Corrigendum: Lanthanide-Doped KLu2F7 Nanoparticles with High Upconversion Luminescence Performance: A Comparative Study by Judd-Ofelt Analysis and Energy Transfer Mechanistic Investigation

Scientific Reports 7: Article number: 43189; published online: 23 February 2017; updated: 06 April 2017 In the original version of this Article, there were errors in Affiliation 1 and 2 which were incorrectly listed as ‘School of Materials Science and Engineering, Sun Yat-Sen University, Guangzhou 510275, Guangdong, China’ and ‘School of Physics and Engineering, Sun Yat-sen Univeristy, Guangzhou 510275, Guangdong, China’ respectively.

Supplementary Figure S7. UCL performance of KLu2F7:Yb,Er versus NaYF4:Yb,Er. The spectra show the stronger UCL intensity of KLu2F7:Yb,Er sample compared to NaYF4:Yb,Er, demonstrating directly that our product can be more efficient host material for UCL than the well-known NaYF4.
Supplementary Figure S8. Luminescence decay curves of three emission bands of Er 3+ for β-NaGdF4:Yb/Er under 980-nm pulsed excitation. Figure S9. Diffuse reflectance spectrum of KLu2F7:Yb/Er UCNPs performed on UV3600 UV-vis-NIR spectrometer, superimposed with electronic energy-level for Er 3+ and Yb 3+ . The green dotted rectangle region includes some stray peaks, which is due to the error generated by switching detector from visible to NIR. The strongest peak is assigned to Yb 3+ 2 F7/2 → 2 F5/2 transition due to the large absorption cross-section of Yb 3+ 2 F5/2 state. Figure S10. Absorption spectra of NaGdF4:Yb/Er, revealing the 4 I13/2 NIR and visible range of Er 3+ .

Judd-Ofelt theory analysis
The Judd-Ofelt model is known to calculate the electric-and magnetic-dipole transition spectra line strength for the rare-earth ions embedded in specific host lattices. Herein, we use this theory to calculate the phenomenological intensity parameters of Er 3+ in Er 3+ /Yb 3+ codoped KLu2F7 and NaGdF4 host matrix, which further predict the luminescent properties and act as the subsequent proof for the proposed upconversion energy transfer mechanism of Er 3+ of our samples. The line strength of electric-and magnetic-dipole transition can be written as follows according to M.J. Weber 3 : The relationship between the absorption spectra and the dipole transition rate is: ( ) is the absorption cross-section; and are correction factor for (n 2 + 2) 2 /9n and n, respectively, where n represents the refractive index of the crystal; ̅ is mean wavenumbers of the transition related to the absorption spectra, in the form of ∫ ( ) ∫ ( ) ⁄ . The absorption spectra reflect the relationship between the optical density ( ) (or absorbance) and frequency , which is ( ) = 0 exp [− ( ) ]. The optical density is defined as: is rare-earth ion density in unit volume and is thickness of the powder sample. However, it is difficult to determine the accurate values of ion density and sample thickness. Hence, it is rational to define a constant parameter = . According to the above discussion, the total Judd-Ofelt model can be re-written as: representing integral optical density for each specific transition; Ω ′ = Ω , representing the redefined intensity parameters. For only electric-dipole transition involved manifolds ( 4 F9/2, 4 S3/2/ 2 H11/2, 4 F7/2, 2 H9/2 and 4 G11/2, which are indicated in Supplementary Figure  S6), the redefined intensity parameters can be evaluated by a least-square method using the spectra data and the double reduced matrix values referred from M.J. Weber 3 . For electric-and magnetic-dipole transition involved manifolds ( 4 I13/2 only in our situation), we can obtain the exact value for and the final intensity parameters. The radiative emission rates ′ , branching ratios and radiative lifetimes of an excited state J can be evaluated from below: ⁄ , ′ = 3 . Since the total lifetime of an excited state is governed by the combination of probabilities for all possible radiative and nonradiative transitions, which is All the used constants and other parameters are listed in Table S1-S3 for KLu2F7:Yb/Er and NaGdF4:Yb/Er, respectively. In the steady-state scenario, the green-and red-emitting population density can be treated and calculated using rate equations. We have used such methods to successfully interpret the energy transfer process between Yb 3+ and Er 3+ in several host matrix [5][6][7] . Generally, the population density of a given transition can be described as:

Supplementary
, + ( +1, +1 − , −1 ) − , is the ET parameters concerned about the donor i to j transition and the acceptor k to l transition. , −1 is the nonradiative MPR rate from the manifold i to the next lower-lying manifold i-1. Ai is the radiative rate of manifold i. Consider the EBT process as main mechanism, all the other cross-relaxation and multiphonon processes can be neglected. Therefore, we have the following equations dealt with the above two proposed energy transfer mechanisms, as shown in Supplementary Table S4. Of all given transitions, the population density of Yb 3+ 2 F5/2 manifold is expressed as: Under the steady-state pumping condition,  From the above results, one can find out that the population density of the violet-, green-and red-emitting manifolds are in similar form in both mechanisms, only with different EBT rates. In our case, ETU is the main depletion of the intermediate states, which means that radiative rates can be neglected compared with UC rate. However, the linear decay is still the main depletion to the luminescent manifolds. Therefore, in EBT1, the population density of the red-emitting state can be expressed as: One can see that the calculated results of EBT1 are corresponding to the experimental data (seen from Figure 5b and 5c). In addition, RGR of EBT1 is independent of pump power, while RGR of EBT2 is proportional to the pump power. Our experimental results (shown in Supplementary Figure S12, demonstrating RGR has nothing to do with excitation power) verify again that the main energy transfer mechanism is EBT1.
Supplementary Figure S12. Red-to-green ratio versus pump power in KLF and NGF.