Ionic Transportation and Dielectric Properties of YF3:Eu3+ Nanocrystals

The ionic transportation and dielectric properties of YF3:Eu3+ nanocrystals are investigated by AC impedance spectroscopy. The ion diffusion coefficient and conductivity increase along with the doping concentration and reach their highest values at 4% of Eu3+. The difference of ionic radius between Eu3+ and Y3+ leads to the structural disorder and lattice strain, which deduces the increase of the ion diffusion coefficient and conductivity before 4% Eu3+ doping; then the interaction of the neighboring doping ions is dominated, which results in the difficulty of ion migration and decreases of the ion diffusion coefficient and conductivity. The strong dispersion of the permittivity in the low frequency region indicates that the charge carrier transport mechanism is the ion hopping in the system. The low-frequency hopping dispersion is affected by an interfacial polarization, which exhibits a Maxwell-Wagner relaxation process, and its loss peak shifts to higher frequency with the ionic conductivity increasing.


Introduction
Rare-earth fluoride nanomaterials have attracted a great deal of interest due to their unique physical and chemical properties and potential applications in luminescence, optoelectronic, down/up conversion devices, etc. [1][2][3][4][5][6]. Among the rare earth fluorides, YF 3 is an important material and has widespread potential applications in optical telecommunication, phosphors, down/up conversion luminescent devices, solid-state batteries, sensors [6][7][8][9][10][11][12][13][14], etc. Due to the closed ionic radius and the same valence, the Y 3+ can be easily replaced by other rare earth ions [15,16]. Moreover, YF 3 has low refractive index and wide bandgap [17,18]. Therefore, YF 3 is an attractive host material for lanthanide-doped phosphors. At the same time, due to its high ionic conduction, YF 3 is a prospective material used as a solid electrolyte of solid-state electrochemical devices.
As the phosphor host and solid electrolyte material, the ionic conductivity and dielectric properties of YF 3 nanocrystals are important subjects. Many investigations have been focused on the structure, synthesis and optical properties of YF 3 nanocrystals [8][9][10][11][19][20][21]. However, few reports have been conducted on the electrical and dielectric properties of YF 3 . Only Sathyamoorthy et al. have investigated the AC conduction of YF 3 thin film, whose structure is amorphous [22]. A thorough study on the carrier transport and dielectric properties of YF 3 nanocrystals is necessary. In this letter, the ionic

Results and Discussion
The structure, component and morphology of YF3 with different Eu 3+ -doping concentrations were investigated by XRD, EDS and TEM as shown in Figures 1-3. It can be seen that all the XRD spectra can be indexed as orthorhombic YF3 structure (JCPDS Card No. 74-0911), and the existence of Eu peak in the EDS spectra proves that the Eu 3+ ion successfully replaces Y 3+ in the Eu 3+ -doping samples. The TEM results show that all the samples are well crystallized and all of their particle sizes are about 28 ± 4 nm. The impedance plots of YF3 with different Eu 3+ -doping concentrations are shown in Figure 4. It shows that all the spectra display a semicircle and a straight line. To obtain the transport parameters, the impedance spectra are usually analyzed by the equivalent circuits. The straight line indicates the existence of the Warburg diffusion process [29]; therefore, a Warburg element was added into the equivalent circuit. The equivalent circuit we used was shown in the insert of Figure  4 and the fitting parameters for the impedance plots were listed in Table 1. The good agreements of the impedance spectra and the simulate plots indicate that the equivalent circuit is appropriate. The impedance plots of YF 3 with different Eu 3+ -doping concentrations are shown in Figure 4. It shows that all the spectra display a semicircle and a straight line. To obtain the transport parameters, the impedance spectra are usually analyzed by the equivalent circuits. The straight line indicates the existence of the Warburg diffusion process [29]; therefore, a Warburg element was added into the equivalent circuit. The equivalent circuit we used was shown in the insert of Figure 4 and the fitting parameters for the impedance plots were listed in Table 1. The good agreements of the impedance spectra and the simulate plots indicate that the equivalent circuit is appropriate.       To the Warburg diffusion process, the real impedance part (Z ′ ) in the low frequency region can be expressed as [29][30][31]:   To the Warburg diffusion process, the real impedance part (Z ′ ) in the low frequency region can be expressed as [29][30][31]: . The impedance plots of YF 3 :Eu 3+ nanocrystals. The DC polarization voltage for the impedance plots (V DC ) is 0 V. The insert is the equivalent circuits, R ct is the ion transfer resistance, W i is Warburg element, C ES is the capacitance between the sample and electrode. To the Warburg diffusion process, the real impedance part (Z ) in the low frequency region can be expressed as [29][30][31]: where σ is Warburg coefficient, Z 0 is constant and ω is frequency. By linear fitting the plots of Z ~ω -1/2 [as shown in Figure 5], the Warburg coefficient σ was obtained.
where σ is Warburg coefficient, is constant and ω is frequency. By linear fitting the plots of Z′~ω -1/2 [as shown in Figure 5], the Warburg coefficient σ was obtained. The diffusion coefficient of Fion can be gained by the following equation, where R is the ideal gas constant, T is temperature, F is the Faraday constant, C is the molar concentration of ions. Let D0 be the F − ion diffusion coefficient of un-doped YF3, then the Di/D0 of different Eu-doping concentration can be gained and was shown in Figure 6a. By simulating the spectra with the equivalent circuit, the ion transfer resistances (Rct) of YF3 with different Eu-doping concentrations are obtained. The ionic conductivity σi can be gained by the following formula: where d is the sample thickness, and A is the electrode area. The Eu-doping concentration dependence of the ionic conductivity was shown in Figure 6b. It can be seen that the ion diffusion coefficient and conductivity increase with the doping concentration until they reach 4% and then decrease. The changing mechanism of the two parameters can be interpreted as the following: the Eu 3+ ionic radius is larger than that of Y 3+ ; while the size mismatch will lead to the structural disorder and lattice strain [1], which finally deduces the The diffusion coefficient of Fion can be gained by the following equation, where R is the ideal gas constant, T is temperature, F is the Faraday constant, C is the molar concentration of ions. Let D 0 be the F − ion diffusion coefficient of un-doped YF 3 , then the D i /D 0 of different Eu-doping concentration can be gained and was shown in Figure 6a. By simulating the spectra with the equivalent circuit, the ion transfer resistances (R ct ) of YF 3 with different Eu-doping concentrations are obtained. The ionic conductivity σ i can be gained by the following formula: where d is the sample thickness, and A is the electrode area. The Eu-doping concentration dependence of the ionic conductivity was shown in Figure 6b. where σ is Warburg coefficient, is constant and ω is frequency. By linear fitting the plots of Z′~ω -1/2 [as shown in Figure 5], the Warburg coefficient σ was obtained. The diffusion coefficient of Fion can be gained by the following equation, where R is the ideal gas constant, T is temperature, F is the Faraday constant, C is the molar concentration of ions. Let D0 be the F − ion diffusion coefficient of un-doped YF3, then the Di/D0 of different Eu-doping concentration can be gained and was shown in Figure 6a. By simulating the spectra with the equivalent circuit, the ion transfer resistances (Rct) of YF3 with different Eu-doping concentrations are obtained. The ionic conductivity σi can be gained by the following formula: where d is the sample thickness, and A is the electrode area. The Eu-doping concentration dependence of the ionic conductivity was shown in Figure 6b. It can be seen that the ion diffusion coefficient and conductivity increase with the doping concentration until they reach 4% and then decrease. The changing mechanism of the two parameters can be interpreted as the following: the Eu 3+ ionic radius is larger than that of Y 3+ ; while the size mismatch will lead to the structural disorder and lattice strain [1], which finally deduces the It can be seen that the ion diffusion coefficient and conductivity increase with the doping concentration until they reach 4% and then decrease. The changing mechanism of the two parameters can be interpreted as the following: the Eu 3+ ionic radius is larger than that of Y 3+ ; while the size mismatch will lead to the structural disorder and lattice strain [1], which finally deduces the increase of the ion diffusion coefficient and conductivity. When the doping concentration is larger than 4%, the interaction of the neighboring doping ions emerges due to the decrease of distance between them [32], which results in the difficulty of ion migration and finally causes the decreases of the ion diffusion coefficient and conductivity.
To further explore the carrier transport mechanism of YF 3 :Eu 3+ , its dielectric properties were investigated. The frequency dependence of the permittivity real part (ε ), imaginary part (ε") and the dielectric loss tangent (tanδ) with different Eu 3+ doping concentration were shown in Figure 7. increase of the ion diffusion coefficient and conductivity. When the doping concentration is larger than 4%, the interaction of the neighboring doping ions emerges due to the decrease of distance between them [32], which results in the difficulty of ion migration and finally causes the decreases of the ion diffusion coefficient and conductivity.
To further explore the carrier transport mechanism of YF3:Eu 3+ , its dielectric properties were investigated. The frequency dependence of the permittivity real part (ε′), imaginary part (ε″) and the dielectric loss tangent (tanδ) with different Eu 3+ doping concentration were shown in Figure 7. It can be seen that with frequency increasing ε′ decreases sharply, then decreases slowly, and finally increases. ε″ decreases almost linearly with frequency increasing and then increases. The strong dispersion of the permittivity in the low frequency region indicates the charge carrier transport mechanism is the ion hopping in the system [33]. Ionic hopping behavior occurs as follows: under the action of electric field, one Fion moves to a more advantageous site (vacancy or interstitial position), then a vacancy is formed at this position and becomes an advantageous site to its surrounding atoms and so on. From Figure 7c, it can be seen that all the dielectric loss tangent plots show well-defined peaks in the frequency region of 0.1-100 HZ, which indicates the existence of the interfacial polarization between the grain boundaries in all of the samples. This loss peak distribution is in agreement with the Maxwell-Wagner relaxation model [34]. It can be deduced that the hopping dispersion in this region is affected by this interfacial polarization, and this phenomenon is similar to the result obtained from AC conduction investigation on YF3 thin film conducted by Sathyamoorthy et al. [22]. From Figure 7, it can be concluded that with the increasing of ionic conductivity, the ε′ and ε″ increase in the low frequency region and the loss peak of tanδ plot shifts to higher frequency. Before 4% Eu 3+ doping, the structural disorder and lattice strain increase with the doping concentration increasing, which are beneficial for the ion migration, and finally result in the ion hopping becoming easier and the interfacial polarization relaxation frequency increasing. When the doping concentration is larger than 4%, the interaction of the neighboring doping ions is strengthened and its effect is dominated; the scattering to ions and dipoles enhances; which finally makes the ion hopping more difficult and makes the interfacial polarization relaxation frequency decrease. It can be seen that with frequency increasing ε decreases sharply, then decreases slowly, and finally increases. ε" decreases almost linearly with frequency increasing and then increases. The strong dispersion of the permittivity in the low frequency region indicates the charge carrier transport mechanism is the ion hopping in the system [33]. Ionic hopping behavior occurs as follows: under the action of electric field, one Fion moves to a more advantageous site (vacancy or interstitial position), then a vacancy is formed at this position and becomes an advantageous site to its surrounding atoms and so on. From Figure 7c, it can be seen that all the dielectric loss tangent plots show well-defined peaks in the frequency region of 0.1-100 HZ, which indicates the existence of the interfacial polarization between the grain boundaries in all of the samples. This loss peak distribution is in agreement with the Maxwell-Wagner relaxation model [34]. It can be deduced that the hopping dispersion in this region is affected by this interfacial polarization, and this phenomenon is similar to the result obtained from AC conduction investigation on YF 3 thin film conducted by Sathyamoorthy et al. [22]. From Figure 7, it can be concluded that with the increasing of ionic conductivity, the ε and ε" increase in the low frequency region and the loss peak of tanδ plot shifts to higher frequency. Before 4% Eu 3+ doping, the structural disorder and lattice strain increase with the doping concentration increasing, which are beneficial for the ion migration, and finally result in the ion hopping becoming easier and the interfacial polarization relaxation frequency increasing. When the doping concentration is larger than 4%, the interaction of the neighboring doping ions is strengthened and its effect is dominated; the scattering to ions and dipoles enhances; which finally makes the ion hopping more difficult and makes the interfacial polarization relaxation frequency decrease.

Conclusions
The structure, component and morphology of YF 3 :Eu 3+ nanocrystals were measured by XRD, EDS and TEM. The ionic transportation and dielectric properties of YF 3 :Eu 3+ nanocrystals are investigated by AC impedance spectroscopy. The ion diffusion coefficient and conductivity increase with the doping concentration increasing and reach their highest values at 4% of Eu 3+ . The difference of ionic radius between Eu 3+ and Y 3+ leads to the structural disorder and lattice strain, which deduces the increase of the ion diffusion coefficient and conductivity before 4% Eu 3+ doping. Afterwards, the interaction of the neighboring doping ions is dominated, which results in the difficulty of ion migration and the decreases of the ion diffusion coefficient and conductivity. The strong dispersion of the permittivity in the low frequency region indicates that the charge carrier transport mechanism is the ion hopping in the system. The low-frequency hopping dispersion is affected by an interfacial polarization, which exhibits a Maxwell-Wagner relaxation process and its loss peak shifts to higher frequency with the ionic conductivity increasing. We have conducted a thorough study on the ionic transportation and dielectric properties of YF 3 nanocrystals with different Eu 3+ doping concentration and it is hoped that the design of YF 3 -based devices could benefit from this investigation.