Evolution of crystallinity of free gold agglomerates and shape transformation

Abstract

We report the shape evolution of free gold agglomerates with different morphologies that transform to ellipsoidal and then to spherical shapes during the heating cycle. The shape transformation is associated with a structural transition from polycrystalline to single crystalline. The structural transition temperature is shown to be dependent on the final size of the particles and not on the initial morphologies of the agglomerates. It is also shown that the transition occurs well below the melting temperature which is in contrast with the melt-freeze process reported in the literature.

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Unique properties of nanoparticles have made them important materials for different applications. Most applications require nanoparticles of a particular shape, preferably spherules, both crystalline and monodisperse. The synthesis of monodisperse nanocrystals is of key importance because the properties of these nanocrystals depend strongly on their dimensions.

Typically, in many industrial aerosol processes and syntheses of nanoparticles (NPs) by the aerosol route,^1–8 a high concentration of very small NPs undergo rapid coagulation and form agglomerates. When sintered at high temperature, the smaller NPs in an agglomerate coalescence, to form larger spherical NPs. However, the crystallinity of spherical NPs has rarely been investigated.

Coalescence of NPs and the evolution of their shapes have been widely investigated, both experimentally^1–15 and theoretically.^15–24 The experiments on supported NPs reveal that the shape and crystallinity of the final product depend on the size, crystallinity, orientation of the initial coalescence, temperature and time.⁹ Molecular dynamic (MD) simulations reveal that the coalescence of NPs occurs below the melting temperature^20,21 and the new particles are polycrystalline and non-spherical at the coalescence temperature.²⁰ Though the crystallinity is not known, the transformation of nanorods and non-spherical NPs to a spherical shape also occurs at incredibly low temperatures.^24–28 On the other hand, multiply twinned Au particles (MTPs) transform to single fcc crystals by a melt-freeze process.^29,30Crystallization of Si has been investigated and found that the crystallization temperature is comparable to the melting temperature of nanoparticles.⁷ It is, therefore of significance to investigate the shape transformation and the crystallinity of agglomerates and non-spherical NPs. Though the shape transformation has been investigated extensively,^1–14 the crystallinity of the products has been rarely investigated.

Here, we report on the evolution of the shape and crystallinity of free non-spherical Au NPs/agglomerates of different sizes and morphologies during the heating cycle. It is shown here that non-spherical particles transform to spherical, while agglomerates transform to non-spherical and then spherical shapes with increasing temperature. The shape transformation is shown to be associated with a change in the structural motifs, from polycrystalline to fcc crystal. A simple and fast technique has been reported and used to evaluate the temperature (T_ST) at which the majority of the polycrystalline particles change to single crystalline. Interestingly, T_ST is found to be independent of the initial morphologies of the agglomerates but depends on the final size of the NPs. It is also found that T_ST is lower than the melting points of the NPs and the structure/shape transformation occurs during the heating cycle. This is in contrast with the melt–freeze process reported for MTPs.^28,29

2. Experimental

Agglomerates or non-spherical Au NPs with different sizes are produced by cooling Au vapor with nitrogen carrier gas (Fig. 1).^1,2Au vapor was obtained by heating Au (99.999%) in a tube furnace at a temperature of 1663 K. NPs/agglomerates are formed as a consequence of vapor condensation followed by coagulation. In order to classify the size of the agglomerates/ particles, they are charged by a radioactive source (⁸⁵Kr), and flown into a differential mobility analyzer (DMA). A DMA selects particles on the basis of their mobility-equivalent diameter which is a function of their size, charge level and shape and is used to characterize the particle size. After the DMA (DMA1), a second tube furnace is used to sinter the free agglomerates and non-spherical NPs to investigate the shape transformation. The time agglomerates or particles spend in the second furnace is ∼35 s for a gas flow rate of 1.0 sL m⁻¹ (standard liter per minute). A tandem DMA technique, i.e. a second DMA (DMA2), as shown in Fig. 1(a), is used to monitor the variation of the mobility-equivalent diameter for different sintering temperatures in the second furnace. For each initial mobility-equivalent diameter d_M0 (selected by DMA1), the particle size distribution (particle number concentration as a function of the mobility equivalent diameter) for a sintering temperature, is measured by an ultrafine condensation particle counter (UCPC, TSI model, 3025) and DMA2. The mobility-equivalent diameter d_M with the maximum particle concentration is considered the representative particle size at the outlet of the sintering furnace, as described in Ref. 2. As shown in Fig. 1(b), the particles can also be deposited on any kind of substrate using an electrostatic precipitator (ESP). The morphology and size of Au NPs/agglomerates are investigated by a transmission electron microscope (TEM). The crystallinity and the equilibrium shape of NPs are examined by high resolution TEM (HRTEM). The instruments used were a Philips CM12 twin microscope, 120 keV with a LaB₆ cathode and a Philips Tecnai F20 electron microscope, 200 keV with a field emission cathode. Using a similar experimental system, thermal recharging of positively charged agglomerates was observed in the second furnace which led to a change in the mobility-equivalent diameter.⁴ Therefore, negatively charged aggregates were investigated which did not show this effect.

Fig. 1 Experimental set up for the investigation of size change (a) using a second DMA (DMA2) and (b) for the deposition of nanoparticles in an ESP.

3. Results and discussion

TEM micrographs of Au agglomerates/particles with d_M0 = 16 nm sintered at different temperatures are presented in Fig. 2. A micrograph of Fig. 2(a) shows open agglomerates consisting of small primary particles. The agglomerates coalesce to yield either compact non-spherical or spherical shapes depending on the sintering temperature, as evidenced from Fig. 2(b–d). To investigate the sphericity of Au NPs, the grid containing the particles is tilted up to 40° (the precision is better than 0.5°), with respect to the electron beam and the TEM images of NPs with d_M0 = 16.0 nm that were sintered at 873 K are shown in Fig. 3. The height d_⊥ is estimated using the equation, d_θ = d_⊥ sin²θ + d₁₁ cos²θ, where d_θ and d₁₁ are the diameters for a tilting angle of θ and 0°, respectively. The diameter-to-height ratio is ∼10 : 8.5 for a sintering temperature of 873 K and slightly non-spherical. Highly monodisperse NPs can also be synthesized by this technique. When d_M0 = 8 nm, non-spherical NPs are obtained even without sintering and undergo a shape transformation to spherical as the sintering temperature is increased. In this context, it is worthy to note that the temperature required to observe the shape transformation, depends on d_M0.

Fig. 2 TEM images of Au NPs (d_M0 = 16.0 nm) at different sintering temperature (a) 298; (b) 723; (c) 873 and (d) 923 K.

Fig. 3 TEM images of Au NPs (d_M0 = 16.0 nm) sintered at 873 K. Micrographs are taken by tilting the TEM grids with the arrow representing the axis of tilting. The angles of tilting are (a) 0; (b) 10; (c) 20; (d) 30; (e) 40°. The diameter-to-height ratio is evaluated to be 10 : 8.5 and the ratio can be lowered by increasing the sintering temperature.

Shown in Fig. 4(a–d) are the HRTEM micrographs of nearly spherical Au NPs for d_M0 = 16.0 nm sintered at 923 K. A few polycrystalline NPs are also observed, as shown in Fig. 4(e) & (f) which suggests that the fraction of fcc particles is ∼2/3. The morphology of best fit is taken from Ref. [31] for comparison and rotated to match the morphology of our NPs (Fig. 4(a–d)) as they are oriented randomly on the TEM grid, as shown in Fig. 4. They resemble the shape of Wulff polyhedra,³² limited by six (100) and eight (111) hexagonal facets and are nearly spherical. NPs sintered at 873 K are non-spherical and polycrystalline as shown in Fig. 5. Based on TEM and HRTEM images, it is observed that NPs/agglomerates sintered at low temperatures are non-spherical and polycrystalline, while NPs are spherical and single crystalline when sintered at higher temperatures. This suggests that the shape transformation of non-spherical NPs/agglomerates is associated with a structural change. The shape as well as the crystallinity of the NPs depends on the sintering temperature. The structure and shape of the final NPs are size-independent for the size range investigated.

Fig. 4 (a–d) HRTEM images revealed that single crystalline Au NPs (d_M0 = 16.0 nm, TSF = 923 K) are enclosed by (111) and (100) crystal faces. The morphology of best fit is taken from Ref. [19] and rotated to match the morphology of our NPs; (e,f) A few polycrystalline NPs are also observed.

Fig. 5 HRTEM images revealed that NPs (d_M0 = 16.0 nm, TSF = 873 K) are non-spherical and polycrystalline.

In order to evaluate T_ST, the reduced mobility-equivalent diameter (d_M/d_M0) is plotted as a function of the sintering temperature for different d_M0 and shown in Fig. 6(a). It can be noted that d_M/d_M0 decreases steadily at first (region I) with increasing T_SF and then gradually (region II) followed by a rapid decrease (region III). The decrease in d_M/d_M0 (region I and II) is associated with the compaction of the agglomerates/particles, as evident from Fig. 2, and the rapid decrease in d_M/d_M0 (region III) is associated with partial evaporation from the NPs.^1,2 Further increasing the sintering temperature leads to a more gradual decrease of d_M/d_M0 (region IV). It is evident from HRTEM studies that the NPs are single crystalline in region IV and polycrystalline in region III. Therefore, the onset temperature of the gradual decrease of d_M can be considered to be T_ST. An interpolation procedure, as demonstrated in Fig. 6(a) is adopted to determine T_ST and the corresponding d_M. In this context, it is worthy to note that the size d determined by TEM is ∼10% smaller than d_M. Taking this deviation of particle size into account, T_ST is plotted as a function of 1/d and shown in Fig. 6(b). It may be noted that T_ST is linear with 1/d in the size range studied.

Fig. 6 (a) The reduced mobility-equivalent diameter as a function of the sintering temperature; (b) size-dependent transition temperature. The melting temperature curve is based on the thermodynamic model.²²

The mean melting temperature, as supported by different experiments and a thermodynamic model,³³ is plotted in Fig. 6(b) for comparison. It may be noted that T_ST is lower than the melting temperature, as is the case with the shape transformation of non-spherical Au NPs and nanorods.^20–29 It has been well established that some facets of fcc crystals melt at much lower temperatures. It is known from experiments that the macroscopic Au (110) surface melts at 770 K,³⁴ (100) surface disorders at 970 K,^35,36 while (111) surface is stable up to, and even above, the bulk melting point.³⁷ This indicates that the Au (110) surfaces first melt with increasing temperature followed by the (100) and then (111) faces. MD simulations reveal that nanorods enclosed by (110) or (100) facets reorganize to form higher stability (111) facets, while rods with (111) facets remain stable with no significant shape or structural rearrangement till the melting temperature.^27,28 The difference is due to the surface melting (SM) of (110) facets and the non-melting of (111) facets suggesting anisotropic thermal stability. The driving force for SM is thought to be a reduction in the total surface energy Δγ :^38,39

Δγ^{hkl} = γ^{hkl}_sv −γ^{hkl}_sl − γ_lv (1)

the γ’s are the surface energies of solid–vapor, solid–liquid and liquid–vapor interfaces of the material and the superscript hkl represents the crystal faces. For most cubic metals, the “average” driving force is close to zero—i.e., Δγ ∼ 0, and subtle changes of surface conditions/surface orientation can have marked effects on the SM for Δγ > 0.

As the NPs are polycrystalline in region III Fig. 6(a), it is expected that SM as well as other surface phenomena such as reconstruction, disordering, and roughening, occur at low temperatures and transform to crystalline and spherical NPs above T_ST. It is possible that an instability of the surface facets nucleates a bulk instability that leads to both surface and bulk reorganization of the agglomerates.^26,40 The surface reorganizes to form new, more stable {111} facets, while the underlying fcc lattice completely reorients to align with this new surface structure. Particles with predominantly {111} facets remain stable until melting so that the shape transformation takes place by a melt–freeze process.^29,30 In region IV, NPs are single crystalline and the gradual decrease of d_M reflects the thermal stability of the (100) and (111) surfaces against evaporation. The results further suggest that the structural transition and the shape transformation take place during the heating cycle. This is in accordance with the shape transformation of nanorods and NPs examined by experiments^24,25 and MD simulations^25,26 but in contrast to the melt–freeze process observed for MTPs where the single crystalline spherical Au NPs are obtained by freezing the droplets.^29,30 As MTPs are enclosed by (111) surfaces, the transition is expected by a melt–freeze process.

It has been shown that agglomerates undergo incomplete or complete coalescence depending on the matching of the crystallographic reorientation.^9,15 In our case, the free agglomerates independent of the morphology transform to crystalline and spherical nanoparticles. The influence of substrates in the coalescence process can be ruled out.¹

Now we discuss the time of complete coalescence of two NPs, though quantitative comparison is not possible as an agglomerate consists of more than two unequal primary NPs. It can be assumed that each agglomerate coalesces to yield agglomerates with two equal size NPs (Step 2) before they coalesce to yield spherical and crystalline NPs, as shown in Fig. 7(a). As the coalescence of small NPs is much faster compared to large NPs, the coalescence time of agglomerates with two equal size NPs just before complete coalescence (Step 2) can be considered as the total coalescence time of the agglomerates. Similarly, the size of the primary particles before coalescence is 2^–1/3d, as two particles coalescence to yield the final particles of size d. For very small objects that facilitate SM, surface diffusion is very efficient as a mass transfer mechanism and the coalescence time of two spheres is given by:⁴¹

t_c = k_BTd⁴/(CD_sγa⁴), (2)

where D_s is the surface diffusion constant, a is the atomic size, γ is the surface energy, d is the initial diameter of the sphere, and C is a numerical constant. The diffusion constant depends on the temperature by

D_s = D_s0 exp(−E_a/RT) (3)

where E_a is the activation energy. Taking D_s0 = 0.3 cm²s⁻¹, t_c = 35 s (the residence time in our case), γ = 1.393 and 8.79 J m⁻²,⁴²C = 225 and solving eqn (2), the average value of E_a is found to be 176.87 T_M J mol⁻¹ where T_M is the bulk melting temperature. Though this value is ∼3.7 times higher than the value used in Ref. [22], the experimental data is comparable with the theoretical curve irrespective of the γ values as shown in Fig. 7(b).

Fig. 7 (a) Schematic of the shape transformation process. Agglomerates follow 1-2-3-4 or 1′-2-3-4 and transform to spherical shape, while non-spherical NPs transform to spherical shape as indicated by 3-4. (b) Comparison of TST with that calculated based on eqn. (2).

4. Summary and conclusions

We report an aerosol route to synthesize monodisperse, spherical and crystalline Au nanoparticles. The shape and structure of free non-spherical NPs/agglomerates change before they melt. Above all, the crystallinity can be improved by sintering agglomerates/non-spherical, polycrystalline spherical NPs, etc. The transition temperature T_ST depends only on the final size of the NPs (not on the initial morphologies) and is linear with the inverse of the particle size.

Acknowledgements

The authors acknowledge Dr B. Rellinghaus for TEM investigations and helpful discussions. The financial support of Deutsche Forschungsgemeinschaft (DFG) in the framework of the special research program “Nanoparticles from the gas phase: formation, structure, properties” (SFB 445, project A7) and priority program “Handling of highly dispersed powders” (SPP 1062).

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