Red shifts of the yellow emission of YAG:Ce³⁺ due to tetragonal fields induced by cationic substitutions

Abstract

Wave function theory ab initio embedded cluster calculations show that Ce³⁺-doped transformed aluminum garnets resulting from Y₃Al₅O₁₂:Ce³⁺ after cationic substitutions that enhance the tetragonal field around Ce³⁺, have their lowest 4f–5d transition red-shifted with respect to the yellow phosphor YAG:Ce³⁺ used in GaN blue-LED based lighting devices. Red shifts in the range of 1000–3000 cm⁻¹ are found in 33 transformed garnets of the types M^IV₂M^IIIM^II₂Al₃O₁₂:Ce³⁺, M^IV₂M^IAl₅O₁₂:Ce³⁺, and M^IVM^IIIM^IIAl₅O₁₂:Ce³⁺. This result shapes the design of new red phosphors by enhancing the tetragonal field around Ce³⁺ via cationic substitutions made in Ce³⁺-doped aluminum garnets.

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I. Introduction

YAG:Ce³⁺ (Ce³⁺-doped yttrium aluminum garnet Y₃Al₅O₁₂) is a key phosphor in InGaN blue-LED based energy efficient white light devices^1,2 because its Ce³⁺ 4f → 5d absorption is well adapted to the blue-LED emission and its yellow 5d → 4f emission³ can be mixed with the residual blue to produce white light. Such a light is cold to the human eye and the demand for a warmer white light for general illumination has led the search for alternative phosphors with a red shifted emission with respect to YAG:Ce³⁺. Among Ce³⁺-doped garnets (with the general formula A₃B′₂B′′₃O₁₂), which enjoy convenient stability and thermal properties, Lu₂CaMg₂Si₃O₁₂:Ce³⁺ has been found to be an orange phosphor.⁴

Here we show, by means of ab initio calculations, that Ce³⁺-doped transformed aluminum garnets resulting from Y₃Al₅O₁₂ after cationic substitutions that enhance the tetragonal field around Ce³⁺, have their lowest 4f–5d transition red-shifted with respect to YAG:Ce³⁺.

This study involves 33 transformed garnets of the types: M^IV₂M^IIIM^II₂Al₃O₁₂, M^IV₂M^IAl₅O₁₂, and M^IVM^IIIM^IIAl₅O₁₂. They can be regarded as resulting from substitutions at the Y dodecahedral and Al octahedral sites of Y₃Al₅O₁₂ by monovalent to tetravalent M^I–M^IV cations. The study is a consequence of the conclusions of previous ab initio studies.^5–7 First, only the cubic field and the tetragonal field (more specifically the D_4h tetragonal (ditetragonal-dipyramidal) field) cause red-shift of the lowest 4f–5d transition in Ce³⁺-doped garnets.⁵ Second, unrelaxed host embedding effects are most important in producing a red shift of the transition with respect to its value in an isolated (CeO₈)¹³⁻ cluster and these effects are largest in aluminum garnets.⁶ And third, local relaxations are only responsible for minor effects, which can establish differences between members of the same family, like Y₃Al₅O₁₂:Ce³⁺ and Lu₃Al₅O₁₂:Ce³⁺, or Y₃Ga₅O₁₂:Ce³⁺ and Lu₃Ga₅O₁₂:Ce³⁺, but not between different families of garnets.⁷

The calculations show that the Ce³⁺ emission shifts towards the red end of the spectrum by 1000–3000 cm⁻¹ in the 33 transformed garnets studied.

II. Method

We performed ab initio wave function theory (WFT) embedded cluster calculations with the MOLCAS suite of programs.⁸ These are two-step spin–orbit coupling calculations on the (CeO₈)¹³⁻ embedded cluster with the many-electron relativistic second-order Douglas–Kroll–Hess (DKH) Hamiltonian,^9,10 using the atomic mean-field integrals approximation (AMFI) for the spin–orbit coupling part.¹¹ We performed SA-CASSCF/MS-CASPT2/RASSI-SO calculations: in the first step, the spin–orbit coupling operator is removed from the Hamiltonian and state-average complete-active-space self-consistent-field^12–14 calculations are done on the many-electron active space that results from distributing the open-shell electrons in 13 active molecular orbitals, mainly of Ce 4f, 5d, 6s character. Subsequent multi-state second-order perturbation theory calculations are performed^15–18 where the dynamic correlation of the 73 electrons corresponding to the 5s, 5p, 4f, 5d, 6s shells of Ce and the 2s, 2p shells of O is taken into account. In the second step, the full Hamiltonian is used and restricted-active-space state-interaction spin–orbit calculations (RASSI-SO)¹⁹ are done using the transformed CASSCF wave functions and MS-CASPT2 energies. All of the calculations are all-electron, with atomic natural orbital (ANO) relativistic basis sets for cerium²⁰ and oxygen,²¹ with respective contractions (25s22p15d11f4g)/[10s8p5d4f2g] and (14s9p4d3f)/[4s3p2d1f].

The Hamiltonian of the otherwise isolated (CeO₈)¹³⁻ cluster was supplemented with the ab initio model potential (AIMP) embedding operators²² of all of the garnets considered. These are made up of the embedding AIMPs of the component ions located at crystallographic positions (see below) within a cube of 3 × 3 × 3 unit cells centered at Ce³⁺, plus a set of ∼10⁵ additional point charges situated at lattice sites, generated by the method of Gellé and Lepetit²³ in order to closely reproduce the Ewald potential²⁴ within the cluster. The effect of the AIMP embedding potentials of the garnets on the (CeO₈)¹³⁻ cluster is to include host electrostatic interactions (made of long-range point-charge (Madelung) and short-range charge density Coulomb contributions), host exchange interactions, and host Pauli repulsion interactions (non-orthogonality contributions due to cluster-host antisymmetry requirements) in the calculations. Electron correlation effects between the cluster and the host are excluded from these calculations. The embedding AIMPs of the ions in all of the transformed garnets considered in this paper have been obtained in this work in self-consistent embedded-ions (SCEI)²⁵ Hartree–Fock (HF) calculations. They are available from the authors²⁶ and presented in the ESI.†

We considered transformed garnets of the types M^IV₂M^IIIM^II₂Al₃O₁₂, M^IV₂M^IAl₅O₁₂, and M^IVM^IIIM^IIAl₅O₁₂, where M^I, M^II, M^III, and M^IV are monovalent, divalent, trivalent, and tetravalent cations respectively. The list is shown in Table 1. Since the goal of the work is to find, possibly, red-shifts of the Ce³⁺ 4f–5d transition with respect to YAG:Ce³⁺, and it has been shown that they do not depend on local relaxations⁷ (which are very costly to handle in ab initio calculations), we made all the calculations on fixed structures corresponding to the experimental crystallographic structure of Y₃Al₅O₁₂ [160 atom body-centered cubic unit cell (80 atom primitive cell) of the Ia3̄d (230) space group, with 8 formula units of A₃B′₂B′′₃O₁₂; a = 12.000 Å, x₀ = 0.0306, y₀ = 0.05120, z₀ = 0.15000, ref. 27] with substitutions of Y³⁺ and Al³⁺ ions by their corresponding M^I, M^II, M^III, and M^IV cations, depending on the garnet. When several substitutions were possible, we chose those which maximized the tetragonal component of the field. E.g., in Th₂YMg₂Al₃O₁₂ the four Th atoms substitute for the Y in the dodecahedral sites that are more equatorial around Ce, whereas the two Y atoms in the axial dodecahedral sites were left unsubstituted. In order to show that the unit cell volume has only a quantitative effect, but not a qualitative one, we repeated all of the calculations with two values of the unit cell constant, the average value for YAG, a = 12.000 Å, and a larger value, a = 12.113 Å, which corresponds to Gd₃Al₅O₁₂ and should increase the energy of the 4f–5d transition with respect to the average value.

Table 1 Shift of the 4f₁–5d₁ transition with respect to YAG:Ce³⁺, in cm⁻¹

	a = 12.000 Å	a = 12.113 Å
Th2YBe2Al3O12:Ce^3+	−2790	−2120
Th2LuBe2Al3O12:Ce^3+	−2790	−2120
Pb2YBe2Al3O12:Ce^3+	−1670	−1010
Pb2LuBe2Al3O12:Ce^3+	−1670	−1010
Zr2YBe2Al3O12:Ce^3+	−2360	−1690
Zr2LuBe2Al3O12:Ce^3+	−2360	−1690
ThPbYBe2Al3O12:Ce^3+	−2230	−1560
ThZrYBe2Al3O12:Ce^3+	−2570	−1910
PbYZrBe2Al3O12:Ce^3+	−2000	−1330
Th2YMg2Al3O12:Ce^3+	−3360	−2720
Th2LuMg2Al3O12:Ce^3+	−3360	−2720
Pb2YMg2Al3O12:Ce^3+	−2230	−1580
Pb2LuMg2Al3O12:Ce^3+	−2230	−1580
Zr2YMg2Al3O12:Ce^3+	−2940	−2280
Zr2LuMg2Al3O12:Ce^3+	−2940	−2280
ThPbYMg2Al3O12:Ce^3+	−2800	−2150
ThZrYMg2Al3O12:Ce^3+	−3150	−2500
PbYZrMg2Al3O12:Ce^3+	−2580	−1930
Th2AgAl5O12:Ce^3+	−3320	−2640
Th2NaAl5O12:Ce^3+	−3320	−2640
Th2LiAl5O12:Ce^3+	−3320	−2640
Pb2AgAl5O12:Ce^3+	−2470	−1760
Pb2NaAl5O12:Ce^3+	−2170	−1500
Pb2LiAl5O12:Ce^3+	−2170	−1500
Zr2AgAl5O12:Ce^3+	−2870	−2190
Zr2NaAl5O12:Ce^3+	−2870	−2190
Zr2LiAl5O12:Ce^3+	−2870	−2190
ThPbNaAl5O12:Ce^3+	−2790	−2120
ThZrNaAl5O12:Ce^3+	−3090	−2420
PbZrNaAl5O12:Ce^3+	−2520	−1850
ThYCaAl5O12:Ce^3+	−1900	−1230
ThYCdAl5O12:Ce^3+	−1900	−1230
ThYHgAl5O12:Ce^3+	−1900	−1230

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III. Results

The results of the calculations are presented in Table 1, which shows the calculated energy shift, in cm⁻¹, of the lowest 4f–5d transition in the transformed garnets with respect to the calculated transition energy of YAG:Ce³⁺, 22 520 cm⁻¹. The transition is red-shifted in all cases. As it can be observed, breathing of the lattice only has a quantitative effect on the red shift, but is unable to change the sign of the shift in spite of its large magnitude.

IV. Conclusions

CASSCF/CASPT2/RASSI-SO wave function theory calculations on Ce³⁺-doped transformed garnets derived from YAG:Ce³⁺ upon cationic substitutions that enhance the tetragonal field around Ce³⁺, have shown that their lowest 4f–5d transition is red-shifted with respect to YAG:Ce³⁺.

Although the set of 33 transformed garnets studied here is limited in number and some of them might face practical difficulties (e.g. the synthesis or handling of hazardous materials and residues), this study suggests as a driving force for the design of new phosphors with an emission red-shifted with respect to YAG:Ce³⁺, the enhancement of the tetragonal field around Ce³⁺ by cationic substitutions in the dodecahedral and octahedral sites.

Acknowledgements

This work was partly supported by a grant from Ministerio de Economía y Competitivad, Spain (Dirección General de Investigación y Gestión del Plan Nacional de I+D+I, MAT2014-54395-P).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra02611g

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