KINETIC CONDENSATION AND EVAPORATION OF METALLIC IRON AND IMPLICATIONS FOR METALLIC IRON DUST FORMATION

Pellets (2 mm in diameter and 1.2 mm in thickness) of metallic iron were put in the ends of a series of alumina tubes, the inner and outer diameters of which were 2 and 3 mm, respectively, and heights ranged from 1.2 to 40 mm. One end of the alumina tube, in which the pellet was put, was covered with an alumina disk, and the tube and disk were inserted into a graphite capsule (Figure 1(a)). The tubes were put in an isothermal region of a tungsten-mesh heater (5 cm in diameter and 10 cm in height), which was set in a vacuum chamber (22 cm diameter and 35 cm height) connected to a turbo molecular pump and a rotary pump (Ozawa & Nagahara 2000; Tachibana et al. 2002), and preheated at 770 K for a few hours to evacuate residual air and gases from furnace materials. The temperature of the furnace was then raised to a desired heating temperature (1720–1350 K), which was calibrated to within an uncertainty of ±5 K using the melting temperatures of Ag, Au, Cu, and Ni, and the eutectic temperature of Ni–C (1600 K), at the rate of ∼20 K minute⁻¹. The tubes were heated at the experimental temperatures for times ranging from 0.75 to 400 hr. Since the tubes have gas flow conductance, part of the evaporated iron gas always resides in the tubes and evaporation occurs in the presence of metallic iron gas (Figure 1(a)). After the desired duration of heating, the samples were quenched by shutting off the power supply. The pressure in the vacuum chamber, which was continuously evacuated during the experiments, was ⩽10⁻³ Pa at higher experimental temperatures (>1550 K) or ∼10⁻⁵ Pa at lower temperatures (<1400 K). The evaporation rate of the pellet was evaluated from the weight loss of the iron pellet, which was measured by an electric microbalance to a precision of 0.01 mg.

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A metallic iron pellet (3–6 mm in diameter and ∼0.5 mm in thickness) was placed at the bottom of a ∼50 mm long alumina crucible, of which the inner diameter ranged from 3 to 6 mm depending on the size of the metallic iron pellet, and preheated at 770 K for a few hours by a tungsten-mesh heater (7 cm in diameter and 10 cm in height) in a vacuum chamber (25 cm diameter and 50 cm height). The temperature of the furnace was raised to a desired heating temperature (1510–1680 K) at a rate of ∼20 K minute⁻¹ and heated for 3–90 hr in order to generate atomic iron gas from the metallic iron pellet (Figure 1(b)). A part of the gas that evaporated through the alumina tube impinged and condensed on an alumina disk (3–10 mm in diameter and ∼1 mm in thickness), which was fixed to a molybdenum plate (2 cm × 3 cm) and hung to the hole of multi-layer molybdenum heat shields (1 cm × 2 cm; Figure 1(b)). The outlet of the alumina tube with a molybdenum plate was placed close to the hole of the innermost heat shield in order to let evaporated iron gas atoms flow only through the hole of the heat shields and to avoid contamination from furnace materials. The distance between the substrate and the outlet of the tube was varied between 5 and 17.5 mm.

The substrate was heated by indirect radiation through the hole of layered heat shields, and its temperature was determined with an uncertainty of ±3 K by calibrating against the melting points of Ag and Au. The pressure in the chamber was kept below 10⁻³ Pa during experiments by continuous evacuation of the chamber with a turbo-molecular pump and a rotary pump. The mean free path of iron atoms that escaped from the tube should be much longer than the distance between the substrate and the outlet of the tube, and direct incoming gas atoms from the tube impinge onto the substrate without thermal accommodation by gas-phase collisions. The direct incoming gas atoms thus have velocities representative of the temperature of the tube, which was almost isothermal in the inside of the tungsten-mesh heater but decreased toward the outlet of the tube. It should be noted however that the temperature of the outlet of the tube was higher than that of the substrate. Because such differences in the gas temperature may affect condensation behavior, condensation experiments at a substrate temperature of 1235 K were carried out for different incoming gas temperatures (1510, 1580, and 1639 K; the temperature of the iron pellet), where the substrate temperature was kept constant for different gas source temperatures by changing the position of the substrate in the furnace and the relative distance from the crucible.

The weight loss of the iron pellet and the weight gain of the alumina substrate were measured by an electric microbalance with a precision of 0.01 mg. The surface and cross section of the condensates were observed with a field-emission scanning electron microscope (FE-SEM), and the chemical composition and crystallinity of the condensates were analyzed with energy dispersive spectroscopy (EDS) and electron back-scattered diffraction (EBSD).

The weight loss of the pellet increases linearly with time; the loss rate is larger in a shorter tube than in a longer tube because a longer tube has much more resistance to the gaseous flow, resulting in a higher iron vapor pressure near the surface of the pellet. We assume that evaporation takes place mostly from the upper surface of the pellet that evaporation from the side and bottom of the pellet is negligibly small and that the vapor pressure just above the upper surface of the pellet affects the evaporation rate. This assumption seems to be valid because the pellet was tightly fitted to the tube even after evaporation of a few tens of percent and step structures that formed by evaporation were observed only on the upper surface of the pellet. Moreover, even if there was a narrow gap between the pellet and the alumina crucible, evaporation from the gap may have been suppressed due to a high local vapor pressure of iron within the gap that should have high conductance for gas flow.

The vapor pressure near the sample surface is estimated from the weight loss of the pellet per unit time (dW/dt), the areas of the tube outlet (A), and the conductance of the tube (C; Paule & Margrave 1967):

$$\begin{equation} p = \frac{{dW/dt}}{A}\left({\frac{1}{C} - 1} \right)\sqrt {{{2\pi kT} / m}},\end{equation} \tag{ 2 }$$

where m is the atomic weight of iron, k is the Boltzmann constant, and T is the absolute temperature. The evaporation flux (J_evap) for different lengths of tubes at temperatures ranging from 1718 to 1347 K are plotted as J_evap/J^id_evap against the undersaturation ratio (S) of p/p^eq in Figure 2, where J^id_evap represents the ideal free evaporation rate (p = 0 and α_e = 1). The measured evaporation rate decreases as S increases due to recondensation from the surrounding gas. Experiments at the same temperature (1548 or 1448 K) with different heating durations show consistent results, which indicate that a steady ambient gas pressure condition was achieved and thus the evaporation rates were constant irrespective of heating duration. It should be noted that the evaporated fraction during heating to the experimental temperature and cooling to the room temperature was estimated to be at most a few percent for the experiments with the shortest duration (0.75 hr at 1720 K) and negligibly small in other cases.

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Energy dispersive spectroscopy and EBSD analyses showed that all the condensates are α-Fe, which may have been transformed from γ-Fe (the stable phase at substrate temperatures) during quench. Alternatively, the condensate might have been α-Fe even during its growth due to Ostwald's step rule, which states that the less stable form is more likely to nucleate from the vapor under the conditions where nucleation occurs. The latter possibility seems to be less likely because the condensed α-Fe would be transformed into γ-Fe at experimental temperatures.

Characteristic structures observed on the surface of condensates were growth steps with an interval of ∼10 nm (Figure 3(a)). Observation of condensates shows that metallic iron nucleates sporadically on the surface of corundum and eventually covers the entire surface, after which metallic iron grows on a compact metallic iron layer (Figure 3(b)).

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The weight of the condensate increases linearly with time, and the weight loss of the gas source also has a linear dependence on time (Figure 4). This suggests steady condensation of metallic iron under conditions of constant supersaturation. The weight gains of the substrates were always smaller than the weight losses of the gas source, and ∼10%–30% of evaporated iron was condensed on the substrate depending on the distance between the outlet of the alumina tube and the substrate: the longer the distance, the smaller the recovered fraction. This is because only a certain fraction of evaporated iron atoms impinge on the surface of the substrate under the low-pressure molecular flow conditions and the incoming flux onto the substrate becomes smaller with increasing distance due to geometric reasons (Figure 1(b)).

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Growth rates under different temperatures and supersaturation ratios were calculated from the steady weight gain of the substrate, the surface of which was covered by a compact metallic iron layer in order to eliminate the effect of heterogeneous nucleation of metallic iron onto the corundum substrate and the subsequent growth of heterogeneously nucleated metallic iron patches.

The evaporation coefficient for free evaporation (p/p^eq = 0) (α_e(0)) is obtained as the ratio between the experimental evaporation rate and the ideal evaporation rate given by Equation (1) with α_e = 1 and p = 0. The obtained α_e(0) ranges from 0.9 at higher temperatures to 0.6 at lower temperatures, and its temperature dependence is expressed by

$$\begin{equation} \ln \alpha _e (0) = 1.44(\pm 0.22) - 2595(\pm 353)/T. \end{equation} \tag{ 3 }$$

The α_e(0) in this study is consistent with that in Tsuchiyama & Fujimoto (1995), but shows a clearer dependence on temperature than in the previous study. The discrepancy may be due to the slight oxidation of metallic iron observed in Tsuchiyama & Fujimoto (1995) that may have affected evaporation. An interesting feature of the obtained temperature dependence is that α_e(0) becomes unity at a temperature close to the melting point of metallic iron (1808 K). Similar temperature dependences of α_e(0) have been reported for refractory oxides such as MgO, Al₂O₃, and Cr₂O₃ (Sata et al. 1978).

The relationship between the evaporation rate and the ambient iron gas pressure is not linear but convex (Figure 2). The evaporation rate should decrease linearly with p (Equation (1)) if α_e and α_c are equal to each other and constant irrespective of p, but this is not the case in the present study. This suggests that α_e and α_c both depend on the pressure of iron vapor. In order to clarify the pressure dependence of α_e and α_c, it is assumed that α_e and α_c are equal to each other and that they have linear dependence on the undersaturation ratio (α_e = α_c = α_e(0) + k (p/p^eq)), which yields a quadratic equation for the evaporation flux as a function of S. The evaporation rates at each temperature are fitted by a least-square technique, and the estimated k are −0.41 ± 0.12 (1σ) at 1718 K, −0.49 ± 0.18 at 1635 K, −0.63 ± 0.12 at 1609 K, −0.66 ± 0.08 at 1548 K, −0.24 ± 0.12 at 1449 K, −0.60 ± 0.05 at 1398 K, and −0.46 ± 0.09 at 1347 K. The negative values of k for all temperatures indicate that the kinetic barriers for evaporation and condensation at undersaturated conditions become larger at higher ambient gas pressure. Metal preferentially evaporates from kinks on the surface because it is easier energetically for atoms to break bonds with adjacent atoms, and condensation of incident metal atoms is also easier on a surface with many kink sites. The surface roughness (number of kinks), which thus affects the kinetic hindrances for evaporation and condensation, may be reduced near equilibrium, where the number of atoms breaking bonds at kink sites is balanced by the number of atoms being incorporated into the crystalline lattice, as long as the temperature of the surface is lower than the thermal roughening temperature. The kinetic hindrance for condensation is therefore expected to be larger near equilibrium than under lower saturation conditions.

k seems to have a weak temperature dependence; however, the mean value of k is −0.54 ± 0.15 (1σ). Thus, α_e and α_c at undersaturation (0 ⩽ S <1) can empirically be expressed by

$$\begin{equation} \alpha _{\rm e} = \alpha _{\rm c} = \exp (1.44 - 2595/T) - 0.54(p/p^{{\rm eq}}) (p/p^{{\rm eq}} < 1) \end{equation} \tag{ 4 }$$

over the temperature range from 1720 to 1350 K. The evaporation rates calculated using Equation (4) are also shown in Figure 2.

A supersaturation ratio S (p/p^eq) at the surface of the substrate was calculated based on the direct incoming flux of iron onto the substrate that could be estimated from the flux distribution of vapor emerging from the tube under molecular flow conditions (Dayton 1956) and the measured evaporation rate of the iron gas source. The fraction of the flux onto the substrate relative to the total evaporation flux of metallic iron from the tube was calculated to range from 0.11 to 0.34 depending on the distance between the substrate and the outlet of the tube. Note that the usage of the tube has the effect of focusing gas flux from the tube outlet (Dayton 1956) and that the estimated fraction of the flux onto the substrate against the total evaporation flux here is much larger than that in the case without the tube.

There might have been other indirect fluxes of iron onto the substrate, which hit the substrate after colliding with the heat shields, and if they were present, the incoming flux onto the substrate would be underestimated. However, the thickness variation of the condensed metallic iron layer agrees well with the predicted spatial variation of direct flux onto the substrate (Figure 5), suggesting that the incoming flux of iron was dominated by the direct flux from the outlet of the tube because the indirect iron gas flux would come from random directions and its spatial variation would be uniform. We also found that condensation of metallic iron occurred on the molybdenum plate used to hold the Al₂O₃ substrate and on the heat shields at the edge of the hole. The temperature of the heat shields should have been lower than that of the substrate because only the edge of the hole was heated by radiation, while the shield was cooled by thermal conduction to the interior. Therefore, the edge of the heat shields may not have acted as a reflector of impinging iron atoms but as a sink for them. This evidence suggests that the indirect iron gas flux onto the substrate was negligibly small, and thus further discussion will be made based on the estimate of the direct incoming flux.

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The calculated direct incoming fluxes onto the substrate yield supersaturation ratios ranging from ∼10 to ∼35 in the present experiments. The condensation flux of metallic iron normalized to the ideal evaporation flux is shown as a function of S in Figure 6. Although the data are scattered to some extent, all of the measured condensation fluxes are close to the ideal value. This indicates that α_c is close to unity irrespective of α_e, because the effect of re-evaporation from the condensates must be small due to the large values of S. It is also seen that α_c at 1235 K does not depend on the temperature of incoming gas atoms, implying instantaneous thermal accommodation of the colliding gas atoms with the substrate surface.

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The ideal condensation behavior of metallic iron in this study suggests that the condensation rate of metallic iron is determined by the supply of atomic iron gas and that surface atomistic processes are not the rate-limiting process at S > 10, i.e., the surface of the condensate is rough enough for all of the adsorbed atoms to find kink sites to be incorporated into the crystal lattice within their lifetime on the surface.