CC BY
33
Near infrared down-conversion luminescence of Ba4Y3F17:Yb3+:Eu3+ nanoparticles
under ultraviolet excitation
S. V. Kuznetsov1*, A. S. Nizamutdinov2, E. I. Madirov2, V. V. Voronov1, K. S. Tsoy2, A. R. Khadiev2, A. D. Yapryntsev3, V. K. Ivanov3, S. S. Kharintsev2, V. V. Semashko2
1Prokhorov General Physics Institute of the Russian Academy of Sciences, Russia 2 Kazan Federal University, Russia 3Kurnakov Institute of General and Inorganic Chemistry of the Russian Academy of Sciences, Russia
PACS 42.70.-a, 81.20.Fw DOI 10.17586/2220-8054-2020-11-3-316-323
The single-phase solid solutions Ba4Y3F17:Yb:Eu with fluorite-type structure were synthesized by co-precipitation from aqueous solution technique. The average particle size was approximately 100 nm without agglomeration. The sensitized down-conversion luminescence of Yb3+ ions was observed under 296 nm excitation. The quantum yield of Yb3+ luminescence was found to reach avalue of 0.4 % for samples with Eu/Yb ratios of 0.1/1.0 and 0.1/10.0.
Keywords: nanofluoride, down-conversion, luminescence. Received: 16 April 2020
1. Introduction
According to the International Energy Agency (IEA) and the European Environment Agency (EEA), the energy consumption increases from year to year. It stimulates the search for new sources of energy and improving the efficiency of existing ones. According to the forecast, the terawatt energy will be generated by means of photovoltaic devices until 2030 years with a simultaneous reduction of kW/h cost [1]. One of the most affordable source of energy is solar energy. Silicon-based solar cells are mostly used for solar energy utilization. Most of this energy will be generated by silicon solar panels. In addition to silicon, various multilayer compositions such as GaAs, CdTe, Cu(In,Ga)Se2, and recently proposed perovskite structures [2, 3]. The latter are expensive and difficult to produce on an industrial scale. Additionally, there is the problem to dispose them after the expiration due to toxic components and use of such compositions is contrary to the principles of green chemistry. The advantages of silicon are chemical availability and the maturity of the technological chains, the disposal of electronic components, including those containing rare-earth elements.
At the same time, one serious drawback of silicon-based solar cells is relatively low light-to-electrical energy conversion efficiency (LECE), namely, no higher than 25 % for the best samples [4,5]. The region of the highest photosensitivity of silicon is located about 1 ^m and his LECE spectrum poorly corresponds the solar emission spectrum.
The enhancement of silicon solar panels efficiency by down-conversion of solar irradiation from ultraviolet and blue spectral range to the 1 ^m spectral range is an urgent task and it is extremely actual for space applications [69]. Prospective emitter is trivalent ytterbium ion due to near-infrared (NIR) luminescence band around 1000 nm (2F5/2-2F7/2 transition) [9-13], which well coincides with the top of LECE spectrum of silicon batteries. One of the new thoroughly investigated luminescence matrices is Ba4Y3F17 [14-17], because it demonstrated the high quantum yield of down-conversion luminescence [14].
Energy transfer from the UV and blue spectral regions to ytterbium is possible for various sensitizing cations absorbing in these spectral regions. One especially efficient mechanism of energy transfer is through stepwise relaxation of a sensitizer ion, resulting in the excitation of two acceptor ions by quantum cutting mechanism [12,13,18,19]. The quantum cutting demonstrated high quantum efficiency coefficient up to 195 % but the quantum yield of NIR luminescence is low. A more efficient pathway is simple downshifting in a systems with higher quantum yield of luminescence. A promising composition is Yb/Eu doping pair, because absorption spectrum of europium comprises several lines in the UV and blue spectral regions. The highest directly measured quantum yield of ytterbium luminescence (2.5 %) upon 266 nm pumping was reached for the SrF2:Yb (1.0 mol %):Eu (0.05 mol %) powder [20].
The purpose of this paper is to synthesize Ba4Y3F17:Yb:Eu solid solution and to study its luminescent properties. This specimen of interest is intended to be utilized for enhancing of LECE of silicon solar cells.
2. Experimental
Ba4Y3Fi7:Yb:Eu powders were synthesized by co-precipitation from aqueous nitrate solutions technique as reported earlier [14]. 99.99 wt. % dihydrate potassium fluoride (REACHEM, Russia), 99.99 wt. % yttrium, ytterbium, and europium nitrate hexahydrates, barium nitrate (all reagents from LANHIT, Russia), and double distilled water were used as starting materials without additional purification. Potassium fluoride was preliminarily dried at 350 °C for 3 hours and it was taken with a 50 % excess from stoichiometry. 0.08 M aqueous solutions of barium nitrate and rare earth nitrate were added dropwise to potassium fluoride (0.16 M) with vigorous stirring. Precipitates were washed several times by double distilled water and collected by centrifugation. The resulting precipitates were dried at 45 °C and annealed in a platinum crucible in air at 600 °C for 1 hour. X-ray powder diffraction analysis was performed on a Bruker D8 Advance diffractometer with CuKa radiation. The TOPAS software (Rwp < 10) was used for calculation of X-ray coherent scattering domain and unit cell parameters. The morphology, particle size, and composition of the samples were analyzed by a Carl Zeiss NVision 40 scanning electron microscope equipped with an EDX detector.
Raman spectra were captured with a multi-purpose analytical instrument NTEGRA SPECTRA™ (NT-MDT) in epi-configuration. The spectrometer was wavelength calibrated with a silicon wafer by registering a first-order Raman band centered at 520 cm-1. A sensitivity of the spectrometer was as high as ca. 3500 photon counts per 0.1 s provided that we used a 100x objective (N.A. = 0.7), an exit slit of 100 ^m and a linearly polarized light with the wavelength of 532 nm and the intensity of 5.4 MW/cm2. The Raman spectra were collected with the EMCCD camera cooled down to -100 °C and registered with spectral resolution of 3 cm-1 using a 600 grooves/mm grating.
Photoluminescence was excited by pulsed UV and visible laser radiation from the H2 Raman shifter cell converting the 266 nm UV radiation from LS2147 laser and/or OPO laser system produced by JV Lotis TII. The pulse duration was 10 ns, repetition rate 10 Hz. The luminescence spectra were registered by a StellarNet EPP2000 portable spectrometer with a spectral resolution of about 0.5 nm. The luminescence kinetics were registered with a MDR-23 monochromator and FEU-100 photomultiplier tube for the UV-visible spectral range and FEU-62 photomultiplier tube for the NIR spectral range and recorded with the 1 GHz 8 bit Rhode-Schwartz oscilloscope. The direct measurements of luminescence quantum yield were performed using the luminescence spectra recorded in a Thorlabs IS200 integrating sphere coupled to a StellarNet EPP2000 spectrometer via an optical fiber. The spectral sensitivity of this system was calibrated using an approach described previously [21].
3. Sample characterization
The samples were single-phase according to X-ray powder diffraction after annealing at 600 °C (Fig. 1). The unit cell parameters are in convenience with preliminary data published elsewhere (Table 1) [14,22].
Fig. 1. X-ray powder diffraction for Ba4Y3F17:Yb(5.0 mol.%): Eu(0.1 mol.%) powder after annealing at 600 °C
Table 1. Unit cell parameters and X-ray coherent scattering domain for Ba4Y3F17: Yb:Eu samples
Nominal composition a, A X-ray coherent scattering domain, nm
Ba4Y3Fi7:Yb(1.0 mol. %):Eu(0.1 mol. %) 5.9252(2) 73 ± 5
Ba4Y3Fi7:Yb(5.0 mol. %):Eu(0.1 mol. %) 5.8960(2) 49 ± 3
Ba4Y3Fi7:Yb(10.0mol. %):Eu(0.1 mol. %) 5.8793(3) 75 ± 11
Ba4Y3Fi7:Yb(1.0mol. %):Eu(0.05 mol. %) 5.8890(3) 96 ± 15
Ba4Y3Fi7:Yb(5.0 mol. %):Eu(0.05 mol. %) 5.8801(3) > 100
Ba4Y3Fi7:Yb(10.0 mol. %):Eu(0.05 mol. %) 5.8843(3) > 100
Scanning electron microscopy revealed that the particles were about 100 nm without agglomeration (Fig. 2). The particle sizes well correlated with X-ray coherent scattering domains (Table 1), which means that all particles are single crystalline.
The real compositions were revealed by energy-dispersion analysis (Table 2). The content of the yttrium and barium are close to nominal content. In contrast, the contents of ytterbium and europium are higher than nominal ones, but it is lower than the error of analysis.
Fig. 2. The typical scanning electron microscopy image for Ba4Y3F17:Yb (5.0 mol.%): Eu (0.1 mol.%) powder after annealing at 600 °C
Table 2. Compositions based on EDX analysis of Ba4Y3Fi7: Yb:Eu samples
Initial nominal compositions Real chemical compositions from EDX analysis
Ba4Y3Fi7:Yb(1.0 mol. %):Eu(0.1 mol. %) Ba0.638 Y0.344 Yb0.0i4Eu0.004F2.362
Ba4Y3Fi7:Yb(5.0 mol. %):Eu(0.1 mol. %) Ba0.568 Y0.364 Yb0.065Eu0.004F2.435
Ba4Y3Fi7:Yb(10.0mol. %):Eu(0.1 mol. %) Ba0.585 K0.02i Y0.363Yb0.i38Eu0.004F2.706
Ba4Y3Fi7:Yb(1.0 mol. %):Eu(0.1 mol. %) Ba0.530 K0.0i4 Y0.387Yb0.065Eu0.003F2.439
Ba4Y3Fi7:Yb(10.0 mol. %):Eu(0.05 mol. %) Ba0.543 Y0.323 Yb0.i3iEu0.003F2.457
The Raman spectrum contains several bands around 300 cm-1 and 600 cm-1, which is characteristic for fluorides with narrow phonon spectra, see Fig. 3. On the other hand, the Raman spectra tail spreads above 800 cm-1, which is non-typical for fluorides and may influence on the energy transfer processes.
Fig. 3. Raman spectrum of Ba4Y3Fi7 sample
Luminescence of Eu3+ ions can be excited by transitions from the 7F0 ground state to the 5D J manifolds, in particular, due to 7F0-5D2 transition located around 465 nm with relatively large cross-section. The excitation of luminescence is also possible in UV spectral range as the result of transitions to 5IJ and 5KJ manifolds or the charge transfer states (Fig. 4). In order to avoid photodynamic processes initiated under intense UV pumping and following color center formation [23], which can distort the spectral-luminescent properties, excitation was performed at 296, 399 and 463 nm (transitions 7F0 ^ 5H5,6, 5L6 and 5D2, correspondingly) only.
Eu3+ Yb3+
Fig. 4. Energy diagram of Eu3+ and Yb3+ ions and the energy transfer processes from Eu3+ to Yb3+ ions [24]
In the case of double doped samples by Eu3+ and Yb3+ ions, the energy gap between 5H5,6 and 5D2 states of Eu3+ ions is close to the 2F7/2-2F5/2 transition energy of Yb3+ ions. Following the results of [24] the energy transfer from Eu3+ to Yb3+ ions may occur through various mechanisms, for example: 5H5 6 (Eu3+ ) + 2F7/2 (Yb3+) ^ D2 (Eu3+) + 2F5/2 (Yb3+), or 5Do (Eu3+) + 2F7/2 (Yb3+) ^ 7Fa (Eu3+) + 2F5/2 (Yb3+) as it is illustrated in Fig. 4.
The luminescence spectrum under pulsed excitation at 296 nm consists of Eu3+ transitions from 5D3, 5D2, 5Di and 5D0 states localized in 400 - 750 nm range, as well as luminescence of Yb3+ ions 2F5/2 F7/2, which is situated around 980 - 1000 nm (Fig. 5). The most intense luminescence bands at 465 nm, 488 nm and 511 nm correspond to 5D2 ^ 7F0,2,3 transitions, at 526 nm, 538 nm and 557 nm bands - to 5Di ^ 7F0,i,2 and at 576 nm, 592 nm, 617 nm and 699 nm - to 5D0 ^ 7F0,i,2,4 transitions, respectively. The NIR luminescence of Yb3+ ions is evidence of the energy transfer processes from Eu3+ to Yb3+ ions. At the same time, the luminescence of 2F5/2-2F7/2 of Yb3+ ions was not detected for the case of excitation at 399 nm or 463 nm.
1-1-1-1-1-■-1-1-1-1-1-■-1
400 500 600 700 800 900 1000 1100
Wavelength, nm
Fig. 5. Typical luminescence spectra of Ba4Y3F17:Yb:Eu samples under pulsed excitation at 296 nm
The energy transfer coefficients from Eu3+ to Yb3+ were estimated from the luminescence spectra using expression (1):
E f IYb(A)dA
= f (IYb{A) + /i(A))dA X 100 % (1)
where IYb(A) is the luminescence intensity of Yb3+ and IEu (A) is the luminescence intensity of Eu3+ (Table 3). The increase of doping level leads to some saturation of energy transfer coefficient most probably due to luminescence concentration quenching effect. Thus there should be some optimal content ratio for Yb/Eu ions contents.
Table 3. Energy transfer coefficients (%) from Eu3+ to Yb3+ in Ba4Y3F17:Yb:Eu samples
Eu content, mol.% Yb content, mol.%
1.0 5.0 10.0
0.05 8 ± 1 5 ± 1 9 ± 1
0.10 11 ± 1 15 ± 1 9 ± 1
It is exhibited in fluorescence kinetics. The luminescence decays of Ba4Y3F17:Yb3+ :Eu3+ samples from 5D1 and 5D0 states of Eu3+at 556 nm and 617 nm, correspondingly, and from 2F5/2 of Yb3+ion (at 1020 nm) were investigated under the excitation at 296 nm (Figs. 6 and 7, respectively). The kinetics from 5D1 state (Fig. 6a) exhibit the long lasting raise (few ms for Ba4 Y3F17:Eu3+ (0.1 mol. %)), which is evidence for cross-relaxation effects between
manifolds of Eu3+ ions [22]. However, the lifetime of 5Di state is weakly dependent on Yb3+ ions' doping level. The luminescence decay from 5D0 state of Eu3+ ions is more complicated and consists of fast and slow components. The contribution of the last one grows with a simultaneous increase of Yb3+ content, which can be attributed to reverse energy transfer from Yb3+ to Eu3+ via cooperative processes [25].
Fig. 6. Luminescence decays of Ba4Y3F17:Eu (0.1 mol.%):Yb (x mol. %), x = 0, 1.0, 5.0, 10.0 samples at 556 nm (from 5D1 state) (a) and 617 nm (from 5D0) (b) under 296 nm excitation
Time, ms Time, ms
Fig. 7. Luminescence decay kinetics of Ba4Y3F17:Yb:Eu samples at 1020 nm upon 296 nm excitation
The luminescence decays of Yb3+ ions registered at 1020 nm under excitation at 296 nm are not exponential too, and look faster with the increase of Yb3+ ions content. It also proves the reverse energy transfer processes from two excited Yb3+ (2F5/2) to 5D1 manifold of Eu3+ ions.
Since the dependence of the luminescence decay of Eu3+ ions at 617 nm differs from the exponential law, the lifetimes were estimated as the average ones according to the formula (2):
ft • I (t)dt f1(t)dt '
where I(t) is dependence of luminescence intensity on time, t - time. The results of calculation are presented in Table 4.
The average luminescence lifetimes of 5D1 manifold of Eu3+ ions decreases with increasing Yb3+ ions concentration, while the lifetimes assumed to 5D0 manifold increases. This suggests that energy transfer from Eu3+
tavg r t/jA _i ± , (2)
Table 4. Average luminescence lifetimes of 5Do, 5D1 of Eu3+ and 2F5/2 of Yb3+ ions in Ba4Y3Fi7:Eu(0.1 mol.%):Yb (x mol.%) x = 0, 1.0, 5.0,10.0 samples under excitation at 296 nm
Registration wavelengths 617 nm (from 5Do) 556 nm (from 5Di) 1020 nm (from 2F5/2)
Eu content, mol.% Eu = 0.10 Eu = 0.10 Eu = 0.05 Eu = 0.10
Yb = 0 3.0 ± 0.1 ms 10.3 ± 0.1 ms — —
Yb = 1.0 2.2 ± 0.1 ms 10.2 ± 0.1 ms 2.0 ± 0.1 ms 2.0 ± 0.1 ms
Yb = 5.0 5.6 ± 0.1 ms 8.4 ± 0.1 ms 0.9 ± 0.1 ms 0.8 ± 0.1 ms
Yb = 10.0 8.8 ± 0.1 ms 7.3 ± 0.1 ms 0.7 ± 0.1 ms 0.5 ± 0.1 ms
to Yb3+ ions occurs from higher-lying states than the 5D0 one, which can cause a low quantum yield of ytterbium down-conversion luminescence, since these states are characterized by shorter lifetimes. Therefore, taking into account the absence of the Eu3+-Yb3+ energy transfer under excitation at 399 nm and 465 nm and despite the fact of existing of luminescence from 5D3 state of Eu3+, the most probable mechanism is 5H5 6(Eu3+)-2F7/2(Yb3+) ^ 5D2(Eu3+)-2F5/2(Yb3+) energy transfer process.
Finally, using the integrating sphere, the quantum yield of Yb3+ luminescence was measured under the 296 nm excitation (Table 5).
Table 5. Quantum yields for Ba4Y3F17: Yb:Eu samples at 296 nm excitation
Eu content mol, % Yb content, mol, %
1.0 5.0 10.0
0.05 0.4 ± 0.05 % 0.2 ± 0.05 % 0.3 ± 0.05 %
0.10 0.3 ± 0.05 % 0.4 ± 0.05 % 0.2 ± 0.05 %
The maximum quantum yields for Ba4Y3F17 samples were recorded for the Eu/Yb ratios of 0.1/1 and 0.1/10.0 and amounted to 0.4 %. It is obvious that competition of mutually oppositely directed energy transfer processes has determined such a small value of quantum yield of down-conversional luminescence of Yb3+ ions in the studied samples.
4. Conclusions
The single-phase solid solutions Ba4Y3F17:Yb:Eu with fluorite-type structure were synthesized by co-precipitation from aqueous solution technique. The average particle size was approximaely 100 nm without agglomeration, which correlated with X-ray coherent scattering domains. The luminescence spectra from all 5Dj manifold of Eu3+ ions were observed under irradiation at various wavelengths, whereas the sensitized down-conversion luminescence of Yb3+ ions, which was detected for the 296 nm excitation only, was not observed for resonant excitation to 5D J states of Eu3+. Moreover, the reverse cooperative energy transfer from a pair of Yb3+ ions in the excited 2F5/2 state to 5D0 state of Eu3+ ions was observed. The quantum yield of Yb3+ down-conversion luminescence was measured using the integrating sphere. The maximal value was 0.4 % for the Eu/Yb ratios of 0.1/1.0 and 0.1/10.0, which appears because of competition of mutually opposite directed energy transfer processes between Eu3+ and Yb3+ ions.
Acknowledgements
This work was supported by the Russian Science Foundation, grant 17-73-20352. Authors thank to M. N. Mayakova for valuable help in sample preparation.
References
[1] Weber E.R. Photovoltaics moving into the terawatt age. Proc. SPIE, Next Generation Technologies for Solar Energy Conversion VIII, 2017, 10368, 1036803.
[2] Lehr J., Langenhorst M., et al. Energy yield of bifacial textured perovskite/silicon tandem photovoltaic modules. Solar Energy Materials and Solar Cells, 2020, 208, 110367 P. 1-9.
[3] Im J.-H., Lee C.-R., et al. 6.5 % efficient perovskite quantum-dot-sensitized solar cell. Nanoscale, 2011, 3, P. 4088-4093.
[4] Han G., Zhang S., et al. Towards high efficiency thin film solar cells. Prog. Mater Sci., 2017, 87, P. 246-291.
[5] Huang X., Han S., Huang W., Liu X., Enhancing solar cell efficiency: the search for luminescent materials as spectral converters. Chem. Soc. Rev., 2013, 42, P. 173-201.
[6] Moraitis P., Schropp R.E.I., Sark W.G.J.H.M. Nanoparticles for luminescent solar concentrators - a review. Opt. Mater., 2018, 84, P. 636-645.
[7] Green M.A., Bremner S.P. Energy conversion approaches and materials for high efficiency photovoltaics. Nat. Mater., 2017, 16, P. 23-34.
[8] Trupke T., Green M.A., Würfel P. Improving solar cell efficiencies by down-conversion of high-energy photons. J. Appl. Phys., 2002, 92, P. 1668-1674.
[9] Yu P., Yao Y., et al. Effects of plasmonic metal core-dielectric shell nanoparticles on the broadband light absorption enhancement in thin film solar cells. Sci. Rep., 2017, 7, P. 7696.
[10] Fang D., Zhang X., et al. Application of bidirectional (up and down)-conversion luminescence material (GdBO3:Yb3+/Tb3+) in CdSe0.4S0.6 quantum dot-sensitized solar cells. Opt. Mater., 2019, 88, P. 80-90.
[11] Gu H., Wang J., et al. The core-shell-structured NaYF4:Er3+, Yb3+@NaYF4:Eu3+ nanocrystals as dual-mode and multifunctional luminescent mechanism for high-performance dye-sensitized solar cells. Mater Res. Bull., 2018, 108, P. 219-225.
[12] Buarque J.M.M., Manzani D., et al. SiO2-TiO2 doped with Er3+/Yb3+/Eu3+ photoluminescent material: a spectroscopy and structural study about potential applicationfor improvement of the efficiency on solar cells. Mater Res. Bull., 2018, 107, P. 295-307.
[13] Rajesh D., Dousti M.R., Amjad R.J., Camargo A.S.S. Quantum cutting and upconversion investigations in Pr3+/Yb3+ co-doped oxyfluoro-tellurite glasses. J. Non-Cryst. Solids, 2016, 450, P. 149-155.
[14] Kuznetsov S.V., Nizamutdinov A.S., et al. Synthesis and down-conversion luminescence of Ba4Y3F17:Yb:Pr solid solutions for photonics. Nanosystems: Physics, Chemistry, Mathematics, 2019, 10, P. 190-198.
[15] Li T., Li Y., et al. Novel Ba(Gdi-xYx)o.7sF6: 20 mol % Yb3+, 2 mol % Tm3+ (0 < x < 1.0) solid solution nanocrystals: A facile hydrothermal controlled synthesis, enhanced upconversion luminescent and paramagnetic properties. J. Alloys Comp., 2018, 740, P. 12041214.
[16] Karbowiak M., Cichos J. Does BaYF5 nanocrystals exist? The BaF2-YF3 solid solution revisited using photoluminescence spectroscopy. Journal of Alloys and Compounds, 2016, 673, P. 258-264.
[17] Fedorov P.P., Kuznetsov S.V., et al. Coprecipitation from aqueous solutions to prepare binary fluorides. Russian J. ofInorg. Chem., 2011, 56, P. 1525-1531.
[18] Kuznetsov S.V., Proydakova V.Yu., et al. Synthesis and quantum yield investigations of the Sr1-x-yPrxYbyF2+x+y luminophores for photonics. Nanosystems: Physics, Chemistry, Mathematics, 2018, 9, P. 663-668.
[19] Kuznetsov S.V., Morozov O.A., et al. Ca1-x-y YbxPryF2+x+y solid solution powders as a promising materials for crystalline silicon solar energetics. Nanosystems: Physics, Chemistry, Mathematics, 2018, 9, P. 259-265.
[20] Kuznetsov S.V., Nizamutdinov A.S., et al. Synthesis and Luminescence of Sr1-x-y YbxEuyF2+x+y. Solid Solutions for Photonics. Inorganic Materials, 2019, 55, P. 1031-1038.
[21] Yasyrkina D.S., Kuznetsov S.V., et al. Dependence of quantum yield of up-conversion luminescence on the composition of fluorite-type solid solution NaY1-x-y YbxEryF4. Nanosystems: Physics, Chemistry, Mathematics, 2013, 4, P. 648-656.
[22] Kuznetsov S.V., Fedorov P.P., et al. Synthesis of Ba4R3F17 (R stands for Rare-Earth Elements) Powders and Transparent Compacts on Their Base. Russian Journal of Inorganic Chemistry, 2010, 55, P. 484-493.
[23] Semashko V.V. Problems in searching for new solid-state UV- and VUV active media: the role of photodynamic processes. Phys. of Solid State, 2005, 47, P. 1507-1511.
[24] Van der Voort D., Dirksen G.J., Blasse G. Luminescence study of Eu3+-O2- associates in fluorides: CaF2, RbCdF3, and RbCaF3. J. Phys. Chem. Solids, 1992, 53, P. 219-225.
[25] Dwivedi Y., Zilio S.C. Infrared cascade and cooperative multicolor upconversion emissions in Y8V2O17 :Eu:Yb nanophosphors. Opt. Express, 2013, 21, P. 4717-4727.
