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Ca9La(PO4)7:Eu2+,Mn2+: an emission-tunable phosphor through efficient energy transfer for white light-emitting diodes

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Abstract

We have synthesized a series of single-composition emission-tunable Ca9La(PO4)7:Eu2+,Mn2+ (CLP:Eu2+,Mn2+) phosphors by solid state reactions. Through an effective resonance-type energy transfer, the CLP:Eu2+,Mn2+ phosphors exhibit a systematically varied hues from green, yellow, and eventually to red and the relative intensity of green and red emissions can be tuned by adjusting the concentration of Mn2+, respectively. The energy transfer from Eu2+ to Mn2+ in CLP:Eu2+,Mn2+ has been studied and demonstrated to be a resonant type via a dipole-quadrupole mechanism based on the decay lifetime data and the energy transfer critical distance was estimated to be 11.36 Å by using the spectral overlap methods. A warm white light emitting diode (WLED) with CIE chromaticity coordinates of (0.35, 0.31), superior color-rendering index (Ra) of 91.5 and lower correlated color temperature (CCT) of 4,496 K was fabricated by combining a 365 nm UV-InGaN chip and a phosphor blend of yellow-emitting (Ca0.98Eu0.005Mn0.015)9La(PO4)7 and blue-emitting BaMgAl10O17:Eu2+.

©2010 Optical Society of America

1. Introduction

In recent years, white light-emitting diodes (white-LEDs) have attracted much attention, in which white light can be generated by a blue-emitting InGaN chip and yellow-emitting phosphor Y3Al5O12:Ce3+ garnet (YAG:Ce3+). However, the disadvantages of this method are low color-rendering index (CRI, Ra = 75) and high color temperature (CCT = 7756 K) [1], due to the lack of red spectral contribution [2,3]. During the past few years, the white LEDs fabricated using (a) near ultraviolet (n-UV) LED or ultraviolet (UV) LED (350~420 nm) coupled with red, green, and blue phosphors [46], (b) n-UV LED (380~420 nm) pumped with a single composition green-to-red emission-tunable [7,8] and blue phosphor to improve the Ra and CCT. From this point of view, single-composition yellow-emitting (green of Eu2+ and red of Mn2+) phosphors for UV or n-UV excitations have drawn much attentions for solid state lighting. As compared to the InGaN-based blue LED chip combined with YAG:Ce3+ phosphor, a white-LED fabricated using a phosphor blend of single-composition emission-tunable phosphor and blue phosphor pumped with UV/NUV chips has advantages of a great Ra, tunable CCT and Commission International de I’Eclairage (CIE) chromaticity coordinates. One of the strategies for generating single-phased emission-tunable phosphor is by co-doping sensitizer and activator into the same host, which is based on the mechanism of energy transfer from sensitizer to activator. The phosphors with energy transfer mechanism of sensitizer/activator, such as Eu2+/Mn2+, have been synthesized and investigated in many hosts. For instance, Ca2MgSi2O7:Eu2+,Mn2+ [7], BaMg2Si2O7:Eu2+,Mn2+ [8], CaAl2Si2O8:Eu2+,Mn2+ [9], SrZn2(PO4)2:Eu2+,Mn2+ [10], SrMg2(PO4)2:Eu2+,Mn2+ [11], KCa10(PO4)7:Eu2+,Mn2+ [12], Ca2P2O7:Eu2+,Mn2+ [13], Sr2P2O7:Eu2+,Mn2+ [14], CaSiO3:Ce3+,Eu2+,Mn2+ [15]. To the best of our knowledge, the crystal structure, luminescence properties and energy transfer of Eu2+/Mn2+ in Ca9La(PO4)7 host have not been reported. We have firstly demonstrated a single-composition green-to-red emission-tunable Ca9La(PO4)7:Eu2+,Mn2+ phosphor by energy transfer mechanism between the luminescence centers Eu2+ and Mn2+, the color can be tuned from green to yellow even to red. We have also proven that a warm white light can be achieved by increasing the dopant contents of Mn2+. The Ca9La(PO4)7:Eu2+,Mn2+ phosphor exhibits great potential for use in white UV-LED applications to serve as a single-phased phosphor that can be pumped with near-UV or UV-LEDs.

2. Experimental

The CLP:Eu2+,Mn2+ phosphors were prepared from stoichiometric starting materials of CaCO3(A.R. 99.9%), Y2O3(A.R. 99.9%), La2O3(A.R. 99.99%), (NH4)2HPO4 (Merck ≥99%), Eu2O3 (A.R. 99.99%), and MnO (A.R. 99.9%). The reactant mixture was first pressed into pellets and calcined at 1,473K for 8 h under ambient atmosphere. The obtained samples were further reduced at 1,273K for 8 h under a reducing atmosphere of 15%H2/85%N2 in an alumina boat. The samples were characterized using powder X-ray diffraction (XRD), photoluminescence (PL) and PL excitation (PLE) spectra, decay lifetime, and CIE chromaticity, as described in our previous work [6,7]. The phase purity of CLP:Eu2+,Mn2+ phosphors was checked by using powder XRD analysis with a Bruker AXS D8 advanced automatic diffractometer with Cu Kα radiation. The measurements of PL and PLE spectra were performed by using a Spex Fluorolog-3 Spectrofluorometer (Instruments S.A., N.J., U.S.A) equipped with a 450W Xe light source and double excitation monochromators. The powder samples were compacted and excited under a 45° incidence angle and the emitted fluorescence was detected by a Hamamatsu Photonics R928 type photomultiplier perpendicular to the excitation beam. Time-resolved measurements were performed with a tunable nanosecond optical-parametric-oscillator/Q-switch-pumped YAG:Nd3+ laser system (NT341/1/UV, Ekspla). Emission transients were collected with a nanochromater (SpectraPro-300i, ARC), detected with photomultiplier tube (R928HA, Hamamatsu), connected to a digital oscilloscope (LT372, LeCrop) and transferred to a computer for kinetics analysis.

White LED lamps were fabricated by integrating a mixture of transparent silicon resin and phosphors blend of Ca9La(PO4)7:0.005Eu2+,0.015Mn2+ and BaMgAl10O17:Eu2+ commodity on an UV-chip (AOT Product No: DC0004CAA, Spec: 370U02C, wavelength peak: 365 ~370 ± 0.6 nm, chip size: 40x40 mil, forward voltage: 3.8 ~4.0 ± 0.02 V, power: 10-20 ± 0.21 mW). The Commission International de I’Eclairage (CIE) chromaticity coordinates for all samples were measured by a Laiko DT-101 color analyzer equipped with a CCD detector (Laiko Co., Tokyo, Japan).

3. Results and discussion

All powder XRD patterns of Ca9Y(PO4)7 (CYP) and CLP:Eu2+,Mn2+ phosphors are shown in Fig. 1 . All phases purity of the as-prepared phosphors was analyzed with JCPDS No. 46-0402 [16] as a reference, indicating that the doped Eu2+ ions or co-doped Eu2+/Mn2+ ions have not caused any observable change in the CLP host structure. The compound Ca9La(PO4)7 is iso-structural to the Ca9Y(PO4)7 [16] and β-Ca9In(PO4)7 [17], Ca9Y(PO4)7 has a rhombohedral crystal structure with a space group of R3c (No.161), and their lattice parameters are a = 10.4442Å, c = 37.324 Å, V = 3525.89 nm3, Z = 6 and Ca2+, Y3+ (La3+) and P5+ ions are have three, one and three crystallographic sites, respectively. The coordination environment of the cations is such that Ca(1) and Ca(2) are eight-coordinated, Ca(3) is nine-coordinated, Y (La) is six-coordinated and P(1), P(2), and P(3) are four-coordinated to oxygen atoms. The ionic radii for eight- and nine-coordinated Eu2+ are 1.25 and 1.3 Å, respectively, and that for eight-coordinated Mn2+ is 0.96 Å; however, the ionic radii for eight- and nine-coordinated Ca2+ cations are 1.12 and 1.18 Å, respectively. Therefore, based on comparison of the effective ionic radii of cations with different coordination numbers, we have proposed that Eu2+ and Mn2+ are expected to randomly occupy the Ca2+ sites in the host structure.

 figure: Fig. 1

Fig. 1 Powder XRD patterns of Ca9Y(PO4)7, Ca9La(PO4)7, Ca9La(PO4)7:Eu2+ and Ca9La(PO4)7:Eu2+,Mn2+ (JCPDS No. 46-0402).

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Figure 2 shows the emission spectra of (Ca0.99)9(Y1-yLay)(PO4)7:0.01Eu2+ with varying amount of La3+ ion concentrations. The PL intensity of (Ca0.99)9(Y1-yLay)(PO4)7:0.01Eu2+ phosphor was found to decrease with increasing La+3 Ion concentration and the blue-greenish emission band centering at 485 nm (sample with y = 0) was observed to red shift to green emission centering at 502 nm (sample with y = 1) with increasing La+3 Ion concentration. According to the reports from Robertson et al. [18] and Jang et al. [19], crystal field splitting (Dq) is expressed as the following equation [20]:

Dq=16Ze2r4R5
where Dq is a measure of the energy level separation, Z is the anion charge, e is an electron charge, r is the radius of d wavefunction, and R is the bond length. When Y3+ site was substituted and occupied by a larger La3+ ion, the distance between Eu2+ and O2- became shorter. Since crystal field splitting is proportional to 1/R5, this shorter Eu2+ O2- distance also increases the magnitude of crystal field, so that it results in lowering of the 5d band of Eu2+.

 figure: Fig. 2

Fig. 2 The PL spectra of (Ca0.99)9(Y1-yLay)(PO4)7:0.01Eu2+ with varying La3+ contents. The inset shows λem and relative intensity as a function of y for (Ca0.99)9(Y1-yLay)(PO4)7:0.01Eu2+ excited at 365 nm.

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The concentration dependence of relative PLE and PL intensity of CLP:xEu2+ (x = 0.001 ~0.1) under 365 nm excitation was shown in Fig. 3 . The PL spectra exhibited a broad band green emission centered at 502 nm, which was imputed to the 4f 65d 1 → 4f 7 of the Eu2+ ion. The optimal Eu2+ dopant content was found to be 0.005 mole and the PL/PLE intensity was observed to increase with increasing x when x < 0.005. For samples with Eu2+ dopant content higher than 0.005 moles, concentration quenching was observed and the PL/PLE intensity was found to decrease with increasing doped Eu2+ content.

 figure: Fig. 3

Fig. 3 Concentration dependence of relative PLE and PL intensity of CLP: xEu2+ (x = 0.001~0.1) under 365 nm excitation.

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As indicated in Fig. 4(a) , the Eu2+ emission of CLP:Eu2+ (solid line) at 400-600nm and centered at 502 nm (solid line) was assigned to the 4f 65d 1 → 4f 7 transition and the Mn2+ excitation of CLP:Mn2+ contains several bands centered at 267, 343, 370, 405, 417, and 454 nm (dash line), corresponding to the transitions from the 6A1(6S) ground state to the excited states of 4T1(4P), 4E(4D), 4T2(4D), [4A1(4G), 4E(4G)], 4T2(4G), and 4T1(4G) levels, as reported by Ravikumar et al. [21]. We have observed a significant spectral overlap at around 454 nm between the Eu2+ PL and Mn2+ PLE spectra, which revealed that the spectral overlap is matched for Eu2+ and Mn2+ and a part of the energy can transfer from Eu2+ to Mn2+. Therefore, there can be a good energy transfer from Eu2+ to Mn2+ in CLP:Eu2+,Mn2+ and an effective resonance-type energy transfer from Eu to Mn (ETEu→Mn) was expected. Figure 4(b) shows the emission spectra of CLP:0.005Eu2+,xMn2+ phosphors (x = 0, 0.01, 0.015, 0.03, 0.05, 0.07 and 0.1). For CLP:0.005Eu2+,xMn2+ samples with 0.01 ≤ x ≤ 0.1, two broad emission bands centered at 502 nm and 635 nm were observed, respectively. The emission band at 502 nm is viewed as the typical Eu2+ emission and the band at 635 nm is due to the Mn2+ emission. The PL intensity of Eu2+ at 502 nm was found to decrease with increasing Mn2+ content, and the PL intensity of Mn2+ at 635 nm increases with increasing Mn2+ content until the appearance of concentration quenching occurred at the sample with Mn2+ content of 0.07, which further supports the occurrence of the ETEu→Mn mechanism. Moreover, the observed variation of emission-tunable PL intensities of Eu2+ and Mn2+ in CLP:0.005Eu2+,xMn2+ strongly support energy transfer from Eu2+ to Mn2+.

 figure: Fig. 4

Fig. 4 (a) Spectral overlap between the Eu2+ PL spectrum of CLP:Eu2+ (solid line) and the PLE spectrum of CLP:Mn2+ (dash line); (b) The emission spectra of CLP:0.005Eu2+, xMn2+ phosphors excited at 365 nm.

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Table 1 reports the chemical compositions and the chromaticity coordinates of CLP:0.005Eu2+,xMn2+ phosphors and Fig. 5 further represents the data in the 1931 CIE chromaticity diagram. The chromaticity coordinates of CLP:0.005Eu2+,xMn2+ ranging from (0.282, 0.445) to (0.406, 0.388) and eventually to (0.637, 0.303), indicate that the color hue is tunable from green to yellow and, eventually, to red in the visible spectral region by changing the doped Mn2+ content. A white light with chromaticity coordinates (0.353, 0.324) was generated by a phosphor blend of a yellow-emitting CLP:0.005Eu2+,0.015Mn2+ and a blue-emitting BaMgAl10O17:Eu2+ (BAM:Eu2+). For comparison, the YAG:Ce3+ with CIE chromaticity of (0.429, 0.553) pumped with an InGaN blue chip with chromaticity of (0.144, 0.030) can give white light with chromaticity of (0.291, 0.300) [22]. The inset of Fig. 5 shows three LEDs fabricated by pumping phosphors of CLP:0.005Eu2+ (photo 1), a mixture of CLP:0.005Eu2+,0.015Mn2+ and blue BAM:Eu2+ (photo w), and CLP:0.005Eu2+,0.1Mn2+ (point 7), respectively, with a 365 nm UV-chip under a forward bias of 350 mA.

Tables Icon

Table 1. Comparison of CIE chromaticity coordinates for CLP:0.005Eu2+,xMn2+ phosphors (λex = 365 nm) and simulated white light using Y3Al5O12:Ce3+ phosphors (λex = 460 nm).

 figure: Fig. 5

Fig. 5 CIE chromaticity diagram of (Ca0.995-x)9La(PO4)7:0.005Eu2+,xMn2+ phosphors excited at 365 nm: x = (1) 0, (2) 0.01, (3) 0.015, (4) 0.03, (5) 0.05, (6) 0.07, and (7) 0.1.

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The decay curves of CLP:0.005Eu2+,xMn2+ phosphors were measured and represented as shown in Fig. 6. The corresponding luminescence decay times can be best fitted with a second-order exponential decay mode (Fig. 6 dash line) by the following equation [23,24]:

I=A1exp(t/τ1)+A2exp(t/τ2)
where I is the luminescence intensity; A1 and A2 are constants; t is the time; and τ1 and τ2 are rapid and slow lifetimes for exponential components. Using these parameters, the average decay times (τ) can be determined by the formula given in the following [25]:

τ=(A1τ12+A2τ22)/(A1τ1+A2τ2)

The values of τ1, τ2, A1 and A2 are analyzed, determined, and summarized in Table 2 , which indicates that in solely Eu2+-activated system, the average decay time is long. However, in the Eu2+/Mn2+ co-doped system, the average decay time was found to be shortened with increasing doped Mn2+ content. Similar observations could be attributed to the formation of paired Mn2+ centers with faster decay than single Mn2+ centers, as proposed by Ruelle et al. [25] The average decay times (τ) were calculated to be 838, 768, 611, 424, 132, 55.7, and 25.8 ns for CLP:0.005Eu2+,xMn2+ with x = 0, 0.01, 0.015, 0.03, 0.05, 0.07, and 0.1, respectively. The inset of Fig. 6 clearly shows the relation between energy transfer efficiency (ηT) and concentration of Mn2+ ions. The ηT from Eu2+ to Mn2+ can be expressed according to Paulose et al. [26]

ηT=1τSτS0
where τS is the lifetime of Eu2+ in the presence of Mn2+ and τS0 is the lifetime of the sensitizer Eu2+ in the sample in the absence of Mn2+. The ηT was determined to be 0%, 18.2%, 41.9%, 59.7%, 81.1%, 89.8% and 95.6% for CLP:0.005Eu2+,xMn2+ with x = 0, 0.01, 0.015, 0.03, 0.05, 0.07, and 0.1, respectively. These results indicate that the ηT of CLP:0.005Eu2+,xMn2+ increases with increasing Mn2+ dopant content.

Tables Icon

Table 2. Decay times of CLP:0.005Eu2+,xMn2+ phosphors excited at 365 nm with emission monitored at 502 nm.

Based on Dexter’s energy transfer formula of multi-polar interaction and Reisfeld’s approximation, the following relation can be obtained [27,28]:

τS0τSCα/3
where C is Mn2+ ions concentration. As (τS0/τS)∝Cα/3 with α = 6, 8, and 10 corresponds to dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interaction, respectively. The relationship of (τS0/τS)∝Cα/3 was illustrated in Fig. 7 and a linear behavior was observed only when α = 8, so that energy absorbed by Eu2+ is transferred to Mn2+ by a nonradiative dipole-quadrupole mechanism. The above results indicate that energy transfer occurs between Eu2+ and Mn2+ in CLP:Eu2+,xMn2+ phosphor and the relative intensity of green and red emission could be tuned by adjusting the relative concentration of Eu2+ and Mn2+, respectively.

 figure: Fig. 7

Fig. 7 Dependence of τS0S of Eu2+ on (a) C6/3 , (b) C8/3 and (c) C10/3.

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According to dipole-quadrupole mechanism, the critical distance of energy transfer from a sensitizer Eu2+ to an activator Mn2+ is given by:

PEuMnDQ=0.63×1028fqλs2QaτS0REuMn8fdEs4Fs(E)Fa(E)dE
where Qa = 4.8 × 10−16 and fd is the absorption coefficient of Mn2+; fd = 10−7 and fq = 10−10 are the oscillator strengths of dipole and quadrupole electrical absorption transitions for Mn2+; λS (Å) and E (eV) are the emission wavelength and emission energy of Eu2+, and ∫FS(E)Fa(E)dE represents the spectral overlap between the Eu2+ and Mn2+ and it was estimated be 1.3565eV−1 [29]. The critical distance Rc of energy transfer from Eu2+ to Mn2+ is defined as the distance for which the probability of transfer equals the probability of radiative emission of Eu2+, i.e., the distance for which PEuMnDQτS0=1. Therefore, Rc can be calculated using the following equation [29,30]:
Rc8=0.63×1028fqλs2QafdEs4Fs(E)Fa(E)dE
In this system, the critical distance of energy transfer in CLP:Eu2+,Mn2+ phosphor was calculated to be about 11.36 Å, which is similar to those obtained for Ca2MgSi2O7:Eu2+/Mn2+ (11.97 Å) [7] and Sr2Zn(PO4)2:Eu2+/Mn2+ (11.4 Å) [10].

Figure 8 shows the PL spectra of CLP:0.005Eu2+,0.015Mn2+ (black line), BAM:Eu2+ commodity (blue line) and a blend of yellow CLP:0.005Eu2+,0.015Mn2+ and blue-emitting BAM:Eu2+ (dash line) commodity pumped with a UV-LED chip (365 nm). Shown in Fig. 9 is the EL spectrum of a white LED lamp fabricated with the above-stated phosphor blend and silicon resin pumped with a 365 nm UV-LED chip and driven with a 350-mA current. The white light generated shows CIE color coordinates (0.35,0.31) and Ra of 91.5, as determined from the full set of the 8 CRIs average Ra values shown in Table 3 . The upper-right inset of Fig. 9 shows the appearance of a phosphor-converted LED lamp under a forward bias of 350 mA. These results demonstrated that our phosphor blend (CLP:Eu,Mn and BAM:Eu2+)-converted white-light UV-LED shows higher Ra value (91.5) and lower CCT (4,496K) than those (i.e., Ra = 75, CCT = 7756K) of a white LED fabricated with YAG:Ce3+ phosphor pumped with blue InGaN chip [1].

 figure: Fig. 8

Fig. 8 The PL spectrum of (Ca0.98)9La(PO4)7:0.005Eu2+,0.015Mn2+, BaMgAl10O17:Eu2+ and the white-emitting phosphors of a mixture of (Ca0.98)9La(PO4)7:0.005Eu2+,0.015Mn2+ and BaMgAl10O17:Eu2+.

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 figure: Fig. 9

Fig. 9 EL spectrum of a white LED lamp fabricated using a UV-chip (365 nm) and a phosphor blend of (Ca0.98)9La(PO4)7:0.005Eu2+,0.015Mn2+ and BaMgAl10O17:Eu2+ under a forward bias of 350 mA.

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Tables Icon

Table 3. Full set of the 8 CRIs and the Ra values of (Ca0.98)9La(PO4)7:0.005Eu2+,0.015Mn2+ and BAM:Eu2+ with a 365 nm UV-LED

4. Conclusion

In conclusion, a series of single-composition emission-tunable CLP:Eu2+,Mn2+ phosphors were synthesized and investigated. The energy transfer from sensitizer Eu2+ to activator Mn2+ in Ca9La(PO4)7 host has been studied and demonstrated to be a resonant type via a dipole-quadrupole mechanism based on the decay lifetime data and the energy transfer critical distance was estimated to be 11.36 Å by using the spectral overlap method. We have improved the Ra and reduced CCT value of white LEDs by using a phosphor blend of yellow-emitting Ca9La(PO4)7:0.005Eu2+,0.015Mn2+ and blue-emitting BaMgAl10O17:Eu2+ commodity pumped with UV-LED chip (365 nm). Our investigation results indicate that the warm white-emitting UV-LED based on phosphor blend of CLP:Eu,Mn and BAM:Eu2+ exhibits superior Ra and CCT to those of conventional white LED based on YAG:Ce3+ pumped with blue LED chips.

Acknowledgments

This research was supported by National Science Council of Taiwan (ROC) under contract No. NSC98-2113-M-009-005-MY3 (T.-M. C.) and, in part, by Industrial Technology Research Institute under contract No. 7301XS1861 (C.-H. H.).

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Figures (8)

Fig. 1
Fig. 1 Powder XRD patterns of Ca9Y(PO4)7, Ca9La(PO4)7, Ca9La(PO4)7:Eu2+ and Ca9La(PO4)7:Eu2+,Mn2+ (JCPDS No. 46-0402).
Fig. 2
Fig. 2 The PL spectra of (Ca0.99)9(Y1-yLay)(PO4)7:0.01Eu2+ with varying La3+ contents. The inset shows λem and relative intensity as a function of y for (Ca0.99)9(Y1-yLay)(PO4)7:0.01Eu2+ excited at 365 nm.
Fig. 3
Fig. 3 Concentration dependence of relative PLE and PL intensity of CLP: xEu2+ (x = 0.001~0.1) under 365 nm excitation.
Fig. 4
Fig. 4 (a) Spectral overlap between the Eu2+ PL spectrum of CLP:Eu2+ (solid line) and the PLE spectrum of CLP:Mn2+ (dash line); (b) The emission spectra of CLP:0.005Eu2+, xMn2+ phosphors excited at 365 nm.
Fig. 5
Fig. 5 CIE chromaticity diagram of (Ca0.995-x)9La(PO4)7:0.005Eu2+,xMn2+ phosphors excited at 365 nm: x = (1) 0, (2) 0.01, (3) 0.015, (4) 0.03, (5) 0.05, (6) 0.07, and (7) 0.1.
Fig. 7
Fig. 7 Dependence of τS0S of Eu2+ on (a) C6/3 , (b) C8/3 and (c) C10/3 .
Fig. 8
Fig. 8 The PL spectrum of (Ca0.98)9La(PO4)7:0.005Eu2+,0.015Mn2+, BaMgAl10O17:Eu2+ and the white-emitting phosphors of a mixture of (Ca0.98)9La(PO4)7:0.005Eu2+,0.015Mn2+ and BaMgAl10O17:Eu2+.
Fig. 9
Fig. 9 EL spectrum of a white LED lamp fabricated using a UV-chip (365 nm) and a phosphor blend of (Ca0.98)9La(PO4)7:0.005Eu2+,0.015Mn2+ and BaMgAl10O17:Eu2+ under a forward bias of 350 mA.

Tables (3)

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Table 1 Comparison of CIE chromaticity coordinates for CLP:0.005Eu2+,xMn2+ phosphors (λex = 365 nm) and simulated white light using Y3Al5O12:Ce3+ phosphors (λex = 460 nm).

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Table 2 Decay times of CLP:0.005Eu2+,xMn2+ phosphors excited at 365 nm with emission monitored at 502 nm.

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Table 3 Full set of the 8 CRIs and the Ra values of (Ca0.98)9La(PO4)7:0.005Eu2+,0.015Mn2+ and BAM:Eu2+ with a 365 nm UV-LED

Equations (7)

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D q = 1 6 Z e 2 r 4 R 5
I = A 1 exp ( t / τ 1 ) + A 2 exp ( t / τ 2 )
τ = ( A 1 τ 1 2 + A 2 τ 2 2 ) / ( A 1 τ 1 + A 2 τ 2 )
η T = 1 τ S τ S 0
τ S 0 τ S C α / 3
P E u M n D Q = 0.63 × 10 28 f q λ s 2 Q a τ S 0 R E u M n 8 f d E s 4 F s ( E ) F a ( E ) d E
R c 8 = 0.63 × 10 28 f q λ s 2 Q a f d E s 4 F s ( E ) F a ( E ) d E
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