Nanoscale inorganic materials with unique electrical, optical and mechanical properties, which are distinct from their bulk counterparts, attract attention in both fundamental scientific research and industrial applications^[1-3]. Investigations on the phase transformation and the structural stability of nanomaterials under high pressure are conducted in physics, materials science, geophysics^[4-9]. Numerous studies on nanomaterials under high pressure have revealed that the grain size plays an important role in the pressure-induced phase transition behaviors. A number of interesting high-pressure behaviors and new properties in nanomaterials appear when the grain size is smaller than a critical size. Studies on CdSe, CdS, ZnO and ZnS nanocrystals observe the size-dependent phase transformations^[10-13]. Lv, et al. ^[14] reports that the Mn₃O₄ nanoparticles show a different phase transformation route and a new high-pressure phase at 14.5–23.5 GPa, which has been recognized to be the orthorhombic CaTi₂O₄-type structure. The crystalline-amorphous transition is discovered in materials such as Y₂O₃, TiO₂, PbTe and BaF₂^[15-19]. Therefore, high-pressure studies on nanomaterials are significant for the discovery of new structures and properties of materials.

Calcium fluoride (CaF₂), a typical face-centered-cubic ionic crystal, has been widely used in many fields^[2-3]. Due to its simple crystal structure, CaF₂ becomes an ideal material for high-pressure research. High-pressure X-ray diffraction (XRD) and Raman spectroscopy studies of bulk CaF₂ have shown that it undergoes two structural transitions and finally reaches highly coordinated structures. The pressure-induced phase transition from the fluorite structure (space group: Fm3m) to the α-PbCl₂-type structure (space group: Pnma) has been found in the pressure range of 8–10 GPa^[20-21]. Dorfman, et al.^[22] have reported that bulk CaF₂ transforms from the α-PbCl₂-type structure into the hexagonal structure at 79 GPa and 2 000 K. Inspired by the size effect of nano-sized materials, our group has made progresses in different structural phase transitions and in the compressibility for nanosized MF₂ (M=Ca, Sr, Ba) particles at high pressures^{[19, 23-26]}. Previous high-pressure studies on the 8 nm CaF₂ nanocrystals reveals that the structural phase transition from the fluorite-type structure into the orthorhombic α-PbCl₂-type structure starts at 14 GPa, and the transition pressure is higher than that of the bulk CaF₂^[23]. Recently, we have performed high-pressure studies on the 23 nm CaF₂ nanocrystals up to 23.5 GPa using synchrotron XRD measurement. We have found that the transition from the fluorite to the orthorhombic phase occurrs at 9.5 GPa, significantly lower than the transition pressure of the 8 nm CaF₂ nanocrystals, but close to that of the bulk materials^[24]. Further analysis indicates that the defect effect in the 23 nm CaF₂ nanocrystals plays a key role in the structural stability. Nevertheless, the high pressure induced structural phase transition of the CaF₂ nanocrystals with other sizes has not been reported. The phase-transition mechanism and the compressibility of the nanoscale CaF₂ are still unclear. In order to further investigate the high pressure behaviors of the nanosized CaF₂, and to confirm whether there is a size-dependent phase transformation at high pressure, more high pressure experimental data for various sized CaF₂ nanocrystals is urgently needed.

Here we investigate the high-pressure behaviors of the CaF₂ nanocrystals with an average grain size of 11 nm using in-situ XRD. We analyse the phase stability, the bulk modulus and the compressibility of the synthesized 11 nm-sized CaF₂ nanocrystals in details. Through comparing the high pressure experimental data of different sized CaF₂ materials, the main factor influencing the structural stability and compression properties of the CaF₂ nanomaterials is explored.

1. Materials and Methods

The 11 nm-sized CaF₂ nanocrystals were prepared by a typical synthesis procedure, as reported in literatures^[27-28]. 2 mmol Ca(NO₃)₂ and 4 mmol NaF were added into a mixture which consisted of ethanol, oil acid, and sodium hydroxide. After being vigorously stirred, the white suspension was transferred into a 40 mL autoclave. The heat-treatment condition at a temperature of 160℃ was maintained for 24 h. Then, the autoclave was cooled down to room temperature, and the final products were collected after centrifugation and drying treatments.

The crystalline structure, the morphology and the particle size of the CaF₂ nanocrystals were examined by XRD (D8 DISCOVER GADDS) with Cu K_α radiation ($\lambda $=1.5418 Å) and by high-resolution transmission electron microscopy (HRTEM, H-7500). The sample was loaded into a diamond anvil cell (DAC) with a culet size of 400 μm for high-pressure analysis. The fluorescence shift of the ruby R1 line was utilized to calibrate the pressure, and an methanol-ethanol mixture with a volume ratio of 4∶1 was chosen as the pressure-transmitting medium. High-pressure XRD experiment was performed at B2 High-Pressure Station of Cornell High Energy Synchrotron Source (CHESS) with a wavelength of 0.485946 Å. MAR165 CCD detector was used to collect the XRD data. The 2D XRD images were integrated using FIT2D software. Materials Studio program was performed to refine the crystal structure using the high-pressure synchrotron XRD patterns.

2. Results and Discussion

Fig.1(a) exhibits the dimension and the morphology of the synthesized CaF₂ nanocrystals, and the corresponding particles’ size distribution histogram is presented in Fig.1(b). Fig.1 reveals that all the nanoparticles are well dispersed and almost sphere with an average diameter of (11 ± 2) nm. The selected-area electron diffraction (SAED) pattern (inset in Fig.1(a)) shows that the major diffraction rings of the fluorite structure, indicating that the synthezied CaF₂ nanocrystals have probably the fluorite structure.

Figure  1.  (a) TEM image of the as-synthesized CaF₂ nanocrystals; (b) particle size distribution of the CaF₂ nanocrystals

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Fig.2 presents the Rietveld refinement of the diffraction pattern of the synthesized CaF₂ nano-particles at ambient conditions. The great agreement between simulations and XRD experiments at ambient conditions with the residuals R_wp=7.73% and R_p=5.99% unraveled that the ambient pressure phase adopts a fluorite structure with a space group of Fm3m. The fluorite structure is constructed by the Ca atoms occupying the (0, 0, 0) positions and by the F atoms occupying the (0.25, 0.25, 0.25) positions. The cubic structure has an lattice constant of 5.461(2) Å. It is consistent with the value of a₀=5.463 Å (JCPDS Card No. 35-0816).

Figure  2.  Rietveld refinement of the diffraction pattern of the synthesized CaF₂ nanoparticles (Red dots, upper (blue), and lower (black) solid lines represent experimental, calculated, and residual patterns, respectively.)

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Fig.3 displays the selected high-pressure XRD patterns of the CaF₂ nanocrystals under different pressures up to 28.6 GPa. At 1.0 GPa, six diffraction peaks of (111)_c, (220)_c, (311)_c, (400)_c, (331)_c and (422)_c of the CaF₂ nanocrystals are observed, together with one peak of the T-301 stainless steel gasket (marked by asterisk). When the pressure reaches 12 GPa, the (111) diffraction peak becomes asymmetric, and a new diffraction peak starts to appear at the right side of the (111) peak, which indicates the occurrence of a phase transition from the fluorite structure to the α-PbCl₂-type structure. The transition pressure is much higher than the one reported in the bulk CaF₂ materials and slightly lower than that of the 8 nm-sized CaF₂ nanocrystals^[23]. When the pressure increases to 20.8 GPa, all the diffraction peaks (120)_o, (111)_o, (121)_o, (211)_o, (031)_o, (002)_o and (240)_o can be assigned to the arised high pressure phase, illustrating the completion of the phase transition. The α-PbCl₂-type structure is stable up to 28.6 GPa (the highest pressure in this study). Then the sample is decompressed to ambient pressure, and it turns out that the pure high-pressure α-PbCl₂-type structure is retained, which indicates the phase transformation is irreversible. Fig.4 presents the Rietveld refinement of the diffraction pattern of the CaF₂ nanocrystals at ambient conditions after decompression, and it shows a quite good agreement with the α-PbCl₂-type structure (with the residual R_wp=0.40 %).

Figure  3.  High-pressure XRD patterns of the CaF₂ nanocrystals, in which the peak (marked by asterisk) is derived from the gasket

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Figure  4.  Rietveld refinement of the diffraction pattern of the CaF₂ nanocrystals at ambient conditions after decompression (Red dots, upper (blue), and lower (black) lines represent experimental, calculated, and residual patterns, respectively.)

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Fig.5 shows the compressibility of the CaF₂ nanocrystals. A third-order Birch-Murnaghan (BM) equation of state (EOS) is fitted to the experimental p-V data^[29]

Figure  5.  Unit-cell volume as a function of pressure determined for the 11 nm-sized CaF₂ nanocrystals (Solid curves are the Birch-Murnaghan EOS fits to the experimental data. Error bars are observed when they are large enough to exceed the sizes of the marked dots.)

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where V₀ is the zero-pressure volume, V is the volume at pressure p given in GPa (V₀ and V were calculated by JADE program), B₀ is the isothermal bulk modulus, ${{B}}_0'$ is the first pressure derivative of the bulk modulus. For the CaF₂ nanocrystals, the fitting yield B₀ = 109(5) GPa, ${{B}}_0'$ = 5 for the fluorite structure, and B₀ = 89(1) GPa, ${{B}}_0' $ = 4 for the α-PbCl₂-type structure. The isothermal bulk modulus of the α-PbCl₂-type phase is lower than that of the fluorite phase. The lower bulk modulus of the high-pressure phase of the CaF₂ nanocrystals at high pressure indicates a higher compressibility. This result is consistent with the previous studies on the bulk CaF₂, but it is different from the bulks SrF₂ and BaF₂ which have lower compressibility under high pressure^{[22, 30]}. The bulk moduli of the 11 nm-sized CaF₂ nanocrystals for the fluorite and the α-PbCl₂-type structure are both significantly larger than those of the bulk CaF₂^[21–22] and the 23 nm-sized CaF₂ nanocrystals^[24], indicating a higher incompressibility for the CaF₂ nanocrystals with smaller grain size. In terms of the Hall-Petch effect^[31-32], a continuous decrease of grain size could further elevate material hardness, thus, the increase in bulk modulus of 11 nm-sized CaF₂ nanocrystals can be easily understood.

Table 1 summarizes the phase transition pressure (p_T), the EOS parameters (B₀ and $B_{0}'$) of the bulk CaF₂ and the CaF₂ nanocrystals with different grain sizes, which clearly reveals the differences between the bulk and the nanoscale CaF₂. It is found that the phase transition pressure and the bulk modulus of the 11 nm-sized CaF₂ nanocrystals are higher than those of the bulk CaF₂ and the 23 nm-sized CaF₂ nanocrystals. A large number of high pressure investigations indicate that many nanomaterials (e.g., CdSe, ZnS and PbS) exhibit obvious elevations of structural stability compared with their bulk materials, which is attributed to the higher surface energies in nanomaterials^{[10, 13, 33]}. Compared with the bulk CaF₂ and the 23 nm-sized CaF₂ nanocrystals, a relatively higher surface energy is expected for the 11 nm-sized CaF₂ nanocrystals, and thus the elevations both in the transition pressure and in the bulk modulus can be easily understood.

Table  1.  Transition pressure (${p}{_{\rm T}}$), and EOS parameters (B₀ and B₀ ′) of the fluorite-type and the α-PbCl₂-type CaF₂

Morphology	Size	$p{_{\rm T}} $/GPa	${B{_0 } } $/GPa			B0 ′
			Fm3m	Pnma		Fm3m	Pnma
Bulk	Micro	9.5[21]	87(5) [21]	74(5) [22]		5	4.7
		9[34]	81(1) [34]			5.22
		8.1[20]	79.54[20]	70.92[20]		4.54	4.38
Nanocrystals	8 nm	14[23]	112(6)	93(9)		5	4
	23 nm	9.5[24]	103(2) [24]	78(2) [24]		5	4
	11 nm	12	109(5)	89(1)		5	4

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Besides the different high-pressure behaviors with the bulk CaF₂ and the 23 nm-sized CaF₂ nanocrystals, Table 1 shows that the 11 nm-sized CaF₂ nanocrystals exhibit a lower transition pressure^[23] and a lower bulk modulus compared with the 8 nm-sized CaF₂ nanocrystals. To the best of our knowledge, defects and grain size are considered to be the main factors in influencing the high-pressure behaviors of the 11 nm-sized CaF₂ nanocrystals and the 8 nm-sized CaF₂ nanocrystals. For further analyses, we have carried out HRTEM measurements of many grains of the 11 nm-sized CaF₂. The HRTEM image is given in Fig.6, it shows that the 11 nm-sized CaF₂ nanocrystals have no visible defects and dislocations, indicating a relatively low defect concentration. Obviously, the decrease of the transition pressure in the 11 nm-sized CaF₂ nanocrystals cannot be attributed to the defects (or dislocation) effect. Therefore, the differences in the phase transformations between the 11 nm and the 8 nm-sized CaF₂ nanocrystals may be caused by the grain size effect. The 8 nm-sized CaF₂ nanocrystals, which have a smaller grain size, possess a higher surface energy, that could result in the elevation of the phase transition pressure.

Figure  6.  HRTEM image of the as-synthesized 11 nm-sized CaF₂ nanocrystals.

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Our results illustrate that the transition pressure dramatically increases as the size of the grains decreases, and the CaF₂ nanocrystals show a noticeable size-dependence of phase transformation at high pressure when the grain size below 11 nm. Therefore, it can be reasonably concluded that the critical size of the CaF₂ nanocrystals, marking the oneset of nanoscal effect, is larger than 11 nm. For the 11 nm-sized CaF₂ nanocrystals, the high-pressure metastable structure (α-PbCl₂-type structure) is retained after the pressure is released, without observing the fluorite structure. This result is in good accordance with the oberservation for the 8 nm-sized CaF₂ nanocrystals^[23], but it is different with those of the bulk CaF₂ and the 23 nm-sized CaF₂ nanocrystals whose transformations are completely or partially reversible^{[21, 24]}. The inreversibility of the 11 nm-sized CaF₂ nanocrystals might be due to the high surface energy, which lead to the solid-solid phase transition hysteresis after decompression. Discovering novel high-pressure metastable structure is one of the main purposes of the high pressure study of the CaF₂ nanocrystals.

3. Conclusions

In summary, the high-pressure behaviors of the CaF₂ nanocrystals with an average grain size of 11 nm have been investigated by in-situ XRD. The phase transition from the fluorite structure to the α-PbCl₂-type structure occurrs at 12 GPa, which is much higher than the value observed for the bulk CaF₂ and slightly lower than that of the 8 nm-sized CaF₂ nanocrystals. The bulk moduli of the CaF₂ nanocrystals with the fluorite or the α-PbCl₂-type structures are all larger than those of the bulk CaF₂, indicating a high incompressibility of nanosized CaF₂. The pure α-PbCl₂-type metastable structure is retained in the 11 nm-sized CaF₂ nanocrystals after decompression. Such distinct high-pressure behaviors of the 11 nm-sized CaF₂ nanocrystals are considered to be mainly due to the grain size effect. When the size is below the critical size, the high surface energy begins directing the enhancement of the structural stability and the increase of the bulk modulus.