The Electrical Properties of Tb-Doped CaF2 Nanoparticles under High Pressure

The high-pressure transport behavior of CaF2 nanoparticles with 3 mol% Tb concentrations was studied by alternate-current impedance measurement. All of the electrical parameters vary abnormally at approximately 10.76 GPa, corresponding to the fluorite-cotunnite structural transition. The substitution of Ca2+ by Tb3+ leads to deformation in the lattice, and finally lowers the transition pressure. The F− ions diffusion, electronic transport, and charge-discharge process become more difficult with the rising pressure. In the electronic transport process, defects at grains play a dominant role. The charge carriers include both F− ions and electrons, and electrons are dominant in the transport process. The Tb doping improves the pressure effect on the transport behavior of CaF2 nanocrystals.

As an important optical and optoelectronic functional material, a thorough study of the electrical transport properties is essential, and the underlying physical transport behaviors, such as charge carrier type and scattering processes, are worthy of exploration.The impedance spectrum measurement method has long been conventional in studies of electrical charge transportation and related physical properties [16][17][18][19][20]. Specially, using the impedance method, the presence of independent pathways for charge transportation in an inorganic material [21], and the mixed electronic and ionic conduction in various organic and inorganic materials have been satisfactorily addressed [22][23][24][25][26].We have investigated the electrical properties of CaF 2 nanoparticles with Tb concentrations from 1 mol% to 5 mol% at atmospheric pressure, and it was found that the resistance of the sample with a concentration of 3 mol% Tb is the smallest.Therefore, in this work, the electrical properties of CaF 2 nanoparticles with 3 mol% Tb concentrations under high pressure were investigated by alternate-current (AC) impedance measurement up to 26 GPa.The underlying physical transport behaviors were discussed.Additionally, the pressure effect on the structural and electrical properties of Tb-doped CaF 2 nanocrystals was compared with that of un-doped nanocrystals.

Materials and Methods
A diamond anvil cell (DAC) was used to generate high pressure.The detailed configuration of the electrodes and sample has been illustrated in previous works [27][28][29].The final microcircuit and the profile of our designed DAC are shown in Figure 1.Pressure was calibrated by using ruby fluorescence.The ruby measurement scale is 100 GPa [30] and the accuracy of our measurement is 0.1 GPa.To avoid additional error on the electrical transport measurements, no pressure-transmitting medium was used.This will cause non-hydrostatic conditions [31]; however, the effects on the transport measurements can be neglected in our experiment pressure range [32].
Crystals 2018, 8, x FOR PEER REVIEW 2 of 8 transport behaviors were discussed.Additionally, the pressure effect on the structural and electrical properties of Tb-doped CaF2 nanocrystals was compared with that of un-doped nanocrystals.

Materials and Methods
A diamond anvil cell (DAC) was used to generate high pressure.The detailed configuration of the electrodes and sample has been illustrated in previous works [27][28][29].The final microcircuit and the profile of our designed DAC are shown in Figure 1.Pressure was calibrated by using ruby fluorescence.The ruby measurement scale is 100 GPa [30] and the accuracy of our measurement is 0.1 GPa.To avoid additional error on the electrical transport measurements, no pressure-transmitting medium was used.This will cause non-hydrostatic conditions [31]; however, the effects on the transport measurements can be neglected in our experiment pressure range [32].Impedance spectroscopy was measured by a Solartron 1260 impedance analyzer (Solartron, Hampshire, England) equipped with a Solartron 1296 dielectric interface.A voltage signal with an amplitude of 1 V was applied to the sample and its frequency ranged from 0.1 to 10 7 Hz.
The sample was prepared by the hydrothermal synthesis method as reported in our previous work [33].The Tb doping concentrations were 3 mol%.The sample was characterized by transmission electron microscopy (TEM) (JEOL Ltd., Tokyo, Japan) and X-ray diffraction (XRD λ = 1.5406Å) (Rigaku, Tokyo, Japan).Figure 2 exhibits the TEM image and the size distribution histogram.It can be seen that the shape of the sample is square with a mean dimension of 8 ± 2 nm.Impedance spectroscopy was measured by a Solartron 1260 impedance analyzer (Solartron, Hampshire, UK) equipped with a Solartron 1296 dielectric interface.A voltage signal with an amplitude of 1 V was applied to the sample and its frequency ranged from 0.1 to 10 7 Hz.
The sample was prepared by the hydrothermal synthesis method as reported in our previous work [33].The Tb doping concentrations were 3 mol%.The sample was characterized by transmission electron microscopy (TEM) (JEOL Ltd., Tokyo, Japan) and X-ray diffraction (XRD λ = 1.5406Å) (Rigaku, Tokyo, Japan).Figure 2 exhibits the TEM image and the size distribution histogram.It can be seen that the shape of the sample is square with a mean dimension of 8 ± 2 nm.
transport behaviors were discussed.Additionally, the pressure effect on the structural and electrical properties of Tb-doped CaF2 nanocrystals was compared with that of un-doped nanocrystals.

Materials and Methods
A diamond anvil cell (DAC) was used to generate high pressure.The detailed configuration of the electrodes and sample has been illustrated in previous works [27][28][29].The final microcircuit and the profile of our designed DAC are shown in Figure 1.Pressure was calibrated by using ruby fluorescence.The ruby measurement scale is 100 GPa [30] and the accuracy of our measurement is 0.1 GPa.To avoid additional error on the electrical transport measurements, no pressure-transmitting medium was used.This will cause non-hydrostatic conditions [31]; however, the effects on the transport measurements can be neglected in our experiment pressure range [32].Impedance spectroscopy was measured by a Solartron 1260 impedance analyzer (Solartron, Hampshire, England) equipped with a Solartron 1296 dielectric interface.A voltage signal with an amplitude of 1 V was applied to the sample and its frequency ranged from 0.1 to 10 7 Hz.
The sample was prepared by the hydrothermal synthesis method as reported in our previous work [33].The Tb doping concentrations were 3 mol%.The sample was characterized by transmission electron microscopy (TEM) (JEOL Ltd., Tokyo, Japan) and X-ray diffraction (XRD λ = 1.5406Å) (Rigaku, Tokyo, Japan).Figure 2 exhibits the TEM image and the size distribution histogram.It can be seen that the shape of the sample is square with a mean dimension of 8 ± 2 nm.The Nyquist impedance spectra of CaF2 nanoparticles with 3 mol% Tb concentrations under several pressures are presented in Figure 4.The Nyquist impedance spectra of CaF 2 nanoparticles with 3 mol% Tb concentrations under several pressures are presented in Figure 4. To analyze the ionic conduction, the impedance spectra were replotted into Z′~ω −1/2 plots, as shown in Figure 5.In the low frequency region, the Z′ can be expressed as:

Results and discussion
where is a parameter independent of frequency, σ is the Warburg coefficient, and ω is the frequency.By linear fitting the Z′~ω −1/2 plots, the Warburg coefficient of various pressure was obtained.The diffusion coefficient of the ions (Di) can be obtained from: where R is the ideal gas constant, T is the temperature, A is the electrode area, F is the Faraday constant, and C is the F − ions molar concentration.We set the F − ion diffusion coefficient at 0 GPa as D0, and the curve Di/D0 under different pressures was obtained and is shown in Figure 6a.
To quantify the pressure effect on the electrical transport properties, the impedance spectra were fitted with the equivalent circuit model (the inset (a) of Figure 4) on the Zview2 impedance analysis software.The obtained bulk and grain boundary resistances (Rb, Rgb) are plotted in Figure 6.The relaxation frequency of bulk (fb) under different pressures was obtained from the Z"~f curve and is presented in Figure 6d.To analyze the ionic conduction, the impedance spectra were replotted into Z ~ω−1/2 plots, as shown in Figure 5.To analyze the ionic conduction, the impedance spectra were replotted into Z′~ω −1/2 plots, as shown in Figure 5.In the low frequency region, the Z′ can be expressed as: where is a parameter independent of frequency, σ is the Warburg coefficient, and ω is the frequency.By linear fitting the Z′~ω −1/2 plots, the Warburg coefficient of various pressure was obtained.The diffusion coefficient of the ions (Di) can be obtained from: where R is the ideal gas constant, T is the temperature, A is the electrode area, F is the Faraday constant, and C is the F − ions molar concentration.We set the F − ion diffusion coefficient at 0 GPa as D0, and the curve Di/D0 under different pressures was obtained and is shown in Figure 6a.
To quantify the pressure effect on the electrical transport properties, the impedance spectra were fitted with the equivalent circuit model (the inset (a) of Figure 4) on the Zview2 impedance analysis software.The obtained bulk and grain boundary resistances (Rb, Rgb) are plotted in Figure 6.The relaxation frequency of bulk (fb) under different pressures was obtained from the Z"~f curve and is presented in Figure 6d.In the low frequency region, the Z can be expressed as: where Z 0 is a parameter independent of frequency, σ is the Warburg coefficient, and ω is the frequency.By linear fitting the Z ~ω−1/2 plots, the Warburg coefficient of various pressure was obtained.The diffusion coefficient of the ions (D i ) can be obtained from: where R is the ideal gas constant, T is the temperature, A is the electrode area, F is the Faraday constant, and C is the F − ions molar concentration.We set the F − ion diffusion coefficient at 0 GPa as D 0 , and the curve D i /D 0 under different pressures was obtained and is shown in Figure 6a.
To quantify the pressure effect on the electrical transport properties, the impedance spectra were fitted with the equivalent circuit model (the inset (a) of Figure 4) on the Zview2 impedance analysis software.The obtained bulk and grain boundary resistances (R b , R gb ) are plotted in Figure 6.The relaxation frequency of bulk (f b ) under different pressures was obtained from the Z"~f curve and is presented in Figure 6d.From Figure 6, it can be seen that all of the parameters vary discontinuously at approximately 10.76 GPa, corresponding to the fluorite-cotunnite (Fm3m-Pnma) structural transition of the sample.According to our previous works [29,33], this phase transition of un-doped CaF2 nanocrystals occurs at about 14 GPa.The variation in the phase transition pressure with the substitution of Ca 2+ by Tb 3+ can be discussed as follows: the ionic radius of Tb 3+ (0.092 nm) is smaller than that of Ca 2+ (0.099 nm), and the valence of Tb 3+ is different with that of Ca 2+ ; these result in deformation in the lattice and the increasing of the deformation potential, and finally make the transition pressure lower.
In the whole pressure range, the diffusion coefficient decreases with pressure; however, the grain and grain boundary resistance increase, indicating that the F − ions diffusion and electronic transport become more difficult with the rising pressure.The grain resistance is larger than the grain boundary resistance, which indicates that defects at grains play a dominant role in the electronic transport process.
The pressure dependence of grain activation energy (dH/dP) can be obtained from: where kB is the Boltzmann constant and T is the temperature.By linear fitting to the curve lnfb~P, the dH/dP of the Fm3m and Pnma phases were obtained and are listed in Table 1.The dH/dP of un-doped CaF2 nanocrystals were obtained by the data of Reference [27] and are also shown in Table 1.The positive values of dH/dP in Fm3m and Pnma phases indicate that the charge-discharge process becomes more difficult under compression.In the Fm3m and Pnma phases, the dH/dP values From Figure 6, it can be seen that all of the parameters vary discontinuously at approximately 10.76 GPa, corresponding to the fluorite-cotunnite (Fm3m-Pnma) structural transition of the sample.According to our previous works [29,33], this phase transition of un-doped CaF 2 nanocrystals occurs at about 14 GPa.The variation in the phase transition pressure with the substitution of Ca 2+ by Tb 3+ can be discussed as follows: the ionic radius of Tb 3+ (0.092 nm) is smaller than that of Ca 2+ (0.099 nm), and the valence of Tb 3+ is different with that of Ca 2+ ; these result in deformation in the lattice and the increasing of the deformation potential, and finally make the transition pressure lower.
In the whole pressure range, the diffusion coefficient decreases with pressure; however, the grain and grain boundary resistance increase, indicating that the F − ions diffusion and electronic transport become more difficult with the rising pressure.The grain resistance is larger than the grain boundary resistance, which indicates that defects at grains play a dominant role in the electronic transport process.
The pressure dependence of grain activation energy (dH/dP) can be obtained from: where k B is the Boltzmann constant and T is the temperature.By linear fitting to the curve lnf b ~P, the dH/dP of the Fm3m and Pnma phases were obtained and are listed in Table 1.The dH/dP of un-doped CaF 2 nanocrystals were obtained by the data of Reference [27] and are also shown in Table 1.The positive values of dH/dP in Fm3m and Pnma phases indicate that the charge-discharge process becomes more difficult under compression.In the Fm3m and Pnma phases, the dH/dP values of the Tb-doped CaF 2 nanocrystals are larger than those of un-doped CaF 2 nanocrystals.This indicates that pressure has a larger effect on the charge-discharge process of the Tb-doped sample.
To distinguish the contributions of F − ions and electrons to the transport process, the transference number were calculated by the following equations [34]: ) where t i is the transference number of F − ions, t e is the transference number of electrons, and R 1 and R 2 are the intercepts on the real impedance axis as shown in the inset (b) of Figure 4. t i and t e under various pressures are shown in Figure 7.It can be seen that electrons play a dominant role in the transport process and the electron transference number slightly increases as the pressure rises.
Crystals 2018, 8, x FOR PEER REVIEW 6 of 8 of the Tb-doped CaF2 nanocrystals are larger than those of un-doped CaF2 nanocrystals.This indicates that pressure has a larger effect on the charge-discharge process of the Tb-doped sample.
To distinguish the contributions of F − ions and electrons to the transport process, the transference number were calculated by the following equations [34]: where ti is the transference number of F − ions, te is the transference number of electrons, and R1 and R2 are the intercepts on the real impedance axis as shown in the inset (b) of Figure 4. ti and te under various pressures are shown in Figure 7.It can be seen that electrons play a dominant role in the transport process and the electron transference number slightly increases as the pressure rises.To further revealing the effect of Tb doping on the high-pressure transport behavior, the resistance variation of Tb-doped CaF2 nanocrystals is compared with that of un-doped CaF2 nanocrystals.The bulk and grain boundary resistances at 0 GPa were set as Rb0 and Rgb0, then the Rb/Rb0 and Rgb/Rgb0 of Tb-doped and un-doped CaF2 nanocrystals were obtained and are shown in Figure 8.It can be observed that both in the bulk and grain boundary, the resistance variation of the Tb-doped sample is larger than that of the un-doped sample.This indicates that the Tb doping improves the pressure effect on the transport behavior of CaF2 nanocrystals.To further revealing the effect of Tb doping on the high-pressure transport behavior, the resistance variation of Tb-doped CaF 2 nanocrystals is compared with that of un-doped CaF 2 nanocrystals.The bulk and grain boundary resistances at 0 GPa were set as R b0 and R gb0 , then the R b /R b0 and R gb /R gb0 of Tb-doped and un-doped CaF 2 nanocrystals were obtained and are shown in Figure 8.It can be observed that both in the bulk and grain boundary, the resistance variation of the Tb-doped sample is larger than that of the un-doped sample.This indicates that the Tb doping improves the pressure effect on the transport behavior of CaF 2 nanocrystals. of the Tb-doped CaF2 nanocrystals are larger than those of un-doped CaF2 nanocrystals.This indicates that pressure has a larger effect on the charge-discharge process of the Tb-doped sample.
To distinguish the contributions of F − ions and electrons to the transport process, the transference number were calculated by the following equations [34]: where ti is the transference number of F − ions, te is the transference number of electrons, and R1 and R2 are the intercepts on the real impedance axis as shown in the inset (b) of Figure 4. ti and te under various pressures are shown in Figure 7.It can be seen that electrons play a dominant role in the transport process and the electron transference number slightly increases as the pressure rises.To further revealing the effect of Tb doping on the high-pressure transport behavior, the resistance variation of Tb-doped CaF2 nanocrystals is compared with that of un-doped CaF2 nanocrystals.The bulk and grain boundary resistances at 0 GPa were set as Rb0 and Rgb0, then the Rb/Rb0 and Rgb/Rgb0 of Tb-doped and un-doped CaF2 nanocrystals were obtained and are shown in Figure 8.It can be observed that both in the bulk and grain boundary, the resistance variation of the Tb-doped sample is larger than that of the un-doped sample.This indicates that the Tb doping improves the pressure effect on the transport behavior of CaF2 nanocrystals.

Conclusions
The electrical properties of CaF 2 nanoparticles with 3 mol% Tb concentrations under high pressure were investigated by impedance measurement.All of the electrical parameters vary abnormally at approximately 10.76 GPa, corresponding to the Fm3m-Pnma structural transition.The substitution of Ca 2+ by Tb 3+ leads to deformation in the lattice, and finally lowers the transition pressure.The F − ions diffusion, electronic transport, and charge-discharge process become more difficult with the rising pressure.In the electronic transport process, defects at grains play a dominant role.The charge carriers include both F − ions and electrons, and electrons are dominant in the transport process.The Tb doping improves the pressure effect on the transport behavior of CaF 2 nanocrystals.Other lanthanides such as Yb, Er, Ce, etc. would cause similar effects and should be explored in the future.

Figure 1 .
Figure 1.The completed microcircuit (left) on diamond anvil and the profile of our designed diamond anvil cell (DAC) (right).

Figure 1 .
Figure 1.The completed microcircuit (left) on diamond anvil and the profile of our designed diamond anvil cell (DAC) (right).

Figure 1 .
Figure 1.The completed microcircuit (left) on diamond anvil and the profile of our designed diamond anvil cell (DAC) (right).

Figure 2 .
Figure 2. The TEM image and the size distribution histogram of 3 mol% Tb-doped CaF2 nanoparticles.

Figure 3
Figure 3 shows the X-ray diffraction pattern of CaF2 nanoparticles with 3 mol% Tb concentrations.The diffraction peaks of the sample match well with the pure cubic (space group: Fm3m (225) α = β = γ = 90°) phase of CaF2 (Joint Committee on Powder Diffraction Standards JCPDS Card No. 35-0816) and the lattice constant is 5.432 Å, which suggests that the original structure of CaF2 was retained after doping.No impurity peaks are observed in the pattern, indicating that the Tb 3+ ions were incorporated into the CaF2 lattice and substitute Ca 2+ ions.The average size estimated from the full width at half maximum (FWHM) using the Debye-Scherrer formula is 8.3 nm, which has good agreement with the TEM result.

Figure 3 .
Figure 3.The X-ray diffraction pattern of CaF2 nanoparticles with 3 mol% Tb concentrations at atmospheric pressure.

Figure 2 .
Figure 2. The TEM image and the size distribution histogram of 3 mol% Tb-doped CaF 2 nanoparticles.

Figure 3
Figure 3 shows the X-ray diffraction pattern of CaF 2 nanoparticles with 3 mol% Tb concentrations.The diffraction peaks of the sample match well with the pure cubic (space group: Fm3m (225) α = β = γ = 90 • ) phase of CaF 2 (Joint Committee on Powder Diffraction Standards JCPDS Card No. 35-0816)and the lattice constant is 5.432 Å, which suggests that the original structure of CaF 2 was retained after doping.No impurity peaks are observed in the pattern, indicating that the Tb 3+ ions were incorporated into the CaF 2 lattice and substitute Ca 2+ ions.The average size estimated from the full width at half maximum (FWHM) using the Debye-Scherrer formula is 8.3 nm, which has good agreement with the TEM result.

Figure 2 .
Figure 2. The TEM image and the size distribution histogram of 3 mol% Tb-doped CaF2 nanoparticles.

Figure 3
Figure 3 shows the X-ray diffraction pattern of CaF2 nanoparticles with 3 mol% Tb concentrations.The diffraction peaks of the sample match well with the pure cubic (space group: Fm3m (225) α = β = γ = 90°) phase of CaF2 (Joint Committee on Powder Diffraction Standards JCPDS Card No. 35-0816) and the lattice constant is 5.432 Å, which suggests that the original structure of CaF2 was retained after doping.No impurity peaks are observed in the pattern, indicating that the Tb 3+ ions were incorporated into the CaF2 lattice and substitute Ca 2+ ions.The average size estimated from the full width at half maximum (FWHM) using the Debye-Scherrer formula is 8.3 nm, which has good agreement with the TEM result.

Figure 3 .
Figure 3.The X-ray diffraction pattern of CaF2 nanoparticles with 3 mol% Tb concentrations at atmospheric pressure.

Figure 3 .
Figure 3.The X-ray diffraction pattern of CaF 2 nanoparticles with 3 mol% Tb concentrations at atmospheric pressure.

Figure 4 .
Figure 4.The Nyquist impedance spectra under several pressures.The inset (a) shows the equivalent circuit model, Rb and Rgb are grain and grain boundary resistance, Cb and Cgb are grain and grain boundary capacitance, and Wi is the Warburg impedance.The inset (b) is the spectroscopy at 1.59 GPa, R1 and R2 are two intercepts on the real impedance axis.

Figure 4 .
Figure 4.The Nyquist impedance spectra under several pressures.The inset (a) shows the equivalent circuit model, R b and R gb are grain and grain boundary resistance, C b and C gb are grain and grain boundary capacitance, and W i is the Warburg impedance.The inset (b) is the spectroscopy at 1.59 GPa, R 1 and R 2 are two intercepts on the real impedance axis.

Crystals 2018, 8 , 8 Figure 4 .
Figure 4.The Nyquist impedance spectra under several pressures.The inset (a) shows the equivalent circuit model, Rb and Rgb are grain and grain boundary resistance, Cb and Cgb are grain and grain boundary capacitance, and Wi is the Warburg impedance.The inset (b) is the spectroscopy at 1.59 GPa, R1 and R2 are two intercepts on the real impedance axis.

Figure 6 .
Figure 6.(a) the diffusion coefficient, (b) the bulk resistance, (c) the grain boundary resistance, (d) the bulk relaxation frequency under high pressure.D0 represents the diffusion coefficient at 0 GPa.

Figure 6 .
Figure 6.(a) the diffusion coefficient, (b) the bulk resistance, (c) the grain boundary resistance, (d) the bulk relaxation frequency under high pressure.D 0 represents the diffusion coefficient at 0 GPa.

Figure 7 .
Figure 7. ti and te under various pressures.

Figure 7 .
Figure 7. t i and t e under various pressures.

Figure 7 .
Figure 7. ti and te under various pressures.

Figure 8 .
Figure 8.The R b /R b0 and R gb /R gb0 of Tb-doped and un-doped CaF 2 nanocrystals.R b0 and R gb0 represent bulk and grain boundary resistances at 0 GPa.

Table 1 .
Pressure dependence of the grain activation energy of Tb-doped and un-doped CaF2 nanocrystals.

Table 1 .
Pressure dependence of the grain activation energy of Tb-doped and un-doped CaF 2 nanocrystals.