Morphology evolution and pure red upconversion mechanism of β-NaLuF4 crystals

A series of β-NaLuF4 crystals were synthesized via a hydrothermal method. Hexagonal phase microdisks, microprisms, and microtubes were achieved by simply changing the amount of citric acid in the initial reaction solution. Pure red upconversion (UC) luminescence can be observed in β-NaLuF4:Yb3+, Tm3+, Er3+ and Li+ doped β-NaLuF4:20% Yb3+, 1% Tm3+, 20% Er3+. Based on the rate equations, we report the theoretical model about the pure red UC mechanism in Yb3+/Tm3+/Er3+ doped system. It is proposed that the pure red UC luminescence is mainly ascribed to the energy transfer UC from Tm3+:3F4 → 3H6 to Er3+:4I11/2 → 4F9/2 and the cross-relaxation (CR) effect [Er3+:4S3/2 + 4I15/2 → 4I9/2 + 4I13/2] rather than the long-accepted mechanism [CR process among Er3+:4F7/2 + 4I11/2 → 4F9/2 + 4F9/2]. In addition, compared to the Li+-free counterpart, the pure red UC luminescence in β-NaLuF4:20% Yb3+, 1% Tm3+, 20% Er3+ with 15 mol% Li+ doping is enhanced by 13.7 times. This study provides a general and effective approach to obtain intense pure red UC luminescence, which can be applied to other synthetic strategies.

host lattice substitutionally or interstitially owing to its small ionic radius, which would reduce the symmetry of crystal field around Ln ions, inducing the enhancement of UC emission intensity. However, there is no report on the increase of pure red UC luminescence by introducing Li + in β -NaLuF 4 :Yb 3+ , Tm 3+ , Er 3+ .
As a typical solution-based approach, the hydrothermal method has been widely applied to synthesize inorganic materials with controllable structures and morphologies 32,33 . During the hydrothermal treatment, a series of external parameters such as the pH value, citrate ions (Cit 3− ) content, NaF content, reaction time and temperature may have significant effects on the morphology evolution of particles 18,[34][35][36] . In particular, the addition of chelating agent has a great impact on the kinetics of crystal growth 37,38 . Cit 3− as a shape modifier plays a critical role in the shape evolution of the final products due to its high thermal stability and ability to form complexes with other metal ions [39][40][41] .
In this article, a series of β -NaLuF 4 crystals were prepared via a hydrothermal method using citric acid as a chelating agent, and their pure red UC luminescence were studied. Hexagonal phase microdisks, microprisms, and microtubes were achieved by simply changing the amount of citric acid in the initial reaction solution. Importantly, pure red UC luminescence can be observed in β -NaLuF 4 :Yb 3+ , Tm 3+ , Er 3+ and Li + doped β -NaLuF 4 :20% Yb 3+ , 1% Tm 3+ , 20% Er 3+ . Based on the rate equations, the theoretical model about the pure red UC mechanism in Yb 3+ /Tm 3+ /Er 3+ doped system is presented. The red UC emission of 660 nm in Li + doped β -NaLuF 4 :20% Yb 3+ , 1% Tm 3+ , 20% Er 3+ is greatly increased compared to the Li + -free sample under 980 nm excitation at room temperature.

Results and Discussion
Morphology evolution of β-NaLuF 4 crystals. Citric acid has been regarded as one of the most effective chelating agents because of its ability to regulate the morphology and dimension of the samples in the hydrothermal process 42 . In the present system, citric acid also plays a critical role in the morphology evolution of β -NaLuF 4 crystals. Figure 1 shows the XRD patterns of the as-prepared β -NaLuF 4 samples with different citric acid contents from 2 to 8 mmol. As can be seen, all the diffraction peaks can be well indexed to pure β -NaLuF 4 , which is consistent with the standard card (JCPDS 27-0726). No other impurity peaks are detected, indicating the high purity of β -NaLuF 4 samples. It is worth to note that the relative intensities of (100), (110), (101) and (201) peaks display some differences from each other, implying the existence of oriented growth under different Cit 3− contents. The above XRD results are supported by the corresponding SEM images, as exhibited in Fig. 2. When the adding citric acid is 2 mmol (Fig. 2a), regular hexagonal phase microdisks with an average size of 0.79 μ m in height and 7.58 μ m in diameter are obtained. As the citric acid content increases to 3 mmol (Fig. 2b), short hexagonal phase microprisms with uniformity and smooth surfaces are achieved. The mean height and diameter of the prisms are 2.12 μ m and 8.51 μ m, respectively. Further increasing the citric acid content to 8 mmol, hexagonal phase microtubes with hollow structure are presented in Fig. 2c. The tubes have an average height of 9.47 μ m and an average diameter of 1.88 μ m. The ratios of height to diameter (H/D ratios) are calculated to be about 0.10, 0.25, and 5.04 when the adding citric acid is 2, 3, and 8 mmol. From the above analysis, it can be concluded that the H/D ratio is increased as the citric acid content increases from 2 to 8 mmol. Based on the high anisotropic structure of β -NaLuF 4 43 , when the adding citric acid increases from 2 to 8 mmol, Cit 3− absorbs onto the {0001} facets more strongly than the {1010} facets. Thus, the growth rate along [0001] direction is faster than that along [1010] direction, resulting in the morphology evolution from disks to tubes and the enhancement of H/D ratio. The hollow structure of the tubes is generated owing to the growth rate at the center is lower than that at the edges 44 . The corresponding schematic diagrams of β -NaLuF 4 crystals under different citric acid contents are displayed in Fig. 2(d-f).
Theoretical model for the first CR effect. The corresponding rate equations are as follows:  As can be seen from Equation (5), the green-emitting level N 4 does not have quasi-quadratic relationship with pump power, which is not corresponding to Fig. 4(a,c) where n are 1.72 and 1.61 in 0.5% Tm 3+ and 1% Figure 6. Proposed ET mechanism of red UC emission in β-NaLuF 4 :Yb 3+ , Tm 3+ , Er 3+ (with high Er 3+ content). The mechanism involves the CR effects among Er 3+ 26-28,46 and ETU from Tm 3+ to Er 3+ 23 .    As can be seen from Equations (7) and (8), red-emitting manifold N 3 and green-emitting manifold N 4 have linear and quasi-quadratic relationships with pump power at high Er 3+ content, which correspond to the relevant results in Fig. 4. The power dependence of RGR for β -NaLuF 4 :20% Yb/1% Tm/20% Er is exhibited in Fig. 7(a). It can be clearly seen that the RGR is decreased with the increase of pump power. The ratio of N 3 to N 4 shows the inverse proportional relationship to pump power [Equation (9)], which is in accordance with the result in Fig. 7(a). From the above analysis, it can be deduced that CR2 maybe makes a contribution to the high RGR when the Yb 3+ / Tm 3+ /Er 3+ system doped with high Er 3+ dose.
Theoretical model for the third CR effect. The corresponding rate equations are as follows:  As can be seen from Equation (10), red-emitting level N 3 ~ aρ + bρ 2 , which is corresponding to the relevant results in Fig. 4(b,d) when we suppose the parameter "b" is close to zero. Equations (11) and (12) show the green-emitting manifold N 4 and ratio of N 3 to N 4 have quasi-quadratic and inverse proportional relationships with pump power, which are in good agreement with the results shown in Figs 4(a,c) and 7(a), respectively. Thus, CR3 can be used to explain the experimental results. On the basis of the above analysis, it can be concluded that both CR2 and CR3 maybe are the appropriate ET mechanisms for the achievement of pure red UC luminescence at high Er 3+ content in Yb 3+ /Tm 3+ /Er 3+ doped system. According to our experimental results, there are three reasons to prove that CR3 (Er 3+ : 4 S 3/2 + 4 I 15/2 → 4 I 9/2 + 4 I 13/2 ) is the main CR effect for the population process of 4 F 9/2 manifold. First, the ratio of NIR to green (NGR) is enhanced with the increase of Er 3+ content in β -NaLuF 4 :20% Yb/1% Tm/xEr (NIR emission corresponds to the 4 I 13/2 → 4 I 15/2 transition of Er 3+ ), as presented in Fig. 7(b). The increasing NGR indicates that the population of Er 3+ 4 I 13/2 level becomes larger and larger compared to Er 3+ 4 S 3/2 / 2 H 11/2 levels. As is known, the probability of MPR from 4 I 11/2 to 4 I 13/2 is quite low due to the low phonon energy in our system. Thus, the increasing NGR is mainly ascribed to CR3. Second, the decay curves of the 4 I 13/2 → 4 I 15/2 transition of Er 3+ in β -NaLuF 4 :20% Yb/1% Tm/0.5% Er and β -NaLuF 4 :20% Yb/1% Tm/20% Er are shown in Fig. 8. The decay lifetime was calculated based on the function: ∫ τ = I t dt I ( ) / P , where I(t) is the emission intensity at time t, and I P is the peak intensity in the decay curve. The calculation results show that τ 0.5% Er = 1.40 ms and τ 20% Er = 0.55 ms. The energy transfer efficiency (ETE) can be evaluated by the following expression: η ETE = 1 − τ 20% Er /τ 0.5% Er , the calculation result shows that η ETE = 60.71%. With the increase of Er 3+ dose, the enhanced red UC emission (660 nm) mainly comes from the enhancement of CR effect between Er 3+ in Yb 3+ /Tm 3+ /Er 3+ doped system. Thus, it is reasonable to consider that the probability of CR3 is 60.71%. Third, the ET process of CR2 (Er 3+ : 4 S 3/2 + 4 I 13/2 → 4 F 9/2 + 4 I 11/2 ) needs the population process of Er 3+ 4 I 13/2 manifold, which is mainly dependent on the ET process of CR3 (Er 3+ : 4 S 3/2 + 4 I 15/2 → 4 I 9/2 + 4 I 13/2 ). Therefore, the CR3 process is required before the CR2 process, resulting in the leading role of CR3 in the CR effects.
Li + doped β-NaLuF 4 :20% Yb 3+ , 1% Tm 3+ , 20% Er 3+ crystals. A series of Li + doped β -NaLuF 4 :20% Yb 3+ , 1% Tm 3+ , 20% Er 3+ crystals were synthesized by adding 3 mmol citric acid. Figure 9 presents the XRD patterns (a) and the main diffraction peak (b) of different Li + doped β -NaLuF 4 :20% Yb 3+ , 1% Tm 3+ , 20% Er 3+ crystals. As shown in Fig. 9(a), all the diffraction peaks of the products can be indexed as pure β -NaLuF 4 (JCPDS 27-0726) even the Li + concentration increases up to 20 mol%, indicating that Li + doping has no influence on the crystal structure of the products. The corresponding UC emission spectra of the products under 980 nm excitation are shown in Fig. 10. As can be seen, the pure red UC luminescence is greatly enhanced after Li + doping. Compared to the Li + -free sample, the pure red UC luminescence in β -NaLuF 4 :20% Yb 3+ , 1% Tm 3+ , 20% Er 3+ with 15 mol% Li + doping is increased by 13.7 times. This phenomenon is mainly caused by the asymmetric surrounding environment around Ln ions after Li + doping. Figure 9(b) exhibits that the main diffraction peak moves to the larger angles when the Li + concentration is from 0 to 15 mol%, whereas shifts in reverse as the Li + concentration increases up to 20 mol%. According to Bragg's law 2dsinθ = nλ, where d represents the interplanar distance, θ represents the diffraction angle, and λ represents the diffraction wavelength. When d decreases, θ increases; when d increases, θ decreases. As is displayed in Fig. 11(a), Na + and Ln 3+ occupy the same lattice site in β -NaLuF 4 lattice. When the Li + is introduced into the host lattice, it can replace Na + (d decreases, θ increases, 0 < Li + concentration ≤ 15 mol%) [ Fig. 11(b)] or occupy the interstitial site (d increases, θ decreases, 15 < Li + concentration ≤ 20 mol%) [ Fig. 11(c)] due to its small ionic radius, leading to the contraction or expansion of unit cell. Both the contraction and expansion of unit cell would reduce the symmetry of crystal field around Ln ions, inducing the sharp increase of pure red UC luminescence intensity [29][30][31] . The strongest UC luminescence intensity is acquired in β -NaLuF 4 :20% Yb 3+ , 1% Tm 3+ , 20% Er 3+ with 15 mol% Li + doping, which is attributed to the most asymmetric surrounding environment around Ln ions, as shown in Fig. 9(b).
Characterization. The phase and structure of the as-prepared products were confirmed by powder X-ray diffraction (XRD) patterns using the D-Max 2200VPC XRD from Rigaku Company. Morphologies and grain sizes were verified by using an Oxford Quanta 400F Thermal Field Emission environmental Scanning Electronic Microscope (SEM). UC photoluminescence spectra were acquired on the Edinburgh Instrument FLSP920 steady-state fluorescence spectrometer equipped with a 2 W 980 nm laser diode. The spot size of the 980 nm laser on the samples is about 0.05 cm 2 . Figure 11. Crystal structure of β -NaLuF 4 (a); possible changes in β -NaLuF 4 crystal lattice after Li + doping: substitution by Li + (b), and interstitial occupation by Li + (c).