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Empirical relation between covalence and the energy position of the Ni2+ 1E state in octahedral complexes
Journal of Luminescence 148 (2014) 338–341
Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Empirical relation between covalence and the energy position of the Ni2 þ 1E state in octahedral complexes M.G. Brik a,n, A.M. Srivastava b, N.M. Avram c,d, A. Suchocki e,f a
Institute of Physics, University of Tartu, Riia 142, Tartu 51014, Estonia GE Global Research, One Research Circle, Niskayuna, NY 12309, USA c Department of Physics, West University of Timisoara, Bd. V. Parvan 4, Timisoara 300223, Romania d Academy of Romanian Scientists, Independentei 54, Bucharest 050094, Romania e Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland f Institute of Physics, Kazimierz Wielki University, Weyssenhoffa 11, 85-072 Bydgoszcz, Poland b
art ic l e i nf o
a b s t r a c t
Article history: Received 14 November 2013 Received in revised form 13 December 2013 Accepted 22 December 2013 Available online 31 December 2013
In this paper, a simple empirical equation that relates the energy of the spin-forbidden 3A2–1E transition qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of the octahedrally coordinated Ni2 þ ion with the recently introduced β1 ¼ ðB=B0 Þ2 þðC=C 0 Þ2 parameter
Keywords: Ni2 þ Covalence β1 parameter
is derived (B, C (B0, C0) are the Racah parameters of Ni2 þ ions in a crystal (free state), respectively). It is shown that the β1 parameter which simultaneously takes into account the reduction in both the Racah parameters B and C due to the nephelauxetic effect, is much more accurate in estimating the energy position of the Ni2 þ 1E state than the commonly used nephelauxetic ratio β¼ B/B0, which completely ignores the reduction in the values of the Racah parameter C when the transition metal ion is introduced in the solid. & 2013 Elsevier B.V. All rights reserved.
1. Introduction Fundamental investigations into crystals doped with the transition metal (TM) ions having unfilled 3d shell continue to be of interest due to their importance in commercial and technological applications [1–3]. As a rule, the spectra of these TM ions are characterized by spin-allowed broad emission bands, which open the possibility, for example, of obtaining tunable laser source. On the other hand, the spin-forbidden transitions of the TM ions are also of great importance. For example, the ruby laser operates on the 2Eg–4A2g emission transition of the Cr3 þ ion (3d3 electronic configuration). The same emission transition of the isoelectronic Mn4 þ ion finds application in the lighting industry [4,5]. The efficient green emission of one of the oldest lighting phosphor, ZnSiO4:Mn2 þ , arises from the spin-forbidden emission transition of the Mn2 þ ions (3d5 electronic configuration) [6]. If the energy separation between the spectral terms of ions with unfilled d-electron shell is considered, one has to keep in mind that there are ten independent interelectronic repulsion parameters (both Coulomb and exchange) [7]. On the other hand, such a large number of parameters simply cannot be extracted from the optical spectra of the TM ions, since the number of the experimental absorption and emission bands is always considerably smaller than 10. Luckily, there is a possibility to reduce this number
n
Corresponding author. Tel.: þ 372 7374751. E-mail address: brik@fi.tartu.ee (M.G. Brik).
0022-2313/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jlumin.2013.12.052
to three Racah parameters A, B and C. Moreover, if the energy levels of only d-electron configuration are concerned with, the A parameter can be further omitted, since it produces only an overall shift of all energy levels without changing the relative separation between them, It is a common practice nowadays that in a cubic crystal-field, the energy levels of any TM ion can be described by three main parameters: crystal-field strength Dq, which defines the crystal-field splitting, and two Racah parameters B and C, which determine the energy intervals between the free ion terms. While the energy of the spin-allowed transitions are largely determined by the crystal field strength Dq, as follows, for example, from the well-known Tanabe–Sugano diagrams [7], the energy of some spin-forbidden transitions of TM ions appears to be practically independent of the crystal-field strength. A good illustration of this statement is given in Fig. 1, where the Tanabe–Sugano diagram for a 3d8 ion in an octahedral crystal field is exhibited. Note that in this case, the energy separation between the ground state spin-triplet 3A2 and the first spin-singlet 1E state is independent of the crystal-field strength. This permits us to distinguish between two limiting cases: (i) weak crystal-field, where the first excited state 3T2 originates from the same 3F term as the ground state 3A2 and, (ii) strong crystal-field, where the first excited state is 1 E which arises from the 1D term of a free ion. The point of intersection of the 3T2 and 1E states serves as a separation between these two situations, as shown by a vertical dashed line in Fig. 1. This behavior of the 1E state suggests that only two Racah parameters B and C are needed to describe its energy position. It is well known that the values of these parameters in a crystal are
M.G. Brik et al. / Journal of Luminescence 148 (2014) 338–341
339
Table 1 The main spectroscopic parameters pertaining to the Ni2 þ 1Eg-3A2g transition in qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi various crystals. β1 ¼ ðB=B0 Þ2 þ ðC=C 0 Þ2 , B0 ¼ 1068 cm 1, C0 ¼4457 cm 1 [11].
E/B
C, β1 B, (cm 1) (cm 1)
Position of the 1E level
Crystal
Ref.
NiCl2 NiI2 NiBr2 Ca3Sc2Ge3O12 MgAl2O4 LiGa5O8 MgF2 AgCl KZnF3 MgO CsCdBr3 CsMgBr3 CsCdCl3 Al2O3 BaLiF3 MgGa2O4 NiCl2(H2O)4 ZAS glass KMgF3 MgBr2 LiNbO3 CdI2 RbCdF3 CdBr2 CdCl2 NiF2 CsMgCl3 CsMgBr3 CsMgI3 WO3–TeO2 glass
[12] [8] [8] [13] [14] [15] [11] [11] [16] [17] [18] [14] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [26] [31] [32] [28] [28] [33]
Calculated Observed Calc. (Eq. (1))
Strong crystal field Weak crystal field
Dq/B Fig. 1. Tanabe–Sugano diagram for an ion with the 3d8 electron configuration in an octahedral crystal field.
reduced relative to their “free ion” counterparts due to the socalled nephelauxetic effect [8]. Since the reduction in the Racah parameters is more pronounced in highly covalent crystals, one may expect the 1E state to be energetically lower in covalently bonded systems than in ionic crystals where the Racah parameters are closer to their free ion values. Recently, Brik and Srivastava have introduced a new parameter (β1) in the spectroscopic properties of the Mn4 þ ion [9,10]. They demonstrated a linear relation between the energetic position of qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the Mn4 þ 2Eg state and the new parameter β1 ¼ ðB=B0 Þ2 þ ðC=C 0 Þ2 (where B and C are the Racah parameters in the crystal and B0 and C0 are the free ion values). In the present paper we will demonstrate that a similar linear relation exists for the energy of the Ni2 þ 1E state. This successful extension to the Ni2 þ ion suggests that the β1 parameter can be used, in general, in the description of the spectroscopic properties of TM ions in crystals.
2. Analysis of spectroscopic data on the energy position of the Ni2 þ 1E state in various crystals Table 1 collects the values of the Racah parameters B and C along with the calculated (from the crystal field theory) and observed energy positions of the Ni2 þ 1E state in a wide variety of crystals. All data collected in the “calculated” and “observed” columns were taken from the references cited in the table. It is evident from the data of Table 1 that the energy of the Ni2 þ 1E state varies considerably: from 11 171 cm 1 in NiI2 to 15 504 cm 1 in BaLiF3. Based on bond covalence considerations, this variation can be qualitatively understood because the iodides are more covalent than fluorides, which tend to be highly ionic compounds. Therefore, the Racah parameters in the iodides are expected to be considerably lower than those in fluorides. The data of Table 1 further show that the Racah B parameter in BaLiF3 (1062 cm 1, the highest value in the compounds under consideration) is about 1.64 times greater than in NiI2 (646 cm 1, which has the lowest B value in this group). It should also be noted that in stoichiometric NiI2, the nickel ions are not impurity ions, but are a part of the crystal lattice. This can explain why, for example, in
785 646 763 935 865 881 995 807 880 935 775.5 782 798.6 900 1062 869 928 940 950 800 816 730 950 675 750 697 868 886 879 958
4045 3851 2772 3503 3254 3225 4192 3141 3696 3330 3041 3026 3142 4250 3865 3150 3764 3919 3990 3200 3224 3450 4000 2975 3150 4035 3869 3952 3918 3330
1.168 1.055 0.947 1.177 1.090 1.097 1.324 1.033 1.169 1.151 0.996 0.999 1.028 1.273 1.319 1.078 1.212 1.244 1.262 1.038 1.052 1.033 1.264 0.919 0.996 1.116 1.189 1.214 1.204 1.167
13,907 11,171 12,550 13,841 13,002 12,986 15,583 12,206 13,891 13,196 11,781 11,800 12,132 15,009 15,504 12,814 14,359 14,124 15,247 12,274 12,120 12,419 14,075 11,963 13,147 13,799 14,435 14,555 14,346 13,831
13,800 11,165 – – 12,987 12,987 15,600 12,470 – 13,535 11,780 11,800 12,700 15,840 15,504 12,870 14,803 14,124 15,156 12,200 12,120 12,450 – 12,104 13,065 – – 14,700 – –
13,805 12,687 11,625 13,890 13,040 13,108 15,345 12,475 13,816 13,637 12,111 12,132 12,420 14,839 15,301 12,915 14,238 14,558 14,734 12,518 12,662 12,469 14,750 11,349 12,110 13,293 14,015 14,263 14,164 13,800
CsMgI3 (where Ni2 þ substitutes for the Mg2 þ ions) the value of B is higher (879 cm 1). The value of the C parameter also varies considerably, from 2772 cm 1 in NiBr2 to 4250 cm 1 in Al2O3 and somewhat close values in fluorides. Again, a qualitative trend is found in that higher values are observed in ionic compounds, like fluorides and oxides, whereas the halogen ligands cause a sharp reduction in the value of the Racah parameter, C. In an attempt to rationalize the data of Table 1, we plotted the calculated and experimental positions of the Ni2 þ 1E state against qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the β1 ¼ ðB=B0 Þ2 þ ðC=C 0 Þ2 parameter. The data were fitted to the linear functions, which turned out to be Eð1 EÞ ¼ 2270:8 þ 9876:0β1
ð1Þ
for the calculated data points and Eð1 EÞ ¼ 1156:3 þ 10; 916:0β1
ð2Þ
for the experimental data points. Both straight lines are fairly close to each other, and the correlation coefficient for both fits is about 0.83, suggesting a similar quality of the fits. Since the number of the experimental data points is less than the number of the calculated data points (not all authors in the cited references have unambiguously determined the energy position of the weak spectral feature that corresponds to the Ni2 þ 1E state), in the following discussions we will restrict ourselves to the data that is obtained via Eq. (1). To assess the quality of the fit and variance of the data presented, we calculated the energy of the Ni2 þ 1E state using
340
M.G. Brik et al. / Journal of Luminescence 148 (2014) 338–341
2
E=1156.3+10916.0 β1 R =0.84086
Al2O3
Position of the 1E level, cm-1
16000 15000
2
E=2270.8+9876.0 β1 R =0.82325 RbCdF3
14000 CdCl2
13000
NiBr2
CdBr2
12000
Calc. Exp.
NiI2
11000 0.8
1.0
1.2
(B
β1 = 2þ
1.4
B0 ) + (C C0 ) 2
2
1
Fig. 2. Energy position of the Ni E state (symbols; the filled/open circles correspond for the calculated/experimental data points from Table 1) against the qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi β1 ¼ ðB=B0 Þ2 þ ðC=C 0 Þ2 parameter.
Position of the 1E level, cm-1
16000
E=5466.8 + 9968.2 β
2
R =0.57335
15000
14000
13000
is only 0.57, which is considerably lower than what was obtained using Eq. (1). This demonstrates the necessity of simultaneous consideration of both Racah parameters B and C when attempting to describe effects due to bond covalence and the energy positions of the spin-forbidden transitions in crystals. It should be also mentioned that the proposed relation between the 1E level and Racah parameters is valid for the zerophonon lines only. Sometimes unambiguous determination of the zero-phonon line position can be complicated due to overlapped vibronic progressions observed in the experimental emission/ absorption spectra, which also may be a factor contributing to the deviation of some experimental/calculated points from the straight line determined by Eq. (1). In this connection we mention here that the data from Table 1 show a significant difference between the calculated 3A2–1E transition for KZnF3 (13,891 cm 1) and that measured for a similar compound of KMgF3 (15,156 cm 1) when compared to the value of the 10Dq-independent 6A2–4A1 transition of Mn2 þ ions measured for both KMgF3:Mn2 þ and KZnF3:Mn2 þ at 25,200 cm 1 [34]. Similarly the position of the 2E–4A2 emission transition for KMgF3:Cr3 þ (15,100 cm 1) [35] is practically identical to that measured for KZnF3:Cr3 þ (15,090 cm 1) [36]. At present we have no explanation why the similar hosts have similar spectral features in the case of some impurity ions, and exhibit considerable difference in the case of other impurities. Hopefully, detailed ab initio studies of these systems may shed more light on their behavior, as was done recently for the Cr3 þ ions in oxides and fluorides [37]. The microscopic studies of the nephelauxetic effect by ab initio calculations of the energy levels of the TM ions in various complexes for different arrangement of ions may also reveal some additional mechanisms for the Racah parameters reduction, e.g., not only sharing electrons between impurity ion and ligands, but also an expansion of the TM d-wave functions due to the net flow of charge from ligands to the central ion [37].
12000 3. Conclusions
11000 0.6
0.8
In this paper we have derived a simple empirical equation that relates the lowest energy spin-forbidden Ni2 þ 3A2–1E transition to qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the recently introduced parameter β1 ¼ ðB=B0 Þ2 þ ðC=C 0 Þ2 . This
1.0
β = B /B 0 Fig. 3. Energy position of the Ni2 þ parameter.
1
E state (symbols) against the β ¼ B/B0
Eq. (1) in the various compounds that are listed in Table 1 and then determined the root-mean-square deviation. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ∑N i ¼ 1 ðEi E iðEq:ð1ÞÞ Þ ; s¼ N
ð3Þ
where Ei and EiðEq:ð1ÞÞ are the data from the fourth and sixth columns of Table 1. The numerical estimations yield the value s ¼489 cm 1. Two dashed straight lines in Fig. 2 are parallel to the straight line given by Eq. (1) and correspond with its upward/ downward shift by s Thus in Fig. 2, the vast majority of the data are within the 7 s interval from the fit line. The data points, which do not fall within the region bordered by the dashed straight lines, correspond to binary compounds NiI2, NiBr2, CdBr2, CdCl2 (which have a layered structure and are highly covalent), Al2O3 and RbCdF3. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi To justify our choice of the β1 ¼ ðB=B0 Þ2 þ ðC=C 0 Þ2 parameter, we exhibit in Fig. 3 the dependence of the calculated (column 4 of Table 1) energy position of the Ni2 þ 1E state against the classic nephelauxetic ratio β¼B/B0. As evident from Fig. 3, the data has considerable scatter and the correlation coefficient of the linear fit
parameter simultaneously takes into account the reduction in the Racah parameters B and C due to the nephelauxetic effect. The linear relation between the energy position of the Ni2 þ 1E state and β1 is much better than between the 1E state energy and the commonly used nephelauxetic ratio β¼B/B0, which ignores the decrease in the values of Racah parameter C. It is reasoned that theβ1 parameter can be used in the description of the spectroscopic properties of TM ions in crystals.
Acknowledgments The cooperation program between Estonian and Polish Academies of Sciences for the years 2013–2015 is kindly acknowledged. This work was partially supported by the European Union within the European Regional Development Fund through the Innovative Economy grant MIME (POIG.01.01.02-00-108/09) and Polish National Science Center (Project no 2012/07/B/ST5/02376). MGB also acknowledges Marie Curie Initial Training Network LUMINET, grant agreement no. 316906. References [1] R.C. Powell, Physics of Solid-State Laser Materials, Springer, Berlin, 1998. [2] S. Kück, Appl. Phys. B 72 (2001) 515.
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[3] S. Kück, in: N.M. Avram, M.G. Brik (Eds.), Optical Properties of 3d-Ions in Crystal: Spectroscopy and Crystal Field Analysis, Tsinghua University Press, Beijing; Springer-Verlag, Berlin, Heidelberg 2013, p. 1. [4] A.A. Setlur, E.V. Radkov, C.S. Henderson, J.-H. Her, A.M. Srivastava, N. Karkada, M.S. Kishore, N.P. Kumar, D. Aesram, A. Deshpande, B. Kolodin, L.S. Grigorov, U. Happek, Chem. Mater. 22 (2010) 4076. [5] A.M. Srivastava, T.F. Soules, fourth ed.,Luminescent Materials (Phosphors), Kirk–Othmer Encyclopedia of Chemical Technology, vol. 15, John Wiley & Sons, New York, 1995. [6] K.H. Butler, Fluorescent Lamp Phosphors, Pennsylvania State University Press, University Park, PA, 1980. [7] S. Sugano, Y. Tanabe, H. Kamimura, Multiplets of Transition-Metal Ions in Crystals, Academic Press, New York and London, 1970. [8] B.N. Figgis, M.A. Hitchman, Ligand Field Theory and Its Applications, WileyVCH, New York, 2000. [9] M.G. Brik, A.M. Srivastava, ECS J. Solid State Technol. 2 (2013) R148. [10] A.M. Srivastava, M.G. Brik, Opt. Mater. 35 (2013) 1544. [11] P.H.M. Uylings, A.J.J. Raassen, J.F. Wyart, J. Phys. B 17 (1984) 4103. [12] M.G. Brik, N.M. Avram, C.N. Avram, Physica B 371 (2006) 43. [13] M.G. Brik, J. Phys. Chem. Solids 67 (2006) 738. [14] M.G. Brik, N.M. Avram, C.N. Avram, C. Rudowicz, Y.Y. Yeung, P. Gnutek, J. Alloys Compd. 432 (2007) 61. [15] M.G. Brik, C.N. Avram, N.M. Avram, J. Phys. Chem. Solids 69 (2008) 1796. [16] M.G. Brik, G.A. Kumar, D.K. Sardar, Mater. Chem. Phys. 136 (2012) 90. [17] N. Mironova-Ulmane, M.G. Brik, I. Sildos, J. Lumin. 135 (2013) 74.
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Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Empirical relation between covalence and the energy position of the Ni2 þ 1E state in octahedral complexes M.G. Brik a,n, A.M. Srivastava b, N.M. Avram c,d, A. Suchocki e,f a
Institute of Physics, University of Tartu, Riia 142, Tartu 51014, Estonia GE Global Research, One Research Circle, Niskayuna, NY 12309, USA c Department of Physics, West University of Timisoara, Bd. V. Parvan 4, Timisoara 300223, Romania d Academy of Romanian Scientists, Independentei 54, Bucharest 050094, Romania e Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland f Institute of Physics, Kazimierz Wielki University, Weyssenhoffa 11, 85-072 Bydgoszcz, Poland b
art ic l e i nf o
a b s t r a c t
Article history: Received 14 November 2013 Received in revised form 13 December 2013 Accepted 22 December 2013 Available online 31 December 2013
In this paper, a simple empirical equation that relates the energy of the spin-forbidden 3A2–1E transition qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of the octahedrally coordinated Ni2 þ ion with the recently introduced β1 ¼ ðB=B0 Þ2 þðC=C 0 Þ2 parameter
Keywords: Ni2 þ Covalence β1 parameter
is derived (B, C (B0, C0) are the Racah parameters of Ni2 þ ions in a crystal (free state), respectively). It is shown that the β1 parameter which simultaneously takes into account the reduction in both the Racah parameters B and C due to the nephelauxetic effect, is much more accurate in estimating the energy position of the Ni2 þ 1E state than the commonly used nephelauxetic ratio β¼ B/B0, which completely ignores the reduction in the values of the Racah parameter C when the transition metal ion is introduced in the solid. & 2013 Elsevier B.V. All rights reserved.
1. Introduction Fundamental investigations into crystals doped with the transition metal (TM) ions having unfilled 3d shell continue to be of interest due to their importance in commercial and technological applications [1–3]. As a rule, the spectra of these TM ions are characterized by spin-allowed broad emission bands, which open the possibility, for example, of obtaining tunable laser source. On the other hand, the spin-forbidden transitions of the TM ions are also of great importance. For example, the ruby laser operates on the 2Eg–4A2g emission transition of the Cr3 þ ion (3d3 electronic configuration). The same emission transition of the isoelectronic Mn4 þ ion finds application in the lighting industry [4,5]. The efficient green emission of one of the oldest lighting phosphor, ZnSiO4:Mn2 þ , arises from the spin-forbidden emission transition of the Mn2 þ ions (3d5 electronic configuration) [6]. If the energy separation between the spectral terms of ions with unfilled d-electron shell is considered, one has to keep in mind that there are ten independent interelectronic repulsion parameters (both Coulomb and exchange) [7]. On the other hand, such a large number of parameters simply cannot be extracted from the optical spectra of the TM ions, since the number of the experimental absorption and emission bands is always considerably smaller than 10. Luckily, there is a possibility to reduce this number
n
Corresponding author. Tel.: þ 372 7374751. E-mail address: brik@fi.tartu.ee (M.G. Brik).
0022-2313/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jlumin.2013.12.052
to three Racah parameters A, B and C. Moreover, if the energy levels of only d-electron configuration are concerned with, the A parameter can be further omitted, since it produces only an overall shift of all energy levels without changing the relative separation between them, It is a common practice nowadays that in a cubic crystal-field, the energy levels of any TM ion can be described by three main parameters: crystal-field strength Dq, which defines the crystal-field splitting, and two Racah parameters B and C, which determine the energy intervals between the free ion terms. While the energy of the spin-allowed transitions are largely determined by the crystal field strength Dq, as follows, for example, from the well-known Tanabe–Sugano diagrams [7], the energy of some spin-forbidden transitions of TM ions appears to be practically independent of the crystal-field strength. A good illustration of this statement is given in Fig. 1, where the Tanabe–Sugano diagram for a 3d8 ion in an octahedral crystal field is exhibited. Note that in this case, the energy separation between the ground state spin-triplet 3A2 and the first spin-singlet 1E state is independent of the crystal-field strength. This permits us to distinguish between two limiting cases: (i) weak crystal-field, where the first excited state 3T2 originates from the same 3F term as the ground state 3A2 and, (ii) strong crystal-field, where the first excited state is 1 E which arises from the 1D term of a free ion. The point of intersection of the 3T2 and 1E states serves as a separation between these two situations, as shown by a vertical dashed line in Fig. 1. This behavior of the 1E state suggests that only two Racah parameters B and C are needed to describe its energy position. It is well known that the values of these parameters in a crystal are
M.G. Brik et al. / Journal of Luminescence 148 (2014) 338–341
339
Table 1 The main spectroscopic parameters pertaining to the Ni2 þ 1Eg-3A2g transition in qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi various crystals. β1 ¼ ðB=B0 Þ2 þ ðC=C 0 Þ2 , B0 ¼ 1068 cm 1, C0 ¼4457 cm 1 [11].
E/B
C, β1 B, (cm 1) (cm 1)
Position of the 1E level
Crystal
Ref.
NiCl2 NiI2 NiBr2 Ca3Sc2Ge3O12 MgAl2O4 LiGa5O8 MgF2 AgCl KZnF3 MgO CsCdBr3 CsMgBr3 CsCdCl3 Al2O3 BaLiF3 MgGa2O4 NiCl2(H2O)4 ZAS glass KMgF3 MgBr2 LiNbO3 CdI2 RbCdF3 CdBr2 CdCl2 NiF2 CsMgCl3 CsMgBr3 CsMgI3 WO3–TeO2 glass
[12] [8] [8] [13] [14] [15] [11] [11] [16] [17] [18] [14] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [26] [31] [32] [28] [28] [33]
Calculated Observed Calc. (Eq. (1))
Strong crystal field Weak crystal field
Dq/B Fig. 1. Tanabe–Sugano diagram for an ion with the 3d8 electron configuration in an octahedral crystal field.
reduced relative to their “free ion” counterparts due to the socalled nephelauxetic effect [8]. Since the reduction in the Racah parameters is more pronounced in highly covalent crystals, one may expect the 1E state to be energetically lower in covalently bonded systems than in ionic crystals where the Racah parameters are closer to their free ion values. Recently, Brik and Srivastava have introduced a new parameter (β1) in the spectroscopic properties of the Mn4 þ ion [9,10]. They demonstrated a linear relation between the energetic position of qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the Mn4 þ 2Eg state and the new parameter β1 ¼ ðB=B0 Þ2 þ ðC=C 0 Þ2 (where B and C are the Racah parameters in the crystal and B0 and C0 are the free ion values). In the present paper we will demonstrate that a similar linear relation exists for the energy of the Ni2 þ 1E state. This successful extension to the Ni2 þ ion suggests that the β1 parameter can be used, in general, in the description of the spectroscopic properties of TM ions in crystals.
2. Analysis of spectroscopic data on the energy position of the Ni2 þ 1E state in various crystals Table 1 collects the values of the Racah parameters B and C along with the calculated (from the crystal field theory) and observed energy positions of the Ni2 þ 1E state in a wide variety of crystals. All data collected in the “calculated” and “observed” columns were taken from the references cited in the table. It is evident from the data of Table 1 that the energy of the Ni2 þ 1E state varies considerably: from 11 171 cm 1 in NiI2 to 15 504 cm 1 in BaLiF3. Based on bond covalence considerations, this variation can be qualitatively understood because the iodides are more covalent than fluorides, which tend to be highly ionic compounds. Therefore, the Racah parameters in the iodides are expected to be considerably lower than those in fluorides. The data of Table 1 further show that the Racah B parameter in BaLiF3 (1062 cm 1, the highest value in the compounds under consideration) is about 1.64 times greater than in NiI2 (646 cm 1, which has the lowest B value in this group). It should also be noted that in stoichiometric NiI2, the nickel ions are not impurity ions, but are a part of the crystal lattice. This can explain why, for example, in
785 646 763 935 865 881 995 807 880 935 775.5 782 798.6 900 1062 869 928 940 950 800 816 730 950 675 750 697 868 886 879 958
4045 3851 2772 3503 3254 3225 4192 3141 3696 3330 3041 3026 3142 4250 3865 3150 3764 3919 3990 3200 3224 3450 4000 2975 3150 4035 3869 3952 3918 3330
1.168 1.055 0.947 1.177 1.090 1.097 1.324 1.033 1.169 1.151 0.996 0.999 1.028 1.273 1.319 1.078 1.212 1.244 1.262 1.038 1.052 1.033 1.264 0.919 0.996 1.116 1.189 1.214 1.204 1.167
13,907 11,171 12,550 13,841 13,002 12,986 15,583 12,206 13,891 13,196 11,781 11,800 12,132 15,009 15,504 12,814 14,359 14,124 15,247 12,274 12,120 12,419 14,075 11,963 13,147 13,799 14,435 14,555 14,346 13,831
13,800 11,165 – – 12,987 12,987 15,600 12,470 – 13,535 11,780 11,800 12,700 15,840 15,504 12,870 14,803 14,124 15,156 12,200 12,120 12,450 – 12,104 13,065 – – 14,700 – –
13,805 12,687 11,625 13,890 13,040 13,108 15,345 12,475 13,816 13,637 12,111 12,132 12,420 14,839 15,301 12,915 14,238 14,558 14,734 12,518 12,662 12,469 14,750 11,349 12,110 13,293 14,015 14,263 14,164 13,800
CsMgI3 (where Ni2 þ substitutes for the Mg2 þ ions) the value of B is higher (879 cm 1). The value of the C parameter also varies considerably, from 2772 cm 1 in NiBr2 to 4250 cm 1 in Al2O3 and somewhat close values in fluorides. Again, a qualitative trend is found in that higher values are observed in ionic compounds, like fluorides and oxides, whereas the halogen ligands cause a sharp reduction in the value of the Racah parameter, C. In an attempt to rationalize the data of Table 1, we plotted the calculated and experimental positions of the Ni2 þ 1E state against qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the β1 ¼ ðB=B0 Þ2 þ ðC=C 0 Þ2 parameter. The data were fitted to the linear functions, which turned out to be Eð1 EÞ ¼ 2270:8 þ 9876:0β1
ð1Þ
for the calculated data points and Eð1 EÞ ¼ 1156:3 þ 10; 916:0β1
ð2Þ
for the experimental data points. Both straight lines are fairly close to each other, and the correlation coefficient for both fits is about 0.83, suggesting a similar quality of the fits. Since the number of the experimental data points is less than the number of the calculated data points (not all authors in the cited references have unambiguously determined the energy position of the weak spectral feature that corresponds to the Ni2 þ 1E state), in the following discussions we will restrict ourselves to the data that is obtained via Eq. (1). To assess the quality of the fit and variance of the data presented, we calculated the energy of the Ni2 þ 1E state using
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M.G. Brik et al. / Journal of Luminescence 148 (2014) 338–341
2
E=1156.3+10916.0 β1 R =0.84086
Al2O3
Position of the 1E level, cm-1
16000 15000
2
E=2270.8+9876.0 β1 R =0.82325 RbCdF3
14000 CdCl2
13000
NiBr2
CdBr2
12000
Calc. Exp.
NiI2
11000 0.8
1.0
1.2
(B
β1 = 2þ
1.4
B0 ) + (C C0 ) 2
2
1
Fig. 2. Energy position of the Ni E state (symbols; the filled/open circles correspond for the calculated/experimental data points from Table 1) against the qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi β1 ¼ ðB=B0 Þ2 þ ðC=C 0 Þ2 parameter.
Position of the 1E level, cm-1
16000
E=5466.8 + 9968.2 β
2
R =0.57335
15000
14000
13000
is only 0.57, which is considerably lower than what was obtained using Eq. (1). This demonstrates the necessity of simultaneous consideration of both Racah parameters B and C when attempting to describe effects due to bond covalence and the energy positions of the spin-forbidden transitions in crystals. It should be also mentioned that the proposed relation between the 1E level and Racah parameters is valid for the zerophonon lines only. Sometimes unambiguous determination of the zero-phonon line position can be complicated due to overlapped vibronic progressions observed in the experimental emission/ absorption spectra, which also may be a factor contributing to the deviation of some experimental/calculated points from the straight line determined by Eq. (1). In this connection we mention here that the data from Table 1 show a significant difference between the calculated 3A2–1E transition for KZnF3 (13,891 cm 1) and that measured for a similar compound of KMgF3 (15,156 cm 1) when compared to the value of the 10Dq-independent 6A2–4A1 transition of Mn2 þ ions measured for both KMgF3:Mn2 þ and KZnF3:Mn2 þ at 25,200 cm 1 [34]. Similarly the position of the 2E–4A2 emission transition for KMgF3:Cr3 þ (15,100 cm 1) [35] is practically identical to that measured for KZnF3:Cr3 þ (15,090 cm 1) [36]. At present we have no explanation why the similar hosts have similar spectral features in the case of some impurity ions, and exhibit considerable difference in the case of other impurities. Hopefully, detailed ab initio studies of these systems may shed more light on their behavior, as was done recently for the Cr3 þ ions in oxides and fluorides [37]. The microscopic studies of the nephelauxetic effect by ab initio calculations of the energy levels of the TM ions in various complexes for different arrangement of ions may also reveal some additional mechanisms for the Racah parameters reduction, e.g., not only sharing electrons between impurity ion and ligands, but also an expansion of the TM d-wave functions due to the net flow of charge from ligands to the central ion [37].
12000 3. Conclusions
11000 0.6
0.8
In this paper we have derived a simple empirical equation that relates the lowest energy spin-forbidden Ni2 þ 3A2–1E transition to qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the recently introduced parameter β1 ¼ ðB=B0 Þ2 þ ðC=C 0 Þ2 . This
1.0
β = B /B 0 Fig. 3. Energy position of the Ni2 þ parameter.
1
E state (symbols) against the β ¼ B/B0
Eq. (1) in the various compounds that are listed in Table 1 and then determined the root-mean-square deviation. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ∑N i ¼ 1 ðEi E iðEq:ð1ÞÞ Þ ; s¼ N
ð3Þ
where Ei and EiðEq:ð1ÞÞ are the data from the fourth and sixth columns of Table 1. The numerical estimations yield the value s ¼489 cm 1. Two dashed straight lines in Fig. 2 are parallel to the straight line given by Eq. (1) and correspond with its upward/ downward shift by s Thus in Fig. 2, the vast majority of the data are within the 7 s interval from the fit line. The data points, which do not fall within the region bordered by the dashed straight lines, correspond to binary compounds NiI2, NiBr2, CdBr2, CdCl2 (which have a layered structure and are highly covalent), Al2O3 and RbCdF3. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi To justify our choice of the β1 ¼ ðB=B0 Þ2 þ ðC=C 0 Þ2 parameter, we exhibit in Fig. 3 the dependence of the calculated (column 4 of Table 1) energy position of the Ni2 þ 1E state against the classic nephelauxetic ratio β¼B/B0. As evident from Fig. 3, the data has considerable scatter and the correlation coefficient of the linear fit
parameter simultaneously takes into account the reduction in the Racah parameters B and C due to the nephelauxetic effect. The linear relation between the energy position of the Ni2 þ 1E state and β1 is much better than between the 1E state energy and the commonly used nephelauxetic ratio β¼B/B0, which ignores the decrease in the values of Racah parameter C. It is reasoned that theβ1 parameter can be used in the description of the spectroscopic properties of TM ions in crystals.
Acknowledgments The cooperation program between Estonian and Polish Academies of Sciences for the years 2013–2015 is kindly acknowledged. This work was partially supported by the European Union within the European Regional Development Fund through the Innovative Economy grant MIME (POIG.01.01.02-00-108/09) and Polish National Science Center (Project no 2012/07/B/ST5/02376). MGB also acknowledges Marie Curie Initial Training Network LUMINET, grant agreement no. 316906. References [1] R.C. Powell, Physics of Solid-State Laser Materials, Springer, Berlin, 1998. [2] S. Kück, Appl. Phys. B 72 (2001) 515.
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