1. Introduction

Recently lanthanides (Ln³⁺) doped upconversion (UC) nanocrystals (NCs) have been expected to be promising materials for the potential applications such as 3D display, bioimaging, photovoltaics, etc. [1–6]. Many efforts have been dedicated to investigating fundamental properties of Ln³⁺-doped fluoride NCs, for example, size-dependent UC luminescence which has attracted lots of research interest [7–12]. Sun et al. reported that the UC emission intensity decreased with increasing particle size in cubic phase NaYF₄:Er³⁺/Yb³⁺ NCs with the size from 30 nm to 300 nm [13]. Whereas Lim et al. reported an increasing tendency of UC emission intensity for Er³⁺/Yb³⁺ co-doped cubic phase NaYF₄ NCs with the size increasing 10 nm to 130 nm [12]. No clear conclusions on the size-dependent UC luminescence have been obtained in either theoretical studies or experimental investigations. Contrary to quantum dots, the size-dependent luminescence of Ln³⁺-doped NCs could not be explained by the theory of quantum confinement of electrons, since the luminescence arises from the electronic transition between the 4f configurations of Ln³⁺ ions. Recently, surface quenching and phonon confinement effects have been reported to explain the size-dependent UC luminescence [8,10]. Zhao et al. reported the quantitative investigation of UC luminescence in NaYF₄:Er³⁺/Yb³⁺ NCs [14]. It was shown that emission lifetimes decreased as the particle size decreased. This was a similar tendency as the results reported by Lim et al. [12]. They formulated a simple mathematical model to explain why emission lifetimes vary with the particle sizes in α-NaYF₄ NCs from 6 to 14 nm and β-NaYF₄ NCs from 20 to 45 nm. Although the explanations of both groups could be useful for understanding of size-dependent UC luminescence, the proposed quenching models still would not be clear to explain the reason why the quenching effect was different for emissions at different wavelengths. For a quantitative investigation, quantum efficiency (QE) can be considered as a crucial criterion to investigate size-dependent UC luminescence. Frank et al. have first reported the absolute UC QE of the colloids containing NaYF₄:Er³⁺/Yb³⁺ NCs [15]. Because of the local field effect and quenching effect of media [16,17], the emission lifetimes of NaYF₄: Er³⁺/Yb³⁺ NCs in liquid should be shorter than those in air. The QE of powder phosphors would be a direct proof of size-dependent luminescence. However, they have not been extensively studied until now.

Moreover, for a more precise comparison, all the samples should be prepared under the same heating condition. Most of the size-dependent luminescence was studied in Ln³⁺-doped NaYF₄ NCs. As well known, heating processes affect the crystallization of NCs and influence the optical properties. To perform reliable investigation, NaYF₄ NCs should be carefully synthesized under the same heating conditions. Besides heating temperature and time, another two methods have been reported to control the grain size of NaYF₄ NCs: one is to adjust the ratio of raw materials and the other is to add other sorts of surfactants [11,18–20]. However, the phase transition between α and β phase and shape transformation would also occur simultaneously during the synthesis processes. It is desired to prepare crystals of single phase with particle size from nanoscale to microscale under a fixed heating condition.

A solid state laser crystal, LiYF₄, which has only tetragonal phase, can be considered as another candidate [6]. LiYF₄ NCs have been successfully synthesized by thermal-decomposition and solvothermal method [21–24]. To the best of our knowledge, no reports on controllable synthesis of LiYF₄ crystals from nanoscale to microscale under the same reaction condition have been found yet.

Here, we report the synthesis of LiYF₄: Er³⁺/Yb³⁺ crystals with tunable sizes via a facile solvothermal method. By adjusting the concentration of LiOH, the grain size can be controlled from 16 nm to 2.0 μm. By the 976 nm excitation, the UC quantum efficiencies (QEs) of LiYF₄: Er³⁺/Yb³⁺ crystals with various sizes were measured. As the particle size changing from 16 nm to 2.0 μm, the QE for UC emissions increased from 0.04% to 2.1%. According to the quantitative comparison of the size-dependent UC luminescence, it showed that UC NCs have lower UC QE compared with microcrystals. It was suggested the quenching of adsorbed oleate ligand would be the main reason for size-dependent luminescence. The physical quenching mechanism of the surface adsorbed oleate ligand was discussed by using a proposed model.

2. Experimental section

2.1 Synthesis of LiYF₄:Er³⁺/Yb³⁺ nanocrystals

Y(NO₃)₃, Yb(NO₃)₃, and Er(NO₃)₃ (99.99%) were supplied by Sigma-Aldrich. Oleic acid (OA), NH₄F, and LiOH were supplied by Kishida Reagents Chemicals. All chemicals were used without further purification. LiYF₄:Er³⁺/Yb³⁺ NCs were synthesized by a solvothermal method [11,18,24]. Typically, 25 mmol of LiOH, 15 mL of OA, 10 mL of ethanol, and 2 mL of distilled water were well mixed under vigorous stirring to obtain a white viscous solution. Then, 2 mL of 0.5 M Ln(NO₃)₃ (Ln = 79%Y, 1%Er, and 20%Yb) stock solution was added into the mixture and kept stirring for 1 h. Then 4 mL of 1 M NH₄F aqueous solution (4 mmol) was dropped into the above solution. After stirring for 1 h, the milky mixture was transferred to a 50 mL Teflon-lined autoclave, and subsequently heated at 180 °C for 12 h. After cooling to room temperature, the products were collected by centrifugation, and washed with ethanol/cyclohexane and ethanol/water several times. The as-obtained sample was denoted as L1. Other samples denoted as L2-L4 were synthesized with different LiOH concentration listed in Table 1.

Table 1. Experimental conditions and the grain size of the corresponding products synthesized at 180 °C for 12h

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2.1 Characterizations

The X-ray diffraction (XRD) patterns of the samples were measured using a LabX XRD-6100 X-ray diffractometer (Shimadzu) with a Cu Kα₁ radiation resource (λ = 1.5405 Å). The morphologies of the samples were characterized by a field emission scanning electron microscope (FE-SEM, JSM-7000F) and transmission electron microscopy (TEM, JEOL 2100). The emission spectra were measured by a monochromator equipped with a H10330A-75 photomultiplier tube (Hamamatsu). The output signal was amplified by the LI5640 digital lock-in amplifier. The emission decay curves were recorded by a 200MHz digital oscilloscope DL-1640 (Yokogawa). A 976 nm laser diode (LD) was used as the pump source. A 300-900 nm band-pass filter was used to remove the scattered light from the pump LD. Under the excitation of the 976 nm LD of 150 mW, the photographs of samples L1-L4 were recorded by a Nikon D70 digital camera with fixed parameters, such as exposure time, shutter time, and ISO. In front of the camera, a 300-900 band-pass filter was used to remove the scattered excitation laser light.

2.3 Quantum efficiency measurements

The absolute QE were measured with an integrating sphere system. The integrating sphere with ultraviolet to near infrared (NIR) reflectance coating (Labsphere 4P-GPS-040-SF) was connected with a fiber-coupled 976 nm LD as an excitation source. A focus lens was setup at the incident port to focus the excitation light on the powder samples. The powder samples were held in a quartz holder and placed inside the integrating sphere. A baffler was mounted at the exit port to prevent the excitation light. The signal was detected with two photonic multichannel analyzers (PMAs): a visible PMA (Hamamatsu, C9220-02) and a NIR PMA (Ohtsuka Denshi, Photal MCPD-5000) [25]. The spectral sensitivities of these PMAs were calibrated with standard tungsten light source by the manufacturers.

3. Results and discussion

Figure 1(a) shows the XRD patterns of the as-obtained NCs (sample L1-L4). The diffraction peaks could be indexed to the standard data of tetragonal LiYF₄ (JCPDS 77-816). When the amount of LiOH decreased from 25 mmol to 10 mmol, the diffraction peak position of these three samples kept the same position. This indicates that all the products were LiYF₄ crystals. But the decreasing width of the diffraction peaks of the sample L1-L4 implies that the grain size of sample increased with decreasing the amount of LiOH. The TEM image in Fig. 1(b) clearly shows that the as-prepared samples were well separated. The average size was about 16 nm which was obtained by measuring more than 300 particles. The high resolution TEM image in Fig. 1(c) shows the as-prepared sample had good crystallinity. The observed interplanar distance between the lattice fringes was about 0.304 nm, which corresponded to that of the (112) plane of tetragonal LiYF₄. It can be observed that the as-prepared particles were in same octahedral shape which is illustrated in Fig. 1(d). In this paper the edge length of octahedral is used as the grain size for comparison (the W value in Fig. 1(d)).

 

Fig. 1 (a) XRD patterns of LiYF₄:Er³⁺/Yb³⁺ crystals prepared with 25, 20, 15, and 10 mmol LiOH. (b) TEM and (c) HR-TEM images of LiYF₄: Er³⁺/Yb³⁺ NCs prepared with 25 mmol LiOH. (d) The schematic graph for shape and size. (e) TEM and (f-g) SEM of LiYF₄:Er³⁺/Yb³⁺ crystals prepared with 20, 15, and 10 mmol LiOH, respectively.

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Figure 1(e)–1(g) show the TEM and FE-SEM images of the sample L2-L4. When the LiOH amount decreased from 25 mmol to 20 mmol, the particle size of the sample L2 increased from 16 nm to 27 nm (Fig. 1(e)). When the LiOH amount was 15 mmol, the grain size increased to about 220 nm with a little broader size distribution. The shape of sample kept octahedral, but the crystal edge became sharper, as shown in Fig. 1(f). When further decreasing the LiOH amount to 10 mmol, the grain size became approximately 2.0 μm, as shown in Fig. 1(g). The sample was not nanocrystals anymore. In this reaction system, LiOH first reacts with OA and forms lithium oleate (RCOOLi). According to the liquid-solid-solution reaction mechanism [26], after exchanged with RE³⁺ ions, Li⁺ would be released. And then it played as a reactant in forming LiYF₄. The reduction of the LiOH amount, namely the RCOOLi amount, would mainly enlarge the size of water drops according to the microemulsion reaction systems. Since the amount of surfactant was not sufficient, the size of separated water drops would not be uniform. Therefore, the grain size of the samples and the size distribution trended to increase with decreasing the LiOH amount.

The role of OA in our reaction system was not merely a solvent. The oleate ligands adsorbed on the surface can keep the particles separated due to the steric repulsions. The surface modification of the LiYF₄: Er³⁺/Yb³⁺ samples with different sizes were analyzed by FTIR, as shown in Fig. 2. The broad band around 3388 cm⁻¹ is ascribed to the −OH stretching vibration. The bands at 2922 and 2850 cm⁻¹ are associated to the asymmetric (υ_as) and symmetric (υ_s) stretching vibration of methylene (−CH₂) in the long alkyl of oleate molecule, respectively. The bands at 1578 and 1464 cm⁻¹ can be assigned to the asymmetric (υ_as) and symmetric (υ_s) stretching vibration of the carboxylic group, respectively. The presence of oleate ligand on the particle surface was confirmed by the FTIR analysis. Although the absolute absorption intensity reduced as the grain size increased from 16 nm to 2.0 μm (sample L1-L4), all the peak positions were the same. It implies that though grain size was different, only oleate ligand adsorbed on the particle surface. Without the influence of distinct ligands, such as TOPO [12], the only one kind of ligand could contribute to a clear understanding of influence of surface ligands. The relative amount of oleate ligand was related with the surface to volume ratio which is defined as Surf/Vol in this paper. For unit volume of crystals, smaller particle size would have larger relative surface area. The 16 nm sample would relatively have more surface ligands. Therefore, the FTIR intensity tended to decrease with the increase of grain size.

 

Fig. 2 FTIR spectra of LiYF₄: Er³⁺/Yb³⁺ with the size of (a) 16 nm, sample L1, (b) 27 nm, sample L2, (c) 220 nm, sample L3, and (d) 1.5 μm, sample L4.

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Under the excitation by a 976 nm LD, the measured emission spectra of LiYF₄: 1%Er/20%Yb (sample L1-L4) are shown in Fig. 3(a). The emission peaks at 379, 408, 522, 550, and 654 nm are assigned to the radiative transitions from the ⁴G_11/2, ²H_9/2, ⁴H_11/2, ⁴S_3/2, and ⁴F_9/2 to the ⁴I_15/2 level. To compare the relative intensity, all the emission spectra were normalized by the peak intensity of the 550 nm emission. Figure 4 shows the possible UC energy transfer processes. Since it has been well investigated by other works [12,15], we do not describe in details here. It is obvious that although blue, green, and red UC emissions can be observed under the 980 nm excitation, the relative intensity of sample of various sizes was different. The integrated intensity ratio of the blue to green and the red to green emission is shown in Fig. 3(b), where I_blue, I_green and I_red are the spectral integrated intensity of the emission from the ²H_9/2→⁴I_15/2, ⁴H_11/2(⁴S_3/2)→⁴I_15/2, and ⁴F_9/2→⁴I_15/2 transitions, respectively.

 

Fig. 3 (a) Emission spectra of LiYF₄: Er³⁺/Yb³⁺ samples with 16, 27, 220 nm, and 1.5μm (L1-L4), respectively, under the 976 nm LD excitation of 300mW. (b) Dependence of B/G and R/G integrated intensity ratio on the average particle size. (c) Schematic energy level diagram of Er³⁺ and Yb³⁺ and possible upconversion emission processes.

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Fig. 4 Dependence of absolute quantum efficiency (QE) of the total emissions and that of UC visible emissions (UC QE) on the average particle size. Inserts are the photography of LiYF₄:Er³⁺/Yb³⁺ crystals under a 976 nm LD pumping.

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It was found that when the grain size increased from 16 nm to 2.0 μm, the I_blue/I_green (B/G) ratio trended to increase, while the I_red/ I_green (R/G) ratio showed a decreasing tendency. It has been reported that the blue UC emission are attributed to a three-photon process, both green and red UC emissions are attributed to two-photon processes. The ⁴F_9/2 level is populated mainly by one process: first the electrons were relaxed to the ⁴I_13/2 level by the nonradiative transition from the ⁴I_11/2 level, then excited to the ⁴F_9/2 level by the energy transfer from a nearby Yb³⁺ ion, as well as excited state absorption (ESA). The electrons kept on the ⁴I_11/2 level could be excited to the ⁴F_7/2 level by the energy transfer energy from Yb³⁺ ions and ESA. Then the ⁴H_11/2(⁴S_3/2) level was populated by the nonradiative transition. The electrons on the ⁴F_9/2 and ⁴H_11/2(⁴S_3/2) level could be further excited to the ⁴G_11/2 and ²H_9/2 level from which the blue light emissions occurred. The key factor is the nonradiative relaxation: from the ⁴I_11/2 to ⁴I_13/2 level, from the ⁴H_11/2(⁴S_3/2) to ⁴F_9/2, and from ⁴F_9/2 to ⁴I_9/2 level. The decreased R/G ratio and increased B/G ratio implies that as the grain size increased from nanoscale to microscale, the nonradiative relaxation became more significant. This hindered the multi-photon UC processes. In this case, compared with in microcrystals, the three-photon UC process became weaker in LiYF₄:Er³⁺/Yb³⁺ nanocrystals. It can be mentioned that the smaller the particle size, the weaker the UC processes. Moreover, because of the stronger nonradiative transition in nanocrystals, it can be expected that the luminescent QE in nanocrystals would be lower than in microcrystals.

To investigate the size-dependence of the UC properties, the comparison of the absolute emission intensity of samples with different sizes was a direct method. However, the results based on such a method gave only phenomenological models, because the absolute emission intensity is related with the absorbed energy and the QE. Experimentally, the absorption can be hardly compared among samples with different sizes, due to the scattering of the pump light. It is extremely difficult to guarantee that all the samples can absorb the same excitation energy. Therefore, the QE comparison of the samples with different size seems to be more reliable. The QE is defined as

The reduction of QE can be explained by the quenching effect. It is easy to accept that the surface quenching would be significant for NCs due to their large Surf/Vol ratio. It should be probable that the surface quenching is caused by the surface defects and the adsorbed ligands on the surface. To investigate the quenching mechanism, the emission decay profiles were measured. The measured decay curves of three emissions, 408, 550 and 650 nm, are shown in Fig. 5. It is obvious that the decay curves for the three emissions decreased with the reduction of grain size. In case of sample sizes in micro- and submicroscale (~200nm), longer emission lifetimes were observed, while LiYF₄: 1%Er³⁺/20%Yb³⁺ nanocrystals exhibited dramatically shortened decay curves. The measured emission lifetime (τ_m) is given by the radiative transition rate (1/τ_R) and nonradiative relaxation rate (W_NR) as follows,

 

Fig. 5 The decay curves of (a) 408 nm, (b) 550 nm, and (c) 650 nm of LiYF₄: 1%Er³⁺/20%Yb³⁺ samples with different size under the excitation of 976 nm LD.

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It is well known that the radiative decay rate of the transition is influenced by the local crystal structure of the dopants. Since the dopant and host were the same, we assumed the radiative decay rate of LiYF₄: Er³⁺/Yb³⁺ samples with different sizes would be similar. The measured lifetime change would be attributed to the different nonradiative relaxation rate. When the particle size decreased, the total surface area for the unit volume of crystal samples would increase due to the enhancement of Surf/Vol ratio. The large surface area would enhance the number of surface quenching center, which is formed by the defects of the crystals, and the total amount of adsorbed oleate ligand on the surface. As mentioned above, oleate ligands were adsorbed on the surface of the as-prepared crystals. The high vibration energy of −CH₂ (~2922 and 2850 cm⁻¹) and −OH (~3300cm⁻¹) in the oleate molecular could bridge the two nearest 4f energy levels of Ln³⁺ ions dopant and quench the luminescence largely. We propose a model to explain the size-dependent luminescent quenching phenomenon as follows.

Assume that oleate molecules with the number of N are adsorbed on the unit area of surface, and some crystal defects with the number of M exist. The effective quenching rates due to oleate ligand and surface defect are assumed as W_ligand and W_surf, respectively. Because only one type of ligand, oleate, adsorbed on the sample surface, the quenching mechanism of the ligand is thought to be the same in the LiYF₄: Er³⁺/Yb³⁺ crystals with different sizes. In Eq. (1) the nonradiative term includes all the factors such as internal crystalline defects, surface defects, and adhered ligands. The modified equation is given by

According to our previous work, a triple exponential function given by

 

Fig. 6 The relation between the Surf/Vol ratio and the reciprocal of measured lifetime for the UC emissions of 408, 550, and 650 nm.

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The plots of blue, green, and red emissions were shown as a function of Surf/Vol ratio. It suggests that the proposed model expressed by Eq. (5) is reasonable. A similar linear relation between the reciprocal of emission lifetime and Surf/Vol ratio has been reported [8,12,14]. In their works, the Stern-Volmer equation was applied to explain the surface quenching, which simply treated all the quenching parameters as one factor. Based on this model, the different quenching effect on the emissions with different wavelengths was not clarified. In our results, the slope of the fitted line for the different emission was found to be different. No explanations have been put forward for this phenomenon to our best knowledge. Based on our model, however, possible mechanisms could be proposed. Typically, the rate of non-radiative relaxation with multi-phonon emission could be simply expressed by

In case of Er³⁺, for the emissions at 408 nm (²H_9/2→⁴I_15/2), 550 nm (⁴S_3/2→⁴I_15/2), and 650 nm (⁴F_9/2→⁴I_15/2), the energy gaps were approximately 2100, 3100, and 2800 cm⁻¹, respectively. Because of the same surface ligand, $\omega$ would be a constant. The W_NR of the emissions will obey the following series,

4. Conclusions

In summary, Er³⁺/Yb³⁺ co-doped LiYF₄ NCs have been synthesized via a facile solvothermal method. By controlling the LiOH concentration, the grain size of LiYF₄:Er³⁺/Yb³⁺ crystals could be controlled from 16 nm to 2.0 μm. The UC QE and relative intensity of I_Blue/I_Green and I_Red/I_Green were measured to investigate the size-dependent UC phenomenon. It was found that increasing grain size would enhance the QE and promote the multi-photon UC process. Based on the emission lifetimes of the transitions from different energy levels, it can be stated that the adsorbed oleate ligands on the surface played an important role in determining the size-dependent luminescent performance. A model was proposed for physically understanding the quenching effect of the oleate ligand.