Effect of Tb-doped Concentration Variation on the Electrical and Dielectric Properties of CaF2 Nanoparticles

Calcium fluoride (CaF2) nanoparticles with various terbium (Tb) doping concentrations were investigated by X-ray diffraction (XRD), transmission electron microscopy (TEM), and alternating current (AC) impedance measurement. The original shape and structure of CaF2 nanoparticles were retained after doping. In all the samples, the dominant charge carriers were electrons, and the F− ion transference number increased with increasing Tb concentration. The defects in the grain region considerably contributed to the electron transportation process. When the Tb concentration was less than 3%, the effect of the ionic radius variation dominated and led to the diffusion of the F− ions and facilitated electron transportation. When the Tb concentration was greater than 3%, the increasing deformation potential scattering dominated, impeding F− ion diffusion and electron transportation. The substitution of Ca2+ by Tb3+ enables the electron and ion hopping in CaF2 nanocrystals, resulting in increased permittivity.

For optical and optoelectronic devices, energy consumption is a key factor in evaluating their performance [18][19][20][21]. Energy consumption is inextricably tied to the electrical and dielectric performance of the material used in a device. Therefore, the electrical and dielectric properties of lanthanide (III)-doped CaF 2 nanoparticles are worth exploring. Due to the presence of numerous grain boundaries, nanocrystals have many unique properties that would not be present in their corresponding bulk counterparts [22,23]. Additionally, electrical and dielectric properties are closely related to the charge carrier types and their scattering processes. However, the above subjects have not been studied in detail.
In this study, the morphology and structure of CaF2 nanoparticles with various Tb doping concentrations are studied using X-ray diffraction (XRD) and transmission electron microscopy (TEM). The electrical and dielectric properties are investigated using alternating current (AC) impedance measurements. The transportation properties of charge carriers are also discussed.

Materials and Methods
A series of Tb-doped CaF2 nanoparticles were synthesized using the liquid-solid-solution (LSS) solvothermal route [24][25][26]. The sample was synthesized as follows: 16.8 mL oleic acid, 48 mL ethanol, and 0.4 g sodium hydroxide (Sinopharm Chemical Reagent Beijing Co., Ltd, Beijing, china) were mixed together and stirred for 10 minutes; 1.888 g Ca(NO3)2·H 2O (Sinopharm Chemical Reagent Beijing Co., Ltd, Beijing, china) dissolved in 20 mL H2O was added to the solution and stirred for 10 minutes. Then, 0.672 g sodium fluoride (NaF) (Sinopharm Chemical Reagent Beijing Co., Ltd, Beijing, china) dissolved in 20 mL H2O was added to the solution and stirred for 1 hour. Finally, the solution was poured into an autoclave. The system was kept at 160 °C for 24 hours and then cooled naturally in air. The product was centrifuged with cyclohexane (Sinopharm Chemical Reagent Beijing Co., Ltd, Beijing, china) and ethanol and dried at 80 °C. To the Tb-doped samples, part of the Ca(NO3)2·H 2O was substituted by Tb(NO3)3·5H2O (Sinopharm Chemical Reagent Beijing Co., Ltd, Beijing, china) and the Tb(NO3)3·5H2O molar fractions were 1, 2, 3, 4, and 5 mol %. Transmission electron micrographs were measured by TEM (JEOL Ltd., Tokyo, Japan). The samples structure and phase were measured by XRD (Rigaku, Tokyo, Japan) with Cu Kα radiation (λ = 1.5406 Å ). The sample we synthesized was powered, which is incompact. However, to complete impedance measurements, the sample must be compact. Therefore, the sample was pressed into a cylinder (ø6 × 1 mm) using a shock pressure (20 MPa). The impedance measurement was measured by parallel plate electrode at atmospheric pressure. The input voltage amplitude was 1 V, and frequency ranged from 0.1 to 10 7 Hz. The output signal was gathered and processed by the impedance analyzer (Solartron 1260, Solartron, Hampshire, UK) with a dielectric interface (Solartron 1260, Solartron, Hampshire, UK). Figure 1 shows the XRD patterns of the Tb-doped CaF2 nanoparticles. The peaks of all the samples matched well with the standard cubic CaF2 phase (JCPDS Card No. 35-0816), and no impurity phase was found in the spectra. Therefore, the crystal structure remained unchanged after doping. Figures 2-4 shows the TEM image, size distribution histogram, and energy dispersive spectrometer (EDS) of the CaF2 nanoparticles with various Tb concentrations. We observed that all samples were square and the mean dimensions were all about 12 ± 3 nm. The presence of Tb in the EDS spectrums of Tb-doped CaF2 nanoparticles indicates that Tb was successfully doped into the samples. The impedance spectroscopy of CaF2 nanocrystals with various Tb concentrations is shown in Figure 5.            To quantify the effect of Tb doping on the electrical transport properties of CaF2 nanocrystals, an equivalent circuit was used to fit the impedance results. The alternative representation Z′~ω −1/2 was used to study the F − ion transport property and the result is presented in Figure 6.  To quantify the effect of Tb doping on the electrical transport properties of CaF 2 nanocrystals, an equivalent circuit was used to fit the impedance results. The alternative representation Z ~ω −1/2 was used to study the F − ion transport property and the result is presented in Figure 6. To quantify the effect of Tb doping on the electrical transport properties of CaF2 nanocrystals, an equivalent circuit was used to fit the impedance results. The alternative representation Z′~ω −1/2 was used to study the F − ion transport property and the result is presented in Figure 6.  In the low frequency region, the Z and ω −1/2 were linear, indicating the existence of F − ion diffusion at low frequency. Thus, a Warburg element was used to depict the F − ion conduction, Nanomaterials 2018, 8, 532 6 of 10 which was added to the equivalent circuit diagram as presented in Figure 7. The fitted spectra agreed well with the experiment results ( Figure 5), indicating that electron and ion conduction coexisted in the sample transport process. In the low frequency region, the Z′ and ω −1/2 were linear, indicating the existence of Fion diffusion at low frequency. Thus, a Warburg element was used to depict the Fion conduction, which was added to the equivalent circuit diagram as presented in Figure 7. The fitted spectra agreed well with the experiment results ( Figure 5), indicating that electron and ion conduction coexisted in the sample transport process. Figure 7. The equivalent circuit used to fit the impedance results. Rb is grain resistance, Rgb is grain boundary resistance, Cb is grain capacitance, Cgb is grain boundary capacitance, and Wi is the Warburg impedance.

Results and Discussion
Considering the charge carriers include both ions and electrons, the transference number was used to describe the contribution of the ions and electrons to the transportation process [27]. The F − ion transference number was defined as ti and electron as te, so ti and te can be expressed as: where R1 and R2 are the X-axis intercepts of the spectroscopy (Figure 5c). The ti and te of CaF2 nanocrystals with various Tb concentrations are presented in Figure 8. In all samples, the electron transport dominated, and the F − ion transference number increased with increasing Tb concentration. The Warburg coefficient (σ) can be obtained by the following equation [28]: Figure 7. The equivalent circuit used to fit the impedance results. R b is grain resistance, R gb is grain boundary resistance, C b is grain capacitance, C gb is grain boundary capacitance, and W i is the Warburg impedance.
Considering the charge carriers include both ions and electrons, the transference number was used to describe the contribution of the ions and electrons to the transportation process [27]. The F − ion transference number was defined as t i and electron as t e , so t i and t e can be expressed as: where R 1 and R 2 are the X-axis intercepts of the spectroscopy (Figure 5c). The t i and t e of CaF 2 nanocrystals with various Tb concentrations are presented in Figure 8. In all samples, the electron transport dominated, and the F − ion transference number increased with increasing Tb concentration. In the low frequency region, the Z′ and ω −1/2 were linear, indicating the existence of Fion diffusion at low frequency. Thus, a Warburg element was used to depict the Fion conduction, which was added to the equivalent circuit diagram as presented in Figure 7. The fitted spectra agreed well with the experiment results ( Figure 5), indicating that electron and ion conduction coexisted in the sample transport process. Figure 7. The equivalent circuit used to fit the impedance results. Rb is grain resistance, Rgb is grain boundary resistance, Cb is grain capacitance, Cgb is grain boundary capacitance, and Wi is the Warburg impedance.
Considering the charge carriers include both ions and electrons, the transference number was used to describe the contribution of the ions and electrons to the transportation process [27]. The F − ion transference number was defined as ti and electron as te, so ti and te can be expressed as: where R1 and R2 are the X-axis intercepts of the spectroscopy (Figure 5c). The ti and te of CaF2 nanocrystals with various Tb concentrations are presented in Figure 8. In all samples, the electron transport dominated, and the F − ion transference number increased with increasing Tb concentration. The Warburg coefficient (σ) can be obtained by the following equation [28]: The Warburg coefficient (σ) can be obtained by the following equation [28]:

of 10
where Z 0 is a constant and ω is the frequency. By performing a linear fit on the Z ~ω −1/2 scatterplot (Figure 6), the Warburg coefficient of CaF 2 nanocrystals with different Tb concentrations was obtained. The ion diffusion coefficient can be expressed as: where R is the ideal gas constant, T is temperature, F is the Faraday constant, and C is the molar concentration of F − ions. The F − ion diffusion coefficient for un-doped CaF 2 nanocrystals was set as D 0 , and the D i /D 0 of various Tb concentrations was obtained, as shown in Figure 9a. Through fitting the impedance spectra by the equivalent circuit, the grain and grain boundary resistances were obtained as shown in Figure 9b. where 0 ′ is a constant and ω is the frequency. By performing a linear fit on the Z′~ω −1/2 scatterplot ( Figure 6), the Warburg coefficient of CaF2 nanocrystals with different Tb concentrations was obtained. The ion diffusion coefficient can be expressed as: where R is the ideal gas constant, T is temperature, F is the Faraday constant, and C is the molar concentration of F − ions. The F − ion diffusion coefficient for un-doped CaF2 nanocrystals was set as D0, and the Di/D0 of various Tb concentrations was obtained, as shown in Figure 9a. Through fitting the impedance spectra by the equivalent circuit, the grain and grain boundary resistances were obtained as shown in Figure 9b. When the Tb concentration was less than 3%, the F − ion diffusion coefficient increased with increasing Tb concentration; when the Tb concentration was greater than 3%, the F − ion diffusion coefficient decreased. The grain and grain boundary resistances decreased with increasing Tb concentration until 3%, and then increased. In all samples, the grain resistance dominated in the total resistance, indicating that the defects in the grain region considerably contribute to the electron transportation process.
The changing of the transport properties with the replacement of Ca 2+ by Tb 3+ was analysed from two aspects: (1) the Tb 3+ ionic radius being smaller than the Ca 2+ ionic radius, which leads to the increasing mobility of the charge carriers [29]; and (2) due to the different valence, the replacement of Ca 2+ by Tb 3+ results in the deformation of the lattice and an increase in the deformation potential scattering, which decreases the mobility of the charge carriers. When the Tb concentration was less than 3%, the effect of ionic radius variation dominated, facilitating both F − ion diffusion and electron transportation. However, when the Tb concentration was greater than 3%, the increasing deformation potential scattering was dominant, impeding F − ion diffusion and electron transportation.
To comprehensively understand the transport properties of Tb-doped CaF2 nanoparticles, the dielectric properties were further studied. The complex permittivity (ε′, ε″) with frequency (f) of CaF2 nanocrystals under different Tb concentrations are shown in Figure 10. When the Tb concentration was less than 3%, the F − ion diffusion coefficient increased with increasing Tb concentration; when the Tb concentration was greater than 3%, the F − ion diffusion coefficient decreased. The grain and grain boundary resistances decreased with increasing Tb concentration until 3%, and then increased. In all samples, the grain resistance dominated in the total resistance, indicating that the defects in the grain region considerably contribute to the electron transportation process.
The changing of the transport properties with the replacement of Ca 2+ by Tb 3+ was analysed from two aspects: (1) the Tb 3+ ionic radius being smaller than the Ca 2+ ionic radius, which leads to the increasing mobility of the charge carriers [29]; and (2) due to the different valence, the replacement of Ca 2+ by Tb 3+ results in the deformation of the lattice and an increase in the deformation potential scattering, which decreases the mobility of the charge carriers. When the Tb concentration was less than 3%, the effect of ionic radius variation dominated, facilitating both F − ion diffusion and electron transportation. However, when the Tb concentration was greater than 3%, the increasing deformation potential scattering was dominant, impeding F − ion diffusion and electron transportation.
To comprehensively understand the transport properties of Tb-doped CaF 2 nanoparticles, the dielectric properties were further studied. The complex permittivity (ε , ε") with frequency (f ) of CaF 2 nanocrystals under different Tb concentrations are shown in Figure 10. The ε′ decreased linearly with increasing frequency in the low frequency region, then remained almost unchanged in the middle frequency region, finally increasing in the high frequency region. The ε″ decreased linearly with increasing frequency and then increased in the high frequency region. The presence of strong low-frequency dispersion in the permittivity implies that the electron and ion are hopping in the transport process [30]. At low frequencies, the ε′ and ε″ of Tb-doped samples were greater than of the un-doped sample, indicating Tb-doping facilitates electron and ion hopping in CaF2 nanocrystals. The substitution of Ca 2+ by Tb 3+ implies the creation of vacancy. Once a vacancy is created, further atom motion is relatively easy, so a neighboring atom hops into the vacancy, which is easily translated to another site, and finally facilitates charge carriers hopping and increases permittivity.

Conclusions
CaF2 nanoparticles with various Tb doping concentrations were characterized by XRD, TEM, and AC impedance. In all samples, the dominant charge carriers were electrons, and the F − ion transference number increased with increasing Tb concentration. The defects in the grain region considerably contributed to the electron transportation process. When the Tb concentration was less than 3%, the ionic radius variation effect dominated and facilitated F − ion diffusion and electron transportation. When the Tb concentration was greater than 3%, the increasing deformation potential scattering dominated, impeding F − ion diffusion and electron transportation. The substitution of Ca 2+ by Tb 3+ enabled electron and ion hopping in CaF2 nanocrystals, and finally led to the increasing permittivity. We concluded that rare-earth-doping treatment is an effective method for modulating the electric conductive and dielectric performance of CaF2 nanoparticles. We expect that the design of CaF2-based optical and optoelectronic devices could benefit from our investigation.
Author Contributions: X.C. conceived and designed the experiments; J.W. and Y.C. fabricated and characterized the sample; X.Z. and J.Z. collaborated in XRD, TEM measurements; T.H., X.L., J.Y. and C.G. analyzed the data. All authors discussed the experiment results and contributed to writing the paper.  The ε decreased linearly with increasing frequency in the low frequency region, then remained almost unchanged in the middle frequency region, finally increasing in the high frequency region. The ε" decreased linearly with increasing frequency and then increased in the high frequency region. The presence of strong low-frequency dispersion in the permittivity implies that the electron and ion are hopping in the transport process [30]. At low frequencies, the ε and ε" of Tb-doped samples were greater than of the un-doped sample, indicating Tb-doping facilitates electron and ion hopping in CaF 2 nanocrystals. The substitution of Ca 2+ by Tb 3+ implies the creation of vacancy. Once a vacancy is created, further atom motion is relatively easy, so a neighboring atom hops into the vacancy, which is easily translated to another site, and finally facilitates charge carriers hopping and increases permittivity.

Conclusions
CaF 2 nanoparticles with various Tb doping concentrations were characterized by XRD, TEM, and AC impedance. In all samples, the dominant charge carriers were electrons, and the F − ion transference number increased with increasing Tb concentration. The defects in the grain region considerably contributed to the electron transportation process. When the Tb concentration was less than 3%, the ionic radius variation effect dominated and facilitated F − ion diffusion and electron transportation. When the Tb concentration was greater than 3%, the increasing deformation potential scattering dominated, impeding F − ion diffusion and electron transportation. The substitution of Ca 2+ by Tb 3+ enabled electron and ion hopping in CaF 2 nanocrystals, and finally led to the increasing permittivity. We concluded that rare-earth-doping treatment is an effective method for modulating the electric conductive and dielectric performance of CaF 2 nanoparticles. We expect that the design of CaF 2 -based optical and optoelectronic devices could benefit from our investigation.