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Allotropic phase transformations in HCP, FCC and BCC metastable structures in Co-nanoparticles
Materials Science and Engineering A304–306 (2001) 923–927
Allotropic phase transformations in HCP, FCC and BCC metastable structures in Co-nanoparticles S. Ram∗ Materials Science Centre, Indian Institute of Technology, Kharagpur 721 302, India
Abstract The effect of particle size on stability of crystal structure of pure cobalt metal is studied. The common HCP allotrope of it is stable in bulk. It assumes an FCC or a BCC structure on reducing its size below a critical value Rc at a nanometer scale. Separated Co-particles coreduced (using a reducing agent) from highly dispersed Co2+ -cations in a liquid or a solid medium have a strict control of size at D = 2–5 nm for the BCC structure and D = 10–20 nm for the FCC structure. Both of them are substantially stable at least within the temperature range of 700◦ C and do not transform to the HCP structure as long as their size is controlled within these regions. The present crystal structure modification in a particle occurs in a manner that it has a minimal value of its total surface energy Ω = Aσ , with A its total surface area and σ the surface-energy density. It yields a stable equilibrium configuration of atoms with its minimal internal energy. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Co-metal; Nanocrystals; Co-allotropes; FCC cobalt; BCC cobalt
1. Introduction Pure cobalt powder samples with diameters (D) of a few nanometers are a subject of intense research due to their unique magnetic and other physical properties which make it very appealing from both the theoretical and the technological points of view [1–3]. It is specially important for information storage systems, ferrofluids, contrast agents in magnetic resonance imaging, and optoelectronic devices [1–7]. Below a critical size Dc ∼ 20 nm, it becomes single domain in nature with unique phenomena of quantum size effects, quantum tunneling of magnetization, superparamagnetism, and unusually large magnetic anisotropies [5–7]. An enhanced surface area A in such small particles induces a modified electronic structure which often results in an enhanced saturation magnetization ρ s by as much as 34% along with an improved value for magnetocrystalline (Ha ) or surface (Hs ) anisotropies over the bulk values [3,7]. It gives a very simple way of improving their energy-product (BH)max . In a solid of finite size, its total surface energy Ω = Aσ , with energy density σ , has a strong correlation with its stability and crystal structure. Thermodynamically, a reduction of its size below a critical value Rc modifies its crystal structure and/or morphology in a manner that the latter is stable with a minimal value of its internal energy ∗
Tel.: +91-03222-55221; fax: +91-03222-55303. E-mail address: [email protected] (S. Ram).
ε0 . In minimizing ε0 , the value of Ω plays a crucial role at R ≤ Rc . As a result, the HCP Co-metal, which is stable in bulk, becomes unstable by an enhanced Ω value in reducing its size to a few nanometers. At this scale, it exists in an FCC or BCC structure [3,7] stabilized with a smaller value of Ω over the HCP structure. This is demonstrated in this paper with synthesis of a pure Co-metal in a strictly controlled 2–20 nm size. 2. Experimental details 2.1. Synthesis Co-nanoparticles of controlled 2–20 nm size were synthesized from highly dispersed Co2+ -cations in (i) a liquid and (ii) a solid matrix by two independent chemical co-reduction reaction methods. The first method involves a rather fast nucleation of the particles from an aqueous Co2+ -solution by a reducing agent NaBH4 . In the other method, similar Co-nanoparticles are produced by thermal decomposition and co-reduction of a Co2+ :AlO(OH)·αH2 O gel in H2 gas. This occurs in a strictly controlled fashion in finely divided reaction centres in a very fine Al2 O3 matrix. Other details are as follows. 2.1.1. Co-reduction reaction in a liquid medium A 10−2 M CoCl2 ·6H2 O solution was obtained in a 10 wt.% DDAB (didodecyldimethyl ammonium bromide),
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Table 1 Crystal lattice parameters, lattice surface area A, lattice volume V, and lattice surface energy Ω for three allotropes of BCC, FCC and HCP crystal structures in a pure cobalt metal Sample
Lattice parameters (nm)
Co-reduced from a Co2+ -solution FCC structure a = 0.3535 Co-reduced from BCC structure FCC structure
Co2+ -cations
Bulk cobalt metal FCC structure HCP structure
in Al2 O3 matrix a = 0.2840 a = 0.3540 a = 0.3545b a = 0.2507b c = 0.4070b
A (10−2 nm2 )
V (10−3 nm3 )
Ω (10−20 J)a
74.98
44.17
204.70
48.39 75.19
22.91 44.36
132.11 205.27
75.40 93.90
44.55 66.50
205.85 261.98
The value of Ω = Aσ is calculated using the reported value of σ = 2.73 J/m2 for the FCC structure and σ = 2.79 J/m2 for the HCP structure in [6]. In absence of a reported σ -value for the BCC structure, it is assumed to be the same as for the FCC structure. b The values of the lattice parameters are taken from Ref. [10]. a
solution in toluene. It is reduced to Co-granules by adding a highly concentrated ∼5 M NaBH4 aqueous solution drop-by-drop while stirring the mixture. The whole reaction is carried out in an argon atmosphere. A highly exothermic reaction occurs and results in black slurries of reduced Co2+ into Co-powders of nanometer size. Average temperature of the solution is controlled at ∼273 K with an ice bath having NaCl impurities. DDAB, which is an established cationic surfactant [3], traps the Co2+ cations in empty micelles and helps the reduction reaction within the micelles by preventing re-oxidation of the sample. After the reaction, the Co-slurries are filtered, carefully washed in deionized water and toluene, and then immediately dried in vacuum or N2 gas at room temperature. 2.1.2. Co-reduction reaction from a gel The Co2+ :AlO(OH)·αH2 O gel was prepared by hydrolysis of Al-metal in an aqueous CoCl2 ·6H2 O solution (∼1.0 M) as described earlier [8,9]. Its thermal decomposition and co-reduction in H2 gas at 500–850◦ C gives separated Co-nanoparticles dispersed in an Al2 O3 matrix of thermal decomposed gel. The samples with different average sizes were obtained by a proper selection of the reduction temperature in this range. A refined microstructure of highly dispersed Al2 O3 matrix in thermal decomposition of the gel supports nucleation of Co-nanoparticles in a strictly controlled size as small as a few nanometers in divided co-reduction reaction centres.
which are given in Table 1. In situ analysis of the compositional maps with an electron microprobe analyzer confirmed absence of byproduct impurities in either series of the specimens. 3. Results and discussion Fig. 1 shows a TEM micrograph of a nanocrystalline sample of pure Co-nanoparticles co-reduced from Co2+ -cations dispersed in the liquid medium as described above. Most of the particles have a shape of well-separated thin platelets of an average diameter D ∼ 10 nm, volume V = Aδ ≡ 150 nm3 , and aspect ratio D/δ ∼ 5, with A ∼ 75 nm2 the surface area for one of the two flat faces. As discussed below, they form a single phase of an FCC crystal structure. The TEM in Fig. 1 contains 2–5% extremely small particles, D = 1–2 nm, which have a spherical shape. A spherical shape presents a minimal surface and in turn a minimal
2.2. Characterization The structure of Co-nanoparticles was analyzed by X-ray diffraction. The diffractogram was recorded with a PW 1710 X-ray diffractometer using filtered Cu K␣ (or Co K␣) radiation of wavelength λ = 0.15406 nm (or 0.17902 nm). Their size/morphology was studied with a JEM 2000cx transmission electron microscope. The positions of the X-ray diffraction peaks were used to calculate the lattice parameters
Fig. 1. TEM micrograph of a typical Co-nanopowder of an FCC crystal structure co-reduced from Co2+ -cations dispersed in an aqueous solution. The scale bar refers to 50 nm.
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Fig. 2. X-ray powder diffractogram of Co-nanoparticles of FCC and BCC crystal structures co-reduced in an Al2 O3 matrix. The peaks of FCC phase are marked by asteriks (∗). Three unassigned peaks (∗∗) around the 2θ values of 37, 44 and 79◦ are due to the matrix. In the inset is shown the diffractogram of a single FCC structure of a Co-nanopowder co-reduced from Co2+ -cations dispersed in an aqueous solution.
value of Ω. This change in the shape of particle from a thin platelet to a spherical one for decreasing D-values in this example demonstrates preponderance of its surface-energy Ω in re-organizing its surface structure in a way that the latter has its minimal Ω-value. In a small particle, the Ω controls distribution of atoms in a specific crystal structure (or configuration of atoms) of a minimal internal energy ε0 . In order to ascertain this conjecture, in a separate experiment, we synthesized finely dispersed Co-metal particles of finite size in a thermally rigid Al2 O3 matrix, as discussed above. The Al2 O3 matrix controls nucleation of very small particles at a moderate rate by inhibiting a fast migration of the reaction species (Co atoms) through it. As a result, the reaction occurs in a controlled manner by nucleation and growth from small nuclei formed according to their basic crystal structures and Ω energies. This is clearly demonstrated by the X-ray diffractogram (Fig. 2) for a Co:Al2 O3 sample obtained by reducing the gel in a flowing H2 gas at 730◦ C for 30 min. The Co-particles, which are dispersed in the Al2 O3 matrix, present two crystalline phases of cobalt of FCC and BCC structures which involve the confined crystal lattices of surface area A∗ = 0.4839 and 0.7519 nm2 or surface energy Ω ∗ = 2.0527 × 10−18 and 1.3211 × 10−18 J, respectively, if compared with A∗ = 0.9390 nm2 and Ω ∗ = 2.6198 × 10−18 J for the bulk HCP structure. The X-ray diffractogram of FCC phase is fairly matching with the standard diffractogram for the bulk sample [10] with a total of three (1 1 1), (2 0 0) and (2 2 0) characteristic peaks (Fig. 2). A lattice parameter a = 0.3540 nm (0.3545 nm the bulk value [10]) has been estimated using their positions. The X-ray diffractogram of
pure Co-powder, obtained in an FCC structure by the other method, are compared in the inset to Fig. 2. It has three sharp peaks at 0.2039, 0.1769 and 0.1248 nm in (1 1 1), (2 0 0) and (2 2 0) lattice reflections with the lattice parameter a = 0.3535 nm. No other diffraction peaks in possible impurities due to an HCP or any other Co-phase have been observed. In the FCC–BCC mixed phase Co-powder dispersed in the Al2 O3 ceramic matrix, a ratio 5:4 between the two phases is estimated according to relative intensities in their most intense peaks at 0.2045 and 0.2015 nm. Several experiments were carried out by reducing the gel of different compositions at different temperatures, in the 500–850◦ C range, in an attempt to have a single phase. It was found that the ratio between the two phases varies with the gel-composition as well as with the reducing temperature but it never gave a single Co-phase. This FCC–BCC biphase structure is stable over a wide range of temperature upto 1000◦ C and at surprisingly large crystallite sizes. Crystallites in either phase are as big as 80 nm as can be determined by an analysis of the widths of the X-ray diffraction peaks. They do not transform to an HCP structure which is the most stable allotrope of cobalt otherwise. The bulk HCP cobalt, as prepared by other methods [2,11], undergoes a reversible martensite transformation to the FCC structure at 427◦ C [11,12]. This transformation is weakly first order with small changes in enthalpy 1H = 440 kJ/mol and volume 1V /V = 0.0036. The two HCP and FCC phases exist in an equilibrium at temperature Teq ∼ 427◦ C, but there is considerable hysteresis between the heating and cooling transformations [12].
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Huang et al. [13] studied allotropic phase transformation in bulk cobalt metal by milling it in an inert gas atmosphere. It follows a sequence of transformation routes of HCP+FCC → HCP, HCP+FCC → HCP → FCC+HCP, and HCP + FCC → HCP → FCC + HCP → FCC, respectively. The results indicate that these phase transformations of bulk cobalt induced by milling are basically determined by a refinement of its microstructure which stores a large amount of surface energy as well as the Gibb’s free energy during the milling process. According to thermodynamics, it follows a self-reorganization of its final structure with creation of new surfaces in stable particles in a specific manner that the latter involves a minimal value of Ω with a minimal value of its internal energy ε0 . In this process, the FCC phase of cobalt which satisfies this conjuncture forms as a stable structure over the HCP phase which involves a rather larger value of Ω (see Table 1) in reducing its size to a confined value of a few nanometers. An enhanced symmetry in the FCC structure in the confined size induced HCP → FCC transformation which supports its stability as it further lowers its total internal energy ε. Formation of a stable structure in a chemical reaction, as used here, occurs by its nucleation followed by its growth in an equilibrium condition. The growth of a structure, which is a natural process, occurs as it lowers its total energy as well as the total energy of the system. For a sample of small critical volume, the Gibb’s free energy is not dependent on a single parameter of its radius r, as in the classical approach, but on the actual average spherical density profile ρ(r) [14]. In general, it can follow infinite numbers of trajectories and a number of metastable phases can be obtained out of it according to the experimental conditions. A stable particle in early stage of its growth is attained in a single non-degenerate process according to the reaction rate and its kinetics. It assumes a specific crystal structure which involves a minimal value of its total internal energy ε0 , which in turn involves a minimal value of its surface energy Ω ∗. In a rate limited process with highly dispersed reaction species in a medium, as in this example, a stable phase is achieved in a single non-degenerate process of such confined particles at moderate reaction rate. It involves small building blocks of a small critical volume Vc or surface energy Ω c as they nucleate first and grow easily in a stable structure at moderate rate. A formation of big building blocks of large Vc or Ω c and their recombination reactions forming bigger building blocks (particles) are not feasible at this moderate reaction rate to make a feasible stable structure in question. This occurs in a bulk reaction at a sufficiently large rate of recombination of the reaction species. It can be shown that growth of small building blocks of small Vc or Ω c value results in a small decrease in the total surface energy Ω(r) of the sample per unit mass as a function of V(r) if compared to that for a sample of big building blocks. As a result, two Ω(r) vs V(r) curves in the two examples intersect at a point Vc (rc ) and the minimum
free energy interface passes through this point. The particles of small size, V (r) ≤ Vc (rc ), are stable below this saddle point with their smaller Ω(r) ≤ Ωc (rc ) values while the bigger r > rc particles become stable in the region above this point by their reduced Ω(r) values under the Ω c (rc ) limit of their stability. Assuming a spherical shape of the particles, it is easy to −GHCP , show that if 1σ = σ FCC −σ HCP and 1Gv = GFCC v v i i where σ and Gv (i = FCC or HCP) refer to the surface energy density and the Gibb’s free energy, then a critical particle size rc exists below which the FCC phase is stable, rc = −
3 1σ 1Gv
(1)
Here, 1Gv is positive, and for positive rc values, 1σ must be negative in accordance with the experimental σ FCC = 2.73 J/m2 and σ HCP = 2.79 J/m2 values [6]. Substituting the value of 1σ = −0.06 J/m2 with 1Gv ∼ = 1.0 × 106 J/m3 [6], this relationship implies an optimal value of rc = 180 nm for particles of spherical shape with Ea = 0 shape anisotropy. In a realistic example, a deviation of their shape from the ideal spherical shape would cause a significant decrease in the final rc value as they involve a manifested 1Gv value by the contribution of the 1Ea = EaFCC − EaHCP shape anisotropy energy. This agrees with the observed size r, as big as r ≡ 21 D = 40 nm, of Co-particles, which are in a shape of thin platelets in this example. The r-value lies within the expected, rc ≤ 180 nm, range of stability of a Co-particle in an FCC or a BCC structure.
4. Conclusions In an FCC crystal structure usually 10 nm or smaller particles of a pure cobalt metal exist. The limit of their stability is extended to as big a size as 80 nm in a biphase FCC–BCC structure dispersed in an Al2 O3 matrix. According to this observation, it is proposed that a small particle of confined size below a critical value Rc assumes its modified crystal structure and/or morphology in a specific manner that the latter has a minimal value of its total surface-energy Ω and in turn a minimal value of its internal energy e0 . The Co-particles, at D ≤ 10 nm, in this example have a stable FCC or a BCC structure as it involves an effectively small value of Ω of 2.0527 × 10−18 J or 1.3211 × 10−18 J if compared with Ω = 2.6198 × 10−18 J in the HCP structure per unit crystal lattice.
Acknowledgements This work has been financially supported by a research grant from the Council of Scientific and Industrial Research (CSIR), Government of India.
S. Ram / Materials Science and Engineering A304–306 (2001) 923–927
References [1] H. Gleiter, Prog. Mater. Sci. 89 (1989) 223. [2] W. Gong, H. Li, Z. Zhao, J. Chen, J. Appl. Phys. 69 (1991) 5119. [3] J.P. Chen, C.M. Sorensen, K.J. Klabunde, G.C. Hadjipanayis, Phys. Rev. B 51 (1995) 11527. [4] L.I. Canham, Appl. Phys. 57 (1990) 1046. [5] M. Lederman, S. Scultz, M. Ozaki, Phys. Rev. Lett. 73 (1994) 1986. [6] H. Sato, O. Kitakami, T. Sakurai, Y. Shimada, Y. Otani, K. Fukamichi, J. Appl. Phys. 81 (1997) 1858.
[7] [8] [9] [10] [11]
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S. Ram, J. Mater. Sci. 35 (2000) 3561. S. Ram, Patent filed. S. Ram, S. Rana, Mater. Lett. 42 (2000) 52. X-ray powder JCPDS diffraction files 15.806 and 5.0727. E. Klugmann, H.J. Blythe, F. Walz, Phys. Stat. Solidi A 146 (1994) 803. [12] M. Erbudak, E. Wetli, M. Hochstrasser, D. Pescia, D.D. Vvedensky, Phys. Rev. Lett. 79 (1997) 1893. [13] J.Y. Huang, Y.K. Wu, H.Q. Ye, Acta Mater. 44 (1996) 1201. [14] R.C. Ashoori, Nature 379 (1996) 413.
Allotropic phase transformations in HCP, FCC and BCC metastable structures in Co-nanoparticles S. Ram∗ Materials Science Centre, Indian Institute of Technology, Kharagpur 721 302, India
Abstract The effect of particle size on stability of crystal structure of pure cobalt metal is studied. The common HCP allotrope of it is stable in bulk. It assumes an FCC or a BCC structure on reducing its size below a critical value Rc at a nanometer scale. Separated Co-particles coreduced (using a reducing agent) from highly dispersed Co2+ -cations in a liquid or a solid medium have a strict control of size at D = 2–5 nm for the BCC structure and D = 10–20 nm for the FCC structure. Both of them are substantially stable at least within the temperature range of 700◦ C and do not transform to the HCP structure as long as their size is controlled within these regions. The present crystal structure modification in a particle occurs in a manner that it has a minimal value of its total surface energy Ω = Aσ , with A its total surface area and σ the surface-energy density. It yields a stable equilibrium configuration of atoms with its minimal internal energy. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Co-metal; Nanocrystals; Co-allotropes; FCC cobalt; BCC cobalt
1. Introduction Pure cobalt powder samples with diameters (D) of a few nanometers are a subject of intense research due to their unique magnetic and other physical properties which make it very appealing from both the theoretical and the technological points of view [1–3]. It is specially important for information storage systems, ferrofluids, contrast agents in magnetic resonance imaging, and optoelectronic devices [1–7]. Below a critical size Dc ∼ 20 nm, it becomes single domain in nature with unique phenomena of quantum size effects, quantum tunneling of magnetization, superparamagnetism, and unusually large magnetic anisotropies [5–7]. An enhanced surface area A in such small particles induces a modified electronic structure which often results in an enhanced saturation magnetization ρ s by as much as 34% along with an improved value for magnetocrystalline (Ha ) or surface (Hs ) anisotropies over the bulk values [3,7]. It gives a very simple way of improving their energy-product (BH)max . In a solid of finite size, its total surface energy Ω = Aσ , with energy density σ , has a strong correlation with its stability and crystal structure. Thermodynamically, a reduction of its size below a critical value Rc modifies its crystal structure and/or morphology in a manner that the latter is stable with a minimal value of its internal energy ∗
Tel.: +91-03222-55221; fax: +91-03222-55303. E-mail address: [email protected] (S. Ram).
ε0 . In minimizing ε0 , the value of Ω plays a crucial role at R ≤ Rc . As a result, the HCP Co-metal, which is stable in bulk, becomes unstable by an enhanced Ω value in reducing its size to a few nanometers. At this scale, it exists in an FCC or BCC structure [3,7] stabilized with a smaller value of Ω over the HCP structure. This is demonstrated in this paper with synthesis of a pure Co-metal in a strictly controlled 2–20 nm size. 2. Experimental details 2.1. Synthesis Co-nanoparticles of controlled 2–20 nm size were synthesized from highly dispersed Co2+ -cations in (i) a liquid and (ii) a solid matrix by two independent chemical co-reduction reaction methods. The first method involves a rather fast nucleation of the particles from an aqueous Co2+ -solution by a reducing agent NaBH4 . In the other method, similar Co-nanoparticles are produced by thermal decomposition and co-reduction of a Co2+ :AlO(OH)·αH2 O gel in H2 gas. This occurs in a strictly controlled fashion in finely divided reaction centres in a very fine Al2 O3 matrix. Other details are as follows. 2.1.1. Co-reduction reaction in a liquid medium A 10−2 M CoCl2 ·6H2 O solution was obtained in a 10 wt.% DDAB (didodecyldimethyl ammonium bromide),
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Table 1 Crystal lattice parameters, lattice surface area A, lattice volume V, and lattice surface energy Ω for three allotropes of BCC, FCC and HCP crystal structures in a pure cobalt metal Sample
Lattice parameters (nm)
Co-reduced from a Co2+ -solution FCC structure a = 0.3535 Co-reduced from BCC structure FCC structure
Co2+ -cations
Bulk cobalt metal FCC structure HCP structure
in Al2 O3 matrix a = 0.2840 a = 0.3540 a = 0.3545b a = 0.2507b c = 0.4070b
A (10−2 nm2 )
V (10−3 nm3 )
Ω (10−20 J)a
74.98
44.17
204.70
48.39 75.19
22.91 44.36
132.11 205.27
75.40 93.90
44.55 66.50
205.85 261.98
The value of Ω = Aσ is calculated using the reported value of σ = 2.73 J/m2 for the FCC structure and σ = 2.79 J/m2 for the HCP structure in [6]. In absence of a reported σ -value for the BCC structure, it is assumed to be the same as for the FCC structure. b The values of the lattice parameters are taken from Ref. [10]. a
solution in toluene. It is reduced to Co-granules by adding a highly concentrated ∼5 M NaBH4 aqueous solution drop-by-drop while stirring the mixture. The whole reaction is carried out in an argon atmosphere. A highly exothermic reaction occurs and results in black slurries of reduced Co2+ into Co-powders of nanometer size. Average temperature of the solution is controlled at ∼273 K with an ice bath having NaCl impurities. DDAB, which is an established cationic surfactant [3], traps the Co2+ cations in empty micelles and helps the reduction reaction within the micelles by preventing re-oxidation of the sample. After the reaction, the Co-slurries are filtered, carefully washed in deionized water and toluene, and then immediately dried in vacuum or N2 gas at room temperature. 2.1.2. Co-reduction reaction from a gel The Co2+ :AlO(OH)·αH2 O gel was prepared by hydrolysis of Al-metal in an aqueous CoCl2 ·6H2 O solution (∼1.0 M) as described earlier [8,9]. Its thermal decomposition and co-reduction in H2 gas at 500–850◦ C gives separated Co-nanoparticles dispersed in an Al2 O3 matrix of thermal decomposed gel. The samples with different average sizes were obtained by a proper selection of the reduction temperature in this range. A refined microstructure of highly dispersed Al2 O3 matrix in thermal decomposition of the gel supports nucleation of Co-nanoparticles in a strictly controlled size as small as a few nanometers in divided co-reduction reaction centres.
which are given in Table 1. In situ analysis of the compositional maps with an electron microprobe analyzer confirmed absence of byproduct impurities in either series of the specimens. 3. Results and discussion Fig. 1 shows a TEM micrograph of a nanocrystalline sample of pure Co-nanoparticles co-reduced from Co2+ -cations dispersed in the liquid medium as described above. Most of the particles have a shape of well-separated thin platelets of an average diameter D ∼ 10 nm, volume V = Aδ ≡ 150 nm3 , and aspect ratio D/δ ∼ 5, with A ∼ 75 nm2 the surface area for one of the two flat faces. As discussed below, they form a single phase of an FCC crystal structure. The TEM in Fig. 1 contains 2–5% extremely small particles, D = 1–2 nm, which have a spherical shape. A spherical shape presents a minimal surface and in turn a minimal
2.2. Characterization The structure of Co-nanoparticles was analyzed by X-ray diffraction. The diffractogram was recorded with a PW 1710 X-ray diffractometer using filtered Cu K␣ (or Co K␣) radiation of wavelength λ = 0.15406 nm (or 0.17902 nm). Their size/morphology was studied with a JEM 2000cx transmission electron microscope. The positions of the X-ray diffraction peaks were used to calculate the lattice parameters
Fig. 1. TEM micrograph of a typical Co-nanopowder of an FCC crystal structure co-reduced from Co2+ -cations dispersed in an aqueous solution. The scale bar refers to 50 nm.
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Fig. 2. X-ray powder diffractogram of Co-nanoparticles of FCC and BCC crystal structures co-reduced in an Al2 O3 matrix. The peaks of FCC phase are marked by asteriks (∗). Three unassigned peaks (∗∗) around the 2θ values of 37, 44 and 79◦ are due to the matrix. In the inset is shown the diffractogram of a single FCC structure of a Co-nanopowder co-reduced from Co2+ -cations dispersed in an aqueous solution.
value of Ω. This change in the shape of particle from a thin platelet to a spherical one for decreasing D-values in this example demonstrates preponderance of its surface-energy Ω in re-organizing its surface structure in a way that the latter has its minimal Ω-value. In a small particle, the Ω controls distribution of atoms in a specific crystal structure (or configuration of atoms) of a minimal internal energy ε0 . In order to ascertain this conjecture, in a separate experiment, we synthesized finely dispersed Co-metal particles of finite size in a thermally rigid Al2 O3 matrix, as discussed above. The Al2 O3 matrix controls nucleation of very small particles at a moderate rate by inhibiting a fast migration of the reaction species (Co atoms) through it. As a result, the reaction occurs in a controlled manner by nucleation and growth from small nuclei formed according to their basic crystal structures and Ω energies. This is clearly demonstrated by the X-ray diffractogram (Fig. 2) for a Co:Al2 O3 sample obtained by reducing the gel in a flowing H2 gas at 730◦ C for 30 min. The Co-particles, which are dispersed in the Al2 O3 matrix, present two crystalline phases of cobalt of FCC and BCC structures which involve the confined crystal lattices of surface area A∗ = 0.4839 and 0.7519 nm2 or surface energy Ω ∗ = 2.0527 × 10−18 and 1.3211 × 10−18 J, respectively, if compared with A∗ = 0.9390 nm2 and Ω ∗ = 2.6198 × 10−18 J for the bulk HCP structure. The X-ray diffractogram of FCC phase is fairly matching with the standard diffractogram for the bulk sample [10] with a total of three (1 1 1), (2 0 0) and (2 2 0) characteristic peaks (Fig. 2). A lattice parameter a = 0.3540 nm (0.3545 nm the bulk value [10]) has been estimated using their positions. The X-ray diffractogram of
pure Co-powder, obtained in an FCC structure by the other method, are compared in the inset to Fig. 2. It has three sharp peaks at 0.2039, 0.1769 and 0.1248 nm in (1 1 1), (2 0 0) and (2 2 0) lattice reflections with the lattice parameter a = 0.3535 nm. No other diffraction peaks in possible impurities due to an HCP or any other Co-phase have been observed. In the FCC–BCC mixed phase Co-powder dispersed in the Al2 O3 ceramic matrix, a ratio 5:4 between the two phases is estimated according to relative intensities in their most intense peaks at 0.2045 and 0.2015 nm. Several experiments were carried out by reducing the gel of different compositions at different temperatures, in the 500–850◦ C range, in an attempt to have a single phase. It was found that the ratio between the two phases varies with the gel-composition as well as with the reducing temperature but it never gave a single Co-phase. This FCC–BCC biphase structure is stable over a wide range of temperature upto 1000◦ C and at surprisingly large crystallite sizes. Crystallites in either phase are as big as 80 nm as can be determined by an analysis of the widths of the X-ray diffraction peaks. They do not transform to an HCP structure which is the most stable allotrope of cobalt otherwise. The bulk HCP cobalt, as prepared by other methods [2,11], undergoes a reversible martensite transformation to the FCC structure at 427◦ C [11,12]. This transformation is weakly first order with small changes in enthalpy 1H = 440 kJ/mol and volume 1V /V = 0.0036. The two HCP and FCC phases exist in an equilibrium at temperature Teq ∼ 427◦ C, but there is considerable hysteresis between the heating and cooling transformations [12].
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Huang et al. [13] studied allotropic phase transformation in bulk cobalt metal by milling it in an inert gas atmosphere. It follows a sequence of transformation routes of HCP+FCC → HCP, HCP+FCC → HCP → FCC+HCP, and HCP + FCC → HCP → FCC + HCP → FCC, respectively. The results indicate that these phase transformations of bulk cobalt induced by milling are basically determined by a refinement of its microstructure which stores a large amount of surface energy as well as the Gibb’s free energy during the milling process. According to thermodynamics, it follows a self-reorganization of its final structure with creation of new surfaces in stable particles in a specific manner that the latter involves a minimal value of Ω with a minimal value of its internal energy ε0 . In this process, the FCC phase of cobalt which satisfies this conjuncture forms as a stable structure over the HCP phase which involves a rather larger value of Ω (see Table 1) in reducing its size to a confined value of a few nanometers. An enhanced symmetry in the FCC structure in the confined size induced HCP → FCC transformation which supports its stability as it further lowers its total internal energy ε. Formation of a stable structure in a chemical reaction, as used here, occurs by its nucleation followed by its growth in an equilibrium condition. The growth of a structure, which is a natural process, occurs as it lowers its total energy as well as the total energy of the system. For a sample of small critical volume, the Gibb’s free energy is not dependent on a single parameter of its radius r, as in the classical approach, but on the actual average spherical density profile ρ(r) [14]. In general, it can follow infinite numbers of trajectories and a number of metastable phases can be obtained out of it according to the experimental conditions. A stable particle in early stage of its growth is attained in a single non-degenerate process according to the reaction rate and its kinetics. It assumes a specific crystal structure which involves a minimal value of its total internal energy ε0 , which in turn involves a minimal value of its surface energy Ω ∗. In a rate limited process with highly dispersed reaction species in a medium, as in this example, a stable phase is achieved in a single non-degenerate process of such confined particles at moderate reaction rate. It involves small building blocks of a small critical volume Vc or surface energy Ω c as they nucleate first and grow easily in a stable structure at moderate rate. A formation of big building blocks of large Vc or Ω c and their recombination reactions forming bigger building blocks (particles) are not feasible at this moderate reaction rate to make a feasible stable structure in question. This occurs in a bulk reaction at a sufficiently large rate of recombination of the reaction species. It can be shown that growth of small building blocks of small Vc or Ω c value results in a small decrease in the total surface energy Ω(r) of the sample per unit mass as a function of V(r) if compared to that for a sample of big building blocks. As a result, two Ω(r) vs V(r) curves in the two examples intersect at a point Vc (rc ) and the minimum
free energy interface passes through this point. The particles of small size, V (r) ≤ Vc (rc ), are stable below this saddle point with their smaller Ω(r) ≤ Ωc (rc ) values while the bigger r > rc particles become stable in the region above this point by their reduced Ω(r) values under the Ω c (rc ) limit of their stability. Assuming a spherical shape of the particles, it is easy to −GHCP , show that if 1σ = σ FCC −σ HCP and 1Gv = GFCC v v i i where σ and Gv (i = FCC or HCP) refer to the surface energy density and the Gibb’s free energy, then a critical particle size rc exists below which the FCC phase is stable, rc = −
3 1σ 1Gv
(1)
Here, 1Gv is positive, and for positive rc values, 1σ must be negative in accordance with the experimental σ FCC = 2.73 J/m2 and σ HCP = 2.79 J/m2 values [6]. Substituting the value of 1σ = −0.06 J/m2 with 1Gv ∼ = 1.0 × 106 J/m3 [6], this relationship implies an optimal value of rc = 180 nm for particles of spherical shape with Ea = 0 shape anisotropy. In a realistic example, a deviation of their shape from the ideal spherical shape would cause a significant decrease in the final rc value as they involve a manifested 1Gv value by the contribution of the 1Ea = EaFCC − EaHCP shape anisotropy energy. This agrees with the observed size r, as big as r ≡ 21 D = 40 nm, of Co-particles, which are in a shape of thin platelets in this example. The r-value lies within the expected, rc ≤ 180 nm, range of stability of a Co-particle in an FCC or a BCC structure.
4. Conclusions In an FCC crystal structure usually 10 nm or smaller particles of a pure cobalt metal exist. The limit of their stability is extended to as big a size as 80 nm in a biphase FCC–BCC structure dispersed in an Al2 O3 matrix. According to this observation, it is proposed that a small particle of confined size below a critical value Rc assumes its modified crystal structure and/or morphology in a specific manner that the latter has a minimal value of its total surface-energy Ω and in turn a minimal value of its internal energy e0 . The Co-particles, at D ≤ 10 nm, in this example have a stable FCC or a BCC structure as it involves an effectively small value of Ω of 2.0527 × 10−18 J or 1.3211 × 10−18 J if compared with Ω = 2.6198 × 10−18 J in the HCP structure per unit crystal lattice.
Acknowledgements This work has been financially supported by a research grant from the Council of Scientific and Industrial Research (CSIR), Government of India.
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References [1] H. Gleiter, Prog. Mater. Sci. 89 (1989) 223. [2] W. Gong, H. Li, Z. Zhao, J. Chen, J. Appl. Phys. 69 (1991) 5119. [3] J.P. Chen, C.M. Sorensen, K.J. Klabunde, G.C. Hadjipanayis, Phys. Rev. B 51 (1995) 11527. [4] L.I. Canham, Appl. Phys. 57 (1990) 1046. [5] M. Lederman, S. Scultz, M. Ozaki, Phys. Rev. Lett. 73 (1994) 1986. [6] H. Sato, O. Kitakami, T. Sakurai, Y. Shimada, Y. Otani, K. Fukamichi, J. Appl. Phys. 81 (1997) 1858.
[7] [8] [9] [10] [11]
927
S. Ram, J. Mater. Sci. 35 (2000) 3561. S. Ram, Patent filed. S. Ram, S. Rana, Mater. Lett. 42 (2000) 52. X-ray powder JCPDS diffraction files 15.806 and 5.0727. E. Klugmann, H.J. Blythe, F. Walz, Phys. Stat. Solidi A 146 (1994) 803. [12] M. Erbudak, E. Wetli, M. Hochstrasser, D. Pescia, D.D. Vvedensky, Phys. Rev. Lett. 79 (1997) 1893. [13] J.Y. Huang, Y.K. Wu, H.Q. Ye, Acta Mater. 44 (1996) 1201. [14] R.C. Ashoori, Nature 379 (1996) 413.