Structural Phase Transition and Compressibility of CaF₂ Nanocrystals under High Pressure

Abstract

The structural phase transition and compressibility of CaF₂ nanocrystals with size of 23 nm under high pressure were investigated by synchrotron X-ray diffraction measurement. A pressure-induced fluorite to α-PbCl₂-type phase transition starts at 9.5 GPa and completes at 20.2 GPa. The phase-transition pressure is lower than that of 8 nm CaF₂ nanocrystals and closer to bulk CaF₂. Upon decompression, the fluorite and α-PbCl₂-type structure co-exist at the ambient pressure. The bulk modulus B₀ of the 23 nm CaF₂ nanocrystals for the fluorite and α-PbCl₂-type phase are 103(2) and 78(2) GPa, which are both larger than those of the bulk CaF₂. The CaF₂ nanocrystals exhibit obviously higher incompressibility compare to bulk CaF₂. Further analysis demonstrates that the defect effect in our CaF₂ nanocrystals plays a dominant role in the structural stability.

1. Introduction

Calcium fluoride (CaF₂)—with low absorption coefficient, high transmittance, anionic conductivity, and high resistivity—has become the focus of fundamental scientific research and industrial applications [1,2,3]. Especially because of its typical crystal structure, CaF₂ becomes the best material for high pressure research. At ambient conditions, bulk CaF₂ crystallizes in the cubic fluorite structure (Fm3m), in which Ca and F atoms occupy Wyckoff position 4a and 8c positions, respectively. Many theoretical and experimental studies on structural phase transition, optical, and electronic properties of CaF₂ under high pressure have been reported [4,5,6,7,8,9,10,11,12,13]. At high pressure, CaF₂ undergoes two structural phase transitions to highly coordinated structures. The first phase transition from the fluorite structure to an orthorhombic α-PbCl₂-type structure (Fm3m to Pnma) is reported to occur at 8–10 GPa [4,5,6]. Theoretical studies of CaF₂ predicted that the second phase transition from α-PbCl₂-type structure to Ni₂In-type structure (Pnma to P6₃/mmc) takes place at 68–278 GPa [6,7]. Experimental research by S M Dorfman et al. reported that bulk CaF₂ transformed from the α-PbCl₂-type structure to the Ni₂In-type structure at 79 GPa with heating to about 2000 K [8]. Although there are widely high-pressure studies on bulk CaF₂, yet very few experimental studies on nanosized CaF₂ exist for comparison.

Because of the surface effect and quantum confinement effect yielded by the significantly decrease in size, applications of high pressure have proven to be an important tool in tailoring the properties of nanomaterials [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]. Previous high-pressure studies on nanomaterials have revealed a set of novel high-pressure behaviors, which different from that of their corresponding bulk materials. The size effect has a great influence on the phase transition pressure [16,17,18,19], the course of amorphization [21,22,23,24,25], and phase transition routines [26]. Our previous high-pressure X-ray diffraction study revealed that CaF₂ nanocrystals with size of 8 nm transformed from fluorite structure into α-PbCl₂-type structure at 14 GPa, and the high-pressure structure was stable up to 46.5 GPa. The enhancement of structural stability is mainly due to the surface energy differences between the cubic and orthorhombic phases [34]. Beyond that, pressure-induced structural transition of nanosized CaF₂ has no other reports, and the bulk modulus of nanoscale CaF₂ is still not well known. In order to further research the high-pressure behaviors of nanosized CaF₂, and explore the important factors to affect the structural stability of nanomaterials, more experimental data for various sized CaF₂ is urgently needed.

Herein, we present our observations on structural phase transition and compressibility of 23 nm CaF₂ nanocrystals using synchrotron X-ray diffraction measurement. We found that the phase-transition pressure from fluorite to α-PbCl₂-type is lower than that previously reported of 8 nm CaF₂ nanocrystals and closer to bulk CaF₂. The bulk modulus of the 23 nm CaF₂ nanocrystals for the fluorite and α-PbCl₂-type structure are both larger than those of the bulk CaF₂. We believe that the enhancement of bulk modulus is due to higher surface energy. We observed that the as-synthesized CaF₂ nanocrystals contain visible dislocations and defects which could play a dominant role in structural stability.

2. Materials and Methods

The 23 nm-sized CaF₂ nanocrystals were synthesized using the solvothermal synthesis method. 0.5 mmol of Ca(NO₃)₂ and 1 mmol of NaF were dissolved in 10 mL distilled water to form clear solutions, respectively. The two solutions were mixed under full stirring to obtain opaque white suspension. The solution was transferred in to a 40ml autoclave which was filled to 85% of its total capacity with ethanol. Then, the system was kept in an oven at 140 °C for 15 h and cooled in air naturally. The final products were obtained after centrifugation and drying treatment.

The crystalline morphology and particle size of synthesized CaF₂ nanocrystals were examined by transmission electron microscopy TEM (200 KV, H-8100IV; HITACHI, Tokyo, Japan) and high-resolution transmission electron microscopy HRTEM (JEM-2100HR; JEOL, Tokyo, Japan). The sample was loaded into a symmetric diamond anvil cell (DAC) with a culet size of 300 μm for high-pressure characterization, and silicon oil was chosen as the pressure transmitting media. The synthesized CaF₂ nanocrystals were enclosed into a 100-μm-diameter hole of the T301 stainless steel gasket. The shift of the ruby R1 line was utilized to calibrate the pressure. A high-pressure X-ray diffraction experiment was performed at BL15U stations of Shanghai Synchrotron Radiation Facility26 (SSRF, λ = 0.6199 Å). A focused beam size of 3 × 3 μm² was used for data collection. MAR165 CCD detector was utilized to collect the X-ray diffraction data. The distance between the sample and CCD detectors was 173 mm which was calibrated using a CeO₂ standard. FIT2D software was used to process the two-dimensional X-ray diffraction images. The ORIGIN8 and MATERIAL STUDIO programs were adopted to refine high-pressure synchrotron XRD patterns.

3. Results and Discussion

Figure 1 shows that the shape of as-prepared CaF₂ nanocrystals is irregular particle with uniform morphology. Selected-area electron diffraction (SAED) pattern (inset in Figure 1a) shows that the major diffraction rings can be indexed into a cubic structure. Figure 1b displays the corresponding particle size distribution histograms. The distribution is narrow, and the average size is 23 ± 4 nm.

Figure 2b presents XRD spectra for the 23 nm CaF₂ nanocrystals collected by increasing the pressure gradually up to 23.5 GPa. Starting at ambient pressure, three diffraction peaks of CaF₂ nanocrystals together with one peak of the gasket material (marked by star) are observed. As shown in Figure 3a, the Rietveld refinement performed at ambient pressure suggests that the nanocrystals diffraction peaks is a good agreement with belong to the fluorite structure with space group of Fm3m (Rwp = 0.98%, Rp = 0.62%). The fluorite structure was characterized by ‘Ca’ and ‘F’ atoms occupying the (0, 0, 0) and (0.25, 0.25, 0.25) position, respectively. We can clearly observe that a phase transition from fluorite structure to α-PbCl₂-type structure takes place at 9.5 GPa. This phase-transition pressure is lower than that the previously reported 8 nm CaF₂ nanocrystals and closes to bulk CaF₂. At pressures higher than 9.5 GPa, additional diffraction new peaks emerge and intensity increases with increasing pressure. At the same time, the diffraction peaks representing the cubic phase become weak. Figure 4 shows the unit-cell parameters as function of pressure. At 9.5 GPa, the cell parameter and unit cell volume of cubic structure were calculated to be a = 5.35(9) Å and V= 153.93 (3) ų. Meanwhile, we obtain the cell parameters and unit cell volume of the α-PbCl₂-type structure (a = 6.90(1), b = 5.83(7) Å, c = 3.45(6) Å, and V= 139.18 (5) ų). The volume change for the fluorite and α-PbCl₂-type structures is a decrease of 9.6% from the low-pressure structure. Complete phase transformation to the high-pressure phase occurs at 20.2 GPa. It is clearly observed that the cubic fluorite structure still exists in the 10–20 GPa range after the phase-transition pressure at 9.5 GPa. The phase transformation is quite sluggish. The Rietveld refinement performed at 20.2 GPa shows that the XRD experimental datum is in a great agreement with an α-PbCl₂-type cell with space group Pnma (Rwp = 1.09%, Rp = 1.07%) with the unit cell volume of 129.95 (2) ų (Figure 3b). The Ca and F ions of the α-PbCl₂-type structure occupy the positions Ca(0.253, 0.25, 0.109), F1(0.859, 0.25, 0.073), and F2 (0.438, 0.25, 0.834), respectively. The high-pressure α-PbCl₂-type structure can be maintained up to the highest studied pressure of 23.5 GPa in our XRD measurements.

Upon decompression, the original fluorite phase of 23 nm CaF₂ nanocrystals is not recovered when the pressure is reduced to 8.4 GPa. The experimental data point that the transition from orthorhombic to cubic phase exhibits strong hysteresis under decompression. After decompression to ambient condition, the sample retains the α-PbCl₂-type structure with for the peaks attributed to fluorite structure remain in the XRD datum. It indicates that the fluorite and α-PbCl₂-type structure co-exist at the ambient pressure after decompression. This result is in good accordance with the reports on the bulk CaF₂ [4], and the hysteresis might be explained as the inherent sluggish nature of CaF₂. For the reported 8 nm-sized CaF₂ nanocrystals, the high-energy hindrance prevents the transition to the fluorite structure which might be the reason for irreversibility at ambient pressure.

Figure 5 demonstrates the EOS data of CaF₂ nanocrystals to pressures of 23.5 GPa. A third-order Birch-Murnaghan (BM) equation of state (EOS) was fitted to the experimental P−V data [35].

P = (3/2)B₀[(V/V₀)^−7/3 − (V/V₀)^−5/3]{1 + (3/4)(B₀′ − 4)×[(V/V₀)^−2/3 − 1]}

(1)

where V and V₀ are the volumes at pressure P given in GPa and ambient pressure, respectively. For the CaF₂ nanocrystals, we yield the bulk modulus B₀ of 103(2) GPa with B₀′ fixed at 5 for the fluorite structure and B₀ of 78(2) GPa with B₀′fixed at 4 for the α-PbCl₂-type structure. The isothermal bulk modulus of α-PbCl₂-type phase at ambient pressure is lower than the fluorite phase. The lower bulk modulus at high pressure indicates higher compressibility of the high-pressure phase of CaF₂ nanocrystals. This result is consistent with previous studies on bulk CaF₂, but it is different from bulk SrF₂ and BaF₂, which have higher incompressibility under high pressure [8,36]. The bulk modulus of CaF₂ nanocrystals for the fluorite and α-PbCl₂-type structure are both significantly larger than those of the bulk CaF₂ (B₀ = 87(5) and 74(5) GPa) [4,8], indicating the high incompressibility of nanosized CaF₂.

Table 1. Transition pressure (P_T), and equation of state parameters (B₀ and B₀′) of fluorite-type and α-PbCl₂-type CaF₂

Morphology	Size	PT (GPa)	B0 (GPa)		B0′
			Fm3m	Pnma	Fm3m	Pnma
Bulk	Micro	9.5 1	87(5) 1	74(5) 2	5	4.7
		9 3	81(1) 3		5.22
		8.1 4	79.54 4	70.92 4	4.54	4.38
Nanocrystals	8 nm	14 5	--	--	--	--
This work	23 nm	9.5	103(2)	78(2)	5	4

¹ Ref. [4]; ² Ref. [8]; ³ Ref. [41]; ⁴ Ref. [6]; ⁵ Ref. [34].

exhibits the phase transition (P_T) starting pressure and the values of B₀ and B₀′ of CaF₂ materials, which clearly revealed the differences between bulk and nanoscale CaF₂. It was found that the high-pressure behavior of the 23 nm CaF₂ nanocrystals is closer to that in bulk CaF₂. However, the bulk modulus of the CaF₂ nanocrystals for the fluorite and α-PbCl₂-type structure are both larger than those of the bulk CaF₂. This indicates that the CaF₂ nanocrystals exhibit obviously higher incompressibility compared to bulk CaF₂. This behavior is different form the results reported for nanocrystalline SnO₂ and TiO² [37,38]. Compared with bulk CaF₂, a relatively higher surface energy is expected in our CaF₂ nanocrystals. Based on the Hall–Petch effect [39,40], a continuous decrease of grain size could further elevate material hardness, and thus the enhancements in bulk modulus can be easily understood.

Extensive high pressure studies indicated that many nanomaterials—such as PbS, CdSe, and ZnS—exhibit obvious enhancement of structural stability compared with the corresponding bulk materials due to higher surface energy [16,17,18,19]. However, for our 23 nm CaF₂ nanocrystals, the higher surface energy does not contribute to the improvement of structural stability. To the best of our knowledge, defects are considered to be one of the most important factors to affect the transition pressure of nanomaterials. In order to prove our deduction, we present the HRTEM image of the 23 nm CaF₂ nanocrystals at ambient condition in Figure 6. It is clear that our sample contains visible structural impurities like dislocations and defects. These dislocations and defects could act as the weak points and induce stress concentration, so a new high-pressure phase prefers to nucleate at such defect sites. Therefore, 23 nm CaF₂ nanocrystals with structural defects has a reduced nucleation pressure. The distortions and defects of the crystal structure play a dominant role in the structural stability. Wang et al. [19] studied bulk and nano ZnS using synchrotron X-ray diffraction and found that when the grain size is larger than 15 nm, the hosted defect acts to behave similarly to that in bulk; below 15 nm, the defect activities turn silent, and surface energy begins directing the enhancement of structural stability. This high-pressure research on ZnS nanomaterials is similar to our studies on CaF₂ nanomaterials.

4. Conclusions

The structural phase transition and compressibility of CaF₂ nanocrystals with size of 23 nm under high pressure were investigated by synchrotron X-ray diffraction measurement. A pressure-induced fluorite to α-PbCl₂-type phase transition starts at 9.5 GPa and completes at 20.2 GPa. The phase-transition pressure is lower than previously reported that of 8 nm CaF₂ nanocrystals and closes to bulk CaF₂. Upon decompression, the fluorite and α-PbCl₂-type structure co-exist at ambient pressure. The bulk modulus B₀ of the 23 nm CaF₂ nanocrystals for the fluorite and α-PbCl₂-type phase are 103(2) and 78(2) GPa, which are both larger than those of the bulk CaF₂. The enhancement of bulk modulus compared with the corresponding bulk materials is due to higher surface energy. The HRTEM image on the sample clearly shows that the as-synthesized CaF₂ nanocrystals contain visible dislocations and defects which act as the weak points and induce stress concentration. The distortions and defects of the crystal structure play a dominant role in structural stability.