Thermodynamic insight into the growth of nanoscale inclusion of Al-deoxidation in Fe–O–Al melt

Products of Al-deoxidation reaction in iron melt are the most common inclusions and play an important effect on steel performance. Understanding the thermodynamics on nano-alumina (or nano-hercynite) is very critical to explore the relationship between Al-deoxidation reaction and products growth in iron melt. In present study, a thermodynamic modeling of nano-alumina inclusions in Fe–O–Al melt has been developed. The thermodynamic results show that the Gibbs free energy changes for the formation of nano-Al2O3 and nano-FeAl2O4 decrease with the increasing size and increase with the increasing temperature. The Gibbs free energy changes for transformation of nano-Al2O3 into bulk-Al2O3 increase with the increasing size and temperature. The thermodynamic curve of nano-alumina (or nano-hercynite) and the equilibrium curve of bulk-alumina (or bulk-hercynite) obtained in this work are agree with the published experimental data of Al-deoxidation equilibria in liquid iron. In addition, the thermodynamic coexisting points about Al2O3 and FeAl2O4 in liquid iron are in a straight line and coincide with the various previous data. It suggested that these scattered experimental data maybe in the different thermodynamic state of Al-deoxidized liquid iron and the reaction products for most of the previous Al-deoxidation experiments are nano-alumina (or nano-hercynite).

www.nature.com/scientificreports/ have been extensively studied since the middle of twentieth century  . However, most of the researchers are focused on the thermodynamic equilibrium between the bulk-alumina and iron melt, while less known about the thermodynamic properties of nano-alumina in liquid iron. Many previous work proved that the thermodynamic properties of the nano-alumina are different from that of the bulk-alumina, and the thermodynamic difference among the nanoscale inclusions is more obvious with the decreasing size of inclusions [31][32][33][34][35][36][37][38] . It was reported that the interfacial free energy between nano-alumina and liquid iron are decreased with the decreasing of the size of alumina, and the Gibbs free energy change of Al-deoxidation reaction has very close relation with the size change of alumina inclusion 31 . Wang et al. [32][33][34] also reported that the thermodynamics of Al-deoxidation reaction in liquid iron is dependent on the size of alumina inclusions. Therefore, a thermodynamic modeling about nano-alumina in liquid iron is necessary. In this paper, the thermodynamic modeling for Al-deoxidation reaction between nano-alumina inclusions and liquid iron has been developed. Base on the density functional theory (DFT) calculations, the thermodynamic curves and coexisting points corresponding to various size alumina and hercynite inclusions in liquid iron have been obtained. The effect of products size on Al-deoxidation equilibrium thermodynamics have been discussed.  38,39 , an internal part that the atoms located in the lattice of Al 2 O 3 crystal and an external part that the atoms situated in the surface layer of Al 2 O 3 particle. Thus, the calculations of thermodynamic properties of nano-Al 2 O 3 should be dealt with separately. The total Gibbs free energy of nano-Al 2 O 3 G can obtained as 38,39 where G s and G i are the Gibbs free energy of the external part and internal part of nano-Al 2 O 3 , x s is the atomic fractions in the surface of nano-Al 2 O 3 . As shown in Fig. 1, the nano-Al 2 O 3 described as a sphere particle with diameter d, contains a shell of δ thickness and a core with diameter (d − 2δ). The atomic fractions x s in the surface of nano-Al 2 O 3 can be obtained as where the subscripts i and s stand for the internal part or the surface part of nano-Al 2 O 3 , N is the atom numbers, V is the volumes, ρ is the atomic densities.
Some experiments reported that the atomic density of nano-particle surface is lower than that of the perfect crystal by 10-30% 39,40 . Thus, the value of ρ i /ρ s was taken as 1.2 in the present calculation. It was reported that the nanocrystalline surface is short-range order structure and there exist a liquid-like structure layer on the surface of nano-particle [41][42][43] . As can be seen from Fig. 2, nano-Al 2 O 3 is the intermediate of Al 2 O 3 product particle growth in the Al-deoxidation reaction, and its surface is formed by the aggregation and phase transformation of (Al 2 O 3 ) n clusters. Therefore, it is logical to conclude that the surface structure of the nano-Al 2 O 3 is a short-range order structure and is similar to the structure of (Al 2 O 3 ) n clusters. Furthermore, some studies reported that the surface of nano-particle usually contains two or three atom layers 5,44 . In this work, for simplicity, the (Al 2 O 3 ) 2 cluster, which contains three-atom thick, was used to describe the surface structure of nano-Al 2 O 3 , and the α-Al 2 O 3 crystal was used to describe the internal part structure of nano-Al 2 O 3 as show in Fig. 1. Thus, the Gibbs free  Table 1.
Calculation methods. The Gibbs free energy of Al 2 O 3 clusters and α-Al 2 O 3 crystal were calculated by DFT method. During the calculations, the generalized-gradient approximation of Perdew-Burke-Ernzerhof (PBE) was applied as the exchange-correlation potential function 46 . The initial structures of (Al 2 O 3 ) 2 cluster and α-Al 2 O 3 crystal were selected from the previous work 33 . The Gibbs free energy of (Al 2 O 3 ) 2 cluster and α-Al 2 O 3 crystal were calculated by the equations [33][34][35][36][37] where E is the total energy of alumina cluster or crystal at 0 K; H and S are the enthalpy and entropy of alumina cluster or crystal, respectively. The H and S were obtained by the analysis of atomic harmonic vibrational frequency of alumina cluster or crystal, which are the functions of temperature T. The calculation details of the relationship among the atomic harmonic vibrational frequency, the thermodynamic properties and temperature can be found in our previous study [33][34][35][36][37] .  Figure 2. Schematic of the nucleation and growth of Al 2 O 3 inclusion.

Gibbs free energy changes for the formation of nano-Al
recommended by JPSP 10 was used in the calculations as: �G θ Al 2 O 3 (s) = − 1,225,000 + 393.8 T J/mol. Figure 3 show the value of �G θ F and �G θ T (from 1500 to 2000 K). It can be seen from Fig. 3, �G θ F decreases with the increasing size of nano-Al 2 O 3 , while �G θ T increases with the increasing size of nano-Al 2 O 3 . It implies that the thermodynamic driving energy for the formation of nano-Al 2 O 3 increases gradually with the increasing of alumina size, while the thermodynamic driving energy for transformation of nano-Al 2 O 3 into bulk-Al 2 O 3 decreases gradually with the increasing of alumina size. On the other hand, the value of �G θ F and �G θ T increase with the increasing temperature. This result indicates that both the formation of nano-Al 2 O 3 and the transformation of nano-Al 2 O 3 into bulk-Al 2 O 3 at the low temperature is more easier than that at the high temperature.

Discussion
Effect of products size on Al-deoxidation equilibrium thermodynamics. The equilibria for Aldeoxidation in liquid iron have been extensively investigated [12][13][14][15][16][17][18][19][20][21][22][23][24][25] . Table 2 lists the experimental conditions and methods of Al-deoxidation equilibrium in liquid iron at 1873 K. Most of the Al-deoxidation equilibria were measured by equilibrating liquid iron with [Al] and pure solid Al 2 O 3 at 1873 K [12][13][14]18,19,[22][23][24][25] . The Al-deoxidation experiments were generally carried out in alumina crucible by using rotating furnace 12 , resistance furnace 19,22 and induction furnace [23][24][25] . Equilibrium concentration of [O] and [Al] were determined by analyzing the composition of experimental sample. The concentration of oxygen was generally analyzed by vacuum fusion method 12,13,18 , inert gas fusion method 14,19,[22][23][24][25] , and neutron activation method 15 , while that of aluminum was obtained by wet-chemical analysis. On the other hand, in order to make the Al-deoxidation reaction more close to the final equilibrium state in liquid iron, Rohde et al. 16     www.nature.com/scientificreports/  www.nature.com/scientificreports/ content is greater than 0.1%, these equilibria curves show different shapes and be away from their experimental data to some extent. Later, the Modified Quasi chemical Model in the pair approximation in consideration of the strong short-range ordering mainly between Al, Fe and O have been used to establish the thermodynamic equilibrium relationship by Paek et al. 25 . It can be concluded from the Fig. 5a that there is not a same curve to describe all these experimental data of Al-deoxidation equilibria in liquid iron. Previous studies reported 29,30 that the atoms of [Al] and [O] could not be independent randomly distributed, but have a strong tendency to form a kind of metastable phase, such as associated compound AlO, Al 2 O etc. In addition, Wang et al. [32][33][34] suggested that the thermodynamic of Al-deoxidation in liquid iron is closely related with the size of alumina. Xiao et al. [35][36][37] reported that the deoxidation thermodynamics of metal in liquid iron have depended on the structures and properties of reaction products. Hence, it can be concluded that there is a close relationship between the thermodynamics of Al-deoxidaiton reaction in liquid iron and metastable phase, such nano-Al 2 O 3 . Wang et al. [32][33][34] reported that the deoxidizers aluminum react with dissolved oxygen in molten steel to form various metastable alumina inclusions at first, and then the metastable alumina inclusion transform into stable crystal. However, the Al-deoxidation reaction in Fe-O-Al melt is very difficult to reach the thermodynamic equilibrium between bulk alumina and Fe-O-Al melt because of low supersaturation. Wasai et al. 31 suggested that the small alumina nuclei are suspended in liquid iron, and this is one reason for the presence of excess oxygen in liquid iron. Later, Wasai et al. 8 found a series of nano-alumina by hold their Al-deoxidation experiments at 1873 K in alumina crucible. In their experiments, the Al-deoxidized iron was maintained at 1873 K for a certain time (1, 5, 15, 30, 60 min), and the Al-deoxidized iron was solidified at 3 different cooling speed. The minimum diameter of alumina inclusions observed in their work is in the range from a few nm to 10 nm. This result indicates that the Al-deoxidation products are nanoscale alumina even 60 min after Al-deoxidation in the liquid iron.
As the reaction proceeds, the thermodynamic driving force of Al-deoxidation in liquid iron decreased gradually with the decreasing supersaturation ratio 31 . Therefore, it is very difficult for the nano-Al 2 O 3 (or nano-FeAl 2 O 4 ) to grow up into the final bulk crystal at the later period of Al-deoxidation. As a result, the nano-Al 2 O 3 (or nano-FeAl 2 O 4 ) are not large enough to float upward, and can appear as the structural units in Fe-O-Al melt and may remain as suspending inclusions in the melt for a long time. Therefore, the reaction products of Aldeoxidation in liquid iron may be various nano-Al 2 O 3 and nano-FeAl 2 O 4 inclusions in many cases.
Based on the Gibbs free energy changes for the formation of different size of Al 2 O 3 and FeAl 2 O 4 in liquid iron at 1873 K, the thermodynamic curves for the Al-deoxidation in liquid iron can be obtained. As shown in Fig. 5b, the thermodynamic curves for different size of alumina (solid line) and hercynite (dash line) means that the product of Al-deoxidation in liquid iron can be different size of alumina and hercynite. It should be noted that the diameter of FeAl 2 O 4 is 1.6 times that of α-Al 2 O 3 when they have the same number of aluminum atoms. This is because of the "molecule densities" of FeAl 2 O 4 is 1.6 times as that of Al 2 O 3 according to the calculation result. It can be seen from Fig. 5b, most of the Al-deoxidation experimental data are covered by the region between the bulk-alumina (or bulk-hercynite) equilibrium curve and the thermodynamic curves of 2 nm alumina (or 3.2 nm hercynite). Such facts indicate that the Al-deoxidation product should not be bulk-crystal but in nanoscale in most of those equilibria experiments. It can be concluded that the Al-deoxidation experiments by various researchers are in different thermodynamic state. These different thermodynamic states in their experiments may lead by the different experimental conditions. In addition, the nano-alumina (or nano-hercynite) thermodynamic curves are close to the bulk-alumina (or bulk-hercynite) equilibrium curve gradually with the increase of size of Al-deoxidation products. It indicates that the Al-deoxidation reaction is gradually close to the equilibrium between bulk alumina (or bulk-hercynite) and liquid iron with the increasing of Al-deoxidation products size during growth process. In other words, the equilibria experiments of various researchers could be in a state away from the final equilibrium between bulk alumina and liquid iron to some extent. thermodynamic coexisting point of the formation of Al 2 o 3 and feAl 2 o 4 in liquid iron. As shown in Fig. 6a, the intersection points of thermodynamic curves for alumina and corresponding hercynite (hercynite have the same number of aluminum atoms with alumina) are the thermodynamic coexisting points, while the intersection of thermodynamic curves for bulk alumina and bulk hercynite is the equilibrium coexisting point. The products in these points are both alumina and hercynite, and their size increase from right to left.
As known, there are three phases (liquid iron, hercynite and alumina) in Fe-Al-O ternary system, so the freedom degree is zero if this ternary system is under the specified pressure and temperature. Consequently, there is only one equilibrium coexisting point when the liquid iron equilibrated with both alumina and hercynite. Such an equilibrium coexisting point at 1873 K has been measured by several researchers [11][12][13]23,31,47,48 Fig. 6b.
These equilibria experiments may be in the different thermodynamic states due to different experimental conditions. Thus, the deoxidation products maybe a series of different size nanoscale hercynite and alumina in their three-phase equilibrium experiments. These different values of equilibrium coexisting points by various researchers may have a close relationship with the size of Al-deoxidation products. In some case of experiments, the three equilibrium coexisting phases in Fe-O-Al melt could be nano-alumina, nano-hercynite and liquid www.nature.com/scientificreports/ iron. Therefore, the coexisting points may be different to each other. As can be seen from Fig. 6b, all the predicted coexisting points are located at the same horizontal line. The concentrate of [Al] at the coexisting point for 2 nm Al 2 O 3 is more than three orders of magnitude less than that for bulk Al 2 O 3 . These results agree well with the previous experimental data [11][12][13]23,31,47,48 . Such a fact indicates that it needs more time for the nano-