Spin-Forbidden Transitions in the Spectra of

ECS Journal of Solid State Science and Technology, 5 (1) R3067-R3077 (2016) 2162-8769/2016/5(1)/R3067/11/$33.00 © The Electrochemical Society

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JSS FOCUS ISSUE ON NOVEL APPLICATIONS OF LUMINESCENT OPTICAL MATERIALS

Spin-Forbidden Transitions in the Spectra of Transition Metal Ions and Nephelauxetic Effect M. G. Brik,a,b,c,d,∗,z S. J. Camardello,e A. M. Srivastava,e N. M. Avram,f,g and A. Suchockic a College

of Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065, People’s Republic of China b Institute of Physics, University of Tartu, Tartu 50411, Estonia c Institute of Physics, Polish Academy of Sciences, Warsaw 02-668, Poland d Institute of Physics, Jan Dlugosz University, PL-42200 Czestochowa, Poland e GE Global Research, Niskayuna, New York 12309, USA f Department of Physics, West University of Timisoara, Timisoara 300223, Romania g Academy of Romanian Scientists, Bucharest 050094, Romania In this paper we review the spectroscopic properties of three transition metal ions - Mn4+ , Cr3+ and Ni2+ - in crystals and establish a relationship between the energies of the lowest in energy spin-forbidden transitions and covalence of the “metal –ligand” chemical 2

2

bonds. A new parameter β1 = ( BB ) + ( CC ) (where (B, C (B0 , C0 ) are the Racah parameters of the ions in a crystal (free state), 0 0 respectively) is shown to determine the energy of the above-mentioned transitions. The considered ions can be used as reliable probes of the covalent effects in various hosts. Several practical recommendations on how to tune the spin-forbidden transitions energy to meet specific needs are suggested. © 2015 The Electrochemical Society. [DOI: 10.1149/2.0091601jss] All rights reserved.

Manuscript submitted July 16, 2015; revised manuscript received August 17, 2015. Published September 11, 2015. This paper is part of the JSS Focus Issue on Novel Applications of Luminescent Optical Materials.

Chemical elements with an unfilled 3d electron shell occupy the fourth row of the periodic table. Their atomic numbers change from 21 (Sc) to 30 (Zn), and their common feature is that in the neutral state that is characteristic for free atoms the 3d electron shell is gradually filled when moving from Sc ([Ar]3d1 4s2 electron configuration) to Zn ([Ar]3d10 4s2 electron configuration). The completed 1s2 2s2 2p6 3s2 3p6 electron configuration of argon is denoted as [Ar]. When these elements are introduced into crystalline solids, they can exist in various oxidation states from +1 to +6, thus losing two 4s and some of 3d electrons. As a result, the unfilled 3d shell becomes to be an outer electron shell, whose electronic states formed due to the coulomb interaction between 3d electrons are strongly affected by the nearest environment of these ions in crystals. These states become split into a number of energy levels, the splitting pattern varies from one host to another, and the electronic transitions between those levels cover a wide spectral range from infrared to ultraviolet. Table I below gives a list of transition metal ions in various oxidation states with an indication of the total number of states allowed (determined by the Pauli exclusion principle), number of the LS terms for a free ion and the ground LS term for each electron configuration (the 2S+1 L notation is used, with S and L being the total spin and orbital momenta of a particular configuration, respectively). In fact, the number of states given in Table I is equal to the maximal number of energy levels of a particular electron configuration in a crystal field (this number should be divided by two for the so called Kramers ions with an odd number of electrons, when an external magnetic field is needed to remove completely the remaining twofold degeneracy). The applications of the 3d ions are numerous, and their description and characterization are not among the main aims of the present paper. We just mention that the first laser was created using the Al2 O3 crystals doped with Cr3+ ions,1 an extensive list of other crystals and impurities used for the solid state lasing is given in Ref. 2, whereas current development of laser crystals with 3d ions is discussed in Ref. 3. Among the 3d ions, a special position is taken by the Mn4+ ions. Although laser generation has not been obtained so far with this ion, ∗ Electrochemical Society Active Member. z E-mail: [email protected]; [email protected]

it is widely used as a color correcting phosphor in high pressure mercury vapor lamps and in fluorescent lamps providing light for the plants growth.4,5 Importance of the Mn4+ ions is also growing due to the fact that the price for the lanthanide ions has been increased drastically over recent years, and red emission that can be obtained from the 2 Eg → 4 A2g transition of tetravalent manganese in a strong crystal field is used for a mixture with green and blue emissions from other activator ions for white LED.6–10 Another example is the YAlO3 perovskite doped with Mn4+ : it is a potential material for several applications, such as holographic recording, optical data storage,11,12 and thermoluminescence dosimetry.13 More recently, several fluoride and oxide systems doped with the Mn4+ ions were also shown to be suitable for the solid state lighting applications.14–17 Speaking about other transition metal ions, of course, one should mention Cr3+ , since it is one of the most popular lasing ions from the 3d group. Laser action was also obtained with other 3d ions, such as Cr4+ , Ni2+ , Co2+ .2 Understanding of peculiar features of transition metal ions spectra in crystalline solids is essential for the assessment of application perspectives of these materials. Such understanding comes from detailed analysis of the energy level schemes, splitting of energy levels in a crystal field and dependence of that splitting on the nature of ligands and chemical bonding properties in a particular crystal. As far as the energy levels of transition metal ions are concerned, the names of Tanabe and Sugano emerge immediately, since they succeeded in calculating the energy level splitting for all configurations in an ideal octahedral crystal field.18–21 Moreover, they proposed very convenient two-dimensional diagrams, widely known as Tanabe-Sugano diagrams, which show how the energy levels behave with increasing crystal field strength. In principle, one has to know three parameters to describe uniquely the energy levels of transition metal ions in a cubic (octahedral and tetrahedral) crystal field. These parameters are the crystal field strength Dq and two Racah parameters B, C (at this point and in what follows the spin-orbit coupling is neglected, which is justified for 3d ions, if the fine structure of the energy levels is not considered). In all Tanabe-Sugano diagrams the horizontal axis is expressed in terms of ratio of Dq over B, whereas the vertical axis shows the energies E of the individual states divided by the same parameter B. The diagrams are also plotted for a fixed C/B ratio, which is usually about 4.5. These diagrams are very efficient tools for an analysis and assignment of the transition metal spectra in

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ECS Journal of Solid State Science and Technology, 5 (1) R3067-R3077 (2016)

Table I. List of transition metal ions with various electronic configurations and their ground LS terms. Electron configuration 3d1 3d2 3d3 3d4 3d5 3d6 3d7 3d8 3d9

Ions Ti3+ ,

V4+ ,

Cr5+ ,

Number of states Mn6+

Ti2+ , V3+ , Cr4+ , Mn5+ , Fe6+ V2+ , Cr3+ , Mn4+ , Fe5+ Cr2+ , Mn3+ , Fe4+ Mn2+ , Fe3+ Co3+ , Fe2+ Co2+ , Ni3+ Ni2+ , Cu3+ Cu2+

10 45 120 210 252 210 120 45 10

solids (although they do not account for a low-symmetry crystal field splitting of degenerated levels). We shall not reproduce here all Tanabe-Sugano diagrams – they can be easily found in a number of papers and books, as well as online – but we show below only two special cases of the d3 and d8 configurations in an octahedral crystal field (Figures 1 and 2), since they are pertinent to the present discussion. A quick glance at both diagrams reveals two important facts. i)

ii)

At some critical value of the Dq/B ratio (denoted by a vertical line in both figures) there is a change of the first excited state. To the left from that point, the multiplicities of the ground and the first excited states are the same, whereas to the right from that point those multiplicities are different. This implies that in the former case the emission spectra consist of a wide band of a spin-allowed transition, while in the latter case the emission appears as a sharp line of a spin-forbidden transition. In the whole range of the Dq/B ratio variation the 2 Eg state (d3 configuration) and 1 Eg state (d8 configuration) are nearly crystal field independent, since they are practically parallel to the horizontal axis.

So, the influence of the crystal field cannot account for an experimental observation that the energies of those spin-forbidden transitions in the strong crystal field case vary in a wide range. It is also easy to see from both diagrams, that the energies of the 2 Eg level for the d3 case and 1 Eg level for the d8 case are close (although somewhat greater) to the separation between the 2 G - 4 F and 1 D - 3 F terms of free ions, respectively. The energy intervals between the free ion electrostatic terms are determined by the Racah parameters B and C, and these parameters are reduced from the free ion values upon introduction of an impurity ion into a crystal due to the nephelauxetic effect.22–26 The nephelauxetic (meaning literally “cloud expansion” from Greek) effect is a common term to describe delocalization of the outer d orbitals of impurity ions because of formation of chemical bonds with ligands. The d electrons then spend some time in the ligands p- and s-orbitals, which leads to a decrease of the inter-electron repulsion within the d shell, and, finally, to a reduction of the B and C values. Since such delocalization effects depend on the nature of ligands and chemical bond lengths, it is natural to expect various degree of B and C reduction in different materials even for the same impurity ion. Therefore, the nephelauxetic effect appears to be one of the main reasons for possible (and indeed encountered experimentally) variation of the energies of the 2 Eg → 4 A2g (d3 configuration) and 1 Eg → 3 A2g (d8 configuration) transitions. The most studied representative ions with these electron configurations are Cr3+ , Mn4+ (d3 ) and Ni2+ (d8 ). A survey of the literature data on the emission transitions of these ions reveals that for the Cr3+ ions the energy of the 2 Eg → 4 A2g emission transition varies between 11975 cm−1 (839 nm) in KZnClSO4 · 3H2 O27 to 15823 cm−1 (632 nm) in CdWO4 28 and 15734 cm−1 (634 nm) in KMgF3 ,29 with the difference in the wavelengths of more than 200 nm. As far as the Mn4+ ions in solids are concerned, the energy of the same 2 Eg → 4 A2g transition can be tuned from 16207

Number of terms

Ground term

Octahedral crystal field

1 5 8 16 16 16 8 5 1

2D

2T 2g 3T 1g 4A 2g 5 E (weak field), 3 T (strong field) g 1g 6 A (weak field), 2 T (strong field) 1g 2g 5 T (weak field), 1 A (strong field) 2g 1g 4 T (weak field), 2 E (strong field) 1g g 3A 2g 2E

3F 4F 5D 6S 5D 4F 3F 2D

cm−1 (617 nm) in Na2 SiF6 30 to 13827 cm−1 (723 nm) in SrTiO3 ,31 thus covering a spectral range with a width of more than 100 nm. If the Ni2+ ions are considered, the position of the spin-singlet state 1 E is shifted from 11165 cm−1 (895 nm) in NiI2 32 to 17757 cm−1 (563 nm) in MgSO3 · 6H2 O,33 again with more than 200 nm difference between these values. In an attempt to model and describe those wide variations of the spin-forbidden transitions energies, in the present paper we offer a quantitative description of such behavior of the three chosen ions, which allows to understand the reasons behind those remarkable spectroscopic features of the Cr3+ , Mn4+ and Ni2+ ions in solids. To the best of our knowledge, there are only a very few papers pertaining to a consistent analysis of the excitation (absorption), emission properties and nephelauxetic effects for these ions in solids. Among those papers, we can mention our earlier publication;34 besides, application of the density functional theory (DFT) to the analysis of the trends in the spectroscopic properties of the Mn4+ ion in solids was published in Ref. 35. Nephelauxetic effect for the Cr3+ ions and pressure effects on their optical spectra was considered in Refs. 36, 37 whereas systematic overview of the Ni2+ ions spectroscopic properties was published in Ref. 38. In the present work we extend our earlier studies34,38,39 to the case of Cr3+ ions and compare degree of

Figure 1. Tanabe-Sugano diagram for the d3 electron configuration in the octahedral crystal field. The thick and thin lines denote the electronic states whose multiplicity is the same or different as that of the ground state, respectively. The subscript “g” is common for all crystal field states and is omitted. The vertical line denotes the point of change of the first excited state and is a border between the weak (to the left from that line) and strong (to the right from that line) crystal fields.



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Table II. Spectroscopic parameters of Mn4+ ions in various crystals. Dq is the crystal field splitting, B and C are the Racah parameters. E(2 Eg ) is energy of the Mn4+ 2 Eg level. Crystal BaGeF6 BaSiF6 BaTiF6 Cs2 GeF6 Cs2 SnF6 K2 GeF6 K2 GeF6 K2 MnF6 K2 SiF6 K2 SiF6 K2 SiF6 Na2 SiF6 Na2 SnF6 ZnSiF6 · 6H2 O ZnSiF6 · 6H2 O Al2 O3 ∗ BaTiO3 Ba2 LaNbO6 CaAl2 O4 CaAl12 O19 CaAl12 O19 CaMg2 Al16 O27 CaZrO3 Gd2 MgTiO6 LaAlO3 α-LiAlO2 MFG∗∗ MgO∗ Mg2 TiO4 PbTiO3 SrTiO3 SrMgAl10 O17 Sr4 Al14 O25 Sr4 Al14 O25 ∗ Sr4 Al14 O25 TiO2 anatase YAlO3 Y2 Sn2 O7 Y2 Ti2 O7

Figure 2. Tanabe-Sugano diagram for the d8 electron configuration in the octahedral crystal field. The notation is the same as in Fig. 1.

nephelauxetic effects experienced by Cr3+ , Mn4+ , Ni2+ ions in various hosts. We also demonstrate that the position of the emitting 2 Eg state (d3 configuration) or 1 Eg state (d8 configuration) is a linear function of 2

2

a recently introduced parameter β1 = ( BB0 ) + ( CC0 ) ,38,39 where B, C (B0 , C0 ) are the Racah parameters of the corresponding ions in a crystal (free state), respectively. In the next section we present the collected literature data on the pertinent spectroscopic properties of the Cr3+ , Mn4+ and Ni2+ ions. After that, we highlight systematic variation of those spectroscopic properties, summarize the results and finish the paper with concluding remarks. We believe that the findings of this paper would be useful for spectroscopists and materials scientists in their attempts of further optimizing the optical properties of these ions for specific applications and will aid in the development of new optical materials with these activator ions. Spectroscopic Properties of the Mn4+ , Cr3+ and Ni2+ Ions in Solids Table II collects a summary of the spectroscopic data for the Mn4+ ions in a number of crystalline solids. The values of the crystal field strength Dq, Racah parameters B and C were extracted from the experimental spectra (if not given directly) that are reported in the cited references. Extraction of the Dq, B, and C values from the d3 ions experimental spectra can be done easily using the energies E(4 T2g ), E(4 T1g (4 F)), and E(2 Eg ) of the 4 T2g , 4 T1g (4 F), and 2 Eg states: E 4 T2g = 10Dq B = Dq E

E Dq

2

15

− 10 E Dq

2

E Dq

−8

Eg 3.05C 1.80B = + 7.90 − B B Dq

where E= E(4 T1g (4 F)) - E(4 T2g ).40

Dq, cm−1 B, cm−1 C, cm−1 E(2 Eg ) energy, cm−1 Ref. 2128 2141 2127 2200 2101 2123 2150 2183 2390 2200 2197 2174 2101 2174 2174 2170 1780 1780 2500 2132 2146 2137 1850 2066 2123 2345 2380 1868 2089 1500 1821 2126 2222 2250 2222 1830 2100 2100 2000

609 568 609 480 589 593 590 604 770 605 599 775 589 590 557 900 738 670 520 807 750 737 754 997 695 729 700 722 790 780 735 802 680 790 794 735 720 700 600

3785 3879 3494 4074 3830 3824 3831 3821 3435 3806 3750 3475 3873 3779 3846 2800 2820 3290 3700 3088 3245 3247 3173 2514 2941 3139 3416 3483 3172 2890 2812 3069 3397 3172 3232 2816 3025 3515 3500

16038 16050 16050 16028 16042 16050 16050 16129 16100 16091 15873 16207 16171 15898 15873 14950; 14 866 13862 14679 15198 15244 15243 15267 15054 14685 14034 14925 15576 15809; 15 279 15193 14236 13827 15151 15361 15361, 15384, 15457 15337 13846 14450 15563 14956

41 42 43 44 45 46 47 48 47 49 50 30 45 51 52 53 54 55 56 57 58 59 39 60 61 62 63 64 65 66 31 67 68 69 70 71 72 73 73

∗ Multicenters and/or various data reported ∗∗ 3.5MgO-0.5MgF -GeO :Mn4+ 2 2

Equations for the energies of the relevant crystal field states arising from the d8 configurations (they can be easily obtained analytically by solving Tanabe-Sugano matrices21 ) are as follows: E 3 T2g = 10Dq E

3

E

1

T1g

3 F = 15Dq + 7.5B − 0.5 100Dq 2 − 180Dq B + 225B 2

E g = 10Dq + 2C + 8.5B − 0.5 400Dq 2 + 40Dq B + 49B 2

There are two types of hosts that can be easily distinguished in Table II. They can be conditionally referred to as “fluorides” and “oxides” (those materials, in which the nearest environment of the Mn4+ ions is made of the fluorine and oxygen ions, respectively). The literature data on spectroscopic properties of the Cr3+ ions in crystals are more abundant (Table III). It also should be kept in mind that despite identical electronic configurations, Cr3+ and Mn4+ ions have, nevertheless, one important difference: if the Mn4+ ions are always experiencing the strong crystal field, the Cr3+ ions can be found at the sites with both weak and strong crystal field, that


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Table III. Spectroscopic parameters of Cr3+ ions in various crystals. Dq is the crystal field splitting, B and C are the Racah parameters. E(2 Eg ) is energy of the Cr3+ 2 Eg level. Crystal Cs2 NaAlF6 M1 site Cs2 NaAlF6 M2 site Cs2 NaGaF6 M1 site Cs2 NaGaF6 M2 site K2 LiAlF6 K2 NaScF6 KMgF3 KZnF3 MgF2 RbCdF3 LiCaAlF6 AlSc(WO3 )4 (550 C) AlSc(WO3 )4 (900 C) Al2 O3 Al2 SiO5 BaAl2 O4 BeAl2 O4 CaYAlO4 CaY2 Mg2 Ge3 O12 Ca3 Ga2 Ge4 O14 CdWO4 Cs2 NaAlF6 Site 1 Cs2 NaAlF6 Site 2 (Ce,Gd)Sc3 (BO3 )4 Cr2 O3 CsAl(MoO4 )2 Cs2 [CrCl2 (H2 O)4 ]Cl3 Cs2 NaYCl6 Ga2 O3 Ga3 Ga5 O12 Gd3 (Sc,Ga)2 Ga3 O12 GdAl3 (BO3 )4 KTiOPO4 KAl(MoO4 )2 KIn(MoO4 )2 KIn(WO4 )2 (7 K) KIn(WO4 )2 (295 K) KSc(WO4 )2 KZnClSO4 · 3H2 O LaGaO3 LaMgAl11 O19 LaSc3 (BO3 )4 LaSc3 (BO3 )4 LaSr2 Ga11 O20 La2.32 Lu2.61 Ga3.07 O12 La2.32 Lu2.61 Ga3.07 O12 (La,Lu)3 Lu2 Ga3 O12 La3 Ga5 SiO14 La3 GaGe5 O16 La3 Ga5.5 Nb0.5 O14 LiAl5 O8 LiGa5 O8 LiIO3 LiIn(WO4 )2 (7 K) LiIn(WO4 )2 (295 K) LiNbO3 LiSc(WO4 )2 LiTaO3 MgAl2 O4 MgAl2 O4 MgO MgSrAl10 O17 MgTiO3 MgWO4 Na3 Ce(PO4 )2 Na3 Li3 In2 F12 NaAl(WO4 )2

Dq, cm−1

B, cm−1

C, cm−1

E(2 Eg ) energy, cm−1

Ref.

1598 1650 1602 1571 1608 1560 1450 1290 1495 1420 1587 1477 1464 1664 ∼1300 1811 1709 1790 1563 1575 1412 1613 1600 1526 1694 1493 1663 1280 1667 1597 1653 1695 1507 1495 1386 1443 1448 1462 1724 1914 1751 1529 1529 1662 1503 1503 1480 1695 1745 1550 1747 1694 1430 1377 1368 1354 1364 1529 1852 1818 1615 1811 1567 1351 1463 1580 1548

730 695 667 740 702 794 760 713 516 800 786 662 653 640 650 533 675 705 632 761 777 740 677 595 462 583 600 600 529 626 638 673 652 586 681 586 671 712 724 589 603 668 675 734 591 412 619 680 654 620 648 565 668 540 534 566 543 667 553 668 586 678 762 525 660 713 615.6

3295 3180 3164 3308 3358 3231 3426 3211 3797 3290 3248 3033 3066 3300 3120 2862 3245 2750 3230 2811 3428 3308 3164 3507 3497 3066 3390 3150 3413 3182 3174 3380 2800 3049 2902 3288 3332 2973 2230 3077 3882 3528 3448 2984 3343 3751 3251 3443 3124 3099 3120 3233 2672 3293 3294 3408 3266 3013 3416 3235 3249 3139 2758 3328 3272 3353 3083

14389 15270 15196 14578 15221 15390 15734 15113 15267 15550 15413 13947 13986 14663 13858 12661 14734 13475 14286 14289 15823 15309 14467 14815 14077 13548 14438 14435 14286 14360 14430 15129 14286 13850 13630 14230 14140 14045 11975 13713 14451 15502 15297 14300 14450 14450 14500 15366 14286 13904 14135 13982 13537 13930 13890 13791 13867 13899 14492 14706 14143 14489 13341 13910 14660 15283 13811

76 76 76 76 77 78 79 80 81 82 83 84 84 85 86 87 88 89 90 91 28 92 92 93 94 95 96 97 98 99 99 100 101 102 103 104 104 105 106 107 108 109 110 111 112 112 99 113 114 115 116 117 118 104 104 119 120 121 122 123 124 125 121 126 127 128 129



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Table III. (Continued).

NaAl(WO4 )2 NaCe(PO3 )4 NaIn(MoO4 )2 NaIn(WO4 )2 (7 K) NaIn(WO4 )2 (295 K) NaMg3 Al(MoO4 )5 NaMg3 Al(MoO4 )5 RbAl(MoO4 )2 (7 K) RbAl(MoO4 )2 (295K) RbIn(WO4 )2 (7 K) RbIn(WO4 )2 (295 K) Sc2 (MoO4 )3 Sc2 O3 YAlO3 YAl3 (BO3 )4 Y2 Sn2 O7 Y3 Al5 O12 Y3 Ga5 O12 Y3 Ga5 O12 (YGG) Y3 (Sc,Ga)2 Ga3 O12 ZnAl2 S4 ZnGa2 O4

Dq, cm−1

B, cm−1

C, cm−1

E(2 Eg ) energy, cm−1

Ref.

1649 1533 1351 1333 1332 1444 1440 1513 1484 1450 1405 1408 1490 1786 1644 1767 1560 1613 1630 1613 1620 1840

710 713 705 536 533 642 676 586 611 764 723 608 590 674 700 590 654 651 639 630 400 553

2875 3434 2859 3332 3329 3025 2945 3058 2992 2891 2979 3054 3227 3088 3163 2800 3290 3214 3180 3195 3228 3461

13834 14705 13740 14010 13980 13780 13738 13550 13500 14150 14130 13641 14084 14286 14147 12315 14550 14472 14450 14440 12970 14569

130 131 103 104 132 131 133 134 134 104 104 135 136 137 138 139 140 141 99 99 142 142

is why in this case we encounter a wider range of the crystal field strength variation. What can be immediately noticed from Tables II and III is that the emitting 2 Eg level in fluorides is always higher than in oxides, which indicates a weaker nephelauxetic effect in fluorides, which are mostly ionic compounds if compared to the covalent oxides. The Racah parameters B0 and C0 for the Mn4+ ion in a free state are 1160 cm−1 and 4303 cm−1 ,74 whereas the same parameters for the Cr3+ are 918 cm−1 and 3850 cm−1 ,75 respectively. All Racah parameters listed in Tables II, III are considerably smaller than those free ion’s values. However, even if we consider only oxides or only fluorides, the degree of the Racah parameters reduction is different for different representatives of the oxide or fluoride materials. Such a difference in the Racah parameters reduction encountered in different hosts indicates that not only the nature of the ligands is an important factor that determines the nephelauxetic effect. Other factors such as different interionic distances and angles between chemical bonds (which may be employed to explain specific features of the chemical bond formation between the impurity ion and the ligands of the host lattice) should be considered too. In other words, the competition between the covalence and the ionicity of the chemical bonds is the key-factor that determines the values of the B and C parameters. As a rule of thumb, it can be stated that in more ionic hosts (such as fluorides), the weak nephelauxetic effect will result in a smaller decrease of the B and C values and will lead to higher energy position of the 2 Eg or 1 Eg levels. In more covalent hosts, such as oxides, covalent interaction between the 3d ions and ligand anions is enhanced with the result that the B and C parameters are strongly decreased. Therefore, relative to fluorides, the first spin-forbidden transition will be shifted to lower energy in oxides. For a long time, a quantitative measure of the nephelauxetic effect was the so called nephelauxetic ratio β = B/B0 .26 Indeed, this parameter provides an insight into the variation of the B parameter in various hosts, but at the same time, by virtue of its definition, it completely ignores the role of the C parameter, which is a rather crude approximation. A good example from Table II is the pair of K2 GeF6 and Y2 Ti2 O7 crystals (other pairs can be found too): the Racah parameters B for Mn4+ ion in these hosts practically coincide and are 593 cm−1 and 600 cm−1 , respectively. Therefore, the nephelauxetic ratio β would be nearly the same in these two materials. However, as the data in Table II reveal, the positions of the 2 Eg energy level in these two lattices are very different (16050 cm−1 and 14956 cm−1 , respectively). Such a difference can be explained if very different values of

the Racah parameter C (3824 cm−1 for K2 GeF6 and 3500 cm−1 for Y2 Ti2 O7 ) will be noticed. The inability of the β parameter to properly describe the variation in the energy of the 2 Eg level is confirmed by Fig. 3, which shows dependence of the Mn4+ 2 Eg level energy on β. All data points are scattered, and no clear trend can be extracted from the graph. This prompted us to introduce a new parameter that quantitatively 4+ describes the nephelauxetic effect in the spectroscopy of the Mn 2

2

ion: β1 = ( BB0 ) + ( CC0 ) .38,39 This parameter has been shown to be successful in predicting the energy of the Mn4+ 2 Eg →4 A2g transition in perovskites39 and the 1 Eg →3 A2g emission transition of the Ni2+ ion in various crystals.38 An advantage of this parameter is that it simultaneously takes into account the reduction in both B and C parameters. The energies of the above-mentioned transitions turned out to be the linear functions of the β1 parameter, which also shows simplicity of the proposed model.

Oxides Fluorides

16500

Position of the 2Eg level, cm-1

Crystal

16000

15500

15000

14500

14000

13500 0.3

0.4

0.5

0.6

0.7

0.8

0.9

β=B/B0 Figure 3. Dependence of energy of the Mn4+ 2 Eg level on the nephelauxetic ratio β = B/B0 .


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Position of the 2Eg level, cm-1

-142.83+15544.02 β1

Oxides Fluorides

Mn4+ doped crystals

16500

σ=365 cm-1 BaTiF6

16000

-142.83+15544.02 β1+σ

15500

-142.83+15544.02 β1−σ MgO

15000

Figure 4. Dependence of energy of the Mn4+ 2 Eg level 2 2 on the new nephelauxetic ratio β1 = ( BB0 ) + ( CC0 ) .

Al2O3 Gd2MgTiO6

14500 PbTiO3

14000

13500 0.88

0.92

0.96

1.00

1.04

Value of β1 Extension of this model to a larger number of Mn4+ activated crystals (Table II) is presented in Fig. 4. Again, a linear dependence of the 2 Eg →4 A2g transition energy is observed; the equation of the linear fit is E(2 Eg →4 A2g ) = − 142.83 + 15544.022 β1 . The root-mean square (rms) deviation of the data points from the fit line (shown by a solid straight line in Fig. 4) is σ = 365 cm−1 , and the two dashed line in Fig. 4 are obtained from the fit line by its up-/downward shift by σ. All data points, excluding Al2 O3 and Gd2 MgTiO6 , fall within the area between those dashed lines. One possible factor, which contributes to deviations of the data points from the straight line of a linear fit, is that very often the Mn4+ 2 Eg →4 A2g emission is accompanied by the vibronic progressions, and the position of the zero-phonon line cannot be always determined unambiguously. We also believe that this is the main reason for those two data points to fall out of the area restricted by the dashed lines in Fig. 4. On the other hand, it can be noticed that this value of σ = 365 cm−1 is close to typical energies

of phonon modes, which coincides with an uncertainty range in determination of the zero phonon line position and deviation of the data points in Fig. 4. The mathematical reason behind such remarkable linearity with respect to the β1 parameter is not yet clear. Several other combinations of the B and C parameters were also tried by us, but none was as successful. From the physico-chemical reasons, it is clear that since the Racah parameters are proportional to the Slater integrals (which in turn are related to the radial distribution of the electron density in the unfilled electron shells), it can be argued that variation in the electron density (or, speaking more precisely, re-distribution of the density of the d-electrons between central ion and ligands) is the prime factor that needs to be considered. However, no further conclusions can be made as of now. Fig. 5 shows a similar diagram for the Cr3+ ions. Again, like in the case of the Mn4+ ions, the linear trend between the position of 3382.80+10021.47* β1

16000

Oxides Fluorides

3+

Cr doped crystals σ=362 cm

3382.80+10021.47* β1+σ

-1

Cs2NaGaF6 M1 site 3382.80+10021.47* β1−σ

15000 KTiOPO4

2

Position of the Eg level, cm

-1

17000

Figure 5. Dependence of energy of the Cr3+ 2 Eg level on 2 2 the new nephelauxetic ratio β1 = ( BB0 ) + ( CC0 ) .

LaMgAl11O19 Cs2NaAlF6 M1 site KIn(WO4)2

14000

MgTiO3

13000 Y2Sn2O7

12000

0.90

KZnClSO43H2O

0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30

Value of β1 Downloaded on 2015-11-02 to IP 148.81.45.170 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).


Table IV. The main spectroscopic parameters pertaining to the Ni2+ 1 Eg →3 A2g transition in various crystals. β1 = B0 = 1068 cm−1 , C0 = 4457 cm−1 .74 Crystal AgCl Al2 O3 β-BaB2 O4 BaLiF3 BeAl2 O4 Be3 Al2 Si6 O18 Ca3 Sc2 Ge3 O12 CdBr2 CdCl2 CdI2 CsCdBr3 CsCdCl3 CsMgBr3 CsMgBr3 CsMgCl3 CsMgBr3 CsMgI3 KMgF3 KZnF3 LiCl LiGa5 O8 α-LiIO3 LiNbO3 MgAl2 O4 MgBr2 MgF2 MgGa2 O4 MgGa2 O4 MgO MgSO3 · 6H2 O NiBr2 NiCl2 NiCl2 (H2 O)4 NiF2 NiI2 [Ni(Im)2 (L-tyr)2 ] · 4H2 O RbCdF3 WO3 -TeO2 ZAS glass ZLKB glass ZLNB glass ZnSiF6 · 6H2 O Zn2 SiO4

R3073 (B/B0 )2 + (C/C0 )2 ,

Dq, cm−1

B, cm−1

C, cm−1

Position of the 1 E level

Ref.

668 1010 900 848 930 835 764 640 720 950 697 634 693 655 695 655 650 698 780 680 977 760 792 1030 706 750 967 1002 800 1016 754 770 828 777 737 1150 660 1099 907 835-850 840-845 915 742

807 900 850 1062 892 860 935 675 750 730 775.5 799 720 886 828 765 750 950 880 870 881 913 816 865 720 995 869 759 935 1000 763 785 928 897 646 630 950 958 940 765-790 780-810 932 1067

3141 4250 3500 3865 3750 3750 3503 2975 3150 3450 3041 3140 2830 3952 3206 2958 2800 3990 3696 4000 3225 4069 3224 3254 2908 4192 3150 3166 3330 4710 2772 4045 3764 3685 3851 4055 4000 3330 3919 3200-3260 3250-3290 4155 4304

12470 15840 15111 15504 14152 13842 13865 12104 13065 12450 11780 12570 11800 14700 14618 13515 13255 15156 15500 15323 12987 15304 12120 12987 11940 15600 12870 12136 13535 17757 13538 13800 14803 13979 11165 12950 16600 13513 14124 12160-12419 12297-12623 15239 10417∗

143 144 145 146 147 147 148 149 149 150 151 151 151 152 153 153 154 155 156, 157 158, 159 143 160 161 162 151 143 163 164 165 32 32 166 167 32 168 169 170 171 172 173 174 175

∗ This

assignment seems to be not correct. With the values of B, C, Dq the 1 E level should be at 18715 cm−1 . Therefore, this entry was excluded from the analysis.

the 2 Eg level and β1 parameter is kept to yield the following relation: E(2 Eg →4 A2g ) = 3382.80 + 10021.47 β1 , with the rms deviation of 362 cm−1 . Finally, Table IV and Fig. 6 present analogous data for the Ni2+ ions. The lowest in energy spin-forbidden transition in this case links together the 1 Eg excited state and the 3 A2g ground states. A linear equation for the energy of this transition is E(1 Eg →3 A2g ) = 2604.42 + 10007.85 β1 , with a considerably higher rms deviation of 797 cm−1 , which merely indicates the more randomly scattered experimental data. The reason for that is that the experimental determination of the 1 Eg level of Ni2+ is very often quite ambiguous task, since this level can be hidden by a wide absorption band for the spin-allowed 3 A2g →3 T2g transition. We also note that in the case of MgSO3 · 6H2 O:Ni2+ the value of the Racah parameter C is greater than the same parameter for a free ion (an obviously unphysical result), which also may reflect certain difficulties in getting the Dq, B and C values from the experimental spectra in that particular case.

As can be easily seen from Figs. 4–6, a common feature of all these systems is that there always exists a certain deviation of the representing data points from the fitting lines. We ascribe this fact to ambiguity in determination of the zero-phonon lines of the corresponding transitions. Very often – even in the low temperature experimental absorption/emission spectra – the zero-phonon lines of the 2 Eg →4 A2g and 1 Eg →3 A2g transitions are masked by pronounced vibronic progressions, especially in the fully symmetric a1g mode. For all three sets of data presented in Tables II–IV, we found a root-mean-square deviation of the data points from the fitting lines. These values are about 350–360 cm−1 for the Mn4+ and Cr3+ ions and about 800 cm−1 ; the typical phonon frequencies (and their multiples – what is important for the vibronic progressions) of a vast majority of solids are somewhere in the range of those estimates. Comparison of the Dq values collected in Tables II–IV highlights a strong crystal field case for the Mn4+ ions: almost for all crystals the value of Dq is greater than 2000 cm−1 . The situation is not


R3074


2+

2604.42+10007.85 β1+σ

Ni doped crystals 18000

σ=797 cm

-1

MgSO3·6H 2O

17000

2604.42+10007.85 β

1

Position of the Eg level, cm

-1

LiCl

16000 BaB2O4

15000

KZnF3

CsMgCl3

14000

2604.42+10007.85 β 1−σ

NiBr2 CsMgBr3

Figure 6. Dependence of energy of the Ni2+ 1 Eg level on the new nephelauxetic ratio β1 =

ZAS glass

2

2

( BB0 ) + ( CC0 ) .

CsMgI3

13000 12000

LiNbO3

11000

NiI2

10000 0.8

1.0

1.2

1.4

Value of β1 straightforward for the Cr3+ and, especially, for the Ni2+ ions, where very large differences in the Dq values in various crystals can be found. It is also interesting to note that the slopes of the fitting lines for the Cr3+ and Ni2+ ions are close. However, we consider this as a merely coincidence, without any far-reaching physical conclusions and consequences. At this point, we would like to emphasize that the developed model is purely empirical, and there is a lot of space for its improvement and further elaboration. The first principles calculations of the microscopic crystal field effects (i.e. dependence of the crystal field splittings and composition of the molecular orbitals composed of the d functions of transition metal ion and s-, p-functions of ligands on the interionic separation) can shed more light on quantitative trends in decreasing behavior of the Racah parameters in crystals. For example, Trueba et al.176 have shown that the value of Dq is determined by mixing of the Cr3+ eg states with the s states of ligands (absence of mixture of the s states of ligands with the t2g states of Cr3+ was also shown in Ref. 177). Decrease of the interionic separation undoubtedly enhances overlap between the d functions of transition metal ions and p functions of ligands. More quantitative calculations are needed to clarify how this enhanced overlap affects the degree of the Racah parameters reduction.

1) 2) 3)

4)

5) Possible Ways to Tune the Spin-forbidden Emission of Transition Metal Ions in Solids The experimental data presented in the previous section unambiguously demonstrate that the energies of the spin-forbidden transitions of the Mn4+ , Cr3+ , and Ni2+ ions are essentially host-dependent and, as such, they can be tuned in a wide range. It has been also shown that the nephelauxetic effect is the physical reason behind this phenomenon. Therefore, these ions can be considered as excellent local probes of the covalent effects in solids. Moreover, given a high practical significance of the considered in the present paper ions for various technological applications (lasing and lighting, first of all), the proper choice of the host materials for a particular application in view acquires special importance. Below we present several empirical observations and deduced from them recommendations, which can be helpful in choosing a proper host for getting emission of these three considered transition metal ions in the desirable wavelength.

6)

7)

If the characteristic emission of the Mn4+ , Cr3+ , Ni2+ ions has to be shifted to the shorter wavelengths, then the highly ionic compounds have to be chosen. If, on the contrary, the same emission is desired to be shifted to the longer wavelengths, then highly covalent hosts (oxides, chlorides, bromides) should be considered. Inside the groups of fluorides and oxide materials, there is an additional degree of freedom that allows to adjust further the 2 Eg (1 Eg ) state position. It is related to different symmetry of the crystal lattice sites occupied by the transition metal ions. If the local symmetry is octahedral, lowering of the 2 Eg level is expected because of enhanced covalency within the octahedral centers (in this case the overlap between the 3d electrons of a central ion and s-, p- functions of ligands is maximal). If, on the other hand, the symmetry of the transition metal site is lower, or (especially) the octahedral complexes are not aligned but tilted with respect to each other, the 2 Eg (1 Eg ) states are prone to shift to higher energies due to the weakened nephelauxetic effect. Additional splitting of the 2 Eg (1 Eg ) orbital doublets can be induced by a low symmetry crystal fields. In this case, the lowest singlet coming from these doublets would become an emitting level. This method can be used to tune the emission energy by a few tens-hundreds wave numbers. Applications of external hydrostatic pressure can considerably change the interionic distances (especially in soft compounds). In the case of the Cr3+ ions an external pressure can change a weak crystal field into a strong crystal field, thus eliminating the broad band 4 T2g →4 A2g luminescence on account of appearance of sharp 2 Eg →4 A2g emission. An external pressure can also enhance nephelauxetic effect, further decreasing the energy of the 2 Eg or 1 Eg states. An illustrative example of this kind is the redshift of the Cr3+ R-lines in ruby with pressure.178–180 Effects of co-doping (“chemical pressure”) can also modify the environment of the transition metal ions in solids. In this connection, it has been shown, for example, that the co-doping with Mg2+ increases greatly efficiency of the Mn4+ luminescence, at the same time solving the problem of charge compensation.58,181,182 Other charge compensating impurities can be also tried, to reach optimized performance of the Mn4+ -based phosphors. Certain interest is now gained by the mixed compounds, in which the nearest environment of the transition metal ion consists of


ECS Journal of Solid State Science and Technology, 5 (1) R3067-R3077 (2016) two types of ligands, which form different chemical bonds. In such compounds, such as oxyfluorides, for example, an interesting interplay of the chemical bond effects within the same impurity center can take place to further change the emission wavelengths.183–185 Conclusions In this paper we have surveyed the literature data and reviewed the spectroscopic properties of three transition metal ions (Mn4+ , Cr3+ and Ni2+ ) in solids. Large arrays of experimental data consisting of the Racah parameters B, C and crystal field strength Dq were composed after an analysis of many papers on experimental spectroscopy and crystal field calculations for the chosen ions. It has been shown that the energies of the lowest in energy spin-forbidden transitions (2 Eg →4 A2g for Mn4+ , Cr3+ and 1 Eg →3 A2g for Ni2+ ) depend on the nature of the ligands and on the nature of chemical bonding formed between these transition metal ions and the host ligands. In highly ionic compounds, such as fluorides, these ions experience a weaker nephelauxetic effect and, as a result, the excited 2 Eg and 1 Eg states move to higher energies. On the contrary, in more covalent oxides, chlorides, bromides the nephelauxetic effect is enhanced (here a word of caution should be said: in these compounds there is a competition between increased covalency due to change of ligands from F to O, Cl, Br, I and increased interionic separations, which would decrease covalency), which eventually moves theselevels to lower energies. 2

2

We also introduced a new parameter β1 = ( BB0 ) + ( CC0 ) in the theory of the nephelauxetic effect, which allows to represent the 2 Eg and 1 Eg levels energy as a linear function of β1 . A key difference between this parameter and an “old” nephelauxetic ratio β = B/B0 is that the new parameter simultaneously considers both B and C parameters, whereas the C parameter was completely omitted previously. Acknowledgment

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