Nanoscale materials have recently attracted considerable attention due to their special properties that are different from those of bulk materials.^[1–4] In general, a decrease in crystal size implies an increased proportion of the surfaces (interfaces) and usually also in increased grain boundary (GB) properties. Therefore, the nanoscale material may have some unique transport properties that would not be presented in the bulk material, which is worth exploring.

The solid fluoride materials have been paid a great deal of attention due to their unique properties, such as low-energy phonons, high ionicity, electron–acceptor behavior, high resistivity, and anionic conductivity.^[5–7] These properties lead to a wide range of potential applications in optics, biological labels, and lenses,^[8,9] as well as components of insulators, gate dielectrics, wide-gap insulating overlayers, and buffer layers in semiconductor-on-insulator structures.^[10] Alkaline earth metal fluorides have been extensively used as solid electrolytes to measure fluorine chemical potentials at high temperatures, and thus, to determine the Gibbs free energies of the formation of metal fluorides, oxides, carbides, and sulfides.^[11,12] Their ambient and moderate temperature conductivities are relatively low.^[13] This is a limitation of the use of alkaline earth metal fluorides as practical electrolytes for low temperature operations. In recent years, it was found that the F ionic conductivity in nanophase fluorides increases greatly in contrast to that in the corresponding coarse or single crystalline phase state.^[14] As a result, with the development of nanometre materials, nanoscale alkaline earth metal fluorides are going to play an essential role in various applications based on their unique optical, electrical and magnetic properties. As an important kind of alkaline earth metal fluoride, strontium fluoride (SrF₂) has attracted a great deal of attention. At ambient conditions, the charge carriers of bulk SrF₂ are only F ions^[12,13] and its conductivity is too small,^[12,13] which limits the application of SrF₂ material. It is well known that both compression and decreasing crystal size treatments are effective methods for improving the material conductivity. However, there are few reports on the conductivity of SrF₂ nanocrystals under high pressures.

In this paper, we conducted an alternate-current (AC) impedance measurement of SrF₂ nanoplates at high pressures up to 35 GPa. The conduction mechanism involved in the charge transport process was studied.

In-situ impedance spectroscopy measurements of SrF₂ nanoplates were conducted at high pressure using a diamond anvil cell (DAC). The diamond culet face was in diameter. A thin film of metal molybdenum was deposited on the surface of the cell by a magnetron sputtering system, and then patterned into a microcircuit with two sections by photoetching. Above the microcircuit, a film of aluminium oxide was sputtered to protect the microcircuit. The electrode ends were in exposure by removing the aluminium oxide chemically to make the probes contact the sample and connect to the electric meters. A detection window ( ) was created in the center of the diamond culet. The distance between electrodes was . The fabrication process of the microcircuit was reported previously.^[15–18] The final microcircuit and the profile of our designed DAC are shown in Fig. 1.

Fig. 1.

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	Fig. 1. (color online) Completed microcircuit on diamond anvil (left) and the profile of our designed DAC (right). Numbers marked on profile represent 1: Mo; 2: alumina layer; 3: insulating layer; 4: sample; 5: ruby; 6: diamond. A and B are the contact ends of the microcircuit.

A T301 stainless steel was pre-indented into in thickness. Using the laser drilling machine, a hole of in diameter was drilled at the centre 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 was drilled. Pressure was calibrated by the R1 fluorescence peak of ruby. To avoid additional error on the electrical transport measurements, no pressure-transmitting medium was used. The impedance spectroscopy was measured by a Solartron 1260 impedance analyser equipped with a Solartron 1296 dielectric interface. A sine signal with amplitude of 1 V and frequency ranging from 0.1 Hz to 10⁷ Hz were applied into the sample. The SrF₂ nanoplates were prepared by a liquid-solid-solution (LSS) solvothermal route. The sample is square with a mean dimension of (21±3) nm.^[19]

The Nyquist representation of the impedance spectroscopy of SrF₂ nanoplates under various pressures is shown in Fig. 2.

Fig. 2.

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	Fig. 2. (color online) Nyquist impedance spectra under various pressures.

As accepted for a solid sample, the equivalent circuit method is a reliable approach to describe the impedance spectra. To the bulk SrF₂, the charge carriers are F ions.^[12,13] To the SrF₂ nanoplates, if the charge carriers are also only F ions, the equivalent circuit would be used as shown in Fig. 3(a), then the impedance spectroscopy would be shown as the hollow circle plot in Fig. 4. Therefore, the charge carriers in SrF₂ nanoplates include both ions and electrons. The equivalent circuit was used as shown in Fig. 3(b).

Fig. 3.

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	Fig. 3. (color online) (a) The equivalent circuit for only F ions conduction and (b) circuit diagram equivalent to the conduction mechanism. The subscripts b and gb of the parallel circuit represent bulk and grain boundary, respectively. Wi denotes the Warburg impedance.

Fig. 4.

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	Fig. 4. (color online) Nyquist diagram at 0.08 GPa. The solid square represents the experimental result. The circle represents the result with only F ions conduction. The continuous line represents the simulated spectrum.

The agreement of the simulated spectra with the experimental data [Fig. 4] indicates the validity of considering both the ionic and electric conductions in SrF₂ nanoplates. The relaxation frequency of grains ( ) can be obtained from the relationship of imaginary part versus frequency. The bulk resistance, grain boundary resistance, and grain relaxation frequency are shown in Fig. 5.

Fig. 5.

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	Fig. 5. Relationships of grain resistance, grain boundary resistance and grain relaxation frequency versus pressure.

From Fig. 5, it can be seen that each parameter changes discontinuously at about 6.71 GPa and 27.56 GPa. Because SrF₂ nanoplates undergo two phase transformations from to Pnma structure at 6.3 GPa, and then to structure at 27.7 GPa,^[19] 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 phase, the grain interior and grain boundary resistance decrease with increasing pressure, while increase in the Pnma phase. This indicates that the grain and grain boundary microstructure are rearranged after the structural phase transition. In the phase, the pressure makes the electronic transport easier. In the Pnma phase, on the contrary, the pressure makes the electronic transport more difficult. In the whole pressure range, the grain boundary resistance shows a relatively larger contribution to the total resistance, which indicates that the defects at grain boundaries dominate the electronic transport process.

Puin et al. measured the conductivity of nanocrystalline CaF₂ at temperatures from 390 K to 500 K and found that the charge carriers are only F ions,^[14] which is different from our results. The difference may be caused by the following reasons. (i) The sample preparation mothed: Puin et al. used the inert gas condensation method; we used the liquid–solid–solution (LSS) solvothermal route, which lead to the difference of the sample microstructure. (ii) The measurement conditions: Puin et al. conducted the measurement at temperatures from 390 K to 500 K, we conducted the measurement at room temperature, the temperature has different effects on the concentration and mobility of electron and ion, which finally leads to the difference of the charge carrier type.

The electron carrier transport in SrF₂ nanoplates grains can be regarded as a charging process in an 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 dependence of activation energy can be obtained by fitting the pressure dependence of the bulk relaxation frequency in Fig. 5(c) to the differential form of the Arrhenius equation,

Table 1.

Table 1.

Table 1. Pressure dependence of grain activation energy. . Pressure region/GPa ( )/(meV/GPa) 0.08 6.71 –4.03 14.88 27.56 0.99

Table 1. Pressure dependence of grain activation energy. .

It can be seen that the activation energy decreases with increasing pressure in the phase, but increases in the Pnma phase. This indicates that the pressure could make the charge–discharge processes in the phase much easier, but make it more difficult in the Pnma phase.

The charge transport behavior of strontium fluoride nanoplates has been investigated by in-situ impedance measurement at pressures up to 35 GPa. Each parameter changes discontinuously at about 6.71 GPa and 27.56 GPa, corresponding to the phase transitions of SrF₂ nanoplates under high pressure. The charge carriers in SrF₂ nanocrystals include both F ions and electrons. In the phase, pressure makes the electronic transport easier, while making it more difficult in the Pnma phase. The defects at grain boundaries dominate the electronic transport process. Pressure could make the charge–discharge processes in the phase much easier, but make it more difficult in the Pnma phase.