Effect of surface pressurization on the growth of α-Fe₂O₃ nanostructures

Abstract

By suitably pressurizing iron substrates under different conditions, the resulting α-Fe₂O₃ nanostructures, formed by its direct thermal oxidation, can gradually change in succession from nanowires to nanoleaves and to micropillars as the pressure is increased. The inter-relation between the pressure conditions and the resulting nanostructure is studied by density functional calculations using ultrasoft pseudopotentials with a plane-wave basis method and with the generalized gradient approximation (GGA). It is shown that the shape of the formed nanostructures is primarily determined by the anisotropic activation energy and, as the latter is lowered, there is a shape change from wire to pillar. A simulation model of diffusion using the Monte Carlo method is applied in the 3-D (dimensional) case to show how the anisotropic activation energy influences the growth process of the α-Fe₂O₃ nanostructure. The present study provides a way to control the shape of the nanostructures grown by the thermal-oxidation method.

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1. Introduction

In the preparation of nanostructures containing transition metal oxides (α-Fe₂O₃,^1–5Co₃O₄,⁶etc.) by the thermal-oxidation method developed in our laboratory, sometimes one gets a mixture of different nanoshapes in the form of particles, wires, leaves, and pillars. Such a situation has been experienced also with other nanosystems, such as ZnO nanobelts⁷ and rings.⁸ The preparation of specific nanoshapes is not easily controlled. It is therefore relevant to ask: what conditions determine the shapes of the nanostructures? Only when this is known can we hope to get the nanoshape we want and avoid the other nanoshapes that are not needed.

In this paper, we start with pre-treated iron substrates formed by subjecting them to different pressures prior to their thermal oxidation. It is found that, as the pressure increases, the resulting nanoshape changes from wires to leaves, and then to pillars. By density functional calculations, it is shown that the anisotropic activation energy determines the shape of the nanostructures. As the anisotropic energy is lowered, the nanostructure gradually transforms from 1D to 3D. Using the Monte Carlo method to simulate the process, the theoretical results obtained are in full accord with the experimental findings.

2. Experimental

The pure iron substrate was pressed with a pellet forming machine at a pressure of about 0.25–1 GPa. After polishing and washing with alcohol in an ultrasonic cleaner, the substrate was placed into a quartz tube within a tubular furnace, where the temperature, pressure, and reaction time were controlled. The sample was heated in a flowing gaseous atmosphere, comprised of 19.4% CO₂, 80.43% N₂ and 0.164% SO₂. The humidity was controlled by mixing the above gas with H₂O vapor produced by heating water. The reaction between iron and the mixed gas, at 450–650 °C for about 10 h, caused the α-Fe₂O₃ nanostructures to grow on the surface of the iron substrate.

The samples were characterized by X-ray diffraction (XRD) (Philips XPert MRD with Cu K_α radiation), field emission scanning electron microscopy (SEM) (FEI Strata DB235 FIB), transmission electron microscopy (FEI Tecnai F30 TEM), and X-ray photoelectron spectroscopy (XPS) (Kratos Analytical Axis Ultra with Mono Al K_α radiation and an excitation energy of 1486.6 eV).

The structure and the growing activation energy of the iron surface have been investigated by density functional calculations using ultrasoft pseudopotentials with a plane-wave basis method⁹ and the generalized gradient approximation (GGA¹⁰) to describe the exchange-correction potential. We have, however, not included the spin polarization and on-site Coulomb interactions for simplification. A kinetic energy cutoff of 300 eV for the plane-wave basis set was adopted. The gamma point (Γ) for the Brillouin zone integrations was used for the energy calculations. The self-consistent field (SCF) tolerance was set to 2.0 × 10⁻⁶ eV atom⁻¹.

Once the different activation energy conditions were known, the growth process was simulated by a Monte Carlo method, which allowed us to confirm whether our analysis was appropriate or not.

3. Results and discussion

The XRD pattern of the obtained nanostructures could be satisfactorily indexed for α-Fe₂O₃ (JCPDS No. 86-0550). The SEM images in Fig. 1 show that three types of nanostructures exist. The first are nanowires (Fig. 1a) of length ∼10–20 μm with diameters ranging from of ∼20–70 nm. The second are nanoleaves (Fig. 1b) with lengths of 1–5 μm, thicknesses of ∼50 nm and widths of ∼1 μm. The third are micropillars (Fig. 1c) with lengths of ∼2–10 μm and diameters of ∼1 μm. Some of the pillars observed are in a quadrangular prism shape. Fig. 1d shows a TEM image of a nanowire. The interplanar spacing of 2.57 Å demonstrates that the α-Fe₂O₃ nanowires grow along the [110] direction (2.52 Å in the reference material) with good crystallinity, which is the same as the direction of the nanoleaves and micropillars (data not shown). This result is corroborated by the corresponding electron diffraction pattern.

Fig. 1 The SEM images of the prepared nanostructures: (a) nanowires (b) nanoleaves (c) micropillars. (d) The TEM images, which prove that the nanostructures are α-Fe₂O₃.

The shape of the nanostructure changes as the substrates are subjected to different pressures. For the original iron substrate heated at 550 °C, nanowires are achieved. For the substrate pressurized at ∼1.0 GPa, micropillars grow on the surface. For the pressure range of 0.5–1.0 GPa, the nanoshapes change, in succession, from wires to leaves and then to pillars.

The XRD pattern shown in Fig. 2 clearly shows that the iron (110) peak shifts by about 0.25° at 1.0 GPa. The inset shows the XRD patterns of the iron surfaces after pressurizing at 0.25–1 GPa. It shows that there are some changes in the iron lattice. The interplanar spacing of the (110) plane changes from 2.027 Å to 2.039 Å. From the XRD data, we obtain the lattice parameters of the iron substrate before and after pressurizing, as shown in Table 1. These lattice parameters were used for the density functional calculations. Fig. 3 depicts the binding energy of Fe 2p in the iron substrates after treatment at different pressures. The inset shows the XPS spectrum for the sample pre-treated under a pressure of 0.75 GPa. The Fe 2p binding energy increases after pressurization, mainly because of the lattice distortion.

Fig. 2 The shift in the iron (110) peak in the XRD pattern of the iron surfaces after pressurizing at different pressures (0.25–1 GPa) in a tablet machine. The inset shows the full patterns.

Table 1 The lattice parameters of the pressurized iron substrate from the XRD data

Pressure (GPa)	a	b	c
0	2.8664	2.8664	2.8664
1	2.8831	2.8831	2.8326

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Fig. 3 The binding energy of Fe 2p at the iron surface after pressurization at different pressures. The inset is the XPS pattern for the sample pre-treated with a pressure of 0.75 GPa.

Comparing the shapes of the nanostructures and the changes in the binding energy after pressurization, we can see that there is a corresponding relationship between the shapes of the nanostructures and the binding energy. It suggests that the change in the nanostructure shape is intimately linked with the activation energy of the surface, which has been investigated by density functional calculations.

In the calculations, the lattice parameters were based on our XRD data. After the pressurization, the lattice changes from the body-centered cubic (Im3̄m) to body-centered tetragonal (I4/mmm). For each lattice, the bare surfaces of (110), (111) and (100) were modeled by slabs, which were periodic within the surface plane with a periodicity of about 20 Å separated by a vacuum. Then, for each slab, an oxygen atom was put on each surface at the lowest energy point after geometric optimization. To determine the activation energy, the final state was chosen such that one of the nearby surface iron atoms had been pulled off the surface. We assume that the iron atom gets to a certain position for comparison. For simplification, the position is chosen to be above the O atom at a distance of 1.888 Å, which is the bond length of Fe–O in Fe₃O₄.

By density functional calculations, the anisotropic activation energy in the [110], [111] and [100] direction was calculated with DFT and the GGA¹⁰ method. They are anisotropic and change with pressure. The calculated activation energy of the [111], [110] and [100] directions at different pressures is shown in Fig. 4. The anisotropic activation is found to be: [111] (4.076 eV) > [110] (3.508 eV) > [100] (3.428 eV). The activation energy in [111] is 0.5 eV higher than the other two directions, and the [110] and [100] activation energies are close to each other. As the pressure increases, the activation energy decreases in all directions, and the [110] and [100] activation energies get mutually closer.

Fig. 4 The calculated activation energies of the [111], [110], and [100] directions at different pressures.

As the activation energy in [111] is 0.5 eV higher than the other two directions, we mainly consider the nanostructures grown on the (110) and (100) surfaces. Fig. 5 is the sketch map of the growth in these directions.

Fig. 5 The central growth direction sketch map: (a) the central [100] and (b) central [110] groths, with lateral growths in the closer direction.

1) The central [100] growth has four [110] easy lateral growths and four hard lateral growths in the [111] direction (Fig. 5(a)). For iron which has not been pressurized, the activation energies of [111] and [110] are high and the lateral growth rate is small, and nanowires are grown. As the pressure increases, the activation energy decreases and the [110] lateral growth rate increases, so micropillars (which are 3-dimentionally more than 10 times thicker than the wires) are formed. The quadrangular prism shape of the pillars may be attributed to the four easy lateral directions.

2) The central [110] growth has two [100] easy lateral growth directions and two [111] hard lateral growths (Fig. 5(b)). The activation energy in [100] is the lowest and there are always two lateral growth directions ([100]). So, the 2D nanoleaf structures are grown on the iron surface.

After discovering that the different shapes of the nanostructures are realized under different activation energy conditions, we tried to simulate the growth process by a Monte Carlo method to find out whether the above analysis was appropriate or not. In our previous work,¹¹ we developed a 2-D simulated model of diffusion using the Monte Carlo method and used it for the growth process of α-Fe₂O₃ nanowires. It can explain the effect of the environment (reaction temperature, the oxide density, and the process of annealing) and why we sometimes get nanowires with large heads. Here, we applied the model in a 3-D case to show how the anisotropic activation energy affects the shape of the nanostructure.

The simulated model from 2D to 3D is developed by assuming the growth is restricted to a cubic lattice. The diffusion process is still modelled using the Monte Carlo method, while the diffusion energy barriers were changed from 2 parameters to 3 parameters and were anisotropic. The diffusion energy barriers are related to the activation energy barriers mentioned above. The vertical direction diffusion energy barrier stands for the central activation energy, and the lateral activation energy concerns the diffusion in the transverse directions. If the activation energy barrier is low, the growth begins in this direction and the diffusion energy in the model is low. Other parameters, like the reaction temperature and the oxygen density, are as has been described in our previous work.¹¹ The density of oxygen molecules can be described as the trial times of all the surface lattices in a unit time. The units of energy, temperature and the lattice length are chosen as 1.

1) To simulate the central [100] growth, we changed the vertical direction diffusion energy barrier to 0.15, and the transverse directions’ energy barrier to 0.52 and 0.52. It is anisotropic and the vertical energy barrier of 0.15 corresponds with the up direction [100] having the lowest activation energy. The central [100] growth has four [110] easy lateral growth sides so that the transverse barrier energy of 0.5 is not so large. The reaction temperature is set at 0.15 and the density of oxygen at 10. The results are shown in Fig. 6(a) and (b) and, accordingly, a nanowire is grown on the surface.

Fig. 6 The simulated nanostructures using a 3D simulated growth model. (a) and (b) nanowire; (c) and (d) micropillar; (e) and (f) nanoleaf.

As the pressure increases, the activation energy decreases in all directions, and the [110] and [100] activation energies get closer. To simulate the energy decrease due to the pressurization of the iron substrate, we changed the vertical direction diffusion energy barrier to 0.13, and the transverse directions’ diffusion energy barrier to 0.45 and 0.45. A micropillar is grown when the reaction temperature is set to 0.15 and the density of oxygen is set to 10, as depicted in Fig. 6(c) and (d).

2) To simulate the central [110] growth, we changed the vertical direction diffusion energy barrier to 0.15, and the transverse directions’ diffusion energy barrier to 0.5 and 2.0. The central [110] growth has two [100] easy lateral growths and two [111] hard lateral growth directions and the energy in the transverse direction is anisotropic. Fig. 6(e) and (f) show the results when the reaction temperature is 0.15 and the density of oxygen is 10. A nanoleaf is accordingly grown on the iron surface. The above simulation substantiates that the anisotropic energy corresponds to the different shapes of the nanostructures. The simulation shows that we get nanowires in the central [100] growth, and nanoleaves in the central [110] growth. As the activation energy decreases in all directions, the [110] and [100] activation energies get closer, and we get micropillars.

4. Conclusion

Pressurization of the iron substrate sensitively influences the shape of the α-Fe₂O₃ nanostructures formed by its thermal oxidation. The shape gradually changes, in succession, from nanowire to nanoleaf to micropillar as the pressure is increased.

It is shown that the anisotropic energy gives rise to the anisotropic growth rate and thereby determines the shapes of the nanostructures formed.

By calculations and simulations, the nanostructures’ growth process is concluded to be the following: for low pressure treated substrates, the central [100] growth is the central part and the lateral growth rate is small, which gives rise to nanowires. As the pressure increases, the [110] activation energy decreases and the central [110] growth becomes relevant. For very high pressures, the activation energies of [110] and [100] decrease and mutually converge, which promotes the formation of micropillars. These theoretical findings corroborate the observations. The study provides a useful pointer to control the shape of the nanostructures in the thermal-oxidation method.

Acknowledgements

The authors are grateful for the support of the State Key Laboratory for Mesoscope Physics at Peking University.

Notes and reference

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