Melting process of nanometer-sized In particles embedded in an Al matrix synthesized by ball milling

Transcription

1 Journal of MATERIALS RESEARCH Welcome Comments Help Melting process of nanometer-sized In particles embedded in an Al matrix synthesized by ball milling H. W. Sheng, J. Xu, L. G. Yu, X. K. Sun, Z. Q. Hu, and K. Lu State Key Laboratory for RSA, Institute of Metal Research, Chinese Academy of Sciences, Shenyang , People s Republic of China (Received 22 June 1995; accepted 10 May 1996) Dispersions of nanometer-sized In particles embedded in an Al matrix (10 wt. % In) have been synthesized by ball milling of a mixture of Al and In powders. The as-milled product was characterized by using x-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive x-ray spectrometer (EDX), transmission electron microscopy (TEM), and high resolution transmission electron microscopy (HREM), respectively. It was found that In and Al are pure components immiscible with each other, with nanometer-sized In particles dispersively embedded in the Al matrix. The melting behavior of In particles was investigated by means of differential scanning calorimeter (DSC). The calorimetric measurements indicate that both the melting point and the melting enthalpy of the In nanoparticles decrease with increasing milling time, or refinement of the In particles. Compared to its bulk melting temperature, a melting point depression of 13.4 K was observed when the mean grain size of In is 15 nm, and the melting point depression of In nanoparticles is proportional to the reciprocal of the mean grain size. The melting enthalpy depression was interpreted according to the two-state concept for the nanoparticles. Melting of the interface was deduced to be an exothermal process due to its large excess energy/volume. I. INTRODUCTION Melting behavior is a common phenomenon in materials research, but it is far from being completely understood. During recent decades, the melting behavior of fine particles has been extensively studied. Methods utilized including analytical, computational, and experimental techniques, abound in various materials. 1,2 Results show the melting points of fine particles exhibit a strong dependence on their sizes. Finite metal particles, e.g., In, Sn, Bi, Pb, Cu, Ag, and Au, have often been found to melt below their bulk melting temperatures, and the melting temperature, in most cases, is inversely proportional to their particle sizes. 3 Meanwhile, superheating of entrained particles was also observed. 4,5 Recently, In and Pb embedded in Al matrixes prepared by using rapid quenching 6 8 and ion implantation techniques, 9 were reported to be greatly superheated above their bulk melting temperatures. Arguments on the melting mechanism for finite particles have never reached an agreement (see e.g., Refs ). Couchman and Jesser 12 stressed the importance of the heterogeneous nucleation of melting at the crystalline surface. The melting point of thin films or fine particles can be either depressed or increased, depending on the nature of the interface. A thermodynamics equation was thus derived to describe the melting of fine particles as 12,16 : T m T s sm r s 2s lm r l r 2DE DH e m where T 0 is the equilibrium melting temperature, s sm and s lm are the interface energies of solid inclusion and matrix, liquid inclusion and matrix, r s and r l are the densities of solid and liquid inclusion, respectively, DE is the change in strain energy density on melting, DHm e is the melting enthalpy, and r is the radius of the particles. Explanations of superheating of In in an Al matrix 7 and melting point depression of In in an Fe matrix 17 have recently been attempted by using this approach. It was suggested that different types of Al In and Fe In interfaces cause the different melting behaviors of the entrained In particles. The melting behavior of the fine particles, however, may be different even in an isotropic matrix. There are some experimental evidences showing the influence of crystallographic shape on the melting point. In the case of free particles, Metois and Heyraud 18 have found the triangularly shaped Pb particles melt 3 K above that for surrounding irregular particles whose melting is assumed to be the equilibrium melting temperature. For the entrained particles, Spiller 19 has reported that small Pb particles, condensed either on graphite or amorphous carbon, of different shapes were found to have qualitatively different melting behaviors. (1) J. Mater. Res., Vol. 11, No. 11, Nov Materials Research Society 2841

2 But, in general, relatively little effort has been devoted to exploring the effect of the interfacial structure of the entrained particles on the melting behavior. With regard to the melting process, the melting enthalpy of fine particles has also been found to vary with the melting point (or the particle size). Such a phenomenon has been reported for In particles confined in porous glasses 20,21 and Sn in the ball-milled Ge Sn dispersions. 22,23 Several interpretations have been suggested regarding the observations of the melting enthalpy depression, such as the two-state model 24,25 or thermodynamic treatments. 20,21 However, the melting enthalpy depression is still not well understood, although it is a fundamental thermodynamic parameter of phase transition. The ball-milling technique provides a new approach for studying melting behavior. 22,23 In this work, it was applied to throw new light on the melting behavior of In particles, and subsequently to reveal the interface as well as the particle size effects on the melting behavior of In. In particular, the melting enthalpy depression will be discussed in detail. II. EXPERIMENTAL In order to obtain homogeneously distributed dispersions of Al In, the mixture of Al 10 wt. % In was ball-milled. Commercial elemental powders of Al (purity % and particle size less than 200 mesh) and granular In (purity % and particle size less than 1 mm) were used as starting materials. The ball-milling process was performed in a vibratory ball mill, at a vibration rate of 10 Hz. The milling media were hardened steel balls and vial. The size of the vial was 54 mm inner diameter and 50 mm in height with a capacity of 115 cm 3. Powders of the desired composition about 5 g were charged into the vial, with a ball-to-powder weight ratio of 30 : 1. At the initial period of milling, 0.5 vol. % of hydrocarbons were added into the powders to prevent them from agglomeration or sticking on the milling tools. The powder mixtures were sealed in a stationary argon atmosphere with an O-ring elastomer ring. The temperature of the vial was kept at room temperature below 60 ± C during the milling by dynamic air cooling. The milling process was interrupted at various time intervals, and powder samples were removed for analysis and characterization. The x-ray diffraction (XRD) was carried out on a Rigaku x-ray diffractometer (D/max-ra, 12 kw) with Cu Ka radiation. The average grain sizes and precise lattice parameters were determined from the half maximum width and peak positions of the diffraction lines, respectively. The microstructures of the Al In composites were examined by electron microscopy. Scanning electron microscopy (SEM) was performed on a Cambridge stereoscan-360 with a backscattering mode. For SEM observations, the as-milled Al In powders were coldcompacted with a uniaxial pressure of 2 GPa into disks (8 mm in diameter), and then mechanically polished. The transmission electron microscopy (TEM) and high resolution transmission electron microscopy (HREM) were conducted on a Philips EM 420 microscope operated at 100 kv and a JEOL 2000 microscope with an accelerating voltage of 200 kv, respectively. Specimens for TEM and HREM observations were milled powders, which were directly supported by copper grids coated with carbon films. Compositions were examined by a Link-AN 1000 energy dispersive x-ray spectrometer (EDX) with a detecting error of less than 0.5%. Oxygen contents were detected by LECO TC-436 Oxygen/Nitrogen Analysis. Thermal analysis was performed in a Perkin-Elmer Differential Scanning Caloimeter (DSC-7), with a sensitivity of 0.02 mj s for energy. Powder compact samples were sealed in aluminum pans and heated in a flowing argon atmosphere at a constant heating rate of 10 ± C min. The temperature of DSC was calibrated with pure In, Zn standard samples, with an accuracy of K. III. RESULTS A. Milling process and characterization Figure 1 shows the XRD spectra of Al 10 wt. % In mixture powders milled for 3 h and 300 h. Up to 300 h, only diffraction peaks for Al and In are observed. No trace of amorphous or other intermediate phases was found. It is also evident that the intensities of both Al and In diffraction peaks decrease while the profile of the pattern broadens, suggesting that grains of Al and In are refined. The apparent grain size of In was calculated using the Scherrer equation. 26 In determining the grain FIG. 1. X-ray diffraction patterns for Al 10 wt. % In samples milled for 3 h (a) and 300 h (b) J. Mater. Res., Vol. 11, No. 11, Nov 1996

3 FIG. 2. Variation of the grain size of In in the milled powders (Al 10 wt. % In) versus the milling time, which was determined from In (101) and In (112) of the XRD profiles. size of In, the effect of the internal strain on the line broadening was neglected. Figure 2 displays the average grain size of In, which was averaged from In (101) and (112) diffraction peaks, as a function of milling time. The grain size of In decreases with an increasing milling time and tends to a steady value (about 15 nm) after 300 h of milling, showing the formation of the nanostructured In component. SEM observations reveal the microstructural evolution of Al In with the milling time, as shown in Fig. 3 (white particles are In). In the early stage of ball milling, the existence of large In particles indicates that In is not pulverized completely all at once. As ball milling proceeds, due to the effects of kneading and fracturing, Al and In are comminuted, while In particles are gradually dispersed into the Al matrix, forming individual fine particle. In the SEM photograph for the Al In milled for 300 h [see Fig. 3(c)], although some pockets of In of a few hundred nanometers are visible, the fine microstructure is beyond the resolution of SEM. Therefore, a TEM is employed to provide more details, as shown in Fig. 4. It can be seen that In particles, in the form of irregular shape, are nanoparticles surrounded by the Al matrix. Figure 5 is the size histogram for In particles in the Al In sample milled for 300 h. The mean diameter, as determined from the dark-field images, is about 13.6 nm, which coincides well with the XRD result (15 nm). The asymmetric bell shape (size distribution function) and the tail toward larger diameters indicate a wide distribution for In in the Al matrix. Since the Al In powders underwent a long period of milling time, contamination from milling media and atmosphere was inevitable. The compositions of the milled dispersion examined by EDX are listed in Table I. The content of Fe, however, reaches a maximum of 1.46 wt. % after 300 h of milling, indicating that the FIG. 3. SEM micrographs of Al 10 wt. % In samples milled for (a) 3 h, (b) 10 h, and (c) 300 h. Bright particles are indications of In. J. Mater. Res., Vol. 11, No. 11, Nov

4 FIG. 5. Histogram of size distribution of In particles in the Al In sample milled for 300 h. TABLE I. Composition of the Al In sample unmilled and milled for 300 h, analyzed by EDX. Content (wt. %) Al In sample Al In Fe Cr Unmilled Milled for 300 h FIG. 4. TEM images of Al 10 wt. % In powders milled for 300 h. (a) Bright-field image, (b) dark image for In, and the inset is the corresponding selected area diffraction pattern. contamination from the milling media is minor. But on the contrary, the oxygen analysis indicates 8 10 at. % oxygen in Al In dispersion milled 300 h. Presumably, the oxygen was most in the form of Al and/or In oxides. HREM of the milled Al In powders shows that the milled particles (about 10 mm in size) are coated with oxide films about 5 nm in depth. Lattice parameters for Al and In in the as-milled sample have been quantitatively determined in order to examine the possible formation of the supersaturated Al In solutions. Table II shows the variation of the lattice parameters for Al and In at room temperature. It is apparent that lattice parameters for Al and In are changed after ball milling. The volume change of the unit cell for Al and In were 20.45% and 0.80%, respectively. According to Vegard s law, it might be expected that the Al lattice would expand and In lattice would contract if solubility extended solutions between Al and In had taken place. Since the opposite was observed, one can exclude the formation possibility of the solid solutions between Al and In. In fact, the lattice contraction of Al resulted from the dissolution of Fe impurity. 27 The reason for the lattice distortion of In remains unknown, and further investigation is in progress. The HREM of Al In milled 300 h was performed to explore the morphologies of embedded In particles, as shown in Fig. 6. Nanosized In particles are evident. Two possible locations are seen for In particles, either inside Al grains or at the grain boundaries of Al grains [Fig. 6(a)], with In particles randomly orienting with the Al matrix. The Al In interfaces are mostly incoherent ones, as shown in Fig. 6(b). Interlayers other than Al In interfaces have not been found. The atoms of In at the interface have low coordination numbers, and are to some extent distorted [see, e.g., the zone circled in Fig. 6(a)]. The microstructure revealed here is quite different from those in the rapidly quenched Al In samples. 6 8,28 B. DSC measurements The melting behavior of the Al In milled samples was measured on DSC with a constant heating rate of 10 K min. An endothermal peak corresponding to melting of the In particles appears in the DSC curve, 2844 J. Mater. Res., Vol. 11, No. 11, Nov 1996

5 TABLE II. Lattice parameters for Al and In in Al In sample under different conditions. Al Al In sample a (nm) a (nm) c (nm) Tabulated Unmilled Milled for 300 h In FIG. 7. DSC scans for In in Al In dispersions milled for different periods of time (as indicated) at a heating rate of 10 K min. The inset is the schematic illustration of the characteristic temperatures of In in the Al In dispersions. FIG. 6. High resolution electron micrographs of Al In milled 300 h, showing (a) In at the Al grain boundaries, and (b) incoherent Al In interface. as shown in Fig. 7, in which three characteristic temperatures were indicated: T s (the starting temperature), T o (the onset temperature), and T p (the peak temperature). Due to the grain size distribution in the as-milled Al In samples, the In particles of different sizes may melt at different temperatures. Therefore, T s corresponds to the melting temperature of the smallest In particles and T o, to that of the In particles with a mean particle size. The equilibrium melting temperature for In and Al are K and K, respectively. The temperature at which the embedded In particles in the Al matrix melt is the eutectic temperature between In and Al. However, since the eutectic point is very close to pure In, it can be taken as the melting temperature of pure In. 29 The unmilled powder mixture of Al In exhibits a sharp endothermal peak with a melting temperature T o of K, which is virtually the equilibrium melting point of the bulk pure In. In the early stage of milling (,3 h), the endothermal peak broadens and shifts toward lower temperatures. Its peak temperature is found to be nearly unchanged but T s becomes smaller, characterized by an J. Mater. Res., Vol. 11, No. 11, Nov

6 TABLE III. Melting temperature and grain size versus milling time. Milling time (h) d (nm) T s (K) T o (K) T p (K) DT o (K) L m (J g) Unmilled (0 h) evident tail at the beginning of the endothermal peak. As the milling proceeds, the melting peak of In gradually shifts toward lower temperatures and further broadens with an extended starting tail. For the sample milled for 300 h, the endothermal peak becomes flattened and spans over a wide temperature range. The characteristic temperatures of T s K, T o K, and T p K indicate that the melting temperature of In is significantly depressed. The magnitude of the melting point depression, DT o, reaches as much as 13.4 K. The values for T s, T o, and T p are listed in Table III and plotted as a function of milling time in Fig. 8. After milling for 10 h, T p of In reaches K, and does not show further substantial depression with an increasing milling time, whereas, T s and T o are monotonically decreasing. By integrating the area under the endothermal peak, we obtain the released heat, L m, for the melting of In particles per gram of the Al In sample. In the unmilled Al In powders, the released heat per gram In is the same as the melting enthalpy of bulk In. With an increasing milling time, or a refinement of the In, L m decreases monotonically. After milling for 300 h, the released heat for In melting is depressed by 61% compared to that of the unmilled Al In sample. The measured values for L m are also listed in Table III. Several melting and solidification cycles have been performed and monitored by DSC for the Al In sample milled for 300 h, as indicated in Fig. 9. The sample was annealed at various temperatures for different periods of time before measurements of the remelting process of In particles in DSC. The sample annealed at a lower temperature (443 K) for 120 s was found to exhibit an identical DSC curve with that of the as-milled sample. No change was detectable in the DSC curves after the same treatment was repeated for a total of 3 times. After the sample annealing at higher temperatures of 120 s, both the melting temperature and the released heat are markedly increased. However, the bulk melting temperature of In is not found to be recovered yet even though the matrix (Al) has been molten at 973 K. The average grain sizes of In in the sample annealed at different temperatures were measured and are listed in Table IV. One can see that the embedded In particles are coarsened upon annealing at high temperatures, but significant grain growth of In is prohibited by the isolation FIG. 8. Plot of the characteristic temperatures of the Al In dispersion as a function of the milling time. The dashed line shows the bulk melting point of In. FIG. 9. DSC scans for the remelting of In in the Al In dispersions milled for 300 h at a heating rate of 10 K min. (a) As-milled, (b) after annealing at 443 K three times, (c) after annealing at 573 K, and (d) 973 K J. Mater. Res., Vol. 11, No. 11, Nov 1996

7 TABLE IV. Characteristic melting temperature (T s, T o, and T p ), mean grain size d of In, and the heat release L m for In melting in the Al In dispersion milled for 300 h and annealed at different temperatures. Remelting run Annealing temperature (K) d (nm) T s (K) T o (K) T p (K) L m (J g) As-milled st nd rd th th th of the Al matrix and/or the oxide coatings. Eckert et al. 30 have explained the melting point depression of pure Al in the ball-milled Al powders by the presence of Al oxides, which might be analogous to our results. IV. DISCUSSION A. Melting point depression In contrast to the observations of the superheat of In nanoparticles embedded in the Al matrix in rapidly quenched samples, 6 8,28 we found the melting point of In is depressed in the same matrix synthesized by ball milling. On account of the different synthesis process in the ball-milled samples, some additional reasons may account for the melting point depression of In particles: for example, the impurities resulting from contamination from the milling media and atmosphere, and the stored energy of cold work. Although traces of iron and oxygen impurities were found in the as-milled samples, T m of equilibrium In was hardly affected by them according to the equilibrium phase diagrams. The stored energy by cold work would serve as another reason for the lowering T m, as in the case of the melting point depression of Cu in the cold-worked CuBeO alloys. Bahk and Ashby 31 found that melting completely removed DT m and recovered the T m of bulk copper. But, in our samples, the subsequent remelting runs do not remove DT m of In nanoparticles and the T m has not recovered to the equilibrium value for the bulk sample, implying that the stored energy by ball milling is not a dominant factor for the melting point depression. The formation of the In Al supersaturated solid solution should be taken into account for the melting point depression of In, as suggested by Uenishi. 32 But both the XRD result and remelting experiments verified that no detectable In Al solid solution has been formed in the as-milled sample. An alternative interpretation of the melting point depression of the In nanoparticles is the size effect (or interface effect), as described by Eq. (1). Neglecting the difference between r s and r l, we get: T m T s sm 2s lm rd 2DE DH e m (2) where r r s 1r l 2, T m is the melting point of the In particles, and T 0 is the equilibrium melting temperature of the bulk In. s sm and s lm are the interface energies of solid In solid Al and liquid In solid Al, DE is the difference of the strain energy densities between solid and liquid In particles, DHm e is fusion enthalpy of the bulk In at the equilibrium state, and d is the mean particle size of In. The predicted 1 d size dependence of the melting temperature can be experimentally verified by plotting the measured melting temperature as a function of the inverse particle size. Taking T o as the melting temperature T m of the In nanoparticles with average grain size, the experimental data of both Al In samples milled for different times and the final sample annealed at different temperatures are plotted in Fig. 10. A straight line is a best fit to the T m 1 d relationship. By extrapolating the straight line to the case of a single crystal 1 d 0, we obtained a melting temperature that coincides with the equilibrium temperature within a few tenths of a degree. This evidence means DE is approximately equal to zero. Therefore, the change in strain energy density due to the volume change on melting of In FIG. 10. Melting temperature as a function of inverse particles size of In in the Al In. The dotted line is the melting temperature of bulk In and the solid line is the best fit straight line to the data. J. Mater. Res., Vol. 11, No. 11, Nov

8 can be neglected. In addition, according to the slope of the best fit straight line in Fig. 10 and Eq. (2), with the available data of DHm e 28.4 J g and r 6.9 g cm 3 (from Ref. 3), we obtained the difference in the interfacial energies s sm 2s lm 16.9 kj m 2. Although the existence of oxides and other impurities is inevitable in the as-milled Al In sample, their influence on the interfacial energy can be neglected. From numerous HREM observations in different regions of the as-milled sample, only the Al In interfaces (other than In oxides one) are detected. Therefore, we may conclude that the interfacial energy difference between solid-in solid-al and liquid-in solid-al is 16.9 kj m 2. From this result, the contact angle (u) between solid matrix and solid In (as shown in Fig. 11) can be evaluated according to s lm 2s sm s sl cos u, where s sl is the interfacial energy between the solid and liquid phases of In. Taking s sl 30 kj m 2 (from Refs. 3 and 33), we obtain u 124 ±. This value of the contact angle in our milled samples (124 ± ) is considerably larger than that reported in the rapidly quenched Al In samples u 84 ±. 7 The difference between these two cases is due to the nature of the Al In interface. In the case of faceted In particles embedded in the Al matrix, 6 8,28 the entrained In particles exhibit an orientation relationship with the fcc Al matrix, and have truncated octahedral shape bounded by 111 Al and 100 Al facets. However, in the milled sample studied in this work, HREM observations indicated that the In nanoparticles are irregular in shape and random in their orientation, and no simple orientation relationship exists between Al and In nanoparticles. The interfacial energy, s, consists of two parts, s s c 1s s, where s c is the chemical contribution and s s is the structural contribution. The chemical contribution, s c, in both dispersions is essentially the same; the structural contribution s s might be different. The randomly oriented crystallites are generally without coherence and have a higher degree of disordering. Both interface enthalpy and entropy are assumed to be higher in comparison to coherent or semicoherent interfaces. 34 FIG. 11. Schematic diagram showing the definition of the contact angle u between the solid In and the Al matrix. Compared with the liquid-in solid-al interface, the solid-in solid-al interface without any orientation relationship, which has an additional structural contribution with a high mismatch between the different solid crystal structures, may have a higher interfacial energy s sm. This might be the origin of the melting point depression, and the higher value for the contact angle u. B. Melting enthalpy depression With an increasing milling time, the heat release for the melting of In nanoparticles in the Al matrix was found to decrease significantly, for which several possible reasons may be responsible: (1) The accumulated cold work during the milling process may energize the In particle and subsequently reduce its melting enthalpy. However, after annealing the as-milled Al In sample at 443 K three times to remove the stored energy, the released heat for the In melting is increased only by about 5%, which is still far below the total depression of the released heat during milling (61%). Besides, the increment in the released heat for the In melting upon annealing may partly result from the grain growth process. Therefore, the cold work during the milling process may not account for depression of the released heat for melting. (2) A mass loss of pure In phase would be another reason for the L m depression. After milling for 300 h, the Al In sample has lost some content of pure In. On one hand, EDX analysis pointed out that in the asmilled sample for 300 h, the content of In decreased from 10 wt. % to 9.6 wt. %, and the content of pure In phase may be even less, for the formation of some In oxides which might be stable beyond 973 K. On the other hand, the possibility of In in solution in the surface of the Al may account for some of the decrease in L m. In the case of Ge Sn, Mössbauer spectroscopy 35 and EXAFS 36 have shown that the melting enthalpy of Sn in Ge Sn nanocomposites decreases because Sn is driven into the near surface layer of Ge, which cannot be revealed by x-ray lattice parameters. However, in the case of Al In, such an effect, if any, on the decrease in L m can be neglected, because of the relatively fewer In atoms in the surface in comparison to the pure In phase. From HREM observations, no intermediate phase between Al and In has been found. (3) The particle size of In may serve as a major effect on the variation of L m for melting of the In nanoparticles. As can be confirmed from that, upon annealing and remelting the In particles of the sample milled for 300 h, in which the content of the pure In phase remains a constant value, the melting enthalpy was obviously increased. Consequently, the released heat depression for the In melting may result from the refinement of In particles 2848 J. Mater. Res., Vol. 11, No. 11, Nov 1996

9 as well as the mass loss of the pure In phase. These two effects will be analyzed as follows. The nanocrystalline material can be treated as a two-state material, consisting of two structural components of (i) the nanometer-sized crystallites and (ii) grain boundaries or interfaces between the crystallites. 37,38 The volume fraction of the interfacial component will be much enhanced when the grain size is reduced to the nanometer scale. This two-state model of nanocrystalline materials has been confirmed by quantitative analysis. 39 It has also been successfully used for characterization of thermodynamics and kinetics of the amorphous-tonanocrystalline transition in metallic alloys. 40,41 Here, we employ the two-state model for the melting of the embedded In nanoparticles. The embedded In particles are assumed to be uniformly spherical with a mean diameter d. An individual In nanoparticle can thus be considered as an interface layer with a constant thickness d, plus a remaining core, or bulk crystal with diameter of d 2 2d. The volume fraction of the interface layer, x in, can be expressed as: x in d d 3 (3) The melting of In particles is a sum of the melting of the interface layer and the crystallite core; i.e., the melting enthalpy of the nanoparticles may be approximated by: DH m x in DH in m xin DH e m (4) where DHm in is the melting enthalpy of the interface layer, which is assumed to be independent of the grain size, and DHm e is the melting enthalpy of the bulk In at the equilibrium state. When Eq. (4) can be rewritten as: DH m DHm e 1 6d DHin m 2DHe m d (5) One can see that a difference between DHm in and DHm e will lead to a variation of DH m, which is inversely proportional to the particle size d. In the milled Al In samples, we have determined the released heat for melting of In nanoparticles, L m, which is actually L m ydh m, where y is the content of the pure In phase in the sample. It is clear that L m is proportional to 1 d if y remains a constant. For the Al In sample milled for 300 h, we have performed melting-solidification cycles to vary the mean grain size. Since the content of the pure In phase stays essentially unchanged after these cycles, Eq. (5) can be used to calculate the content of pure In in the sample. Figure 12 is a plot of L m as a function of 1 d in terms of the measurement data, as listed in Table III. It can be seen that the experimental data are approximately in a straight line. By extrapolating the straight line to 1 d 0, we FIG. 12. Heat release for In melting, L m, after the Al In sample (milled for 300 h) annealing at different temperatures as a function of the inverse grain size. have ydhm e 1.96 J g; i.e., y (where DHm e 28.4 J g). The result shows that, compared with the starting material y 0.10, only 69% of the pure In remains after 300 h of ball milling. The mass loss of In will cause depression of the heat release for the melting of the In by about 31%. Evidently, the other 30% of the released heat depression in the as-milled sample is the result of the size effect, as described by Eq. (5). Unruh et al. 20,21 have found that melting enthalpy of In particles of several nanometers confined in porous glasses was reduced to about one third of the bulk value, which may also be attributed to the size effect. During the ball-milling process, the influence of the mass loss of In on the deficit of the heat release can be reasonably extracted by assuming that the mass loss of In during the milling process is proportional to the milling time. The values for melting enthalpy of pure In nanoparticles in Al In milled samples were calculated and are listed in Table V. Figure 13 is a plot of the melting enthalpy of the In particles, DH m vs 1 d, for the Al In samples. The best fit to the data is a straight line. The intercept of the straight line is about 28.6 J g, which agrees well with the bulk melting enthalpy of In (28.4 J g). If assuming interface thickness d 1 nm (about four atomic layers thick) of the embedded In nanoparticles, and substitution DHm e 28.4 J g, we obtain DH in m 24.7 J g (20.54 kj mol). DH in, 0 implies that the melting of the interface is an exothermal process. This behavior might be understood according to the nature of the interface. The microstructure and properties of the interface are manifested by its excess volume DV in (DV in V in V c 2 1, where V in and V c are the specific volumes for the boundary and the perfect crystal, respectively) J. Mater. Res., Vol. 11, No. 11, Nov

10 TABLE V. Content of pure In phase y, grain size d, heat release for In melting in Al In sample L m, and melting enthalpy of pure In phase DH m, versus milling time. Milling time (h) d (nm) y (wt. %) L m (J g) DH m (J g) Unmilled (0 h) FIG. 13. Melting enthalpy for pure In particles as a function of the inverse grain size of In. due to a decrease in the coordination number in the interface. Theoretical analysis and computation modeling indicated that excess volume of the interface is an important parameter designating the thermodynamic parameters of the interfaces. According to the model of the universal equation of state, 42,43 one may estimate the thermodynamic properties of the interface. Calculation results show that the excess energy of 3.80 kj mol DH in m 2DHe m for the In nanoparticles corresponds to an excess volume of 14.7%, which is quite reasonable compared to the interfacial excess volume of 10 30% for nanocrystalline materials. 37 V. CONCLUSIONS (1) Nanostructured dispersions of Al In are synthesized by high energy ball milling. The grain size of In particles decreases with the increasing milling time. Up to 300 h, the grain size of In reaches 15 nm. The refined In particles are irregular in shape and randomly oriented with the Al matrix. (2) The melting point as well as melting enthalpy for In nanoparticles in the Al In dispersions are much depressed. The magnitude of the melting point depression, DT m, of pure In reaches as much as 13.4 K for Al In milled for 300 h. The released heat for In melting in the Al In dispersion is decreased by 61% of the unmilled Al In sample. (3) The melting point depression can be described by the equation T m T s sm 2s lm rd 2DE DH e m The interfacial energy of solid In solid Al is determined to be higher than that of liquid In solid Al by 16.9 kj m 2. The contact angle between solid In and solid Al in the milled samples is determined as 124 ±, which is different from that in the rapidly quenched Al In samples. Both the interfacial energies and the contact angle may vary with the structure of the interface. (4) Besides mass loss of the pure In phase, the interface effect may also be responsible for the melting enthalpy depression of In in the Al In dispersion, which can be described by DH m DHm e 1 xin DHm in 2 DHm e. The melting of the Al In interface is predicted as exothermal, and the value of the interfacial melting enthalpy is 24.7 J g. The interfacial excess energy as a function of excess volume may account for variation of the interfacial melting enthalpy. ACKNOWLEDGMENTS Financial support from the Chinese Academy of Sciences and the National Science Foundation of China (Grant No ) is acknowledged. REFERENCES 1. Ph. Buffat and J-P. Borel, Phys. Rev. A 13, 2287 (1976) and references therein. 2. L. L. Boyer, Phase Trans. 5, 1 (1985) and references therein. 3. G. L. Allen, R. A. Bayles, W. W. Gile, and W. A. Jesser, Thin Solid Films 144, 297 (1986). 4. J. Däges, H. Gleiter, and J. H. Perepezko, Phys. Lett. 119, 79 (1986). 5. C. J. Rossouw and S. F. Donnelly, Phys. Rev. Lett. 55, 2960 (1985). 6. K. Sasaki and H. Saka, Philos. Mag. A 63, 1207 (1991). 7. H. Saka, Y. Nishikawa, and T. Imura, Philos. Mag. A 57, 895 (1988). 8. D. L. Zhang and B. Cantor, Acat Metall. Mater. 39, 1595 (1991). 9. L. Gråbæk, J. Bohr, E. Johnson, A. Johansen, L. Sarholt- Kristensen, and H. H. Anderson, Phys. Rev. Lett. 64, 934 (1990). 10. F. A. Lindemann, Z. Phys. 11, 609 (1910). 11. M. Born, J. Chem. Phys. 7, 591 (1939). 12. P. R. Couchman and W. A. Jesser, Philos. Mag. 35, 787 (1977). 13. R. W. Cahn, Nature 323, 668 (1986). 14. H. J. Fecht, Nature 356, 133 (1992). 15. F. G. Shi, J. Mater. Res. 9, 1307 (1994). 16. G. L. Allen, W. W. Gile, and W. A. Jesser, Acta Metall. 28, 1695 (1980). 17. T. Ohashi, K. Kuroda, and H. Saka, Philos. Mag. B 65, 1041 (1992) J. Mater. Res., Vol. 11, No. 11, Nov 1996

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