Effect of Lanthanum-Cerium Rare Earth Elements on Steel at Atomic Scale: A Review

Abstract

Lanthanum-cerium rare earth (RE) elements play a vital role in metallurgy as essential microalloying elements. Their addition significantly modifies inclusion characteristics, enhances mechanical properties, and improves corrosion resistance. This review emphasizes the distinct and synergistic roles of lanthanum (La) and cerium (Ce) in steel at the atomic scale, elucidated through first-principles calculations based on density-functional theory (DFT). The primary focus includes the nucleation mechanisms and characteristics of rare earth inclusions, the solid solution and segregation behavior of rare earth atoms, and their microalloying effects on electronic structure and interfacial bonding. Although both elements form stable inclusions Re₂O₃ and ReAlO₃ and exhibit grain refinement effects, Ce exhibits a unique dual valence state (Ce³⁺/Ce⁴⁺). This results in nucleation behavior and oxide stability for Ce ions that differ slightly from those of La. Both elements alter the electronic structure of the Fe matrix through hybridization with d-orbitals, reducing magnetic moment and enhancing toughness. Compared to other alloying elements, La and Ce exhibit unique behaviors due to their large atomic radii and high chemical reactivity, which influence their solid solubility, segregation tendencies, and interactions with other atoms such as Cr, C, and N. Finally, this paper discusses the challenges that exist when first-principles computational methods are used to study the mechanism of action of RE elements in steel, and proposes measures and methods to address these challenges, aiming to provide an in-depth understanding of the mechanism of action of REs in steel at the microscopic level and to promote the application of computational chemistry in the field of metallurgy.

1. Introduction

The Baiyun Ebo mine in the Inner Mongolia Autonomous Region in northern China is rich in rare earth (RE) elements such as neodymium (Nd) and samarium (Sm), which are widely used in electronics and machinery [1,2]. However, light REs such as lanthanum (La) and cerium (Ce) are chronically oversupplied due to imbalanced utilization across industries. In recent years, researchers have begun to explore the addition of lanthanum-cerium to steel to improve its performance index [3,4,5]. RE steels have gradually become a research hotspot in the field of iron and steel metallurgy due to their excellent performance and wide application prospects.

Studies have shown that the role of lanthanum-cerium RE elements in steel mechanism is mainly reflected in two aspects. Firstly, adding REs to steel modifies the original inclusions, creating fine, diffuse RE inclusions. Secondly, it is solidly dissolved in steel in the form of atoms, exerting the microalloying effect and thus enhancing the properties of steel [6,7,8,9,10,11]. Although experimental studies have made significant progress in characterizing the macroscopic properties of RE steels, the traditional experimental methods are not ideal for investigating the microscopic behaviors and intrinsic mechanisms of RE elements in steels due to the overly microscopic and complex processes of RE atoms acting in steels [12,13]. For example, for the phenomenon that RE elements can enhance the impact properties of steel, the study of Song et al. [14] demonstrated that the addition of 0.021% of RE elements significantly improves the impact properties of C-Mn steel. However, Gao et al. [15] found that increasing the RE element content from 0.015% to 0.025% will reduce the impact toughness of high-alloy Cr-Mo-V steel. The first-principles calculations can explain this phenomenon well from the perspective of solution enthalpies. Cr atoms increase the solution enthalpy of Ce in steel, reducing the solid solution of Ce in steel, which in turn reduces the RE microalloying effect [16,17]. It is necessary to clarify the underlying mechanism of the action of RE elements in steel at the microscopic scale.

With the advancement of modern physical chemistry and computational science, an increasing number of simulation methods have been widely applied in the study of material micro-mechanisms, for example, molecular dynamics (MD), Monte Carlo (MC), phase field methods, and first-principles calculations based on density functional theory (DFT) [10,18,19,20]. MD can simulate dynamic processes and diffusion behavior at the atomic scale. The MC method is applicable for studying thermodynamic equilibrium and atomic arrangement. Phase field methods are commonly used to simulate microstructural evolution and phase transformation processes. The first-principles calculations, based on the fundamental laws of quantum mechanics, can precisely determine a material’s electronic structure, mechanical properties, and chemical reaction mechanisms without requiring empirical parameters. As a highly precise computational method, first-principles calculations can provide key physical parameters for material properties. Therefore, they demonstrate unique advantages in investigating the atomic-scale mechanisms of RE elements in steel. First-principles calculations enable researchers to characterize and analyze the structure and properties of target substances using parameters such as formation energy, electronic work function, lattice constant, interface adsorption energy, and electron density [21,22,23]. By calculating the changes in the system structure and chemical bonding, first principles is able to explain the behavior of REs in steel at the microscopic level [24].

Firstly, this paper summarizes the process of characterizing and calculating the properties of substances by the first-principles calculation method as well as its application in the research of RE-containing steels. Secondly, the progress of research on first-principles calculations for the two main existing forms of REs after their incorporation into steel is summarized. For RE inclusions, this paper summarizes their nucleation behavior, intrinsic properties, and mechanism of action on the mechanical properties of steel. For RE atoms, it summarizes their solid solution sites, microalloying mechanisms, and interaction mechanisms with other alloying atoms. Finally, this paper clarifies the limitations of applying first-principles calculations to the study of RE-containing steels and presents an outlook for future research directions. This study contributes to advancing the application of computational chemistry in the field of metallurgy, deepens the microscopic understanding of the role of RE elements in steel, and provides guidance for the development of high-performance RE-containing steels.

2. Overview of First Principles

First principles considers that multiple electrons and multiple nuclei together make up the whole system, the theoretical basis of which is quantum mechanics [25]. After some approximation, first principles investigates the properties of substances by solving the Schrodinger Equation. At the heart of first-principles calculations are calculations of atomic structure. Currently, commonly used computational software mainly includes the CASTEP [26] module of Materials Studio, VASP [27], Gaussian [28], Siesta [29], CP2K [30], Wien2K [31], etc. Commonly used software in metallurgy is CASTEP and VASP. Figure 1 summarizes the steps of first-principles calculations of properties of substances. It can be found that first principles predicts the properties of substances by performing calculations such as electronic structures and related parameters based on a structurally optimized model.

The application of first-principles calculations to RE steels focuses on calculations of the properties of RE inclusions and the microalloying mechanism of RE atoms.

Table 1. Summary of research on first-principles calculations for RE steels.

Element	Software	Research Content	Refs.
Ce	VASP	Calculation of surface energy, solvation energy, adsorption energy, electronic structure and work function of Fe-Ce surface model to study the effect of Ce on the corrosion of steel	[22]
Ce	VASP	Calculation of formation energies, elastic constants and coefficients of thermal expansion of Ce2O3, CeAlO3, Ce2O2S, and study of their basic physical properties	[32]
Ce	VASP	Calculation of the electronic structure and elastic constants of the Fe-Ce system and study of the effect of solid solution RE atoms on the mechanical properties of steels	[24,33]
Ce	VASP	Calculation of the solution enthalpies of Ce atoms in iron, segregation energy at grain boundaries (GBs), and interaction of REs with vacancies in iron to study the segregation behavior of RE atoms	[5]
Ce	VASP	Calculating the work function of La2O2S to study the mechanism of RE inclusion-induced corrosion	[34]
Ce	DMol3	Study of the thermodynamic properties and nucleation mechanism of Ce2O3	[35]
Ce	VASP	Calculation of the electronic structure of the Fe-Ce-Cr system and study of the interaction of solid solution RE atoms with Cr atoms	[16,17]
La	CASTEP	Calculated interaction energies of La atoms with C and N atoms to study the mechanism of RE nitriding and carburizing on iron-based alloys	[36]
La	CASTEP	Calculation of the elastic modulus, Poisson’s ratio and anisotropy of the system when La atoms are in different sites of γ-Fe, and study of the solid solution strengthening mechanism and diffusion behavior of RE atoms	[20]
La	VASP	Calculation of work functions of La2O3, LaAlO3, La2O2S and Fe to study the corrosion tendency of RE inclusions	[37,38]
La	CASTEP	Calculation of formation energies and elastic constants of La2O3, La2O2S and LaAlO3, and study of their basic physical properties	[39]
Ce, La	WIEN2k	Calculation of lattice constants, ground state energies, electromagnetism and resistivity of the La/CeFe2 system, and study of the structural, electronic, magnetic and elastic properties of the La/CeFe2	[40]
Ce, La	VASP	Calculation of surface energies and adsorption energies of C and N atoms in the system before and after doping with RE Ce and La, and study of the effect of solid solution RE atoms on the diffusion of C and N atoms	[41]
Ce, La	CASTEP	Calculation of the electronic structures, interfacial ideal adhesion work and interfacial energies of ReAlO3(100)/γ-Fe(100) to study the conditions under which RE inclusions act as heterogeneous nucleation sites for γ-Fe	[42]
Ce, La, Y	VASP	Calculation of vacancy binding energies, migration energies, pre-factors, and activation energies for Y, La, and Ce to study the diffusivity of RE atoms in bcc-Fe	[43]

summarizes the application of first-principles calculation to RE steels.

It is noteworthy that the valence state of cerium (Ce) can significantly influence its thermodynamic and electronic properties. Ce commonly exists in two stable oxidation states, Ce³⁺ and Ce⁴⁺, which exhibit distinct electronic structures and formation energies. This valence dependency must be carefully considered in first-principles calculations, particularly when evaluating Gibbs free energy, formation enthalpies, and electronic properties of cerium-containing compounds. Proper treatment of Ce valence is essential for accurate predictions of its behavior in steel, including inclusion stability and microalloying effects.

3. Behavior of RE Inclusions in Steel

As the first substances formed after the addition of RE elements to steel, understanding the behavior of inclusions in steel is essential for the efficient use of RE elements [44,45]. Therefore, this section summarizes the nucleation, formation rules, properties and effects of RE inclusions on steel properties.

3.1. Nucleation of RE Inclusions

The nucleation of RE inclusions is essential to study the fundamental properties of such inclusions [46]. Currently, the in-situ observation of inclusion collisions and phase transitions is mainly realized by high-temperature confocal scanning laser microscopy (CSLM), and the nucleation of inclusions is investigated with the support of classical nucleation theory [47,48,49,50]. However, the intrinsic nucleation mechanism of RE inclusions is difficult to observe directly due to the rapid nucleation process and the high-temperature environment in which it occurs. The first-principles calculations based on DFT become an effective tool for studying the inclusions nucleation [51,52,53,54].

When added to steel, RE elements first react with oxygen to form RE oxides. Li et al. [35] constructed (CeO₂)_n and (Ce₂O₃)_n (n = 1–6) clusters, calculated the nucleation behavior of RE oxides using the first-principles approach, and evaluated the stability of the formed substances via Gibbs free energy. The Gibbs free energy is calculated using the following equation.

$$\mathrm{G}=\mathrm{H}-\mathrm{TS}+\mathrm{E}(0\mathrm{K})$$

(1)

where H is enthalpy, T is absolute temperature, S is entropy, and E(0 K) is the total energy at 0 K.

Figure 2a shows the Gibbs free energy changes of these clusters, nanoparticles and bulk materials at 1873 K. The valence state of cerium plays a crucial role in the nucleation process. CeO₂ inclusions contain Ce⁴⁺, while Ce₂O₃ inclusions contain Ce³⁺. The different valence states of cerium influence the Gibbs free energy and stability of cerium oxides, thereby affecting nucleation pathways and inclusion morphology. The Gibbs free energy of Ce₂O₃ is more negative at high temperatures, indicating that the RE oxide that exists stably in this state is Ce₂O₃ rather than CeO₂. Based on the two-step nucleation theory, the nucleation process of Ce oxides is summarized in Figure 2b: [Ce] + [O] → (CeO₂)_n/(Ce₂O₃)_n → (Ce₂O₃)_n → (Ce₂O₃)₂ → core(Ce₂O₃ crystal)–shell((Ce₂O₃)₂ cluster) nanoparticles → (Ce₂O₃)bulk. This study reveals the nucleation mechanism of RE oxides at multiple scales, including atomic, molecular, cluster and nanoparticle, and provides a theoretical basis for the nucleation behavior of RE inclusions.

The first-principles calculations provide new insights into the nucleation behavior of RE inclusions. However, the nucleation pathways of La oxides at the atomic scale have not yet been fully established through first-principles calculations. Future research should focus on clarifying the nucleation mechanisms of La-based inclusions to more comprehensively supplement current studies.

3.2. Properties of RE Inclusions

3.2.1. Formation Rule of RE Inclusions

Understanding the formation mechanism of inclusions facilitates more effective control over their generation. First principles can evaluate the formation capability of inclusions from an energetic perspective by calculating their formation enthalpy. A negative value of the formation enthalpy indicates that the inclusion can be generated stably, and the more negative the value is, the more stable the inclusions are. The formation enthalpy can be calculated using the following equation [55]:

$${∆}_{\mathrm{r}}{\mathrm{H}}_{\mathrm{m}}={\displaystyle \frac{1}{\mathrm{n}}}({\mathrm{E}}_{\mathrm{tot}}-{\mathrm{E}}_{\mathrm{bluk}})$$

(2)

where ${∆}_{\mathrm{r}}{\mathrm{H}}_{\mathrm{m}}$ is the formation enthalpy, ${\mathrm{E}}_{\mathrm{tot}}$ is the total cell energy, ${\mathrm{E}}_{\mathrm{bluk}}$ is the total energy of the atoms that constitute the crystal in the ground state, and n is the number of atoms.

Differences in the chemical bonding properties and crystal structure of the RE inclusions result in notable differences in their formation enthalpies. Figure 3 summarizes the results of formation enthalpy calculations for common RE inclusions. Although different calculation parameters (e.g., LDA or GGA approximation, k-point, etc.) may cause minor differences in the results, a comprehensive analysis shows that the rule of inclusions formation remains stable. The formation of inclusions presents the following sequence: Re₂O₃ > ReAlO₃ > Re₂O₂S > ReS_x. Studies have shown that when REs are added to steel, inclusions evolve in the order of oxides, oxysulfides, and sulfides.

3.2.2. Mechanical Properties of RE Inclusions

First principles can predict the mechanical properties of RE inclusions by establishing correlations between crystal information and mechanical property parameters such as bulk modulus (B), shear modulus (G), Young’s modulus (E), and Poisson’s ratio (ν), and by the Viogt–Reuss–Hill (VRH) approximation [59,60,61]. The formulas are given in Equations (3)–(6).

$$\mathrm{B}={\displaystyle \frac{1}{2}}({\mathrm{B}}_{\mathrm{V}}+{\mathrm{B}}_{\mathrm{R}})$$

(3)

$$\mathrm{G}={\displaystyle \frac{1}{2}}({\mathrm{G}}_{\mathrm{V}}+{\mathrm{G}}_{\mathrm{R}})$$

(4)

$$\mathrm{E}={\displaystyle \frac{9\mathrm{B}\mathrm{G}}{3\mathrm{B}+\mathrm{G}}}$$

(5)

$$\mathrm{v}={\displaystyle \frac{3\mathrm{B}-2\mathrm{G}}{2(3\mathrm{B}+\mathrm{G})}}$$

(6)

where ${\mathrm{B}}_{\mathrm{V}}$ and ${\mathrm{G}}_{\mathrm{V}}$ are the Voigt bulk and shear moduli, GPa, respectively. ${\mathrm{B}}_{\mathrm{R}}$ and ${\mathrm{G}}_{\mathrm{R}}$ are the Reuss bulk and shear moduli, GPa, respectively. Figure 4 summarizes the mechanical properties of various RE inclusions, including B, G, E and ν, as calculated by multiple researchers.

The results indicate significant variations in mechanical properties among different RE inclusions, which can be attributed to differences in their crystal structures and chemical bonding characteristics. Notably, ReAlO₃ exhibits higher values of B, G, and E compared to other RE inclusions and pure Fe, suggesting stronger interatomic bonding and greater resistance to deformation and fracture. This makes ReAlO₃ particularly effective in enhancing the mechanical performance of steel matrices. In contrast, Re₂O₃, Re₂O₂S, and ReS show mechanical properties comparable to or lower than those of Fe, indicating similar or weaker bonding strengths. In addition, Poisson’s ratio indicates the strength of covalent bonds and can be used to predict the ductility and brittleness of a material, with larger values being associated with better toughness [67,68]. When Poisson’s ratio is greater than 0.26, the material exhibits toughness [32]. By further comparing the Poisson’s ratio values of the inclusions, it can be found that the Fe, Re₂O₃, Re₂O₂S and ReS belong to the ductile materials, while the other RE inclusions exhibit brittle characteristics. This distinction is crucial for understanding how RE inclusions influence the toughness and fracture behavior of steel.

In addition to the intrinsic mechanical properties of RE inclusions, their role in dispersion hardening should also be considered. Fine and dispersed RE inclusions such as Re₂O₃, ReAlO₃, and Re₂O₂S can act as effective barriers to dislocation motion, thereby enhancing the strength of steel through the Orowan mechanism [8,69]. This dispersion hardening effect is particularly significant when the inclusions are nanoscale and uniformly distributed, which is often achieved through controlled RE addition and processing conditions. Future studies combining first-principles calculations with dislocation dynamics simulations could provide deeper insights into the interaction between dislocations and RE inclusions at the atomic scale.

3.3. Effect of RE Inclusions on Steel Properties

3.3.1. Corrosion Behavior of RE Inclusions

The electronic work function has been widely used in investigating the corrosion behavior of inclusions and steel matrices, and preliminary findings have been achieved [69,70,71]. Lower values of the electronic work function indicate that the surface electrons of the inclusions are more likely to escape, thus creating an environment at the interface between the inclusions and the corrosion medium where electron transfer is more likely to occur. This condition facilitates corrosion reactions, which in turn enhances the probability of inclusion-induced corrosion initiation [72]. The formula for the electronic work function is given in Equation (7):

$$\mathrm{W}={\mathrm{E}}_{\mathrm{V}}-{\mathrm{E}}_{\mathrm{F}}$$

(7)

where W is the electronic work function, eV; E_V is the electrostatic potential energy of the material, eV; and E_F is the Fermi energy inside the material, eV.

Corrosion usually occurs at the surface of a given crystal [72]. Therefore, when using the electronic work function to investigate inclusion-induced corrosion, the primary step is to identify the specific surface where corrosion occurs. The three low-index crystal surfaces commonly used in such calculations are the (100), (110), and (111) surfaces, respectively [37,38,73]. Current methods for determining the electronic work function of corrosion are mainly based on comparing the average work function of two selected crystalline surfaces with lower surface energies or the average work function of all selected crystalline surfaces [37,73].

For La-containing inclusions, Wei et al. [73] compared the average work function of La₂O₂S and Fe and found that the theoretical corrosion tendency of La₂O₂S was higher than that of Fe. Zhang et al. [38] further investigated the work function of La₂O₂S, LaAlO₃ and Fe, and the results showed that the corrosion tendency of LaAlO₃ is between La₂O₂S and Fe. Figure 5a shows the planar model of LaAlO₃. Tang et al. [37] calculated the corrosion tendency of sulfides (oxysulfides) and oxides of La and found that sulfides (oxysulfides) are more prone to corrosion. For the theoretical corrosion tendency of Ce-containing inclusions, the average work function order of inclusions calculated by Liu et al. [56] was CeAlO₃ > Fe > CeS > Ce₂O₂S > Ce₂O₃. The results indicated that Ce₂O₃ exhibited the highest probability of inducing corrosion, whereas CeAlO₃ could effectively enhance the corrosion resistance of steel. Figure 5b presents the planar view model of Ce₂O₂S.

First principles can also provide new insights into the conductive properties of such inclusions by calculating their energy band structures [19]. Conductivity determines how inclusions participate in electrochemical reactions. Hou et al. [74] investigated the properties of the RE inclusions LaAlO₃ and La₂O₂S in terms of their energy band structures, as shown in Figure 6. The results show that LaAlO₃ belongs to the class of insulator materials, while La₂O₂S belongs to the class of typical semiconductor materials. This indicates that La₂O₂S participates in corrosion by achieving effective electron transfer, while LaAlO₃ resists corrosion.

First-principles calculation of the electronic work function of inclusions can reveal the nature of the corrosion process in depth from the atomic and electronic levels, thereby providing an important theoretical basis for understanding the corrosion mechanism and predicting the corrosion behavior.

3.3.2. Performance of RE Inclusions on Grain Refinement

RE inclusions can act as effective heterogeneous nucleation cores for ferrite or austenite, thereby refining grains [75,76,77,78,79,80]. However, visualization of the nucleation process is very difficult due to technical limitations of the experiments. First-principles calculations offer new insights into the investigation of heterogeneous nucleation between RE inclusions and matrix phases.

Jiao et al. [81] used a 2D lattice mismatch model to demonstrate that the lattice mismatch between CeO₂(111)/γ-Fe(100) satisfies the crystallographic conditions for effective heterogeneous nucleation, and calculations further showed that the O1-Fe structure was preferentially formed at the initial stage of nucleation and that the highest interfacial bond strength was the O2-Fe structure under the same conditions. This demonstrates at the atomic level that CeO₂ can form a stable interfacial structure with γ-Fe and act as an effective heterogeneous nucleation core to refine austenite grains. Using the same approach, Zhou et al. [82] demonstrated that La₂O₂S does not serve as an effective heterogeneous nucleation core for γ-Fe. Yang et al. [42] calculated the charge density and charge density difference at the ReAlO₃(100)/γ-Fe(100) interface as shown in Figure 7. The blue areas indicate that the corresponding atoms have lost charge, while the red areas indicate that the corresponding atoms have gained charge during the interface formation process. The results show that more charge is transferred from Fe atoms to O atoms at the AlO₂-terminated structure interface than at the ReO-terminated structure. It is demonstrated that the AlO₂-terminated interface exhibits higher stability compared to the ReO-terminated interface. It is further shown that ReAlO₃ can act as a γ-Fe heterogeneous nucleation core under the following conditions: the chemical potential of La ranges from −11.59 eV to −11.22 eV or −1.94 eV to −1.56 eV, and the chemical potential of Ce ranges from −6.27 eV to −5.97 eV. In response to the question of whether RE inclusions can serve as the core of ferrite heterogeneous nucleation, calculations by Yang et al. [83] show that LaAlO₃ (100) can serve as an effective heterogeneous nucleation core for ferrite (100 and 110) when the terminal interface is LaO and the chemical potentials of La are −2.447 eV and −1.009 eV, respectively.

Jiao et al. [84] demonstrated that the interaction force between the interfacial structure formed by La₂O₃ (001) and γ-Fe (110) is mainly repulsive from the point of view of the interaction force between the interfaces. This inhibited the expansion of γ-Fe grain surfaces at the interface, which led to the refinement of austenite grains.

RE inclusions can provide a heterogeneous nucleation core by forming a stable interfacial structure with ferrite or austenite, thus refining the grain. The chemical bonding and electronic interactions at the interface are the key factors affecting their nucleation efficiency. Future research could improve the accuracy of the prediction of the effect of RE inclusions on grain refinement by taking crystal defects, etc., into account.

4. Behavior of Solid Solution RE Atoms

During solidification, segregation of RE atoms occurs at GBs and exerts a microalloying effect. Currently, more advanced techniques have been used to characterize the atomic positions of REs, such as the three-dimensional atom probe (3DAP) [85], electron probe microanalysis (EPMA) [86] and secondary ion mass spectrometry (SIMS) [87]. These characterization results confirm significant segregation of RE elements at grain and phase boundaries. Liu et al. [88] demonstrated the clustering behavior of RE atoms at the dendritic interface by controlling the conditions of the CSLM in-situ experiments and combining them with the elemental distribution of EPMA. The results of the experiment are shown in Figure 8. However, due to the limitations of the characterization techniques, the extremely low solid solubility of REs and the high cost of the experiments, the mechanism of RE action at the microscopic level is difficult to be explained experimentally.

First-principles calculations provide an efficient method for characterizing the location of the presence of RE atoms. This section summarizes the first-principles calculations of the behavior of RE atoms in steel, and systematically analyzes the location of RE atoms in steel, microalloying mechanisms and interactions with other atoms. The aim is to provide a micro-level explanation of the mechanism of action of RE elements in steel.

4.1. Solid Solution Positions of RE Atoms

By calculating the solvation energies of RE atoms at different positions by first principles, the position of their solid solution in steel can be determined. Negative solvation energy indicates a stable system, and the larger the absolute value, the higher the stability [89,90]. The foreign atoms mainly occupy O-point positions (octahedral positions), T-point positions (tetrahedral positions) and S-point positions (substitution positions). Figure 9 shows a schematic diagram of the possible positions occupied by RE atoms in γ-Fe and α-Fe.

You et al. [91] showed that La preferentially occupies the S site in α-Fe, as the relaxation of Fe atoms in the structure is minimal when La atoms substitute for Fe atoms. The results of Fan et al. [20] showed that La can be stabilized at all three sites of γ-Fe and the order of stability is S > O > T. Liu et al. [24,33,92] further demonstrated the stability of Ce solid solution in α-Fe and γ-Fe at the S-point position and pointed out that the fundamental reason for the solid solution of RE elements in steel lies in their electron release and polarization effects in the Fe matrix. Specifically, in the Ce doping system, Ce triggers polarization by releasing electrons, leading to a reduction in atomic radius and thus facilitating its solid solution in steel. On this basis, Yang et al. [41] further showed that RE atoms are more inclined to displace surface S sites on the surface and subsurface of α-Fe (100).

4.2. Segregation of RE Atoms

The large radii of the RE atoms lead to significant lattice distortions and elevated supercell energies when replacing Fe matrix atoms. In contrast, RE atoms are more likely to segregate at GBs and dislocations, thus enhancing GB cohesion [93,94,95]. The first-principles approach provides theoretical support for solid solution atomic segregation phenomena by studying the interaction of liquid metal solutes with GBs and free surfaces at the atomic level [96,97]. Wang et al. [98] demonstrated that La atom doping led to a significant reduction in electron density within the GB region and a transition in bonding mode from metallic to ionic, which in turn stabilized the GBs. Li et al. [5] revealed that the vacancy of Fe energetically favors the formation of RE nanoclusters, as seen in Figure 10, which indicates that the presence of an Fe monovacancy can at most help stabilize a local nanocluster composed of 14 RE atoms.

First-principles calculations can provide a theoretical basis for segregation of RE elements from an energetic perspective by calculating GB energies [99]. Liu et al. [88] showed that the enthalpy of solid solution of Ce at α-FeΣ5(310) [001] GBs is negative and the GB energy is significantly reduced by RE doping. This proves that Ce can be stabilized in the GB region and enhance the GB stability. Chen et al. [100] further showed that La and Ce atoms stabilize the GBs by bonding with Fe atoms at the Σ5(310) [001] GBs, and that the stability of GB segregation of La is better than that of Ce. Results from first-principles calculations show that the dendritic interface in steel is capable of efficiently capturing RE elements, thereby overcoming the limitations of traditional characterization techniques for analyzing the distribution of RE atoms.

4.3. Mechanism of Microalloying of RE Atoms

Solid solution RE atoms have a significant effect on the electronic structure of the Fe matrix. Wang et al. [101] analyzed the projected density of states (PDOS) of RE atoms and their first-nearest-neighbor Fe atoms, as shown in Figure 11. The d- and f-orbitals of RE atoms in solid solution undergo significant hybridization with the d-orbitals of neighboring Fe atoms. This hybridization alters the density of states (DOS) distribution of Fe and reduces the difference between the number of spin-up and spin-down electrons, thereby leading to a decrease in the magnetic moment of the system. In addition, Liu et al. [24,33] found that Ce atoms increased the electron cloud density of the α-Fe and γ-Fe systems while decreasing the metal bond strength of the systems. This reduces the incompressibility and rigidity of the system and improves the toughness of the system.

Microalloying with RE atoms has the property of increasing the corrosion resistance of steel. Liu et al. [22] calculated the adsorption energies and the binding energies between the surface and inner layers of the systems doped with Ce atoms on the surface and subsurface of α-Fe (100) with different Cl-atom coverages by first principles. Figure 12 shows the optimum structure of Ce doped on the surface and subsurface of Fe (100) with different concentrations of Cl atoms and the calculation of each system parameter. Studies have shown that Ce doping on the Fe surface is beneficial for preventing the detachment of Fe atoms, while Ce doping on the subsurface increases the binding strength of Fe atoms between the surface and inner layers. This finding indicates that Ce atoms enhance the corrosion resistance of the system by strengthening both interfacial bonding and electron localization.

4.4. Interactions of RE Atoms with Other Atoms

Due to their unique electronic structure and large atomic radii, RE atoms in solid solution induce the transfer of electrons, the formation and breaking of chemical bonds, and the emergence of antibonding states within the system; these processes in turn interact with other atoms in the steel. Studies by Li et al. [17] and Shi et al. [16] showed that Ce atoms provide electrons to Fe atoms in γ-Fe and α-Fe, which enhances the Fe-Cr interactions and thus promotes the solid solution of Cr atoms in steel. You et al. [91,102] revealed the interactions between La atoms solidly dissolved in α-Fe and other alloy atoms from the point of view of interaction energies and chemical bonding characteristics. The interaction between La and Cu atoms is attractive, Co and Ni have almost no interaction with La atoms, and the interaction with C, N, Al, Si, Ti, V, Cr, Mn, Nb and Mo atoms is repulsive. Solid solution La or Ce atoms increase the adsorption capacity and diffusion rate of C and N atoms on the Fe surface by providing electrons to the system, which in turn increases the surface C/N concentration [36,41,91,103].

First-principles calculations have broken through the limitations of traditional characterization techniques and thus can provide theoretical support for the behavior of solid solution RE atoms at the microscopic level. First-principles calculations in the future should be combined with multi-scale models such as molecular dynamics and experimental verification to take into account a more realistic system environment and reveal the behavior of RE atoms in steel more comprehensively [104].

5. Conclusions and Outlook

In this paper, the mechanism of RE elements in steels is reviewed based on DFT, including the nucleation mechanism, properties, and effects of RE inclusions on steel properties, as well as the positions, microalloying, and interactions of solid solution RE atoms with other atoms. Specific conclusions are as follows:

• The nucleation process of RE oxides involves the gradual evolution of RE elements combined with O to form crystals, nanoparticles and final phases. The formation of RE inclusions is prioritized as Re₂O₃ > ReAlO₃ > Re₂O₂S > ReS_x.
• The theoretical corrosion tendency of RE inclusions is associated with the system composition. Lanthanum-containing inclusions show the following order: LaS > La₂O₂S > LaAlO₃ > Fe, and the theoretical corrosion tendency of cerium-containing inclusions is Ce₂O₃ > Ce₂O₂S > CeS > Fe > CeAlO₃.
• Mechanical property analysis shows that ReAlO₃ significantly enhances the deformation and fracture resistance of steel. Re₂O₃, Re₂O₂S and ReS behaved as ductile materials, while other RE inclusions behaved as brittle.
• Studies on the effect of RE inclusions on the heterogeneous nucleation of γ-Fe and α-Fe indicate that CeO₂ and La₂O₃ can act as heterogeneous nucleation cores for γ-Fe, whereas La₂O₂S cannot, and ReAlO₃ can act as a γ-Fe heterogeneous nucleation under the following conditions: the chemical potential of La ranges from −11.59 eV to −11.22 eV or −1.94 eV to −1.56 eV, and the chemical potential of Ce ranges from −6.27 eV to −5.97 eV. LaAlO₃ can act as an α-Fe nucleation core at La chemical potentials of −2.447 eV and −1.009 eV.
• RE atoms tend to occupy S-point sites in the Fe matrix and segregate at GBs or vacancies, where up to 14 RE atoms can be stabilized at the vacancies. The interaction of RE atoms with other alloying elements in steel promotes or inhibits their solid solution behavior.

The first-principles insights summarized in this paper can be translated into practical strategies for designing high-performance RE steels. The results obtained from the first-principles calculations regarding the formation sequence and properties of RE inclusions can be used to guide the determination of optimal RE element addition levels. This enables the development of RE steels with the most favorable performance characteristics for different application scenarios, such as those requiring high toughness or high corrosion resistance. First-principles calculations reveal the interfacial structure of rare-earth inclusions and the interactions between RE elements and other atoms. This not only provides a theoretical basis for guiding the controlled formation of inclusions to achieve grain refinement but also offers design guidance for optimizing the alloying effects of other elements in steel. However, the behavior of RE elements in steel involves multiscale processes from the atomic scale to the macroscopic scale. Therefore, more in-depth studies are needed on the coupling relationship between multiple scales and the mechanism influencing the macroscopic performance.