Review—Photoluminescence Properties of Cr3+-Activated Oxide Phosphors

Sadao Adachi

doi:10.1149/2162-8777/abdc01

A variety of rare-earth-free phosphors emitting in the red spectral region have drawn much interest for realizing warm white-LED (w-LED) devices with high color rendering index and high luminous efficacy.^1–3 From this point of view, the most important non rare-earth ions with currently receiving great attention are Mn⁴⁺ and Cr³⁺ ions. Note that Cr³⁺ ion has the same electronic configuration, 3d³, as Mn⁴⁺ and V²⁺. The most common oxidation state of Cr used in phosphor applications is +3, though oxidation states from +2 to 6 + have been observed. The intra-d-shell electrons in Cr³⁺ ion can be well characterized by the standard crystal-field theory.^4,5

Near-IR radiation is known to have good penetration for organic matter and, therefore, it has drawn attention for application in monitoring foods and medicines, bioimaging, and night vision (see Refs. 6 and 7, and therein). Doping of Cr³⁺ ions into various hosts enables to emit light in the near-IR to red spectral region. Therefore, some Cr³⁺-activated phosphors that emit in the near-IR spectral region are not suitable for use in warm w-LED applications. However, their efficient emission/excitation properties can be successfully explained by the same electronic configuration, 3d³, as Mn⁴⁺ ion. As a result, near-IR LEDs inherit the traits of w-LEDs using Mn⁴⁺-doped phosphors, such as environmental friendliness, compactness, and high energy efficiency.^6,7 Therefore, the development of InGaN-chip excitable phosphors not only for w-LED but also for near-IR-emitting LED devices is of great importance.

Like Mn⁴⁺ ion, a sequence of its energy states can be described by the symmetry of ion site, by the crystal-field parameter Dq, and by interelectronic interaction strength determined by the Racah parameters B and C. Although the luminescence behaviors of the 3d³-configuration Mn⁴⁺ ions doped into various oxide hosts have been clarified in detail,^1–3 similar studies on Cr³⁺ ions introduced into oxide hosts have not been performed until now.

Here, we discuss the photoluminescence (PL) and PL excitation (PLE) properties of Cr³⁺-activated phosphors of oxide hosts, including borates, phosphates, silicates molybdates, tungstates, and similar. The zero-phonon line (ZPL) emission and excitation energies of the Cr³⁺ ions are determined from PL and PLE spectra by performing the Franck−Condon analysis within the configurational-coordinate (CC) model. Such ZPL emission and excitation energies are used to calculate the crystal-field and Racah parameters of Cr³⁺ in the various oxide hosts. A method for obtaining reliable crystal-field and Racah parameters of the Cr³⁺ ions doped into the oxide hosts is proposed for more deep understanding of such very important but, at present, largely scattered parameter values.

Tanabe−Sugano Energy-Level Diagram

The most of the fundamental optical properties of various 3dⁿ transition-metal ions doped into crystalline hosts can be interpreted in terms of the crystal-field model. Figures 1a and 2a show the effects of Dq/B, the crystal-field strength (Dq) divided by the Racah parameter (B), on the electronic energy levels of the 3dⁿ (n = 3) electron system based on the Tanabe−Sugano energy-level diagram scheme.^4,5 The optical properties of such transition-metal ions with the 3d³ configuration (Cr³⁺, Mn⁴⁺, V²⁺, etc) can be successfully interpreted by this energy-level diagram scheme.

**Figure 1.** (a) Tanabe–Sugano energy-level diagram for a 3d³ ion in octahedral symmetry of an oxide host crystal. The highlighted regions in the diagram correspond to those for phosphors of types O–Cr–A, O–Cr–B, and O–Mn (see text). Here, ⁴ F, ⁴ P, and ² G on the vertical axis represent the free-ion ground (⁴ F) and excited states (⁴ P and ² G). The CC model analyses for phosphors of types O–Cr–A (LaAlO₃:Cr³⁺), O–Cr–B (β-Ga₂O₃:Cr³⁺), and O–Mn (CaAl₁₂O₁₉:Mn⁴⁺) are shown in (b)–(d), respectively. The horizontal bars in each PLE spectrum of (b)−(d) represent the theoretical fits using Eq. 9. S = Stokes; a-S = anti-Stokes; CTB = charge transfer band.
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**Figure 2.** (a) Tanabe–Sugano energy-level diagram for a 3d³ ion in octahedral symmetry of a fluoride host crystal. The highlighted regions in the diagram correspond to those for phosphors of types F–Cr and F–Mn (see text). Here, ⁴ F, ⁴ P, and ² G on the vertical axis represent the free-ion ground (⁴ F) and excited states (⁴ P and ² G). The CC model analyses for phosphors of types F–Cr (LiSrGaF₆:Cr³⁺) and F–Mn (K₂SiF₆:Mn⁴⁺) are shown in (b) and (c), respectively. The horizontal bars in each PLE spectrum of (b) and (c) represent the theoretical fits using Eq. 9. S = Stokes; a-S = anti-Stokes; CTB = charge transfer band.
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In Figs. 1a and 2a, ⁴ A_2g represents the ground state of the 3d³ electron, which is a component of the free-ion ground state ⁴ F. Note that the crystal-field strength Dq is dependent on the distance R between the ion and ligands. The electronic energies of the higher-lying states like ⁴ T_2g, ⁴ T_1g, and ² A_1g are, therefore, strongly dependent on the type of lattice and ligands through R.

In the very small crystal-field region of Dq/B < 0.4, the first and second excited states are ⁴ T_2g and ⁴ T_1g,a, respectively, which are components of the free-ion ground state ⁴ F. In the small crystal-field region of 0.4 < Dq/B < 1.4, the first and second excited states are the same as those for Dq/B < 0.4, but the third excited state changes from ⁴ T_1g,b (⁴ P) to ² E_g (² G). In the region of 1.4 < Dq/B < 2.1, the second excited state exchanges from ⁴ T_1g,a to ² E_g with keeping the first excited state to be ⁴ T_2g.

Note that the optical transitions of ⁴ A_2g ↔ ² E_g, ² T_1g, and ² T_2g are both parity and spin forbidden and, therefore, any ² E_g, ² T_1g, and ² T_2g-related optical transitions cannot be clearly observed in principle. However, the ² E_g-related optical transitions are gained by the activation of local vibrations and become observable.⁸ Consequently, the ² E_g-related optical transitions are clearly observed in the crystal-field region of Dq/B > 2.1. The optical transitions of ⁴ A_2g ↔ ⁴ T_2g are spin allowed but parity forbidden. The ⁴ T_2g-related optical absorption and emission transitions can then be observed as a broad and strong band caused by an interaction with the specific lattice vibration mode.^1–3

Crystal-Field and Racah Parameters

The Tanabe−Sugano energy-level diagrams in Figs. 1a and 2a suggest that a curve of E(² E_g)_ZPL/B exhibits no strong dependence on Dq/B, where E(² E_g)_ZPL represents the ZPL energy of the ² E_g state. However, the E(² E_g)_ZPL/B plots determined from the generally used calculation model usually show an almost linear increase with increasing Dq/B, in clear disagreement with the Tanabe−Sugano diagram. As we will see latter, such an obvious disagreement comes from a large error in the determination of the ZPL energies required as input parameters in the general calculation model.^9–13 It should be noted that the E(² E_g)_ZPL and E(⁴ T_2g)_ZPL energies can be accurately determined from analyzing experimental PL and PLE spectra; however, accurate or reliable values of the higher-lying excited-state ZPL energies, such as E(⁴ T_1g,a)_ZPL, E(² A_1g)_ZPL (⁴ A_2g → ² A_1g), and E(⁴ T_1g,b)_ZPL (⁴ A_2g → ⁴ T_1g,b), are very difficult to obtain from any optical spectra. Because of this, an energy at each emission or excitation intensity maximum was previously regarded as its ZPL energy.^12,8 Of course, this assumption is a last resort.

Obtaining the Racah (B and C) and crystal-field parameters (Dq) requires at least three energy values those popularly used were E(² E_g)_ZPL, E(⁴ T_2g)_ZPL, and E(⁴ T_1g,a)_ZPL. As just mentioned above, it is very difficult and, in many cases, impossible to exactly determine the higher-lying ZPL energy, E(⁴ T_1g,a)_ZPL. Considering only exactly determinable E(² E_g)_ZPL and E(⁴ T_2g)_ZPL values, therefore. one can obtain expressions for B, C, and E(⁴ T_1g,a)_ZPL from the standard crystal-field theory (in cm⁻¹) as Refs. 12, 14

$\begin{eqnarray}\begin{array}{lll}B & = & \left(0.85r+2.19\right)Dq-\displaystyle \frac{1}{2}\left\{{\left[\left(1.69r+4.39\right)Dq\right]}^{2}\right.\\ & & -\,{\left.2.22E{({}^{2}E_{g})}_{{\rm{ZPL}}}Dq\right\}}^{1/2}\end{array}\end{eqnarray} \tag{ 1 }$

$\begin{eqnarray}&&\displaystyle \frac{C}{B}\equiv r\end{eqnarray} \tag{ 2 }$

$\begin{eqnarray}\begin{array}{lll}E{({}^{4}T_{1g,{\rm{a}}})}_{{\rm{ZPL}}} & = & 7.5B+15Dq\\ & & -\,\displaystyle \frac{Dq}{2}{\left[{\left(\displaystyle \frac{15B}{Dq}+10\right)}^{2}-\displaystyle \frac{480B}{Dq}\right]}^{1/2}\end{array}\end{eqnarray} \tag{ 3 }$

with

$\begin{eqnarray}&&Dq=\displaystyle \frac{1}{10}E{({}^{4}T_{2g})}_{{\rm{ZPL}}}\end{eqnarray} \tag{ 4 }$

An idea of obtaining Eqs. 1–3 is to reduce unknown input energy parameters from three to two [i.e., no need of E(⁴ T_1g,a)_ZPL] by assuming C/B ≡ r, where r is an optional constant. An algebra teaches us that determining two unknown variables, in the present study B (C = rB) and Dq, only two known energy parameters, in the present study only E(² E_g)_ZPL and E(⁴ T_2g)_ZPL, are required. Note that the Racah parameter ratios C/B for many 3d³-ion-activated oxide and fluoride phosphors are reported to fall in the range of 3 to 6 (Refs. 5 and 15) or can be assumed to be ∼4.7.¹⁶ The higher-lying E(⁴ T_1g,a)_ZPL energy can then be calculated by inputting only B and Dq values obtained from Eqs. 1 and 2 into Eq. 3.

Analysis Model for PL and PLE Spectra

Some of the optical spectra have been successfully analyzed by considering an interaction with the lattice vibrations. Let us consider the Franck−Condon analysis with the CC model to explain the peculiar optical absorption spectra in the 3d³ (Cr³⁺)-ion-activated phosphors. The optical transition energies in the CC model can now be written as Refs. 1–3, 17, 18

$\begin{eqnarray}&&h{\nu }_{{\rm{ex}}}={E}_{{\rm{ZPL}}}+kh{\nu }_{p,\mathrm{ex}}\end{eqnarray} \tag{ 5 }$

$\begin{eqnarray}&&h{\nu }_{{\rm{em}}}={E}_{{\rm{ZPL}}}-lh{\nu }_{p,\mathrm{em}}\end{eqnarray} \tag{ 6 }$

where E_ZPL is the ZPL transition energy, h is the Planck constant, hν_p,ex and hν_p,em are the lattice vibronic quanta for the excited and ground states, respectively, and k and l are positive integers. The experimental absorption and emission bands are regarded as envelopes of numerous lines; each is due to a transition between one vibration level, k, of the excited electronic state and one vibration level, l, of the ground electronic state.

The optical emission spectrum in the CC model can be written as Refs. 1–3

$\begin{eqnarray}&&{I}_{{\rm{PL}}}(E)=\displaystyle \displaystyle \sum _{n}{I}_{n}^{{\rm{em}}}(n)\exp \left[-\displaystyle \frac{{\left(E-{E}_{{\rm{ZPL}}}\pm nh{\nu }_{p,\mathrm{em}}\right)}^{2}}{2{{\sigma }_{{\rm{em}}}}^{2}}\right]\end{eqnarray} \tag{ 7 }$

with

$\begin{eqnarray}&&{I}_{n}^{{\rm{em}}}(n)={I}_{0}^{{\rm{em}}}\exp (-S)\displaystyle \frac{{S}^{n}}{n!}\,(n=0,1,2,\ldots )\end{eqnarray} \tag{ 8 }$

Here, σ_em is the broadening energy of each Gaussian component, ${I}_{0}^{{\rm{em}}}$ is the ZPL emission intensity, and S is the mean local vibration number (Huang−Rhys factor) defined by the Poisson statistics (Eq. 8). The upper and lower signs in Eq. 7 correspond to the Stokes and anti-Stokes luminescence, respectively.

The spectral distribution of the optical absorption spectrum in the CC model can be written essentially the same form as Eq. 7

$\begin{eqnarray}&&{I}_{{\rm{PLE}}}(E)=\displaystyle \displaystyle \sum _{n}{I}_{n}^{{\rm{ex}}}(n)\exp \left[-\displaystyle \frac{{\left(E-{E}_{{\rm{ZPL}}}-nh{\nu }_{p,\mathrm{ex}}\right)}^{2}}{2{\sigma }_{{\rm{ex}}}^{{\rm{2}}}}\right]\end{eqnarray} \tag{ 9 }$

with

$\begin{eqnarray}&&{I}_{n}^{{\rm{ex}}}(n)={I}_{0}^{{\rm{ex}}}\exp (-S)\displaystyle \frac{{S}^{n}}{n!}\,(n=0,1,2,\ldots )\end{eqnarray} \tag{ 10 }$

where σ_ex is the broadening energy of each Gaussian component in the PLE process and ${I}_{0}^{{\rm{ex}}}$ is the ZPL excitation transition intensity.

It should be noted that the higher the lattice temperature, the stronger is the electron–phonon coupling interaction and, as a result, the larger is the broadening parameter of σ_ex (σ_em). The fit-determined σ_ex values previously reported were in the order of a few tens of millielectron volts at temperatures from cryogenic up to 300 K.^1,2,14 For simplicity, let us assume σ_em = σ_ex = 0 meV in the present study. Assuming σ_ex → 0 (σ_em → 0) in Eq. 9 (Eq. 7), an absorption (emission) line-shape of I_PLE (I_PL) can be simply characterized only by the Poisson distribution function of Eq. 10 (Eq. 8), as depicted by the vertical bars in the PLE spectra of Figs. 1b−1d and 2b−2c.

Let us show in Fig. 3 the PL and PLE spectra for the MgCa₂WO₆:Cr³⁺ phosphor observed in the ⁴ A_2g ↔ ⁴ T_2g transition region at 300 K. The experimental data are taken from Xu et al.¹⁹ The vertical bars represent the results calculated using Eqs. 7 and 9. The fit-determined parameters here are: E(⁴ T_2g)_ZPL = 1.54 eV, hν_p,ex = 60 meV, and S = 2 (Stokes PL); E(⁴ T_2g)_ZPL = 1.54 eV, hν_p,ex = 60 meV, and S = 1 (ant-Stokes PL); E(⁴ T_2g)_ZPL = 1.54 eV, hν_p,ex = 60 meV, and S = 4 (PLE).

**Figure 3.** PL and PLE spectra for the MgCa₂WO₆:Cr³⁺ phosphor observed in the ⁴ A_2g ↔ ⁴ T_2g transition region at 300 K.¹⁹ The vertical bars represent the results calculated using Eqs. 7 and 9 (see text). The dashed lines also represent an oscillatory structure observed in the PLE spectrum, suggesting an energy interval of hν_p,ex ∼ 60 meV.
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As we will see more details in the next section, the vibronic quantum energies required in Eqs. 7 and 9 for the Cr³⁺-activated phosphors are hν_p,em = hν_p,ex ∼ 60 meV, which are slightly smaller than those for the Mn⁴⁺-activated ones (∼65 meV).^1–3 It should be noted that the weak, but clear multiple-peak structure can be found in the PLE spectrum of Fig. 3. An oscillatory energy interval is determined to be hν_p,ex ∼ 60 meV. More remarkable multiple-peak structures were observed in Mn⁴⁺-activated fluoride phosphors with an oscillatory energy interval of hν_p,ex ∼ 65 meV that was especially when PLE spectra were measured at cryogenic temperature.^10,20

Vibration Frequencies of ${{\rm{CrO}}}_{6}^{9-}$ Octahedron Molecule

Luminescence from Cr³⁺ and Mn⁴⁺ ions can be observed only when such ions are substituted for the octahedral site in the host lattice. Then, the complex peak structure has been observed in many PL and PLE spectra of Cr³⁺ and Mn⁴⁺-activated phosphors. Note that an octahedral molecule like ${{\rm{CrO}}}_{{\rm{6}}}^{9-}$ (CrO₆) or ${{\rm{MnO}}}_{{\rm{6}}}^{8-}$ (MnO₆) has 3N − 6 = 15 normal vibration modes (N = 7) with six coordinates required to describe the translational and rotational motions, six independent vibration modes of ν_i (i = 1 − 6) needed to represent its crystallographic symmetry properties, and the remining three modes come from the acoustic phonons with one longitudinal and two transverse modes (6 + 6 + 1 + 2 = 15).^21,22

We summarize in Table I the local vibration frequencies of ν_i (i = 1 − 6) for the Cr³⁺ and Mn⁴⁺ ions in the oxide and fluoride hosts.²³ The IR-active (ν₃ and ν₄) and silent vibration frequencies (ν₆) can in principle be obtained from measuring PL spectra, whereas the Raman-active ν₁, ν₂, and ν₅ frequencies are determined from Raman scattering measurements. Generally speaking, the vibration frequencies of the local ${{\rm{MnF}}}_{{\rm{6}}}^{2-}$ octahedron in the various fluoride hosts are not so largely dependent on a kind of surrounding metal species M (e.g., M = Si, Ge, Sn, Ti, Zr, or Hf in A₂MF₆ fluoride host).²³ Similarly, those of the ${{\rm{MnO}}}_{{\rm{6}}}^{8-}$ octahedron are not so largely dependent on a kind of oxide host materials. The same situation may hold for the Cr³⁺ ion in the various fluoride or oxide hosts.²³

Table I. Vibronic frequencies, ν₁ − ν₆, of ${{\rm{CrO}}}_{6}^{9-},$ ${{\rm{MnO}}}_{{\rm{6}}}^{8-},$ ${{\rm{CrF}}}_{{\rm{6}}}^{3-},$ and ${{\rm{MnF}}}_{6}^{2-}$ molecules in Cr³⁺ and Mn⁴⁺-doped oxide and fluoride crystals at 300 K (in meV).²³ R = Raman active; IR = IR active.

			Oxide		Fluoride
Mode	Polarization	Activity	Cr³⁺	Mn⁴⁺	Cr³⁺	Mn⁴⁺
ν₁	a_1g	R		∼74.4	∼68.2	∼74.4
ν₂	e_1g	R	∼60.1	∼63.2	∼55.8	∼63.2
				∼65.1^{^a)}		∼65.1^{^a)}
ν₃	t_1u	IR		∼81.2	∼71.3	∼81.2
ν₄	t_1u	IR		∼44.0	∼39.0	∼44.0
ν₅	t_2g	R		∼37.8	∼31.0	∼37.8
ν₆	t_2u	Silent		∼29.7	∼26.6	∼29.7

^a)Ref. 2.

Figure 4 shows the ² E_g-related PL spectra for some Mn⁴⁺-activated fluoride phosphors, together with those for the Cr³⁺-activated oxide phosphors at 300 K. The experimental data are taken for K₂TiF₆:Mn⁴⁺ and Na₂TiF₆:Mn⁴⁺ from Xu and Adachi,²⁴ for Ca₁₄Zn₆Al₁₀O₃₅:Cr³⁺ from Sun et al.,²⁵ for LaAlO₃:Cr³⁺ from Zhang et al.,²⁶ for La₂ZnTiO₆:Cr³⁺ from Ou et al.,²⁷ for MgAl₂O₄:Cr³⁺ from Karthik et al.,²⁸ and for MgSrAl₁₀O₁₇:Cr³⁺ from Singh et al.²⁹ The Stokes ν₃, ν₄, and ν₆ vibronic modes and anti-Stokes ν₄, and ν₆ vibronic modes are marked on the PL spectrum of the K₂TiF₆:Mn⁴⁺ phosphor.

In Ref. 23, each local vibronic frequency of the ${{\rm{CrF}}}_{6}^{3-}$ octahedron is found to be smaller than that of the ${{\rm{MnF}}}_{6}^{2-}$ one. This is not surprising because of the fact that the smaller the mass number of ligand metal ion, the smaller is its local vibronic frequency, i.e., in the present case, the mass number of Cr is smaller than that of Mn.³⁰ Similarly, each local vibronic frequency of the ${{\rm{CrO}}}_{6}^{9-}$ octahedron in Fig. 4 is understood to be slightly smaller than that of the ${{\rm{MnF}}}_{6}^{2-}$ one. It should be noted that the Raman-active mode energy of hν₂ corresponds to the vibronic energy of hν_p,em (hν_p,ex) involved in the PL (PLE) process.^1,3 Therefore, we can use a value of hν_p,em (hν_p,ex) ∼ 60 meV for the ${{\rm{CrO}}}_{6}^{9-}$ and ${{\rm{CrF}}}_{6}^{3-}$ octahedra that is slightly smaller than the value of ∼65 meV used for the Mn⁴⁺-activated oxide and fluoride phosphors.^1–3 The local vibronic energies of ν₂ ∼ 60 meV in K₂NaGaF₆:Cr³⁺ have also been determined from luminescence (59.5 meV) and Raman-scattering measurements (59.6 meV).³¹

Classification of Cr³⁺ and Mn⁴⁺-Activated Oxide and Fluoride Phosphors

Oxide phosphors

From a spectroscopic point of view, we classify the "oxide" phosphors doped with Cr³⁺ and Mn⁴⁺ ions into three different groups: (i) type O–Cr–A, (ii) type O–Cr–B, and (iii) type O–Mn (Fig. 1a). The crystal-field strength of type O–Cr–A phosphors certainly falls in the region of Dq/B > 2.1 and, therefore, their luminescence properties can be mainly determined by the ² E_g-related luminescence transitions [E(² E_g)_ZPL < E(⁴ T_2g)_ZPL; see Fig. 1b]. Similarly, the crystal-field strength of type O–Cr–B phosphors falls in the region of Dq/B < 2.1 and, therefore, their luminescence properties can be mainly determined by the ⁴ T_2g-related optical transitions [E(⁴ T_2g)_ZPL < E(² E_g)_ZPL; see Fig. 1c].

The luminescence properties of type O–Mn phosphors are essentially the same as those of type O–Cr–A phosphors and, therefore, the dominant luminescence comes from the ² E_g-related optical transitions [E(² E_g)_ZPL < E(⁴ T_2g)_ZPL; see Fig. 1d].³² To the best of our knowledge, there has not been reported any oxide phosphor doped with Mn⁴⁺ ion and clearly exhibiting the ⁴ T_2g-related luminescence peak or band. Table II summarizes a classification scheme for the Cr³⁺ and Mn⁴⁺-activated oxide and fluoride phosphors.

Table II. Classification scheme of Cr³⁺ and Mn⁴⁺-activated oxide and fluoride phosphors.

	Oxide		Fluoride
Ion	² E_g < ⁴ T_2g	² E_g > ⁴ T_2g	² E_g < ⁴ T_2g	² E_g > ⁴ T_2g
Cr³⁺	Type O–Cr–A	Type O–Cr–B	—	Type F–Cr
Mn⁴⁺	Type O–Mn	—	Type F–Mn	—

"—" means no any phosphor reported to date.

Fluoride phosphors

From a spectroscopic point of view, we classify the "fluoride" phosphors doped with Cr³⁺ and Mn⁴⁺ ions into two groups: (i) type F–Cr and (ii) type F–Mn (Fig. 2a). The crystal-field strength Dq/B of the Cr³⁺-doped fluoride phosphors [type F–Cr (Fig. 2b); E(⁴ T_2g)_ZPL < E(² E_g)_ZPL] is usually smaller than that of the Mn⁴⁺-doped fluoride ones [type F–Mn (Fig. 2c); E(² E_g)_ZPL < E(⁴ T_2g)_ZPL].^14,32 As a result, any Cr³⁺-activated fluoride phosphor with the crystal-field strength of Dq/B larger than that of a Mn⁴⁺-doped fluoride phosphor is nothing and, vice versa, any Mn⁴⁺-activated fluoride phosphor with the crystal-field strength of Dq/B smaller than that of a Cr³⁺-doped fluoride phosphor is nothing. This means that, to the best of our knowledge, almost all the Cr³⁺-doped (Mn⁴⁺-doped) phosphors belong to type F–Cr (type F–Mn), as depicted in Fig. 2a. This fact further promises that the ⁴ T_2g-related (² E_g-related) luminescence is usually observed in Cr³⁺-activated (Mn⁴⁺-activated) fluoride phosphors. As in type O–Cr–B phosphors, the luminescence spectra of type F–Cr phosphors can therefore be explained by the broad emission band caused by the spin-allowed ⁴ T_2g-related transitions (see Fig. 2b).¹⁴

Cr³⁺-Activated Oxide Phosphors of Type O–Cr–A: Specific Spectral Analysis

Bi₂Al₄O₉:Cr³⁺ phosphor

As mentioned previously, the Cr³⁺-activated "oxide" phosphors can be classified into two groups: types O–Cr–A and O–Cr–B. The luminescence properties of type O–Cr–A phosphors are essentially the same as those of the Mn⁴⁺-activated oxide and fluoride phosphors (types O–Mn and F–Mn)^10,32 and, therefore, the dominant luminescence comes from the ² E_g-related optical transitions [E(² E_g)_ZPL < E(⁴ T_2g)_ZPL; Fig. 1b (see also Fig. 1d)].

The Bi₂Al₄O₉:Cr³⁺ phosphor is of type O–Cr–A. Figure 5a shows the PL and PLE spectra of the Bi₂Al₄O₉:Cr³⁺ phosphor measured at 300 K. The experimental data are taken from Chen et al.³³ Because of the energy inequality relation of E(² E_g)_ZPL < E(⁴ T_2g)_ZPL for type O–Cr–A phosphors, this phosphor shows the PL and PLE spectra that are almost the same as those of the Mn⁴⁺-activated oxide and fluoride phosphors (i.e., types O–Mn and F–Mn phosphors). Thus, the PL spectrum can be characterized only by the sharp ² E_g-related ZPL emission peak and its Stokes and anti-Stokes counterparts. The lattice vibrations made possible a breaking of the parity and spin-forbidden selection rules and, therefore, gaining of the ² E_g → ⁴ A_2g luminescence intensity. The dominant lattice vibrations here are of the IR-active ν₃ and ν₄ modes and silent-mode ν₆ phonons in the ${{\rm{CrO}}}_{{\rm{6}}}^{9-}$ octahedron complex, but not of the Raman-active ν₁, ν₂, and ν₅ modes (see Table I).

The strong and sharp PL peaks at ∼1759 and 1.775 eV in Fig. 5a are due to the ² E_g-relaed ZPL emission peaks (R₁ and R₂ lines). The vertical bars in the PLE spectrum show the results calculated using Eq. 9. The fit-determined parameters here are: E(⁴ T_2g)_ZPL = 1.82 eV, hν_p,ex = 60 meV, and S = 4. As has been mentioned before, the ZPL energies of the first [E(² E_g)_ZPL] and second lowest excited states [E(⁴ T_2g)_ZPL] can be relatively easily and accurately determined from PL and PLE spectra. The "center of gravity" energy of the spin–orbit split R₁ and R₂ lines is given by E(² E_g)_ZPL = 1.767 eV. Introducing this value of E(² E_g)_ZPL = 1.767 eV and PLE value of E(⁴ T_2g)_ZPL = 1.82 eV into Eqs. 1–3, we obtain the Racah-related parameters of B = 82.5 meV, C = 388 meV, E(⁴ T_1g,a)_ZPL = 2.62 eV, and Dq/B = 2.207 (≅2.21). In Table III, we summarize some important excited-state ZPL energies, together with the Racah (B and C) and crystal-field parameters (Dq/B) for the various Cr³⁺-activated oxide phosphors of type O–Cr–A determined in the present study.^{25–29,33–131}

Table III. Summary of host materials, ZPL transition energies [E(² E_g)_ZPL, E(⁴ T_2g)_ZPL = 10Dq, and E(⁴ T_1g,a)_ZPL], and Racah parameters (B and C) for the Cr³⁺-activated oxide phosphors of type O–Cr–A. Values of E(⁴ T_1g,a)_ZPL were calculated from Eq. 3 (C/B = 4.7).

Host	² E_g (R₁/R₂) (eV)	⁴ T_2g (eV)	⁴ T_1g,a (eV)	B (meV)	C (meV)	T (K)	References
α-Al₂O₃	1.787/1.791	2.07	2.90	83.1	391	115	34
	1.785/1.788	1.94	2.76	83.2	391	300	34
Al₁₀Ge₂O₁₉	1.774	2.02	2.84	82.5	388	300	35
Al₅NO₆	1.789	2.02	2.85	83.2	391	300	36
BaAl₂O₄	1.759/1.773	1.92	2.73	82.3	387	300	37
BaAl₁₂O₁₉	1.767	2.03	2.85	82.1	386	300	38
Ba₂LaNbO₆	1.709/1.713					10	39
BaMgAl₁₀O₁₇	1.794	1.92	2.74	83.6	393	300	40
	1.782	1.89	2.70	83.1	390	300	41
Ba₂Mg(BO₃)₂	1.777	1.84	2.64	82.9	390	77	42
BeAl₂O₄	1.826/1.831^{^a)}	1.93^{^a)}	2.76	85.3	401	12	43
	1.817/1.822^{^b)}	1.89^{^b)}	2.71	84.9	399	300	44
Bi₂Al₄O₉	1.759/1.775	1.82	2.62	82.5	388	300	33
	1.756	1.84	2.64	81.9	385	300	45
	1.757/1.773	1.84	2.64	82.3	387	300	46
CaAl₁₂O₁₉	1.811	1.93	2.75	84.4	397	300	47
	1.810	1.89	2.71	84.4	397	300	48
CaAl₆Ga₆O₁₉	1.789	1.89	2.70	83.4	392	300	49
Ca₃Al₂Ge₂O₁₀	1.778	1.92	2.73	82.8	389	300	50
CaGa₂O₄	1.790	1.82	2.62	83.6	393	300	51
CaGdAlO₄	1.665	1.82	2.58	77.5	364	300	52
Ca₂NbAlO₆	1.663	1.74	2.49	77.6	365	300	53
Ca₂NbGaO₆	1.676	1.77	2.53	78.2	367	300	53
CaTiO₃	1.619	1.81	2.56	75.3	354	77	54
CaYAlO₄	1.668	1.79	2.55	77.7	365	300	55
Ca₁₄Zn₆Al₁₀O₃₅	1.742	1.87	2.66	81.2	382	300	25
CdAl₂O₄	1.794	1.90	2.72	83.6	393	300	56
Cd₂Nb₂O₇	1.683						57
(CH₃)₂NH₂Al(SO₄)₂ · 6H₂O	1.761	1.80	2.59	82.2	386	300	58
(CH₃)₂NH₂Ga(SO₄)₂ · 6H₂O	1.750/1.757	1.78	2.57	81.9	385	300	58
Cr₂O₃	1.704^{^c)}	1.77^{^c)}	2.54	79.5	374	77	59
	1.707^{^d)}	1.77^{^d)}	2.54	79.7	374	77	59
GdAlO₃	1.705	2.03	2.83	79.2	372	300	60
GdAl₃(BO₃)₄	1.808	1.82	2.63	84.5	397	300	61
	1.816	1.82	2.63	84.9	399	300	62
GdY₂Al₃Ga₂O₁₂	1.795	1.82	2.63	83.8	394	300	63
LaAlO₃	1.688	1.96	2.74	78.4	369	300	26
	1.688	1.95	2.73	78.5	369	300	64
LaGaO₃	1.677/1.701	1.75	2.51	78.8	370	300	65
	1.700	1.80	2.57	79.3	373	300	66
	1.698	1.79	2.56	79.2	372	300	67
La₃GaGe₅O₁₆	1.769	1.77	2.56	82.7	389	300	68
	1.781	1.81	2.61	83.2	391	300	69
LaMgAl₁₁O₁₉	1.789	1.86	2.67	83.5	392	300	70
LaMgGa₁₁O₁₉	1.680	1.75	2.51	78.4	368	300	71
La₂MgGeO₆	1.783	1.84	2.64	83.2	391	300	72
La₂ZnTiO₆	1.672	2.28	3.08	77.3	363	300	27
LiAl₅O₈	1.737/1.771	1.95	2.76	81.6	384	300	73
LiGa₅O₈	1.731/1.766	1.85	2.64	81.6	383	300	74
	1.734/1.768	1.80	2.59	81.7	384	300	75
	1.727/1.763	1.83	2.62	81.4	383	300	76
	1.726/1.763	1.84	2.63	81.4	382	300	77
Li₅Zn₈Al₅Ge₉O₃₆	1.772	1.90	2.71	82.6	388	300	78
	1.772	1.88	2.69	82.6	388	300	79
Li₅Zn₈Ga₅Ge₉O₃₆	1.772	1.83	2.63	82.7	389	300	79
Li₂ZnGe₃O₈	1.732	1.78	2.56	80.8	380	300	80
Lu₃Al₅O₁₂	1.796	1.98	2.80	83.6	393	300	81
Lu₃Ga₅O₁₂	1.802	1.84	2.65	84.1	395	300	82
MgO	1.776^{^e)}	1.91^{^e)}	2.72	82.8	389	77	83
	1.761^{^f)}	1.86^{^f)}	2.66	82.1	386		84
MgAl₂O₄	1.801	1.88	2.70	84.0	395	300	28
	1.806	1.94	2.76	84.2	396	300	85
	1.804	1.94	2.76	84.1	395	300	86
MgAlGaO₄	1.754	2.05	2.87	81.5	383	300	87
MgGa₂O₄	1.746	1.76	2.54	81.6	383	300	88
	1.753	1.81	2.60	81.8	385	300	89
Mg₃Ga₂GeO₈	1.663	1.72	2.47	77.6	365	300	90
Mg₄Ga₄Ge₃O₁₆	1.791	1.86	2.67	83.6	393	300	91
Mg₄Ga₈Ge₂O₂₀	1.790	1.87	2.68	83.5	392	300	92
MgGaInO₄	1.743	1.98	2.79	81.1	381	300	93
Mg₂SiO₄	1.788/1.813^{^g)}	1.83^{^g)}	2.64	84.1	395	10	94
	1.725	1.78	2.56	80.5	378	300	95
MgSrAl₁₀O₁₇	1.798	1.92	2.74	83.8	394	300	29
MgSr₂Al₂₂O₃₆	1.800	1.85	2.66	84.0	395	300	96
MgY₂Al₄SiO₁₂	1.799	1.88	2.69	83.9	394	300	97
NaGdTi₂O₆	1.634	1.70	2.44	76.2	358	300	98
Na₂TiGeO₅	1.613	1.80	2.54	75.1	353	300	99
SrAl₂O₄	1.791	1.96	2.78	83.4	392	300	100
SrAl₁₂O₁₉	1.813	1.84	2.65	84.7	398	300	48
	1.804	1.84	2.65	84.2	396	300	100
Sr₄Al₁₄O₂₅	1.798	2.00	2.83	83.7	393	300	101
SrGa₁₂O₁₉	1.786	1.80	2.60	83.4	392	300	102
SrLaAlO₄	1.666	1.72	2.47	77.8	365	300	103
Sr₂LaGa₁₁O₂₀	1.773/1.790	1.91^{^h)}	2.72	83.0	390	300	104
YAlO₃	1.766	2.02	2.84	82.1	386	300	105
Y₃Al₅O₁₂	1.805	1.84	2.65	84.3	396	300	106
	1.800	1.81	2.62	84.1	395	300	107
	1.753	1.80	2.59	81.8	385	300	108
YAl₃(BO₃)₄	1.808	1.82	2.63	84.5	397	300	61
	1.807	1.82	2.63	84.4	397	300	62
	1.810	1.82	2.63	84.6	397	300	109
Y₃Al₂Ga₃O₁₂	1.799	1.80	2.60	84.1	395	300	110
ZnAl₂O₄	1.802	2.02	2.85	83.8	394	300	111
	1.802	2.01	2.84	83.9	394	300	112
	1.805	2.01	2.84	84.0	395	300	113
	1.809	2.00	2.83	84.2	396	300	114
ZnAlGaO₄	1.805	2.01	2.84	84.0	395	300	115
Zn₃Al₂GeO₈	1.805	1.90	2.72	84.2	396	300	114
Zn₃Al₂Ge₂O₁₀	1.768	1.92	2.73	82.4	387	300	116
Zn₃Al₂Ge₃O₁₂	1.802	1.88	2.70	84.1	395	300	117
Zn₆Al₈GeO₂₀	1.799	1.97	2.79	83.8	394	300	118
ZnGa₂O₄	1.802	2.00	2.83	83.9	394	300	119
	1.801	1.96	2.78	83.9	394	300	120
	1.808	1.96	2.79	84.2	396	300	121
	1.808	1.96	2.79	84.2	396	300	122
	1.808	1.99	2.82	84.2	396	300	123
Zn₃Ga₂GeO₈	1.782	1.87	2.68	83.1	391	300	124
Zn₃Ga₂Ge₂O₁₀	1.776	1.80	2.60	82.9	390	300	125
Zn₅Ga₆GeO₁₆	1.774	1.85	2.65	82.8	389	300	126
Zn₈Ga₁₂Ge₃O₃₂	1.780	1.91	2.72	83.0	390	300	127
	1.775	1.82	2.62	82.9	389	300	128
Zn₃Ga₂SnO₈	1.782	1.90	2.71	83.1	390	300	124
Zn₆Ga₈TiO₂₀	1.749	1.90	2.70	81.5	383	300	129
Zn₂SnO₄	1.766	1.78	2.57	82.5	388	300	130
	1.766	1.86	2.66	82.4	387	300	131

^a) E ∣∣ b.^b) E ∣∣ x, y, z ( E ∣∣ a, b, c; i.e., no strong polarization dependence).^c) E ⊥ c.^d) E ∣∣ c.^e)Cubic site.^f)Tetragonal site.^g) E ∣∣ a, b; T = 150 K (PL); Mg(I) site.^h) E ∣∣ π, σ, α (i.e., no strong polarization dependence).

Figure 6 shows the effects of crystal field on the energy levels of Cr³⁺ ion in the Tanabe−Sugano energy-level diagram.^4,5 Here and below, we assume C/B ≡ r to be 4.7.^5,15,16 The symbols plotted correspond to those for the Bi₂Al₄O₉:Cr³⁺ phosphor (see Fig. 5a). The E(² E_g)_ZPL, E(⁴ T_2g)_ZPL = 10Dq, E(⁴ T_1g,a)_ZPL, B, and C values were taken from a list in Table III. One can see in Fig. 6 an excellent agreement of the excited-state ZPL energies, E(² E_g)_ZPL, E(⁴ T_2g)_ZPL, and E(⁴ T_1g,a)_ZPL, divided by B, with the theoretical Tanabe−Sugano diagram curves. The Tanabe−Sugano diagram curves at Dq/B = 2.207 also provide the ZPL-related parameter values of E(² T_1g)_ZPL/B = 23.0 with E(² T_1g)_ZPL = 1.90 eV and E(² T_2g)_ZPL/B = 31.7 with E(² T_2g)_ZPL = 2.62 eV. These E/B values are also plotted by the shaded triangles in Fig. 6.

Note that the weak, spin-forbidden ⁴ A_2g → ² T_1g transition energy of E(² T_1g)_ZPL = 1.90 eV nearly coincides with the strong, spin-allowed ⁴ A_2g → ⁴ T_2g transition one. Therefore, the former contribution can be successfully neglected in the present PLE spectral analysis of Fig. 5a. The vertical arrows in Fig. 5a indicate the positions of the various excited-state ZPL energies obtained in the present analysis.

An anomaly in PLE spectra of many Cr³⁺-activated "fluoride" phosphors can be sometimes observed.¹⁴ This anomaly is due to the Fano resonance (protuberances) or anti-resonance (small dips) caused by the spin−orbit interaction between the sharp spin-forbidden ² E_g (² G) or ² T_1g ⁽² G) state and broad spin-allowed ⁴ T_2g (⁴ F) state.^132,133 The theoretical Fano profile was discussed in detail by Sturge et al.¹³⁴ The same resonance/anti-resonance interaction may occur in Cr³⁺-activated "oxide" phosphors. In fact, a weak anomaly in the ⁴ A_2g → ⁴ T_2g transition region of the PLE spectrum is observed at ∼1.90 eV in Fig. 5a. Such a peculiar spectral feature sometimes makes possible to accurately determine the spin-forbidden ZPL transition energies at the various excited states like ² E_g, ² T_1g, and ² T_2g from actual optical spectra. In fact, we can determine in Fig. 5a the E(² T_1g)_ZP energy to be ∼1.9 eV. This value is in good agreement with the E(² T_1g)_ZPL = 1.90 eV value estimated from the Tanabe−Sugano diagram curve in Fig. 6. Moreover, we can find in Fig. 5a an energy of ∼2.6 eV at which new excitation absorption transitions start to occur. This energy may correspond to the ⁴ T_1g,a and ² T_2g-related ZPL transition energies, in good agreement with the values of E(⁴ T_1g,a)_ZPL = E(² T_2g)_ZPL = 2.62 eV estimated from the Tanabe−Sugano diagram curves in Fig. 6 (open circle and shaded triangle).

GdAlO₃:Cr³⁺ phosphor

The PL and PLE spectra of the GdAlO₃:Cr³⁺ phosphor measured at 300 K are shown in Fig. 7. The experimental data are taken from Eldridge.⁶⁰ The sharp and strong PL peak can be easily found at ∼1.705 eV, which is caused by the ⁴ A_2g → ² E_g transition peak. Similarly, the largest PLE band peaking at ∼2.2 eV is due to the ⁴ A_2g → ⁴ T_2g excitation absorption transitions. The corresponding PLE component calculated using Eq. 9 with the fitting parameters of E(⁴ T_2g)_ZPL = 2.03 eV, hν_p,ex = 60 meV, and S = 3 is shown by the vertical bars.

**Figure 7.** PL and PLE spectra for the GdAlO₃:Cr³⁺ phosphor measured at 300 K. The experimental data are taken from Eldridge.⁶⁰ The vertical bars in the PLE spectrum show the results calculated using Eq. 9. The vertical arrows indicate the positions of the various excited-state ZPL energies, E(² E_g)_ZPL, E(⁴ T_2g)_ZPL, E(² T_2g)_ZPL, E(⁴ T_1g,a)_ZPL. S = Stokes; a-S = anti-Stokes.
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The values of E(² E_g)_ZPL = 1.705 eV and E(⁴ T_2g)_ZPL = 2.03 eV introduced into Eqs. 1−3 give the Racah-related parameters of B = 79.2 meV, C = 372 meV, E(⁴ T_1g,a)_ZPL = 2.83 eV, and Dq/B = 2.56 (Table III). The determined E(⁴ T_1g,a)_ZPL value then makes possible to calculate Eq. 9 for the PLE component caused by the ⁴ A_2g → ⁴ T_1g,a excitation transitions. This calculation yielded the best-fit parameters of E(⁴ T_1g,a)_ZPL = 2.83 eV, hν_p,ex = 60 meV, and S = 3, and the result is shown by the vertical bars in Fig. 7.

The Tanabe−Sugano diagram plots for the GdAlO₃:Cr³⁺ phosphor are shown in Fig. 8. The E/B plots for the ² E_g, ⁴ T_2g, and ⁴ T_1g,a states are found to fall on the Tanabe−Sugano diagram curves very well. Further, the curve crossing at Dq/B = 2.56 gives the value of E(² T_2g)_ZPL/B = 32.4 with E(² T_2g)_ZPL = 2.57 eV. The open triangle in Fig. 8 represents this data point of E(² T_2g)_ZPL/B. The corresponding PLE contribution calculated using Eq. 9 with E(² T_2g)_ZPL = 2.57 eV, hν_p,ex = 60 meV, and S = 4 is shown by the vertical bars in Fig. 7. An improvement of fit between the experimental and theoretical data can be obtained by adding this extra absorption term of E(² T_2g)_ZPL.

**Figure 8.** Tanabe–Sugano energy-level diagram for a 3d³ (Cr³⁺) ion in octahedral symmetry with r = 4.7. The circular symbols represent the various ZPL energies for the GdAlO₃:Cr³⁺ and ZnGa₂O₄:Cr³⁺ phosphors plotted against the crystal-field parameter Dq, both axes divided by B. The Racah and related parameters are determined by analyzing PL and PLE spectra in Fig. 7 (GdAlO₃:Cr³⁺) and 11 (ZnGa₂O₄:Cr³⁺).
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La₂ZnTiO₆:Cr³⁺ phosphor

Figure 9 shows the PL and PLE spectra of the La₂ZnTiO₆:Cr³⁺ phosphor measured at 300 K. The experimental data are taken from Ou et al.²⁷ Note that the PL spectrum plotted in Fig. 9 is the same as that in Fig. 4g. At first glance, it is very difficult to conclude which peak is the ZPL peak or those originate from the Stokes and anti-Stokes sidebands. However, many PL spectral plots of various phosphors facilitate the ZPL peak determination very easy. Based on this, one can conclude the weak, but sharp peak at ∼1.672 eV in Fig. 4g to be due to the ZPL emission peak of the ² E_g state. The PLE analysis using Eq. 9 also determines the following best-fitting parameters for the ⁴ A_2g → ⁴ T_2g excitation transitions: E(⁴ T_2g)_ZPL = 2.28 eV, hν_p,ex = 60 meV, and S = 6.

Introducing E(² E_g)_ZPL = 1.672 eV and E(⁴ T_2g)_ZPL = 2.28 eV into Eqs. 1−3, we obtain B = 77.3 meV, C = 363 meV, E(⁴ T_1g,a)_ZPL = 3.08 eV, and Dq/B = 2.95 for the La₂ZnTiO₆:Cr³⁺ phosphor. The corresponding Tanabe−Sugano energy-level diagram plots are shown in Fig. 10. The E/B curve crossings at Dq/B = 2.95 give the following ZPL energy parameters: E(² T_2g)_ZPL/B = 33.1 with E(² T_2g)_ZPL = 2.56 eV and E(² A_1g)_ZPL/B = 48.0 with E(² A_1g)_ZPL = 3.71 eV (open triangles).

**Figure 10.** Tanabe–Sugano energy-level diagram for a 3d³ (Cr³⁺) ion in octahedral symmetry with r = 4.7. The circular symbols represent the various ZPL energies for the La₂ZnTiO₆:Cr³⁺ phosphor plotted against the crystal-field parameter Dq, both axes divided by B. The Racah and related parameters are determined by analyzing PL and PLE spectra in Fig. 9.
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As in Fig. 7, the addition of the ⁴ A_2g → ² T_2g excitation transition component with the fitting parameters of E(² T_2g)_ZPL = 2.56 eV, hν_p,ex = 60 meV, and S = 8 in Eq. 9 can improve the fit with the experimental PLE spectrum in the spectral region between the E(⁴ T_2g)_ZPL and E(⁴ T_1g,a)_ZPL excitation transitions. Moreover, the broad excitation band peaking at ∼3.7 eV cannot be explained only by considering the ⁴ A_2g → ⁴ T_1g,a excitation transition component. Therefore, we further consider the ⁴ A_2g → ² A_1g excitation transition component with E(² A_1g)_ZPL = 3.71 eV, hν_p,ex = 60 meV, and S = 3 in Eq. 9. An improvement of the fit with the experimental PLE spectrum is easily understood in Fig. 9.

ZnGa₂O₄:Cr³⁺ phosphor

Figure 11 shows the PL and PLE spectra of the ZnGa₂O₄:Cr³⁺ phosphor measured at 300 K. The experimental data are taken from Li et al.¹²⁰ As in Fig. 9, it is very difficult to determine the ² E₂ → ⁴ A_2g ZPL transition energy in the PL spectrum. Plotting PL intensities on the horizontal axis of E − E(² E_g)_ZPL in Fig. 4, we determine the E(² E_g)_ZPL ∼ 1.801 eV value for the ZnGa₂O₄:Cr³⁺ phosphor. Note that the strongest PL peak in Fig. 11 appears at ∼1.751 eV. If we assume its peak as the E(² E_g)_ZPL emission peak, some contradiction arises that is the Stokes emission component is much weaker than the anti-Stokes emission one. Thus, the E(² E_g)_ZPL energy position should be larger in energy than ∼1.751 eV. The peak energy of E(² E_g)_ZPL ∼ 1.801 eV was determined by satisfying this requirement. The spectral PLE calculation using Eq. 9 also determines the value of E(⁴ T_2g)_ZPL = 1.96 eV with hν_p,ex = 60 meV and S = 5, as shown in Fig. 11.

The ZPL energies of E(² E_g)_ZPL = 1.801 eV and E(⁴ T_2g)_ZPL = 1.96 eV, and the use of Eqs. 1−3 provide B = 83.9 meV, C = 394 meV, E(⁴ T_1g,a)_ZPL = 2.78 eV, and Dq/B = 2.34 for the ZnGa₂O₄:Cr³⁺ phosphor. The corresponding Tanabe−Sugano energy-level diagram is shown in Fig. 8. The E/B curve crossing at Dq/B = 2.34 gives E(² T_2g)_ZPL/B = 32.0 with E(² T_2g)_ZPL = 2.68 eV (open triangle). The PLE spectrum coming from these ⁴ A_2g → ² T_2g excitation transitions is also calculated and plotted in Fig. 11. The best-fit parameters of Eq. 9 are: E(⁴ T_2g)_ZPL = 2.68 eV, hν_p,ex = 60 meV, and S = 2.

Cr³⁺-Activated Oxide Phosphors of Type O–Cr–B: Specific Spectral Analysis

Bi₂Ga₄O₉:Cr³⁺ phosphor

Bi₂Al₄O₉ and Bi₂Ga₄O₉ compounds are isostructural materials and crystallize in the orthorhombic structure. The Cr³⁺-doped Bi₂Al₄O₉ phosphor is of type O–Cr–A, and its fundamental phosphor properties were discussed before (Figs. 5a and 6). Let us show in Fig. 5b the PL and PLE spectra of the Bi₂Ga₄O₉:Cr³⁺ phosphor measured at 300 K.³³ The sharp PL peaks at ∼1.747 and 1.768 eV are due to the E(² E_g)_ZPL energy peaks (R₁ and R₂ lines) with the "center-of-gravity" energy of E(² E_g)_ZPL = 1.758 eV. The lower-energy broad luminescence band peaking at ∼1.6 eV is attributed to the ⁴ T_2g → ⁴ A_2g emission transitions. The best fit of this broad luminescence band using Eq. 7 is shown by the vertical bars in Fig. 5b, giving E(⁴ T_2g)_ZPL = 1.72 eV, hν_p,em = 60 meV, and S = 2. Thus, the energy inequality relation of E(⁴ T_2g)_ZPL < E(² E_g)_ZPL holds for the Bi₂Ga₄O₉:Cr³⁺ phosphor and suggests its phosphor type being of O–Cr–B. The large ⁴ T_2g-related excitation band peaking at ∼2.0 eV has also been analyzed using Eq. 9 and obtained E(⁴ T_2g)_ZPL = 1.72 eV, hν_p,ex = 60 meV, and S = 5 as best-fit parameters.

The "center of gravity" energy of the spin–orbit split R₁ and R₂ peaks is given by E(² E_g)_ZPL = 1.758 eV. Using this value and E(⁴ T_2g)_ZPL = 1.72 eV, we obtain B = 82.2 meV, C = 386 meV, E(⁴ T_1g,a)_ZPL = 2.50 eV, and Dq/B = 2.092 (≅2.09) for the Bi₂Ga₄O₉:Cr³⁺ phosphor. Table IV summarizes some important excited-state ZPL energies, together with the Racah and crystal-field parameters B, C, and Dq/B, for the various Cr³⁺-activated oxide phosphors of type O–Cr–B determined in the present study.^{7,19,33,61,84,94,135–203} The excited-state ZPL energies of E(² E_g)_ZPL, E(⁴ T_2g)_ZPL, and E(⁴ T_1g,a)_ZPL vs Dq, divided by B, are also plotted on the Tanabe−Sugano energy-level diagram in Fig. 6.

Table IV. Summary of host materials, ZPL transition energies [E(² E_g)_ZPL, E(⁴ T_2g)_ZPL = 10Dq, and E(⁴ T_1g,a)_ZPL], and Racah parameters (B and C) for the Cr³⁺-activated oxide phosphors of type O–Cr–B. Values of E(⁴ T_1g,a)_ZPL were calculated from Eq. 3 (C/B = 4.7).

Host	² E_g (R₁/R₂) (eV)	⁴ T_2g (eV)	⁴ T_1g,a (eV)	B (meV)	C (meV)	T (K)	References
Al₂(WO₄)₃	1.734	1.67	2.44	81.2	381	300	135
AlSc(WO₄)₃	1.741^{^a)}	1.58^{^a)}	2.34	81.7	384	300	136
Al₂SiO₅	1.791	1.79	2.59	83.7	393	300	137
BaZrSi₃O₉	1.837	1.70	2.50	86.1	405	300	138
Bi₂AlGa₃O₉	1.746/1.767	1.70	2.48	82.2	386	300	33
Bi₂Al₂Ga₂O₉	1.753/1.770	1.72	2.50	82.4	387	300	33
Bi₂Al₃GaO₉	1.756/1.772	1.75	2.54	82.5	388	300	33
Bi₂Ga₄O₉	1.747/1.768	1.72	2.50	82.2	386	300	33
	1.747/1.767	1.68	2.46	82.3	387	300	139
Ca₃Al₂Ge₄O₁₄	1.818	1.72	2.52	85.2	400	300	140
Ca₃Ga₂Ge₃O₁₂	1.845	1.72	2.53	86.5	406	300	138
Ca₃Hf₂Al₂SiO₁₂	1.795	1.71^{^b)}	2.50	84.1	395	300	141
	1.795	1.66^{^c)}	2.44	84.2	396	300	141
Ca₂LuHf₂Al₃O₁₂	1.795	1.71	2.50	84.1	395	300	141
	1.814	1.65	2.44	85.1	400	300	142
Ca₂LuScGa₂Ge₂O₁₂	1.83	1.71	2.51	85.8	403	300	143
Ca₂LuZr₂Al₃O₁₂	1.810	1.68	2.47	84.9	399	300	144
CaSc₂O₄	1.770	1.66	2.44	82.9	390	2.7	145
Ca₃Sc₂Ge₃O₁₂	1.828	1.72	2.52	85.6	403	10	146
	1.825	1.72	2.52	85.5	402	300	146
Ca₃Sc₂Si₃O₁₂	1.788	1.69	2.48	83.8	394	300	7
	1.771	1.70	2.48	82.9	390	300	147
CaY₂Mg₂Ge₃O₁₂	1.775	1.72	2.51	83.1	390	300	148
CaZnGe₂O₆		1.70				300	149
CdWO₄	1.760	1.26	1.95	83.6	393	10	204
(Ce_0.82Gd_0.18)Sc₃(BO₃)₄	1.840^{^d,^e)}	1.61^{^d,^e)}	2.40	86.5	407	300	150
CsAl(MoO₄)₂	1.673	1.64	2.38	78.2	368	300	151
β-Ga₂O₃	1.777/1.798	1.77	2.57	83.6	393	300	152
Gd₃Ga₅O₁₂	1.782	1.78	2.58	83.3	391	300	153
	1.798	1.76	2.56	84.1	395	85	154
GdSc₃(BO₃)₄	1.830	1.57	2.35	86.1	405	300	61
Gd₃Sc₂Ga₃O₁₂	1.795	1.77	2.57	83.9	394	300	155
	1.830	1.77	2.58	85.6	402	300	156
Gd₃(Sc_1−xGa_x)₂Ga₃O₁₂	1.789	1.72	2.51	83.7	394	300	153
In₂(WO₄)₃	1.734	1.57	2.32	81.4	382	300	157
KAl (MoO₄)₂	1.681	1.65	2.40	78.6	369	300	158
K₂Ga₂Sn₆O₁₆	1.746	1.64	2.41	81.8	385	300	159
KIn(MoO₄)₂	1.715	1.50	2.24	80.6	379	5	160
	1.713	1.50	2.23	80.5	378	300	160
KIn(WO₄)₂	1.749	1.55	2.30	82.2	386	300	161
K₃(Mg_0.3Sc_0.7)₁₀(MoO₄)₁₅	1.710	1.58	2.33	80.2	377	300	162
KSc (WO₄)₂	1.736	1.58	2.33	81.5	383	300	163
KTiOPO₄	1.755^{^d)}	1.62^{^d)}	2.39	82.3	387	300	164
La₃Ga₅GeO₁₄	1.781/1.802^{^f)}	1.78^{^f)}	2.58	83.8	394	300	165
		1.45^{^g)}				300	165
La₆Ga₁₁NbO₂₈		1.83^{^h)}				300	166
		1.47^ⁱ)				300	166
La₃Ga₅SiO₁₄	1.782^{^j)}	1.65^{^k)}	2.43	83.6	393	15	167
	1.782^{^j)}	1.70^{^l,^m)}	2.49	83.4	392	15	167
(La_1−xLu_x)₅Ga₃O₁₂	1.792	1.62	2.40	84.1	395	300	153
LaSc₃(BO₃)₄	1.833^{^a)}	1.61^{^a)}	2.40	86.2	405	300	168
	1.842	1.51	2.28	86.9	408	300	169
La₃Sc₂Ga₃O₁₂		1.65				300	155
LiCrSi₂O₆	1.809^ⁿ)	1.63^ⁿ)	2.41	84.9	399	300	170
LiGa(WO₄)₂	1.680	1.58	2.32	78.7	370	300	171
LiIO₃	1.760	1.54	2.29	82.7	389	300	172
LiInSiO₄	1.825^{^o)}	1.55^{^p)}	2.32	85.9	404	300	173
		1.35^{^q)}				300	173
LiInSi₂O₆	1.817	1.62	2.40	85.3	401	300	174
LiIn(WO₄)₂	1.715	1.40	2.12	80.9	380	300	161
LiLaP₄O₁₂	1.580	1.55	2.25	73.9	347	273	175
LiNbO₃	1.714	1.64	2.40	80.2	377	15	176
	1.718	1.68	2.44	80.4	378	300	177
	1.720^{^d,^e)}	1.60^{^d,^e)}	2.35	80.6	379	300	178
LiScP₂O₇	1.847	1.60	2.39	86.9	408	300	179
LiSc(WO₄)₂	1.714	1.34	2.04	81.0	381	300	180
LiTaO₃	1.729	1.58	2.33	81.1	381	5	181
	1.726^{^k)}	1.58^{^k)}	2.33	81.0	381	300	181
	1.726^{^l)}	1.60^{^l)}	2.35	80.9	380	300	181
Li_1.6Zn_1.6Sn_2.8O₈	1.753	1.64	2.41	82.2	386	300	182
Lu₃Sc₂Ga₃O₁₂	1.797	1.77	2.57	84.0	395	300	155
MgO	1.785^{^r)}	1.69^{^r)}	2.48	83.6	393	77	84
MgCaSi₂O₆	1.819	1.47	2.23	85.8	403	300	183
MgCa₂WO₆		1.54				300	19
Mg₂CaY₂Ge₃O₁₂	1.775	1.76	2.55	83.0	390	300	7
MgLa₂ZrO₆		1.64				300	184
MgMoO₄	1.716	1.58	2.33	80.5	378	10	204
Mg₂SiO₄	1.682^{^s)}	1.64^{^s)}	2.39	78.7	370	10	94
MgSr₈La(PO₄)₇		1.56				300	185
MgSr₂WO₆	1.642	1.57	2.29	76.9	361	300	186
MgTa₂O₆		1.57				300	187
MgWO₄	1.729	1.44	2.17	81.5	383	10	204
	1.726	1.42	2.14	81.4	382	300	188
	1.724^{^a)}	1.44^{^a)}	2.17	81.2	382	300	189
Mg₃Y₂Ge₃O₁₂		1.73				300	190
NaAl(WO₄)₂	1.714	1.67	2.43	80.2	377	10	191
	1.750	1.70	2.48	81.9	385	300	192
Na₂CaGe₃Sn₂O₁₂		1.70				300	193
Na₂CaTi₂Ge₃O₁₂		1.70				300	193
Na₃Ce(PO₄)₂	1.740	1.63	2.39	81.5	383	300	194
NaCrSi₂O₆	1.808^ⁿ)	1.63^ⁿ)	2.41	84.9	399	300	170
NaIn(MoO₄)₂	1.715	1.35	2.06	81.1	381	300	160
NaIn(WO₄)₂	1.740	1.40	2.12	82.1	386	300	161
Na₂Mg₅(MoO₄)₆	1.719	1.55	2.29	80.7	379	300	195
NaMg₃Al(MoO₄)₅	1.787	1.62	2.40	83.9	394	8	196
NaScSi₂O₆	1.805	1.62	2.40	84.7	398	300	197
RbAl(MoO₄)₂	1.673	1.62	2.36	78.3	368	300	151
RbIn(WO₄)₂	1.740	1.60	2.36	81.6	384	300	161
Sc₂O₃	1.726^{^f)}	1.64^{^f)}	2.40	80.8	380	300	198
		1.20^{^g)}				300	198
ScBO₃		1.70				300	199
	1.865	1.67	2.48	87.6	412	300	200
Sc₂(MoO₄)₃	1.692	1.54	2.28	79.4	373	300	201
Sc₂(WO₄)₃	1.734	1.58	2.33	81.4	382	300	157
ScIn(WO₄)₃	1.732	1.58	2.33	81.3	382	300	157
SrGa₄O₇	1.782	1.69	2.47	83.5	392	300	202
SrSc₂O₄	1.770	1.62	2.39	83.0	390	2.7	145
Y₃Ga₅O₁₂	1.791	1.79	2.59	83.7	393	300	153
	1.793	1.78	2.58	83.8	394	300	203
YSc₃(BO₃)₄	1.820	1.63	2.42	85.5	402	300	61
Y₃Sc₂Ga₃O₁₂	1.794	1.77	2.57	83.9	394	300	155
Y₃(Sc_1−xGa_x)₂Ga₃O₁₂	1.790	1.78	2.58	83.7	393	300	153
ZnWO₄	1.724	1.44	2.17	81.2	382	10	204

^a) E ∣∣ x, y, z ( E ∣∣ a, b, c; i.e., no strong polarization dependence).^b)Cr (I) site.^c)Cr (II) site.^d) E ∣∣ c.^e) E ⊥ c.^f)Center I.^g)Center II.^h)Octahedral site.ⁱ⁾Tetrahedral site.^j)Assuming no polarization dependence.^k) π polarization.^l) σ polarization.^m) α polarization.ⁿ⁾ E ∣∣ α, β, γ (i.e., no strong polarization dependence).^o)Estimated from an optical absorbance spectrum.^p)Octahedral site (I).^q)Octahedral site (II).^r)Rhombic site.^s) E ∣∣ a, b; Mg(II) site.

Note that the weak Fano resonance/antiresonance structures can be observed at ∼1.92 and 2.60 eV in the PLE spectrum of Fig. 5b. The positions of these structures may correspond to the E(² T_1g)_ZPL and E(² T_2g)_ZPL energies, respectively. The shaded triangles in Fig. 6 represent these spin-forbidden excited-state ZPL energies divided by B. All the Fano resonance/antiresonance-estimated E/B values for the Bi₂Al₄O₉:Cr³⁺ and Bi₂Ga₄O₉:Cr³⁺ phosphors fall on their Tanabe−Sugano diagram curves reasonably well; however, only the E(² T_1g)_ZPL/B plot for the Bi₂Ga₄O₉:Cr³⁺ phosphor is seemed to be slightly larger than the Tanabe−Sugano diagram value.

Ca₃Sc₂Ge₃O₁₂:Cr³⁺ phosphor

The Ca₃Sc₂Ge₃O₁₂:Cr³⁺ phosphor is of type O–Cr–B. Figure 12 shows the PL and PLE spectra of the Ca₃Sc₂Ge₃O₁₂:Cr³⁺ phosphor measured at 10 K. The experimental data are taken from Cavalli et al.¹⁴⁶ Because of the energy inequality relation of E(⁴ T_2g)_ZPL < E(² E_g)_ZPL for type O–Cr–B phosphors, their PL and PLE spectra are quite different from those of type O–Cr–A phosphors. The resultant PL spectrum for the Ca₃Sc₂Ge₃O₁₂:Cr³⁺ phosphor can be characterized by a broad ⁴ T_2g-related emission band, and is fitted using Eq. 7 in Fig. 12. Since the PL spectrum was measured at cryogenic temperature of T = 10 K, the best fit required only the Stokes emission component with E(⁴ T_2g)_ZPL = 1.72 eV, hν_p,em = 60 meV, and S = 2.

The PL spectrum measured at 300 K is also shown by the dashed line in Fig. 12.¹⁴⁶ Because of the high temperature measurement of 300 K, its PL spectrum shows relatively broader emission band than that at 10 K with the maximum peak energy being slightly shifted toward the low-energy side. The high-energy luminescence tail is also observed to be due to the anti-Stokes emission component.

The first excitation band peaking at ∼1.9 eV in Fig. 12 is analyzed using Eq. 9. The resulting best-fit parameters are: E(⁴ T_2g)_ZPL = 1.72 eV, hν_p,ex = 60 meV, and S = 4. Because of the mirror reflection relation between the PL and PLE spectra in Fig. 12, we used the same ZPL energies of E(⁴ T_2g)_ZPL = 1.72 eV in Eqs. 7 and 9. An agreement between the theory and experiment is excellent for both PL and PLE spectra in the ² E_g ↔ ⁴ A_2g transition region (∼1.3 − 2.3 eV).

Note that the first excitation band in the PLE spectrum of Fig. 12 shows singularities arising from the Fano resonance/antiresonance interaction between the sharp spin-forbidden ² E_g and ² T_1g states with broad spin-allowed ⁴ T_2g state. From these spectral singularities, we can estimate the spin-forbidden excited-state ZPL energies of E(² E_g)_ZPL = 1.828 eV and E(² T_1g)_ZPL = 1.94 eV. We can also find singularity in the PLE spectrum at ∼2.6 eV. This singularity is caused by the Fano resonance/antiresonance interaction between the spin-forbidden ² T_2g and spin-allowed ⁴ T_2g states, suggesting the spin-forbidden transitions being occur at E(² T_2g)_ZPL = 2.60 eV.

Introducing E(² E_g)_ZPL = 1.828 eV and E(⁴ T_2g)_ZPL = 1.72 eV into Eqs. 1−3, we obtain B = 85.6 meV, C = 403 meV, E(⁴ T_1g,a)_ZPL = 2.52 eV, and Dq/B = 2.01 for the Ca₃Sc₂Ge₃O₁₂:Cr³⁺ phosphor. The corresponding E(² E_g)_ZPL/B, E(⁴ T_2g)_ZPL/B, and E(⁴ T_1g,a)_ZPL/B vs Dq/B plots on the Tanabe−Sugano energy-level diagram are shown in Fig. 13. The PLE contribution coming from the ⁴ T_1g,a excited state is also shown by the vertical bars in Fig. 12.

**Figure 13.** Tanabe–Sugano energy-level diagram for a 3d³ (Cr³⁺) ion in octahedral symmetry with r = 4.7. The circular symbols represent the various ZPL energies for the Ca₃Sc₂Ge₃O₁₂:Cr³⁺ phosphor plotted against the crystal-field parameter Dq, both axes divided by B. The Racah and related parameters are determined by analyzing PL and PLE spectra in Fig. 12.
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Note that the spin-forbidden ⁴ A_2g → ² T_1g and ⁴ A_2g → ² T_2g transition intensities may be definitely weaker than those of the spin-allowed ⁴ A_2g → ⁴ T_2g and ⁴ A_2g → ⁴ T_1g,a transitions. Therefore, the former contributions may be nearly completely masked by the latter ones. Because of this, we did not add such weak excitation absorption components in Fig. 12. However, the values of E(² T_1g)_ZPL/B = 22.7 [E(² T_1g)_ZPL = 1.94 eV] and E(² T_2g)_ZPL/B = 30.4 [E(² T_2g)_ZPL = 2.60 eV], determined from the Fano resonance/antiresonance structures in Fig. 12 are plotted by the shaded triangles in Fig. 13. All these E/B vs Dq/B plots in Fig. 13 fall on the Tanabe−Sugano diagram curves very well.

LiInSi₂O₆:Cr³⁺ phosphor

The PL and PLE spectra for the LiInSi₂O₆:Cr³⁺ phosphor measured at 300 K are shown in Fig. 14. The experimental data are taken from Xu et al.¹⁷⁴ The same authors also measured diffuse reflectance spectra. The optical spectrum on the top of Fig. 14 represents their obtained diffuse reflectance spectrum. Some Fano resonance/antiresonance singularities appear in both PLE and diffuse reflectance spectra at ∼1.8 eV. These singularities enabled determination of a value of E(² E_g)_ZPL = 1.817 eV. Further weak Fano singularities can be found at energies higher than ∼1.9 eV, giving E(² T_1g)_ZPL = 1.96 eV and E(² T_2g)_ZPL = 2.65 eV. Such a Fano interaction-induced singularity between the spin-forbidden ² E_g and spin-allowed ⁴ T_2g states has also been observed in diffuse reflectance spectrum of LiScP₂O₇:Cr³⁺ phoshor.¹⁷⁹

**Figure 14.** Diffuse reflectance, PL, and PLE spectra of the LiInSi₂O₆:Cr³⁺ phosphor measured at 300 K. The experimental data are taken from Xu et al.¹⁷⁴ The vertical bars in the PL and PLE spectra show the results calculated using Eqs. 7 and 9, respectively. The vertical arrows indicate the positions of the various excited-state ZPL energies, E(⁴ T_2g)_ZPL, E(² E_g)_ZPL, E(² T_1g)_ZPL, E(⁴ T_1g,a)_ZPL, and E(² T_2g)_ZPL. The open circles in red color also show the regions occurring Fano resonance/antiresonance interaction. S = Stokes; a-S = anti-Stokes.
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The PL spectrum analyzed using Eq. 7 in Fig. 14 gives E(⁴ T_2g)_ZPL = 1.62 eV, hν_p,em = 60 meV, and S = 3. The same analysis, but for the PLE spectrum using Eq. 9 also gives E(⁴ T_2g)_ZPL = 1.62 eV, hν_p,ex = 60 meV, and S = 4. Introducing E(² E_g)_ZPL = 1.817 eV and E(⁴ T_2g)_ZPL = 1.62 eV into Eqs. 1−3, we obtain the Racah-related energy parameters of B = 85.3 meV, C = 401 meV, E(⁴ T_1g,a)_ZPL = 2.40 eV, and Dq/B = 1.90 for the LiInSi₂O₆:Cr³⁺ phosphor.

Determination of the ZPL energies of E(² T_1g)_ZPL and E(⁴ T_1g,a)_ZPL makes possible to obtain each PLE spectral component using Eq. 9. The results obtained are shown by the vertical bars in Fig. 14 with the following parameters: E(² T_1g)_ZPL = 1.96 eV, hν_p,ex = 60 meV, and S = 2 for the ⁴ A_2g → ² T_1g excitation transitions; E(⁴ T_1g,a)_ZPL = 2.40 eV, hν_p,ex = 60 meV, and S = 5 for the ⁴ A_2g → ⁴ T_1g,a excitation transitions. The E/B vs Dq/B plots are also shown in Fig. 15, indicating an excellent agreement with the Tanabe−Sugano energy-level diagram values.

**Figure 15.** Tanabe–Sugano energy-level diagram for a 3d³ (Cr³⁺) ion in octahedral symmetry with r = 4.7. The circular symbols represent the various ZPL energies for the LiInSi₂O₆:Cr³⁺ phosphor plotted against the crystal-field parameter Dq, both axes divided by B. The Racah and related parameters are determined by analyzing PL and PLE spectra in Fig. 14.
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MgCaSi₂O₆:Cr³⁺ phosphor

The PL and PLE spectra for the MgCaSi₂O₆:Cr³⁺ phosphor measured at 300 K are shown in Fig. 16. The experimental data are taken from Huang et al.¹⁸³ The PL spectrum in Fig. 16 reveals the double peak structure at ∼1.3 and 1.6 eV. The vertical vars on its spectrum show the analysis results using Eq. 7 with E(⁴ T_2g)_ZPL = 1.47 eV, hν_p,em = 60 meV, and S = 4 (Stokes luminescence component peaking at ∼1.3 eV); with E(⁴ T_2g)_ZPL = 1.47 eV, hν_p,em = 60 meV, and S = 2 (anti-Stokes luminescence component peaking at ∼1.6 eV).

**Figure 16.** Diffuse reflectance, PL, and PLE spectra of the MgCaSi₂O₆:Cr³⁺ phosphor measured at 300 K. The experimental data are taken from Huang et al.¹⁸³ The vertical bars in the PL and PLE spectra show the results calculated using Eqs. 7 and 9, respectively. The vertical arrows indicate the positions of the various excited-state ZPL energies, E(⁴ T_2g)_ZPL, E(² E_g)_ZPL, E(² T_1g)_ZPL, E(⁴ T_1g,a)_ZPL, and E(² T_2g)_ZPL. The open circles in red color also show the regions occurring Fano resonance/antiresonance interaction. S = Stokes; a-S = anti-Stokes.
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The PLE spectrum in Fig. 16 reveals the Fano resonance/antiresonance structures near the maximum of the ⁴ A_2g → ⁴ T_2g excitation transition band. From these Fano resonance/antiresonance structures, the ZPL transition energies are determined to be given by E(² E_g)_ZPL = 1.819 eV and E(² T_1g)_ZPL = 1.93 eV for the MgCaSi₂O₆:Cr³⁺ phosphor. The spectral analysis of the ⁴ A_2g → ⁴ T_2g excitation transition band using Eq. 9 also provides the fitting parameters of E(⁴ T_2g)_ZPL = 1.47 eV, hν_p,ex = 60 meV, and S = 7.

Introducing E(² E_g)_ZPL = 1.819 eV and E(⁴ T_2g)_ZPL = 1.47 eV into Eqs. 1−3, we obtain B = 85.8 meV, C = 403 meV, E(⁴ T_1g,a)_ZPL = 2.23 eV, and Dq/B = 1.71 for the MgCaSi₂O₆:Cr³⁺ phosphor. The E/B vs Dq/B data obtained from the PL and PLE analyses and Fano resonance/antiresonance structures in Fig. 16 are also plotted in Fig. 17 and are found to be in good agreement with the Tanabe−Sugano energy-level diagram values.

**Figure 17.** Tanabe–Sugano energy-level diagram for a 3d³ (Cr³⁺) ion in octahedral symmetry with r = 4.7. The circular symbols represent the various ZPL energies for the MgCaSi₂O₆:Cr³⁺ phosphor plotted against the crystal-field parameter Dq, both axes divided by B. The Racah and related parameters are determined by analyzing PL and PLE spectra in Fig. 16.
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Recapitulation of Spectroscopic Properties of Cr³⁺-Activated Oxide Phosphors

We summarized in Tables III and IV some important excited-state ZPL energies and Racah parameters for the Cr³⁺-activated oxide phosphors of types O–Cr–A and O–Cr–B, respectively. The first and second lowest excited-state ZPL energies E(² E_g)_ZPL and E(⁴ T_2g)_ZPL for phosphors of type O–Cr–A, respectively, or those of E(⁴ T_2g)_ZPL and E(² E_g)_ZPL for phosphors of type O–Cr–B, respectively, listed in these tables were determined by analyzing the experimental PL and PLE spectra of such oxide phosphors ever-reported. The second highest spin-allowed ZPL transition energies of E(⁴ T_2g,a)_ZPL and Racah parameters B and C were then obtained from analytical expressions of Eqs. 1−3.

Figure 18 plots the excited-state ZPL energies, E(² E_g)_ZPL, E(⁴ T_2g)_ZPL, and E(⁴ T_1g,a)_ZPL, against Dq, divided by B, for (a) the Cr³⁺ and Mn⁴⁺-activated "oxide" phosphors and (b) those of the "fluoride" phosphors. The data values of the Cr^3--activated oxide phosphors plotted were taken from Tables III and IV. The same, but those for the Cr³⁺-activated "fluoride" phosphors were taken from Ref. 14. The Mn⁴⁺-activated "oxide" and "fluoride" phosphor data were taken from a list in Ref. 10 (see also Ref. 32).

As mentioned earlier, all the Mn⁴⁺-activated "oxide" phosphors belong to type O–Mn [E(² E_g)_ZPL < E(⁴ T_2g)_ZPL]. All the Mn⁴⁺-activated "fluoride" phosphors also belong to type F–Mn [E(² E_g)_ZPL < E(⁴ T_2g)_ZPL]. Similarly, all the Cr³⁺-activated "fluoride" phosphors belong to type F–Cr [E(⁴ T_2g)_ZPL < E(² E_g)_ZPL]. The present investigation suggested that such spectroscopic properties of the Cr³⁺-activated "oxide" phosphors are dependent on the crystal-field strength Dq (Dq/B), namely, type O–Cr–A [E(² E_g)_ZPL < E(⁴ T_2g)_ZPL] of relatively larger Dq values and type O–Cr–B [E(⁴ T_2g)_ZPL < E(² E_g)_ZPL] of relatively smaller Dq values. It should be noted that the data points for the La₂ZnTiO₆:Cr³⁺ oxide phosphor were neglected in the plots of Fig. 18a (also Figs. 19–21 below). The reason is that only this phosphor showed an extremely large Dq/B value of 2.95 (see Table III) compared to other Cr³⁺-activated oxide phosphors. The relatively large Dq/B value of this phosphor corresponds to its large E(⁴ T_2g)_ZPL value (Table III; see also Fig. 9).

**Figure 19.** (a) B vs Dq, (b) C vs Dq, and (c) C vs B plots for the various Cr³⁺-activated oxide and fluoride phosphors. The numeric data plotted here are taken from Tables III and IV for the Cr³⁺-activated oxide phosphors and from Ref. 14 for the Cr³⁺-activated fluoride ones. The solid lines show the average values or least-squares-fit results (see text).
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**Figure 20.** Plots of E(² E_g)_ZPL vs (a) Dq, (b) Dq/B, and (c) B for the various Cr³⁺-activated oxide and fluoride phosphors. The numeric data plotted here are taken from Tables III and IV for the Cr³⁺-activated oxide phosphors and from Ref. 14 for the Cr³⁺-activated fluoride ones. The solid lines show the average values or least-squares-fit results (see text). The dashed line at Dq/B ∼ 2.14 in (b) represents the boundary of types O–Cr–A [E(² E_g)_ZPL < E(⁴ T_2g)_ZPL] and O–Cr–B (F–Cr) [E(⁴ T_2g)_ZPL < E(² E_g)_ZPL].
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**Figure 21.** Plots of E(⁴ T_2g)_ZPL vs (a) Dq, (b) Dq/B, and (c) B for the various Cr³⁺-activated oxide and fluoride phosphors. The numeric data plotted here are taken from Tables III and IV for the Cr³⁺-activated oxide phosphors and from Ref. 14 for the Cr³⁺-activated fluoride ones. The solid lines show the average values or least-squares-fit results (see text). The dashed line at Dq/B ∼ 2.14 in (b) represents the boundary of types O–Cr–A [E(² E_g)_ZPL < E(⁴ T_2g)_ZPL] and O–Cr–B (F–Cr) [E(⁴ T_2g)_ZPL < E(² E_g)_ZPL].
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Figure 19 shows the plots of (a) B vs Dq, (b) C vs Dq, and (c) C vs B for the Cr³⁺-activated oxide and fluoride phosphors. The numeric data were taken from Tables III and IV for the Cr³⁺-activated oxide phosphors and from a list in Ref. 14 for the Cr³⁺-activated fluoride phosphors. The Racah parameters plotted in Figs. 19a and 19b show no strong dependence on Dq, represented by B ∼ 81.7 meV and C ∼ 385 meV for the oxide phosphors; B ∼ 89.7 meV and C ∼ 422 meV for the fluoride phosphors. No large difference has also been found for phosphors of types O–Cr–A and O–Cr–B. In Fig. 19c, a value of C increases with increasing B at a slope of r = 4.7, in accord with its assumed ratio of Eq. 2.

The plots of E(² E_g)_ZPL vs (a) Dq, (b) Dq/B, and (c) B for the Cr³⁺-activated oxide and fluoride phosphors are shown in Figs. 20a–20c, respectively. The numeric data were taken from the same sources as in Fig. 19. The values of E(² E_g)_ZPL show no strong dependence on the horizontal axis quantity Dq, Dq/B, or B, represented approximately by E(² E_g)_ZPL ∼ 1.77 eV for the Cr³⁺-activated oxide phosphors and ∼1.91 eV for those of the fluoride phosphors. However, the oxide and fluoride phosphor plots in Fig. 20c show almost linear increase with increasing B given by [E(² E_g)_ZPL in eV; B in meV]

$\begin{eqnarray}&&E{({}^{2}E_{g})}_{{\rm{ZPL}}}=0.021B+0.03\end{eqnarray} \tag{ 11 }$

The same as in Fig. 20, but those for E(⁴ T_2g)_ZPL are shown in Fig. 21. One can find that the results shown in Fig. 21 are quite different from those in Fig. 20. The values of E(⁴ T_2g)_ZPL in Fig. 21a are given, as expected from Eq. 4, by

$\begin{eqnarray}&&E{({}^{4}T_{2g})}_{{\rm{ZPL}}}=0.01Dq\end{eqnarray} \tag{ 12 }$

with E(⁴ T_2g)_ZPL in eV and Dq in meV, and in Fig. 21b by

$\begin{eqnarray}&&E{({}^{4}T_{2g})}_{{\rm{ZPL}}}=0.73(Dq/B)+0.21\end{eqnarray} \tag{ 13 }$

with E(⁴ T_2g)_ZPL in eV, that are, regardless of type O–Cr–A, O–Cr–B, or F–Cr.

The values of E(² E_g)_ZPL in Fig. 21c tend to show no strong dependence on B, approximately given by E(⁴ T_2g)_ZPL ∼ 1.87 and ∼1.63 eV for the Cr³⁺-activated oxide phosphors of types O–Cr–A and O–Cr–B, respectively, and E(⁴ T_2g)_ZPL ∼ 1.71 eV for the Cr³⁺-activated fluoride ones. The results given in Figs. 19–21 can be used to predict an energy of the Cr³⁺ emission and/or to check a validity of the Racah parameters determined from a variety of Cr³⁺-activated oxide and fluoride phosphors.

The room-temperature PL spectra observed for some Cr³⁺-activated oxide phosphors of (a) type O–Cr–A and (b) type O–Cr–B are shown in Fig. 22. The oxide phosphors plotted are selected to have the smallest and largest ZPL emission energies of E(² E_g)_ZPL in Table III and of E(⁴ T_2g)_ZPL in Table IV . Such phosphors are: Na₂TiGeO₅:Cr³⁺ (1.613 eV) (Ref. 99) and BeAl₂O₄:Cr³⁺ (∼1.82 eV) (Ref. 44) in Fig. 22a; CdWO₄:Cr³⁺ (1.26 eV; T = 10 K) (Ref. 204) and La₆Ga₁₁NbO₂₈:Cr³⁺ (1.83 eV) (Ref. 166) in Fig. 22b. It should be noted that the PL spectrum for the CdWO₄:Cr³⁺ phosphor in Fig. 22a corresponds to that measured at 10 K. It is known that the E(⁴ T_2g)_ZPL value usually decreases with increasing T, but its degree of decrease is not so large.

**Figure 22.** Room-temperature PL spectra for some Cr³⁺-activated oxide phosphors of (a) type O–Cr–A and (b) type O–Cr–B. The oxide phosphors plotted here are selected to have the smallest and largest ZPL emission energies of E(² E_g)_ZPL in Table III and of E(⁴ T_2g)_ZPL in Table IV. These phosphors are: Na₂TiGeO₅:Cr³⁺ (1.613 eV) (Ref. 99) and BeAl₂O₄:Cr³⁺ (∼1.82 eV) (Ref. 44) in (a); CdWO₄:Cr³⁺ (1.26 eV; T = 10 K) (Ref. 204) and La₆Ga₁₁NbO₂₈:Cr³⁺ (1.83 eV) (Ref. 166) in (b).
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As evidenced from Fig. 22, the E(² E_g)_ZPL emission wavelength for phosphors of type O–Cr–A varies not so largely from ∼680 nm (BeAl₂O₄:Cr³⁺) to ∼770 nm (Na₂TiGeO₅:Cr³⁺). Contrarily, the E(⁴ T_2g)_ZPL emission wavelength of type O–Cr–B phosphors ranges widely from ∼675 nm (La₆Ga₁₁NbO₂₈:Cr³⁺) to ∼985 nm (CdWO₄:Cr³⁺). Note that the first and second broad luminescence bands observed in the La₆Ga₁₁NbO₂₈:Cr³⁺ phosphor can be attributed to Cr³⁺ ions situated in the octahedral and tetrahedral sites of La₆Ga₁₁NbO₂₈ lattice, respectively. The E(⁴ T_2g)_ZPL value for the Cr³⁺ ion in the tetrahedral site of this phosphor can also be determined using Eq. 9 to be given by ∼1.47 eV ( Table IV).

Conclusions

The Cr³⁺-activated oxide phosphors were discussed in detail from an aspect of spectroscopic point of view. The PL and PLE spectra were analyzed on the basis of the Franck−Condon principle with the CC model. The results suggested that the Cr³⁺-activated oxide phosphors can be classified into two groups: types O–Cr–A and O–Cr–B. Phosphors of type O–Cr–A are defined by an energy inequality relation of E(² E_g)_ZPL < E(⁴ T_2g)_ZPL, promising an observation of a series of the sharp emission peaks caused by the ² E_g → ⁴ A_2g transitions. Similarly, phosphors of type O–Cr–B can be defined by an energy inequality relation of E(⁴ T_2g)_ZPL < E(² E_g)_ZPL, promising an observation of a broad emission band attributed to the ⁴ T_2g → ⁴ A_2g transitions. A modified approach was proposed based on the general ligand field theory for obtaining reliable crystal-field, Dq, and Racah parameters, B and C, with drawing an attention to difficulty in exactly determining such very important phosphor parameters. The analysis results of the various Cr³⁺-activated oxide phosphors were summarized in graphical and tabular forms. The excited-state ZPL energies, such as E(² E_g)_ZPL, E(⁴ T_2g)_ZPL, and E(⁴ T_1g,a)_ZPL, in such oxide phosphors were also successfully determined and plotted against Dq in the Tanabe−Sugano energy-level diagram chart. The facts justify a validity of our proposed model and make possible to classify various 3d³-ion-activated oxide and fluoride phosphors into types of O–Cr–A [E(² E_g)_ZPL < E(⁴ T_2g)_ZPL] and O–Cr–B [E(⁴ T_2g)_ZPL < E(² E_g)_ZPL] for Cr³⁺-activated oxide phosphors, type of F–Cr [E(⁴ T_2g)_ZPL < E(² E_g)_ZPL] for Cr³⁺-activated fluoride phosphors, type of O–Mn [E(² E_g)_ZPL < E(⁴ T_2g)_ZPL] for Mn⁴⁺-activated oxide phosphors, and type of F–Mn [E(² E_g)_ZPL < E(⁴ T_2g)_ZPL] for Mn⁴⁺-activated fluoride phosphors.

Review—Photoluminescence Properties of Cr³⁺-Activated Oxide Phosphors

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Abstract

Tanabe−Sugano Energy-Level Diagram

Crystal-Field and Racah Parameters

Analysis Model for PL and PLE Spectra

Vibration Frequencies of ${{\rm{CrO}}}_{6}^{9-}$ Octahedron Molecule