Cite this Article
Dou Xi-Long, Kuang Xiao-Yu, Xia Xin-Xin, Ju Meng. Exploration of the structural and optical properties of a red-emitting phosphor K2TiF6:Mn4+. Chinese Physics B, 2019, 28(1): 017107  
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Exploration of the structural and optical properties of a red-emitting phosphor K2TiF6:Mn4+
Dou Xi-Long1, Kuang Xiao-Yu1, †, Xia Xin-Xin1, Ju Meng2, ‡
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China
School of Physical Science and Technology, Southwest University, Chongqing 400715, China

 

† Corresponding author. E-mail: scu_kuang@163.com mengju@swu.edu.cn

Project supported by the National Natural Science Foundation of China (Grant No. 11574220), Fundamental Research Funds for the Central Universities, China (Grant No. SWU118055), and the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase), China.

Abstract

The exploration of the appropriate red phosphor with good luminescence properties is an important issue in the development of current white light-emitting diode (WLED) devices. Transition metal Mn-doped compounds are fascinating luminescent materials. Herein, we performed a systematic theoretical study of the microstructure and optical properties of K2TiF6:Mn4+ using the CALYPSO structure search method in combination with first-principles calculations. We uncovered a novel structure of K2TiF6:Mn4+ with space group P-3m1 symmetry, where the impurity Mn4+ ions are accurately located at the center of the MnF6 octahedra. Based on our developed complete energy matrix diagonalization (CEMD) method, we calculated transition lines for 2Eg → 4A2, 4A2 → 4T2, and 4A2 → 4T2 at 642, nm, 471 nm, and 352 nm, respectively, which are in good agreement with the available experimental data. More remarkably, we also found another transition (4A2 → 2T2) that lies at 380 nm, which should be a promising candidate for laser action.

PACS: 71.15.Mb;71.20.-b;61.50.-f
Keyword:crystal structures;first-principles calculations;K2TiF6
1. Introduction

Since their discovery in the 1990s, white light-emitting diodes (WLEDs) have received widespread attention because of their unique advantages, such as low loss, long lifetime, high efficiency, low environmental harm, and high thermal stability.[1–8] However, WLEDs fabricated by the yellow phosphor YAG:Ce and a blue InGaN chip[9,10] have a poor color rendering index (< 80) and a high correlated color temperature (> 6000 K) due to the lack of red emission components in their spectra,[11–13] which severely limits their application. To solve this problem, a significant amount of effort has been made to develop red-emitting materials. Interestingly, M2Si5N8:Eu2+ (M = Ca, Sr, and Ba) and CaSiAlN3:Eu2+ can make up for defects in the color rendering index and color temperature, but the serious reabsorption between nitride phosphors and YAG:Ce3+ reduces the luminous efficiency of these WLEDs.[14,15] In addition, their broadband emissions are over 650 nm, beyond the applicable bounds of human eyes.[16] It is therefore necessary to explore a new red luminescent material for WLEDs.

Mn4+-doped fluorides have the characteristics of low phonon energy and high stability and thus are highly suitable red-emitting phosphors for use in WLEDs. In comparison with rare earth ions, the transition metal Mn4+ ion has a 3d3 valence electronic configuration and is extremely sensitive to different lattice environments. Many researchers have made great effort to investigate various Mn4+-activated fluoride phosphors, such as AXF6:Mn4+ (A = K, Na, Rb, Cs, NH4, Ba, Zn and X = Si, Ge, Zr, Ti, Sn). Interestingly, Mn4+-doped K2TiF6 was evaluated to be an excellent candidate because of its many unique advantages, particularly its higher thermal stability and fine color stability, which make this material very popular.[17–28] Experimental results suggested that K2TiF6 has a hexagonal crystal structure in space group P-3m1.[29] The Ti4+ ion is located at the center of six nearest-neighbor F ions and forms an octahedral structure, and the K+ ion combines with the nearest-neighbor F ions to form a polyhedral structure. Mn4+ in Mn4+-doped K2TiF6 prefers substitution of the Ti4+ ion and is coordinated with six F− ions to form an octahedral structure. The high positive charge of the Mn4+ ion easily causes a strong crystal field, which can lead to energy-level splitting when Mn4+ is located at the geometric center of K2TiF6. Experimental results revealed that emission lines located at approximately 630 nm should be attributed to the spin-forbidden transition 2Eg → 4A2. Another two broadband absorption peaks are located at approximately 360 nm and 460 nm, corresponding to the spin-allowed transitions 4A2 → 4T1 and 4A2 → 4T2, which match well with the other components of WLEDs. Furthermore, the loss of the spectrum at 550 nm effectively avoids reabsorption and improves the efficiency of WLEDs. To date, many research groups have successfully synthesized the red K2TiF6:Mn4+ phosphor using different methods, such as wet chemical etching, coprecipitation, and cation exchange procedures.[30–32] Excitingly, the photoluminescence quantum efficiency can reach as high as 98% through cation exchange synthesis. Liao et al.[30] investigated the properties of the K2TiF6:Mn4+ phosphor by x-ray diffraction, scanning electron microscopy, Raman spectroscopy, decay curve analysis, Fourier transform infrared spectroscopy, and photoluminescence. Bicanic et al.[33] devised a model phosphor mixture composed of YAG:Ce and K2TiF6:Mn4+ by the color-corrected analysis of multiple phosphors (CCAMP), which improved warm white light emission at powers up to 5 kW/cm2. Zhou et al.[34] successfully developed a waterproof, narrow-band fluoride phosphor, K2TiF6:Mn4+, through a facile superhydrophobic surface-modification strategy (i.e., using superhydrophobic surface modification with octadecyltrimethoxysilane on K2TiF6 surfaces), making WLEDs more accessible. However, to the best of our knowledge, there are no theoretical studies on the local structure, location site, or electronic structure of Mn4+-doped K2TiF6, and absorption spectra have not been reported either experimentally or theoretically.

Density functional theory (DFT) is one of the most popular approximation methods in computational physics and materials research and has been widely used to address such problems.[35–40] In particular, strong on-site Coulomb repulsion (U) is introduced based on first principles, which greatly improves the reliability of the calculation result of systems with strong electronic correlations.[41–44] In this work, we first obtained ground-state structures, addressed the location site, and explored the electronic structure of Mn4+-doped K2TiF6 using the CALYPSO (crystal structure analysis by particle swarm optimization)[45–49] structural prediction method combined with first-principles calculations. Next, we calculated the optical absorption of the octahedral Mn4+ center in K2TiF6 by diagonalizing the complete energy matrices for a 3d3 ion configuration in a trigonal ligand field. Simultaneously, to confirm the correctness of our method and provide a reliable method for other transition metal-doped systems, we used the same method to study the spectrum of Mn4+ in Cs2TiF6 systems.

2. Computational methods

Extensive structural searches of K2TiF6:Mn4+ under 1 atm are performed using the CALYPSO structure prediction method. This method has been demonstrated to be efficient for a variety of systems, ranging from elements to binary and ternary compounds.[50–53] The variable-cell approach is used with up to 108 atoms. The top 30 structures with relatively low energy are reoptimized in the structure searches. The structural relaxation and electronic property calculations are performed using the Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) as implemented in theVienna ab-initio simulation package (VASP) code.[54,55] The frozen-core all-electron projector-augmented wave (PAW) method is applied to 3s23p64s, 3s23p63d24s2, 1s22s22p5, and 3s23p63d54s2, which are the valence electrons for K, Ti, F, and Mn, respectively. A cut-off energy of 500 eV is chosen for the total energy calculations of all structures, which is sufficient for the electron wavefunction extending to the plane-wave functions. A 3×3×2 Monkhorst–Pack k mesh is used as the integration space over the Brillouin zone to ensure that the total energy is well converged to less than 1 meV/atom. To further adjust the 3d electron configuration contribution of Mn4+, the DFT+U method is employed to handle the strong exchange correlation function of electrons, and the value of U added on the Mn 3d orbital is 4.0 eV.[56,57]

Mn4+ belongs to the 3d3 electronic configuration, with the high-spin ground-state spectral term 4A2 (S = 3/2). In the absence of a magnetic field, the interaction Hamiltonian in the crystal field for a 3d3 ion configuration can be expressed as[58]

where represents the contribution of spherical symmetric partial interactions, is the interaction between electrons, is the interaction of the electron spin–orbit coupling, and is the interaction between electrons and ligands. The ligand field potential (Vi) and ligand field parameter are described in the supporting information. Utilizing the |J,MJ〉 basis functions, the 120 × 120 energy matrix is derived according to the perturbation Hamiltonian (1) for the 3d3 ion configuration, where the matrix elements are the functions of the Racah parameters B and C and the spin–orbit coupling coefficient ζ.

3. Results and discussion
3.1. Structure and electronic properties

The space group of K2TiF6 is P-3m1, its unit cell contains two potassium atoms, one titanium atom, and six fluorine atoms. We first performed the ground-state structure prediction of K2TiF6 by CALYPSO using the chemical composition K: Ti: F = 2: 1: 6 as the input information under ambient pressure conditions and found the K2TiF6 structure to be in space group P-3m1, which is in accordance with the experimental results. This fact further confirms the reliability of the prediction method. Next, we reoptimized the structure of K2TiF6 using the local density approximation (LDA) and generalized gradient approximation (GGA) within the VASP code for the lowest energy structure. The calculated results are listed in Table S1 (supporting information), which shows that the GGA is a more accurate method for optimizing the structure of K2TiF6 than the LDA. To further explore the structure of Mn4+-doped K2TiF6 at the nominal concentration,[59] we searched the evolutionary variable-cell structure prediction structure up to 108 atoms with the input chemical composition ratio of Mn: K: Ti: F = 1: 24: 11: 72 at ambient pressure. The lowest energy structures of pure K2TiF6 and Mn4+-doped K2TiF6 are displayed in Fig. 1. Figure 1 shows that the Mn4+ ion will be more inclined to replace the vertex Ti atom and locate on Wyckoff 1a (0.0, 0.0, 0.0) and, along with six F− ions, will form a regular octahedral [MnF6]2− cluster in the D3d point symmetry group. There is no apparent distortion compared to the octahedral [TiF6]2− cluster structure, and their bond lengths and bond angles are very close, which may be attributed to the similar radius and identical valence state of the Ti4+ (0.605 Å) and Mn4+ (0.53 Å) ions. At the same time, in Fig. S1, we give another structure of Mn4+-doped K2TiF6 whose energy is very close to the ground-state one. From Fig. S1, we find that Mn substituted Ti at different sites and located on Wyckoff 1b (0.0, −1.0, 0.5), with the same space group (P-3m1) as the one in Fig. 1. The lattice constants, unit cell volumes, and corresponding relative energies are listed in Table S2, which indicate that the two structures are very similar. Thus, this structural information and the lowest energy structure have equally important theoretical significance for understanding the experimental observations, as well as mining the application potential of the Mn-doped K2TiF6 system. As an effective means of structural analysis, the XRD patterns of pure and doped K2TiF6 were calculated to further identify the accuracy of the predicted structures by comparing these spectra to the experimental results. As displayed in Fig. 2, the peaks and intensities of the spectra for (a) K2TiF6 and (b) Mn-doped K2TiF6 are in good agreement with the experimental data in the 2θ range of 15° to 50°,[59] which indicates that our predicted structures are reasonable. To determine the thermodynamic stability of Mn4+ in the K2TiF6 system, the formation energies (Ef) are computed by the following equation:[60]

where E1 and E0 are the total energies of the system with and without Mn4+, respectively; m and n are the numbers of dopant (Mn) atoms and substituted (Ti) atoms in the host lattice, respectively; and μm and μn are the chemical potentials for Mn and Ti atoms, respectively. We chose stable bulk MnF4 and TiF4 as references to evaluate the chemical potentials of the Mn and Ti atoms; for F atoms, μf is half the chemical potential of gas-phase F2. The calculated formation energy is −1.5442 eV, which indicates that Mn atoms substitute vertex Ti atoms and that K2TiF6 is able to form a stable structure with exothermic energy.

Fig. 1. Coordination structures of optimized (a) K2TiF6 (KTF) and (b) Mn4+ doped KTF. The pink, green, red, and yellow spheres represent K, Ti, F, and Mn, respectively.
Fig. 2. Comparison of the simulated XRD patterns with experimental data for (a) K2TiF6 and (b) K2TiF6:Mn crystals.

Figure 2 shows the energy-band structure and the total and partial density of states (DOS) for pure and Mn-doped K2TiF6 along the high-symmetry direction of the Brillouin zone, including the spin–orbit effect. It should be noted that all the values are subtracted by the Fermi energy, and the zero-point energy is equivalent to the Fermi level. K2TiF6 is an insulator with a direct gap of 4.33 eV, which is close to the value (4.73 eV) calculated by Jain et al.[61] In terms of the calculated band gap, the true band gap is estimated to be approximately 7–8 eV. To provide a better description of the d states of Mn4+ and obtain an appropriate band structure, we used the GGA+U approach to examine the Mn-doped K2TiF6 system, choosing Ueff = 4.0 eV. This method has been successfully applied to the study of transition element-doped systems.[62] The results show that the band gap is reduced to 2.12 eV for Mn-doped K2TiF6. The small band gap suggests that Mn4+ can effectively improve electron transport from the valence band to the conduction band when doped into K2TiF6 systems, leading to a shift from an insulator to a semiconductor. The formation of these gaps and the origin of all calculated bands can be well interpreted and extended by means of the DOS diagram. Figure 3 shows that the conduction band and valence band are mainly composed of p and d states. Most notably, unlike pure K2TiF6, the hybridization between the d state of Mn and the p state of F leads to some additional peaks in the DOS diagram of Mn-doped K2TiF6, which decreases the total energy and has a great influence on the emission energy.[63] We hope that our current theoretical results can provide useful guidance for further experimental investigations.

Fig. 3. Calculated band structures and total and partial DOS of (a) K2TiF6 and (b) K2TiF6:Mn. The dotted line represents the Fermi level.
3.2. Spectra properties

The Mn4+ ion has a 3d3 configuration, which possesses five-fold degenerate d orbitals and splits into two-fold and three-fold degenerate eg and t2g states due to the octahedral field, as shown in Figs. 4(a) and 4(b). The energy gap between the t2g and eg levels is 10Dq, where Dq is the crystal field parameter. There are 120 possible scenarios for electronic placement, and the interaction of electrons in the 3d3 configuration may induce eight spectral terms (namely, 4F, 4P, 2P, 2D1,2, 2F, 2G, and 2H, where the 4F term represents the ground state). The effect of a crystal field splits the 4F term further into 4A2, 4T1, and 4T2 levels, and the 2G term splits into 2E, 2T1, and 2T2 levels. To determine the transition energy, we construct a 120×120 energy matrix for a 3d3 ion configuration, employing the |J,MJ〉 basis functions. The matrix elements are the functions of the Racah parameters B and C, the spin–orbit coupling coefficient ζ, and the ligand field parameters B20, B40, , and . B and C are mainly dependent on the repulsive energy between the individual d electrons, and the values of the Racah parameters B and C are 605 and 4061, which was reported by Zhu et al.[32] The spin–orbit coupling coefficient can be expressed as ζ = N2ζ0 to reduce the adjustable factor in relation to the covalence reduction effect, where N is the covalence reduction factor, which can be obtained from the approximate formula ,[64] and B0, C0, and ζ0 represent the free Mn4+ ion parameters, whose values are B0 = 1160, C0 = 4303, and ζ0 = 405.[65] Because [MnF6]2− belongs to the D3d point group, the ligand field parameter term is zero, and the other ligand field parameters are described in the supporting information. We introduce two parameters R and θ to describe the Mn–O bond length and the angle between the Mn–O bond and the C3 axis, which are 1.8478 Å and 56.12°, respectively, in Fig. 1. A4 (see the Supporting Information) is almost constant and can be determined from the optical spectrum and the Mn–F bond length. Thus, A4 = 30.06 a.u. and A2 = 12.41 a.u. were estimated and used in our calculation. The optical spectra of the Mn4+-doped K2TiF6 crystal were calculated via diagonalized complete matrices, and the results are shown in Table 1. According to the Tanabe–Sugano energy diagram and configurational coordinate[66,67] model of Mn4+ in octahedral coordination shown in Figs. 4(c) and 4(d), the absorption peaks located at 471 nm and 352 nm are assigned to the spin-allowed transitions 4A2 → 4T2 and 4A2 → 4T1. The emission peak at 642 nm is derived from the spin-forbidden transition 2Eg → 4A2, which is not susceptible to the crystal field strength, such that the energy of the emission peak will not change too drastically with the crystal field strength, as shown in Table S3. Our results are consistent with the experimental results.[32,59,68] The 4A2 → 2T1 transition is located at 578 nm, which is in good agreement with the result reported by Zhu et al.[32] The 4A2 → 2T2 transition lies at 380 nm, which is distributed between the ultraviolet and visible regions and was first reported by us. To further verify the reliability of our calculation method, we calculated the spectrum of Cs2TiF6. Cs2TiF6 is an analog of K2TiF6 in the same space group.[69] Experiments have shown that Mn substitutes Ti in the Cs2TiF6 system, forming octahedral [MnF6]2− clusters with D3d symmetry. We obtained its structure using the atomic substitution method and list the structure and its structural parameters in Fig. S2 and Table S4, respectively. The Racah parameters are B = 657 and C = 3695, which were reported by Hasan and Manson.[70] Our calculation results are in good agreement with the experimental data reported by Zhou et al.[71] shown in Table 1. In addition, we first identified two other absorption lines located at 603 nm and 408 nm, corresponding to the 4A2→ 2T1 and 4A2→ 2T2 transitions, respectively. These findings will be of great significance for guiding future experiments and developing applications of laser materials.

Table 1.

The calculated and observed optical absorption spectra for Mn4+ ions in K2TiF6. All values are in units of nm.

.
Fig. 4. (a) Energy level splitting of d3 configuration in octahedron field. (b) Atomic orbital angle distribution diagram of d. (c) Tanabe–Sugano diagram for the d3 electron configuration in the octahedral crystal field. (d) Configurational coordinate diagram for Mn4+ in K2TiF6.
4. Conclusions

We performed a comprehensive study of K2TiF6:Mn4+ using the CALYPSO structural search method and first-principles calculations. We identified the P-3m1 structure of Mn4+-doped K2TiF6 under atmospheric pressure, which shows that the Mn ion substitutes the vertex Ti ion and then forms an octahedron with local D3d symmetry. The accurate energy-band and DOS calculations indicate that the doped Mn ion reduces the band gap of K2TiF6 to 2.12 eV, which leads to an insulator-to-semiconductor transition in K2TiF6:Mn4+. We calculated the optical absorption spectrum of K2TiF6:Mn4+ using the CEMD method. The calculated transition lines are in good agreement with the available experimental data. Furthermore, we found another promising transition line (4A2→ 2T2) located at 380 nm, which enriches the energy transition of K2TiF6:Mn4+. We expect this new transition to be experimentally identified in the near future.

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