li 2s valence electron and to a lesser extent, the two Y 5s electrons and one Y 4d electron have been transferred to F. The upper valence band derived from F 2p is very narrow, only 4.02 eV. The semi-core-like Y 4p levels interact rather strongly with the deep F 2s levels to produce two segments of bands centered at 28 and 22 eV in the deep valence band. The lower one is dominated by Y 4p states and the higher one by the F 2s states. The lower part of the conduction band in YLF is mainly derived from the Y 4d and F 2p orbital. Once the V Li is created in YLF, it needs a positive charge to maintain the local electrical neutrality. The main problem is what may trap the hole to compensate the electrical negativity of the V Li? So TDOS and the PDOS of YLF crystal containing VLi are also calculated. The calculated results are shown in Fig. 4. Compared with the perfect YLF, the top of valence band and the bottom of conduction band are still mainly composed of the 2p state of F and the 2s state of Li. The main difference between perfect crystal and defect crystal is the energy gap of the defect crystal being narrower than that of the perfect crystal and there is a new electronic state peak appearing within the forbidden band. The calculation indicated that the new electronic state peak is attributed to the 2p states of the F ions. According to the Fermi–Dirac distribution, the average number of electrons at the state is 1 f ¼ m=kT þ1 e
(1)
herein m is the Fermi level. From Eq. (1), it can be concluded that electrons near to the Fermi level could be easily excited to a higher level and hence leave a hole at the site. Therefore, the F ions near to V Li would more easily lose electrons or trap holes to compensate for V Li. The question is which fluorine ions nearest to the V Li may share a hole to compensate the electrical negativity of V Li? According to the calculated results, as shown in Fig. 5, the partial
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J. Yin et al. / Physica B 404 (2009) 1053–1057
1200 1000 800 600 400 200 0
E EF
450 300 PDOS
150
π
4p
0
300 2s
0 2p
750
F
2s
500
2p
250 0 -30
-20
-10
0 Energy(eV)
10
20
30
Fig. 4. Total densities of states and partial densities of states of LiYF4 containing V Li.
160 F32p
120 80
EF
40 0 120
F42p
80 40 0 120
F12p
80 40 0 120
F22p
80 40 0 -30
-20
-10
0 Energy(eV)
10
2
∏g
Fig. 6. Energy level scheme of F 2.
2s
150
∏u
2 + ∑u
Li
450
2
σ
Y
4d
PDOS
2 + ∑g
Total
20
30
Fig. 5. Scheme of the 2p states of the F(1–4) ions.
densities of four F ions nearest to the V Li can be distinguished for labeling from 1 to 4. From Fig. 5, it can be seen that the new electronic state peak within the forbidden band is attributed to the 2p states of the F3 and F4 ions. Comparing the distances
between the F(1–4) ions before and after optimization. It is found that the distance between the F3 and F4 becomes 1.4421 A˚, which ˚ tends to the chemical bond length of F–F in F 2 (1.41 A) [17]. Compared to the formation of hole centers in alkali halides, once a negative alkali ion vacancy is formed, the compensator is a hole shared by two halide ions nearest to the alkali ion vacancy forming a halide diatomic molecular ion rather than being trapped by one halide ion nearest to the alkali vacancy forming a halide atom [18]. It might be believable that the hole is shared by the F3 and F4 ions, forming a diatomic molecular ion F 2 rather than trapped by a single F in YLF–V Li crystals to compensate for V Li. The reaction formula can be written as 2F þ h ¼ F 2 According to the definition of color centers in alkali halides [18], this hole center is defined by VF. According to the molecular-orbital linear combination of atomic orbital (MO-LCAOs) theory [18], the configuration energy level scheme of the F 2 molecular ion is as illustrated in Fig. 6. Only 2 2 þ the transitions from the ground state 2 Sþ u to Pg and Sg are parity allowed. The absorption features of F2 exhibit two bands 2 þ named the s band corresponding to the 2 Sþ u Sg transition and 2 þ 2 the p band corresponding to the Su Pg transition. The 2 transition probability from 2 Sþ u Pg is much smaller than that 2 þ from 2 Sþ S . This results in the intensity of the longer u g wavelength side (p band) being much smaller than that of the s band, and usually the p band can be neglected in the absorption spectrum of the molecular ion F 2 . In most alkali halides the intensity ratio of the two bands is larger than about 200 [18]. The s band absorbs light with its E vector parallel to the symmetric axis of F 2 ; however, the p band absorbs light with its E vector perpendicular to the symmetric axis of F 2 . Compared to the alkali halides, e.g. LiF [18], VF center is the independent fluorine diatomic molecular ions F 2 perturbed by a lithium vacancy. The amount of outer 2p orbital electron in the fluorine molecular ion F 2 is 11. The amount of outer electron occupying 2p orbital in the fluorine molecular ions F 2 of VF in YLF is 11. Thus, VF in YLF would have similar absorption features with the VF center in alkali halides. The s band of F 2 in VF center in LiF peaks at about 340 nm [9,10,18]. Therefore the s band of F 2 in VF center YLF peaks at about 340 nm too, which is in agreement with the experimental results. Thus the 337 nm band of the YLF crystal is attributed to the VF center.
4. Conclusions The electronic structures of perfect LiYF4 (YLF) and the YLF containing V Li with the lattice structure optimized are studied
ARTICLE IN PRESS J. Yin et al. / Physica B 404 (2009) 1053–1057
within the framework of the DFT. By analyzing the lattice relaxation and electronic structure of the YLF containing V Li we can reasonably believe that once V Li is formed in YLF crystal, its compensating hole will turn out to be shared by two F nearest to V Li forming a diatomic fluoride molecular ion (F2 ) perturbed by VLi, or to say VF color center. According to the molecular-orbital linear combination of atomic orbital (MO-LCAOs) theory, compared to the alkali halides, e.g. LiF, the F 2 in VF center in YLF peaks at about 337 nm. The calculated results agree well with the experimental results. For the YLF crystal, it would be desirable to study different rare-earth ions at the Y site since this is the main experimental interest. Such calculations will be much more demanding because the multiplet structure of rare-earth ions in a crystal field is much more complex than that of a transition-metal ion. It would also be of interest to see if excited-state absorption exists in this crystal [19]. Symmetry allowed transitions from the doping levels in the gap to excited states either in the gap or to the conduction band have implications on the durability and stability of laser pumping, and also offer potential avenue for up-conversion channels in laser operation. Such studies can lead to a better understanding of the factors governing laser degradation and eventually improve their performances. Another area of significant interest is that the same fluoride crystals can be used as phosphor materials with very practical applications in the mercury-free fluorescent lamps and color plasma display panels [20]. In YLF, and in other laser crystals, one would eventually like to understand the roles of defects and the effect of ion–ion interaction based on a more
1057
realistic first-principles approach. Therefore, we expect fundamental studies in the fluoride laser crystals will be an active area of research in years to come.
References [1] A.A. Kaminskii, Laser Crystals, Springer, Berlin, 1990. [2] G.J. Quarles, L. Esterowitz, G.M. Rosemblat, R. Uhrin, R.F. Belt, Proc. Adv. Solid State Lasers 13 (1992) 306. [3] J.S. Griffith, The Theory of Transition Metal Ions, Cambridge University Press, London, 1961. [4] C.J. Balhausen, Introduction to Ligand Field Theory, McGraw Hill, New York, 1962. [5] S. Sugano, Y. Tanabe, H. Kamimura, Multiplets of Transition Metal Ions in Crystals, Academic, New York, 1970. [6] M. Louis, E. Simoni, S. Hubert, J.Y. Gesland, Opt. Mater. 4 (1995) 657. [7] G.M. Renfro, L.E. Halliburton, W.A. Sibley, R.F. Belt, J. Phys. C 13 (1980) 1941. [8] S.P. Deshpande, S.J. Dhoble, W.K. Pokale, B.T. Deshmukh, R.B. Pode, T.K. Gundurao, Nucl. Instrum. Methods Phys. Res. B 134 (1998) 385. [9] W. Kanzig, J. Phys. Chem. Solids 17 (1960) 80. [10] W. Kanzig, J. Phys. Chem. Solids 17 (1960) 88. [11] E. Garcia, R.R. Ryan, Acta Crystallogr. C 49 (1993) 2053. [12] A.V. Goryunov, I. Popov, Russ. J. Inorg. Chem. 37 (1992) 126. [13] W.Y. Ching, Yong-Nian Xu, Phys. Rev. B 63 (2001) 115101. [14] X. Gonze, et al., Comput. Mater. Sci. 25 (2002) 478. [15] N.M. Khajdukov, A.V. Goryunov, P.P. Fedorov, A.I. Popov, Mater. Res. Bull. 27 (1992) 213. [16] E. Garcia, R.R. Ryan, Acta Crystaliogr. Sect. C 49 (1993) 2053. [17] H. Shen, Inorganic Chemistry, Chemistry Industry Press, 2004. [18] S.G. Fang, Q.R. Zhang, Physics of Colour Centres in Crystal, Shanghai Jiaotong University Press, Shanghai, 1989 (in Chinese). [19] B.K. Brickeen, W.Y. Ching, J. Appl. Phys. 88 (2000) 3073. [20] S. Shionoya, W.M. Yen (Eds.), Phosphor Handbook, CRC, Boca Raton, 2000.
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Physica B journal homepage: www.elsevier.com/locate/physb
Ab initio lattice relaxation and electronic structures of LiYF4 crystals containing VF color center Jigang Yin, Qiren Zhang , Tingyu Liu, Xiaofeng guo, Min Song, Xien Wang, Haiyan Zhang College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
a r t i c l e in fo
abstract
Article history: Received 29 June 2008 Received in revised form 27 September 2008 Accepted 31 October 2008
The electronic structures of perfect LiYF4 and the LiYF4 containing lithium vacancy V Li with the lattice structure optimized are studied within the framework of the density functional theory. By analyzing the lattice relaxation and electronic structure of the LiYF4 containing V Li we can reasonably believe that once V Li is formed in LiYF4 crystal, its compensating hole will turn out to be shared by two F nearest to VLi forming a diatomic fluoride molecular ion (F2 ) perturbed by VLi, or to say VF color center. According to the molecular-orbital linear combination of atomic orbital (MO-LCAOs) theory, compared to the alkali halides, e.g. LiF, the F 2 in VF center in LiYF4 peaks at about 337 nm, which is in agreement with the experimental results. & 2008 Elsevier B.V. All rights reserved.
PACS: 61.72.Ji 61.72.Bb 71.15.Mb Keywords: LiYF4 crystal Absorption band Lattice relaxation VF color center ABINIT
1. Introduction Considering the high technological importance of LiYF4 (YLF), it is not surprising, that during the last years, it has been the subject of many experimental and theoretical studies [1–5]. Certain aspects of this research recently gained large interest in the context of the use of YLF as an optical material for the deep ultraviolet (DUV) and vacuum ultraviolet (VUV) spectral regions. Many alkali halides and fluorides provide an attractive medium for color center research because of the ease with which they can be grown in reasonably pure single-crystal form and because they may be colored by ionizing radiations. 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 concentration of defects in a material so as to tune its properties in a desired manner to generate different behavior. YLF could become an important optical material if one could avoid or, at least, control the photo-induced defect formation, which so far in applications degrades its optical quality. Therefore, it is important to understand the nature of defects in YLF.
The experiment of pure YLF single crystal under gamma ray irradiation has been performed by Louis et al. [6]. The irradiated crystal exhibits five absorption spectrum peaks at 268, 337, 420, 530 and 640 nm. Two kinds of intrinsic color center have been observed in YLF by electron spin-resonance techniques. One is an X2-like center, whose resonance has been reported by Renfro et al. [7]. The other is the F center, an electron trapped in an anion vacancy, whose resonance has been found by Deshpande et al. [8]. As in the case of other fluorides for example in LiF [9,10], gamma ray irradiation-induced absorption spectrum of YLF supports the idea that several kinds of color centers are related to the lithium vacancy (V Li), however, which has seldom been discussed yet. This work reports our study on the electronic structure of perfect YLF and the YLF containing V Li with the lattice structure optimized are studied within the framework of the density functional theory (DFT). In this paper, the ab initio calculation (ABINIT package) is employed.
2. Computational model and method 2.1. Computational model
Corresponding author. Tel.: +86 021 55274943; fax: +86 021 55274057.
E-mail address: [email protected] (Q. Zhang). 0921-4526/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2008.10.052
The tetragonal cell belongs to the space group I4I/a with four formula units per cell [11,12]. The crystal is birefringent since it
ARTICLE IN PRESS 1054
J. Yin et al. / Physica B 404 (2009) 1053–1057
Table 1 The distances between ions before and after optimization.
Y
System
VLiLi (A˚)
VLiF (A˚)
VLiY (A˚)
Pre-optimized
3.7252
1.897
3.6514 3.7252
Optimized
3.5643
1.905 1.907 1.574 1.576
3.6414 3.7187
Li F Table 2 Calculated properties of perfect YLF crystal. Property
z
Calculated
Experimental Ref. [15]
Ref. [16]
5.171 10.748
5.16 10.74
Lattice energy (Ha/formula) LiYF4 98.1348 Lattice parameters (A˚) a¼b c
5.164 10.741
x
y Fig. 1. Structure of the LiYF4.
has a scheelite structure as shown in Fig. 1. The as-grown crystal contains a significant amount of rare-earth impurities so the structure for a pure YLF may be slightly different. The Li ion has four and the Y ion has eight nearest-neighbor (NN) F ions. The two Y–F NN distances of 2.244 and 2.297 A˚ are much larger than the single Li–F NN distance of 1.897 A˚ [13].
Density (g cm3)
3.957
3.98
4.00
Interatomic distance (A˚) Li–F Y–F Y–F F–F F–F F–F F–F Li–F F–F
1.8975 2.2437 2.3043 2.6142 2.7815 2.7820 2.8523 2.9334 3.0516
1.89 2.24 2.29 2.60 2.75 2.76 2.82 2.90 2.95
1.89 2.24 2.29 2.59 2.74 2.76 2.83 2.89 2.95
2.2. Computational method All ab initio calculations were performed within the framework of the DFT. We use the ABINIT package [14], based on pseudopotentials and plane waves. It relies on an efficient fast Fourier transform algorithm for the conversion of wave functions between real and its reciprocal space, on the adaptation to a fixed potential of the band-by-band conjugate-gradient method and on a potential-based conjugate-gradient algorithm for the determination of the self-consistent potential. In order to access to the real gap, we combine the new generated pseudopotentials and the pseudopotentials of the Troullier–Martins type in the local density approximation (LDA). The equilibrium parameters were computed using 8 8 8 K-point mesh in Brillouin zone, and plane-wave cut-off kinetic energy was 40 Hartree (about 1088.44 eV). It is necessary to optimize the lattice structure before calculating the electronic structures of the crystal since the existence of fluorine vacancy V Li would cause lattice distortion. For geometry relaxation we combine the minimizations of conjugate-gradient energy and the force acting on ions were less than 1.0 104 eV/A˚ and the energy difference between two consecutive cycles was less than 1.0 1010 Hartree. The maximal permitted scaling of the lattice parameters is 1.05 when the cell shape and dimension is varied. Once the defect is created in cluster, it would change the total energy of the cluster. Since there are many ions in cluster, the total energy of the cluster would be different, depending on which kind of the defect forms. The most probable defect that might appear
Table 3 The total energy of cluster containing the different defects. Kinds of defect
Energy (Ha)
Kinds of defect
Energy (Ha)
Perfect V3+ Y
392.53923618 101.97249965
V Li V+F
400.76925129 395.34679243
should correspond to the lowest total energy of the cluster. Therefore, the conjugate gradient energy minimization method is used to optimize lattice, in the procedure of the lattice relaxation, to keep the total energy of the cluster low. Comparing with the calculated results, it is found that the total energy is the lowest when the V Li is appearing. The calculated results are listed in Table 1.
3. Results and discussion 3.1. Structure optimization The calculated results of lattice parameters and interatomic distances are listed in Table 2. They are seen to match fairly, with the experimentally observed values, justifying the viability of our model to correctly account for the further calculations. The results of the optimized lattice structure are listed in Table 3. Compared with the perfect YLF structure, the optimized
ARTICLE IN PRESS J. Yin et al. / Physica B 404 (2009) 1053–1057
1055
1200
1
Total
800 EF
400
4 0 450
Y
4d
300 PDOS
150
4p
0 150
3
Li 2s
100 2s
50 0
2
750
VLi-
F
hole
F
2s
2p
500 250
Fig. 2. Scheme of the F ions around the V Li, the small hollow circle is a hole shared by two F3,4 ions forming a diatomic molecular ion F 2.
lattice structures containing V Li exhibit the following characteristics: (1) the cations (Li+ and Y3+) nearest to the V Li slightly shift + towards the V Li and the displacement of the Li is larger than that of the Y3+; (2) each V Li is surrounded by four neighboring F . The lattice relaxation results show that two F ions shifted towards the V Li, while other F ions shifted outwards from the VLi. In order to be distinguished, they are labeled from 1 to 4, as shown in Fig. 2. The distortion of the structure of the YLF is obvious. This distortion will significantly affect the electronic structures of the YLF crystal with lithium vacancy. Once the lithium vacancy V Li is created in YLF, there would be two types of potentials caused by the fluorine vacancy V Li: one is the electrical potential caused V Li, the other is the mechanical potential originated from the structure deficiency of the Li ion. The latter attracts all the ions towards the V Li, while the former only attracts the cations Li+ and Y3+ nearest to the V Li and simultaneously repulses the anions F nearest to the V Li. Since the electrical forces are larger than the mechanical ones, the cations Li+ and Y3+ shift towards the V Li. This coincides with the calculated results. The anions F should have been repulsed by the V Li and shifted outwards. However, two F3,4 ions were attracted and shifted towards V Li, while F1,2 ions are repulsed and shifted outwards. This seems to be contradicted with the physical analyses. In order to explain this abnormal phenomenon, the electronic structure of the perfect YLF and the YLF containing V Li should be calculated in detail. The densities of states are calculating by Tetrahedron method. The Gaussian smearing parameter is chosen as 0.01 Hartree in calculating the total densities of states.
3.2. Electronic structure The electronic structures are calculated in the region from 30 to 30 eV. The total density of states (TDOS) and partial densities of states (PDOS) of the perfect YLF crystal are given in Fig. 3. Comparing the TDOS and PDOS, it is easy to find that the ionic nature of YLF is very obvious. First, the gap is much larger and there are very little PDOS components from Li and Y ions in the
2p
0 -30
-20
-10
0 Energy(eV)
10
20
30
Fig. 3. Total densities of states and partial densities of states for the perfect LiYF4 crystal.
upper valence band. Most of the Li 2s valence electron and to a lesser extent, the two Y 5s electrons and one Y 4d electron have been transferred to F. The upper valence band derived from F 2p is very narrow, only 4.02 eV. The semi-core-like Y 4p levels interact rather strongly with the deep F 2s levels to produce two segments of bands centered at 28 and 22 eV in the deep valence band. The lower one is dominated by Y 4p states and the higher one by the F 2s states. The lower part of the conduction band in YLF is mainly derived from the Y 4d and F 2p orbital. Once the V Li is created in YLF, it needs a positive charge to maintain the local electrical neutrality. The main problem is what may trap the hole to compensate the electrical negativity of the V Li? So TDOS and the PDOS of YLF crystal containing VLi are also calculated. The calculated results are shown in Fig. 4. Compared with the perfect YLF, the top of valence band and the bottom of conduction band are still mainly composed of the 2p state of F and the 2s state of Li. The main difference between perfect crystal and defect crystal is the energy gap of the defect crystal being narrower than that of the perfect crystal and there is a new electronic state peak appearing within the forbidden band. The calculation indicated that the new electronic state peak is attributed to the 2p states of the F ions. According to the Fermi–Dirac distribution, the average number of electrons at the state is 1 f ¼ m=kT þ1 e
(1)
herein m is the Fermi level. From Eq. (1), it can be concluded that electrons near to the Fermi level could be easily excited to a higher level and hence leave a hole at the site. Therefore, the F ions near to V Li would more easily lose electrons or trap holes to compensate for V Li. The question is which fluorine ions nearest to the V Li may share a hole to compensate the electrical negativity of V Li? According to the calculated results, as shown in Fig. 5, the partial
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1200 1000 800 600 400 200 0
E EF
450 300 PDOS
150
π
4p
0
300 2s
0 2p
750
F
2s
500
2p
250 0 -30
-20
-10
0 Energy(eV)
10
20
30
Fig. 4. Total densities of states and partial densities of states of LiYF4 containing V Li.
160 F32p
120 80
EF
40 0 120
F42p
80 40 0 120
F12p
80 40 0 120
F22p
80 40 0 -30
-20
-10
0 Energy(eV)
10
2
∏g
Fig. 6. Energy level scheme of F 2.
2s
150
∏u
2 + ∑u
Li
450
2
σ
Y
4d
PDOS
2 + ∑g
Total
20
30
Fig. 5. Scheme of the 2p states of the F(1–4) ions.
densities of four F ions nearest to the V Li can be distinguished for labeling from 1 to 4. From Fig. 5, it can be seen that the new electronic state peak within the forbidden band is attributed to the 2p states of the F3 and F4 ions. Comparing the distances
between the F(1–4) ions before and after optimization. It is found that the distance between the F3 and F4 becomes 1.4421 A˚, which ˚ tends to the chemical bond length of F–F in F 2 (1.41 A) [17]. Compared to the formation of hole centers in alkali halides, once a negative alkali ion vacancy is formed, the compensator is a hole shared by two halide ions nearest to the alkali ion vacancy forming a halide diatomic molecular ion rather than being trapped by one halide ion nearest to the alkali vacancy forming a halide atom [18]. It might be believable that the hole is shared by the F3 and F4 ions, forming a diatomic molecular ion F 2 rather than trapped by a single F in YLF–V Li crystals to compensate for V Li. The reaction formula can be written as 2F þ h ¼ F 2 According to the definition of color centers in alkali halides [18], this hole center is defined by VF. According to the molecular-orbital linear combination of atomic orbital (MO-LCAOs) theory [18], the configuration energy level scheme of the F 2 molecular ion is as illustrated in Fig. 6. Only 2 2 þ the transitions from the ground state 2 Sþ u to Pg and Sg are parity allowed. The absorption features of F2 exhibit two bands 2 þ named the s band corresponding to the 2 Sþ u Sg transition and 2 þ 2 the p band corresponding to the Su Pg transition. The 2 transition probability from 2 Sþ u Pg is much smaller than that 2 þ from 2 Sþ S . This results in the intensity of the longer u g wavelength side (p band) being much smaller than that of the s band, and usually the p band can be neglected in the absorption spectrum of the molecular ion F 2 . In most alkali halides the intensity ratio of the two bands is larger than about 200 [18]. The s band absorbs light with its E vector parallel to the symmetric axis of F 2 ; however, the p band absorbs light with its E vector perpendicular to the symmetric axis of F 2 . Compared to the alkali halides, e.g. LiF [18], VF center is the independent fluorine diatomic molecular ions F 2 perturbed by a lithium vacancy. The amount of outer 2p orbital electron in the fluorine molecular ion F 2 is 11. The amount of outer electron occupying 2p orbital in the fluorine molecular ions F 2 of VF in YLF is 11. Thus, VF in YLF would have similar absorption features with the VF center in alkali halides. The s band of F 2 in VF center in LiF peaks at about 340 nm [9,10,18]. Therefore the s band of F 2 in VF center YLF peaks at about 340 nm too, which is in agreement with the experimental results. Thus the 337 nm band of the YLF crystal is attributed to the VF center.
4. Conclusions The electronic structures of perfect LiYF4 (YLF) and the YLF containing V Li with the lattice structure optimized are studied
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within the framework of the DFT. By analyzing the lattice relaxation and electronic structure of the YLF containing V Li we can reasonably believe that once V Li is formed in YLF crystal, its compensating hole will turn out to be shared by two F nearest to V Li forming a diatomic fluoride molecular ion (F2 ) perturbed by VLi, or to say VF color center. According to the molecular-orbital linear combination of atomic orbital (MO-LCAOs) theory, compared to the alkali halides, e.g. LiF, the F 2 in VF center in YLF peaks at about 337 nm. The calculated results agree well with the experimental results. For the YLF crystal, it would be desirable to study different rare-earth ions at the Y site since this is the main experimental interest. Such calculations will be much more demanding because the multiplet structure of rare-earth ions in a crystal field is much more complex than that of a transition-metal ion. It would also be of interest to see if excited-state absorption exists in this crystal [19]. Symmetry allowed transitions from the doping levels in the gap to excited states either in the gap or to the conduction band have implications on the durability and stability of laser pumping, and also offer potential avenue for up-conversion channels in laser operation. Such studies can lead to a better understanding of the factors governing laser degradation and eventually improve their performances. Another area of significant interest is that the same fluoride crystals can be used as phosphor materials with very practical applications in the mercury-free fluorescent lamps and color plasma display panels [20]. In YLF, and in other laser crystals, one would eventually like to understand the roles of defects and the effect of ion–ion interaction based on a more
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realistic first-principles approach. Therefore, we expect fundamental studies in the fluoride laser crystals will be an active area of research in years to come.
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