PHYSICAL REVIEW B 70, 125421 (2004) Determination of pressure effect on the melting point elevation of Al nanoparticles encapsulated in Al 2 O 3 without epitaxial interface Q. S. Mei, S. C. Wang, H. T. Cong, Z. H. Jin, and K. Lu* Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, People s Republic of China (Received 2 June 2004; published 24 September 2004) We report a quantitative measurement of the pressure effect on melting point elevation of encapsulated nanoparticles without epitaxial interfaces. By means of in situ x-ray diffraction, a substantial melting point elevation of about 15 K in encapsulated Al nanoparticles in Al 2 O 3 shells without epitaxial interfaces was observed. Meanwhile, a pressure buildup of about 0.25 GPa on the Al nanoparticles was determined due to constraint of the rigid Al 2 O 3 shell. The correlation between the measured pressure and melting point elevation in the present system verified that the observed melting point elevation is a pressure-induced phenomenon and the pressure effect on melting point for encapsulated nanoparticles follows the rule for bulk solids. DOI: 10.1103/PhysRevB.70.125421 PACS number(s): 61.10. i, 61.46. w, 64.10. h, 64.70.Dv I. INTRODUCTION Following the pioneering study on superheating of Ag particles by Daeges et al., 1 superheated metal particles (of which the sizes are usually in the nanometer scale), embedded within matrices of high melting points, have been observed in a number of systems, and the superheating phenomenon has been studied extensively. 2 13 Previous investigations indicated that there are basically two major effects responsible for the observed superheating. Firstly, formation of low-energy epitaxial (coherent or semicoherent) interfaces is effective in suppression of melt nucleation at the particle/matrix interfaces, hence elevate the melting point. The second one is the pressure effect. Due to the difference in thermal expansion coefficients (TECs) between the particles and the matrix and the volume change upon melting, a compression pressure is usually generated onto the embedded particles prior to melting. The pressure buildup was considered to be effective in elevating the melting point of the encapsulated nanoparticles, 3 6 analogous to that for the bulk solids which is well known from the classical thermodynamics. (The term superheating has been used to mean melting above the equilibrium melting point in previous studies; in this paper we use melting point elevation for clarification if the melting thermodynamics is changed.) Meanwhile the effect of epitaxial interfaces on superheating of encapsulated nanoparticles has been experimentally demonstrated in many systems; 5 7 the pressure effect on the melting point variation for nano-sized particles, to the authors knowledge, has not yet been testified by quantitative experimental measurements in the literature. In most previous studies, superheating was usually observed in metal particle/metal matrix systems with epitaxial particle/matrix interfaces, which means both metals should have the same lattice structure and very similar lattice constants to ensure a small lattice mismatch at the interface. If incoherent interfaces are formed, the embedded metal nanoparticles will not be superheated and pre-melting occurs, as demonstrated experimentally by Sheng et al. 7 In these systems, the pressure effect was considered to be minor relative to the epitaxial interface effect due to the small difference in TECs and relaxation of the pressure by the metallic matrix. 3 6 Isolating the pressure effect on the melting point from other effects is difficult in these samples. For metal nanoparticles embedded in a rigid ceramic or carbon matrix without an epitaxial particle/matrix interface, a substantial superheating has also been observed experimentally. For example, a superheating of up to 270 K was observed in encapsulated metal particles (Pb, Sn) in fullerenelike shells. 14 A pressure induced melting point elevation was also observed in tin particles embedded in amorphous carbon films. 15 Although the observed superheating was attributed to the high pressure buildup in these studies, no quantitative measurement was performed to verify the pressure effect. At this point, another important question is still remaining that whether the same pressure effect as in the bulk solids can be applied to the nanoparticle systems where surfaces and/or interfaces play a crucial role. To answer those questions, quantitative determination of pressure buildup in nanoparticles as well as its correlation to the melting point variation is necessary. Determination of the pressure effect on melting point elevation in nanoparticle systems is practically difficult. To isolate the pressure effect from other influencing factors of the melting point variation for nanoparticles, one has to find a suitable system with the following conditions: (1) A rigid matrix or shell to sustain the pressure buildup without relaxation; 16 (2) a large TEC difference to ensure a large pressure build-up in the encapsulated nanoparticles that facilitates the pressure measurement; (3) formation of incoherent particle/matrix interfaces to exclude the possible interface effect on suppression of melt nucleation. The objective of this work is to quantitatively determine the pressure effect on melting point elevation in nanoparticles, with a metal/ceramic system, Al nanoparticles encapsulated in rigid Al 2 O 3 shells. II. EXPERIMENTAL PROCEDURES Al nanoparticles were prepared by means of active H 2 plasma evaporation and condensation. The nanoparticles 1098-0121/2004/70(12)/125421(5)/$22.50 70 125421-1 2004 The American Physical Society
MEI et al. PHYSICAL REVIEW B 70, 125421 (2004) FIG. 1. HRTEM observations of the original Al nanoparticles (a), and typical oxidized Al nanoparticles (b) and (c). were in situ passivated at room temperature before exposing to air (original sample). Oxidation of the passivated original Al nanoparticles was performed at 773 K for 3 h in air followed by a further oxidation at 873 K for 3 h. Transmission electron microscopy (TEM) and highresolution electron microscopy (HRTEM) observations were performed on a Philips EM 420 microscope with an accelerating voltage of 100 kv and a JEM 2010 high-resolution microscope with an accelerating voltage of 200 kv, respectively. In situ x-ray diffraction (XRD) experiments were conducted on an x-ray diffractometer (Brueker D8 Discover) with a high-temperature attachment for investigating the melting process and the thermal expansion behavior of the oxidized sample. For comparison, a bulk Al sample with coarse grains (grain size 100 m) and the original Al powder sample were also tested. The Cu K wavelengths were selected using a goeble mirror. The divergence, scattering and receiving slits were chosen with the width of 1, 1, and 0.1 mm, respectively. A platinum thermocouple was used to monitor the sample temperature, of which the accuracy is ±1 K. A step size of 0.02 and counting time of 3 5 s were used, depending on the diffraction intensity of the samples. All experiments at high temperatures were carried out under vacuum conditions 2 10 3 Pa. The sample was heated to each temperature at a heating rate of 18 K/min and held for 5 min before collecting the x-ray diffraction profiles of four Bragg reflection peaks of Al, (111), (200), (220), and (311), respectively. Al particles. The thickness of the oxide shells varies from particle to particle, with an average value of 20 nm. Statistic measurements of a large number of particles under HRTEM indicated that the relative shell/core size ratio, t/ r (where t is the shell thickness and r is the core radius), is about 0.60±0.30. The t/r ratio was also estimated from the weight gain after oxidation and an average value of about 0.68± 0.20 was obtained for the oxidized sample. Clearly, both measurement results are consistent, which are much larger than that in the original sample 0.13. The Al/ -Al 2 O 3 interfaces are mostly curved and no sharp edged particles with strong facets were observed by HRTEM [Fig. 1(c)]. The curved Al/ -Al 2 O 3 interface is an indication that no epitaxial relationship exists between Al and -Al 2 O 3, since an epitaxial interface would be faceted (flat) due to fixed crystallographic orientation relationship. Observations of a large number of particles indicated that the Al/ -Al 2 O 3 interfaces are random without epitaxial relationship, which is confirmed by electron diffraction analysis. Therefore, possible effect of particle surface/interface on superheating can be excluded. Figure 2 collects in situ XRD profiles of Al (111) peak for the oxidized sample heated to various temperatures. The diffraction intensity of Al (111) peak reduces gradually as temperature rises, especially around the equilibrium melting point of Al T 0 =933 K. It was expected that the Al diffrac- III. RESULTS AND DISCUSSION TEM and HRTEM observations showed that the original Al nanoparticles are spherical with a size distribution between 30 nm and 200 nm, averagely 80 nm. An amorphous Al 2 O 3 shell of about 5 nm thick was found on each particle [Fig. 1(a)], which was formed in the passivation process. For the oxidized Al nanoparticle sample, -Al 2 O 3 was found in the XRD analysis at room temperature. HRTEM observations [Figs. 1(b) and 1(c)] showed that much thicker oxide shells were formed in the oxidized sample. The Al cores in the oxidized sample remain roughly spherical without facets, but with smaller diameters relative to the original FIG. 2. In situ XRD profiles of Al (111) in the oxidized sample at different temperatures as indicated. 125421-2
DETERMINATION OF PRESSURE EFFECT ON THE PHYSICAL REVIEW B 70, 125421 (2004) FIG. 3. Variation of the integrated intensity of Al (111), (200), (220), and (311) peaks with temperature for the original sample (a) and the oxidized sample (b) and (c). I 298 : The integrated intensity at room temperature 298 K. FIG. 4. Temperature dependence of lattice spacing of Al (111) planes d 111 for different samples as indicated. The inset is an enlargement of the part at high temperatures. tion line would disappear around this temperature if no melting point elevation exists. However, an evident Al (111) profile with a substantial intensity (about 40% of the intensity at room temperature) still exists at 934 K. Even at 948 K, 15 K above T 0, the diffraction peak is clearly visible. The observation means some Al crystals in the sample can survive above T 0, i.e., the melting point Al crystals is elevated at least by 15 K beyond T 0. At 953 K, the (111) peak starts to disappear. Figure 3 shows variations of integrated intensities of Al (111), (200), (220), and (311) diffraction peaks with temperature for the original and the oxidized Al nanoparticle samples. For the original sample, the integrated intensities of these diffraction peaks reduce gradually with an increase of temperature due to thermal scatterings. When temperature approaches T 0, those intensities begin to decline rapidly at about 10 K below T 0 and tend to zero at T 0. It suggests a pre-melting process occurred at about 10 K below T 0, which can be understood in terms of the small particle sizes and insufficient constraint of the thin amorphous Al 2 O 3 shell. For the oxidized sample, the diffraction intensities begin to decrease markedly at similar temperatures, indicating the premelting in some particles without effective constraint. However, the intensities do not drop to zero at T 0. From the relative intensities at T 0, one can speculate that approximately 20% 40% volume fraction of the Al particles remains in crystalline state at the equilibrium bulk melting point of Al. The intensity gradually diminishes at about 15 K beyond T 0. With consideration of the x-ray diffraction resolution and the substantial holding time scale at elevated temperatures above T 0, we believe that a considerable number of Al nanoparticles have elevated melting point. After cooling down the oxidized sample to room temperature, we reheated the sample again, and the melting point elevation phenomenon can be reproduced, as demonstrated in Fig. 3(c). To understand the origin of the observed melting point elevation in the encapsulated Al nanoparticles, we determined the pressure build-up on the Al nanoparticles according to their thermal expansion behavior around the melting point. The thermal expansion behavior can be obtained by means of in situ x-ray diffraction measurements of lattice spacing at elevated temperatures, d hkl = /2 sin hkl. 17 Figure 4 shows the lattice spacing of Al (111) plane d 111 as a function of temperature for three samples. It is obvious that the lattice spacing values in three different samples are approximately identical from room temperature to 800 K. The thermal expansion coefficients of the samples derived from the temperature dependence of the lattice spacing are consistent with the literature data in this temperature range. 18 When temperature approaches T 0, no difference can be identified in the lattice spacing values between the original sample and the bulk Al. However, a pronounced difference appears in the oxidized sample, as shown in Fig. 4. The lattice spacing values are smaller than those in the original sample when temperature exceeds 880 K, and the slope of the temperature dependence of d 111 is much smaller than those in other two samples. It means the thermal expansion coefficient of Al lattice is decreased in the oxidized sample around the equilibrium melting point. Measurements on other crystallographic planes showed the same behavior. The reduced thermal expansion coefficient of Al lattice in the oxidized sample is an indication of pressure build-up on the nm-sized Al core. Based on a simple elastic consideration, the pressure build-up on the Al core at T 0 in the oxidized sample can be estimated by P=K Al d b d s /d b, where d s is the lattice spacing measured at T 0 for the oxidized sample, d b is the corresponding bulk value measured at the same temperature, K Al is the bulk modulus of Al. The estimated pressures from the x-ray diffraction measurement of d values in four crystallographic planes are 0.25 GPa for (111), 0.23 GPa for (200), 0.26 GPa for (220), and 0.26 GPa for (311), respectively. Apparently, the resulted values are rather consistent with an average value of 0.25± 0.03 GPa. The pressure onto the Al cores is resulted from different thermal expansion coefficients between the shell and the core and/or the volume change upon melting. According to the 125421-3
MEI et al. PHYSICAL REVIEW B 70, 125421 (2004) shell model, in the case of an Al core encapsulated by the Al/ -Al 2 O 3 shell, the overpressure on the Al core can be calculated by 19,20 P = 4 2 + 1 1+ + 4, 3K 1 where is the shear modulus of the shell, K is the bulk modulus of the core, is the Poission s ratio for the shell, is the misfit parameter, which is defined as T, where T is the temperature difference, and is the TEC difference between Al and Al 2 O 3, and = 2r3 + r + t 3 2 r + t 3 r 3, 2 is a geometrical factor. The pressure can be calculated as a function of relative shell/core ratio t/r. Based on the measured average t/r values in the oxidized sample 0.60, a pressure of about 0.33 GPa is obtained from equation (1). This value agrees reasonably with our measured result 0.25± 0.03 GPa from the lattice spacing measurements. In the above calculation, the excess volume of the interface was not taken into account. This may account for the slight difference between the measured and the calculated pressures. The pressure effect on the melting point can be analyzed by using Clausius-Clapeyron equation 21 dp/dt= VL/T (where P is the pressure, T is the absolute temperature, L is the latent heat of fusion and V is the relative volume change of Al). Taking the measured pressure on the Al core, one may get a melting temperature elevation for the oxidized sample of 13±2 K, which is coincident with the experimentally observed one. The melting temperature of Al nanoparticles is also related to their sizes, i.e., the Gibbs-Thompson effect or the capillary effect due to small sizes. 22 For a sample of nanoparticles with a certain size distribution, melting should take place in a temperature range due to the size effect. We measured by in situ XRD the temperature at which melting ends, which corresponds to the highest melting temperature of the particles. For the original sample, melting ends at 2 K before T 0, so we know the size effect is minor at the highest melting temperature. Besides, the difference between the Al s /Al 2 O 3 and Al l /Al 2 O 3 interfacial energies in the oxidized Al nanoparticles may be reduced [e.g., 8 mj/m 2 (Ref. 23)] compared with that of freestanding Al nanoparticles [ 167 mj/m 2 (Ref. 24)], which will weaken the size effect. 15 Therefore, it is reasonable that the size effect is neglected when interpreting the highest melting temperature of the oxidized Al nanoparticles (the melting point elevation we observed by in situ XRD). IV. CONCLUSION The coincidence between the observed melting point elevation and that based on the classical thermodynamics (Clausius-Clapeyron equation) in the present sample verifies that the observed melting point elevation is dominated by the pressure effect induced by the constraint of the Al 2 O 3 shell, and the pressure effect on melting point in the nanoparticle systems still follows the rule for bulk solids. We report quantitative measurements of the pressure and melting point elevation at the same time in a system of encapsulated nanoparticles without epitaxial interfaces. ACKNOWLEDGMENTS Financial support from the National Science Foundation of China (Grant Nos. 59801011, 59931030, 59971057, and 59841004), the Ministry of Science and Technology of China and the Max-Plank Society of Germany is gratefully acknowledged. *Author to whom correspondence should be addressed. Telephone: 86-24-23906826; Fax: 86-24-23998660. Electronic mail address: lu@imr.ac.cn 1 J. Daeges, H. Gleiter and J. H. Perepezko, Phys. Lett. A 119, 79 (1986). 2 H. Saka, Y. Nishikawa and T. Imura, Philos. Mag. A 57, 895 (1988). 3 D. L. Zhang and B. Cantor, Acta Metall. Mater. 39, 1595 (1991). 4 R. Goswami and K. Chattopadhyay, Acta Metall. Mater. 43, 2873 (1995). 5 L. Gråbaek, J. Bohr, E. Johnson, A. Johansen, L. Sarholt- Kristensen, and H. H. Andersen, Phys. Rev. Lett. 64, 934 (1990). 6 J. Zhong, L. H. Zhang, Z. H. Jin, and K. Lu, Acta Mater. 49, 2897 (2001). 7 H. W. Sheng, G. Ren, L. M. Peng, Z. Q. Hu, and K. Lu, Philos. Mag. Lett. 73, 179 (1996). 8 K. Lu and Y. Li, Phys. Rev. Lett. 80, 4474 (1998). 9 J. G. Dash, Rev. Mod. Phys. 71, 1737 (1999). 10 K. Lu and Z. H. Jin, Curr. Opin. Solid State Mater. Sci. 5, 39 (2001). 11 Z. H. Jin, P. Gumbsch, K. Lu, and E. Ma, Phys. Rev. Lett. 87, 055703 (2001). 12 R. W. Cahn, Nature (London) 323, 668 (1986); 413, 582 (2001). 13 L. Zhang, Z. H. Jin, L. H. Zhang, M. L. Sui, and K. Lu, Phys. Rev. Lett. 85, 1484 (2000). 14 F. Banhart, E. Hernandez, and M. Terrones, Phys. Rev. Lett. 90, 185502 (2003). 15 G. L. Allen, W. W. Gile, and W. A. Jesser, Acta Metall. 28, 1695 (1980). 16 A. K. Malhotra and D. C. Van Aken, Philos. Mag. A 71, 949 (1995). 125421-4
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