Pressure Effects on the Charge Carrier Transportation of BaF$_{2}$ Nanocrystals

Xiao-Yan Cui(崔晓岩)$^{1}$, Ting-Jing Hu(胡廷静)$^{1\hyperlink{s}{**}}$, Jing-Shu Wang(王婧姝)$^{1}$, Jun-Kai Zhang(张俊凯)$^{1}$, Xue-Fei Li(李雪飞)$^{1}$, Jing-Hai Yang(杨景海)$^{1}$, Chun-Xiao Gao(高春晓)$^{2\hyperlink{s}{**}}$

doi:10.1088/0256-307X/34/4/046401

⇦Chinese Physics Letters, 2017, Vol. 34, No. 4, Article code 046401⇨ Pressure Effects on the Charge Carrier Transportation of BaF$_{2}$ Nanocrystals * Xiao-Yan Cui(崔晓岩)1, Ting-Jing Hu(胡廷静)1**, Jing-Shu Wang(王婧姝)1, Jun-Kai Zhang(张俊凯)1, Xue-Fei Li(李雪飞)1, Jing-Hai Yang(杨景海)1, Chun-Xiao Gao(高春晓)2** Affiliations 1Key Laboratory of Functional Materials Physics and Chemistry of the Ministry of Education, Jilin Normal University, Siping 136000 2State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012 Received 27 December 2016 ^*Supported by the National Natural Science Foundation of China under Grant Nos 11374131, 11674404, 11404137 and 61378085, the Program for New Century Excellent Talents in University under Grant No NCET-13-0824, the Program for the Development of Science and Technology of Jilin Province under Grant Nos 201201079 and 20150204085GX, and the Twentieth Five-Year Program for Science and Technology of Education Department of Jilin Province under Grant No 20150221.
^**Corresponding author. Email: tjhumars@126.com; cc060109@qq.com; gaocx@jlu.edu.cn Citation Text: Cui X Y, Hu T J, Wang J S, Zhang J K and Li X F et al 2017 Chin. Phys. Lett. 34 046401 Abstract The charge transport behavior of barium fluoride nanocrystals is investigated by in situ impedance measurement up to 35 GPa. It is found that the parameters change discontinuously at about 6.9 GPa, corresponding to the phase transition of BaF$_{2}$ nanocrystals under high pressure. The charge carriers in BaF$_{2}$ nanocrystals include both F$^{-}$ ions and electrons. Pressure makes the electronic transport more difficult. The defects at grains dominate the electronic transport process. Pressure could make the charge–discharge processes in the $Fm3m$ phase more difficult. DOI:10.1088/0256-307X/34/4/046401 PACS:64.60.-i, 72.20.-i, 07.35.+k © 2017 Chinese Physics Society Article Text Transport properties of nanoscale materials have attracted a great deal of interest due to great potential for applications.[1-3] Generally speaking, a decrease in crystal size implies an increased proportion of the surfaces (interfaces) and usually also an increased contribution of grain boundary (GB) to the total material properties. Therefore, the nanoscale material may have some unique transport properties that would not be presented in the bulk material, which is worth exploring. A well-established method to separate the processes of grain and the grain boundary is the alternating current impedance spectroscopy. In recent years, impedance measurements have been shown a powerful tool for analyzing the conduction mechanism of grain and grain boundary.[4-6] Barium fluoride (BaF$_{2}$), which holds intrinsic optical and lattice-dynamical properties, has been widely studied as a type of important alkaline earth metal fluoride.[7] In particular, the BaF$_{2}$ crystal is an excellent high-density luminescent material and is extensively used for $\gamma$-ray and elementary particle detection.[8] As a typical ionic conductivity material, BaF$_{2}$ nanocrystal conductive property is an interesting subject. Despite there being many high-pressure studies on phase transitions of BaF$_{2}$,[9-12] few experimental and theoretical works have reported its transport properties under high pressure. In this Letter, the alternating current impedance spectroscopy of BaF$_{2}$ nanocrystals is conducted under high pressure up to 35 GPa. The conduction mechanism involving the charge transport process is studied. Our in situ impedance spectroscopy measurements of BaF$_{2}$ nanocrystals under high pressure were conducted on a diamond anvil cell (DAC). The diamond culet face was 400 μm in diameter. We chose molybdenum (Mo) as the electrodes and alumina as their protecting layer. The fabrication process of the microcircuit was reported previously.[13-16] The final microcircuit and the profile of our designed DAC are shown in Fig. 1. The distance between electrodes was 50 μm. A T301 stainless steel was pre-indented into 60 μm in thickness. Using the laser drilling machine, a hole of 250 μm in diameter was drilled at the center of the indentation. Then, the insulating layer that mixed cubic boron nitride powder and epoxy was compressed into the indentation. Subsequently, a sample chamber of 150 μm was drilled. Pressure was calibrated by R1 fluorescence peak of ruby. No pressure-transmitting medium was used. The alternating current impedance spectral measurements involve an ac source signal, $U(\omega,t)=U_{0}\cos(\omega t)$, loaded onto a sample, and a response current signal determined as $I(\omega,t)=I_{0}\cos(\omega t -\gamma)$. The complex impedance is obtained by $Z=U/I=Z'+iZ''$, where $Z'$ is the real part of impedance, and $Z''$ is the imaginary part of impedance. The impedance spectroscopy was measured by a Solartron 1260 impedance analyzer equipped with Solartron 1296 dielectric interface. The signal had amplitude of 1 V and frequency ranging from 0.1 to 10$^{7}$ Hz was applied into the sample. The BaF$_{2}$ nanocrystals were prepared by a liquid-solid-solution (LSS) solvothermal route. The length of the sample is around 14$\pm$3 nm.[17] The Nyquist representation of the impedance spectroscopy of BaF$_{2}$ nanocrystals under various pressures is shown in Fig. 2. The $x$ axis is the real part of the impedance ($Z'$), and the $y$ axis is the imaginary part of the impedance ($Z''$). As accepted for the solid sample, the equivalent circuit method is a reliable approach to describe the impedance spectra. To the bulk BaF$_{2}$, the charge carriers are F$^{-}$ ions. To the BaF$_{2}$ nanocrystals, if the charge carriers are also only F$^{-}$ ions, the impedance spectroscopy would be an arc (in the high frequency region) and a line (in the low frequency region), such as the hollow circle plot shown in Fig. 3.

Fig. 1. Completed microcircuit on diamond anvil (left) and the profile of our designed DAC (right). Here 1 is Mo, 2 is an alumina layer, 3 is an insulating layer, 4 is the sample chamber and 5 is the ruby. A and B are the contact ends of the microcircuit.

Fig. 2. Nyquist impedance spectrum under various pressures. Here $Z'$ is the real part of impedance, and $Z''$ is the imaginary part of impedance.

Fig. 3. Nyquist diagram at 0.7 GPa. Here $Z'$ is the real part of impedance, and $Z''$ is the imaginary part of impedance. The solid square represents the experimental result. The hollow circle represents the result with only F$^{-}$ ions conduction. The continuous line represents the simulated spectra.

Therefore, the charge carriers in BaF$_{2}$ nanocrystals include both ions and electrons. The transport processes include the ion and electron transport ($R$), the dipole polarization ($C$) and the ion diffusion ($W_{\rm i}$). The grain and grain boundary have different electrical transport properties, two RC circuits were used to describe the electrical transport processes of grain and grain boundary, respectively. The equivalent circuit was used as shown in Fig. 4(a). Above 22.2 GPa, the sample transformed into an amorphous phase,[17] therefore the equivalent circuit was simplified to Fig. 4(b).

Fig. 4. (a) The equivalent circuit below 22.2 GPa. Here $R_{\rm b}$ is the grain resistance, $R_{\rm gb}$ is the grain boundary resistance, $C_{\rm b}$ is the grain capacitance, $C_{\rm gb}$ is the grain boundary capacitance, and $W_{\rm i}$ denotes the Warburg impedance. (b) The equivalent circuit above 22.2 GPa.

The agreement of the simulated spectra with the experimental data (Fig. 3) indicates the validity of considering both the ionic and electric conductions in BaF$_{2}$ nanocrystals. The bulk resistance and grain boundary resistance below 22.2 GPa are shown in Fig. 5, and the resistance of the amorphous phase is also shown in Fig. 5.

Fig. 5. Relationships of resistance versus pressure. Below 22.2 GPa, the square represents the grain resistance, the circle represents the grain boundary resistance, and the triangle represents the resistance of the amorphous phase.

From Fig. 5, it can be seen that the bulk and grain boundary resistances change discontinuously at about 6.9 GPa. Because BaF$_{2}$ nanocrystals undergo the phase transformation from $Fm3m$ to $Pnma$ at 6.8 GPa,[17] the discontinuous changes can be attributed qualitatively to the pressure-induced structural phase transition. These results show that the phase transition is accompanied by the detectable changes in the electrical transport behavior. In the $Fm3m$ and $Pnma$ phases, the grain and grain boundary resistances increase with pressure, indicating that the pressure makes the electronic transport more difficult. In the pressure range of 0–22.2 GPa, the grain resistance shows a relatively larger contribution to the total resistance, compared with the grain boundary resistance, which indicates that the defects at grains dominate the electronic transport process. Above 22.2 GPa, the sample transformed into an amorphous phase, the resistance increases with the pressure, indicating that the pressure makes the electronic transport more difficult. The relaxation frequency of grains ($f_{\rm b}$) can be obtained from the relationship of imaginary part $Z''$ versus frequency. The grains relaxation frequency of the $Fm3m$ phase is shown in Fig. 6.

Fig. 6. The grains relaxation frequency of the $Fm3m$ phase under various pressures.

The electron carrier transport in BaF$_{2}$ nanocrystals grains can be regarded as a charging process in an RC resonance circuit and the relaxation frequency actually denotes the charge–discharge rate of the dipoles' oscillation process, and its activation energy represents the energy to activate the resonance. The pressure-dependent activation energy can be obtained by fitting the pressure dependence of the bulk relaxation frequency in Fig. 6 to the differential form of the Arrhenius equation $$ \frac{d(\ln f_{\rm b})}{dp}=-\frac{1}{k_{\rm B}T}\frac{dH}{dp}, $$ where $H$ represents the activation energy, $k_{\rm B}$ is the Boltzmann constant, and $T$ represents the temperature. The results are listed in Table 1. It can be seen that the activation energy decreases with the increasing pressure in the $Fm3m$ phase, which indicates that the pressure could make the charge–discharge processes more difficult.

**Table 1.** Pressure dependence of the grain activation energy.
Pressure region (GPa)	$dH/dp$ (meV/GPa)	Error (%)
0–6.2	3.2	4.3

In summary, the charge transport behavior of barium fluoride nanocrystals has been investigated by in situ impedance measurement up to 35 GPa. Each parameter changes discontinuously at about 6.9 GPa, corresponding to the phase transition of BaF$_{2}$ nanocrystals under high pressure. The charge carriers in BaF$_{2}$ nanocrystals include both F$^{-}$ ions and electrons. Pressure makes the electronic transport more difficult. The defects at grains dominate the electronic transport process. Pressure could make the charge–discharge processes in the $Fm3m$ phase more difficult. References Magnetic recording: advancing into the futurePhysical and chemical properties of nanoscale magnetite-based solvent extractantPreparation, characterization, and performance of magnetic iron–carbon composite microparticles for chemotherapyGrain boundaries in high-

T_{c}

superconductorsCharacterisation of ZnO-based varistors prepared from nanometre Precursor powdersGrain boundaries in dielectric and mixed-conducting ceramicsFirst-principles study of structural stabilities, electronic and elastic properties of BaF2 under high pressureFirst-principles study of structural, electronic and optical properties of BaF ₂ in its cubic, orthorhombic and hexagonal phasesPhase transitions and equations of state of alkaline earth fluorides

{CaF}_{2}

{SrF}_{2}

, and

{BaF}_{2}

to Mbar pressuresPressure induced structural phase transitions and metallization of BaF2The Radiations of

{Ce}^{141}

and

{Pa}^{233}

High-pressure x-ray- and neutron-diffraction studies of

{BaF}_{2}

: An example of a coordination number of 11 in

{AX}_{2}

compoundsIn situ Hall effect measurement on diamond anvil cell under high pressurePhase Transition Behavior of LiCr _0.35 Mn _0.65 O ₂ under High Pressure by Electrical Conductivity MeasurementIn Situ Electrical Resistivity and Hall Effect Measurement of β-HgS under High PressureCarrier behavior of HgTe under high pressure revealed by Hall effect measurementPressure-Induced Amorphization in BaF ₂ Nanoparticles

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