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

Abstract

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.

1. Introduction

Recently, rare earth (RE)-doped nanomaterials have attracted much attention [1,2,3,4,5], due to their potential applications such as advanced phosphor [6], display monitors [7], light amplification [8], and biological labeling [9,10], etc. Among these host materials, calcium fluoride (CaF₂) is an attractive host for RE doping because of its high transparency in a wide wavelength region and low phonon energy [11,12,13,14,15].

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 CaF₂ 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 CaF₂ 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 CaF₂ nanocrystals was compared with that of un-doped nanocrystals.

2. 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, 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 10⁷ 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 = 1.5406 Å) (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.

3. Results and Discussion

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 Tb³⁺ ions were incorporated into the CaF₂ lattice and substitute Ca²⁺ 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.

The Nyquist impedance spectra of CaF₂ 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:

$$Z^{\prime }=Z_0^{\prime }+\sigma {\omega }^{-1/2},$$

(1)

where $Z_0^{\prime }$ 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:

$$D_i=0.5(\frac{RT}{A{F}^2\sigma C}{)}^2,$$

(2)

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 D_i/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 (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 Ca²⁺ by Tb³⁺ can be discussed as follows: the ionic radius of Tb³⁺ (0.092 nm) is smaller than that of Ca²⁺ (0.099 nm), and the valence of Tb³⁺ is different with that of Ca²⁺; 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:

$$\mathrm{d}\left(\ln f_b\right)/\mathrm{dP}=-\left(1/k_{B}T\right)\left(dH/dP\right),$$

(3)

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

Phase	dH/dp (meV/GPa) (Tb-dDoped)	dH/dp (meV/GPa) (Un-Doped)
Fm3m	4.70	3.12
Pnma	2.97	1.44

. 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 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]:

$$t_i=\left(R_2-R_1\right)/R_2,$$

(4)

$$t_e=R_1/R_2,$$

(5)

where t_i is the transference number of F⁻ ions, t_e 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. 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.

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 R_b0 and R_gb0, then the R_b/R_b0 and R_gb/R_gb0 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.

4. Conclusions

The electrical properties of CaF₂ 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 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. Other lanthanides such as Yb, Er, Ce, etc. would cause similar effects and should be explored in the future.