The densities of the light metals, Mg and Al, which have close-packed structures ^[1][2].[1,2], Their densities are about one-fifth and one-third of that of iron, respectively. Moreover, Mg and Al metals have unique properties, such as high specific strengths and excellent castability. Thus, Mg and Al alloys have been widely used in a variety of engineering fields, particularly in the automotive and aerospace industries ^[3][4][3,4]. The current regulations on environmental protection demand further improvements in the chemical and mechanical properties of light alloys. One important approach is to achieve solidified products of fine and uniform microstructures by controlling the solidification processes ^[5][6][7][5,6,7].

The conventional way to obtain a fine and uniform microstructure of cast alloys is via the addition of grain refiners during casting ^[4][7][4,7]. The added chemicals remain in the cast parts, which may hinder the recycling of the products. Recently, Fan and co-workers developed a new approach to grain refinement using native oxide particles as nucleation sites [6]. This approach is helpful not only for obtaining cast parts of increased integrity, improved mechanical properties, and reduced casting costs but also for facilitating metal recycling. Meanwhile, the application of this approach for casting alloys of desirable microstructure and properties demands knowledge about the atomic ordering at the interfaces between the liquid metals and the oxide substrates.

There have been both experimental and theoretical efforts to obtain insight into the formation, polymorphs, and morphologies of oxide particles and atomic arrangements at liquid–metal/oxide (noted as M(l)/oxide) interfaces. Here, reswearchers provide an overview of the recent advances in the understanding of prenucleation at the M(l)/oxide interfaces using ab initio molecular dynamics (AIMD) techniques.

A pseudo-potential plane-wave approach based on the density-functional theory (DFT) was used for the present study. This approach was implanted into the first-principles code VASP (Vienna ab initio simulation package) ^[8][65]. VASP permits variable fractional occupation numbers, which worksing well for insulating/metallic interfaces ^[8][9][65,66]. The molecular dynamics simulation uses the finite-temperature density functional theory of one-electron states, the exact energy minimization and calculation of the exact Hellmann-Feynman forces after each MD step using the preconditioned conjugate techniques, and the Nosé dynamics for generating a canonical NVT ensemble. The Gaussian smearing was employed with the width of smearing (0.1 eV). The code also utilizes the projector augmented-wave (PAW) method ^[10][67] within the generalized gradient approximation ^[11][68]. The electronic configurations used are Mg ([Ne] 3s² 3p⁰), Al ([Ne] 3s² 3p¹) and O ([He] 2s² 2p⁴). 

For electronic structure calculations, reswearchers used cut-off energies of 400.0 eV for the wave functions and 550.0 eV for the augmentation functions. Reasonably dense k-meshes were used for sampling the electronic wave functions, e.g., a 2 × 2 × 1 (8 k-points) in the Brillouin zone (BZ) of the supercell of the interfaces, based on the Monkhorst-Pack scheme ^[12][69]. For the AIMD simulations of the interfaces, rwesearchers employed cut-off energy of 320 eV and the Γ-point in the BZ, considering the lack of periodicity of the whole system in molecule/solid-substrate and liquid/solid interfaces ^{[9][13][14][15][16]}[66,70,71,72,73]. Test simulations using different cut-off energies demonstrated that the settings are reasonable.

ThWe researchers prepared liquid Al or Mg samples by equilibrating at 3000 K for 2000 steps (1.5 fs per step). Then the obtained liquid was cooled to the desired temperature. researchersWe used the obtained liquid Al or Mg samples together with the oxide substrates for building the M(l)/oxide simulation systems. resWearchers employed two different approaches in the AIMD simulation depending on the systems. Full relaxation of atoms is used all the time. The other adopted a two-step approach: researchersWe first performed AIMD simulations with the substrate O atoms pinned for about 2 ps (1.5 ps per step). Then, researcherswe equilibrated the systems further with full relaxation of the substrate atoms for another 4000 to 7000 steps. The time-averaged method was used to sample the interfaces over 3.0 to 4.5 ps to ensure statistically meaningful results ^[9][13][66,70].

ThWe researchers first discuss the atomic evolutions at the M(l)/oxide interfaces using the Al(l)/Al₂O₃ interfaces at 1000 K as an example. During simulations, rwesearchers observed that the liquid Al atoms move quickly to the oxide substrates, forming a terminating layer. The number of atoms in this newly formed metal layer becomes gradually stabilized, forming a new substrate surface within 2 ps. Then, the atoms/ions in the oxide substrates vibrate around their equilibrium positions, while the liquid metal atoms away from the interfaces move around freely. The simulations revealed that the behavior of liquid atoms near the substrates varies depending on the nature of the substrate surfaces.

The terminating Al layers at the Al(l)/γ-Al₂O₃{1 1 1}_{Al_2} interface are flat and contain vacancies. The terminating Al layers at the Al(l)/γ-Al₂O₃{1 1 1}_{Al_1} and Al(l)/α-Al₂O₃{0 0 0 1} interfaces contain both vacancies and displacements along the direction perpendicular to the substrates. Analysis showed that there is moderate atomic ordering in the first Al layer but little in the second Al layer in the Al(l)/γ-Al₂O₃{1 1 1}_{Al_2} interface. At the Al(l)/γ-Al₂O₃{1 1 1}_{Al_1} and Al(l)/α-Al₂O₃{0 0 0 1} interfaces even the first Al layer has little atomic ordering.

There are apparent holes at the termination layers of the Al(l)/γ-Al₂O₃{1 1 1} systems. The occupation of the octahedral sites in the terminating layers was analyzed using the time-averaged atomic positions over 3 ps: The occupation rate at the terminating layer by Al is 54.0% in the Al(l)/γ-Al₂O₃{1 1 1}_{Al_1} system and 58.1% in the Al(l)/γ-Al₂O₃{1 1 1}_{Al_2} system. These values are lower than that in the bulk alumina (66.7%), but they are comparable with that for the Al(l)/α-Al₂O₃{1 1 1} system (55.9%). These occupation rates of the terminating Al layers are notably lower than those in the Al(l)/MgAl₂O₄{1 1 1} system (70.4 to 75.0%) ^[20][64]. This reflects the role of the crystal chemistry of the substrates. The simulations also revealed structural coupling of the terminating Al layer to the γ-Al₂O₃{1 1 1} substrate: In the Al(l)/γ-Al₂O₃{1 1 1}_{Al_1} system, the multiple-peaked terminating Al layer is coupled to the single peak in the subsurface Al layer, whereas in the Al(l)/γ-Al₂O₃{1 1 1}_{Al_2} system the single-peaked Al terminating layer is accompanied by the multiple-peaked subsurface Al layer in the substrate.

In summary, researchwers have the following conclusions:

(i).

The Al and O atoms/ions in the substrates form layers of atomic ordering;

(ii).

The substrates are terminated by a layer of Al atoms. The terminating Al atoms form a single peak at the Al(l)/γ-Al₂O₃{1 1 1}_{Al_2} interface, whereas they form multiple peaks (three sublayers) at the Al(l)/γ-Al₂O₃{1 1 1}_{Al_1} interface;

(iii).

The Al-O interatomic distances between the terminating Al atoms and the outmost O ions are close to those in the bulk substrate. This indicates that the terminating Al atoms are chemically bonded to the substrates, becoming an integrated part of the substrates;

(iv).

Both layering and in-plane ordering at the Al(l)/γ-Al₂O₃{1 1 1}_{Al_2} interface are more pronounced than that at Al(l)/γ-Al₂O₃{1 1 1}_{Al_1} and Al(l)/α-Al₂O₃{0 0 0 1}.

(v).

There are atomic vacancies in the terminating Al layers.

The O and Al ions in the substrates are charged with −1.3e and +2.0e, respectively. The Al away from the substrates is electronically neutral. The terminating Al atoms are positively charged with electrons transferred to the outmost O ions. Thus, chemically the terminating Al ions/atoms are bonded to the substrates, being the integrated part of the substrates.

In summary, the AIMD simulations revealed an Al layer terminating the Al(l)/Al₂O₃ substrate. The terminating Al atoms are positively charged, chemically bonded to the outmost O ions, thus being an integral part of the substrates. The terminating Al layers contain vacancies and displacements vertical to the substrate surface, resulting in atomic roughness. Consequently, the prenucleation at the Al(l)/Al₂O₃ interfaces is overall weakened, and they are impotent substrates for heterogeneous nucleation of solid Al.

The Mg and O layers in the MgO{1 1 1} substrates are well-ordered and solid-like. This corresponds to the strong chemical bonding in MgO. Although the liquid metal atoms away from the substrates display disordering and behave liquid-like, those near the interfaces exhibit layering. There is a metal layer terminating the MgO{1 1 1} substrates. The terminating Mg atoms at the M(l)/MgO{1 1 1}_Mg form a single peak, whereas the terminating Al atoms at Al(l)/MgO{1 1 1}_Al form a peak and a shoulder at 0.8Å away from the artificial dividing interface. There is an isolated Al layer (the first metal layer) at the Al(l)/MgO{1 1 1}_Mg interface, whereas the first Al layer at the Al(l)/MgO{1 1 1}_Al interface is admixed with the second Al layers.

In the Al(l)/MgO{1 1 1}_Mg system, the terminating Mg layer at the Al(l)/MgO{1 1 1}_Mg interface has a sharp peak in the atomic density profile, and the Al atoms in the first layer display significant ordering. Similarly, the terminating Mg atoms at the Mg(l)/MgO{1 1 1} interface form a sharp peak in the density profile and display strong localization. Meanwhile, there are some unoccupied sites at the terminating layer. Statistics provided the site occupation of 92% ^[21][50]. Comparatively, the terminating Al atoms at the Al(l)/MgO{1 1 1}_Al interface are less localized and contain some disordering. This is reflected in the in-plane ordering coefficients (Figure 10). The in-plane ordering coefficients of the terminating Mg layers at both Mg(l)/MgO{1 1 1} and Al(l)/MgO{1 1 1}_Mg interfaces are close to around 0.6, being significantly larger than that (about 0.2) at the Al(l)/MgO{1 1 1}Al interface.

The present study reveals that the atomic structure and the interfacial interactions are crucial in the determination of the prenucleation at a liquid/solid interface. This also indicates possibilities to control the prenucleation or nucleation potency of the substrates via, e.g., segregating impurity atoms at the interfaces.

TheOur investigation revealed a wide variety of atomic arrangements at the M(l)/oxide interfaces, as exampled in the previous sections. The systematic study revealed the common features of the M(l)/oxide interfaces.

As mentioned previously, Mg and Al have different valence electrons. To keep charge balance, the different valences of Al (3+ in ionic model) and Mg (2+) cause different occupation ration (N_metal/N_O) in the bulk substrate: 100.0% for MgO, 66.7% (2/3) for Al₂O₃ and 75.0% (3/4) for MgAl₂O₄. Such charge balance influences the composition and structure of the terminating metal layer at the M(l)/oxide interfaces. This normalization has been applied to calculate the atomic roughness ^[18][62].

Interface	f(%)	M

l)/oxide interfaces at thermal equilibrium are summarized in Table 1, and the key points from Table 1 are as follows:

• Crystallographically, there is a range of lattice misfit, from moderate (1.4%) to high (7.9%);
• Geometrically, although the terminating M layer may have a single peak in the atomic density profiles, it contains atomic vacancies and/or vertical atomic displacements and, therefore, is atomically rough.
• Chemically, atoms in the terminating M layer are positively charged and are bonded to the substrates, becoming an integral part of the substrates;
• The terminating metal atoms exhibit structural coupling with the metal atoms at the substrate subsurface layer, which influences the prenucleation at the interfaces.

Oc.(%)	R	(%)	q	(e/M)	nLayers	SM(z) 1st LM	Prenucl.
Al(l)/Al{111}Al [22][10]	0.0	SP 100.0	0.0	0.0	6	0.50	Strong
Mg(l)/MgO{111}Mg [21][50]	+7.9	SP, vac. 92.0	4.0	+0.60	3–4	0.01	rWesearchersaak
Al(l)/MgO{111}Mg [17][23][49,63]	−2.2	SP 100	0.0	+0.69	4	0.30	Moderate-strong
Al(l)/MgO{111}Al [17][23][49,63]	−2.2	MP, vac. 73.3	8.2	+0.94	3–4	0.01	rWesearchersak
Al(l)/α-Al2O3{0001}Al [17][49[23],63]	+5.6	MP, vac. 55.9	30.8	+0.95	3	0.01	rWesearchersaak
Al(l)/MgAl2O4{111}Al_2 [20][64]	+1.4	SP, vac. 70.4	5.3	+1.07	3–4	0.18	Moderate
Al(l)/MgAl2O4{111}AlAlAl [20][64]	+1.4	MP, vac. 71.8	18.7	+0.40 to +1.42	3	0.01	rWesearchersaak
Al(l)/MgAl2O4{111}MgAlAl [20][64]	+1.4	MP, vac. 75.0	14.7	+0.44 to +1.17	3	0.05	rWesearchersaak
Al(l)/MgAl2O4{111}MgAlMg [20][64]	+1.4	MP, vac. 75.0	11.2	+0.21 to +1.11	3	0.02	rWesearchersaak
Al(l)/γ-Al2O3{111}Al_2 [18][62]	+3.3	SP, vac. 58.1	11.1	+0.80 to +1.20	3–4	0.03	rWesearchersak
Al(l)/γ-Al2O3{111}Al_1 [18][62]	+3.3	MP, vac. 54.0	31.1	+0.40 to +1.50	3	0.01	rWesearchersaak

The key characteristics of the terminating M layers at the M(

In addition, Table 1 shows that layering at the M(l)/oxide interfaces (n_Layer ≤ 4) is notably weaker than that of the M(l)/M(s) interface ^[22][24][9,10]. For instance, there is a flat and charged Mg terminating layer at the Al(l)/MgO{1 1 1}_Mg interface. It has four recognizable layers, and the in-plane ordering coefficient of the first layer is 0.18 ^[17][23][49,63]. This suggests that the positive charging of the terminating metal atoms influences the ordering of the nearby metal atoms and thus hinders prenucleation at the interfaces.

Clearly, the atomic roughness of the terminating metal layer reduces the in-plane ordering in a more or less linear way with R < 10%. When R > 10%, the in-plane ordering coefficients at the M(l)/oxide interfaces are small.

According to the heterogeneous nucleation theory, potency represents the intrinsic capability of a substrate to nucleate a solid phase in the liquid ^[6][7][25][6,7,15]. The prenucleation at a liquid/solid interface also relates to the intrinsic capability of the substrate to atomic template ordering in the liquid adjacent to the interface and, therefore, corresponds to the potency of the substrate for nucleation of the solid ^[22][24][26][9,10,11]. From Table 1, rwesearchers can rank the M(l)/oxide interfaces in terms of their capability for prenucleation (nucleation potency from high to low): Al(l)/MgO{1 1 1}_Mg > Al(l)/MgAl₂O₄{1 1 1}_{Al_2} > Al(l)/γ-Al₂O₃{1 1 1}_{Al_2} > Mg(l)/MgO{1 1 1}~Al(l)/α-Al₂O₃{0 0 0 1}~Al(l)/γ-Al₂O₃{1 1 1}_{Al_1}.

The prenucleation at Al(l)/MgO{1 1 1}_Mg and Al(l)/MgAl₂O₄{1 1 1}_{Al_2} is more pronounced than that at the other interfaces. This suggests that the atomic roughness of the terminating metal layer hinders prenucleation. This is confirmed by the weak prenucleation at Al(l)/γ-Al₂O₃{1 1 1}_{Al_2} interface, which has a notable lattice misfit and high atomic roughness caused by vacancies.

Heterogeneous nucleation depends on the nucleation potency of substrates or the prenucleation at the M(l)/oxide interfaces. The stronger the prenucleation is, the smaller the driving force it requires.

In order to obtain cast products of fine and uniform microstructures, attention has been paid to the potent particles as potential nucleation sites for grain refinement. The most successful grain-refiners for Al alloys are Al-Ti-B master alloys which contain TiB₂{0 0 0 1} substrates ^{[7][27][28][29][30][31][32][33]}[7,55,56,57,58,59,77,78]. Recently, HR-TEM observations revealed that the TiB₂{0 0 0 1} substrates are covered by a two-dimension compound (2DC), most likely TiAl₃ 2DC ^[31][59]. This 2DC enhances the potency of the TiB₂{0 0 0 1} substrate for Al nucleation. In this case, the size of the TiB₂ particles plays a crucial role in grain initiation ^{[5][7][34][35]}[5,7,16,17]. However, heterogeneous nucleation occurs on the TiB₂ particles of all sizes at the same temperature. When the temperature lowers to the grain initiation temperature, grain initiation starts with the large particles first and gradually occurs at the smaller ones with increasing undercooling. This grain initiation process is considered progressive ^[5][34][5,16], in which only a small number of large-sized particles function as grain-refinement sites.

The oxides are impotent nucleation substrates for Al and Mg alloys. Thus, they require larger nucleation undercooling, which might be lower than that of the corresponding grain initiation temperature if no other more potent particles of significance exist. Under such a situation, when the temperature reaches the nucleation temperature, the nucleation and grain initiation may occur almost simultaneously, in an explosive way ^[5][6][34][5,6,16]. On most of the substrates, grain initiation occurs. This means large fractions of particles become grain-initiation sites, and thus, the cast products may have fine and uniform microstructures.

Experimental observations revealed the formation of different oxide particles in alloys, e.g., coexisting of MgO and MgAl₂O₄ spinel particles in Al-Mg alloys and α- and γ-Al₂O₃ particles in Al-rich alloys. These oxide particles exhibit a wide variety of nucleation potency. Moreover, one type of oxide particle, e.g., γ-Al₂O₃ particles, may have terminating surfaces of different nucleation potency ^[18][62]. In liquid, these oxide particles compete for heterogeneous nucleation, and consequently, only some oxide particles of higher potency may participate in the nucleation process ^[5][34][5,16].

Wang et al. investigated the cast samples of Mg-0.5Ca alloy and observed segregation of impurities, including Ca on the MgO{1 1 1} substrates ^[36][79]. Ma et al. studied the effects of Cu segregation at the sapphire substrate on the nucleation of Al using an AIMD simulation technique ^[37][80]. Recently, Wang et al. observed the segregation of La and Y atoms on Al(l)/γ-Al₂O₃{1 1 1} substrates using the HR-TEM techniques ^[38][81]. To have a better knowledge of the segregation of the nd¹ elements, Sc, Y, and La atoms at the oxide interfaces, reswearchers performed systematic AIMD simulations ^[39][82]. 

The AIMD simulations revealed the formation of a 2DC layer of Al₂La at both Al(l)/γ-Al₂O₃{1 1 1}_{Al_1} and Al(l)/γ-Al₂O₃{1 1 1}_{Al_2} interfaces. The terminating Al/La layers are composed of multiple peaks and thus become atomically rougher as compared with those Al(l)/γ-Al₂O₃{1 1 1} interfaces without segregation. Such surface roughening deteriorates the terminating capability of the Al(l)/γ-Al₂O₃{1 1 1}_{Al_2} interface. Consequently, the nucleation potency of both γ-Al₂O₃{1 1 1}_{(Al/La)_1} and γ-Al₂O₃{1 1 1}_{(Al/La)_2} substrates is reduced.