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Formation Mechanism of Fe Nanocubes by Magnetron Sputtering Inert Gas Condensation Junlei Zhao, Ekaterina Baibuz, Jerome Vernieres, Panagiotis Grammatikopoulos, Ville Jansson, Morten Nagel, Stephan Steinhauer, Mukhles Sowwan, Antti Kuronen, Kai Nordlund, and Flyura Djurabekova ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.6b01024 • Publication Date (Web): 10 Mar 2016 Downloaded from http://pubs.acs.org on March 13, 2016

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Formation Mechanism of Fe Nanocubes by Magnetron Sputtering Inert Gas Condensation Junlei Zhao,∗,† Ekaterina Baibuz,† Jerome Vernieres,‡ Panagiotis Grammatikopoulos,‡ Ville Jansson,† Morten Nagel,† Stephan Steinhauer,‡ Mukhles Sowwan,‡,¶ Antti Kuronen,† Kai Nordlund,† and Flyura Djurabekova† Department of Physics and Helsinki Institute of Physics, University of Helsinki, P.O. Box 43, FI-00014 Helsinki, Finland, Nanoparticles by Design Unit, Okinawa Institute of Science and Technology (OIST) Graduate University, 1919-1 Tancha, Onna-Son, Okinawa, 904-0495, Japan, and Nanotechnology Research Laboratory, Al-Quds University, East Jerusalem, P.O. Box 51000, Palestine E-mail: [email protected]

Abstract In this work, we study the formation mechanisms of iron nanoparticles (Fe NPs) grown by magnetron sputtering inert gas condensation and emphasize the decisive kinetics effects that give rise specifically to cubic morphologies. Our experimental results, as well as computer simulations carried out by two different methods, indicate that the cubic shape of Fe NPs is explained by basic differences in the kinetic growth modes of {100} and {110} surfaces rather than surface formation energetics. Both ∗

To whom correspondence should be addressed Department of Physics and Helsinki Institute of Physics, University of Helsinki, P.O. Box 43, FI-00014 Helsinki, Finland ‡ Nanoparticles by Design Unit, Okinawa Institute of Science and Technology (OIST) Graduate University, 1919-1 Tancha, Onna-Son, Okinawa, 904-0495, Japan ¶ Nanotechnology Research Laboratory, Al-Quds University, East Jerusalem, P.O. Box 51000, Palestine †

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our experimental and theoretical investigations show that the final shape is defined by the combination of the condensation temperature and the rate of atomic deposition onto the growing nanocluster. We, thus, construct a comprehensive deposition rate– temperature diagram of Fe NP shapes and develop an analytical model that predicts the temporal evolution of these properties. Combining the shape diagram and the analytical model, morphological control of Fe NPs during formation is feasible; as such, our method proposes a roadmap for experimentalists to engineer NPs of desired shapes for targeted applications.

Keywords Fe nanocubes, Kinetic effect, Molecular Dynamics, Kinetic Monte Carlo, Inert gas condensation The shape of nanoparticles (NPs) is usually determined by surface energy minimization; therefore, rather intuitively, spherical or roughly spherical polyhedral shapes with the lowest surface-to-volume ratio (i.e. number of surface atoms over number of bulk atoms) are the most likely to form. 1–3 On the other hand, practical applications often benefit from utilizing metastable structures with larger surface-to-volume ratios. One such example is catalytic applications, 4–6 where NPs of non-spherical morphologies can often provide more active sites for catalytic reactions. 7 The formation of non-spherical NPs is, however, difficult to reconcile with the surface energy minimization argument mentioned above. Therefore, it comes as no surprise that prediction and control of NP shapes (of metallic NPs, in particular) has been a topic of intense research over the last decade. 8–15 In the current paper, we study the influence of the synthesis parameters on the shape of iron (Fe) NPs obtained by magnetron sputtering inert gas condensation, a method that has been widely used during recent years since it allows simultaneous control of composition, magnetron power, inert gas pressure, NP drift velocity and aggregation zone length. 16 Fe NPs have been reported in several cases to grow in cubic rather than in spherical or close2 ACS Paragon Plus Environment

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to-spherical polyhedral shapes, both by chemical 17 and physical methods. 18–20 For chemical synthesis, a shape-formation mechanism has been proposed, 21–23 concerning the ability of surfactant ligands to move on the NP surface, which allows specific facets to grow instead of others, inducing different growth rates that dictate the NP shapes. In contrast, for physical methods, a possible shape-formation mechanism has been proposed, 17,18 but no theory or simulation verifying the hypothesis was provided. Here, we combine high resolution transmission electron microscopy (HRTEM) structural analysis with classical molecular dynamics (MD) and kinetic Monte Carlo (KMC) computer simulations in order to elucidate the growth mechanism of Fe NPs at the atomic scale. Our results show that in the high temperature or high deposition rate regime the NPs remain spherical (or close to spherical), as expected from thermodynamic considerations of surface energy minimization; clearly, such conditions cannot account for the non-spherical shapes of Fe NPs that have been observed in numerous previous experimental investigations. 17–20 Most importantly, however, we report that within a clear range of combinations of deposition rates and NP temperatures during vapor phase synthesis, the competition between two different surface growth modes on low-index {100} and {110} facets is responsible for the formation of NPs with cubic shapes. More specifically, nanoislands grown on each surface type contain sides of the other type; therefore, rather counter-intuitively, adatom diffusion on {100} facets governs the growth of {110} surfaces and vice versa, leading to unequal growth rates and eventually to the formation of Fe nanocubes.

Results and discussion Equilibrium shapes of Fe NPs. Before investigating the mechanisms that drive NPs towards metastable configurations, it is reasonable to identify possible stable structures first. Under thermodynamic equilibrium, NPs eventually assume energetically favorable shapes due to surface energy minimization. In order to determine these optimal structures for NP sizes


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of relevance to our experimental findings (see below), we analyzed a number of possible Fe NP shapes by means of molecular statics (MS) simulations; the shape with the minimum potential energy per atom is expected to be thermodynamically stable. For consistency, the number of atoms for each NP shape was approximately the same (with 1% variation). A corresponding imaginary spherical NP with a certain diameter was assigned to each NP of every shape, such that it contained the same number of atoms; this way a comparison of the original shapes was readily possible according to the diameters of the corresponding spherical NPs. Molecular statics results of all investigated NP shapes and sizes are presented in Fig. 1, revealing that the rhombic or truncated rhombic dodecahedron (RD and TRD, respectively) shaped NPs are the most stable structures. With increasing diameter, the difference in energy between these two shapes and the sphere is diminishing, and at NP sizes larger than 16 nm (in corresponding spherical diameter) it practically disappears. This observation can be explained by the low surface energy of the close packed {110} and {100} facets 24,25 terminating the RD and TRD NPs, and infers that the equilibrium shape of the NPs must have a large fraction of such surfaces, to comply with the aforementioned surface energy minimization argument. The shape with the highest potential energy per atom for all NP sizes is consistently the cube. However, the potential energy difference among all shapes, including the cubic, is rather limited, around 15 meV for the larger sizes. This fact can, in principle, allow for shape transitions to occur readily and can also lead to the simultaneous co-existence of NPs of more than one shape under real experimental conditions at non-zero temperatures– we will return to this point later on. Next, we verified the stability of RD or TRD shapes under realistic temperature conditions in order to approximate sputtering experiments more accurately. Assuming that nascent NPs are in a liquid state during early growth stages, we used MD to simulate the subsequent cooling process. Liquid Fe nanoclusters of various sizes were cooled down from 1800 to 1000 K. Below this temperature, we observed no significant advancement of any


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Figure 1: Potential energy as a function of Fe NP size for the five shapes shown on the righthand side. The truncated rhombic dodecahedron (TRD) is consistently the most stable structure in the investigated range of NP sizes.

shape transformation until the end of the simulations (120 ns). The dynamics of the process for a Fe NP 13 nm in diameter is presented in Fig. 2(a). During the first 45 ns, the Fe NP cools down from 1800 K to the phase transition temperature at about 1000 K. At this point, an abrupt first-order phase transition occurs, that results in crystallization of the NP in a body-centered cubic (BCC) structure. The corresponding initial and final structures are shown in Fig. 2(b) and (c). It is evident that the final structure is a TRD with 6 {100} and 12 {110} planes, perfectly comparable to the TRD shape constructed by surface energy minimization on different planes using the Wulff method. 24–27 This result is also consistent with our MS simulations. More importantly, though, such conditions correspond to the high temperature deposition in Ref., 28,29 indicating that, provided their initial temperature is sufficiently high, the NPs are able to reach equilibrium attaining the most energetically favorable configuration. In order to explain cubic NP structures obtained experimentally, and knowing that the sputtering power in a magnetron gun affects decisive growth parameters (e.g. Fe plasma density and temperature), this observation signifies the necessity to tackle subtle growth kinetics such as


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the competition between the rates of atomic deposition and surface diffusion. Once more, we will revisit this point after discussing our experimental results.

Figure 2: (a) Evolution of temperature (top) and cooling rate (bottom) of an Fe NP 13 nm in diameter. The initially liquid NP (b) solidified into an α-Fe bcc NP of TRD shape with 6 {100} and 12 {110} planes (c) after 120 ns. The abrupt first-order liquid-to-crystalline phase transition occurs at 45 ns. The fitting curve to the temperature evolution is based on the approach developed in Ref. 2

Experiments Fe NPs deposited on silicon nitride TEM grids by the magnetron sputtering inert gas condensation technique (see Section Methods) are shown in the low-magnification TEM images of Fig. 3. We distinguish three groups of NPs obtained at different DC magnetron powers: Fe-50W (Fig. 3a), Fe-70W (Fig. 3c) and Fe-100W (Fig. 3e). Their corresponding size histograms of Figs. 3b, 3d, and 3f show well-dispersed NPs with no sign of post-growth agglomeration, as indicated by their Gaussian, rather than log-normal, distribution. Interestingly, in the intermediate power case (Fe-70W), the presence of both spherical NPs and nanocubes with two distinct size distributions is revealed in Figs. 3(c) and (d), experimentally confirming the possibility for co-existence of two distinct shapes, 6 ACS Paragon Plus Environment

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as theoretically explained above. Gaussian fits result in a mean cluster width of 15.9 ± 1.3 and 12.5 ± 0.9 nm for the spherical and cubic NPs, respectively. However, by adjusting only a single experimental parameter, i.e. the DC magnetron power, one can control the shape of the NPs, shifting them towards either the purely-spherical or purely-cubic directions, as demonstrated in Figs. 3(a)-(b) and (e)-(f), respectively. Thus, in the low-power Fe-50W deposition, spherical Fe NPs grew, with a narrow size distribution and a mean diameter of 13 ± 1 nm, whereas in the high-power Fe-100W case, Fe nanocubes with a similarly narrow size distribution and a cluster width of 10.5 ± 0.8 nm were produced. In order to obtain further details of the morphology and crystalline structure of the NPs, we used high-resolution TEM (HRTEM) analysis, as shown in Fig. 4. The presence of coreshell structures with a crystalline core and polycrystalline shell is clearly demonstrated in Figs. 4(a) and 4(c). The core-shell structures arose due to oxidation of the metallic NPs after exposure to air. The corresponding Fast-Fourier Transform (FFT) of the cubic NP (Fig. 4(b)) clearly displays the (110) and (200) reflections of the BCC structure, corresponding to the metallic α-Fe phase. Main (111) and (200) reflections of the spherical NP are indexed in Fig. 4(d), and correspond to the FCC structure of Fe, the so-called γ-Fe phase. Since crystallization from the liquid state is expected to lead the NPs to a BCC phase, the presence of FCC structures may be explained either by subsequent coalescence between still-amorphous solid Fe nanoclusters later on in the growth process, inside cooler regions of the aggregation zone, or by the higher tendency of nanospheres to oxidize after exposure to air, compared to the nanocubes, thus producing an extensive FCC oxide shell which triggers a phase transition within the core, too. Either mechanism indicates that, at least partially, growth of the Fe-50W sample happens after the plasma zone, once more underlining the subtle interplay between growth parameters and resultant structures. Growth kinetics during formation of Fe NPs. It was mentioned above that high magnetron power leads to high plasma temperature 30 and fast NP growth rate, 31 which, in turn, result in high initial NP temperature during the condensation process; surface diffusion is thus


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Figure 3: Low magnification TEM images (left column) and corresponding size distributions (right column) of well-dispersed Fe NPs deposited on silicon nitride grids using different dc magnetron powers: (a)-(b) Fe-50W, (c)-(d) Fe-70W and (e)-(f) Fe-100W, respectively.

enhanced, enabling the NPs to obtain the equilibrium shape. Thus, it is clear that thermodynamic considerations alone are unable to explain the cubic shapes formed experimentally using different magnetron powers. This is why we now turn our focus to the study of growth kinetics during the formation of Fe nanocubes.


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Figure 4: High-resolution TEM images and corresponding FFT patterns of an exemplary Fe nanocube (a)-(b) and a spherical Fe NP (c)-(d), respectively. Core-shell structures can be observed, with characteristic FFT patterns of BCC and FCC Fe phases.

We analyzed NP growth kinetics by simulating uniform depositions of Fe atoms on initially spherical Fe NP nuclei by means of MD and KMC methods (see Section Methods for details). Since the difference in nuclei temperatures may result in NPs of different final shapes, it is important to understand which processes take place at each temperature to be able to explain the observed experimental results via computer simulations. Therefore, we studied the temperature effect on growth kinetics for two cases with distinct NP temperatures of 500 K (low-T ) and 1000 K (high-T ). In the MD simulations, the temperature was controlled only within the initial nucleus; the temperature of the growing surface was


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allowed to evolve, determined by the latent heat released during atomic adsorption on the NP and by exchanges with the thermal bath of the NP core. As clearly evident in Fig. 5, both simulation methods agree closely on the final NP shapes, both at high and low temperatures. During the low-T deposition, the Fe NPs grew in a rather cubic shape with six well pronounced {100} surfaces (yellow surfaces in Fig. 5), whereas the high-T deposition runs led to the TRD shape, as expected from the surface energy minimization discussion above. This result is consistent with the experimental observations in Ref. 18 and emphasizes the importance of growth kinetics specifically on {100} and {110} facets for determining the formation of one or the other final shape under different growth conditions. This is our next point of focus: we used both MD and KMC to simulate growth on these two surface types, and developed an analytical model that describes the experimental growth dynamics of Fe NPs to compare our simulation results with our experimental findings. Growth modes of {100} and {110} facets: MD simulation results. In order to elucidate the formation mechanism of Fe nanocubes, we investigated the growth modes specific to the {100} and {110} surfaces in the temperature range of interest. By exploiting the symmetry of the system, we narrowed down the problem into a two dimensional one, substituting the NP nucleus with an infinite-length nanowire (NW) that contains a surface consisting of a large fraction of {100} and {110} facets. Therefore, periodic boundary conditions were applied in the z direction, along the major axis of the NW, whereas open surfaces were used in the x and y directions. We simulated the deposition process by adding an isolated Fe atom into the simulation box every 100 or 1000 MD steps. These frequencies of atomic addition correspond to different deposition rates, which we simply refer to as high–Rd and low–Rd , respectively. The simulations were performed at three different initial temperatures: 700 K, 1000 K, and 1200 K, under both high– and low–Rd . The applied temperature control was similar as in the case of NP growth described above: only the atoms of the initial NW – the core – were controlled, while the temperature of the deposited atoms was allowed to evolve naturally.


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As a result, in the high–Rd case the temperature in the surface layer was constantly higher than in the core temperature. Additionally, in order to assess the effect of surface diffusion on growth, we determined the migration barriers for a single adatom migrating on {100} and {110} surfaces. The calculated values clearly indicate fast adatom diffusion on {110} surfaces with a minimal barrier of 0.27 eV, while surface diffusion on {100} facets is markedly slower (minimal barrier of 0.72 eV). More information on how migration barriers were calculated can be found in Section Methods.

Figure 5: (Color online) Cross sections (left) and 3D images (right) of the resultant Fe NPs obtained by MD and KMC simulations after atomic deposition at 500 (low T) and 1000 K (high T). For the cross sections, the inner (green atoms) and outer (blue atoms) regions correspond to the initial NP and deposited atoms, respectively. For the 3D images, the different colors of the surface atoms represent {100} (yellow), {110} (red) and other faceted surfaces (blue).

As the NWs grew in size, they obtained different shapes, according to their core temperatures and deposition rates, as shown in Fig. 6, where the initial core and the adatoms are depicted in green and blue color, respectively. The temperature indicated next to each cross section corresponds to the average surface temperature of the NW over the simulation time. A first observation in Fig. 6 is that, for both deposition rates, the NW cross sections are round-shaped at the high ends of the investigated temperature ranges; however, with decreasing temperatures, they gradually obtain an increasingly square-like shape. Strikingly, 11 ACS Paragon Plus Environment

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for each high–Rd NW cross section of a certain shape, there corresponds a low–Rd cross section of an almost identical shape, signified in Fig. 6 with the oval backgrounds correlating NWs (a) and (d), (b) and (e), and (c) and (f). The temperature difference between these pairs of NWs is consistently around 200 K, indicating that the final shape of the NW cross section depends on the combination of surface temperature and deposition rate. A schematic illustration of the nanocube formation process is shown in Fig. 7, decomposing the atomic deposition and diffusion mechanisms that make an initially TRD-shaped nanocluster (depicted in green) grow into eventually obtaining a cubic shape. Temporal evolution is implied by the alternating light and dark blue colors of the newly-deposited layers of adatoms. It is clear from the atomic-scale representations of the two surface types that different growth modes dominate on {110} and {100} facets, resulting in different effective growth rates. Analysis of the atomic-scale mechanisms of NP growth for the simulated conditions shows that atoms landing on {110} surfaces diffuse rapidly, and almost immediately form singlelayer nanoislands, even at low temperatures, due to low migration (∼ 0.27 eV) and relatively high detachment barriers (∼0.58 to 1.0 eV). The newly deposited atoms which land on top of the already existing nanoislands diffuse only within the latter, barely having an opportunity to climb down (in this case, the Ehrlich-Schwoebel barrier is between 0.64 and 0.72 eV, depending on specific diffusion pathway). This fact explains why these islands are stable and grow in all dimensions until they finally take over the entire {110} surface in accord with a Volmer-Weber-like (VW) growth mechanism. This process is schematically illustrated in the top-right corner of Figure 7: the specific hill-like structures at the corners of the final tetragonal shape are also clearly visible in NWs (a) and (d) of Fig. 6. On the other hand, growth on the {100} surfaces (as seen in the same NWs of Fig. 6) appears to be rather flat. However, closer inspection shows limited nanoscale roughness on the {100} facets as well. This is explained by the high atomic migration (Em ≥ 0.72 eV) and Ehrlich-Schwoebel barriers (1.04 eV) that allow nanoislands to grow initially upwards.


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However, since the sides of the growing nanoislands have preferentially {110} facets, after the formation of about three layers only, the fast diffusion specific to {110} surfaces comes into play, as shown in the top-middle atomic-scale schematic of Fig. 7. The phenomenon is well studied in thin film growth, usually referred to as downward funnelling. 32,33 This prevents further upward growth of the nanoisland and leads to its flattening; thus the overall growth is dictated by a Frank-van-der-Merwe-like (FM) mechanism.

Figure 6: (Color online.) Final shapes of Fe NW cross sections, obtained by MD simulations of the atomistic deposition process at high and low deposition rates, Rd . High and low Rd correspond to random introduction of a new surface atom every 100 and 1000 MD steps, respectively. The temperature indicated next to each cross section corresponds to the average surface temperature of the NW over the simulation time. The oval backgrounds correlate NWs obtained at different deposition rates of nearly identical cross sections, indicating an approximate temperature difference of 200 K between each pair.

Growth modes of {100} and {110} facets: KMC simulation results. We also performed similar simulations by means of the KMC technique (See section Methods), which is wellsuited to simulate diffusion processes since their duration is typically beyond the time span of MD simulations. Hence, it was possible to extend the results of MD simulations to time scales comparable with experimental ones. Although there is a clear difference in deposition rates between the MD and KMC simulations, we clearly observe that the final shapes of the NW cross sections once more depend on the combination of temperature and deposition rate, just 13 ACS Paragon Plus Environment

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Figure 7: (Color online.) Schematic illustration of an initially faceted TRD NP growing into a cubic shape via competing atomic deposition and surface diffusion mechanisms. The alternating light and dark blue colors of the newly-deposited adatom layers imply temporal evolution. Nanoislands of {110} and {100} sides are grown on {100} and {110} facets, respectively, as shown in the zoomed in areas. Different growth modes – {110} facets grow via a Volmer Weber-like mechanism and {100} facets via a Frank-van-der-Merwe-like mechanism – lead to the different effective growth rates.

like the MD results discussed previously. By running a series of KMC simulations, we were able to map a comprehensive deposition rate–temperature diagram of final NP shapes (see Fig. 8), henceforth referred to as the “shape diagram” in a fashion analogous to the phase diagram concept. Although the simulations were performed for an infinite-length Fe NW,


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we propose that these results are also valid for the case of NPs, since the main assumption applies for both geometries: the final shape is defined by the competition of growth modes on the {100} and {110} surfaces. The shape diagram of Fig. 8 is mainly composed by two regions: the blue (dark) region is defined by conditions which favor the formation of cubic Fe NPs, and the yellow (light) region, where the shape of the formed NPs is spherical or close-to-spherical. The chosen temperature range extends between room temperature and the melting point, 34,35 which corresponds to the experimental solidification conditions of the NP nuclei. The axes of the diagram indicate the two competing processes that govern the growth modes, i.e. temperature-assisted surface diffusion versus atomic deposition. In the low deposition rate limit, surface diffusion is unrestricted and various diffusion barriers on different facets define the final shapes of the NPs; therefore, with rising temperatures the NPs increasingly attain surface energy minimization, approaching a close-to-spherical, TRD shape. This happens at temperatures near the melting point, when the difference between diffusional barriers is negligible, and diffusional jumps in all directions become equally probable. On the other hand, in the high deposition rate limit, surface diffusion is fully restricted, and the growth modes on all surfaces resemble the FM growth mode, preserving the original near-spherical shape of the NPs. However, the most interesting region of the shape diagram lies between these extreme deposition rate regimes, encompassing the interplay between surface diffusion and atomic deposition; the subtle balance between temperature and deposition rate can be used to explain the different shapes formed at the end of the condensation process. Analysis of Fe nanoparticle shape diagram In the previous section, a rather qualitative description of the deposition and diffusion processes was given, emphasizing on their rates, the competition between them, and its effect on the resultant NP shape. Here, we give a more in-depth, quantitative analysis of these processes, which, in the next section, will enable the construction of a full analytical model that can be useful as a reference guide for


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future NP growth experiments. The average residence time ∆tr before a diffusional jump of a surface atom occurs at a given temperature, T , can be defined as the inverse of the diffusion transition rate given by the Boltzmann equation: 36

∆tr = (γ0 exp(−hEm i/kB T ))−1

(1)

Here γ0 is a prefactor which includes the number of available transitions and the attempt frequency of a jumping atom, and kB and hEm i are the Boltzmann constant and the effective migration barrier for an average diffusional jump of a surface atom, respectively. On the other hand, we can estimate the time, ∆td , needed to cover the entire surface via the deposition.

∆td =

Na Rd Ahkl

(2)

Here, Rd is the deposition rate, whereas Ahkl is the area per unit cell with the corresponding Miller indices hkl for the (100) or (110) surfaces. Na is the number of atoms, which is unity if growth of a single atomic layer is considered. If this time, ∆td , is shorter than the residence time between diffusion transitions, diffusion is restricted and both surfaces grow uniformly, inducing no change to the initial shape, which remains spherical. By equalizing these two time periods, we can designate points in the Fe NP shape diagram (see Fig. 8) that correspond to final shapes in-between cubic and spherical, as obtained by our MD and KMC simulations. The curve going through these points constitutes a border separating the areas of clearly cubic and clearly spherical final shapes of the Fe NPs.

Rd =

Na · γ0 exp(−hEm i/kB T ) Ahkl

(3)

In our fitting procedure, we combine all factors before the exponent as a single fitting


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parameter γ =

Na ·γ0 , Ahkl

since, with the exception of Na , the contribution of the other two

parameters can vary during the deposition process. Also hEm i is fitted as a single value, even though, strictly speaking, it depends on the local environment prior to the diffusion jump and, as a consequence, on the combination of temperature and deposition rate. For our MD results, using the least square fitting procedure, 37 we found 0.94 ± 0.2 eV for the 32 effective migration barrier hEm i and 6+14 Hz for γ. These values change when fitting −2 × 10

the data obtained by KMC simulations, with hEm i = 0.72 ± 0.04 eV and γ = 6 ± 4 × 1031 Hz, respectively. Since we were able to run only single cases for each point, during the fitting we have assumed ±50% uncertainty margins for the input data. The results of the fit show that the main diffusion transitions that compete with atomic deposition, i.e. the cause of diffusion restriction, are the jumps on a {100} surface (Em ∼ 0.72 eV) and detachment of atoms from the forming nanoislands on a {110} surface (Em between ∼ 0.58 and 1.0 eV). Both are energetically more expensive compared to the free-hopping events (Em ∼ 0.27 eV) or the jumps towards the bound states within a forming island (≤ 0.1 eV). We note that the curves fitted to the MD and KMC results are described by similar but not identical fitting parameters. The most intriguing difference is in the hEm i value, which is higher for the MD results and amounts to 0.94 ± 0.11 eV compared to 0.72 ± 0.04 eV for KMC. This divergence stems from the contribution of diffusion barriers that cannot be predicted by KMC. For instance, collective many-body or concerted jumps become possible on a {100} surface at high temperatures. These barriers were estimated as hEm i ∼ 1.0 to 1.22 eV and only allow jumps very rarely at low temperatures. This is why the MD and KMC results converge at low temperatures and low deposition rates; it is also worth noting that this is the regime relevant to the experimental conditions of the magnetron sputtering inert gas condensation method. At very high deposition rate, there is a small area where the final shape remains spherical, although the temperatures are rather low. We successfully fitted the border curve in this


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regime with the exponential function with the fitting parameter hEm i ∼ 0.27 eV, which corresponds to the lowest migration barrier on a {110} surface. This indicates that above this curve no diffusional jump takes place and the growth proceeds uniformly, preserving the original spherical shape of the Fe NP.

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Figure 8: Comprehensive deposition rate–temperature diagram of final Fe NP shapes. Results were obtained by simulating Fe NWs by KMC. Square and circular markers indicate cubic and spherical shapes, respectively. The yellow markers are MD results. The dashed and dotted curves are the exponential fits to the KMC and MD results, respectively. The hatched area between two exponential fits indicates the uncertainty of the present simulations due to the use of different methods. However, the two simulation methods converge at low deposition rates relevant to the experiment.

Comparison of simulations and experiments The simulation results have shown that the balance between deposition rate and temperature is the key factor for the final shape of Fe NPs. In order to enable comparison of these results to the experiment, we estimate the temperature evolution of Fe NPs in the aggregation zone and in the deposition chamber by developing the following analytical model.


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For simplicity, we consider a single Fe NP that grows via deposition of sputtered Fe atoms, and cools down through interactions with ambient Ar atoms. The density of Ar atoms depends on the working pressure PAr in the gas aggregation source, and can be calculated as ρAr = PAr /kB TAr , where kB is the Boltzmann constant and the temperature TAr is the second order exponential decay function fitted to experimental literature results. 30 This value is fixed in all three cases of the different values of sputtering ion current, ρAr = 3 × 1021 m−3 . The number density of the sputtered Fe atoms is controlled by the dc voltage and current, and can be calculated as in Ref.: 30

ρF e =

− YFAr e Id /e φAr · Pat /PAr

(4)

38 Id is the where the Fe sputtering yield, YFAr e , is taken as 0.64 at 180 eV and 0.6 at 170 eV,

dc current, φAr is the gas flow rate, and Pat denotes the atmospheric pressure. The NP temperature evolves via heating – through latent heat released upon atomic depositions – and cooling – through collisions with Ar atoms and black-body radiation. We can write a system of differential equations which describe the simultaneous, in-flight, temporal evolution of the NP temperature and the number of Fe atoms bound in the NP (which correspond to its size):        

dN (t) N (t) = π · rc2 · (ρF e − ) · vF e dt V dT (t) πrc2 N (t) = · [3kB ρAr vAr (TAr − T (t)) + 2(ρF e − ) · vF e Eco ]  dt 3kB N (t) V      4  −8πrc2 σ(T (t)4 − TAr )/(3kB N (t))

(5)

Here rc is the radius of the Fe NP, rc = [3hV0 iN (t)/4π]1/3 , where hV0 i is the average atomic volume of Fe atoms; V is the constant volume which contains 150,000 Fe atoms, vi = (3kB TAr /mi )1/2 , where i stands for Ar or Fe, are the average velocity of the Ar and Fe gas atoms, respectively, Eco is the cohesive energy of Fe atoms, which is released in form of latent heat during the deposition event, σ is the Stefan-Boltzmann constant, and is the 19 ACS Paragon Plus Environment

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emissivity. The values of the key parameters for all three cases is shown in Tables 1 and 2. Table 1: Experimental condition and resultant NP parameter values. Experiments Id [mA] U [Volt] Fe-50W 200 250 Fe-70W 300 233 Fe-100W 400 250

φAr [sccm] PAr [Bar] ρF e [m−3 ] 55 2 × 10−4 1.7 × 1020 55 2 × 10−4 2.4 × 1020 55 2 × 10−4 3.4 × 1020

Cluster size [nm] 13 ± 1 15.9 ± 1.3/12.5 ± 0.9 10.5 ± 0.8

Table 2: Input parameters for the analytical model. Parameters hV0 i [nm3 ] Value 1.169 × 10−2

ρAr [m−3 ] Eco [eV] 3 × 1021 2.1

σ [eV nm−2 ns−1 K −4 ] 3.54 × 10−16 0.1

kB [eV K −1 ] 8.62 × 10−5

The numerical solution of Eq. 5 is shown in Fig. 9. The growth time-of-flight is set to 4.0 × 104 µs (40 ms). This parameter is fixed for all three cases since the condensation time depends on the gas flow and the length of the aggregation chamber. As can be seen in Fig. 9a, the NP final sizes calculated with the analytical model agree with the experimental values (dots in Fig. 9a). At the very early stage of each condensation process, the temperature rises rapidly, as shown in the inset of Fig. 9b. The attained high temperatures can be explained by the high number density of Fe atoms, which heats the NPs more effectively since it leads to an increased probability of heat-releasing Fe-Fe collisions. In the same graph, the evolution of the deposition rate is also shown, which can be derived from the growth rate of the NP, dN (t)/dt, divided by the surface area of the NP, Ac (t) = 4πrc2 (t). Then, from the first equation of the system of equations (5), we obtain

Rd =

1 dN (t)/dt = (ρF e − N (t)/V ) · vF e Ac (t) 4

(6)

These results follow a trend similar to the time evolution of temperature. The initially faster growing NPs, i.e. Fe-70W and Fe-100W, end up with lower deposition rates at the final stages of the growth process. By plotting the NP temperature as a function of deposition 20 ACS Paragon Plus Environment

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Figure 9: Evolution of diameter (a – solid line), number of atoms (a – dash line), temperature (b – solid line) and deposition rate (b – dash line) of an Fe NP, as functions of time-of-flight. The capital letters D, N, T and R correspond to the diameter, number of atoms in the NP, temperature and deposition rate, respectively. The numbers 50, 70 and 100 are used to distinguish between the Fe-50W, Fe-70W and Fe-100W samples. The inset figure shows the temperature evolution at the very early stage, before 5 µs. Small dots on the top right corner of figure (a) indicate the widths of experimentally obtained NPs.

rate, we can compare the result of our analytical model to the shape diagram in Fig. 8, as shown in Fig. 10, where the relevant part of the shape diagram is zoomed in for clarity. The curves show the solutions of Eqs. 5 for the three different power values, Fe-50W, Fe-70W and Fe-100W. It is evident that the experimental conditions, which correlate deposition rate and temperature, vary over the condensation process. Initially, in the region of the highest deposition rate – after exiting the hot plasma region – the NP temperature is still increasing due to condensation, while the deposition rate remains constant. This lasts for


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some time, which explains the short horizontal lines at the top of the curves. When the Fe NP flies within the condensation chamber, its size is increasing, while the temperature and the deposition rate are monotonically decreasing. Eventually, at the exit of the condensation chamber, no atoms are available for deposition, and the condensation process stops. The duration of condensation process is defined by the length of the condensation chamber and the gas flow velocity; thus, taking a gas flow velocity around 2 to 3 meters per second and a chamber length of 90 mm, we estimated this time to be around 40 ms. As can be seen in Fig. 10, the curve that corresponds to the lowest sputtering power, Fe-50W, is fully located in the spherical-shape region, as deduced from both the MD and KMC simulations. This fully agrees with the experimental finding for the Fe-50W sample (Cf. Fig. 3a) showing spherical NPs. Both curves for the higher sputtering ion currents (Fe-70W and Fe-100W) intersect the border between the regions of clearly spherical or cubic shapes. The Fe-100W NPs reach much lower deposition rates at the same temperatures as Fe-70W NPs (see Fig. 10), which explains stable formation of cubic NPs (Cf. Fig. 3c), while the Fe-70W NPs show both cubic and spherical NP shapes (Cf. Fig. 3b). These results are also in good agreement with experiment, as the dominant shape of the Fe-100W NPs is cubic, while the Fe-70W sample contains a significant amount of NPs of both shapes, cubic and spherical. The temporal evolution of NP temperature and deposition rate shown in Fig. 9b further supports this argument. The figure shows that, although initially both the temperature (inset of Fig.9b) and the deposition rate of Fe-100W NPs are the highest among the three cases, these values drop more rapidly at the later growth stages (after 100 µs) compared to the Fe-50W and Fe-70W cases. This is explained by the faster growth rate of Fe-100W NPs (see Fig. 9a); in contrast, the growth of Fe-50W NPs is the slowest one and, hence, the temperature and the deposition rate at the end of the condensation process remains the highest, leading the NPs into the spherical shape regime. The Fe-70W NPs remain hot for longer than the Fe-100W NPs, but eventually their deposition rate and temperature end up


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1E22 Spherical/TRD Region

1E21

Fe-1 Fe-2 Fe-3

1E20 200

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Figure 10: Correlation of deposition rate and NP temperature during growth, juxtaposed with the shape diagram. At the beginning of the condensation process the clusters are formed in a high-density region, leading to their rapid heating at the same depostion rate (horizontal top part of the three curves). Beyond the hot plasma region, the deposition rate decreases and the clusters cool down due to collisions with the carrier gas 2,31 and black-body radiation. The decrease of deposition rates and temperatures ends (cross markers) at the exit of the Fe NPs from the condensation chamber.

with values comparable to the Fe-100W case; hence the result shown in Fig. 3b, where NPs of both spherical and cubic shapes are clearly visible.

Conclusion In this contribution, we used both experiment, as well as MD and KMC simulation methods to demonstrate that the formation of Fe nanocubes in magnetron sputtering condensation can be explained by the different diffusion behaviors of atoms deposited on {100} and {110} surfaces at different temperatures. The results reveal that, under certain combinations of atomic deposition and surface diffusion rates, Fe NPs grow in cubic rather than a close23 ACS Paragon Plus Environment

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to-spherical shape, despite the former being energetically unfavorable at thermodynamic equilibrium. The combined MD, KMC and analytical models introduced in this study can be potentially applied to a wide range of materials systems, with a view to improving current experimental techniques towards precise control of NP shapes.

Methods Experiments Three Fe NP samples were fabricated and characterized for this study, using a dc magnetron sputtering gas phase condensation source; 39,40 namely Fe-50W, Fe-70W and Fe-100W samples, with corresponding magnetron powers, were prepared using different sputtering ion currents (Id ) equal to 200, 300 and 400 mA, respectively. Fe NPs were initially formed through a supersaturated vapor of metal atoms by dc sputtering of a high-purity Fe target (99.9%, 2 inch diameter × 0.3 mm thickness) in argon (Ar) atmosphere. The NPs were directly deposited onto silicon nitride TEM grids under high vacuum conditions (base pressure around 1×10−8 mbar) for further characterization. Fe NP growth was controlled by adjusting deposition parameters such as magnetron power, aggregation length, gas flow, and differential pressure. Between these experiments, the gas flow and the aggregation length were kept constant at 55 sccm and 90 mm, respectively. During NP growth, the pressure was 2 × 10−1 mbar in the aggregation zone and 5.6 × 10−4 mbar in the main chamber. The shape, size, morphology and crystal structure of the Fe NPs were evaluated using an FEI Titan 80-300 kV image-corrected transmission electron microscope (TEM) operated at 300 kV. All measurements were performed after exposure to ambient air. Simulation Cooling of Fe NPs was simulated in the Ar atmosphere following similar a procedure as in Ref. 2 In order to study kinetics effects, we used the MD and KMC methods to simulate the growth process of Fe NPs. In MD simulation, a 7.6 nm spherical Fe NP was placed in the center of a 20 nm × 20 nm × 20 nm simulation box. The ambient atmosphere consisted of isolated Fe atoms. The initial velocities of all atoms were generated according


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to the Maxwell-Boltzmann distribution to ensure the desired initial temperature. The NoséHoover thermostat was applied to the atoms initially located within the 5 nm spherical region at the center of the NP. The deposition rate was simulated by adding a new atom every 20 MD steps. We compared the shape of the grown particles at 500 K and 1000 K to analyze kinetics effects. The simulations were carried out for 1200 ps with a time step of 1 fs (Supplementary Information Movie S1). In order to reach beyond the MD time span, we used the KMC model Kimocs, recently developed by our group to study evolution of metal surfaces (personal communication in Supplementary Information). The model is based on rigid lattice approximation and was extended to include the body centered cubic (BCC) structure for the current work. The calculation of the energy barriers of all the possible diffusion jumps was made using the Nudged Elastic Band (NEB) method 41,42 implemented in the PARCAS code. 43 The time scale of the KMC simulations is in the order of a few milliseconds. Atomic deposition was performed by randomly adding Fe atoms on the NP surfaces at the desired deposition rate, which was controlled by keeping the number of deposited atoms per second per square meter constant (see Supplementary Information Movie S2.) The Fe-Fe interactions in both the MD and KMC simulations were based on the EAM potential developed by Mendelev et. al. 44

Acknowledgement Research performed at the University of Helsinki was supported by the doctoral program MATRENA. E. Baibuz was supported by a CERN K-contract. V. Jansson was supported by Academy of Finland (grant No. 285382), Ruth och Nils-Erik Stenbäcks Stiftelse and Waldemar von Frenckells Stiftelse. Work performed at OIST was supported by funding from the Okinawa Institute of Science and Technology Graduate University. The authors are also grateful to the Finnish IT Center of Science, CSC, for grants of computational time.


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