Interfacial interaction and prenucleation at liquid-Al/γ-Al2O3{1 1 1} interfaces

Alumina (α- and γ-Al2O3) particles are formed in liquid Al-Mg alloys during the liquid dealing and cast processes. These native oxide particles have non-trivial influences on the microstructures and properties of the solidified parts, and may act as potential heterogenous nucleation sites during solidification. At present there is still a lack of understanding about the interaction and atomic arrangements at the interfaces between liquid-Al and γ-Al2O3 substrates. Here we investigate the liquid-Al/γ-Al2O3{1 1 1} interfaces by means of ab initio molecular dynamics simulations and electronic structure calculations. We found that the interfacial interaction at the interfaces leads to formation of an ordered terminating Al layer. This newly formed terminating Al layer is positively charged and chemically bonded to the substrate and thus, becomes part of the substrate. Analysis showed that the terminating Al layer contains vacancies and displacements, being atomically rough. The newly-formed Al layer is also structurally coupled with the substrates. These γ-Al2O3 particles are weak templates for nearby liquid to nucleate. The present study sheds some light on the role of alumina particles in grain refinement of Al-based alloys during solidification processing.

Recent study revealed that the early stage of solidification processes contains several steps [10,11]. The initiating step is prenucleation which refers to the atomic ordering in liquid atoms near a solid substrate at temperatures above the nucleation temperature [10][11][12][13]. The epitaxial nucleation model [14] suggested that heterogeneous nucleation builds on the ordering created by prenucleation and proceeds in a layer-by-layer growth mechanism. The substrate surface provides a structural template to induce atomic ordering in the liquid or prenucleation. Prenucleation provides a precursor at the nucleation temperature for heterogeneous nucleation of the solid phase. Therefore, knowledge about prenucleation at the interfaces between liquid Al and γ-A 2 O 3 {1 1 1} surfaces is crucial to obtain insight into the role of the alumina particles in heterogeneous nucleation during solidification of Al-based alloys.
Chemically, alumina is an ionic compound due to the electronegativity difference between Al (1.61 in Pauling scale) and O (3.44). Crystallographically, αand γ-Al 2 O 3 phases are very different. α-Al 2 O 3 exhibits a trigonal lattice, in which the Al ions are in distorted octahedral coordination of O ions [15,16]. Meanwhile, γ-Al 2 O 3 has a cubic lattice with the Al ions being coordinated both tetragonally and octahedrally by O [17][18][19][20].  [18,20]. Along its [1 1 1] axis, there are two types of Al layers ( figure 1(a)). At the Al2 layer which is below the O1 layer, the Al ions occupy two thirds of the octahedral sites [10]. The Al1 layer below the O2 layer (figure 1(a)) is composed of three sublayers: a sublayer of octahedrally coordinated Al being sandwiched by two tetragonally coordinated Al sublayers ( figure 1(a)). Such rich Al arrangements in the alumina phases shall have impacts on the prenucleation at the interfaces between liquid aluminum and alumina.

Simulation techniques and settings
For the ab initio molecular dynamics simulations and electronic structure calculations, we employed a pseudopotential plane-wave approach based on the density-functional theory (DFT), which was implanted into the code VASP (Vienna ab initio simulation package) [44,45]. This code permits variable fractional occupation numbers, working well for insulating/metallic interfaces [22,24,[39][40][41][42]. 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 [44]. The Gaussian smearing was employed with the width of smearing, SIGMA=0.1eV. The code also utilizes the projector augmented-wave (PAW) method [46] within the generalized gradient approximation [47]. The atomic electronic configurations used are Al ([Ne] 3s 2 3p 1 ) and O ([He] 2s 2 2p 4 ).
For electronic structure calculations, we used cut-off energies of 400.0eV for the wave functions and 550.0 eV for the augmentation functions. The default energies of the potentials are E nmax /E aug =240.3 eV/ 291.1 eV for Al and 400.0eV/605.4eV for O. 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 [48]. For the ab initio MD simulations of the interfaces, we employed a cut-off energy of 320 eV, and the Γ-point in the BZ with considering the lack of periodicity of the whole system in such liquid/solid interfaces [37][38][39][40][41][42]. Test simulations using different cut-off energies ranging from 200.0 eV to 400.0 eV demonstrated that the settings are reasonable.
We prepared liquid Al samples by equilibrating at 3000K for 2000 steps (1.5 fs per step). Then the obtained liquid was cooled to the desired temperature. We used the obtained liquid Al samples together with the oxide substrates for building the L-Al/γ-Al 2 O 3 {1 1 1} interfaces. A two-step approach was applied in our simulations. We first performed ab initio molecular dynamics simulations with the substrate O atoms pinned for about 2ps (1.5fs per step). Then, we equilibrated further the systems with full relaxation of the substrate atoms for another 4,000 to 7,000 steps (figure 2). The two-step approach avoids risk of collective atomic movements occurring often when we relax all atoms from start. The time-averaged method was used to sample the interfaces over 3.0-4.5 ps to ensure statistically meaningful results [39][40][41][42]49].

Parameters describing atomic ordering at the L-Al/oxide interfaces
In order to assess the atomic ordering at the equilibrated L-Al/γ-Al 2 O 3 {1 1 1} interfaces three coefficients are employed as follows.

Atomic density profile
In order to provide a quantitative measure of atomic layering at a liquid/solid interface, we use the atomic density profile, ρ(z) which is defined as [12,13,34,50,[39][40][41][42]: here, L x and L y are the in-plane x and y dimensions of the unit cell, respectively, and z the dimension perpendicular to the interface. Δz is the bin width, and N z (t) is the number of atoms between z − (Δz/2) and z+(Δz/2) at time t. 〈N z (t)〉 means a time-averaged number of atoms in the duration. The unit of the atomic density profile is (Å −3 ).

In-plane (atomic) ordering coefficient
In-plane ordering coefficient, S(z) can assess the atomic ordering in an individual layer [34,50]. It is defined as: here, the summation is over all atoms within a layer with a bin of width, Δz=z − (Δz/2) and z+(Δz/2). Q is the reciprocal lattice vector in the x-y plane, r i is the Cartesian coordinates of the ith atom, and N z is the number of atoms in the layer, respectively.

Atomic roughness of an individual layer
Atomic roughness (R) of an individual layer [39,42] is quantified as: where Δz(i) is the deviation of the ith atom from the atomic plane along the z-axis, d 0 (>0) is the interlayer spacing of the metal, and N z is the total number of atoms in the layer. When an atom is located in the lattice of the plane, Δz(i)/d 0 =0, when an atomic site is unoccupied, |Δz(i)|/d 0 =1.0. Ab initio molecular dynamics simulations are performed at elevated temperature at which atoms move around their equilibrium positions. Therefore, we use the atomic density profiles for estimation of the atomic roughness. The base-plane is set to be the peak/center at the atomic density profile.

Results
3.1. Atomic evolution at the L-Al/γ-Al 2 O 3 {1 1 1} interfaces During the ab initio molecular dynamics simulations, some liquid Al atoms moved quickly towards the O ions terminating the substrates. Correspondingly, the total energies of the systems decrease sharply at the first 0.4ps, and then level off slowly with time ( figure 2). Full relaxation of all atoms in the system causes some changes in atomic rearrangement as indicated by the energy changes ( figure 2). After about 1ps, the systems reached thermal equilibrium and the total energy curves of the two systems overlap with each other, being consistent with the fact that these two systems have the same atomic species and numbers in the unit cells of the same dimensions. This also indicates the similar stability of the two γ-Al 2 O 3 {1 1 1} surfaces in liquid Al. Furthermore, the simulations showed that the two-step approach provided quick and steady convergence and avoided collective movements of the atoms. The latter happened using one step approach [38][39][40][41]. The simulations also showed that at thermal equilibrium, the liquid Al atoms at the terminating layer exhibit ordering and are more solid-like (details in next section). Meanwhile, the Al atoms adjacent to the substrates were moving around and even moved to neighboring layers. But, the numbers of Al atoms at each layer keep statistically constant.    between the 1st Al and the substrate ( figure 4(a)), which is similar to that at the L-Al/α-Al 2 O 3 {0 0 0 1} interface, where the terminating Al layer is composed of two Al subpeaks and admixed with the 1st Al layer [36,40]. Figure 4 shows structural coupling between the terminating Al atoms and those at the subsurface Al layer in the substrate below the outmost O layer. At L-Al/γ-Al 2 O 3 {1 1 1} O1 the multiply peaked terminating Al layer is coupled to the single peak at the subsurface Al layer ( figure 4(a)), whereas at L-Al/γ-Al 2 O 3 {1 1 1} O2 the singlepeaked Al terminating layer is accompanied by the multiply peaked subsurface Al layer in the substrate. From another angle, the atomic arrangements of the terminating Al atoms are similar to those at its 3rd Al layer in the substrate at each L-Al/ γ-Al 2 O 3 {1 1 1} interface, respectively. ( figure 4(b)).

In-plane ordering at the L-Al/γ-Al 2 O 3 {1 1 1} interfaces
The epitaxial nucleation model suggested that the substrate surface provides a structural template for nucleation of the solid phase [14]. The prenucleation at the interface relates to the capability of the substrate to nucleate the solid phase in liquid. Figure 5 presents snapshots for the terminating Al, the 1st and 2nd Al layers at the L-Al/γ- The terminating Al layers at both interfaces contain vacancies, and displacements ( figure 5). There are moderate atomic ordering at the 1st Al layer but little at the 2nd Al layer at L-Al/γ-Al 2 O 3 {1 1 1} O2 . At L-Al/γ-Al 2 O 3 {1 1 1} O1 even the 1st Al layer seems hardly any atomic ordering.
The in-plane ordering coefficients for the atomic layers near the interfaces were obtained using the configurations summed over 3ps via equation (2). The results are plotted in figure 6.

Atomic roughness of the terminating Al layer
For the L-Al/γ-Al 2 O 3 {1 1 1} interfaces, one issue is the occupation of metallic sites at the termination metal layer [42]. Charge balance in bulk Al 3+ 2 O 2− 3 requires a N metal /N O ratio to be 66.7% (two thirds). The triple nature of the metal atoms and the related ordering at the terminating metal layer provides a constant free electron density at the substrate surfaces to interact with the nearby liquid Al atoms. N z is the same as that in a substrate metal layer.
Using equation (3) with N z /N 0 =2/3 (N 0 is the number of sites produced by the outmost O layer), we can estimate R values for the terminating Al layers at the L-Al/alumina interfaces. The terminating Al layer at L-Al/γ-Al 2 O 3 {1 1 1} O2 is flat with an occupation of 58.1% and therefore, R=12.9%. The terminating Al layer at L-Al/γ-Al 2 O 3 {1 1 1} O1 has an Al occupation of 54.0% which contributes 19.0% to R. Moreover, the Al atoms also display splitting along the z-axis and analysis produces another 14.5%. Overall, the R=33.5% for the terminating Al layer at L-Al/γ-Al 2 O 3 {1 1 1} O1 . Similar analysis produced R=33.6% for the terminating Al layer at L-Al/α-Al 2 O 3 {0 0 0 1} [40,41].

Chemical interaction at the L-Al/γ-Al 2 O 3 {1 1 1} interfaces
The chemical interaction between the substrate and liquid affects the atomic ordering of the liquid adjacent to the substrate [10,13]. Here, we employed Bader charge model [51] to analyze the atomic charges at the interfaces. The results for the systems are plotted in figure 7.
The oxygen ions in both substrates have an average charge value of −1.3e/O, whereas the Al in the substrates are positively charged with an averaged value of +2.0e/Al. Therefore, the substrates can be described with the formula, (Al 2.0+ ) 2 (O 1.3− ) 3 . These charge values are smaller than the ionic model with Al 3+ and O 2− at the atomic sites, indicating some covalent nature of alumina. Meanwhile, the Al atoms away from the interface are electronically neutral. Figure 7 shows that the terminating Al atoms are charged partially. There is charge transfer from the terminating Al atoms to the outmost O atoms, indicating strong chemical bonding between the terminating Al atoms and the substrates. Therefore, the terminating Al atoms are better regarded as part of the substrate. The charge at a terminating Al-layer decreases strongly with the distance from the outmost O atoms, agreeing well with the chemical bonding theory [52].

Discussion
The present ab initio molecular dynamics simulations revealed the formation of an ordered Al layer terminating the γ-Al 2 O 3 {1 1 1} substrates in liquid Al. Charge transfer occurs from the terminating Al to the outmost O. Consequently, the terminating Al atoms are positively charged and chemically bonded to the outmost O. The terminating Al atoms/ions exhibit ordering and are more solid-like, and therefore, belong to the substrates. The simulations also discovered that the terminating Al are structurally coupled with the Al ions at the subsurface. The origin of the structural coupling comes from the Coulomb repulsion between the Al ions at the terminating layer and the subsurface cross the outmost O layer, similar to that at the L-Al/MgAl 2 O 4 {1 1 1} interfaces [42]. Such structural coupling is a general phenomenon, found at the other interfaces between liquid-metal and oxide substrates [39][40][41][42]. This unusual structural coupling between the newly formed terminating metal layer to the oxide substrate helps us to obtain some insight into the growth of the oxide particles. Here we try to make a scenario of γ-Al 2 O 3 {1 1 1} growth in liquid Al. In liquid Al, the solute O ions/atoms aggregate at the space between the terminating Al layer and the 1st Al layer due to the Coulomb interaction, forming a new O outmost later at L-Al/MgAl 2 O 4 {1 1 1}. During the formation of the new O outmost layer, the composition and atomic arrangements at the original terminating layer are adjusted into those in the corresponding bulk. Consequently, a new Al terminating layer with structural coupling to the substrate will be formed to terminating this new O outmost layer. This process continues until the O ions/atoms in the liquid are consumed up. A detailed discussion is beyond the scope of the present manuscript.
Prenucleation is related to the intrinsic capability of the substrate surface to induce atomic ordering in the liquid adjacent to the interface. Therefore, it corresponds to the potency of the substrate for nucleation of the solid [10,11,53]. Recent studies revealed three factors affecting prenucleation at a liquid-metal/solid-substrate interface [10]. Firstly, at a flat substrate, the lattice misfit between a metal and a substrate ( f ) hinders strongly the in-plane ordering, but affects little on the atomic layering (structural factor, f ) [12]. Secondly, the chemical interaction between liquid metal and a flat substrate influences the atomic ordering at the interface. A chemically affinitive substrate promotes atomic ordering at the interface, whereas a repulsive substrate weakens prenucleation (chemical factor) [13]. Furthermore, the atomic roughness of a substrate surface deteriorates both layering and in-plane ordering at the interface (effect of atomic roughness, R) [35,42].
The present study revealed charging of the terminating Al at the L-Al/γ-Al 2 O 3 {1 1 1} interfaces (q), which can be considered as a measure of the interfacial chemical interaction. We summarize the factors, lattice misfits ( f ), the atomic roughness of the terminating metal layer (R), and the charges at the interfacial atomic sites (q) in table 1. These factors affecting prenucleation at the L-Al/γ-Al 2 O 3 {1 1 1} interface are listed in table 1 in comparison with those at L-Al/α-Al 2 O 3 {0 0 0 1} from the literature [40,41]. Table 1 shows that all the terminating Al atoms at the L-Al/alumina interfaces are charged. Moreover, the lattice misfits were moderate for Al/α-Al 2 O 3 {0 0 0 1} (4.8%) [5] and Al/γ-Al 2 O 3 {1 1 1} (5.6%). Table 1 shows overall weak prenucleation at the at the three L-Al/alumina interfaces as compared with the liquid-metal/solid-metal interfaces [12,13]. The observed layering at Al/α-Al 2 O 3 {0 0 0 1} is in line with the experimental observations [21][22][23][24][25][26][27].The atomic roughness of the terminating layer is different at the three interfaces: R=12.9% for L-Al/γ-Al 2 O 3 {1 1 1} O2 , which is notably smaller than those of L-Al/γ-Al 2 O 3 {1 1 1} O1 and L-Al/α-Al 2 O 3 {0 0 0 1}. Consistently, the prenucleation at the L-Al/γ-Al 2 O 3 {1 1 1} O2 interface is more pronounced than that at the other two interfaces. This indicates the atomic roughness is the dominating factor at these interfaces. However, the moderate/weak prenucleation at the L-Al/alumina interfaces is not determined by a sole factor, such as atomic roughness, but a combination of the lattice misfit, chemical interaction (charging) and atomic roughness.
The poor prenucleation at the L-Al/Al 2 O 3 interfaces indicates requirements of large drive forces (undercoolings) to nucleate the solid Al phase. The nucleation temperatures at these interfaces might be even lower than the corresponding grain initiation temperatures. In this case, as soon as the grain initiation temperature is reached, heterogeneous nucleation and grain initiation occur in a narrow time interval, leading to explosive grain initiation [10,11]. This indicates that more alumina particles can act as potential sites for nucleation and growth of solid aluminum. This explosive nucleation may help to materialize fine particles of solidified metals if no other more potent particles of significance exist [10,11].

Conclusions
We performed ab initio molecular dynamics simulations with a two-step approach and electronic structure calculations for the L-Al/γ-Al 2 O 3 {1 1 1} interfaces. The simulations showed that the two-step approach is helpful in avoiding risk of collective movements of atoms during ab initio MD simulations. This study revealed the formation of an ordered Al layer terminating the γ-Al 2 O 3 {1 1 1} substrates in liquid Al at thermal equilibrium. The terminating Al are electronically charged and chemically bonded to the outmost O ions, becoming part of the substrates. Moreover, the terminating Al atoms/ions at the L-Al/γ-Al 2 O 3 {1 1 1} interfaces are structurally ordered but are topologically rough. This leads to its weak templating capability and therefore, poor prenucleation at the interfaces. Moreover, the investigations also discovered structural coupling between the terminating Al ions with the those at the subsurface layer in the substrates. This is helpful to understand the growth mechanism of oxide particles in the liquid metals.  [40,41]