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Shape-dependent local internal stress of α-Cr2O3 nanocrystal fabricated by pulsed laser ablation
ARTICLE IN PRESS Journal of Physics and Chemistry of Solids 70 (2009) 1505–1510
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Technical note
Shape-dependent local internal stress of a-Cr2O3 nanocrystal fabricated by pulsed laser ablation C.H. Lin a, S.Y. Chen b, N.J. Ho a, D. Gan a, P. Shen a, a
Department of Materials and Optoelectronic Science, Institute of Materials Science and Engineering, Center for Nanoscience and Nanotechnology, National Sun Yat-sen University, Kaohsiung, Taiwan, ROC b Department of Mechanical and Automation Engineering, I-Shou University, Kaohsiung, Taiwan, ROC
a r t i c l e in fo
abstract
Article history: Received 15 June 2009 Received in revised form 30 July 2009 Accepted 23 September 2009
The a-Cr2O3 single-crystal nanocondensates were fabricated by pulsed laser ablation in air and characterized by analytical electron microscopy regarding shape-dependent local internal stress of the anisotropic crystal. The nanocondensates formed predominantly as rhombohedra with well-developed f0 1 1 2g surfaces and occasionally hexagonal plate with thin f1 1 2 0g edges and blunt corners. Such nanocondensates showed Raman shift for the CrO6 polyhedra, indicating a local compressive stress up to ca. 4 GPa on the average. Careful analysis of the lattice fringes revealed a local compressive stress (0.5% strain) at the thin edge of the hexagonal plates and a local tensile stress (0.3–1.0% strain) near the relaxed f1 0 1 2g, f1 0 1 1g, and (0 0 0 1) surfaces of truncated rhombohedra. The combined effects of nanosize, capillarity force at sharp edge, and specific surface relaxation account for the retention of a local internal compressive stress built up in an anisotropic crystal during a very rapid heating–cooling process. & 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Nanostructure B. Laser annealing C. Raman spectroscopy D. Surface properties D. Elastic properties
1. Introduction It is a common knowledge that size-dependent pressure due to capillarity force follows a simple relation 2g/r for a spherical particle, where g is the surface energy and r the radius of curvature [1]. On the other hand, shape-dependent local internal stress involving capillarity force and specific surface relaxation of an anisotropic nanocrystal is less understood. Here we report such experimental evidences for a representative anisotropic nanocrystal formed via a pulsed laser ablation (PLA) technique. We focused on the corundum-type a-Cr2O3 system because it has well-developed surfaces with periodic bond chains (PBCs), i.e., strong bonding directions [2,3], and theoretically calculated surface relaxations of various surfaces [4]. The purpose is to study the variation of the shapes of the nanocrystals and hence the local internal stresses built up in a dynamic heating–cooling process. The spectroscopic evidence of a very large internal compressive stress in the a-Cr2O3 nanocrystals was provided. The cause and mechanism of sustaining a large internal stress without breaking down the crystal core was rationalized by the presence of a (h k i l)-specific relaxation shell as observed for the first time by careful measurements of the lattice plane spacing. The a-Cr2O3 material is also of engineering interest for
Corresponding author. Fax: +886 7 525 4099.
E-mail address: [email protected] (P. Shen). 0022-3697/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2009.09.015
potential applications in optoelectronics such as components for flat-panel display devices [5].
2. Experimental Cr (Solar Applied Materials Technology, 99.9% pure) plate 1 mm in thickness was subjected to energetic Nd-YAG-laser (Lotis, 1064 nm in wavelength, beam mode: TEM00) pulse irradiation. The laser beam was focused to a spot size of 0.03 mm2 on the target inside the ablation chamber for ablation in air. Oxygen gas (99.999% purity) at a flow rate of 50 L/min was supplied into the chamber to oxidize and cool the as-formed condensates. A specified laser power density of 1.5 108 W/cm2, i.e. 1100 mJ/pulse with a pulse time duration of 240 ms at 10 Hz on a focused area of 0.03 mm2, was employed. The condensates were collected with Cu grid covered with a carbon-coated collodion film for direct observation. The composition and crystal structures of the condensates were characterized by analytical electron microscopy (AEM, Tecnai G2 F20 at 200 kV) with selected area electron diffraction (SAED), and point-count energy dispersive X-ray (EDX) analysis with a beam size of 10 nm. Bright field images (BFI) taken by transmission electron microscopy (TEM) were used to study the general morphology and agglomeration of the nanocrystals. Lattice imaging coupled with two-dimensional (2-D) Fourier transform and inverse transform was used to characterize the crystal structure of the individual
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nanoparticles. The d-spacings were averaged from ca. 30 lattice fringes in magnified TEM images for improved accuracy ( 70.0002 nm) to evaluate local internal strain and stress with respect to the exposed surfaces and sharp edges. The condensates collected on soda-lime glass were used for Raman spectroscopic study of the retained internal stress. Raman spectra were made using semiconductor laser excitation (532 nm) having a frequency resolution of 2 cm 1 and a beam diameter of 1 mm using Opympus MPlan 100 objective (Jobin-Yvon Triax 320 Micro-Raman microprobe). The analysis typically covered more than 1000 nanoparticles less than 100 nm in size accumulated up to 1 mm thick. The reagent-grade a-Cr2O3 powder (Cerac, 5 mm in diameter, 99.8% pure) and other PLA samples fabricated in vacuum, air or water [6] were used to calibrate the Raman shifts. The same sample was also used for X-ray photoelectron spectroscopy (XPS, JEOL JPS-9010MX Photoelectron spectrometer with Mg Ka X-ray source), calibrated with a standard of C 1s at 284 eV, to analyze the position of Cr 2p3/2 peak for the possible presence of Cr2 + in the condensates. The condensates were mostly formed in air before being collected by Cu grid or glass substrate.
The a-Cr2O3 condensates formed predominantly rhombs with sharp corners occasionally truncated. Hexagons were also observed but were much less in number. These nano condensates tended to coalesce over well-developed surface into nano-chain aggregate or into close-packed groups. The electron diffraction ring patterns showed significant line broadening and hence were difficult, if not impossible, to measure the d-spacings with sufficient accuracy for least-squares refinement of precise lattice parameters regarding possible retention of the internal stress.
3. Results 3.1. TEM observations The condensates collected on a carbon-coated collodion film were identified by BFI and SAED pattern as randomly oriented a-Cr2O3 nanocrystals ranging from 30 to 100 nm in size (Fig. 1).
Fig. 1. TEM (a) BFI and (b) corresponding SAED pattern and index of rhombohedral and hexagonal-shaped a-Cr2O3 condensates ranging from 30 to 100 nm in size and randomly oriented as indicated by ring pattern. (c) BFI of another area of the aCr2O3 condensates showing coalescence of rhombs and hexagons (denoted by an arrow) into nano-chain aggregate. Sample produced by laser ablation on pure Cr target at 1100 mJ/pulse and oxygen flow rate of 50 L/min in air and collected by a carbon-coated collodion film.
Fig. 2. TEM (a) lattice image of a truncated rhombohedral a-Cr2O3 particle, magnified from inset, showing well-developed {0 0 0 1}, f1 0 1 2g, and f1 0 1 1g surfaces viewed edge on in the ½1 2 1 0 zone axis. The lattice fringe spacings of ð1 0 1 2Þ, ð2 0 2 2Þ, and (0 0 0 6) all increase from core to edge as shown by the average values in three adjoined regions denoted by arrows. (b) Another magnified area showing the increased d-spacing of {1014} planes toward the surface. (c) and (d) 2-D forward and inverse Fourier transform of the square region in (a), showing dislocation-free lattice. It is the same specimen as in Fig. 1.
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Lattice imaging was used to identify the {h k i l} surfaces and associated strain for the a-Cr2O3 nanocrystals in the form of truncated rhomb and hexagonal plate. The truncated rhombohe-
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dral a-Cr2O3 nanoparticle has {0 0 0 1} and f1 0 1 1g surfaces besides well-developed f1 0 1 2g surfaces as viewed edge on in the ½1 2 1 0 zone axis (Fig. 2). Careful measurement of the magnified lattice fringe spacings of ð1 0 1 2Þ, ð2 0 2 2Þ, and (0 0 0 6) showed unambiguous increase of d-spacing from core to edge as shown by the average values in three adjoined regions indicated in Fig. 2a. There is also increased d-spacing of f1 0 1 4g planes toward the surface (Fig. 2b), indicating that the capillarity force can be ignored in this case. No dislocation was observed in this nanocrystal. Fig. 3a shows a hexagonal a-Cr2O3 nanoplate in the [0 0 0 1] zone axis with well-developed (0 0 0 1) terraces on top and f1 1 2 0g lateral surfaces viewed edge on. The magnified lattice image shows a decreasing f1 1 2 0g d-spacing toward the edge as indicated by the average values in three regions indicated in Fig. 3b. The nanoplate is also dislocation free as indicated by 2-D forward and inverse Fourier transform (Figs. 3c and d). Alternatively, the hexagonal a-Cr2O3 nanoplate showed gradual change of the plate thickness fading from the central thick area toward sharp edge (not shown). Point-count EDX spectrum of the nanoplate shows the presence of Cr and O and negligible impurities (Fig. 3e). It should be noted that the hexagonal undoped aCr2O3 nanoplate has a blunt corner at f1 1 2 0g junctions (Fig. 3a). In contrast, Si4 + -doped Cr2O3 condensate produced by the same PLA method has six sharp/concave corners at the junction of f1 1 2 0g vicinal surfaces [7] (see Fig. 5 of Ref. [7]). Reasons for such a difference will be addressed later. The lattice-fringe interplanar spacing variations from core to edge of the a-Cr2O3 nanocondensates in Figs. 2 and 3 are compiled in Table 1. In comparison with the calculated ambient values based on the reported lattice parameters a =0.4959 nm and c=1.3594 nm (JCPDS file# 38-1479), the d-spacing is significantly smaller at the core but larger at the edge of the nanoparticle. The only exception is ð1 1 2 0Þ, which shows an opposite trend due to the thin edge with a large capillarity force. It should be noted that the theoretical calculation [4] indicates a more complicated manner of surface relaxation than the interspacing variation of the present nanocondensates produced by a dynamic PLA process. The relaxation of the a-Cr2O3 (0 0 0 1) plane was theoretically suggested to involve a decreased separation between the Cr and O ions at the surface and an increased side length of the equilateral O triangle, while the ð1 0 1 2Þ plane to involve a 8%, 20%, 6%, and 15% change in the top four interplanar spacings, respectively [4]. On the other hand, the low-energy electron diffraction of the (0 0 0 1) surface indicates a significant charge reduction and Table 1 Lattice fringe interspacing variation from core to edge of the a-Cr2O3 nanocondensates. hkil
Surface relaxation
Core
Middle
Edge
Calculated
0112
0.3597
0.3617
0.3652 (+0.0021)
0.3631
0.58%
1014
0.2631
0.2659
0.2673 (+ 0.0008)
0.2665
0.30%
1120 0006
0.2511
0.2490
0.2467 ( 0.0013)
0.2480
NA
0.2264 0.2014
0.2274 0.2029
0.2288 (+0.0022) 0.2066 (+ 0.0018)
0.2266 0.2048
0.97% 0.88%
2022
Fig. 3. TEM (a) lattice image of hexagonal a-Cr2O3 nanoplate with well-developed (0 0 0 1) terraces in top view and f1 1 2 0g lateral faces edge on in [0 0 0 1] zone axis. (b) Magnified image showing its blunt corner. (c) and (d) 2-D forward and inverse Fourier transform of the square region. (e) Point-count EDX spectrum showing Cr and O counts, the C and Cu counts being from the carbon-coated collodion film and copper holder. Note the d-spacing of ð1 1 2 0Þ plane in (b) decreases toward the thin edge as indicated by the average values in three adjoined regions. It is the same specimen as in Fig. 1.
d-spacing (nm)a
The bulk ambient values are calculated from the reported lattice parameters a= 0.4959 nm and c =1.3594 nm (JCPDS file# 38-1479). The differences between the d-spacings at edge and those of ambient values are also given in parenthesis. a The d-spacings (7 0.0004 nm) were averaged from about 30 lattice fringes in Figs. 2 and 3. Note in comparison with the calculated ambient values, there is a significantly smaller d-spacing at the core and a larger d-spacing at the edge of the nanoparticle, except ð1 1 2 0Þ which shows opposite trend with a 0.52% decrease near the surface. This statement is supported by three more independent observations of the nanocondensates [6].
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depolarization to stabilize the surface [8]. In the present case, the local strain of the nanocondensates can be reasonably estimated to be 0.5% at the thin edge of the hexagonal nanoplates and 0.3–1.0% for the well-developed and relaxed f1 0 1 2g, f1 0 1 1g, and {0 0 0 1} surfaces.
3.2. Spectroscopy The Raman spectra of the reagent-grade a-Cr2O3 powders and the a-Cr2O3 nanocondensates deposited on silica glass under the same conditions as the TEM samples are shown in Figs. 4a and b, respectively. The standard powders under ambient condition have five characteristic Raman peaks at 296, 328, 484, 536, and 590 cm 1 whereas the nanocondensates show peak shifting to 268, 301, 510, 548, and 610 cm 1, respectively, with an additional peak at 697 cm 1. The shift of the most intense Raman peak, assigned as A1g symmetry [9], from 536 to 548 cm 1 indicates a compressive stress of 4 GPa for the constituting CrO6 polyhedra of the nanocondensates, according to the Raman shift dependence on applied compressive pressure [9]. The binding energy of the a-Cr2O3 nanocondensates deposited on glass is characterized by Cr 2p1/2 and Cr 2p3/2 and O 1s peaks with peak binding energy at 587, 577, and 530 eV, respectively (Fig. 4c), indicating that the Cr2 + content is negligible [10]. The Cr2 + presence would otherwise cause a lower binding energy for Cr 2p3/2 and less sharp peaks for Cr 2p1/2 and O 1s [10]. 4. Discussion 4.1. Shape change of the nanocondensates
Fig. 4. Raman spectra of a-Cr2O3: (a) ambient reagent-grade powders with five characteristic Raman peaks at 296, 328, 484, 536, and 590 cm 1. (b) Nanocondensates deposited on silica glass by pulsed laser ablation showing shifts of corresponding Raman peaks to 268, 301, 510, 548, and 610 cm 1, respectively, with additional 697 cm 1. The strongest peaks with Lorentzian curve fittings inset in (a) and (b) are used for internal stress estimation (cf. text). (c) XPS spectrum of the same a-Cr2O3 condensates as in (b) showing Cr 2p1/2, Cr 2p3/2 and O 1s peaks, indicating a negligible Cr2 + content (cf. text) [10].
According to the ideal unrelaxed atom disposition [11], the f1 1 0 4g, f1 1 2 0g, and f0 1 1 2g of a-Cr2O3 are K, S and energetically favorable F faces having the cation-filled octahedral sites assembled as 0, 1, and 2 PBCs, respectively [2]. The (0001), despite having 3 PBCs, is energetically less favorable than f0 1 1 2g in theory [4,12]. (For example, the surface energies of (0 0 0 1) and ð0 1 1 2Þ are 2.95 and 2.37 J m 2, respectively, for relaxed geometries and are 5.06 and 2.84 J m 2, respectively, for unrelaxed geometries according to recent first-principles Hartree-Fock calculations [4].) In addition, the multiplicity factor of (0 0 0 1) is one-sixth that of f0 1 1 2g. Thus, rhomb shape with well-developed f0 1 1 2g surfaces, occasionally truncated by (0 0 0 1), is favored for the present a-Cr2O3 nanocondensates. The truncation by f1 0 1 1g is less favored because its surface energy is higher than (0 0 0 1) and f0 1 1 2g after relaxation [4]. The nanocondensates were occasionally found to be hexagonal in shape having well-developed {0 0 0 1} terraces and f1 1 2 0g lateral edges with blunt corners, implying a combined growth mechanism of basal surface nucleation and lateral ledge growth. According to first-principles Hartree-Fock calculations [4], the (0 0 0 1) has a lower surface energy than f1 1 2 0g in relaxed state (2.95 and 3.10 J m 2, respectively), but is higher than f1 1 2 0g in unrelaxed state (5.06 and 3.81 J m 2, respectively). The (0 0 0 1) surface thus needs to be relaxed in order to form a hexagonal plate with well-developed (0 0 0 1) surface and rapid growth edges of f1 1 2 0g. Precondensation during solidification or crystallization from melt/solutions may affect the attachment of ions/atoms on specific F faces in terms of PBCs and hence may favor unexpected faces not following the PBC predictions [3]. The Si4 + -doped a-Cr2O3 nanocondensates, being in the form of corrugated hexagons with well-developed (0 0 0 1) surface and f1 1 2 0g edges with sharp corners and concave edges [7], suggest that they were formed by a combined effect of precondensation and constitutional supercooling. It is possible that the Si4 + dopant lowers the surface energy of (0 0 0 1) and hence promotes its surface nucleation and lateral growth. On the other hand, the curved f1 1 2 0g surfaces of Si4 + -doped a-Cr2O3 [7] may be related to the orientation-dependent incorporation of solute, as illustrated by experimental [13] and theoretical [14,15] works on the preferred
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incorporation of solute at flat Si(111) face rather than its rough interface for a higher distribution coefficient, b = avDm/DkbT (where a is the interatomic spacing, v is the growth rate, Dm is the chemical potential driving force for the crystallization process, and D is the diffusion coefficient) and an extended solid solubility. In fact, enhanced solute incorporation, or so-called solute trapping, via a very rapid growth rate was proved experimentally by laser-melted Bi-doped silicon wafers showing orientation dependence on the nonequilibrium partition coefficient of Bi in Si [13] and by computer modeling [14]. Note also the S- and K-faces of barite crystal were suggested to be favored by dehydration and impurities [16]. Diamonds also tend to form dendrite with unusual faces such as (1 0 0) rather than (111) under the combined effects of H2O and a large driving force [17]. In any case, the above impurity effect can be neglected for the present a-Cr2O3 condensates by the absence of Si based on the EDX spectrum (Fig. 3) and the Cr 2p1/2, Cr 2p3/2 and O 1s peaks by XPS (Fig. 4c) showing negligible Cr2 + content.
4.2. Internal stress state of the nanocondensates There is a significant compressive stress for the constituting CrO6 polyhedra in the present a-Cr2O3 nanocondensates, similar to the cases of Si4 + -doped a-Cr2O3 [7] and the partially crystallized chromium oxide lamellae, which were fabricated by PLA in vacuum with a much finer nanosize and hence a higher heating/cooling rate [11]. However, according to lattice fringe interspacings, there is a significant local compressive stress at the core and local tensile stress near the relaxed surfaces of the a-Cr2O3 nanocondensates (Table 1). The bulk compressibility of a-Cr2O3 was reported to be 240 GPa based on experiments under isotropically compressed conditions [18]. We suggest that the combined effects of nanosize, capillarity force at thin edges, dislocation-free state as well as (h k i l)-specific (i.e., (0 0 0 1), f1 0 1 2g, and f1 0 1 1g) relaxation may contribute to the buildingup of a rather complicated local internal compressive stress for the nanoparticles, which would otherwise relax to ambient cell volume without the large internal stress. This argument is supported by a rather tight 6-coordination of Cr3 + in the corundum-like structure or even amorphous phase formed upon rapid quenching [11]. It is also similar to the graphite anion-like nanopressure cell with a progressively smaller basal interplanar spacing to generate diamond at its core upon very intense electron irradiation [19]. The various extents of surface relaxation on the well-developed (0 0 0 1) and f1 0 1 2g, and minor f1 0 1 1g shed light on the shape-dependent local internal stress of the condensates. According to Mougin et al. [9], a-Cr2O3 typically shows five Raman modes in the range of 200–800 cm 1 under ambient pressure conditions. These Raman bands, except the one with the lowest wave number, were found to shift toward higher wave numbers with an increased applied pressure because of a decreased interatomic distance [9]. In the present study, both bulk powder and nanocondensates displayed five Raman peaks. However, compared to the bulk samples, three high-wave number Raman peaks in the nano samples shifted to higher wave number (i.e. from 484, 536, 590 to 510, 548, 610 cm 1, respectively, with an additional peak at 697 cm 1), and two low-wave number peaks shifted to lower wave number (i.e. from 296 and 328 to 268 and 301 cm 1, respectively). These changes could possibly be related to the observed surface compression and relaxation at different facets of the nanocondensates as a result of anisotropic (i.e. {h k i l}-specific) internal stress via a dynamic PLA process. However, the extent of deviatoric stress is difficult, if not impossible, to analyze in this complicated case. Still, the shift of
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the most intense Raman peaks of A1g symmetry, from 536 to 548 cm 1, and the additional peak assigned as Eg symmetry near 700 cm 1 indicates a significant compressive stress at least up to ca. 4 GPa for the constituting CrO6 polyhedra according to the equation of state by Mougin et al. [9]. This statement is justified by comparable frequencies of the strongest Raman band for other PLA samples fabricated in vacuum, air, and water [6] under power density known to produce high-pressure phases [20,21]. The other Raman modes are too weak and broad to be fitted by appropriate mathematical functions (Figs. 4a and b) and to provide meaningful insight into the internal stress. Rapid quenching can sometimes result in the formation of high-pressure phase, such as the a-PbO2- and fluorite-type TiO2 [20,21], with a significant activation energy to suppress the backtransformation to ambient structure. In the present case, a large local stress is retained without forming the high-pressure phase. The theoretical strength of materials was estimated to be 1/10 of its Young’s modulus G based on the Griffith criteria [22]. The yielding strength of a crystalline bulk material can be orders-ofmagnitude (10 1–10 3) lower than its theoretical strength due to the presence of dislocations. Thus, the present a-Cr2O3 nanocondensates, being free of dislocations, may have a high yield stress and therefore are expected to be capable of retaining a high local internal stress, maybe up to the theoretical strength. In this connection, the maximum sustained tensile strain on the outside surface of a bent carbon nanotube was estimated to be as large as 16% [23], which corresponds to a tensile stress of 288 GPa, 1/16 of its Young’s modulus 1.8 TPa [24]. Without experimental data on Young’s modulus, the bulk modulus reported to be 240 GPa [18] can be used as a substitute as adopted in the high-pressure study of other close-packed crystal, e.g. ZnS [25]. The theoretical strength of the a-Cr2O3 nanocondensates is therefore estimated to be about 24 GPa, i.e. one-tenth of G as mentioned. The internal stress of the nanocondensates, estimated by the Raman shift to be ca. 4 GPa, is less than that. The d-spacing differences at the cores of the nanocondensates with respect to the values calculated from bulk samples (Table 1) provide another rough estimate to be 0.21, 2.2, 3.1, and 4.0 GPa for (0 0 0 6), ð0 1 1 2Þ, ð1 0 1 4Þ, and ð2 0 2 2Þ, respectively. The high internal stresses estimated by both methods are in the same order of magnitude and are still less than the theoretical strength. Therefore these are reasonable estimates.
5. Conclusions The a-Cr2O3 nanocondensates fabricated by pulsed laser ablation in air with very rapid heating and cooling showed a significant internal stress. Compressive stress up to 5 GPa on the average was formed. Local compression at thin edge and local tensile stress near the relaxed surfaces of the anisotropic single crystal were also carefully measured based on the average from about 30 lattice fringes for a meaningful accuracy improvement. The relaxed surface enabled the retention of compressive internal stress, analogous to carbon anions as nanoscopic pressure cells for diamond formation, and may shed light on the stress state of sesquioxide nanocondensates in natural and engineering dynamic settings.
Acknowledgments We thank Dr. C.N. Huang for PLA runs with us, Miss S.Y. Shih for the help with XPS analysis and anonymous referees for constructive comments. This work was supported by Center for Nanoscience and Nanotechnology at NSYSU and National Science Council, Taiwan, ROC.
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References [1] D.A. Porter, K.E. Easterling, Phase Transformations in Metals and Alloys, second ed., Van Nostrand, Reinhold, 1981. [2] P. Hartman, W.G. Perdok, Acta Crystallogr. 8 (1955) 49. [3] P. Hartman, W.G. Perdok, Acta Crystallogr. 8 (1955) 521. [4] J. Sun, T. Stirner, A. Matthews, Surf. Coat. Technol. 201 (2006) 4205. [5] M. Tabbal, S. Kahwaji, T.C. Christidis, B. Nsouli, K. Zahraman, Thin Solid Films 515 (2006) 1976. [6] C.H. Lin, Chromium oxide condensates fabricated by pulsed laser ablation in air, vacuum and water, Ph.D. Thesis, National Sun Yat-sen University, Taiwan, ROC, 2009. [7] C.H. Lin, S.Y. Chen, P. Shen, J. Cryst. Growth 310 (2008) 245. ¨ [8] F. Rohr, F. B¨aumer, H.J. Freund, J.A. Mejias, V. Staemmler, S. Muller, L. Hammer, K. Heinz, Surf. Sci. 372 (1997) L291. [9] J. Mougin, T.L. Bihan, G. Lucazeau, J. Phys. Chem. Solids 62 (2001) 553. [10] A.K. Sinha, K. Suzuki, Appl. Catal. B: Environ. 70 (2007) 417.
[11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
C.H. Lin, P. Shen, S.Y. Chen, Y. Zheng, J. Phys. Chem. C 112 (2008) 17559. C. Rehbein, F. Michel, N.M. Harrison, A. Wander, Surf. Rev. Lett. 5 (1998) 337. M.J. Aziz, C.W. White, Phys. Rev. Lett. 57 (1986) 2675. K.M. Beatty, K.A. Jackson, J. Cryst. Growth 174 (1997) 28. K.A. Jackson, J. Cryst. Growth 198/199 (1999) 1. P. Hartman, W.G. Perdok, Acta Crystallogr. 8 (1955) 525. I. Sunagawa, J. Cryst. Growth 99 (1990) 1156. S. Rekhi, L.S. Dubrovinsky, R. Ahuja, S.K. Saxena, B. Johansson, J. Alloys Compd. 302 (2000) 16. F. Banhart, P.M. Ajayan, Nature 382 (1996) 433. S.Y. Chen, P. Shen, Phys. Rev. Lett. 89 (2002) 096106. S.Y. Chen, P. Shen, Jpn. J. Appl. Phys. 43 (2004) 1519. M.F. Ashby, Acta Metall. 37 (1989) 1273. M.R. Falvo, G.J. Clary, R.M. Taylor, V. Chi, F.P. Brooks, S. Washburn, R. Superfine, Nature 389 (1997) 582. M.M.J. Treacy, T.W. Ebbesen, J.M. Gibson, Nature 381 (1996) 678. Z.W. Wang, Q.X. Quo, J. Phys. Chem. C 113 (2009) 4286.
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Technical note
Shape-dependent local internal stress of a-Cr2O3 nanocrystal fabricated by pulsed laser ablation C.H. Lin a, S.Y. Chen b, N.J. Ho a, D. Gan a, P. Shen a, a
Department of Materials and Optoelectronic Science, Institute of Materials Science and Engineering, Center for Nanoscience and Nanotechnology, National Sun Yat-sen University, Kaohsiung, Taiwan, ROC b Department of Mechanical and Automation Engineering, I-Shou University, Kaohsiung, Taiwan, ROC
a r t i c l e in fo
abstract
Article history: Received 15 June 2009 Received in revised form 30 July 2009 Accepted 23 September 2009
The a-Cr2O3 single-crystal nanocondensates were fabricated by pulsed laser ablation in air and characterized by analytical electron microscopy regarding shape-dependent local internal stress of the anisotropic crystal. The nanocondensates formed predominantly as rhombohedra with well-developed f0 1 1 2g surfaces and occasionally hexagonal plate with thin f1 1 2 0g edges and blunt corners. Such nanocondensates showed Raman shift for the CrO6 polyhedra, indicating a local compressive stress up to ca. 4 GPa on the average. Careful analysis of the lattice fringes revealed a local compressive stress (0.5% strain) at the thin edge of the hexagonal plates and a local tensile stress (0.3–1.0% strain) near the relaxed f1 0 1 2g, f1 0 1 1g, and (0 0 0 1) surfaces of truncated rhombohedra. The combined effects of nanosize, capillarity force at sharp edge, and specific surface relaxation account for the retention of a local internal compressive stress built up in an anisotropic crystal during a very rapid heating–cooling process. & 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Nanostructure B. Laser annealing C. Raman spectroscopy D. Surface properties D. Elastic properties
1. Introduction It is a common knowledge that size-dependent pressure due to capillarity force follows a simple relation 2g/r for a spherical particle, where g is the surface energy and r the radius of curvature [1]. On the other hand, shape-dependent local internal stress involving capillarity force and specific surface relaxation of an anisotropic nanocrystal is less understood. Here we report such experimental evidences for a representative anisotropic nanocrystal formed via a pulsed laser ablation (PLA) technique. We focused on the corundum-type a-Cr2O3 system because it has well-developed surfaces with periodic bond chains (PBCs), i.e., strong bonding directions [2,3], and theoretically calculated surface relaxations of various surfaces [4]. The purpose is to study the variation of the shapes of the nanocrystals and hence the local internal stresses built up in a dynamic heating–cooling process. The spectroscopic evidence of a very large internal compressive stress in the a-Cr2O3 nanocrystals was provided. The cause and mechanism of sustaining a large internal stress without breaking down the crystal core was rationalized by the presence of a (h k i l)-specific relaxation shell as observed for the first time by careful measurements of the lattice plane spacing. The a-Cr2O3 material is also of engineering interest for
Corresponding author. Fax: +886 7 525 4099.
E-mail address: [email protected] (P. Shen). 0022-3697/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2009.09.015
potential applications in optoelectronics such as components for flat-panel display devices [5].
2. Experimental Cr (Solar Applied Materials Technology, 99.9% pure) plate 1 mm in thickness was subjected to energetic Nd-YAG-laser (Lotis, 1064 nm in wavelength, beam mode: TEM00) pulse irradiation. The laser beam was focused to a spot size of 0.03 mm2 on the target inside the ablation chamber for ablation in air. Oxygen gas (99.999% purity) at a flow rate of 50 L/min was supplied into the chamber to oxidize and cool the as-formed condensates. A specified laser power density of 1.5 108 W/cm2, i.e. 1100 mJ/pulse with a pulse time duration of 240 ms at 10 Hz on a focused area of 0.03 mm2, was employed. The condensates were collected with Cu grid covered with a carbon-coated collodion film for direct observation. The composition and crystal structures of the condensates were characterized by analytical electron microscopy (AEM, Tecnai G2 F20 at 200 kV) with selected area electron diffraction (SAED), and point-count energy dispersive X-ray (EDX) analysis with a beam size of 10 nm. Bright field images (BFI) taken by transmission electron microscopy (TEM) were used to study the general morphology and agglomeration of the nanocrystals. Lattice imaging coupled with two-dimensional (2-D) Fourier transform and inverse transform was used to characterize the crystal structure of the individual
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nanoparticles. The d-spacings were averaged from ca. 30 lattice fringes in magnified TEM images for improved accuracy ( 70.0002 nm) to evaluate local internal strain and stress with respect to the exposed surfaces and sharp edges. The condensates collected on soda-lime glass were used for Raman spectroscopic study of the retained internal stress. Raman spectra were made using semiconductor laser excitation (532 nm) having a frequency resolution of 2 cm 1 and a beam diameter of 1 mm using Opympus MPlan 100 objective (Jobin-Yvon Triax 320 Micro-Raman microprobe). The analysis typically covered more than 1000 nanoparticles less than 100 nm in size accumulated up to 1 mm thick. The reagent-grade a-Cr2O3 powder (Cerac, 5 mm in diameter, 99.8% pure) and other PLA samples fabricated in vacuum, air or water [6] were used to calibrate the Raman shifts. The same sample was also used for X-ray photoelectron spectroscopy (XPS, JEOL JPS-9010MX Photoelectron spectrometer with Mg Ka X-ray source), calibrated with a standard of C 1s at 284 eV, to analyze the position of Cr 2p3/2 peak for the possible presence of Cr2 + in the condensates. The condensates were mostly formed in air before being collected by Cu grid or glass substrate.
The a-Cr2O3 condensates formed predominantly rhombs with sharp corners occasionally truncated. Hexagons were also observed but were much less in number. These nano condensates tended to coalesce over well-developed surface into nano-chain aggregate or into close-packed groups. The electron diffraction ring patterns showed significant line broadening and hence were difficult, if not impossible, to measure the d-spacings with sufficient accuracy for least-squares refinement of precise lattice parameters regarding possible retention of the internal stress.
3. Results 3.1. TEM observations The condensates collected on a carbon-coated collodion film were identified by BFI and SAED pattern as randomly oriented a-Cr2O3 nanocrystals ranging from 30 to 100 nm in size (Fig. 1).
Fig. 1. TEM (a) BFI and (b) corresponding SAED pattern and index of rhombohedral and hexagonal-shaped a-Cr2O3 condensates ranging from 30 to 100 nm in size and randomly oriented as indicated by ring pattern. (c) BFI of another area of the aCr2O3 condensates showing coalescence of rhombs and hexagons (denoted by an arrow) into nano-chain aggregate. Sample produced by laser ablation on pure Cr target at 1100 mJ/pulse and oxygen flow rate of 50 L/min in air and collected by a carbon-coated collodion film.
Fig. 2. TEM (a) lattice image of a truncated rhombohedral a-Cr2O3 particle, magnified from inset, showing well-developed {0 0 0 1}, f1 0 1 2g, and f1 0 1 1g surfaces viewed edge on in the ½1 2 1 0 zone axis. The lattice fringe spacings of ð1 0 1 2Þ, ð2 0 2 2Þ, and (0 0 0 6) all increase from core to edge as shown by the average values in three adjoined regions denoted by arrows. (b) Another magnified area showing the increased d-spacing of {1014} planes toward the surface. (c) and (d) 2-D forward and inverse Fourier transform of the square region in (a), showing dislocation-free lattice. It is the same specimen as in Fig. 1.
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Lattice imaging was used to identify the {h k i l} surfaces and associated strain for the a-Cr2O3 nanocrystals in the form of truncated rhomb and hexagonal plate. The truncated rhombohe-
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dral a-Cr2O3 nanoparticle has {0 0 0 1} and f1 0 1 1g surfaces besides well-developed f1 0 1 2g surfaces as viewed edge on in the ½1 2 1 0 zone axis (Fig. 2). Careful measurement of the magnified lattice fringe spacings of ð1 0 1 2Þ, ð2 0 2 2Þ, and (0 0 0 6) showed unambiguous increase of d-spacing from core to edge as shown by the average values in three adjoined regions indicated in Fig. 2a. There is also increased d-spacing of f1 0 1 4g planes toward the surface (Fig. 2b), indicating that the capillarity force can be ignored in this case. No dislocation was observed in this nanocrystal. Fig. 3a shows a hexagonal a-Cr2O3 nanoplate in the [0 0 0 1] zone axis with well-developed (0 0 0 1) terraces on top and f1 1 2 0g lateral surfaces viewed edge on. The magnified lattice image shows a decreasing f1 1 2 0g d-spacing toward the edge as indicated by the average values in three regions indicated in Fig. 3b. The nanoplate is also dislocation free as indicated by 2-D forward and inverse Fourier transform (Figs. 3c and d). Alternatively, the hexagonal a-Cr2O3 nanoplate showed gradual change of the plate thickness fading from the central thick area toward sharp edge (not shown). Point-count EDX spectrum of the nanoplate shows the presence of Cr and O and negligible impurities (Fig. 3e). It should be noted that the hexagonal undoped aCr2O3 nanoplate has a blunt corner at f1 1 2 0g junctions (Fig. 3a). In contrast, Si4 + -doped Cr2O3 condensate produced by the same PLA method has six sharp/concave corners at the junction of f1 1 2 0g vicinal surfaces [7] (see Fig. 5 of Ref. [7]). Reasons for such a difference will be addressed later. The lattice-fringe interplanar spacing variations from core to edge of the a-Cr2O3 nanocondensates in Figs. 2 and 3 are compiled in Table 1. In comparison with the calculated ambient values based on the reported lattice parameters a =0.4959 nm and c=1.3594 nm (JCPDS file# 38-1479), the d-spacing is significantly smaller at the core but larger at the edge of the nanoparticle. The only exception is ð1 1 2 0Þ, which shows an opposite trend due to the thin edge with a large capillarity force. It should be noted that the theoretical calculation [4] indicates a more complicated manner of surface relaxation than the interspacing variation of the present nanocondensates produced by a dynamic PLA process. The relaxation of the a-Cr2O3 (0 0 0 1) plane was theoretically suggested to involve a decreased separation between the Cr and O ions at the surface and an increased side length of the equilateral O triangle, while the ð1 0 1 2Þ plane to involve a 8%, 20%, 6%, and 15% change in the top four interplanar spacings, respectively [4]. On the other hand, the low-energy electron diffraction of the (0 0 0 1) surface indicates a significant charge reduction and Table 1 Lattice fringe interspacing variation from core to edge of the a-Cr2O3 nanocondensates. hkil
Surface relaxation
Core
Middle
Edge
Calculated
0112
0.3597
0.3617
0.3652 (+0.0021)
0.3631
0.58%
1014
0.2631
0.2659
0.2673 (+ 0.0008)
0.2665
0.30%
1120 0006
0.2511
0.2490
0.2467 ( 0.0013)
0.2480
NA
0.2264 0.2014
0.2274 0.2029
0.2288 (+0.0022) 0.2066 (+ 0.0018)
0.2266 0.2048
0.97% 0.88%
2022
Fig. 3. TEM (a) lattice image of hexagonal a-Cr2O3 nanoplate with well-developed (0 0 0 1) terraces in top view and f1 1 2 0g lateral faces edge on in [0 0 0 1] zone axis. (b) Magnified image showing its blunt corner. (c) and (d) 2-D forward and inverse Fourier transform of the square region. (e) Point-count EDX spectrum showing Cr and O counts, the C and Cu counts being from the carbon-coated collodion film and copper holder. Note the d-spacing of ð1 1 2 0Þ plane in (b) decreases toward the thin edge as indicated by the average values in three adjoined regions. It is the same specimen as in Fig. 1.
d-spacing (nm)a
The bulk ambient values are calculated from the reported lattice parameters a= 0.4959 nm and c =1.3594 nm (JCPDS file# 38-1479). The differences between the d-spacings at edge and those of ambient values are also given in parenthesis. a The d-spacings (7 0.0004 nm) were averaged from about 30 lattice fringes in Figs. 2 and 3. Note in comparison with the calculated ambient values, there is a significantly smaller d-spacing at the core and a larger d-spacing at the edge of the nanoparticle, except ð1 1 2 0Þ which shows opposite trend with a 0.52% decrease near the surface. This statement is supported by three more independent observations of the nanocondensates [6].
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depolarization to stabilize the surface [8]. In the present case, the local strain of the nanocondensates can be reasonably estimated to be 0.5% at the thin edge of the hexagonal nanoplates and 0.3–1.0% for the well-developed and relaxed f1 0 1 2g, f1 0 1 1g, and {0 0 0 1} surfaces.
3.2. Spectroscopy The Raman spectra of the reagent-grade a-Cr2O3 powders and the a-Cr2O3 nanocondensates deposited on silica glass under the same conditions as the TEM samples are shown in Figs. 4a and b, respectively. The standard powders under ambient condition have five characteristic Raman peaks at 296, 328, 484, 536, and 590 cm 1 whereas the nanocondensates show peak shifting to 268, 301, 510, 548, and 610 cm 1, respectively, with an additional peak at 697 cm 1. The shift of the most intense Raman peak, assigned as A1g symmetry [9], from 536 to 548 cm 1 indicates a compressive stress of 4 GPa for the constituting CrO6 polyhedra of the nanocondensates, according to the Raman shift dependence on applied compressive pressure [9]. The binding energy of the a-Cr2O3 nanocondensates deposited on glass is characterized by Cr 2p1/2 and Cr 2p3/2 and O 1s peaks with peak binding energy at 587, 577, and 530 eV, respectively (Fig. 4c), indicating that the Cr2 + content is negligible [10]. The Cr2 + presence would otherwise cause a lower binding energy for Cr 2p3/2 and less sharp peaks for Cr 2p1/2 and O 1s [10]. 4. Discussion 4.1. Shape change of the nanocondensates
Fig. 4. Raman spectra of a-Cr2O3: (a) ambient reagent-grade powders with five characteristic Raman peaks at 296, 328, 484, 536, and 590 cm 1. (b) Nanocondensates deposited on silica glass by pulsed laser ablation showing shifts of corresponding Raman peaks to 268, 301, 510, 548, and 610 cm 1, respectively, with additional 697 cm 1. The strongest peaks with Lorentzian curve fittings inset in (a) and (b) are used for internal stress estimation (cf. text). (c) XPS spectrum of the same a-Cr2O3 condensates as in (b) showing Cr 2p1/2, Cr 2p3/2 and O 1s peaks, indicating a negligible Cr2 + content (cf. text) [10].
According to the ideal unrelaxed atom disposition [11], the f1 1 0 4g, f1 1 2 0g, and f0 1 1 2g of a-Cr2O3 are K, S and energetically favorable F faces having the cation-filled octahedral sites assembled as 0, 1, and 2 PBCs, respectively [2]. The (0001), despite having 3 PBCs, is energetically less favorable than f0 1 1 2g in theory [4,12]. (For example, the surface energies of (0 0 0 1) and ð0 1 1 2Þ are 2.95 and 2.37 J m 2, respectively, for relaxed geometries and are 5.06 and 2.84 J m 2, respectively, for unrelaxed geometries according to recent first-principles Hartree-Fock calculations [4].) In addition, the multiplicity factor of (0 0 0 1) is one-sixth that of f0 1 1 2g. Thus, rhomb shape with well-developed f0 1 1 2g surfaces, occasionally truncated by (0 0 0 1), is favored for the present a-Cr2O3 nanocondensates. The truncation by f1 0 1 1g is less favored because its surface energy is higher than (0 0 0 1) and f0 1 1 2g after relaxation [4]. The nanocondensates were occasionally found to be hexagonal in shape having well-developed {0 0 0 1} terraces and f1 1 2 0g lateral edges with blunt corners, implying a combined growth mechanism of basal surface nucleation and lateral ledge growth. According to first-principles Hartree-Fock calculations [4], the (0 0 0 1) has a lower surface energy than f1 1 2 0g in relaxed state (2.95 and 3.10 J m 2, respectively), but is higher than f1 1 2 0g in unrelaxed state (5.06 and 3.81 J m 2, respectively). The (0 0 0 1) surface thus needs to be relaxed in order to form a hexagonal plate with well-developed (0 0 0 1) surface and rapid growth edges of f1 1 2 0g. Precondensation during solidification or crystallization from melt/solutions may affect the attachment of ions/atoms on specific F faces in terms of PBCs and hence may favor unexpected faces not following the PBC predictions [3]. The Si4 + -doped a-Cr2O3 nanocondensates, being in the form of corrugated hexagons with well-developed (0 0 0 1) surface and f1 1 2 0g edges with sharp corners and concave edges [7], suggest that they were formed by a combined effect of precondensation and constitutional supercooling. It is possible that the Si4 + dopant lowers the surface energy of (0 0 0 1) and hence promotes its surface nucleation and lateral growth. On the other hand, the curved f1 1 2 0g surfaces of Si4 + -doped a-Cr2O3 [7] may be related to the orientation-dependent incorporation of solute, as illustrated by experimental [13] and theoretical [14,15] works on the preferred
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incorporation of solute at flat Si(111) face rather than its rough interface for a higher distribution coefficient, b = avDm/DkbT (where a is the interatomic spacing, v is the growth rate, Dm is the chemical potential driving force for the crystallization process, and D is the diffusion coefficient) and an extended solid solubility. In fact, enhanced solute incorporation, or so-called solute trapping, via a very rapid growth rate was proved experimentally by laser-melted Bi-doped silicon wafers showing orientation dependence on the nonequilibrium partition coefficient of Bi in Si [13] and by computer modeling [14]. Note also the S- and K-faces of barite crystal were suggested to be favored by dehydration and impurities [16]. Diamonds also tend to form dendrite with unusual faces such as (1 0 0) rather than (111) under the combined effects of H2O and a large driving force [17]. In any case, the above impurity effect can be neglected for the present a-Cr2O3 condensates by the absence of Si based on the EDX spectrum (Fig. 3) and the Cr 2p1/2, Cr 2p3/2 and O 1s peaks by XPS (Fig. 4c) showing negligible Cr2 + content.
4.2. Internal stress state of the nanocondensates There is a significant compressive stress for the constituting CrO6 polyhedra in the present a-Cr2O3 nanocondensates, similar to the cases of Si4 + -doped a-Cr2O3 [7] and the partially crystallized chromium oxide lamellae, which were fabricated by PLA in vacuum with a much finer nanosize and hence a higher heating/cooling rate [11]. However, according to lattice fringe interspacings, there is a significant local compressive stress at the core and local tensile stress near the relaxed surfaces of the a-Cr2O3 nanocondensates (Table 1). The bulk compressibility of a-Cr2O3 was reported to be 240 GPa based on experiments under isotropically compressed conditions [18]. We suggest that the combined effects of nanosize, capillarity force at thin edges, dislocation-free state as well as (h k i l)-specific (i.e., (0 0 0 1), f1 0 1 2g, and f1 0 1 1g) relaxation may contribute to the buildingup of a rather complicated local internal compressive stress for the nanoparticles, which would otherwise relax to ambient cell volume without the large internal stress. This argument is supported by a rather tight 6-coordination of Cr3 + in the corundum-like structure or even amorphous phase formed upon rapid quenching [11]. It is also similar to the graphite anion-like nanopressure cell with a progressively smaller basal interplanar spacing to generate diamond at its core upon very intense electron irradiation [19]. The various extents of surface relaxation on the well-developed (0 0 0 1) and f1 0 1 2g, and minor f1 0 1 1g shed light on the shape-dependent local internal stress of the condensates. According to Mougin et al. [9], a-Cr2O3 typically shows five Raman modes in the range of 200–800 cm 1 under ambient pressure conditions. These Raman bands, except the one with the lowest wave number, were found to shift toward higher wave numbers with an increased applied pressure because of a decreased interatomic distance [9]. In the present study, both bulk powder and nanocondensates displayed five Raman peaks. However, compared to the bulk samples, three high-wave number Raman peaks in the nano samples shifted to higher wave number (i.e. from 484, 536, 590 to 510, 548, 610 cm 1, respectively, with an additional peak at 697 cm 1), and two low-wave number peaks shifted to lower wave number (i.e. from 296 and 328 to 268 and 301 cm 1, respectively). These changes could possibly be related to the observed surface compression and relaxation at different facets of the nanocondensates as a result of anisotropic (i.e. {h k i l}-specific) internal stress via a dynamic PLA process. However, the extent of deviatoric stress is difficult, if not impossible, to analyze in this complicated case. Still, the shift of
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the most intense Raman peaks of A1g symmetry, from 536 to 548 cm 1, and the additional peak assigned as Eg symmetry near 700 cm 1 indicates a significant compressive stress at least up to ca. 4 GPa for the constituting CrO6 polyhedra according to the equation of state by Mougin et al. [9]. This statement is justified by comparable frequencies of the strongest Raman band for other PLA samples fabricated in vacuum, air, and water [6] under power density known to produce high-pressure phases [20,21]. The other Raman modes are too weak and broad to be fitted by appropriate mathematical functions (Figs. 4a and b) and to provide meaningful insight into the internal stress. Rapid quenching can sometimes result in the formation of high-pressure phase, such as the a-PbO2- and fluorite-type TiO2 [20,21], with a significant activation energy to suppress the backtransformation to ambient structure. In the present case, a large local stress is retained without forming the high-pressure phase. The theoretical strength of materials was estimated to be 1/10 of its Young’s modulus G based on the Griffith criteria [22]. The yielding strength of a crystalline bulk material can be orders-ofmagnitude (10 1–10 3) lower than its theoretical strength due to the presence of dislocations. Thus, the present a-Cr2O3 nanocondensates, being free of dislocations, may have a high yield stress and therefore are expected to be capable of retaining a high local internal stress, maybe up to the theoretical strength. In this connection, the maximum sustained tensile strain on the outside surface of a bent carbon nanotube was estimated to be as large as 16% [23], which corresponds to a tensile stress of 288 GPa, 1/16 of its Young’s modulus 1.8 TPa [24]. Without experimental data on Young’s modulus, the bulk modulus reported to be 240 GPa [18] can be used as a substitute as adopted in the high-pressure study of other close-packed crystal, e.g. ZnS [25]. The theoretical strength of the a-Cr2O3 nanocondensates is therefore estimated to be about 24 GPa, i.e. one-tenth of G as mentioned. The internal stress of the nanocondensates, estimated by the Raman shift to be ca. 4 GPa, is less than that. The d-spacing differences at the cores of the nanocondensates with respect to the values calculated from bulk samples (Table 1) provide another rough estimate to be 0.21, 2.2, 3.1, and 4.0 GPa for (0 0 0 6), ð0 1 1 2Þ, ð1 0 1 4Þ, and ð2 0 2 2Þ, respectively. The high internal stresses estimated by both methods are in the same order of magnitude and are still less than the theoretical strength. Therefore these are reasonable estimates.
5. Conclusions The a-Cr2O3 nanocondensates fabricated by pulsed laser ablation in air with very rapid heating and cooling showed a significant internal stress. Compressive stress up to 5 GPa on the average was formed. Local compression at thin edge and local tensile stress near the relaxed surfaces of the anisotropic single crystal were also carefully measured based on the average from about 30 lattice fringes for a meaningful accuracy improvement. The relaxed surface enabled the retention of compressive internal stress, analogous to carbon anions as nanoscopic pressure cells for diamond formation, and may shed light on the stress state of sesquioxide nanocondensates in natural and engineering dynamic settings.
Acknowledgments We thank Dr. C.N. Huang for PLA runs with us, Miss S.Y. Shih for the help with XPS analysis and anonymous referees for constructive comments. This work was supported by Center for Nanoscience and Nanotechnology at NSYSU and National Science Council, Taiwan, ROC.
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References [1] D.A. Porter, K.E. Easterling, Phase Transformations in Metals and Alloys, second ed., Van Nostrand, Reinhold, 1981. [2] P. Hartman, W.G. Perdok, Acta Crystallogr. 8 (1955) 49. [3] P. Hartman, W.G. Perdok, Acta Crystallogr. 8 (1955) 521. [4] J. Sun, T. Stirner, A. Matthews, Surf. Coat. Technol. 201 (2006) 4205. [5] M. Tabbal, S. Kahwaji, T.C. Christidis, B. Nsouli, K. Zahraman, Thin Solid Films 515 (2006) 1976. [6] C.H. Lin, Chromium oxide condensates fabricated by pulsed laser ablation in air, vacuum and water, Ph.D. Thesis, National Sun Yat-sen University, Taiwan, ROC, 2009. [7] C.H. Lin, S.Y. Chen, P. Shen, J. Cryst. Growth 310 (2008) 245. ¨ [8] F. Rohr, F. B¨aumer, H.J. Freund, J.A. Mejias, V. Staemmler, S. Muller, L. Hammer, K. Heinz, Surf. Sci. 372 (1997) L291. [9] J. Mougin, T.L. Bihan, G. Lucazeau, J. Phys. Chem. Solids 62 (2001) 553. [10] A.K. Sinha, K. Suzuki, Appl. Catal. B: Environ. 70 (2007) 417.
[11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
C.H. Lin, P. Shen, S.Y. Chen, Y. Zheng, J. Phys. Chem. C 112 (2008) 17559. C. Rehbein, F. Michel, N.M. Harrison, A. Wander, Surf. Rev. Lett. 5 (1998) 337. M.J. Aziz, C.W. White, Phys. Rev. Lett. 57 (1986) 2675. K.M. Beatty, K.A. Jackson, J. Cryst. Growth 174 (1997) 28. K.A. Jackson, J. Cryst. Growth 198/199 (1999) 1. P. Hartman, W.G. Perdok, Acta Crystallogr. 8 (1955) 525. I. Sunagawa, J. Cryst. Growth 99 (1990) 1156. S. Rekhi, L.S. Dubrovinsky, R. Ahuja, S.K. Saxena, B. Johansson, J. Alloys Compd. 302 (2000) 16. F. Banhart, P.M. Ajayan, Nature 382 (1996) 433. S.Y. Chen, P. Shen, Phys. Rev. Lett. 89 (2002) 096106. S.Y. Chen, P. Shen, Jpn. J. Appl. Phys. 43 (2004) 1519. M.F. Ashby, Acta Metall. 37 (1989) 1273. M.R. Falvo, G.J. Clary, R.M. Taylor, V. Chi, F.P. Brooks, S. Washburn, R. Superfine, Nature 389 (1997) 582. M.M.J. Treacy, T.W. Ebbesen, J.M. Gibson, Nature 381 (1996) 678. Z.W. Wang, Q.X. Quo, J. Phys. Chem. C 113 (2009) 4286.