**1. Introduction**

The mechanical properties and service life of steel are seriously affected by inclusions. After the proposal of the concept of oxide metallurgy [1], researchers have realized that it is important to control the size of inclusions [2–4] rather than increase the smelting cost [5–8]. Formation of inclusions begins with nucleation, and exploring the nucleation mechanism and properties of inclusions in steel is important to control the inclusion size. However, owing to the high speed of inclusion nucleation and high smelting temperature, the inclusion-nucleation process is difficult to detect and observe directly. Therefore, research on the inclusion of nucleation in steel is a challenge.

Researchers have found that Zr-containing inclusions can promote acicular ferrite transformation in Zr-deoxidized steel under certain conditions [9–13]. Zr-containing inclusions in Zr-deoxidized steel also play an important role in oxide metallurgy. On the one hand, they can induce nucleation of intragranular ferrite. There are several theories about the nucleation mechanism of ferrite. The change in the chemical composition of austenite around inclusions promotes nucleation. Inclusions and precipitates are coherent with ferrite to reduce the potential nucleation barrier and promote nucleation. In addition, the strain energy caused by the difference in thermal shrinkage between inclusions and austenite, as well as inclusions acting as an inert interface, promotes nucleation [14]. Among the proposed theories, the Mn-depleted-zone mechanism formed by the precipitation of MnS

**Citation:** Li, Y.; Wang, L.; Chen, C.; Yang, S.; Li, X. New Insights into the Mechanism of Nucleation of ZrO2 Inclusions at High Temperature. *Materials* **2022**, *15*, 7960. https:// doi.org/10.3390/ma15227960

Academic Editor: Daniela Kovacheva

Received: 17 October 2022 Accepted: 3 November 2022 Published: 10 November 2022

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on ZrO2 is considered to be one of the most effective mechanisms for intragranular ferrite nucleation [15,16]. On the other hand, Zr-containing inclusions play an important role in controlling the distribution of MnS inclusions in the steel. The density of ZrO2 is close to that of liquid steel, and the volume is small. Therefore, it is not easy for ZrO2 to float up in liquid steel, and it is easier for ZrO2 to disperse and distribute in steel to improve the distribution of sulfide through heterogeneous nucleation. Theoretical calculation shows that the lattice mismatch degree between MnS and ZrO2 is only 5.2%, and ZrO2 is the most effective nucleation core to promote MnS nucleation [17]. The thermodynamics from first-principles calculation show that Mn will diffuse into ZrO2 because ZrO2 has cationic vacancies and can absorb Mn [18]. Whether it induces intragranular ferrite nucleation or acts as a heterogeneous nucleation core, the key is the size control of ZrO2. However, there has been limited research on the nucleation mechanism and size control of ZrO2. In addition, the inclusion-nucleation speed is fast and the smelting temperature is high, so the inclusion-nucleation process is difficult to detect and observe directly.

To study the evolution of alumina inclusions at the atom scale, Wang et al. [19–21] investigated the cluster structure from experimental and theoretical aspects, and they proposed a two-step nucleation mechanism. Using quenching and three-dimensional atomic-probe detection technology, Zhao et al. [22] captured the intermediate structure of titanium oxide, and they proposed the cluster-assisted nucleation mechanism. Yang et al. [23] simulated the growth process of clusters by molecular dynamics, and they found that clusters grow through collision. However, there has been limited research on the nucleation of zirconium oxide. Thus, it is necessary to study the nucleation process of zirconium oxide.

In this study, a high-temperature Zr deoxidation experiment was carried out, and the characteristics of the zirconium oxide inclusions in liquid steel, such as the composition, morphology, size, quantity, and area density, were statistically analyzed. According to classical thermodynamic nucleation theory, the relationships between the solute element activities and the nucleation radius and nucleation rate of inclusions were obtained, and the theoretical nucleation rate was compared with the experimental nucleation rate. Cluster models of zirconium oxide were constructed by Materials Studio software. The cluster structure and thermodynamic properties of nanoparticles after geometric optimization were calculated, and the accuracy of the first-principles calculation was verified. By combining the high-temperature experimental results, classical nucleation calculations, and first-principles analysis, the nucleation mechanism of zirconium oxide inclusions is proposed.

#### **2. Materials and Methods**

#### *2.1. Sample Preparation*

Pure iron was used as the raw material, and it was heated in a Si–Mo heating electric resistance furnace (Braveman Special Testing Furnace CO. LTD., Luoyang, Henan, China). The chemical composition of the pure iron sample is shown in Table 1. The pure iron sample was heated to 1873 K (1600 ◦C) in an alumina crucible in the Si–Mo heating electric resistance furnace. After the temperature was maintained at 1873 K for 30 min, the Zr–Fe alloy (60% Zr) wrapped in a high-purity iron belt was added to the melted pure iron, followed by stirring for 10 s to ensure uniform distribution of the Zr–Fe alloy. Finally, 120 s after adding the Zr–Fe alloy, samples were removed in quartz tubes, followed by quenching in water. The whole experimental process was protected by high-purity argon gas.

**Table 1.** Chemical contents of the impurities in the pure iron sample (wt%).


The inclusions were extracted by electrolysis. A copper plate was used as the cathode, and the sample was the anode. After electrolysis, the anode was placed in anhydrous ethanol. By ultrasonic cleaning, the inclusions attached to the anode were dispersed in anhydrous ethanol. Finally, the inclusions extracted by electrolysis were analyzed by micro X-ray diffraction (μXRD, Bruker D8 Advance, Bruker, Berlin, Germany) and transmission electron microscopy (TEM, JEOL JEM-F200, JEOL, Tokyo, Japan).

#### *2.2. Microstructure and Composition Characterization*

To measure the composition and morphologies, the samples were processed into ∅5 mm × 15 mm metallographic samples. Scanning electron microscopy with energydispersive X-ray spectroscopy (SEM-EDS) (EM-30PLUS, COXEM, Daejeon, Korea) was then performed. In addition, the samples were processed into ∅5 mm × 10 mm bars for total oxygen and nitrogen content detection by the fusion-infrared absorption method. The oxygen and nitrogen contents were measured three times to investigate the uniformity of the total oxygen and nitrogen contents in the molten iron. In addition, the total Zr content was measured by inductively coupled plasma–atomic emission spectroscopy. The chemical contents of oxygen, nitrogen, and zirconium are given in Table 2.

**Table 2.** Chemical contents of O, N, and Zr in the steel sample after Zr addition.


To measure the composition of the inclusions in the steel after zirconium addition, the inclusions extracted by electrolysis were observed by μXRD and TEM. The results provided an experimental reference for subsequent first-principles calculation of inclusion crystal-type selection.

#### *2.3. Nucleation Calculation*

According to classical nucleation theory, the critical nucleation size and nucleation rate *I* [cm−3·s<sup>−</sup>1] can be calculated by [24]

$$\ln I = \frac{16\pi\gamma\_{SL}^3 V\_O^2}{3k\_B R^2 T^3} \left( \frac{1}{\left(\ln S\_O^\*\right)^2} - \frac{1}{\left(\ln S\_O\right)^2} \right) \tag{1}$$

$$\sigma\_{\mathbb{C}} = -\frac{2\gamma\_{SL}}{\Delta G\_V} = \frac{2r\_{SL}V\_{\mathbb{O}}}{RT\ln S\_{\mathbb{O}}} \tag{2}$$

where *kB* is the Boltzmann constant (1.38 × 10−<sup>23</sup> J/K), *R* is the gas constant (8.314 J/(mol K)), *T* [K] is the absolute temperature, and *VO* [m3/mol] is the molar volume of oxide. *γSL* [J/m2] is the interfacial energy between the oxide and liquid steel, and it can be expressed by Young's equation:

$$
\gamma\_{SL} = \gamma\_{SV} - \gamma\_{LV}\cos\theta \tag{3}
$$

$$
\gamma\_{LV} = 1.75 - 0.279 \ln(1 + 140 \cdot a\_O) \tag{4}
$$

where *γSV* is the surface energy of the solid inclusion, *γLV* is the surface energy of the liquid steel, which has been calculated in previous studies [25,26], and *θ* is the contact angle between liquid steel and the inclusion, as illustrated at Table 3.

**Table 3.** Data related to the calculation of the critical nucleation size and nucleation rate of oxide inclusions.


The experimental values of the nucleation rate *I* can be obtained by [24]

> *I*

$$\mathbf{f} = \frac{f\_v}{\frac{4}{3}\pi r^3 \cdot t} \tag{5}$$

where *t* is the nucleation time (generally taken to be 0.2 s [29]) and *r* is the critical nucleation radius obtained by Equation (2). *fv* is the volume fraction of oxide particles: [24]

$$f\_v = \frac{\rho\_{F\varepsilon}}{\rho\_{ZrO\_2}} \cdot \frac{M\_{ZrO\_2}}{xM\_{Zr}} \cdot [\text{ppm insol. Zr}] \times 10^{-6} \tag{6}$$

where *ρFe* and *ρZrO2* are the densities of Fe and ZrO2, respectively (*ρFe* = 7.8 g/cm3, *ρZrO2* = 5.85 g/cm3) [30], *MZrO2* is the molecular weight of ZrO2, *Mzr* is the atomic weight of Zr, and [ppm insol. Zr] represents the Zr content.

#### *2.4. First-Principles Calculation*

The DMol [3] module based on density functional theory in the Materials Studio software package (Materials Studio8.0, Accelrys, California, America) was used for cluster optimization and thermodynamic property calculation. The Broyden–Fletcher–Goldfarb– Shanno mechanism was used for geometric optimization. The Perdew–Burke–Ernzerhof functional with the generalized gradient approximation was selected as the electron exchange–correlation potential function [31].
