Specific Heat, Melting, Crystallization, and Oxidation of Zinc

Figure 1 shows the plots of Cp of zinc nanoparticles, and bulk zinc against T, where the Cp data for bulk zinc from Grønvold and Stølen(15) are incl...
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J. Phys. Chem. C 2008, 112, 20159–20166

20159

Specific Heat, Melting, Crystallization, and Oxidation of Zinc Nanoparticles and Their Transmission Electron Microscopy Studies Lina Gunawan and G. P. Johari* Department of Materials Science and Engineering, McMaster UniVersity, Hamilton, Ontario L8S 4L7, Canada ReceiVed: September 19, 2008; ReVised Manuscript ReceiVed: October 28, 2008

The specific heat, Cp, of zinc nanoparticles (size distribution 30-180 nm and peak at 30 nm) was measured, and their melting behavior was investigated as the ZnO shell grew around the metal particles and thickened. Both structural and chemical analyses were performed by using Transmission Electron Microscopy and techniques of energy filtering and energy dispersive X-ray analyses. The Cp of Zn nanoparticles is slightly higher than that of bulk metal. The melting point of Zn nanocrystals confined to the ZnO shell is only 1-2 K less than that of bulk Zn, much less than that expected from the Gibbs-Thomson equation. This is attributed to the increase in pressure on the zinc core because (i) zinc expands more on heating and on melting than ZnO, (ii) the ZnO shell thickens at the expense of the zinc core, and (iii) there is an epitaxial interaction between Zn and the ZnO shell. The enthalpy of melting decreases on thermal cycling. Nanodroplets of Zn supercooled by a few degrees before crystallizing in two steps. The high temperature step is attributed to heterogeneous nucleation at the core-shell interface, and the low temperature step to homogeneous nucleation in the particle core. The amount crystallized on homogeneous nucleation decreased on thermal cycling as the ZnO shell thickened when oxygen diffused through this layer. The enthalpy of crystallization also decreased on thermal cycling. 1. Introduction Change in thermodynamic properties of a material on reduction in size has been a subject of interest since the 19th century.1,2 The effect arises from an additional free energy term that increases with decrease in the radius of the particle, as formulated by Thomson1 (later Lord Kelvin) for a liquid droplet whose vapor pressure depends upon its curvature. Gibbs1 discussed the surface energy contribution2 to a material’s thermodynamics and its melting point. Defay et al.3 showed that an extension of the Thomson formalism to small crystals yields the same equation as obtained from the Gibbs theory.2 For details, a monograph3 on the Gibbs-Thomson effect and related interfacial properties may be consulted. Various equations used for describing the Gibbs-Thomson effect have also been briefly reviewed.4 Recognition of the change in a material’s property on size reduction to nanometer scale has led to wider use of the Gibbs-Thomson equation in geology, pharmaceutical and food sciences, and in bio- and nanomaterials technology. As nanoparticles, single crystals have their own size- and crystal plane-dependent surface energy. Their properties have been studied usually when surface melting of nanoparticles occurs at the inert gas/solid interface. But when nanoparticles form large aggregates, they produce a large grain boundary area that contains, in some cases, as many atoms as in the nanocrystals itself. Consequently, the vibrational and configurational parts of their thermodynamic functions depend upon the amount and the structure of the grain boundary regions. In addition, the interfacial energy of a nanocrystal itself varies with its environment and pressure. The effects become distinguished when nanocrystals are confined to a rigid shell and/or their shape is non spherical. As a part of our investigation of these effects, here we report the specific heat of zinc nanoparticles and their * To whom correspondence should be addressed. E-mail: joharig@ mcmaster.ca.

melting and refreezing behavior in two conditions: (i) when the zinc particles are in isolated states and (ii) when they are confined by a ZnO shell of increasing thickness formed by the surface oxidation. We also provide a detailed electron microscopy study of the particle size distribution and of the processes of their melting. A recent study on melting of (broad and narrow size distribution in the 8 to 50 nm range) aluminum particles with the oxide passivation layer by differential scanning calorimetry (DSC)5 is somewhat related to our study but discusses different aspects. In that study, the melting point and the heat of melting of Al were found to decrease with size reduction according to the Gibbs-Thomson equation. Zinc is widely used in galvanizing steel products to prevent surface corrosion and in a variety of alloys. ZnO nanoparticles are used for ultraviolet radiation absorption, as electro-optic and piezoelectric materials,6,7 as a catalyst for accelerating the adsorption of gases on gas sensor materials,7,8 in the production of an n-type metal oxide semiconductor sensor for detecting CO, H2, and NO2, 9 and as a material for wear resistance, shock resistance, sound insulation, photosensitization, fluorescence, and catalytic purposes in the form of tetrapod shape nanocrystals.10 As part of their review on the subject, Wu et al.10-13 have provided a brief discussion of thermal properties of Zn and ZnO. Therefore, in addition to providing thermodynamic insight into melting and crystallization of Zn, our findings may be useful in investigating corrosion of galvanized products and in the use of ZnO nanoparticles in electroluminescent and semiconducting devices, in pharmaceutical drug design, and in cosmetics. 2. Experimental Methods Nanocrystalline zinc in the form of powder was purchased from Nanostructured and Amorphous Materials Inc. Its purity was 99.9 + %, as the average particle size was stated to be in the 35-80 nm range, with no specification of their size

10.1021/jp808341k CCC: $40.75  2008 American Chemical Society Published on Web 12/02/2008

20160 J. Phys. Chem. C, Vol. 112, No. 51, 2008 distribution, and the specific surface area was stated as 30-50 m2/g. The container of the powder was opened in a glovebox containing high purity Argon gas, and small stocks of zinc nanoparticles were stored in several sealed glass vials. These were kept in a desiccator until the measurements were performed. Bulk zinc metal was purchased in the form of “metal shots” of >99.9% purity from Fisher Scientific Company. Two calorimeters were used: One was a Perkin-Elmer Pyris Diamond differential scanning calorimeter and the second a Thermal Analysis Q-100 assembly. The purge gas used for the first instrument was ultra high purity Ar and for the second equipment was ultra high purity N2. The instruments were calibrated against the melting point and enthalpy of melting of indium. For measuring the specific heat, Cp, of zinc nanoparticles over the 623 to 703 K range, the calorimeter was calibrated with sapphire of known Cp.14 It was determined by using the multiple curves specific heat software available for the PerkinElmer Pyris Diamond DSC equipment. A baseline was obtained by averaging several heating scans at 20 K/min of two empty aluminum DSC pans, which differed in weight by (0.5 mg. One of the two empty pans was then used as sample container for sapphire standard, bulk zinc, and zinc nanoparticles. The baseline was subtracted from the measured heat flow curve. Thus, errors from the weight difference between two DSC pans were eliminated. Measurements were repeated for samples of bulk zinc, zinc nanoparticles, and sapphire. In each experiment a new sample was used, and it was ensured that the oxidation of the nanoparticles to ZnO was minimum or negligible. A relatively low temperature range was chosen for measuring Cp to avoid agglomeration of nanoparticles and any further ZnO formation on the nanoparticles surface. Also, the heating scans for the same sample were made for different rates. The Cp values measured by the two methods agreed within (1%, for both the bulk and the nanoparticles of zinc. Its value is accurate to within 1%. Both calorimeters were calibrated before the measurements, and the temperature correction arising from thermal lag was automatically made. Because of the further slow oxidation of zinc in nanoparticles, measurements were made in two ways. In one, nanoparticles were transferred to the DSC pan in Ar gas atmosphere, crimp sealed, weighed, and placed in the DSC sample holder. In the second, the nanoparticles were transferred to a glass vial and left exposed to air for at least 1 h. The sample was then transferred to the sample pan, crimp-sealed, weighed, and then placed in the calorimeter. Bulk Zn crystals had been stored at ambient conditions in a sealed container. These were studied in the same manner as nanoparticles except that in one set of measurements, the sample pan was not crimp-sealed. To determine accuracy and self-consistency of the measured Cp values, their variation with T, and features of melting and crystallization, samples of different amounts were cycled several times in the 573 and 713 K range by heating and cooling at different rates. For brevity, only data for the10, 20, and 40 K/min rates are included here. For microstructural observations and chemical analysis, two transmission electron microscopes were used, namely JEOL 2010F TEM/STEM and a Philips CM12 TEM. The latter had a specimen holder equipped with molybdenum heating filament for in situ bright field imaging of melting of nanoparticles. In this procedure, the nanoparticles were dispersed in toluene to reduce their reactivity and flammability in case the air contained moisture. A drop of this very dilute dispersion was then placed on a holey (containing holes) carbon film supported by a Cu grid and left in open air to allow the solvent to evaporate. The

Gunawan and Johari

Figure 1. Specific heat of nanoparticles and bulk zinc is plotted against the temperature. The specific heat data for bulk zinc from Grønvold and Stølen15 are plotted for comparison.

process also led to formation and/or thickening of the ZnO shell on the particles. 3. Results (i) Calorimetric Studies. Figure 1 shows the plots of Cp of zinc nanoparticles, and bulk zinc against T, where the Cp data for bulk zinc from Grønvold and Stølen15 are included for comparison. Our data for bulk zinc are about 2.3% higher than the average Cp reported by them. Values of Cp measured here have (1% error, and their data show variation by at least ( 0.5%. The difference may arise partly from the difference between the respective samples and partly from the experimental procedures used. Nanoparticle samples weighed before and after the Cp measurements showed no increase in their mass, which indicated that no further oxidation occurred during the Cp measurement. Figure 1 shows that Cp for nanoparticles is about 13% higher than that of bulk zinc and increases much more sensitively with increase in T than for bulk zinc. Such Cp values and increasing trend are likely to originate from particles with Zn nanocore and a rigid shell of ZnO that did not grow during the course of measurements. More than three sets of differential scanning calorimetric (DSC) scans were obtained during heating and cooling between 298 and 723 K. Since the plots were featureless over most of the lower temperature range, only features in the interesting range of 623 to 723 K are relevant. Typical plots of dH/dT [) (dH/dt)/q], which is equivalent to Cp with q being the heating or cooling rate, of zinc nanoparticles measured during heating at 10 K/min are shown against the temperature, T, in Figure 2A. Since dH/dT of nanodroplets (molten zinc) on cooling from 723 K show different features, these are plotted separately against T in Figure 2B, where curve 1′ was obtained after curve 1 in Figure 2A, curve 2′ after curve 2, and so on. For comparison, the corresponding plot for bulk zinc measured during the heating is shown in Figure 2A and that on subsequent cooling of the melt in Figure 2B. The dH/dT against T plots for a new sample obtained during the heating at 20 K/min rate and subsequent cooling at the same rate are shown in Figure 3 panels A and B, and those on another new sample heated and cooled at 40 K/min are shown in Figure 4 panels A and B. (ii) Electron Microscope Studies of Nanoparticles. The size distribution of Zn nanoparticles was displayed in a histogram obtained by measuring the size of every single particle of the as-received sample recorded in TEM images, which in turn were acquired by using Philips CM12 120 kV, the agglomerated state

Zinc Nanoparticles

Figure 2. (A) Plots of dH/dT of zinc nanoparticles and bulk Zn against the temperature during heating. The curves are numbered in the sequence in which they were obtained. (B) Plots of dH/dT of Zn nanodroplets and bulk Zn against the temperature during cooling. In this figure and Figures 2-5, Curve 1′ was obtained during cooling of the molten (nm size droplets) from 573 K after heating to 713 K in curve 1 in panel A, curve 2 ′ after the sample had been heated to 723 K in curve 2 in panel A, and so on. The samples were heated and cooled at 10 K/min.

Figure 3. (A) Plots of dH/dT of zinc nanoparticles and bulk Zn against the temperature during heating. The curves are numbered in the sequence in which they were obtained. (B) Plots of dH/dT of Zn nanodroplets and bulk Zn against the temperature during cooling. The samples were heated and cooled at 20 K/min.

of the sample showed sharp facets of the nanoparticles pointing outward. In the TEM experiment, under the focused electron beam, the nanoparticles from the agglomerates spread out onto the holey carbon film and showed their triangular, hexagonal, and so forth, faceted shapes. From multiple pictures, the

J. Phys. Chem. C, Vol. 112, No. 51, 2008 20161

Figure 4. (A) Plots of dH/dT of zinc nanoparticles and bulk Zn against the temperature during heating. The curves are numbered in the sequence in which they were obtained. (B) Plots of dH/dT of Zn nanodroplets and bulk Zn against the temperature during cooling. The samples were heated and cooled at 40 K/min.

Figure 5. (A) Size distribution of zinc nanoparticles. (B) The TEM bright field image of zinc nanoparticles at 298 K before heating to 20 K above its Tm () 693.2 K) and (C) after heating to 20 K above its Tm.

histogram was obtained and it is shown in Figure 5A. Because of the irregular shape of the particles, the size of each particle was determined as (a2 + b2)1/2, where a and b are respectively

20162 J. Phys. Chem. C, Vol. 112, No. 51, 2008 the longest and the shortest end-to-end distance measured for each particle. This particle size is in the 30-200 nm range, instead of the 35-80 nm range specified by the supplier. Most of the particles were found to be of 30-40 nm width and an equal proportion is of 50-70 nm width. The radius of the particle is taken as half of this size. Also, typical bright field TEM image of the (spread-out) nanoparticles was obtained by means of Philips CM12 120 kV. Figure 5B shows that the shapes are similar to those reported by Yan et al.,16 who referred to these as zinc nanodiscs and nanobelts. To examine the effect of melting and the possibility of oxidation of the Zn nanoparticles, the spread-out particles while still in TEM holder were heated from 298 to 713 K, which is 20 K above its melting point, and then cooled at an unknown rate to 298 K. During heating, the image intensity decreased, which indicated the beginning of their melting at a temperature in the 633-653 K range. This fading continued until all particles reached the same intensity at about 673 K. After the temperature had reached 713 K, the sample was cooled back to 298 K. The TEM picture of the particles taken at 298 K after the thermal cycling is shown in Figure 5C. The particles contrast has faded, they appear as a skeletal shell with only the surfaces showing, and there is no change in the shape. Had the zinc melted and then all of it solidified, the image intensity would have returned to its initial intensity. Therefore, loss of intensity on thermal cycling indicates that during the heating process, the sample did not only melt but that its melt also vaporized in the vacuum of the TEM. Finally, only the ZnO shell skeleton, which had likely formed during the evaporation of toluene from the sample before it was placed in the microscope at 298 K, remained. To understand the evaporation of zinc in the vacuum of the TEM, we recall that vapor pressure increases as particle size sat decreases, according to the equation ln(psat r /p∞ ) ) 2γVL/RTr, sat sat where pr and p∞ are respectively the vapor pressures of particle of radius r and of bulk, γ is surface tension () 0.99 J m-2, ref 17), VL is molar volume, for zinc melt () 9.88 × 10-6 m3 mole-1), R the gas constant, and T the temperature. Accordingly, psat r will be ∼ exp(4/r) times the vapor pressure of the bulk melt at 692.68 K, and this makes their complete evaporation much more probable. Some of the solid particles would also sublimate on heating toward the melting point, Tm. We conclude that in the vacuum of 10-7 Torr, Zn nanoparticles evaporated at a temperature far below the bulk zinc’s boiling point of 1180 K. However, the rigid ZnO shell persisted because of its much higher melting point and lower vapor pressure. To confirm whether or not the shell was composed entirely of ZnO, energy filtered TEM (EFTEM) and scanning TEM (STEM) studies were performed by using JEOL 2010F (S)TEM. The image of the region to be analyzed was taken by using a zero loss filtering technique, in which the zero loss peak is aligned with the optical axis. The energy slit width for filtering transmitted electrons was chosen to be 50 eV, so that the image contained only elastically scattered electrons, and the imageblurring caused by inelastically scattered electrons was avoided. The zero-loss filtered image of a nanoparticle after heating to 713 K and cooling back to room temperature showed a clear contrast between the skeletal shell and the core. Several energy dispersive X-ray spectra were obtained at different locations of the inner surface and the edge regions of the particle. These locations appeared hollow as a result of sample loss by drilling on penetration of electrons through the sample. The spectra were analyzed using INCA, an elemental concentration analysis software. The atomic percentage of both

Gunawan and Johari Zn and O obtained from the outer region of the particle showed stoichiometry for ZnO. Thus, only ZnO was present after the zinc particles had been melted and evaporated on heating up to 713 K, and there was no indication for formation of ZnO2. The EFTEM elemental mapping was performed using the three-window technique. The Zn and O elemental maps showed that both Zn and O were more concentrated at the edge than at the inner region of the particle. This indicated that the 30-50 nm thick ZnO shell around the particle was non-uniform in thickness. The non-uniformity appeared mainly in the regions where the shell had cracked as a result of hydrostatic stress. The very weak signals of both Zn and O from the inner region showed less concentration of both elements. The EFTEM and STEM line profiling specifically showed that the shell is ZnO and the Zn content decreasing from outside of the shell to the inside. This confirmed that as Zn melted and evaporated on heating, O2 entered in the empty core of the particles. The STEM line profiling was also done to investigate the distribution of Zn and O along the shell of the particle. The results showed that the concentration of Zn and O decreases as one moves from the outer edge toward the inner region of the particle. The concentration of zinc at ∼60 nm depth from the surface plummeted down to nearly zero, indicating that all zinc metal was lost in the procedure of heating in the TEM study. We now consider at what stage of the thermal treatment ZnO could have formed on the surface of Zn nanoparticles. Since thermal cycling was done in the vacuum of TEM, surface oxidation did not occur in the TEM. It could have occurred either during the production of the particles or during the handling of the particles prior to the TEM observations. In that case, it is necessary to explain how zinc metal could have escaped in vacuum through the ZnO shell of the nanoparticles. To do so, we recall that Tm of ZnO is 2248 K, much higher than 692.7 K for Zn, and its thermal expansion coefficient is 4 × 10-6 K-1, which is much less than that of 60.8 × 10-6 K-1 for zinc in the c-axis direction.10,11 It would be even lesser than that of the zinc melt. During heating in the TEM experiment, zinc expands more than its ZnO shell, which would produce a hydrostatic pressure within both solid zinc and liquid zinc inside a sealed particle. Since the elastic modulus of ZnO, 228 GPa,18 is higher than that of the Zn metal, 70-140 GPa,19 and its thermal expansion coefficient is much less than that of zinc, and ZnO is brittle, the hydrostatic pressure would rupture the ZnO shell at its thinnest part, thus exposing the molten zinc to vacuum, causing it to vaporize. Thus only the ZnO shell would be left. In case, the ZnO shell already had a crack, the pressure generated by expansion of the metal zinc would widen it, allowing easier escape of the zinc core into vacuum. Although any oxygen present in the atmosphere would increase the ZnO shell thickness by diffusing through it and oxidizing the zinc core, in the 10-7 Torr vacuum such a probability is small and thickening of the ZnO shell would be slow, if any. The lower concentration of zinc in the inner region than that in the edge region observed in the STEM linescan confirms that molten zinc extruding from the ZnO shell evaporated in the vacuum. On heating at ambient pressure, molten zinc may extrude through the cracks and oxygen from the atmosphere may enter, thus sealing the crack, but in the vacuum of TEM, a crack would not seal. 4. Discussion (i) Specific Heat of Nanoparticles. In Figure 1, Cp of the nanoparticles is higher than that of the bulk zinc. Our TEM studies have shown that the nanoparticles consist of a zinc core

Zinc Nanoparticles and a few nanometer-thick ZnO shell. Therefore, Cp of the nanoparticles would be equal to the weighted sum of the respective Cp’s of the zinc nanocore and the ZnO nanoshell. To estimate the Cp contributions from ZnO and zinc in nanoparticles, we recall that the Cp of ZnO is 44.34 J mol-1 K-1 (ref 19) and that of the Zn nanoparticles 30.15 J mol-1 K-1, at 373 K. In comparison, the Cp of bulk zinc is 26.75 J mol-1 K-1 at 373 K. By using the additivity of Cp of ZnO and of zinc in a two-phase material, we estimate the mole fraction of ZnO in the nanoparticles as 0.19 [) (Cp,Zn-nanoparticles - Cp,Zn)/ (Cp,ZnO - Cp,Zn)]. The molar volume of ZnO is 14.53 mL () 81.41/5.6) and of zinc is 9.17 mL () 65.41/7.13) at 298 K, a ratio of 1.58. Thus, a mole fraction of 0.19 corresponds to a volume fraction of 0.30 () 0.19 × 1.58). TEM studies of the ZnO skeleton after zinc had evaporated show that for the mean diameter of 100 nm, and a ZnO shell thickness of ∼ 5 nm estimated from Figure 5C, the maximum volume fraction of ZnO is 0.27, which is less than that calculated above. Accordingly, the increased Cp of the nanoparticles cannot be entirely attributed to the presence of the ZnO shell. We conclude that the Cp of zinc nanocore would be slightly higher than that of bulk zinc. It may be noted also that the plots of the enthalpy of a liquid, that is, the integral of Cp dT, and of its crystal phase approach each other as T is decreased. Therefore, the heat of melting of nanoparticles is generally expected to be less than that of the bulk crystals, and the difference is expected to vary with the material and may even be within experimental error in some measurements. Cp values of nanoparticles higher than that of bulk (polycrystalline) solids have been found for Pd (50% higher),20 Cu (10% higher), and Pd (40% higher).21 It has been concluded that nanocrystalline materials consist of comparable volume fractions of (i) a core component in which atoms are on the lattice of the crystallites or grains and (ii) an interfacial component or grain boundaries. The higher Cp and thermal expansion coefficient of nanoparticles has been attributed to (i) a large fraction of atoms in the disordered interfacial structure and a more open structure (∼85% of the bulk density) and hence a weaker interatomic coupling that decreases the vibrational frequencies and increases the vibrational and configurational entropy,20 (ii) thermally induced variation of the vibrational and configurational entropy of materials because of lattice vibrations and variation of equilibrium defect concentration, especially in the disordered structures (grain boundaries),21 and (iii) strong anharmonic forces that lower the vibrational frequencies because of increased interatomic spacing.22 The increased Cp has been modeled in terms of the Einstein and Debye theories,23 discussed in terms of the difference between the vibrational modes of surface and interior atoms,24 and phonon scattering by the boundary of nanocrystals that generates new phonon frequencies that contribute to the specific heat.25 In general, the disordered interfacial atoms of metals have a higher vibrational and configurational Cp, expansivity21,26 and entropy contribution than the bulk. Kirchheim et al.27 have calculated the configurational entropy of the grain boundaries for three metals, that is, Cu, Ni, Pd, at 330 K. They showed that the configurational entropy and hence configurational Cp of the grain boundary atoms of nanocrystalline (aggregate) metals is much higher than the corresponding entropy typical of coarse polycrystalline metals. The increased Cp of zinc nanocore may also be attributed to lowering of the vibrational frequencies and increase in the configurational Cp at surface and interfacial regions of nanoparticles.

J. Phys. Chem. C, Vol. 112, No. 51, 2008 20163 (ii) Source of Low Temperature Endotherm on Heating Zinc Nanoparticles. In Figures 2A, 3A, and 4A, a very small endothermic feature appears on the low temperature side of the melting peak in the first heating cycle of all nanoparticle samples irrespective of the heating rate. This feature vanishes in the subsequent scan and does not reappear on thermal cycling. In Figures 2A-4A, the onset and the end temperatures of the small endothermic feature are 632 and 639.5 K for 10 K/min rate, 652.6 and 674.4 K for 20 K/min rate, and 666.3 and 685.3 at 40 K/min rate. The Tms of nanoparticles for the first heating cycle are, respectively, 690.8, 691.3, and 691.6 K. In Wu et al.’s11 preliminary study of zinc nanoparticles by DSC, one heating scan for 20 K/min rate in O2 atmosphere had shown a sharp endothermic peak at ∼ 639 K. This is comparable to the peak at ∼648 K in curve 1 in Figure 3A. The ratio of this peak’s height to the melting endotherm peak height is less than 1%, in comparison with the corresponding ratio of 50%, reported in Figure 3 of ref 11. They tentatively attributed this endotherm to the heat absorbed on evaporation of the sample when the ZnO shell ruptured. To investigate the origin of this feature, DSC scans of several new samples of nanoparticles were obtained during both heating and cooling at rates of 10, 20, and 40 K/min but in the low temperature range of 573-673 K in which zinc nanocore did not melt. The small endothermic feature was observed only on the first heating. For higher heating rates, its position shifted to higher T, from 632.0 to 666.3 K when the heating rate was increased from 10 to 40 K/min, as seen in Figures 2A and 4A. Although the size and the ZnO shell thickness of nanoparticles in our study differs from those studied by Wu et al., the small endotherm appears at about the same T in the two studies. We first consider whether the small endotherm at 652 K in Figure 2A could be due to melting of relatively small nanoparticles in the sample. Since the endotherm’s temperature increases with increase in the heating rate, and it appears only on first heating, the endotherm would be attributable to a kinetically controlled process instead of a thermodynamic equilibrium process. The feature may be attributed to melting of very small nanoparticles only if the Gibbs-Thomson equation was obeyed, as for example Tm of unconfined gold nanoparticles is known to decrease by as much as 700 K.28 If it were due to such melting, it would reappear on second thermal cycling unless the zinc nanocore oxidized or else it partly oxidized and reduced the nanocore to a size which could not exist in the crystal form. Alternatively, if the molten zinc nanoparticles coalesced, the resulting increase in size would raise their Tm, and the feature would appear at a higher T. This is not observed. We conclude that the small endotherm is likely to be due to the melting of some of the smallest nanocores of zinc metal in the particles and not due to evaporation of zinc metal on rupture of the ZnO shell. The endotherm’s temperature became heating rate dependent because of a large thermal lag between the zinc metal and the instrument sensor, with ZnO shell acting as a thermal insulator and adding to the thermal lag that increased with increase in the heating rate. (iii) Melting Point in Nanoconfinement. In Figures 2A-4A, Tm of nanoparticles for the first heating cycle is 690.9 K for 10 K/min, 691.4 K for 20 K/min, and 691.7 K for 40 K/min rate. These values gradually decrease respectively to 688.6 K, 689.8 K, and 690.1 K in the fifth heating cycle after the samples had been cooled at the same rate as heated. In comparison, Tm of the bulk sample remains at 692.7 K for the three heating rates. The difference, ∆T, between the onset and end temperatures of the melting endotherm is 15 K for 10 K/min, 16.8 K for 20

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K/min, and 20.2 K for 40 K/min heating, and it decreases respectively to 7.5, 14.3, and 17.8 K on the fifth heating cycle. According to the Gibbs-Thomson equation,2,29 the equilibrium melting temperature TmR of a crystal of radius R with a free surface,

TmR Tmbulk also written as,

[( )]

(1)

[ ( )]

(1a)

) exp -

TmR ) Tmbulk 1 -

2γs,lVs 1 ∆HmR R

2γs,lVs 1 ∆Hmbulk R

where Tmbulk is the melting point of the bulk solid, γs,l is the interfacial tension between the solid and its melt, Vs is the molar volume of the solid, and ∆HmR is the molar enthalpy of melting at TmR, which is taken to be equal to that of the bulk ∆Hmbulk in eq 1a. We use the known value for γs,l ) 993 mJ/m2 (ref 17), Vs ) 9.16 mL/mol (atomic wt ) 65.4 Da and density ) 7.14 g/mL) and ∆Hmbulk ) 7.07 kJ/mol15 equal to ∆HmR, the enthalpy of melting of bulk zinc, and Tbulk m ) 693.2 K in eq 1 to determine TmR. Thus for 35-80 nm size (spherical) nanoparticles (R ) 17.5-40 nm), TmR is in the range 598-650 K and lower for smaller nanocore of zinc. In contrast, the result obtained here shows that the minimum TmR is 687.2 K, which is 37-89 K higher than the value calculated from eq 1. Evidently, the decrease in Tm is much less than that expected from the Gibbs-Thomson equation. In principle, the width of a melting endotherm may indicate the percentage of particles of a given size melting at a certain temperature. Without the knowledge of the size-dependent surface or interfacial energy of anisotropic crystals, it does not seem possible to determine this percentage from our studies. It is not generally recognized that use of the Gibbs-Thomson equation between R and Tm was derived for equilibrium with its own vapor phase and not for crystals tightly confined within a cavity, where the pressure may change with change in both T and the volume on melting. In this study, its use serves merely an instructive purpose in view of the fact that the zinc nanocore expands more on heating than the rigid ZnO shell, thereby producing a hydrostatic pressure on the nanocore. This pressure would increase further when the zinc nanocore melts, which in turn would raise the melting point of the nanocore. The magnitude of the increase would depend upon the volume and the entropy change on melting, and a condition may be reached when Tm would cease to decrease on thermal cycling. This is an effect opposite to that of eq 1 according to which Tm would only decrease. There is also a further aspect that prevents the use of eq 1 for determining Tm. Both zinc and ZnO have close-packed hexagonal structure, but different unit cell parameters. In a study of the gas-sensing properties of ZnO, Lin et al. 30 have shown that there is a good epitaxial relationship between zinc and ZnO shell. The singular fringe spacing of high-resolution TEM of zinc is 0.24 nm while that of ZnO was about 0.28 nm.30 Such good epitaxial relationship may result in surface interactions between zinc and ZnO not included in eq 1. Therefore, we conclude that the use of the Gibbs-Thomson equation should be restricted to particles at equilibrium with their vapor. Moreover, for confined nanoparticles, for example, those embedded in a matrix, it has been suggested that Tm is higher than that of free nanoparticles,31,32 particularly when the interface between nanoparticles and matrix is coherent or semi-coherent.33 Therefore, the Gibbs-Thomson equation itself would not be

able to accurately predict the decrease in melting temperature of confined nanoparticles, such as Zn confined in the ZnO shell. We now consider the effect of thermal cycling on Tm. For the 10 K/min rate, it decreases from 690.9 to 689.6 K from first to the second cycle and finally to 688.6 K in the fifth cycle, for the 20 K/min rate from 691.4 to 689.7 K and thereafter remains constant, and for the 40 K/min rate from 691.7 to 690.3 K and finally to 690.1 K. The initial decrease in Tm indicates reduction in the zinc nanocore on oxidation and consequent thickening of the ZnO layer and ultimately sealing of the ZnO shell. After that has occurred, oxygen diffuses far too slowly through the ZnO shell to further oxidize significantly the zinc nanocore during the measurement period. As seen in Figures 2-4 for the first heating and cooling cycle at the 10 K/min rate, melting begins at 690.9 K and crystallization at 688.5 K. For the 20 K/min rate, it begins at 691.4 K and crystallization at 689.2 K, and for the 40 K/min rate, it begins at 691.7 K, and crystallization at 688.2 K. The 2.2 to 3.5 K difference between the melting and the crystallization temperatures shows that zinc nanodroplets supercool before crystallization begins. Both the melting and the crystallization temperature ranges are broadened with increase in heating/ cooling rates. (iv) Enthalpy of Melting and of Crystallization. The change in enthalpy from T1 to T2 is equal to the integral of Cp dT. In a DSC measurement, the heat of melting, ∆Hm, and the heat of crystallization, ∆Hcryst, are determined by integrating the area of the endotherm and exotherms, respectively, between the onset and the end temperatures. The heat flow data are thus used to determine the enthalpy difference from the relation,

∆H(T) - ∆H(Tref) )

dT ∫TT ( ∂H ∂T ) ref

(2)

where Tref is the reference temperature which we take as 640 K for 10, 20, and 40 K/min heating in Figures 2-4. This integral is plotted against T in Figures 6A and B. ∆Hm was determined from the difference between the extrapolated value of the enthalpies of solid and liquid at Tm. ∆Hcryst was determined from the difference between the extrapolated enthalpies of the solid and the liquid at Tcryst, the onset temperature for crystallization, and using Tref as 700 K for the three cooling rates. For the bulk zinc, ∆Hm is 7.16, 7.07, and 7.05 kJ/mol for 10, 20, and 40 K/min heating rates and ∆Hcryst is 7.05, 7.06, and 7.00 kJ/mol. These ∆Hm and ∆Hcryst are within the experimental and analytical errors of (1.2%, and they agree with the known ∆Hm of 7.07 kJ/mol (ref 15). For the nanoparticles, ∆Hm is 5.46 ( 0.06 kJ/mol. In the fifth thermal cycle, ∆Hm decreases to 2.87 for 10 K/min, to 4.49 for 20 K/min, and to 5.13 kJ/mol for 40 K/min rate. In contrast, ∆Hcryst varies with the cooling rate, and it is 4.6, 4.4, and 5.0 ( 0.06 kJ/mol, respectively, for 10, 20, and 40 K/min cooling rate. In the fifth thermal cycle it decreases to 2.2 kJ/mol for 10 K/min, to 3.8 kJ/mol for 20 K/min, and to 4.85 kJ/mol for 40 K/min rate. Thus, ∆Hm and ∆Hcryst decrease to about half of their values when thermally cycled at 10 K/min, but only by 2-6% on thermal cycling at 40 K/min. This indicates that the decrease is due to reduction of the zinc core’s mass as it is consumed to form ZnO, and the reduction was more for slower rate of thermal cycling than for the faster rate. Thus, the decrease in ∆Hm and ∆Hcryst would be an artifact of our use of the initial mass of nanoparticles as the mass of zinc for calculating these quantities. Without correcting for the amount of zinc in nanoparticles, it is not possible to ascertain how much of the decrease in ∆Hm and ∆Hcryst is due to the size effect.

Zinc Nanoparticles

Figure 6. (A) Enthalpy of Zn nanometer size particles and melt in units of J mol-1 K-1 plotted against the temperature. The sample was heated at 10 K/min, and the curves numbered are in the sequence in which they were obtained. Also plotted is the enthalpy of bulk Zn in J mol-1 K-1. (B) The enthalpy of Zn nm-size droplets during crystallization on cooling is plotted against the temperature.

However, ∆Hm decreases on further thermal cycling even though Tm does not change. The constant Tm does not correspond to a constant particle size distribution, instead it indicates thickening of the ZnO shell on large particles, whose melting does not determine the endotherm’s onset temperature. This is supported by the fact that while the onset temperature does not change, the end melting temperature is slightly shifted to lower T. Moreover, the 13% higher Cp of the nanoparticles implies that the integral of Cp dT for the nanoparticles is higher than for bulk zinc. Since dCp/dT seen in Figure 1 is also higher, this means that not only its enthalpy is higher but also the slope of the enthalpy in the T plane is higher. If the corresponding dCp/ dT for the melt did not greatly change, then the ∆Hm of nanoparticles would be lower than that of the bulk. This is a general feature of melting of all nanoparticles and is in addition to the decrease in ∆Hm due to any change in the high-energy surface structure of the nanoparticles. (v) Two-Step Crystallization on Cooling. Upon crystallization during cooling, bulk zinc melt shows only one exothermic minimum in Figures 2B-4B and the nanomelt shows two exothermic minima, indicating two mechanistically different stages of crystallization inside the ZnO shell. The temperature range of the two minima becomes narrower on thermal cycling, as the ZnO shell thickens and zinc is consumed. The first (higher temperature) minimum is deeper in Figures 2B-4B than the second (low temperature) minimum, and both lose strength as they mutually approach on thermal cycling. The extent of the approach varies with thermal cycling rate. The self-diffusion coefficient in the melt is usually high, and therefore a rapid nucleation and crystallization is expected. However, the crystallization exotherms are broad, which may occur if different regions in the nanomelt or different nanocore melt crystallize at different T. To investigate whether or not the two minima on cooling could be due to a possible thermal barrier for heat propagation between two crystallizing nanodroplets, we performed separate

J. Phys. Chem. C, Vol. 112, No. 51, 2008 20165 experiments: In one, two indium metal particles were separated by a 0.5 mm thick glass disk and its DSC scans were obtained. The scans showed two endothermic peaks on heating and two exothermic minima on subsequent cooling. In the second, zincAl2O3 mixture was ball-milled. DSC scans of the powder (Al2O3 acting as thermal barrier) showed two endothermic peaks but only a one exothermic minimum. Since there is only one endothermic peak on heating in Figures 2B-4B and the exothermic minima observed on cooling are widely separated, these two minima are not an artifact of thermal barrier between nanodroplets. Since the first minimum appears at a T higher than that of the bulk zinc, it is attributable to heterogeneous nucleation and growth on the inner surface of the ZnO shell. The activation energy of this nucleation is less than that for homogeneous nucleation of zinc nanodroplets. Briefly, ∆G*het ) ∆G*hom × S(θ), where S(θ) ) (2 + cos θ)(1 - cos θ)2/4, where ∆G*het and ∆G*hom are the energy barriers for respective nucleation, and θ, the “wetting” angle of the melt with the substrate determines the magnitude of the shape factor S(θ), as described in detail in refs 34 and 35. A low θ value corresponds to a good lattice matching between the nucleating substance and the free surface. In a study of ZnO as gas sensor29 it has been reported that ZnO and zinc have the same hexagonal close packed cell structure but different unit cell parameters, thus indicating their good epitaxial relationship. As mentioned earlier here, the singular fringe spacing of high-resolution TEM of Zn was measured to be 0.24 nm while that of ZnO was about 0.28 nm. The 17% lattice mismatch is considered to provide a semicoherent interface, which would make heterogeneous nucleation favorable. We have already discussed that the ZnO shell thickens on thermal cycling at the expense of zinc nanocore, and the rate of this process decreases with increasing thickness of the ZnO nanoshell and hence increasing diffusion time for oxygen through the shell. As a result, the interface of the nanomelt core with ZnO decreases as the inner curvature of the shell increases. This would decrease the surface available for heterogeneous nucleation, change the epitaxial mismatch for heterogeneous nucleation, and decrease the volume of the nanomelt core available for homogeneous nucleation. Altogether, they would cause the minima arising from heterogeneous and homogeneous nucleation mechanisms to mutually approach and their relative strength to become thermal cycle rate dependent, higher for the 10 K/min than for 40 /min rate as seen in Figures 2B-4B. 5. Conclusions The specific heat of zinc nanoparticles is slightly higher than that of the bulk zinc and is more sensitive to temperature, and the heat of melting is less for the nanoparticles than for the bulk. The melting point of nanoparticles is only 1.5 K less than that of the bulk. Although this is consistent with the GibbsThomson equation, it is argued that the equation should be used only in cases where the solid particles or liquid droplets are at equilibrium with their vapor, and not confined in a rigid cavity or shell. The much higher thermal expansion of zinc and its melt relative to that of the more rigid ZnO shell produces a hydrostatic pressure on the zinc core as the nanoparticles are heated, and this raises their melting point. An apparently good epitaxial ratio of zinc and ZnO seems to have a further effect on the melting thermodynamics. A minute endotherm is observed on the first heating of zinc nanoparticles before their melting. This is attributed to the melting of the smallest particles. The peak vanishes on second

20166 J. Phys. Chem. C, Vol. 112, No. 51, 2008 and further heating partly because most of the zinc core oxidizes and the amount of zinc left is either too small to crystallize, or its melting temperature is further reduced with greatly reduced endotherm intensity. Increase in hydrostatic pressure because of the difference in the thermal expansion coefficient of the zinc nanocore and the ZnO shell, and because of the volume increase on melting of zinc nanocore, is expected to increase the measured ∆Hm and ∆Hcryst. In contrast, thickening of the ZnO shell at the expense of the zinc nanocore during thermal cycling yields a lower ∆Hm and ∆Hcryst if, as in our estimate, the mass of zinc is not corrected. The uncorrected ∆Hm and ∆Hcryst decrease more for the slow rate of thermal cycling than for the fast rate. The zinc core in the ZnO nanoshell crystallizes on cooling first by heterogeneous nucleation on the ZnO surface and second by homogeneous nucleation. During thermal cycling, the amount of nanomelt decreases in a ZnO shell of increasing curvature, the relative magnitudes of the two crystallization steps change, and their peak temperatures merge. These observations have been confirmed by structural and chemical analysis using techniques of TEM and STEM. Since most nanoparticles are highly reactive and susceptible to oxidation in air, the effect of a rigid oxide shell studied here would be helpful in interpreting their properties and the properties of nanoconfined materials in rigid cavities. Acknowledgment. This study is part of the M.A.Sc. thesis of Lina Gunawan, dated June 2005, which may be consulted for more details. The research was supported by a Discovery Grant from Natural Sciences and Engineering Research Council of Canada to G.P.J. References and Notes (1) Gibbs, J. W. Collected Works of J. W. Gibbs; Dover, NY, 1928. (2) Thomson, W. (Lord Kelvin) Proc. R. Soc. Edinburgh 1871, 7, 63; Philos. Mag. 1871, 42, 448. (3) Defay, R.; Prigogine, I.; Bellemans, A. Surface Tension and Adsorption; translated by D. H. Everett; Longmans: London, 1966. (4) Johari, G. P. Philos. Mag. A 1998, 77, 1367. (5) Sun, J.; Simon, S. L. Thermochim. Acta 2007, 463, 32. (6) Puchert, M. K.; Timbrell, P. Y.; Lamb, R. N. J. Vac. Sci. Technol. A 1996, 14, 2220.

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