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Color-tunable visible photoluminescence of Eu:CaF2 single crystals: variations of valence state and local lattice environment of Eu ions

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Abstract

In this article, Eu-activated CaF2 single crystals were synthesized by Bridgman-Stockbarge method. The dependence of photoluminescence properties of Eu: CaF2 crystals in UV-Vis regions on EuF3 doping concentrations were investigated. While the EuF3 doping concentration is increased from 0.6% to 6.0%, the CIE (Commission Internationale de L'Eclairage) color coordinates of Eu: CaF2 crystals can be tuned from (0.28, 0.12) to (0.60, 0.38), corresponding to the luminescence color from blue to orange. XPS (X-ray Photoelectron Spectroscopy) measurements indicated that Eu2+ and Eu3+ ions both existed in the crystals. With EuF3 doping concentration increasing, the proportion of Eu3+ ions increase from 16.73% to 39.00%, while that of Eu2+ ions decrease from 83.27% to 61.00%. Moreover, the integrated intensity ratio (R) of the 614 nm to 593 nm of Eu3+ ions increase from 0.38 to 0.44, indicating the local lattice environment symmetry of Eu3+ ions become lower with higher EuF3 doping concentrations. Furthermore, the CIE chromaticity coordinates of Eu: CaF2 crystals greatly depend on the excitation wavelength. The warm white-light emission has been realized in 0.6%Eu: CaF2 crystal when the excitation wavelength is around 322 nm.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The luminescence of Eu doped materials has attracted extensive research due to their applications in displays, optical communication, solar cells and biological fields [1–6]. Eu shows two valence states trivalent (Eu3+) and divalent (Eu2+) in certain compounds. Eu2+ ions have a broad excitation band, which could offer tunable emission colors ranging from light blue to the deep red region depending on the host materials [7,8]. Eu3+ ions show characteristic emissions resulting from 5D07FJ (J = 1,2,3,4) transitions [9]. There is a coincident region between the excitation spectra of Eu3+ ions and the emission spectra of Eu2+ ions in the UV region, which provides the possibility of highly efficient Eu2+→Eu3+ energy transfer or synchronous excitation of Eu2+ and Eu3+ ions in a single-phase valence-varied Eu-doped phosphor. Therefore, the white-light emission can be realized by changing the ratios of Eu2+ to Eu3+ ions. However, the coexistence of Eu2+ and Eu3+ activators in a single host lattice is still very difficult, especially for obtaining white light.

CaF2 doped with rare-earth ions gain much attention because of its excellent optical properties (broad transmission range, low phonon energy) as well as physical properties (good thermal conductivity, high radiation resistance and low refraction index) [10–13]. Among the lanthanide rare-earth ions, Eu: CaF2 materials have attracted more attention because of the emission and excitation characteristics of europium ions. Samuel et al reported that the divalent Eu ions are dominant at lower concentration whereas trivalent states become dominant as the concentration was increased in Eu doped transparent CaF2 ceramics [14]. Dr. Masai in Kyoto University reported on the Eu doped 80LiF-20 CaF2 with different concentrations. Divalent and trivalent Eu ions are contained and the divalent per trivalent Eu ions ratio drastically decreases with increasing total Eu concentration [15]. It is well known that the doping of trivalent lanthanide ions into the alkali-earth fluorides (CaF2, SrF2, BaF2, etc.) occupy the Ae2+ (Ae = Ca, Sr, Ba, etc.) site [16] and are accompanied by interstitial F- ions as charge compensators, which give rise to multiple luminesce centers coexist in the host lattices [17–21]. The trivalent Eu ions in CaF2 are charge compensated by either fluoride interstitials which are so distant that the dopant has cubic symmetry or very near enough to change the local symmetry [22]. Therefore, it indicates that the emission spectra of Eu: CaF2 single crystals could be tuned by changing Eu ion concentrations and local lattice environment. In addition, there is a coincident region between the excitation spectra of Eu3+ ions and the emission spectra of Eu2+ ions in the UV region, which provides the possibility of highly efficient Eu2+−Eu3+ energy transfer to impact the emission spectra of Eu: CaF2. As far as we know, there have been hardly any reports about the emission color tuning of Eu: CaF2 single crystals through modulation of Eu ion concentrations, local lattice environment and energy transfer from Eu2+ ions to Eu3+ ions to obtain the white light.

Herein, in this article, we successfully prepared Eu: CaF2 single crystals with different Eu ion contents by Bridgman-Stockbarge method and their luminescence properties were studied. With excitation of UV light, the Eu: CaF2 single crystals show not only the characteristic 5d−4f transition of Eu2+ ions in the blue-green region but also the characteristic f−f transition of Eu3+ ions in the orange-red region. Further investigation shows that the luminescence colors of the Eu: CaF2 single crystals can be tuned from blue to orange-red by changing Eu ion concentrations and local lattice environment. In addition, the energy transfer from Eu2+ ions to Eu3+ ions are also attributed to the color-tunable of Eu: CaF2 single crystals. The warm white-light emission has been realized in the Eu:CaF2 single crystal. The obtained Eu: CaF2 single crystals have potential applications in the areas of UV white-light-emitting diodes.

2. Materials and methods

In our experiments, the x%Eu: CaF2 (x = 0.6, 1.2, 3.0, 6.0) crystals were grown by Bridgman-Stockbarge method. All calculations were performed assuming that Eu3+ replace Ca2+. High purity (>99.995%) CaF2 and EuF3 fine powders were used as raw materials. The raw materials were mixed and sealed into a platinum crucible, which were grown in the air at the same time. In order to ensure the observed data quality, all the samples were obtained from the same position of the crystals. Moreover, the samples were cut into a cuboid with the dimensions of 5*5*15 mm3 and fine polished for spectral measurements.

X-ray diffraction (XRD) spectra were carried out with a Bruker-D8 X-ray diffractometer using Cu-Kα radiation. The actual concentrations of Eu ions in these samples were measured by ICP-AES (Inductively Coupled Plasmas Atomic Emission Spectroscopy) method. XPS data were obtained from the argon-ion etching (2 kV, 10 s) by using an ESCALAB 250 X-ray photoelectron spectrometer (Thermo Fisher, England) with the resolution of 0.5 eV. An ESCALAB 250Xi spectrometer equipped with a monochromatized Al Kα (1486.6 eV) source was used for XPS analysis. Photoluminescence, excitation, and fluorescence lifetime tests were recorded with 1.0 nm resolution using a FLS 980 time-resolved fluorescence spectrometer (Edinburgh Instruments, England). The xenon lamp was exploited as an excitation source. The visible emissions were measured by PMT photodetector. Luminescence decay curves were detected with a μF900 microsecond lamp. All tests were conducted at room-temperature.

3. Results and discussion

The photograph of the as-grown Eu: CaF2 single crystals is shown in Fig. 1(a). The crystal is approximately 16 mm in diameter and 60 mm in length. The cylindrical was transparent and cut into a cuboid with the dimensions of 5*5*15 mm3 and all surfaces were polished for spectral measurements. The crystal structure is drawn using the VESTA software and shown in Fig. 1(b). It can be described as a cubic unit cell with a simple lattice, of which Ca atoms are at the corners, while F atoms lie at the centers of the octants. In the lattice, each Ca atom coordinates with two F atoms and each F atom is surrounded by four Ca atoms. Both Eu2+ and Eu3+ occupy the Ca2+ sites.

 figure: Fig. 1

Fig. 1 (a) The photograph of as-grown Eu: CaF2 single crystal. (b) Crystal structure of Eu:CaF2 single crystal. (c) XRD patterns of x%Eu: CaF2 (x = 0.6, 1.2, 3.0, 6.0) crystals.

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The XRD patterns of the as-prepared Eu: CaF2 single crystals with different Eu doping concentrations are shown in Fig. 1(c). It is observed that all diffraction peaks of samples can be indexed to pure cubic phase CaF2 without any impurity peaks. In Fig. 1(c), a magnification of the (111) reflection is reported. As the concentration of Eu ions increase, the (111) peak gradually shift toward high angles. This phenomenon may be explained by the ionic radii of the doping ions and the charge balance due to the Eu ions is supposed to substitute Ca2+, which can be compensated with additional fluoride ions. According to the ionic radii among Ca2+, Eu3+ and Eu2+ in eightfold coordination, that is REu2+ (1.25 Å)>RCa2+(1.12 Å)>REu3+(1.07 Å), the lattice expansion or constriction effect can serve as a criterion to identify the Eu valence state [23]. In our experiments, a lattice shrink effect was observed as the Eu dopant concentration increased from 0.6 at. % to 6.0 at. %, the offset angle gradually increased, which means smaller ions, i.e. divalent Eu2+ was gradually decreased relation to the Eu3+.

The emission spectra of all Eu: CaF2 single crystals with different doping concentrations of Eu ions are shown in Fig. 2(a). From this figure, it can be observed that a strong and broad blue emission peak around 424 nm and several red weak sharp emission peaks in the range 550-750 nm appear upon 398 nm excitation. They are ascribed to the 5d-4f transition of Eu2+ and the 5D0-7Fj (j = 0, 1, 2, 3, 4) transitions of Eu3+, respectively. The emission intensity of f-f transitions of Eu3+ initially increased with the increase of Eu contents. When the concentration of Eu ions is increased to 3.0%, the single crystal yields the highest emission intensity. However, further increase Eu doping concentration leads to decrease on emission intensity, which could be ascribed to the quenching effect. As for Eu2+ ions, it can be observed that the emission intensity of Eu2+ decreased monotonously with increasing Eu ion doping contents. The emission intensity ratio of Eu3+/Eu2+increases with increasing Eu concentrations in the CaF2 single crystal, as shown in Fig. 2(b). Based on the fact that Eu2+ processes blue-green emission and Eu3+ owns orange-red emission, so the emission color of Eu: CaF2 can be tuned by changing the doping concentration of Eu ions. The color chromaticity coordinates were calculated using the CIE 1931, and the chromaticity diagram of the samples is shown in Fig. 2(c). It can be seen that, with excitation of UV light at 398 nm, the luminescence color of x% Eu: CaF2 crystals with the Eu doping concentration of 0.6%, 1.2%, 3.0% and 6.0% can be changed from blue (0.28, 0.12), pink (0.41, 0.22), orange-red (0.58, 0.36) to orange (0.60, 0.38) regions, respectively.

 figure: Fig. 2

Fig. 2 (a)Emission spectra of x%Eu: CaF2 (x = 0.6,1.2,3.0,6.0) crystals. (b) The intensity ratio between Eu3+ (593 nm) /Eu2+ (424 nm) as a function of Eu doping concentrations. (c) CIE chromaticity diagram of x%Eu: CaF2 (x = 0.6,1.2,3.0,6.0) crystals.

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The emission spectra and luminescence color are tuned with an increase in the Eu concentration, which can be attributed to different factors:

  • (1) Variation of atomic concentration ratios of Eu2+/Eu3+;
  • (2) Variation of local lattice environment of Eu ions;
  • (3) The presence of energy transfer from Eu2+ ions to Eu3+ions.

In order to prove our conjecture, the valence state of the Eu ions in Eu doped CaF2 single crystals were measured by the X-ray photoelectron spectroscopy (XPS) method. As shown in Fig. 3, the Eu3d3/2 and Eu3d5/2 of both Eu2+ and Eu3+ ions are observed in all Eu: CaF2 samples. The XPS peaks centered at 1167.15 eV, 1156.65 eV, 1137.05 eV and 1126.35 eV could be attributed to Eu3+ (Eu3d3/2), Eu2+ (Eu3d3/2), Eu3+ (Eu3d5/2) and Eu2+ (Eu3d5/2) spin-orbit splitting core levels, respectively, which is quite similar with the previous reported data [24–26]. Thus, the concomitant valence states of Eu2+ and Eu3+ could be proved in Eu doped CaF2 single crystals. This implies that the reduction of Eu3+ to Eu2+ took place effectively when synthesizing CaF2 single crystals at high temperatures.

 figure: Fig. 3

Fig. 3 The Eu3d XPS spectra of x%Eu: CaF2 (x = 0.6, 1.2, 3.0, 6.0) crystals.

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For the mechanism of reduction of Eu3+ to Eu2+, it can be explained by the charge compensation model based on substitution defect mechanisms [27]. When trivalent Eu3+ ions are doped into CaF2, the Ca2+ ions are replaced. In order to keep the charge balance, two Eu3+ ions should be needed to substitute for three Ca2+ ions to form a cation vacancy. Then, one vacancy defect Vca (Ca2+ is missing from the lattice), two negative charges and two positive defects of Euca· (the Eu3+ ion occupied the site of Ca2+) would be formed, as indicated in Eq. (3.1). Vca and Euca· acted as donors and acceptors of electrons, respectively. Consequently, the negative charges in the vacancy defects would tend to transfer to Eu3+ sites and causing the reduction of Eu3+ ions to Eu2+ ions, as shown in Eq. (3.2) and (3.3). The whole processes could be explained in the following equations:

3CaCa+2Eu3+=3Ca2++2Euca'+Vca''
Vca''=Vcax+2e
2Euca'+2e=2Eucax

In addition, the atomic concentration ratios of Eu3+ and Eu2+ ions in the as prepared samples were also measured by XPS, as shown in Table 1. It was also observed that the Eu3+ ion proportion ratio increased with increasing Eu concentrations in the Eu: CaF2 crystals, which is in agree with the previous report [19]. Meanwhile, the divalent Eu ions are more dominant at a lower Eu concentration (0.6%) whereas the trivalent charge states become predominant as the Eu concentration reaches to 6.0%, which is attributed to the special structure of the CaF2 matrix. When a small amount of Eu3+ ions were doped into CaF2, the intrinsic vacancies and vacancy defects of Vca· would reduce Eu3+ to Eu2+, so the divalent Eu ions are more dominant. Due to the fact that Eu3+ ions are more stable than Eu2+ ions and the defect numbers in CaF2 would be decreased, the trivalent charge states become predominant with the further increase of Eu contents. The luminescence color of Eu2+ and Eu3+ ions shows blue, orange-red and orange, respectively. Thus, the luminescence color can be tuned by the Eu doping concentrations.

Tables Icon

Table 1. Relative percentage for ionic concentrations of Eu3+ and Eu2+ ions of x%Eu: CaF2 (x = 0.6, 1.2, 3.0, 6.0) crystals obtained from XPS data.

The Eu3+ ions are substituted in the CaF2 matrix, the excess positive charges are compensated by additional interstitial fluorine ions (F-). The fluorine ions can substitute locally or in a distant position inside the lattices leading to a change in the local environment. In order to verify the local environment around the Eu3+ ions which affect the emission spectral intensity ratios between Eu3+ and Eu2+, the integrated intensity ratio (R) of the I (5D0-7F2) to (5D0-7F1) for Eu3+ ions are measured. Because the 5D0-7F1 transition is a magnetic dipole transition, which is insensitive to the local environment around Eu3+ and the 5D0-7F2 transition is a forced electronic dipole transition, which is sensitive to the local environment around Eu3+. The lower symmetry is the environment around Eu3+ in the crystals, the higher ratio (R) will be obtained [21]. The R values for Eu: CaF2 single crystal with Eu doping concentration of 0.6%, 1.2%, 3.0% and 6.0% are 0.38, 0.40, 0.43, and 0.44, respectively, as shown in Fig. 4. This indicates the local environmental symmetry around Eu3+ ions become lower with increasing Eu doping concentrations, which aggravated the local lattice structure distortion and led to a further broken of the 4f-4f parity-forbidden transition. Thus, the probability of the radiative transition increased, which caused a more intensive fluorescence [28,29].

 figure: Fig. 4

Fig. 4 The integrated intensity ratio (R) of I (5D0-7F2) to I (5D0-7F1) for x%Eu: CaF2 (x = 0.6,1.2,3.0,6.0) crystals.

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The energy transfer from Eu2+ ions to Eu3+ ions is studied by using the excitation and emission spectra of the 0.6%Eu: CaF2 single crystal. The luminescence excitation spectra of Eu3+ (593 nm) and Eu2+ (424 nm) emission of the 0.6%Eu: CaF2 is shown in Fig. 5(a). The excitation spectrum of Eu:CaF2 single crystal, monitoring the 5D0-7F1 transition of Eu3+ at 593 nm, consists of some narrow lines at 316 nm (7F05H6), 362 nm (7F05D4), 380 nm (7F05L7), 398 nm (7F05L6), 416 nm (7F05D3) and 464 nm (7F05D2), assigned to the characteristic f-f transition of Eu3+ [30]. In the excitation spectrum of the 424 nm luminescence, the 4f→5d transitions of the Eu2+ ions are monitored, which consists of a broad band ranging from 300 to 420 nm peaking at 338 nm, 354 nm, 367 nm, 377 nm and 388 nm with a shoulder at 400 nm. It also can be seen that there are overlaps between the characteristic f-f transitions of Eu3+ ions and the 4f→5d transition of the Eu2+ ions from 300 to 420 nm. This means that the UV light in this range can excite not only the divalent europium ions but also the trivalent europium ions. Therefore, with the excitation of UV light in this range, the luminescence excitation spectra can be controlled by the excitation wavelengths.

 figure: Fig. 5

Fig. 5 (a) Luminescence excitation spectra of Eu2+ and Eu3+ emissions in 0.6%Eu: CaF2 together with emission spectrum excited at 398 nm; (b) Emission spectra measured of 0.6%Eu: CaF2 at different wavelengths from 320 to 330 nm; (c) Emission spectra measured of 0.6%Eu: CaF2 at different wavelengths of 300, 330 and 350 nm; (d) Decay curves of the Eu3+:5D0 (593 nm) energy level;(e) Configuration coordination diagram for Eu3+ and Eu2+ energy levels;(f) CIE chromaticity diagram of 0.6%Eu: CaF2 crystal under different excitation wavelength from 320 to 330 nm.

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Figure 5(b) presents emission spectra of 0.6%Eu: CaF2 recorded upon stimulation into different wavelength in the range of 320-330 nm. From this figure, it can be seen that the relative emission intensities of Eu2+ and Eu3+ ions obviously vary with the change of excitation wavelengths. At higher excitation energy (320 nm), Eu3+ line-type emission intensity is much higher than that of the 5d→4f transition of Eu2+ ions. Then, with the excitation wavelength increasing, the broad-band emission intensity of Eu2+ ions get increased gradually. When the excitation energy reaches 330 nm, the emission intensity of the 5d→4f transition of Eu2+ ion is much higher than that of the f-f transition of Eu3+ ion. This phenomenon could be due to the variation of absorption intensity for Eu2+ and Eu3+. Figure 5(c) shows emission spectra of 0.6%Eu: CaF2 excited at 300 nm (Eu3+ selectively excited), 330 nm (Eu2+ exclusively excited) and 350 nm (Eu2+ and Eu3+ simultaneously excited), respectively. When excited at 300 nm, one can see that the emission peak of Eu2+ could hardly be seen because of the weak intensity. As the excitation wavelength increased from 330 to 350 nm, the emission intensity of Eu2+ ions increased. Moreover, the emissions of Eu3+ ions could be observed, which means an energy transfer from Eu2+ to Eu3+ occurs. Meanwhile, the emission intensity of Eu3+ ions decreased, which may be due the weaken energy transfer process.

The luminescence decay curves of the 0.6%Eu: CaF2 crystal with different excitation wavelengths (320 to 330 nm) were measured for the emission band at Eu3+:5D0 (593 nm) levels at room temperature, as shown in Fig. 5(d). The decay curves are well described form single-exponential function:

It=I0etτ

Where It is the emission intensity at 593 nm, I0 is the emission intensity at the beginning of the decay process, t is the time and τ is the decay time. The lifetimes of Eu3+:5D0 level were fitted to be 7.92 ms, 7.89 ms, 7.84 ms, 7.79 ms, 7.68 ms and 7.53 ms for different excitation wavelengths of 320 nm, 322 nm, 324 nm, 326 nm, 328 nm and 330 nm, respectively. The decrease of lifetimes for the Eu3+:5D0 (593 nm) energy level might be ascribed to the excitation of different luminescent centers with varying the excitation wavelengths from 320 to 330 nm. As we know that Eu3+ ions occupy multiply sites in CaF2 crystals [31]. The energy transfer mechanism from the excited 4f-5d states of Eu2+ to the 4f-4f states of Eu3+ ions is schematically shown in Fig. 5(e). Two energy transfer channels were proposed, labeled as ET1 and ET2. As for ET1, energy absorbed from Eu2+ excited at 398 nm directly transferred to the 5L6 state of Eu3+ ions, by non-radiative dipole interaction. For the ET2, the radiative energy from Eu2+ is absorbed by Eu3+ ions. It is important to note that 4f-5d transition of Eu2+ is a fully allowed transition, however, the 4f-4f transition of Eu3+ is parity forbidden and has a relatively low absorption cross-section. Though both Eu2+ and Eu3+ ions could be excited at 398nm due to the overlap of absorption, Eu2+ ions absorb most of the incident energy. So ET2 might be the main energy transfer process. Besides, the overlapping area (around 300 to 420 nm) of the photoluminescence excitation spectra for the Eu2+ and Eu3+ ions varies according to the excitation wavelength, as shown in Fig. 5(a). Therefore, tunable colors could be obtained by adjusting the excitation wavelength within one single crystal sample. The CIE chromaticity coordinates of the 0.6%Eu: CaF2 crystal were calculated to be (0.43, 0.29), (0.38, 0.24), (0.33, 0.20), (0.28, 0.14), (0.24, 0.10) and (0.22, 0.08) from the emission spectra, with 2 nm interval from 320 to 330 nm as shown in Fig. 5(f). It can be found that the CIE color coordinates depend greatly on the excitation wavelength. The color is changed from warm white to blue by adjusting the excitation wavelength from 320 to 330 nm, which indicates that the crystal can be used for WLEDs.

4. Conclusion

In summary, as-prepared Eu: CaF2 single crystals are successfully synthesized by the Bridgman-Stockbarge method. The XPS results show that both the Eu2+ and Eu3+ valance states coexist in the Eu: CaF2 single crystals. Under 398 nm excitation, the emission spectrum of Eu: CaF2 single crystals show not only the characteristic f−f transitions of Eu3+ ions but also the 5d→4f transition emission of Eu2+ ions. And the emission spectrum of Eu: CaF2 single crystal can be impacted by the atomic concentration ratios of Eu2+/Eu3+, local lattice environment of Eu ions and energy transfer from Eu2+ ions to Eu3+ ions. The corresponding luminescence color can be tuned from blue, pink, orange-red to orange. In addition, the warm white light can be obtained in 0.6%Eu: CaF2 single crystal when the excitation wavelength is around 322 nm. So, Eu: CaF2 single crystal has potential applications in the areas of UV white-light-emitting diodes.

Funding

National Key Research and Development Program of China (2016YFB0701002); National Natural Science Foundation of China (NSFC) (61635012, 51432007); Strategic Priority Program of the Chinese Academy of Sciences (XDB16030000).

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Figures (5)

Fig. 1
Fig. 1 (a) The photograph of as-grown Eu: CaF2 single crystal. (b) Crystal structure of Eu:CaF2 single crystal. (c) XRD patterns of x%Eu: CaF2 (x = 0.6, 1.2, 3.0, 6.0) crystals.
Fig. 2
Fig. 2 (a)Emission spectra of x%Eu: CaF2 (x = 0.6,1.2,3.0,6.0) crystals. (b) The intensity ratio between Eu3+ (593 nm) /Eu2+ (424 nm) as a function of Eu doping concentrations. (c) CIE chromaticity diagram of x%Eu: CaF2 (x = 0.6,1.2,3.0,6.0) crystals.
Fig. 3
Fig. 3 The Eu3d XPS spectra of x%Eu: CaF2 (x = 0.6, 1.2, 3.0, 6.0) crystals.
Fig. 4
Fig. 4 The integrated intensity ratio (R) of I (5D0-7F2) to I (5D0-7F1) for x%Eu: CaF2 (x = 0.6,1.2,3.0,6.0) crystals.
Fig. 5
Fig. 5 (a) Luminescence excitation spectra of Eu2+ and Eu3+ emissions in 0.6%Eu: CaF2 together with emission spectrum excited at 398 nm; (b) Emission spectra measured of 0.6%Eu: CaF2 at different wavelengths from 320 to 330 nm; (c) Emission spectra measured of 0.6%Eu: CaF2 at different wavelengths of 300, 330 and 350 nm; (d) Decay curves of the Eu3+:5D0 (593 nm) energy level;(e) Configuration coordination diagram for Eu3+ and Eu2+ energy levels;(f) CIE chromaticity diagram of 0.6%Eu: CaF2 crystal under different excitation wavelength from 320 to 330 nm.

Tables (1)

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Table 1 Relative percentage for ionic concentrations of Eu3+ and Eu2+ ions of x%Eu: CaF2 (x = 0.6, 1.2, 3.0, 6.0) crystals obtained from XPS data.

Equations (4)

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3 C a C a + 2 E u 3 + = 3 C a 2 + + 2 E u c a ' + V c a ''
V c a '' = V c a x + 2 e
2 E u c a ' + 2 e = 2 E u c a x
I t = I 0 e t τ
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