Characterization of nano-size YVO/sub 4/:Eu and (Y,Gd)VO/sub 4/:Eu phosphor via low voltage cathodoluminescence

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Characterization of nano-size YVO4 : Eu and „Y , Gd…VO4 : Eu phosphors by low voltage cathodo- and photoluminescence Jong Hyuk Kang,a兲 Michael Nazarov, and Won Bin Im Department of Material Science and Engineering, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea

Jin Young Kim Electronic Materials Lab., Samsung Advanced Institute of Technology, P. O. Box 111, Suwon 440-600, Republic of Korea

Duk Young Jeon Department of Material Science and Engineering, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea

共Received 1 October 2004; accepted 27 December 2004; published 7 April 2005兲 Low voltage cathodoluminescence 共LVCL兲 and photoluminescence measurement were carried out to better understand the role of Gd in 共Y , Gd兲VO4 : Eu phosphor and to compare two different synthesis methods 共solid-state reaction, coprecipitation reaction兲 and their preparing conditions. From the analysis of LVCL measurement, it is understood that the luminescence of YVO4 : Eu and 共Y , Gd兲VO4 : Eu phosphors might be interpreted as originating from a two-level system and for reasons of enhanced luminescence intensity of 共Y , Gd兲VO4 : Eu phosphor, the effect of Gd on the symmetry of Eu sites dominates over that of interaction between Gd and Eu. It is also found that nano-size phosphor of YVO4 : Eu synthesized by coprecipitation reaction shows lower quantum yield in comparison with that synthesized by solid-state reaction due to the presence of secondary phase produced after heat treatment. © 2005 American Vacuum Society. 关DOI: 10.1116/1.1861048兴

I. INTRODUCTION Yttrium orthovanadate 共YVO4兲 is an attractive host lattice for several lanthanide ions to produce efficient phosphors emitting a variety of colors.1–4 Especially, europium doping gives a red emission in YVO4 with three main group of lines at 593 nm 共5D0 → 7F1兲, 619 nm 共5D0 → 7F2兲, and 700 nm 共5D0 → 7F4兲. Recently YVO4 : Eu phosphor is considered as a candidate for red phosphor for flat panel displays 共FPDs兲 because of its good color purity.5 It has been reported that when the Eu ion is located in a host lattice lacking inversion symmetry such as YVO4, luminescent properties of Euactivated phosphor are affected by the crystal symmetry of the Eu site.6 As a result, YVO4 : Eu phosphor shows good color purity. In this study, to improve the PL intensity of YVO4 : Eu phosphor, Gd was investigated as host cation substituting Y of YVO4 : Eu phosphor because Gd and Y have the same valency electron configuration 共d1s2兲 and are optically inert, and their ionic radii in the trivalent state are very similar.7 Generally, to synthesize ceramic powders, solidstate reaction has been widely adopted. In conventional solid-state reaction, extensive ball milling is required, however, it may lead to possible contamination by unwanted impurities and degradation of the luminescent properties. To avoid such problems, various soft-chemical synthesis techniques have been extensively studied.8,9 Among these, coprecipitation reactions which offer molecular or nano-level mixa兲

Author to whom correspondence should be addressed; electronic mail: [email protected]

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ing of constituents leading to chemical homogeneity are very useful to synthesize novel nano-size compounds with high crystallinity. When a phosphor is adopted for flat panel display 共FPD兲 applications, it might be the case that design constraints in FPD limit the amount of excitation power available to excite phosphors. A good example can be found in field emission displays where highly energetic electrons and substantial beam current cannot be used unlike cathode ray tube display.10 As a result, the emission efficiency of phosphor becomes an issue of major concern. To achieve the high emission efficiency under low voltage excitation, high purity and low electrical resistivity of phosphor components must be insured and in advance of these factors it is very important to understand precisely about behavior of phosphors by low voltage excitation.11–13 Moreover, cathodoluminescence 共CL兲 measurement of a rare earth activated phosphor can give us better understanding about the luminescence mechanism of phosphor.14 The aim of this study is to compare the luminescence characteristics of YVO4 : Eu phosphors which were synthesized by two different synthesis methods 共solid-state reaction, coprecipitation reaction兲 and understand the role of Gd in 共Y , Gd兲VO4 : Eu via low voltage cathodoluminescence 共LVCL兲 and photoluminescence 共PL兲 measurements. II. EXPERIMENT Polycrystalline YVO4 : Eu and 共Y , Gd兲VO4 : Eu phosphors were prepared by solid-state reaction and coprecipitation reaction. The particle sizes and morphologies of the samples

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©2005 American Vacuum Society

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Kang et al.: Characterization of nano-size YVO4 : Eu and „Y , Gd…VO4 : Eu

obtained by both methods were investigated by a FEI XL30SFEG scanning electron microscope 共SEM兲. The crystal structures of the samples were investigated by x-ray diffraction 共XRD兲 spectra obtained by a Rigaku D/max-RC x-ray diffractometer with Cu K␣ radiation 共␭ = 1.5406 Å兲. In order to investigate the luminescence properties, PL measurement was carried out with Perkin-Elmer Instruments LS50B luminescence spectrometer at room temperature. The excitation was performed with a 254 nm ultraviolet 共UV兲 radiation. For LVCL measurement, the samples were placed inside a vacuum chamber that employed a Kimball Physics FRA-2X1-2/EGPS-2X1 electron gun system. All luminescence measurements were conducted on powder samples. Initially the CL spectra were recorded at accelerating voltage of 500 or 1000 eV and at emission current of 100 A / cm2 for all phosphors under vacuum level of 1 ⫻ 10−7 Torr. Then the dependence of the luminescence properties on electron beam current 20–100 A / cm2 and accelerating voltage 100–1000 V was investigated.

III. RESULTS AND DISCUSSION A. Chemical synthesis

Nano-size Y0.95VO4 : Eu0.05 phosphor powder was synthesized by coprecipitation reaction.15 First of all, three solutions were prepared. In solution 共A兲, Y2O3 共99.99%, Aldrich兲 and Eu2O3 共99.99%, Aldrich兲 were taken in equimolar ratios and dissolved in HCl 共30%, Aldrich兲. In solution 共B兲, V2O5 共99.99%, Aldrich兲 was dissolved in HCl separately because vanadium exists as a form of not vanadate 共VO3− 4 兲 but vanadyl radical VO2+ in hydrochloric solution. Subsequently, solutions 共A兲 and 共B兲 were diluted with distilled water in the ratio of 1 to 3, respectively. Solution 共C兲 is a mixture of NH4OH and H2O2 with 3:1 ratio. Finally, a diluted solution 共A兲 was added to a diluted solution 共B兲, and pH of the resulting mixture was brought to 8.0 by adding the solution 共C兲. The resulting mixture was stirred and heated to about 80 °C until the precipitate formed. The overall process is explained by the following reaction: 2共1 − x兲Y3+ + 2xEu3+ + 2VO2+ + 10OH− + H2O2 → 2共Y1−x , Eux兲VO4 + 6H2O. After allowing the solution to cool down and the precipitates to settle, the precipitates were washed with distilled water to remove useless resultants, filtered and substantially separated from the aqueous mother liquor. The dried precipitate was then loaded into trays with a large exposed surface area, and fired in air for about 2 h at 300, 1100, 1200, 1300, and 1400 °C. YVO4 : Eu and 共YX , Gd1−X兲VO4 : Eu 共0 艋 x 艋 1.0兲 were also synthesized by solid-state reaction. Abovementioned high purity oxides and Gd2O3 共99.99⫹%, Aldrich兲 were used as raw materials. For the present studies, we fixed the amount of dopant europium to be 5 mole %. The raw materials were thoroughly mixed by using ethanol as liquid phase for mixing. Initially these oxides were calcined at 900 °C for 10 h and then calcined again at 1200 °C for 20 h. After these procedures, the samples were washed with distilled water to remove useless resultants, filtered, and dried at 80 °C. J. Vac. Sci. Technol. B, Vol. 23, No. 2, Mar/Apr 2005

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FIG. 1. SEM micrographs of YVO4 : Eu powder synthesized by 共a兲 coprecipitation reaction and 共b兲 solid-state reaction.

Figure 1 shows morphologies and sizes of YVO4 : Eu phosphor powder prepared by the two aforementioned methods. As shown in Fig. 1共a兲, the particle size of YVO4 : Eu prepared by coprecipitation reaction was below 200 nm. And it also shows narrow particle size distribution, spherical shape, and a small degree of agglomeration. B. Structural characterization

Figure 2共a兲 shows powder x-ray diffraction patterns of nano-size YVO4 phosphor. Nano-size YVO4 : Eu powder obtained after coprecipitation reaction which was done completely at 100 °C showed a single and partly crystallized phase even before heat treatment. From the analysis of the XRD pattern, it was understood that the introduction of activator Eu3+ did not influence the crystal structure of the phosphor matrix. As shown in Fig. 2共b兲, after subsequent heat treatment at 1200 °C for 2 h, the XRD pattern of polycrystalline YVO4 : Eu powder was observed. And also small diffraction peaks are observed at 28.8 and 29.2°, which might be due to the formation of secondary phase Y8V2O17.

FIG. 2. Powder XRD patterns of YVO4 : Eu powder synthesized by coprecipitation reaction: 共a兲 as-synthesized sample, 共b兲 heat treated sample, 共c兲 YVO4 : Eu and 共d兲 共Y , Gd兲VO4 : Eu synthesized by solid-state reaction. The 19-0341 and 44-0390 Joint Committee on Powder Diffraction Standards files 共see Ref. 24兲 can be also seen to identify the obtained crystalline phases.

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FIG. 3. Normalized PL intensity of YVO4 : Eu synthesized by coprecipitation reaction 共inset: PL spectrum of as-synthesized sample兲.

It has been reported that surface area affect its evaporation rate and temperature, namely, high surface to volume ratio of nano-size particles can reduce evaporation temperature compared to bulk particles.16 Therefore, it is believed that relatively easy formation of vanadium-deficient secondary phase in the case of nano-size YVO4 : Eu might be due to a reduction of evaporation temperature by high surface area of nanosize particles. As shown in Figs. 2共c兲 and 2共d兲, YVO4 : Eu and 共Y0.4 , Gd0.6兲VO4 : Eu synthesized by solid-state reaction showed the same crystal structure which is tetragonal with a little different lattice constant. Lattice constants of YVO4 : Eu are: a = b = 7.112 Å and c = 6.290 Å. And lattice constants of 共Y0.4 , Gd0.6兲VO4 : Eu are a = b = 7.178 Å and c = 6.329 Å, respectively. From the analysis of XRD, it was revealed that all three axes of YVO4 : Eu were elongated by an introduction of Gd because the ionic radius of Gd ion is bigger than that of Y ion.17 And as a result of that, it is believed that a small degree of distorted crystal symmetry could be obtained. C. Photoluminescence characterization

PL measurements were carried out to investigate the effect of Gd addition upon PL property of YVO4 : Eu and to compare solid-state reaction with coprecipitation reaction. As shown in the inset of Fig. 3, as-synthesized YVO4 : Eu phosphors by coprecipitation reaction show specific luminescence spectrum even before heat treatment and YVO4 : Eu fired at 1200 °C shows the highest PL intensity. Figure 4 shows the PL excitation and emission spectra of red-emitting YVO4 : Eu and 共Y0.4 , Gd0.6兲VO4 : Eu phosphors excited by 254 nm. The measured excitation spectra of YVO4 : Eu phosphors was in fair agreement with ones available from the literature.18 YVO4 lattice is responsible for the absorption present in the spectra. It is most likely due to excitation from the filled oxygen 2p levels in the valence band to the empty V 3d levels of the conduction band. In the case of emission spectrum, it has been reported that the pure YVO4 shows blue JVST B - Microelectronics and Nanometer Structures

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FIG. 4. PL excitation and emission spectra of 共a兲 共Y , Gd兲VO4 : Eu, 共b兲 YVO4 : Eu synthesized by solid-state reaction, and 共c兲 YVO4 : Eu synthesized by coprecipitation reaction.

emission, which is due to energy transition of a molecular 19 orbital VO3− 4 group inside YVO4. As shown in Fig. 4, however, when Eu replaces Y in the host material, very sharp peaks appear in the red region instead of broadband blue emission. The emission spectrum of YVO4 : Eu3+ presents the characteristics of Eu3+ emission transitions arising mainly from the 5D0 level to the 7FJ 共J = 0, 1, 2, 3, 4兲 manifolds. Among these transitions, the major emission peak of Eu3+ ion observed at 619 nm is assigned to the transition of the electric dipole 5D0 → 7F2 which is sensitive to the site symmetry around the activator ion. As shown in Fig. 4共a兲 when some of Y3+ ions in YVO4 : Eu phosphor were replaced by Gd3+ ions, it was found that the shape of the PL spectrum was changed very little, while relative PL intensity was increased in comparison with YVO4 : Eu shown in Fig. 4共b兲. It has been reported that the improvement of luminescence intensity of Y-based phosphor with Eu by adding Gd3+ ions is due to distortion of site symmetry around Eu3+ ion6 or the creation of Gd3+–Eu3+ energy transfer process by introduction of Gd.20,21 Luminescence spectrum of nano-size YVO4 : Eu phosphor shown in Fig. 4共c兲 is almost the same as the one observed in Fig. 4共b兲. And the corresponding excitation spectrum was also observed. This is in agreement with the mechanism known to be responsible for the luminescence of the YVO4 : Eu shown in Fig. 4共b兲. In brief, the absorption of UV photons by the VO3− 4 groups inside the host material is followed by a nonradiative transfer to the europium.22 Subsequently, it relaxes to the ground state through a radiative transition. Under 254 nm excitation, it showed lower PL intensity than YVO4 : Eu did as shown in Fig. 4共b兲. Considering the existence of secondary phase Y8V2O17 observed from XRD analysis, low PL intensity of YVO4 : Eu phosphor might be due to creation of defects such as vanadium or oxygen vacancy produced on surfaces of the sample16 or reduction of VO43− group playing an important role in luminescence of YVO4 : Eu phosphor.22

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TABLE I. Relative PL intensity ratios 共R兲 for the measured emission levels of Eu3+ doped YVO4 phosphor. 5

Phosphor

5

共Y , Gd兲VO4 : Eu 共SSR兲a YVO4 : Eu 共SSR兲 YVO4 : Eu 共CM兲b

D 0 → 7F 1 D 0 → 7F 1

5 5

1.000 1.000 1.000

D 0 → 7F 2 D 0 → 7F 1 3.170 3.340 2.867

5 5

D 0 → 7F 3 D 0 → 7F 1 0.074 0.081 0.058

5 5

D 0 → 7F 4 D 0 → 7F 1 0.113 0.099 0.143

a

SSR: solid-state reaction. CM: coprecipitation reaction.

b

In the case of some phosphors having Eu3+ ion as an activator, the 5D0 → 7FJ emission is very suitable to survey the environmental effects 共of surrounding ions兲 on the sites of Eu3+ ion in a host lattice lacking inversion symmetry such as YVO4. While the 5D0 → 7F4 transition is sensitive to longrange environmental effects, the 5D0 → 7F2 transition which originates from interactions with neighbors is hypersensitive to, especially short-range, environmental effects.23 However, the 5D0 → 7F1, the allowed magnetic-dipole transition, is not affected by neighbors of the Eu3+ ion, so that luminescence intensity of 5D0 → 7F1 transition among radiative transitions of Eu3+ ion is usually utilized as a reference. Table I shows the relative PL intensity ratios 共R兲 for the measured emission levels of Eu3+ doped YVO4 and 共Y0.4 , Gd0.6兲VO4 phosphors. The intensity ratios of 5D0 → 7F2 and 5D0 → 7F4 transitions to 5 D0 → 7F1 transition in PL spectrum of 共Y , Gd兲VO4 : Eu phosphor represent that Eu3+ ions occupied yttrium sites of YVO4 lattice and the short-range environments of Eu3+ ions in 共Y , Gd兲VO4 are somewhat different from that of Eu3+ in YVO4, which might be due to introduction of Gd3+ ions. D. Low voltage cathodoluminescence characterization

To compare the luminescence characteristics of YVO4 : Eu phosphors which were synthesized by solid-state reaction and coprecipitation reaction, respectively, and understand the role of Gd in 共Y , Gd兲VO4 : Eu, LVCL measurements were carried out. Figure 5 shows the CL emission spectra of the samples. When we compare CL emission spectra with PL emission spectra in terms of relative intensity and spectra shape, each emission peak was shown in the same wavelength, the shape of spectra was almost identical with that of PL spectra. In addition the relative CL intensity of the samples was also in agreement with the relative PL intensity shown in Fig. 4. In general the CL intensity depends not only on the investigated sample but is also an unknown function of emission current and accelerating voltage ICL = Kf 1共J兲f 2共U兲,

ICL = KJ.

共2兲

The coefficient K differs for YVO4 : Eu synthesized by coprecipitation reaction. In any case if there is a linear dependence of Eu3+ main peak intensity 共␭ = 619 nm兲 versus emission current and no saturation one can see, we can establish that at these activator concentrations no Gd–Eu energy transfer was formed and all emission is attributed to the electronic transition from emitting level 5D0 to 7FJ 共J = 1, 2, 3, 4, 5, 6兲 for trivalent ions of europium. In this case a twolevel model14 can be considered, taking into account the stationary conditions of excitation 共dn/ dt= 0兲, the number of luminescent ions in excited state is given by

共1兲

where K is a certain constant depending on the sample, J is density of emission current and U is accelerating voltage between cathode and anode in CL installation. Knowledge of these functions f 1 and f 2 could help us in modeling emission process and energy transfer in the investigated sample. They can be received from direct experiJ. Vac. Sci. Technol. B, Vol. 23, No. 2, Mar/Apr 2005

ments changing J and U. Especially, in our previous study we have investigated successfully that energy transfer from Tb to Eu occurs inside CaWO4 : Eu, Tb phosphor by analyzing the relation between CL intensity and activator concentration.14 For fixed accelerating voltage U = 1 kV the current dependences for the samples are shown in Fig. 6. One can see the linear intensity dependence for all the phosphors

FIG. 5. CL emission spectra of 共a兲 共Y , Gd兲VO4 : Eu, 共b兲 YVO4 : Eu synthesized by solid-state reaction, and 共c兲 YVO4 : Eu synthesized by coprecipitation reaction.

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atoms in the host lattice, Gd changes the parameters of lattice and it can also influence the forced electric dipole transition of Eu3+ ion and improve the CL and PL intensity. IV. CONCLUSION

FIG. 6. Current dependence on CL intensity of 共a兲 共Y , Gd兲VO4 : Eu, 共b兲 YVO4 : Eu synthesized by solid-state reaction, and 共c兲 YVO4 : Eu synthesized by coprecipitation reaction 共U = 1 kV兲.

n1 =

LJN , LJ + ␶−1

共3兲

where n1 gives the number of luminescent ions in excited state, ␶−1 is the probability for spontaneous emission excited state 共1兲→ ground state 共0兲, J is an electron beam density, L is a quantum yield of CL, and N is the total number of luminescent ions 共n1 + n0兲. Obtained expression explains the linear dependence of CL intensity on the emission current if LJⰆ ␶−1. Thus, the CL intensity assumes a form ICL ⬇ n1 = LJN␶ = KJ,

共4兲

where K = LN␶. This derived Eq. 共4兲 is the same as the experimental Eq. 共2兲. Therefore, from the consideration of LVCL measurement of YVO4 : Eu and 共Y , Gd兲VO4 : Eu phosphors, it is found that the luminescence of both YVO4 : Eu and 共Y , Gd兲VO4 : Eu phosphor could be explained by a two-level model. And for the same activator concentration and total number of luminescent ions N, and for the constant probability for spontaneous emission, the coefficient K is determined by quantum yield L. Consequently, as shown in Fig. 6, YVO4 : Eu phosphor synthesized by coprecipitation reaction has a low quantum yield in comparison with one synthesized by solid-state reaction, which might be due to the presence of secondary phase Y8V2O17. From the literature of Eu3+ ion as an activator, the analysis of XRD, PL, and LVCL measurement, the effect of Gd in 共Y , Gd兲VO4 : Eu phosphor can be summarized as follows: The choice of host lattices for Eu3+ activator is very important because the luminescence properties of Eu3+ ion doped phosphors depend to a great extent on the site symmetry around Eu3+ ion. In this study, the luminescence spectrum of 共Y , Gd兲VO4 : Eu is dominated by the peak at 619 nm due to the forced electric dipole 5D0 → 7F2 transition of Eu3+, which is typical behavior of Eu3+ ions occupying noncentrosymmetric sites. Consequently, when Gd replaces some of the Y JVST B - Microelectronics and Nanometer Structures

We have successfully synthesized zircon-type YVO4 : Eu phosphor with solid-state reaction and coprecipitation reaction, respectively. It was found that YVO4 : Eu phosphor synthesized by coprecipitation reaction shows the nano-size, spherical shape but lower emission efficiency than that synthesized by solid-state reaction. From the analysis of XRD and PL emission spectra, it was found that Gd ions in 共Y , Gd兲VO4 : Eu phosphor improve the PL intensity of YVO4 : Eu phosphor, which might be due to the changed site symmetry of Eu3+ ions. And we have also used LVCL measurement to get better understanding about the characteristics of YVO4 : Eu and 共Y , Gd兲VO4 : Eu phosphors. Based on the LVCL measurement, we have successfully established a twolevel model as a luminescence mechanism of 共Y , Gd兲VO4 : Eu and YVO4 : Eu phosphor. And it is thought that for reasons of enhanced luminescence intensity of 共Y , Gd兲VO4 : Eu phosphor, the effect of Gd on the symmetry of Eu sites dominates over that of interaction between Gd and Eu. It is also found that nano-size YVO4 : Eu phosphor synthesized by coprecipitation reaction shows low quantum yield in comparison with that synthesized by solid-state reaction due to the presence of secondary phase. ACKNOWLEDGMENT This research was supported by a Grant 共M102KR010024-04K1801-02413兲 from Information Display R&D Center, one of the 21st Century Frontier R&D Programs funded by the Ministry of Science and Technology of the Korean government. A. K. Levine and F. C. Palilla, Appl. Phys. Lett. 5, 118 共1964兲. L. Ozawa, Cathodoluminescence 共Kodansha, Tokyo, and VCH, New York, 1990兲. 3 J. L. Sommerdijk and A. Bril, J. Electrochem. Soc. 122, 952 共1975兲. 4 G. Blasse and A. Bril, J. Chem. Phys. 48, 217 共1968兲. 5 T. Hisamune, in Proceedings of the 9th International Display Workshops, 2002, p. 685. 6 R. D. Peacock, Struct. Bonding 共Berlin兲 22, 83 共1975兲. 7 L. H. Ahrens, Geochim. Cosmochim. Acta 2, 155 共1952兲. 8 A. Huignard, T. Cacoin, and J.-P. Poilot, Chem. Mater. 12, 1090 共2000兲. 9 S. Erdei, R. Schlecht, and D. Ravichandran, Displays 19, 173 共1999兲. 10 S. Shionoya and W. M. Yen, Phosphor Handbook 共CRC, Boca Raton, FL, 1998兲. 11 C. H. Seager, D. R. Tallant, and W. L. Warren, J. Appl. Phys. 82, 4515 共1997兲. 12 S. A. Bukesov and D. Y. Jeon, Appl. Phys. Lett. 81, 2184 共2002兲. 13 J. Bang, B. Abrams, B. Wagner, and P. H. Holloway, J. Appl. Phys. 95, 7873 共2004兲. 14 M. V. Nazarov, D. Y. Jeon, J. H. Kang, E.-J. Popovici, L.-E. Muresan, M. V. Zamoryanskaya, and B. S. Tsukerblat, Solid State Commun. 131, 307 共2004兲. 15 R. C. Ropp, US Patent No. 3,580,861 共1971兲. 16 Ph. Buffat and J.-P. Borel, Phys. Rev. Lett. 91, 106102 共2003兲. 17 CRC Handbook of Chemistry and Physics, 81st ed., edited by D. R. Lide 共CRC, Boca Raton, FL, 1991兲, pp. 12–14. 18 A. Newport, J. Silver, and A. Vecht, J. Electrochem. Soc. 147, 3944 共2000兲. 1 2

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R. C. Ropp, Luminescence and the Solid State 共Elsevier, Amsterdam, 1991兲. 20 F. G. Anderson, H. Weidner, P. L. Summers, R. E. Peale, X. X. Zhang, and B. H. T. Shai, J. Lumin. 60, 150 共1994兲. 21 R. T. Wegh, H. Donker, K. D. Oskam, and A. Meijerink, J. Lumin. 82, 93 19

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共1999兲. K. Riwotzki and M. Haase, J. Phys. Chem. B 105, 12709 共2001兲. 23 L. D. Carlos and A. L. L. Videira, Phys. Rev. B 49, 11721 共1994兲. 24 Powder Diffraction File, Joint Committee on Powder Diffraction Standards, Swarthmore, PA, 1991. 22

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