Unusual Compression Behavior of Nanocrystalline CeO₂

Abstract

The x-ray diffraction study of 12 nm CeO₂ was carried out up to ~40 GPa using an angle dispersive synchrotron-radiation in a diamond-anvil cell with different pressure transmitting medium (PTM) (4:1 methanol: ethanol mixture, silicone oil and none) at room temperature. While the cubic fluorite-type structure CeO₂ was retained to the highest pressure, there is progressive broadening and intensity reduction of the reflections with increasing pressure. At pressures above 12 GPa, an unusual change in the compression curve was detected in all experiments. Significantly, apparent negative volume compressibility was observed at P = 18–27 GPa with silicone oil as PTM, however it was not detected in other circumstances. The expansion of the unit cell volume of cubic CeO₂ was about 1% at pressures of 15–27 GPa. To explain this abnormal phenomenon, a dual structure model (hard amorphous shell and relatively soft crystalline core) has been proposed.

Introduction

Nano materials attract much attention not only for their unique enhanced properties, which are different from those of the bulk materials, but also for their fundamental scientific and technological applications. Series of interesting phenomena and novel properties have been revealed when nanosized materials were investigated under high pressures. As an important material in many technological applications including gate for metal-oxide semiconductor devices, ultraviolet (UV) blockers, solar cell, catalysts and solid oxide fuel cells, the rare earth oxide CeO₂, with a cubic fluorite structure, is considered to be important in the high P-T processing of advanced engineering materials^1,2,3,4. Due to its promising technological applications, numerous investigations have been reported on the structure stabilities and compressibility of different sized CeO₂ under high pressure^{5,6,7,8,9,10,11,12,13}. It is reported that the phase transformation pressure of nanosized CeO₂ decreased compared to that of bulk counterpart^8,9, whereas other studies hinted that nano-CeO₂ remains stable to much higher pressures than the bulk^7,10,11,14. Moreover, an anomalous compressive behavior of CeO₂ nanocubes, which is due to the strengthening of the surface Ce-O bonds, was observed by Ge et al.⁵ Therefore, series of interesting phenomena and novel properties have attracted much interest and continuous high pressure investigations are conducting to reveal the details of the behavior of nano-CeO₂.

In this work, we have carried out three high pressure angle-dispersive x-ray diffraction (ADXD) studies to investigate the structure stabilities and compressibility for 12 nm nanocrystalline (nc) CeO₂ with two different and without pressure transmitting medium (PTM). We found that at pressures above 12 GPa, an unusual change in the compression curve was detected in each experiment. Significantly, in the pressure range of 18–27 GPa, suspected negative volume compressibility (NVC) was observed with silicone oil as PTM, however it was not detected in experiment with mixture of methanol-ethanol (M-E) (4:1 by volume) as PTM or without PTM. High-pressure in situ x-ray diffraction experiments showed that the expansion of the unit cell volume of cubic CeO₂ was about 1% at pressures of 18–27 GPa. Based on previous high pressure works, a dual structure model (hard amorphous shell and relatively soft crystalline core) has been proposed. This unusual NVC phenomenon is not really a characteristic for nc CeO₂ itself, but a false appearance induced by the formation and thickens of a stiff shell in nanograin under compression with silicone oil as PTM.

Results

Figure 1 displays angle dispersive x-ray diffraction spectra taken at pressure for the 12 nm CeO₂ with silicone oil as PTM. The patterns for other two experiments are similar with Fig. 1 (shown in Fig. S1). While the cubic fluorite-type structure was retained to the highest pressure, there is progressive broadening and intensity reduction of the reflections due to increasing strain inhomogeneity and microstrains with increasing pressure. Differences in the elastic properties of nanoparticle interiors and their grain-boundary regions, particle aggregation and increased nonhydrostaticity due to unavoidable solidification of liquid pressure media likely account for local strain inhomogeneity, but the peak positions used to determine lattice parameters, which contain the information of macrostrain in the elastic deformation, are not affected¹⁵. Therefore, full XRD spectrum fitting was carried out to obtain the pressure-dependent variations in relative d-spacing (d/d₀) as shown in Fig. 2. Upon initial compression, a consistent shift of angle dispersive x-ray diffraction lines to smaller d-spacings indicates tighter packing of the atoms with compression. When the pressure increases to 15 GPa, there are clearly unusual stiffness changes in the shift of peak positions as a function of pressure with M-E (4:1) or silicone oil as PTM or without PTM. More significantly, obvious shifts toward large d-spacings are observed for all diffraction lines as compared to those at 18.5 GPa under compression with silicone oil as PTM. This tendency continues with further compression and a progressive peak broadening and intensity reduction are accompanied. At pressures beyond 27 GPa, the weak and broad Bragg reflections of the cubic structure start to shift normally to smaller d-scale. Above 39 GPa, both with silicone oil as PTM and without PTM, a weak new peak of the high-pressure phase (α-PbCl₂-type) was faintly visible as shown in Fig. 3, indicating that the cubic fluorite-type structured nc-CeO₂ begins to transform to the high-pressure phase (α-PbCl₂-type).

Figure 1

Integrated in situ XRD spectra at various pressures under compression up to 40 GPa with silicone oil as PTM.

Figure 2

Variation of relative d-spacing (d/d₀) for 12 nm CeO₂ for different Bragg reflections as a function of pressure.

(a) with methanol: ethanol mixture (4:1) as PTM. (b) with silicone oil as PTM. (c) Nonhydrostatic compression.

Figure 3

X-ray diffraction of nano-CeO₂ at the highest pressure under compression with methanol: ethanol mixture (4:1) (a) or silicone oil as PTM (b) and without PTM (c).

The downward arrow (↓) represents the appearance of the most intense peak of the high pressure CeO₂ phase.

Table 1 summarizes the main experimental results of high-pressure studies of CeO₂. The differences in the transition pressures at which the structural transitions occur may depend on the nature of the starting materials and the experimental conditions. Considering the detection methods of the determination of the grain size, this work along with a reanalysis of previous studies on nc CeO₂^{5,6,7,10,11,14,16} allow us to reach consistency among several studies of the size dependence of the phase transitions, that is the nanocrystals exhibit elevated phase transition pressures as compared to bulk materials^6,14,17. This may due to the initial peak broadenings of nanosized starting material and progressive broadening and intensity reduction of the reflections which result from the increasing pressure. Therefore the weak peaks of the high-pressure phase can be identified at higher pressure compared to that for the bulk counterpart.

Table 1 Summary of the main results of high-pressure studies of CeO₂^a

Figure 4 displays the variations of refined unit cell parameters for CeO₂ to 40 GPa under compression. Also shown in the figure are data on previous works. At lower pressures (P < 12 GPa), the compressibilities of nano-CeO₂ samples are similar to bulk-CeO₂. However, abrupt changes in the compression curves were observed in all data for the nanosized samples at P > 12 GPa as shown in Fig. 4. Here we discuss the unusual compressibilities of nano-CeO₂ in two parts, before and after 15 GPa. The pressure-volume (P-V) data for cubic fluorite-type CeO₂ at P < 15 GPa was fitted by using a second-order Birch-Murnaghan EOS (BM-EOS)¹⁸ to more easily compare with previous studies (Table 2). Our measured second-order BM-EOS for 12 nm CeO₂ gives a bulk modulus B₀ = 282(5) GPa with V₀ = 158.64 (0.15) ų under compression with silicone oil as PTM; whereas for nonhydrostatic condition, we obtain a slight higher value B₀ = 289 (13) GPa. It is found that the bulk modulus increases as the particle size decreases to ~10 nm and then decreases in particles less than ~10 nm (Table 2, Fig. S2). Above 15 GPa, clear stiffness changes in the compression curves were observed in all data for the nanosized samples at P > 12 GPa as shown in Fig. 4. Remarkably, negative volume compressibility was observed for 12 nm CeO₂ at P = 21.8–27 GPa with silicone oil as PTM in this study. And the unit cell volume of the cubic CeO₂ was expanded for nearly 1% at pressures of 15.8–27 GPa. With further compression to a critical pressure of about 27 GPa, normal volume contraction recovered and the unit cell volume started to decrease.

Table 2 Bulk modulus of CeO₂ with a series of particle sizes^a

Figure 4

The pressure-dependent variations of the unit cell volume for CeO₂.

Open triangle: 4.7 nm data from Ref. 5; inverted triangle: 5.6 nm data from Ref. 5; star: 10 nm data from Ref. 10; squares (red): 12 nm CeO₂ of this study without PTM; diamonds (blue): 12 nm CeO₂ of this study with silicone oil as PTM; circle (green): 12 nm CeO₂ of this study with M-E (4:1) as PTM; dash line (black): bulk data from Ref. 6.

It is thermodynamically impossible for a closed system to have a negative volumetric compressibility¹⁹. Therefore findings about this phenomenon were disconfirmed as a result of an uptake of additional interstitial molecules^20,21, e.g., hydration²² or the intercalation of a component of the pressure transmitting medium¹⁹. However, in this study, the unusual compression phenomenon is not a result of an uptake of the silicone oil for the NVC phenomenon did not happened for bulk-CeO₂ using the same DAC techniques as illustrated in the supplementary materials (Fig. S3). Since the NVC phenomenon was not observed during nonhydrostatic compression up to 39 GPa, we believe that the nonhydrostaticity is not responsible for the formation of the NVC phenomenon. The overall results together with previous works indicate that the NVC phenomenon observed in this study is related with PTM used and the average grain size of the starting material.

Discussion

Surface atoms are different from those of atoms located inside the crystallites for they have fewer interatomic bonds than those in the bulk²³. Due to the high surface to volume ratio, a nanocrystal cannot be represented uniquely by a unit cell. And the properties of nanocrystalline depend critically on the properties of internal interfaces such as grain boundaries and interphase boundaries²⁴. It is reasonable to interpreted a nanograin as a two-phase system^25,26 where a structurally crystalline core is surrounded by a surface disordered (low density amorphous, LDA) shell at room temperature and pressure. Based on the main experimental and theoretical results as below:

• i First-principles electronic calculations reported by Ge et al. show that the increased bulk modulus of the nanocrystal is due to the strengthening of the surface Ce-O bonds resulting in a much larger shear modulus than in the bulk and consequently hardening the shell surface. In other words, results suggested that the shorter and stronger Ce-O bonds are near the surface of the nanocrystal forming a hard shell which is harder to compress⁵. Here we consider the harden shell surface with shorter an stronger Ce-O, which is different from the initially LDA, as high density amorphous (HDA);

• ii A larger fraction of the atoms belongs to the grain boundaries as the pressure elevated during compression²⁷,

we propose a mechanism here to explain the observed negative volume compressibility in 12 nm CeO₂ by extending the core-shell dual structure model. The initially LDA state will transform to a HDA state upon compression at a critical pressure. In other words, the surface shell get stiffer due to the LDA-HDA transformation under compression as compared to the nanocrystalline core⁵. Further compression, the core atoms near the interface transform to the amorphous state that belongs to the shell. At the same time, the residual core where XRD can detect relaxed due to the thicken of denser shell.

Schematic diagrams for the detailed structure evolution of the nanograin core-shell model under compression are shown in Fig. 5. The surface atoms exist in a form of LDA state upon initial compression and the stress is continuous across the interface between LDA shell and crystalline core (so called isostress condition). The unit cell volume of nc CeO₂ decreases under compression at this stage (I: 0–15.1 GPa). A “hard” HDA shell²⁶ of the individual nanograin comes into being at stage II (P ~ 15.1–21.8 GPa). Due to the support of the “hard” amorphous shell (arching effect), the environment pressure is not timely delivered to the crystalline nanograin core, resulting in a pressure difference between the crystalline core and PTM. In other words, there exists pressure gradient from the HDA shell to the crystalline core (P_i2 < P₂). Unlike isostress condition, the strain is continuous across the interface between HDA shell and crystalline core (isostrain condition) at stage II. Due to the epitaxial effect of HDA at stage III (P ~ 21.8–27 GPa, Fig. 6), further compression can leads more crystalline core atoms, which are near to the shell-core interface, transform to the HDA shell atoms, which is a slow but continuous process²⁸. Meanwhile, the residual crystalline core is relaxed owing to the thickening of HDA shell as the crystalline core has a lower density (longer Ce-O bonds) than that of the HDA shell (shorter Ce-O bonds). That means the increasing environmental P gradually thicken the HDA shell and lessen the volume of the crystalline core where the actual pressure is becoming smaller because of the core's relaxation. In this case, the pressure obtained by ruby R₁-luminescence line shift is the environmental pressure of the nanograins and the pressure corresponding to the unit cell volume of cubic CeO₂ determined from in situ ADXD reflects the inner pressure of crystalline nanograin core. This created an illusion of (environmental) pressure induced unit cell volume expansion of nc CeO₂ at stage III (NVC region). The differential stress between inside and outside the HDA shell increased with compression. In conjunction with Fig. 5a, we may obtain that the maximal differential stress (p_c) which the HDA shell can support is about 17.5 GPa between the crystalline core and PTM. After that the “hard” HDA shell start to yield at ~30 GPa, the unit cell volume decreases with increasing pressure (IV: P > 27 GPa). However, the ADXD observed compression curve of 12 nm CeO₂ in stage IV drifts rightward rather than returns to normal as a result of the differential stress (~17.5 GPa).

Figure 5

(a) The pressure-dependent variations of the unit cell constants. (b) Compression mechanism in nc CeO₂ according to core-shell model, exaggerated for illustrative purposes. I: 0–15.1 GPa, isostress condition between low density amorphous (LDA) shell and crystalline core; II: 15.1–21.8 GPa, LDA → HDA transformations on the shell with compression; III: 21.8–27 GPa, negative volume compressibility region; IV: P > 27 GPa, the NVC phenomenon disappears owing to the yielding of the “hard” shell.

Figure 6

Negative volume compressibility region (III: 21.8–27 GPa).

(a) the light blue and red part: crystalline core; the blue part: HDA shell; (b) the blue part: HDA shell; the red part: residual crystalline core.

According to the above discussion, the unusual NVC phenomenon observed in nc CeO₂ is attributed to the following two conditions: a) a stiff HDA shell can be formed under compression and the caused nano arching effect is strong enough to maintain an apparent stress difference between inside and outside of the shell; and b) part of the relative low density crystalline core atoms can transform to high density shell atoms, which can lower the actual core pressure.

For the first condition, it depends on the external environment and the intrinsic properties of the nanograin. With regard to the external environment, the degree of hydrostaticity plays an important role to maintain the HDA shell. When pressure acts on the core-shell structure, it is easier for the uniaxial pressure to break the shells due to the shear stress, whereas the shells could endure much higher hydrostatic pressure since the applying force is isotropic. As the grain core size is reduced a larger fraction of the atoms belongs to the grain boundaries, the pressure thicken the HDA shell under hydrostatic compression. However, under nonhydrostatic compression, the grain cores immediately experience the compression because the shells were smashed at lower pressure. On the other hand, when the shells were subjected to the hydrostatic compression, the thickening HDA shell was able to sustain higher pressure^26,27,29,30. Therefore, as shown in Fig. 4, the pressure evolution of cell volume under nonhydrostatic compression exhibits unusual (work hardening) behavior immediately after the formation of the HDA shell at P > 12 GPa. However, the nonhydrostaticity in the chamber destroy the HDA shell upon further compression.

Nanoparticles have a tendency to strongly aggregate for the high surface-to-volume ratios. Using a soft PTM will not provide hydrostatic compression of all the particles and the intergrain contacts will lead anyway to strong shear stresses even if the medium is still hydrostatic³¹. It is well known that silicon oil is a poor PTM, being “quasihydrostatic” only up to 3 GPa³². In fact, the bad hydrostaticity character of silicon oil might be the reason why the NVC could be observed. Ideally, the PTM will be located between the grains, hindering the grains to touch each other, phenomenon that will provoke strong uniaxial strains and transmit the pressure to the inner crystalline core. However, good PTM like helium or neon are too soft to hinder the grains to touch each other, which would have the same effect than no PTM. Therefore, the compressibility for experiments used M-E as PTM, both previous works and our experiment, are similar to that of no PTM.

When it comes to the intrinsic properties of the nanograin, it depends on the strength and thickness of the shell, as well as the size of individual nanograin. After the formation of the hard amorphous shell, every grain can be viewed as a perfect spherical shell under uniform external pressure for simplicity's sake. For a perfect spherical shell, there are two possible failure modes (the HDA shell is yield or break). One is the maximum stresses reaching the yield condition and then yielding zone spread leading to final plastic collapse and the other is elastic or elastic-plastic buckling leading to collapse³³.

The maximum stress (p_c) supported by the hard HDA shell can be calculated by the following formula³⁴:

where

E = modulus of elasticity, GPa;

r = shell thickness, nm;

d = particle diameter, nm;

k = constant.

Here we make a qualitative discussion using the simplest type, therefore k is a certain coefficient without an exact value.

As reported in this work, p_c is about 17.5 GPa as the grain size is ~12 nm for CeO₂. The estimated maximum stress p_c for 12 μm CeO₂ is then ~0.18 bar, for the case where the HDA thickness r contribution has been neglected in equation (1). If it was to be included, then the maximum stress p_c may be far less than 0.18 bar. This demonstrates that p_c could be ignored as it is only 0.18 bar, which is comparable with the error brought by pressure standard. Let alone the fine crystallinity for micron materials on the surface which will hinder the shape up of HDA shell. Since the spherical shell is becoming a failure mode, the NVC phenomenon won't happen for 12 μm CeO₂.

The compression curve will be hardening after the formation of the stiff HDA shell that is strong enough to maintain an apparent stress difference between inside and outside of the shell for smaller grain size particle. However, whether NVC phenomenon will happen or not is depend on the second condition, since the initial nanocrystalline core should be larger than the critical nucleus as the size of any stable single crystal cannot be infinitely small. Fig. 7 illustrates this point. The critical diameter for nucleation and growth of the HDA phase is δ. When the grain diameter d = 5δ as shown in Fig. 7a, the lower compressibility occurs when the first shell formed and the NVC take place when the second shell comes into being; however, as shown in Fig. 7b (d = 3δ), nothing but the lower compressibility occurs when the one and only first shell formed. This may be the reason why, without NVC phenomenon, only lower compressibility of 4.7 nm (5.6 nm) CeO₂ at P > 10 GPa (16 GPa) was observed in Ref. 5.

Figure 7

Schematic diagrams for small grain size effect on abnormal compressibility.

d is grain size and δ is the critical diameter for nucleation and growth of the HDA phase. (a) d = 5δ. (b) d = 3δ.

Therefore, the NVC phenomenon may only be observed in nanomaterials with an average grain size around a critical dimension d_c. A potentially interesting subject for future high pressure studies of nanostructured materials is to check whether there is an indeed critical grain size d_c around which NVC would happen by a mechanism result from the dual structure model. On the other hand, the unusual structural stability and hardening of longitudinal modulus^9,35,36 for many nanostructured materials like nc CeO₂ under compression may also be rationalized by the hard-shell model mentioned above.

However, we present an analysis of such a structure under ideal conditions. Particle aggregation, dislocation activity in the grains, sliding motions at grain boundaries and increased nonhydrostaticity due to unavoidable solidification of liquid pressure media will hinder the shape up of, even break the HDA shell. Anyhow, this peculiar hard-shell structure is still suggested to be responsible for the observed increasing strength and toughness in some materials as the grain size decreases from micro to nano- scale.

In summary, we have identified the occurrence of “negative cell volume compressibility” in 12 nm CeO₂ via the use of in situ angle-dispersive synchrotron XRD. While the nanoscale CeO₂ has XRD characteristic of cubic fluorite phase up to ~40 GPa, the expansion of the unit cell causes a negative volume compressibility of the material under quasihydrostatic compression. This unusual behavior can be attributed to the formation and thicken of the stiff high density amorphous shell under compression, which causes a strong nano arching effect and lowers the actual crystalline core pressure for the individual nano grain.

Methods

Materials

The commercial nanocrystalline CeO₂ used in this study was purchased from Nanostructured & Ammorphous Materials Incorporated. The structure of the starting material was confirmed to be pure cubic fluorite phase (Fm3m) CeO₂ by ambient-pressure x-ray diffraction (XRD). The Scherrer formula has been used to deduce an average particle size of 12 nm from the (111), (200), (220), (311), (222), (400), (331), (420) and (422) diffraction linewidths, consistent with the value (12 ± 3 nm) of the dimension of the platelet grains discerned in the TEM micrograph of Fig. 8a.

Figure 8

(a) Transmission electron micrograph (TEM) of ~12 nm nc CeO₂. (b) An example of Rietveld refinement for nc CeO₂ under quasihydrostatic compression (P = 0.1 GPa, a = 5.410129(74) Å, V = 158.3517(65) ų).

DAC experiments

A modified Mao-Bell type DAC with a culet size of 300 μm was used to generate high pressures up to ~40 GPa. A piece of ~20-micron sample in thickness was loaded into a 100 μm diameter hole of a stainless steel (T301), which was preindented to 40 micron thickness. The thickness of squeezed sample powder at the highest pressure (~35 GPa) should be less than the gap between the diamond anvils. We conducted three separated experiments using the same starting material. In the first or second run, M-E (4:1) or silicone oil was used as a PTM and the internal pressure was measured using the ruby fluorescence lines³⁷. In the third run, no PTM was used to achieve a maximum nonhydrostatic stress and a small amount of gold powder (<2%) was included to determine the pressure, using the equation of state of gold³⁸.

X-ray diffraction measurements

In situ high pressure angle dispersive diffraction experiments were performed at the High-Pressure Station, 4W2 beamline at Beijing Synchrotron Radiation Facility (BSRF). The x-ray was monochromatized to 0.6199 Å using double crystal (silicon 220). All of the measurements were conducted at room temperature. The two dimensional diffraction patterns were integrated by Fit2D³⁹ obtain the 2θ intensity curves, which were then analyzed by GSAS + EXPGUI Rietveld package^40,41 (Fig. S4) and PeakFit (Fig. 8b).