Pressure-Induced Structural Transition Trends in Nanocrystalline Rare

Article pubs.acs.org/JPCC

Pressure-Induced Structural Transition Trends in Nanocrystalline Rare-Earth Sesquioxides: A Raman Investigation Nita Dilawar Sharma,* Jasveer Singh, Aditi Vijay, K. Samanta, S. Dogra, and A. K. Bandyopadhyay Pressure and Vacuum Standards, National Physical Laboratory, Dr. K. S. Krishnan Road, New Delhi 110012, India ABSTRACT: The article presents a concise review of our investigations on the preferred transition paths followed as well as high-pressure-induced structural changes in nanocrystalline rare-earth sesquioxides that include Y2O3, Sm2O3, Gd2O3, Eu2O3, Dy2O3, Ho2O3, and Yb2O3. The starting phase in all samples was predominantly cubic, as characterized using X-ray diffraction and Raman spectroscopy. The pressure-induced structural changes were primarily tracked via changes in phonon modes in the Raman spectra. The structural transition sequences demonstrated behaviors differing from the polycrystalline trends usually observed; however, it was interesting to note that the onset pressures and subsequent shifts in the phonon modes followed a trend similar to the unpressurized samples when observed with respect to the f-electron number. The mode Grüneisen parameters were estimated from the high-pressure data, which indicated a swifter response to external stimuli as the particle size reduced below an average of 50 nm. It was also inferred that the presence of traces of disordered/nonstoichiometric material directly affected the structural transition sequence. A summary of the results and the mechanisms leading to such structural transitions is discussed. fine polishing, catalytic converters and catalysis, high-efficiency luminescent materials (for flat panel displays, plasma displays), red powder activation of color TV, sintering aids, rare earth magnets, control rod material for fast breeder reactors, and so on.8,9 Dy2O3 in nanoform has potential to be used as a dopant for fluorescent materials, as glass material with a Faraday rotation effect for optical and laser-based devices, as magnetooptical recording material, and for materials with a large magnetostriction.10 Various types of experimental techniques have been used to study the behavior of this series; however, to investigate the interplay between local lattice fluctuation effects and long-range ordering, Raman scattering technique is one of the best experimental tools. Raman spectroscopic study distinctly identifies many interesting phenomena such as metal−insulator transition, structural progressions, charge transfer, orbital and spin ordering, properties of nanomaterials, and so on. Because interatomic interactions can be altered by temperature, chemical substitution, and pressure, the Raman scattering investigations under the influence of these external effects reveal many important aspects of structural and physical properties of rare-earth sesquioxides; however, the overall effect of the change of interatomic space by temperature or chemical substitution is very small compared with the effect brought about by the application of external pressure. Because of the change of pressure, there is an increasing overlap of the electron cloud, which brings about a rearrangement of band

1. INTRODUCTION The rare-earth sesquioxides have been the subject of great interest owing to the fact that these compounds are quite important, scientifically as well as technologically.1,2 They exhibit various polymorphic forms with structures from cubic, monoclinic, hexagonal, and so on under different external conditions.3−6 Furthermore, in the form of nanoparticles they exhibit other modified properties and behavior that require extensive studies. It is known that the ground state of the rare earth atoms in these sesquioxides [Ln2O3] is in the trivalent [Ln3+] configuration except Ce metal, which oxidizes in the tetravalent Ce4+ configuration. From Nd onward, all rare-earth oxides, with the exception of Tb, occur naturally as Ln2O3, but Tb oxide occurs naturally as Tb4O7 and transforms into TbO2 under positive oxygen pressure. As far as the crystallographic structure of these compounds is concerned, under ambient temperature and pressure, they are known to exist in three structural modifications that are designated as A, B, and C, corresponding to hexagonal (in most cases space group P3m1), monoclinic (in most cases space group C2/m) and cubic phase (in most cases space group Ia3), respectively. The cubic phase unit cell has bixbyite structure that contains 16 molecules of Ln2O3 (Th7Ia3), and the resulting structure has 24 Ln3+ ions on sites with C33i(S6) symmetry.7 In the form of nanostructures, these rare-earth sesquioxides hold potential as highly functionalized materials as a result of both enhanced surface area and quantum confinement effects. These nanosized rare-earth sesquioxides have shown potential for a wide variety of possible applications, including fuel cells, solid-state light-emitting devices or as luminescent probes in immunoassays, chemical−mechanical polishing (CMP), ultra© XXXX American Chemical Society

Received: February 29, 2016 Revised: May 9, 2016

A

DOI: 10.1021/acs.jpcc.6b02104 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. AFM micrographs for the samples investigated along with bar graphs for the estimation of particle sizes using the “Image tool” software.

subjected to any pretreatments. The phase characterizations at ambient were carried out using X-ray diffraction and atomic force microscopy apart from Raman spectroscopy. The samples were subjected to high pressures in a Mao-Bell-type diamond anvil cell with ruby crystals as pressure markers. The structural transitions were primarily investigated using changes in the phonon modes of the samples tracked using a single-stage Jobin Yvon Spex Raman spectrometer with 514.5 nm line of an Ar ion laser. The details of the characterizations at ambient have already been reported in detail elsewhere,11−16 which reveal that the sesquioxides are cubic in structure at ambient with particle sizes ranging from an average of 34 nm for Gd2O3 to 96 nm for Yb2O3; however, Sm2O3, Eu2O3, and Ho2O3 were also found to have very slight traces of either nonstoichiometric or monoclinic phases, which were revealed either through X-ray diffraction pattern, XPS, or Raman spectra under ambient conditions.12,13,16 It was established that the samples under atmospheric pressure were nanocrystalline in nature through atomic force micrographs as well as X-ray diffraction studies. Figure 1 shows the atomic force micrographs of most of the samples investigated along with the bar charts for the particle size analysis carried out using “Image tool” software. The average particles sizes were estimated to be ∼70 nm for Y2O3, 45−50 nm for Sm2O3, 60−70 nm for Eu2O3, 20−40 nm for Gd2O3, 60 nm for Dy2O3, 50 nm for Ho2O3, and finally 96 nm for Yb2O3.

structure, leading to band overlap metallization in otherwise semiconductors or insulators, which is reflected through electrical, optical, and many other properties. The free energy of the system often assumes minimum for a spatial arrangement of the atoms different from the initial, resulting in a structural phase transition. Hence, the high-pressure behavior of these materials is expected to give insight into some of the above factors governing the variation in the structural changes. With the application of pressure the expected normal transition sequence goes from cubic to monoclinic to hexagonal; however, transition route of these sesquioxides is expected to alter when these sesquioxides are in the form of nanoparticles. In view of these we have been investigating the pressure induced effects when these samples are in the form of nanoparticles and present a summarized account of the evolution of these strategic materials under the influence of pressure. This article discusses the results we obtained for nanocrystalline Y2O3, Sm2O3, Eu2O3, Gd2O3, Dy2O3, Ho2O3, and Yb2O3. The investigations were carried out at ambient temperatures. The details of each sample have already been published; however, the present article focuses on the transition trends down the series in detail, which become apparent on analyzing the results relatively.

2. MATERIALS AND METHODS The samples investigated include rare-earth sesquioxides Y2O3, Sm2O3, Gd2O3, Eu2O3, Dy2O3, Ho2O3, and Yb2O3. All samples were procured from M/s Johnson Matthey, U.K. and were not B


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3. RAMAN STUDIES AT AMBIENT According to the group theory, the Raman modes of the ideal cubic Ln2O3 are as follows17 4A g + 4Eg + 14Tg

shift with increase in f-electron number. The Tg mode is observed at 377.8 cm−1 for Y2O3, 343.5 cm−1 for Sm2O3, 336 cm−1 for Eu2O3, 362 cm−1 for Gd2O3, 374 cm−1 for Dy2O3, 375 cm−1 for Ho2O3, and 363.8 cm−1 for Yb2O3. A number of other relatively weaker bands are also observed and are tabulated in Table 1. The corresponding most probable assignments are also listed in Table 1. The phonon modes for these sesquioxides and oxides have been discussed in detail elsewhere.12−16 Figure 3

That is, there are four Ag or the Raman-active symmetric stretching vibrations, four Eg or the Raman-active symmetric doubly degenerate bending vibrations, and 14 Tg or the Ramanactive triply degenerate symmetric stretching vibrations, and hence, in total there are 22 Raman bands; however, smaller numbers of modes are observed in the actual Raman spectra. This is possible due to the fact that some of the observed modes are actually superposition of closely spaced different type of modes, which are unseparated owing to weak factor− group interactions.7 It is observed that Tg mode is usually assigned as the major peak obtained from the samples. Sometimes Ag plus Tg combination also contributes. Because the strong Raman intensity measured for this band indicates a large polarizability change during the vibration; therefore, these bands are expected to be more sensitive to changes in chemical bonding in the series and highly indicative of the structural variations suffered by the sample under the influence of external factors such as pressure or temperature. Figure 2 shows the Raman modes observed at ambient for all samples, and as discussed, the most intense Tg mode shows a

Figure 3. Comparison of the most prominent Tg mode positions observed for the current nanocrystalline samples.

graphically depicts plot of the frequency variation of the prominently observed Tg modes for the nanocrystalline sesquioxides for our studies.18 It is clearly seen that excluding Y2O3, which has zero f electrons, the Raman frequencies shift to higher wavenumbers with the increasing number of f electrons, in a sequential manner except for Eu2O3 with 6 f electrons and Yb2O3 with 13 f electrons. This general trend of increasing wavenumber, in the present case from Sm (f = 5) to Yb (f = 13) across the period has been explained in terms of lanthanide contraction, which is caused by an increase in the effective nuclear charge across the series due to the poor shielding ability of 4f electrons. With an increase in nuclear charge, all electrons get pulled in closer so that the radii of the rare-earth ions decrease slightly, while in contrast the radii should have increased with the increasing charge across the period. The lower value of wave numbers for Eu2O3 and Yb2O3 has been attributed to the reduction of the force constant, which could be associated with unique electronic structures that broaden the potential well.

Figure 2. Raman spectra of the samples under ambient conditions. The peak identifiers are listed in Table 1 along with their possible assignments.

Table 1. Phonon Modes and Their Assignments for the Studied Samples under Ambient Conditions mode I1 I2 I3 I4 I5 I6 I7 I8 I9 I10

Y2O3 (cm−1)

Sm2O3 (cm−1)

316 331

262 295

377.8

343.5

433

383 417 465

470.8 592

Eu2O3 (cm−1)

Gd2O3 (cm−1)

Dy2O3 (cm−1)

Ho2O3 (cm−1)

Yb2O3 (cm−1)

assignment (refs 17 and 18)

266.4 295 311.4 336 354 380 409.7 459 483

274 317

273 327.5

362

374

314.7 330 354.5 375

269.6 310.9 337.5 363.8

398

420

433.8

447 489 568

464

469.6

Tg+Eg Eg Γel(C3i) Tg(+Ag) B-phase Ag Tg B-phase Ag Tg

585

588.7

613.5

Tg

C


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phase phonon modes at and above 12.62 GPa. Sm2O3 showed a weakening of cubic phase peaks, while monoclinic phase peaks gained significant intensity at a pressure of 6.79 GPa. In the latter sample, as a result of increase in pressure, the system progressed toward a mixture of monoclinic and amorphous disordered state at the expense of the starting cubic phase, which again remained irreversible.13 Eu2O3 showed similar behavior and underwent an early transition.12 It was observed that the material underwent a structural change from cubic to monoclinic structure with an onset transition pressure at ∼2.1 GPa and completed at ∼8 GPa. The XRD studies also showed that above ∼2.0 GPa the peaks corresponding to monoclinic phase emerged, which showed a slight increase in preferred orientation as the pressure increased.12 Dy2O3, also cubic at ambient, turned into hexagonal structure with increase in pressure.14 Under ambient conditions, the cubic phase Tg peak occurring at ∼374 cm−1 steadily shifted to higher wavenumbers. At 14.6 GPa, another broad band started developing around 542 cm−1, which split into two distinct peaks corresponding to the hexagonal structure as the pressure was further increased. Ho2O3, with traces of disordered monoclinic phase at ambient, went into monoclinic phase. At a pressure of ∼17.8 GPa, the predominant cubic phase peak completely disappeared. In fact, at the highest studied pressure of ∼28.8 GPa, most other peaks disappeared, and the peaks that remained were the result of monoclinic phase.16 Yb2O3 showed transition to hexagonal phase from the initial cubic phase. The cubic Yb2O3 transformed to the hexagonal phase at 20.6 GPa; however, the mixed phase of cubic and hexagonal was identified at and above ∼12.8 GPa. The phase transition was irreversible as observed after release of pressure. In the hexagonal phase that belongs to the space group P3m1 (D33d), the two RE atoms and two oxygen atoms are in the (2d) position with site symmetry C3v, and the remaining one oxygen atom is in the (1a) position with site symmetry D3d. The oxygen atom at (1a) position is octrahedrally surrounded by six RE atoms, whereas the same at (2d) position is surrounded by RE atoms at the corner of the slightly distorted tetrahedron.25 The irreducible representations of the vibrations of the atoms in hexagonal RE2O3 give four vibrational Raman modes that correspond to two stretching vibrations, that is, A1g and Eg modes, and two bending vibrations of the A1g and Eg modes.25,26 Out of these, the bending vibrations occur at low wave numbers, typically between 100 and 200 cm−1, while the stretching occurs at higher wave numbers between 400 and 600 cm−1. Consequently, the transition sequences for Gd2O3, Dy2O3, and Yb2O3 displayed the replacement of cubic phase peaks with stretching vibrations for the hexagonal phase occurring around 400−600 cm−1, and the bending vibrations also developed in the low wavenumber ranges.12−14 In B-type, RE atoms are located in three different 4i positions. The 18 oxygen atoms of the unit cell occupy five different crystallographic sites: four in 4i (m or Cs symmetry) = O (1), O (2), O (3), O (4), that is, 16 O in 4i, and one in 2b (2/m or C2h symmetry) = O (5), that is, two O in 2b.24,27,28 Hence, the irreducible representation according to group theory gives 21 Raman-active modes among, which 14 are Ag modes and 7 are Bg modes; however, all of the modes are rarely observed in practice. The detailed transition sequences, the peak positions, as well as the shifts have been reported in detail elsewhere in refs

It has been reported that the small physical dimensions of the scattering crystals cause the confinement of optical phonon in the finite region and lead to a downshift of the first-order Raman line,19−21 which has been suggested to occur due to cohesive bond weakening of the lower coordinated atoms near the surface region of the nanograin. An additional factor governing this shift may also be the relaxation in momentum conservation when the size is decreased, and consequently, the Raman active modes will not be limited at the center of the Brillouin zone; however, there are conflicting reports on this aspect wherein as compared with frequencies reported by Urban and Cornilsen,18 there is indeed a red shift in our samples; however, some of the more recent reports contradict this theory and report comparable frequencies for powder samples.22,23 From Figure 3 it is also seen that Yb2O3 and Eu2O3 behave differently from other rare-earth sesquioxides and display a relatively larger decrease in vibrational numbers for the Tg mode as well as peak broadening. This occurs due to significant variation in force constants and chemical bonding despite having no anomalies in lattice constants or bond distances, as compared with other rare-earth sesquioxides. It is known that this decrease in force constants is caused by unique electronic structures that broaden the potential well that result from the proximity of the f-electron states to the Fermi level and electron phonon interactions, which result in the previously mentioned behavior.18 Another observation, clear from Table 1 and Figure 2, is the detection of a weak band designated as I3, which is referred to as a Stark level assignment for RE3+ ion in C3i site.24 The spin− orbit and crystal-field interaction splits the f orbital into the multiplets of 2F7/2 and 2F5/2 levels. The electronic transition from the ground state of 2F7/2 to the 2F5/2 level gives the Stark line, which is observed in some of the samples.

4. HIGH-PRESSURE STUDIES The detailed high-pressure behavior for each of the samples studied has already been reported.12−16 This section discusses the characteristic modes of the structural phase transitions observed, the similarities/dissimilarities, and the trends observed with respect to the nanosize of the samples, the felectron number and the effect of starting phases in and among the investigated rare-earth sesquioxides. In brief, yttrium sesquioxide (Y2O3), gadolinium sesquioxide (Gd2O3), and samarium sesquioxide (Sm2O3) were pressurized up to ∼19 GPa.13 Eu2O3 was pressurized up to 16 GPa,12 Dy2O3 to ∼25 GPa,14 Yb2O3 to 27 GPa,15 and Ho2O3 to 29 GPa.16 As mentioned, most of the rare-earth sesquioxides were cubic in nature in the starting material with the exception of Eu2O3, Sm2O3, and Ho2O3, which showed traces of either nonstoichiometric/monoclinic phase in small fractions.12,13,16 A brief summary of the observed phase progressions shows that Y2O3 underwent a crystalline to partial amorphous transition when pressurized up to ∼19 GPa, with traces of hexagonal phase;13 however, on release of pressure, the hexagonal phase developed into the dominant phase. The most predominant Tg mode was observed at 378 cm−1. Up to a pressure of 15.49 GPa, this Tg mode displayed a continuous shift to higher wavenumbers while losing intensity, and a slight increase in the background was observed.13 Gd2O3 also developed into a mixture of amorphous and hexagonal phases on pressurizing, while Sm2O3 became monoclinic. Gd2O3 showed the development of the hexagonal D


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The Journal of Physical Chemistry C 12−16; however, for the sake of completeness, we reproduce the transition sequences for two of the samples, namely, Dy2O3 and Ho2O3 in Figures 4 and 5, respectively, depicting the

Figure 6. Shifts observed in the Tg phonon mode for the samples as observed with increasing applied pressure.

comparison of Figure 7, plotted for Tg mode observed at various pressures versus the f-electron number, compares well

Figure 4. Progression in phonon modes of Dy2O3 with increasing pressures depicting development of hexagonal phase at the expense of cubic phase.

Figure 7. Graphical depiction of the shifting of the Tg mode with increasing pressures in Re2O3 samples as a function of f-electron number. Figure 5. Raman spectra of Ho2O3 as a function of increasing pressure showing the development of monoclinic phase at high pressures.

with the trend observed under ambient conditions (Figure 3). The variation follows a similar trend even up to the pressures of 15 GPa. It is clear that up to the pressures where it is still discernible, the Tg mode shift follows similar behavior, which is true despite the fact that the particle sizes for all samples, although in the nanorange, are quite different. Furthermore, with increase in pressure the half width of the predominant Tg + Ag peak for all the samples is seen to increase. A representative variation for the Tg modes of Dy2O3 and Gd2O3 is shown in Figure 8. Broadening in Raman lines occurs because the molecules in the fluid phase experience pressure-induced bond length variations related to instantaneous changes in the local environment.18 It can also occur due to nonhydrostatic pressure conditions; however, we could observe distinct R1 and R2 Raman lines of Ruby up to the highest studied pressures in the samples studied. Hence we can

typical cubic to hexagonal and cubic to monoclinic phase transitions, respectively. The Figures depict the hexagonal phase and monoclinic phase peaks as previously described. Figure 6 shows the quantitative shift observed in the Tg mode of the samples investigated with an increase in applied pressure. With an increase in the pressure, all Ln2O3 generally showed shifting and broadening of the cubic phase peaks. This shifting of cubic phase T g peak of Ln 2O3 to higher wavenumbers signifies destabilization prior to phase transitions. Most Ln2O3, with exception of Eu2O3, which had an early transition, showed clearly observable Tg modes up to a pressure of ∼15 GPa. Interestingly, it has been experimentally observed that the progressive shifting of the Tg mode follows more or less a similar trend as was seen under ambient conditions. A E


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Figure 9. Transition pressures of Re2O3 as a function of f-electron number demonstrating a variation similar to Figure 3.

Figure 8. Variation in half-width of the Tg modes of Dy2O3 and Gd2O3 showing a sharp increase near the transition pressure.

on the particle size, as would be discussed in the subsequent sections. Furthermore, the anomalous behavior seen in the case of Eu2O3 and Yb2O3 is also reflected in the high-pressure behavior with reduced transition pressures as compared with the other Ln2O3 with increasing f electrons.

safely conclude that an increase in defects in the system occurs, leading to destabilization of the system. Figure 8 shows a sharp increase in the line-width just prior to onset of the phase transitions and is another indication of the breakdown of the starting structure. Table 2 summarizes the observed high-pressure-induced structural phases and their transition pressures for all samples studied. In short, the samples with purely cubic phase at ambient largely showed a cubic to hexagonal phase transition, while the samples with traces of either nonstoichiometric or monoclinic phase exhibited a cubic to monoclinic phase transition. All transitions, with the exception of Y2O3, were irreversible in nature and more or less showed the hysteresis effect. Because in the case of Eu2O3,12 Sm2O3, and Ho2O313,16 the starting material itself contained monoclinic/nonstoichiometric phase, the kinetic barrier for the formation of monoclinic phase is expectedly lowered and the predominant phase obtained is monoclinic. On the contrary, all other samples proceed to hexagonal phase only with no signals of the monoclinic phase in the intermediate pressures. Another interesting observation may be made from Figure 9, wherein the transition onset pressures are plotted as a function of the f-electron number. Again, the trend in the curve is seen to follow the one seen in Figures 3 and 7. This may be remarkably indicative of the fact that the lanthanide contraction also plays a significant role in the restructuring as a result of applied pressure, which to some extent is not wholly dependent

5. MODE GRÜ NEISEN PARAMETERS The mode Grüneisen parameter is a valuable parameter in solid-state physics because it provides a dimensionless estimate of the response of the sample to externally applied pressure. It is obtained from the measured pressure dependence of the mode frequencies and the isothermal compressibility of a material. We have calculated the mode Grüneisen parameters using the equation. γi = (B0 /ω0)(dω/dP)

wherein the pressure coefficients of Raman modes can be obtained from the linear fitting using the equation ω = ω0 + (dω/dP)P

Here Bo is the isothermal bulk modulus for the cubic phase of the rare-earth sesquioxide under study29,30 and ω0 is the mode frequency at ambient. In our studies, because Eu2O3 showed a very early transition, γ could not be estimated using the experimental data; however, for other samples an indicative trend was observed in the response to external pressure application. Table 3 shows the values obtained for γ for the prominent bands for the samples under study.

Table 2. Summary of the Phase Transitions Observed S. no.

material

f-electron number

maximum pressure (GPa)

final phase

initial phase

1

Y2O3

0

19

cubic

2

Sm2O3

5

19

3

Eu2O3

6

16.4

4 5 6 7

Gd2O3 Dy2O3 Ho2O3 Yb2O3

7 9 11 13

19 25.5 28.8 27.43

cubic with small traces of monoclinic cubic with small traces of nonstoichiometric material cubic cubic cubic with traces of monoclinic cubic F

amorphous with hexagonal monoclinic

transition pressure 16.15 6.79

monoclinic

2.1

hexagonal hexagonal monoclinic hexagonal

12.62 14.6 15.5 12.81

reversible/irreversible partially reversible cubic with hexagonal irreversible

reference no. 13 13 12

irreversible irreversible, monoclinic irreversible irreversible

13 14 16 15


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relaxed to monoclinic phase;36 however, a polycrystalline sample of Gd2O3 has also been shown to partially convert to monoclinic phase at very low pressures, followed by a hexagonal phase transition at ∼9 GPa.37 Angle-dispersive X-ray diffraction studies on Eu2O3 have also shown cubic to hexagonal phase transition starting at 5 GPa and finishing at 13.1 GPa;38 however, luminescence studies on Eu3+ demonstrated initiation of a sluggish phase transition from a C-type bcc to B-type monoclinic phase at ∼8 GPa39,40 completing at 14 GPa, which remained irreversible. In the case of Dy2O3, the high-pressure-induced studies have not been reported except by the authors; however, the effect of high-energy ion irradiation was studied by Tang et al.,41,42 who reported that 300 keV Kr ion irradiation transformed cubic Dy2O3 into monoclinic phase at cryogenic temperatures. The phase-transition temperature/pressures for cubic to monoclinic transitions up to a temperature of 1386 K and pressures of 1.81 GPa in Dy2O3 were reported by Seck et al.43 Wu et al.44 had predicted the B → A phase transition of Ho2O3 at ∼17.0 GPa based on the density functional theory. Ctype Ho2O3 was found to transform to the monoclinic phase at 1.5 GPa and 1000 °C by Hoekstra.45 An irreversible structural phase transition in the case of Ho2O3 has been observed at ∼9.5 GPa to a low-symmetry monoclinic type structure by Lonappan et al.46 The two phases were reported to coexist to ∼16 GPa, and thereafter the parent phase was found to have disappeared; however, Jiang et al.47 have recently reported a C → B → A transition sequence in Ho2O3 with all three phases coexisting at ∼15 GPa. High-pressure XRD studies on C-type Yb2O3 by Meyer et al.29 revealed a transformation to monoclinic B-type structure above 13 GPa, which remained in its high-pressure phase on decompression. Hoekstra et al.48 obtained B-type Yb2O3 and Ho2O3 from C-type at 40 kbar pressure/1000 °C and 25 kbar pressure/1000 °C, respectively. Both of the transitions were irreversible. Recently, Yusa et al.49 found the conversion of Ctype Yb2O3 into A-type at 19.6 GPa via an intermediate B type phase, which was observed at 15.9 GPa.

Table 3. Mode Frequencies, Pressure Coefficients, and Grüneisen Parameters (γi) for Phonon Modes in Studied Samplesa avg. particle size (nm)

phase

Y2O3

60−80

cubic

Sm2O3

45−50

cubic

Gd2O3

20−40

cubic

Dy2O3

60

cubic

Ho2O3

50

cubic

Yb2O3

96

cubic

RES

a

ωo (cm−1)

dω/dP (cm−1/GPa)

γ

381.3 472 598.1 343 420.7 477.4 317.8 363.3 447.2 374 464 586 330.2 375.2 468 301.9 363.8 613.5

3.794 5.016 4.582 4.61 0.705 2.691 2.749 3.863 3.060 3.587 4.824 4.533 3.19 3.89 3.05 2.364 3.102 4.363

1.35 1.44 1.027 1.916 0.48611 0.8004 1.626 1.99 1.286 1.4446 1.5659 1.1651 1.99 2.14 1.34 1.417 1.543 1.287

Modes in bold indicate the most prominent Tg mode.

From the table, the most significant observation is the fact that for all of the samples studied, the most intense Tg mode demonstrated the highest values of dω/dp as well as γ values, which confirms the expectation that the phonon modes with the highest polarizability changes are most responsive to external influences. Another interesting point is the fact that both Sm2O3 and Ho2O3, which showed traces of monoclinic phase at ambient, showed the highest γ values for the Tg mode, indicating again that the breakdown of the cubic phase is faster as compared with the other samples. Although our investigation did not explicitly examine the effect of varying particle size for each sample, we may still make a general observation from the Table, which shows that the samples with smaller particle sizes demonstrated relatively higher values of the mode Grüneisen parameters for the most prominent Tg mode.

7. DISCUSSION It is known that the stability of the rare-earth sesquioxides at room temperature and pressure depends on a number of factors, which also include cation and anion radius ratios.50 Atype phase with space group P3m ̅ 1 is usually found to be stable from La to Nd, B type with space group C2/m from Sm to Gd, and cubic with space group Ia3̅ for other rare-earth sesquioxides. In the cubic phase the RE atoms occupy two octahedral sites: 8 atoms in (a) positions with 3-fold inversion symmetry C3i and 24 atoms in (d) positions with 2-fold symmetry C2. For the C3i site two oxygen atoms are missing across the body diagonal, while for the C2 site they are missing across a face diagonal.25 Under normal conditions, a comparison of molar volumes of the three structure types of the rare-earth sesquioxides suggests that application of high pressure should lead to a shift in phase boundaries. The hexagonal and monoclinic phases in rare-earth sesquioxides have smaller molar volumes as compared with the cubic phase. Furthermore, the hexagonal phase has smaller molar volume than monoclinic phase, and application of pressure is thus favorable for the formation of hexagonal phase. It must be pointed out that cubic to monoclinic phase change produces a substantial volume decrease of ∼8%, while the monoclinic to hexagonal phase change produces only a minor

6. WHAT’S BEEN REPORTED? A look at the reported studies also shows that a few rare-earth sesquioxides show preference for cubic to hexagonal structural transition under pressure. Y2O3 has been shown to transform to A-type structure at 12.1 GPa;31 however, a single-crystal sample for the same transformed to a B-type structure at 12 GPa, followed by an Atype structure at 19 GPa.26 Y2O3 powder has also been reported to turn into monoclinic structure at 13 GPa.32 The X-ray diffraction data reported by Jiang et al.33 indicate that a mixture of monoclinic and cubic phases of Sm2O3 begin to transform to a hexagonal phase at 2.5 and 4.2 GPa, respectively. The hexagonal phase is stable up to at least 40.1 GPa and could not be quenched to ambient conditions. Gd2O3:Eu nanoparticles as well as bulk samples have been reported to turn into a hexagonal phase at ∼13.4 GPa, relaxing into monoclinic structure at release.34 A mixture of nanocrystalline cubic and monoclinic phases has been reported to turn into hexagonal structure at ∼10.35 GPa;35 however, polycrystalline powder of Gd2O3 has also shown a transition to A phase at as low as 4.6 to 5.2 GPa pressure, which again G


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The Journal of Physical Chemistry C volume change.51 Hence pressure is also expected to give changes commiserate with such volume collapses. It has been reported that phases obtained under pressure are metastable at atmospheric pressure.48 Hence the structural transformation should take place in the order C → B→A when the sesquioxides are subjected to increasing pressure. Hyde and Anderson52 showed that the A-type structure resembles very closely the B-type structure and very small amount of anion shuffling would convert the A-type structure to B-type structure. The preferred structural phases that would be attained under the application of pressure are also likely to have contributions from a number of other factors such as structure of the starting phases, particle sizes, kinetic factors, effects due to the f electrons, and so on. A brief consideration of these factors can help us understand the experimental outcomes previously described. To begin with Y2O3 with zero f electrons does not display a clear transition and goes into a partial amorphous state, followed by the development of hexagonal phase. The crystalline to amorphous phase transformation occurs when the free energy of the amorphous phase is less than the combined free energy of the high-pressure crystalline phase and the defects. In nanomaterials the defect-controlled term becomes important due to the presence of increased volume fraction of grain boundaries. Hence the crystalline-toamorphous phase transformation in nanomaterials under external stimuli such as pressurization, irradiation, or milling, in particular, below a critical particle size, becomes possible. On application of pressure the nanoparticle size of the sesquioxides further reduces due to compression, leading to further increase in the fraction of the grain boundary component. This causes a constant increase in the defect energy term, eventually leading to amorphization of the material below some critical particle size at the expense of the normally observed high-pressure phase. It has also been suggested that for certain materials at the ambient the kinetics of the phase transformation reactions are slow and therefore intermediate structural disarray is frozen in, resulting in amorphous form.53 This finding also suggests that the structural transformation with large volume changes may always proceed via an intermediate amorphous phase and subsequently settle into the lowest energy crystalline phase. Before a consideration of the pressures values at which transitions have been observed, it may be interesting to note that Gschneidner et al.54 suggested a test for 4f contribution to bonding in a series of rare earth compounds wherein pressure determines the stability of a polymorph. If at a constant temperature increasing pressure is required with increasing atomic number to form one of the polymorphs, then 4f electrons are contributing to the bonding. If increasing pressure is required with decreasing atomic number, then 4f bonding is not involved. It has also been reported that at ambient temperature the C → A transformation pressure in Ln2O3 increases with decreasing ion radius of the rare-earth cation.55 Among the samples studied presently, Gd2O3, Dy2O3, and Yb2O3 showed a direct cubic to hexagonal phase transition. Consequently, it is significant to note that we observed the C → A transition in Gd2O3 completing at ∼14.01 GPa,13 while in the case of Dy2O3 the transition completes at ∼17.81 GPa;14 finally, for Yb2O3, the transition completes at 20.59 GPa.15 It is noteworthy that Gd2O3 has larger ionic radius as compared with Dy2O3. Similarly, Yb2O3 with the smallest ionic radius also showed a complete transition to hexagonal phase at a still

higher pressure of 20.6 GPa, although the transition was seen to commence at a pressure of 12.8 GPa. As mentioned, the ionic radii are affected by the number of f electrons;11 that is, the larger the number of f electrons, the smaller the radii. These smaller radii occur due to lanthanide contraction; therefore, the higher the pressure required to transform the structure. This observation is indicative of the possibility that the 4f electrons do play a crucial role in the high-pressure transitions in the present studies. This may indicate the delocalization of 4f electrons participating in bonding to form the new polymorphs.43 Further credence to this fact is given by the observation that the transition onset pressures, as shown in Figure 9, also show a behavior similar to the phonon behavior at ambient. Hence it reinforces the possibility that the f electrons also play a vital role in the anomalous behavior observed in the present case. It is pertinent to mention here that Zhang et al.56 reported a phase diagram for Gd2O3 according to which at low temperatures the cubic to hexagonal phase transition is favored with application of pressure while at high temperatures the monoclinic phase is favored. Furthermore, in the case of bulk crystals, the C → B and C → A phase transitions in Ln2O3 are reconstructive and they usually have a large kinetic energy barrier, and as a result, the transformation rate would be very small and excess compression is required to drive the phase transition. It is well known that the kinetics of phase transformation depend, in general, on the pressure, temperature, and the amount of nonhydrostatic stresses as well as the existence of defects; therefore, the barrier heights would also depend on these parameters.53 Because nanosized samples have increased defects, the previously mentioned barriers to transition can also be altered at finite size of the nanocrystals,57,58 as they are further fragmented into finite domains upon transition. Although in our studies the effect of size variation of the nanoparticles was not investigated, a few general observations are in order vis-avis the reported results. The nanocrystalline materials have a higher percentage of grain boundaries that due to their high energy are more responsive to the external influences and hence have also been shown to demonstrate a size-dependent transition pressure. Because of Gibbs−Thomson effect an additional hydrostatic pressure component occurs owing to the surface curvature of the nanoparticles, which below a critical particle diameter may contribute to making high-pressure phases with higher density become thermodynamically favorable.58 Hence, compared with conventional polycrystalline materials, nanometer-sized particles can form in new phases and exhibit new or enhanced optical, electronic, or structural properties.59,60 Indeed, in most reports of samples with a higher number of f electrons, the polycrystalline/powder samples show C → B transitions.29,30,39,46 Gd2O3 has been found to be an exception, with the C → A transition reported for powder samples, too.36,56 Sm2O3, Eu2O3, and Ho2O3 show a different response to the applied pressure and convert to the monoclinic phase.12,13,16 In the case of Eu2O3 and Sm2O3, the starting material was found to contain traces of nonstoichiometric phase and monoclinic phase, respectively. In the case of Ho2O3 a broad hump is seen around 600−700 cm−1 in the Raman spectra at ambient and at a low pressure of 1.32 GPa, which increases with applied pressure. Although our XRD studies did not indicate the presence of another phase in Ho2O3, it may be possible that some amount of disordered state was present in the sample, H


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sensitive to a number of observable factors, which include the felectron number, the presence of monoclinic/nonstoichiometric components, and, to some extent, the particle size and so on. The transition onset pressures interestingly followed a sequence similar to the phonon mode variations under ambient conditions. The observed sequence followed all the way to the pressures where the cubic phases were no longer discernible, thereby indicating that the ionic radii as well as f-electron numbers affect the structural variations under pressure. The samples with smaller nanocrystals showed a higher response to externally applied pressure. The samples with purely cubic phases preferred to transform to hexagonal phase, while samples with a small amount of noncubic content transformed to monoclinic phases. The kinetic factors due to the combined effects observed led to differences in the final phases achieved on application of pressure.

which facilitates the growth of monoclinic phase at the expense of cubic phase. It is noteworthy that there exist several ways of transformation between the various phases depending on temperature and pressure conditions. Additional reaction components can also help to transform the sesquioxides during the temperature treatment. For example, Foex et al. achieved a transformation from the C-type to the B-type structure by adding some lime5 or by offering support with oxides like CaO and SrO.61 In addition, for the case of nanocrystals where the surface energy makes a major contribution to the total free energy of the system, the transition path can actually determine the final state of the system. These effects are masked in bulk systems whereas nanocrystals provide an opportunity to observe the effects of transition path. Hence, in the present case, the presence of monoclinic/nonstoichiometric phase is expected to lower the energy barrier for the formation of monoclinic phase. The higher values of the dω/dp for the Tg mode of these samples further strengthen this observation. After phase transition the cubic phase has not been completely recovered in any of the samples, which may be the result of the large energy barrier to the reverse transition. In general, any phase transition is controlled by both energy barrier of the phase transition and the difference of lattice energies. In their study of the stability of the sesquioxide polymorphs, Goldschmidt and coworkers considered all phase transitions to be reversible.60 However, Tolbert et al.62 argued that high-pressure solid−solid transitions are generally hysteretic and occur over a range of pressures. In observations on nanoparticles, Alivisatos et al.63 reported a hysteresis loop with a width of a few gigapascals relative to a limiting thermodynamic transition pressure. This hysteresis loop was found to be narrow at elevated temperatures, and the position of the hysteresis loop was controlled by the size of the nanocrystals. This hysteresis effect is expected to allow the formation/trapping of the nanoparticles in metastable structures following a pressurization-depressurization cycle. Furthermore, the thermodynamic surface considerations previously discussed apply to the down stroke transition also, and the thermodynamic pressure for the reverse transition will be lowered. If the hysteresis loop is wide enough, the practical reverse transition pressure may become negative, so that the nanoparticles will remain in the high-pressure structure for a very long time under ambient conditions. Furthermore, a different distribution of surfaces may lead to an otherwise favored transition pathway (such as the reverse of the path adopted on the upward transition) being blocked, resulting in an alternative pathway being adopted. This implies that phases different from the starting phases may become possible in the case of pressurization−depressurization cycles in the case of nanocrystals.64 In particular, in the case of nanocrystals, where the surface energy makes a major contribution to the total free energy of the system, the transition path can actually determine the final state of the system.61 Thus, the stabilization of metastable phases (amorphous/hexagonal) in the present study on subjecting the sesquioxides to pressurization−depressurization cycle may be the result of the size-induced hysteresis.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +91-11-45608488. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to Director, NPL for his constant encouragement. The financial grant from network project NWP-45 is also acknowledged. We are also thankful to Dr. S. M. Sharma and Dr. H. Poswal, at BARC, Mumbai for collaborative experimental work.

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REFERENCES

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Pressure-Induced Structural Transition Trends in Nanocrystalline Rare

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