Atomic Distance Tuning Effect for Nucleation in Liquid Iron

Abstract

Liquid structural evolution of iron with various oxides was tracked from above liquidus to undercooling temperatures using an in situ high-energy X-ray diffraction method. The icosahedral-like orders and its enhancement with the decreasing temperature in all the liquids investigated suggest that icosahedral-like orders are not the sole reasons responsible for the variation of undercooling. The reduction of nearest-neighbor distance (r₁) tuned by catalyzers contributes to the enhanced nucleation behavior of liquid iron.

Turnbull[1] proposed that nucleation behavior of crystals in an undercooled liquid is related to the catalyzer it contains, which can be estimated by lattice disregistry between the catalyzer and the nucleated solid. However, even under the same thermal and substrate conditions, a nucleation system can exhibit distinct undercooling values.[2,3,4] This phenomenon suggests that there are unknown factors affecting nucleation process. To comprehend this puzzle, liquid structure was proposed as an important clue responsible for the variations observed in undercooling.[5,6] Frank[7] hypothesized a theory to explain the origin of undercooling by assuming liquid is composed of icosahedral short-range orders (ISROs). The proposed ISRO has six fivefold symmetry axes,[7] which is incompatible with the crystal translational periodicity. This structural dissimilarity is regarded as the atomic structural origin of the detected undercooling (nucleation energy barrier).

Many experimental and simulation evidences have verified the Frank’s hypothesis, where ISRO was identified in metallic liquids, especially in liquid iron.[8,9,10] The ISRO can be a perfect or distorted fivefold symmetry structure,[11] both can decrease the barrier to nucleation of the metastable i-phase[12] or metallic glass.[13] More recently, the concept of ISRO was considered as the leading structure for icosahedral quasicrystals (iQC) to act as a template for nucleation of crystalline solids, e.g., face-centered-cubic (fcc)-Al in Al-Zn-Cr alloys.[14] Thus, the obtained results suggest that ISRO might be a key intermediate structure for crystal nucleation, i-phase formation, and glass transition during liquid-to-solid transition process.

The earlier study on the effect of the substrate on atomic ordering in liquid was observed through high-resolution transmission electron microscopy (HRTEM) by Howe[15] and Oh et al.[16] Layer ordering and in-plane ordering were identified simultaneously in the first few layers adjacent to the liquid/substrate interface.[15,16,17,18] Greer[19] pointed out that such ordering could affect the nucleation either positively or negatively, depending on substrate template effect. State-of-art experimental studies[20,21,22,23] have shown that indeed the substrate can affect the nucleation behavior of new crystals but the ordering effect on the liquid is missed in these studies. For instance, there is little information about how the liquid ordering takes part in the nucleation process and how the ordering itself is affected by the substrate. In these researches, Schülli et al.[20] investigated the substrate template’s effects of three different Si substrates on the undercooling of AuSi droplets, but the real reconstruction process of liquid atoms was not observed. Reichert et al.[21] pointed out that the substrate was able to capture liquid clusters in preferred orientations, giving rise to orientational alignment of new crystals during nucleation. The other evidences can be referred to the nucleation of Al[22] and Al-Cu[23] on various substrates but there is no discussion of the role of the substrate on liquid structure as well.

In this paper, we focus on identifying the atomic structural evolution of liquid iron under the influence of the in situ-formed iron oxides during the freezing process. These oxides normally lead to different undercoolings even under the same thermal conditions.[24,25] In order to understand the atomic structural origin of the difference in undercooling, structure factors and pair distribution functions of the liquid are tracked from above the liquidus to the undercooled state. The mechanism behind the difference is discussed based on the atomic structural similarity among the investigated iron liquids, the corresponding substrates and the final iron crystal.

Ingot samples with or without oxides were prepared by arc-melting of high-purity elemental Fe (99.99 pct) in a water-cooled copper hearth under an oxygen-filled atmosphere (400 Pa). The preparation details and oxide identification can be found in Reference 25. The mean spatial diameter and the number density are 3.08 ± 0.43 (μm) and (5.5 ± 0.9) × 10¹³ (m⁻³) for Fe₃O₄, and 3.28 ± 0.49 (μm) and (4.3 ± 0.4) × 10¹³ (m⁻³) for FeO, respectively. The average distances between the oxide particles were 26.3 ± 1.5 μm for Fe₃O₄ particles and 28.5 ± 0.9 μm for FeO particles. Levitated samples with different oxides were then used to investigate liquid structural evolution during cooling procedure. High-energy X-ray diffraction (HE-XRD) measurements were performed at specific collection temperatures on BL13W1 at Shanghai synchrotron radiation facility (SSRF) equipped with a monochromatic beam which had an energy level of 72.095 keV and a wavelength of 0.17199 Å. The diffraction patterns were recorded using a Perkin Elmer Si 1621 detector, and the exposure time for data collection was 6 seconds. The raw 2D data were integrated from X-ray intensity profiles using FIT2D program (ref. Supplementary Data),[26] and transformed to 1D profile. The scattering intensities were corrected for absorption, polarization, coherent scattering, Compton scattering, and multiple scattering contributions. Then, structure factor S(Q) of liquid can be derived from diffraction intensity as a function of Q (ref. Supplementary Data), where Q is the scattering vector magnitude. The measurement was acquired over a range of Q values from 1 to 16 Å⁻¹ using a rapid-acquisition pair distribution function technique.

Figure 1 displays the S(Q) and the corresponding enlarged second peaks. For oxide-free pure iron, we chose eight temperatures ranging from 1810 °C, i.e., 272 °C above T_m, to 1380 °C, i.e., 158 °C below T_m for survey experiments in order to capture significant evidence for structural changes in the liquid on nucleation. For oxide-contained liquid iron, two temperatures were selected in both the superheating and undercooling zones for a comparison.

Fig. 1

Structure factors inferred from high-energy X-ray diffraction experiments and the enlarged second peaks of S(Q) marked in red squares for pure iron liquids (a, d), FeO-contained iron liquids (b, e), and Fe₃O₄-contained iron liquids (c, f) (Color figure online)

The S(Q) for all liquids oscillated well around unity over the entire range of Q values, reflecting the quality of the experimental data.[27] The primary peak increased in intensity and shifted to the high Q value end with a decrease in temperature, as shown in the insets (Figures 1(a) through (c)). It indicates that the degree of order in the liquid becomes increasingly pronounced, corresponding to the expected increase in density. A shoulder on the right-hand side of the second peak is observed for all measured S(Q) curves of the three different liquids, as clearly seen in Figures 1(d) through (f). Such a feature has been identified as a signature of ISRO from the theoretical study of Sachdev and Nelon[28] and was evidenced in liquid iron elsewhere.[8,9,10] It should be noticed that this feature becomes more pronounced with the decreasing temperature and also more prominent in the Fe₃O₄-contained liquid as indicated by the enhanced intensity (Figures 1(d) through (f)).

The pair distribution function, g(r), was calculated from Fourier transformation of S(Q) as shown in Figure 2. The nearest-neighbor distances (r₁) can be obtained from the location of the first maximum of g(r), which is approximately 2.550 Å for both pure iron liquid and FeO-contained liquid iron at the given undercooled temperature. Compared with those of pure liquid iron and FeO-contained liquid iron, the value of r₁ for Fe₃O₄-contained liquid iron slightly decreases to about 2.544 Å at the same temperature. The intensity of g(r) increases with the decreasing temperature and is slightly higher in Fe₃O₄-contained liquid as displayed in the insets of Figure 2. The same temperature effect on atomic g(r) were also found in Al, Cu, and Cu-Zr melts[29] which suggests that the variation of g(r) with temperature is a common phenomenon of liquid metal. The coordination number, $Z = \mathop \smallint \nolimits_{{r^{1} }}^{{r^{2} }} 4\pi \rho r^{2} {\text{g(r)dr}}$, of the liquid was calculated from the entire area under the first peak by using the first (r¹) and second (r²) minima as integration boundaries, where ρ denotes the atomic density. From Figure 2, the r¹ and r² have similar values in all three liquids, which lead to an approximate Z = 12. The observed values (Z ~ 12) at ~ T_m and the shoulder on the second peak of S(Q) are compatible with a few types of SRO including icosahedral-like, fcc-like or hexagonal close packing-like (hcp). However, further evaluation by simulation[28] suggested that the SRO tends to be icosahedral-like orders in liquid iron.

Fig. 2

The pair distribution functions g(r) for pure iron liquids (a), FeO-contained iron liquids (b), and Fe₃O₄-contained iron liquids (c)

The atomic structure difference was further verified by plotting r₁ and Z values against liquid temperatures as shown in Figure 3. For the liquid without oxide, the r₁ value shifted from 2.555 ± 0.001 Å at 1810 °C to 2.547 ± 0.000 Å at 1380 °C as shown in Figure 3(a). The r₁ value of FeO-contained liquid iron showed nearly the same trend with that of the pure iron liquid from 2.553 ± 0.001 Å at 1565 °C to 2.549 ± 0.001 Å at 1428 °C. As for the Fe₃O₄-contained liquid iron, the r₁ value also decreased with the decreasing temperature but with a much smaller value from 2.547 ± 0.001 Å at 1580 °C to 2.544 ± 0.001 Å at 1478 °C. In fact, the r₁ value of iron crystal is 2.539 Å at the T_m, which is smaller than those of all three liquids but closer to that of the Fe₃O₄-contained liquid iron. It decreases as temperature drops (2.534 Å at 1400 °C), considering the thermal contraction of the crystal.[30] From the above analysis, we have the following sequence of r₁ at ~ T_m, i.e., r₁ (liquid iron) ≈ r₁ (FeO-contained liquid iron) > r₁ (Fe₃O₄-contained liquid iron) > r₁(solid iron). However, the Z increases linearly with the decreasing temperature as shown in Figure 3(b). The regression coefficient (R²) of the best fitting is 0.99, indicating an intimate relationship of Z with temperature regardless of the catalyzer. The trends observed in oxide-contained iron liquids indicate that oxide does not affect the coordination number of the liquid but changes the nearest atomic distance depending on the substrate.

Fig. 3

(a) The nearest-neighbor distances, (b) coordination numbers of pure iron liquid (square symbol), FeO-contained iron liquid (diamond symbol), Fe₃O₄-contained iron liquid (circular symbol), iron crystal (star symbol), FeO crystal (down-triangle symbol), and Fe₃O₄ crystal (up-triangle symbol) change with temperature

It should be noticed that solute element affects the nucleation efficiency in terms of growth restriction factor Q and the formation of a compound.[31,32,33] In our study, the samples are taken from the same arc melted ingot, undergoing the same thermal cycle condition. Therefore, the oxygen content in the iron melts contained two different oxide particles are consistent with each other, resulting in a slight difference in liquid structures between them. Apart from solute effect, substrate particles are also able to tune the nucleation behavior in terms of ordering and undercooling through the substrate template effect as discussed in previous sections.[14,15,16,18,21] But the information about the effect of substrate on the structure of SRO remains ambiguous. Schneider[34] indicated that Cu segregated to a crystalline Si/liquid Al-alloy interface in terms of nanoscale islands rather than monolayer. Pouget[35] found that the aggregation of prenucleation clusters led to the nucleation of amorphous nanoparticles which assembled at the template and formed calcium carbonate crystals after reaching a critical size. These clusters may disperse in the melt under the role of melt flow, resulting in a reduction of the nearest-neighbor distance (Figure 3(a)).

In Figures 4(a) through (d), we present the deduced XRD pattern and reduced pair distribution function G(r) curves of the catalyzing oxides based on the ordinary X-ray diffraction data with the wave length λ = 1.54 Å obtained from the standard powder diffraction file [PDF, card numbers 19-0629 for Fe₃O₄ and 06-0615 for FeO], with a view to correlating the atomic structure of the nucleating liquid with the corresponding substrate. The first peak was observed at 1.99 Å for Fe₃O₄ crystal, which is very close to the first nearest distance between iron and oxygen (i.e., the length of Fe-O bond) at room temperature.[36,37] According to the thermal expansion of the crystal,[38] the change in the r₁ value of Fe₃O₄ crystal with the increasing temperature is shown in Figure 3(a). At T_{m, Fe} of pure iron, the r₁ value can be extrapolated as 2.168 Å, which is much smaller than those of the liquids and pure iron crystal at the same temperature. Figures 4(c) and (d) give the r₁ value of FeO crystal obtained from the G(r) at room temperature, 2.120 Å and the extrapolated r₁ value for FeO at T_{m, Fe}, 2.248 Å. The r₁ value is much larger than that of Fe₃O₄ at the same temperature but close to that of iron. Here, we obtain r₁ sequence for two oxides at T_{m, Fe} as r₁ (FeO crystal) > r₁ (Fe₃O₄ crystal). Combining the r₁ sequence of the liquids and pure iron crystal, this leads to an assumption that a larger r₁ of substrate (FeO) will lead to a larger r₁ of liquid. Apart from this, the approximate equal r₁ values of liquid iron with and without FeO particles also indicate FeO catalyzer has a weaker effect on liquid structure compared with Fe₃O₄.

Fig. 4

(a) The X-ray diffraction intensity of Fe₃O₄ crystal as a function of Q and (b) the corresponding reduced pair distribution function G(r), (c) The XRD intensity of FeO crystal as a function of Q, and (d) the corresponding G(r)

In our experiment, a denser atomic distance was obtained in Fe₃O₄-contained iron liquid with the smallest substrate r₁, while the larger r₁ of FeO leads to a less dense atomic distance in the liquid. This finding indicates that the liquid system is more likely to be a tension system. The denser substrate will attract the atoms in liquid toward a closer atomic distance and a similar Z but may not be close enough to the same as the substrate, as indicated in Figure 3(a). The nucleation energy barrier depends on the atomic distance difference between SRO structure of the liquid and the corresponding crystal structure, given a similar atomic structural type (an identical Z value). If the atomic distance of SRO is close to the crystal structure, the required nucleation energy is thus much lower than those liquid with a larger atomic distance. In this study, the r₁ of Fe₃O₄-contained liquid is much smaller than that of FeO-contained liquid and close to that of iron crystal. Hence, a smaller undercooling (75 °C) was obtained for Fe₃O₄-contained iron liquid.[23] Although the structural template effect of the substrate on liquid structure can not be directly observed in this experiment, it indicates that the atomic distance of the substrate does affect the nucleation barrier of the liquid in terms of undercooling.

In summary, the liquid structure of pure iron was modified through the in situ-formed oxide particles. Synchrotron HE-XRD investigation indicates that a distinguished shoulder was observed at the high Q side of second peak of structure factors. It suggests that icosahedral-like orders should exist during the nucleation of the liquid investigated. The Z values of the liquids with and without oxides have the same trends with the decreasing temperature, but the r₁ reveals distinguished differences. The value of r₁ follows the sequence of r₁ (liquid iron) ≈ r₁ (FeO-contained liquid) > r₁ (Fe₃O₄-contained liquid) > r₁ (solid iron) > r₁ (FeO crystal) > r₁(Fe₃O₄ crystal) at T_{m, Fe} accompanying with the undercooling sequence of ΔT_{pure liquid} (304 °C) > ΔT_{FeO-contained liquid iron} (223 °C) > ΔT_{Fe3O4-contained liquid iron} (75 °C). It indicates that the liquid structural evolution during the cooling procedure can be manipulated by a proper substrate. A smaller atomic distance difference between the liquid and target crystal promises a decreased nucleation energy barrier for the new crystals in the liquid. The current study gives an unambiguous experimental proof of the atomic structural origin for the various undercoolings of the liquids cooled under a similar thermal condition and even containing similar liquid structure.