Effect of pentagonal-coordinated surface on crystal nucleation of an undercooled melt

Bringing a liquid into contact with a solid is known to generally promote crystal nucleation at the freezing temperature. In contrast, it is much more difficult to conceive that a solid surface may hinder nucleation and favor large undercooling effects. Here we report on ab initio and classical molecular dynamic simulations to capture the underlying structural mechanism responsible for this striking effect. We find that the substrate/liquid interactions exert an important influence on in-plane ordering of the adjacent liquid layers in the undercooling regime. In particular, we identify that the presence of atomic arrangements with five-fold symmetry (FFS) on the substrate surface in the form of pentagonal atomic motifs allows the liquid to be undercooled well below its freezing temperature. Our findings clearly demonstrate that this pentagonal-coordinated surface enhances the presence of local arrangements with FFS in the adjacent liquid layers that prevents the crystal nucleation. Finally we suggest new technological developments to attain large undercooling effects.


Simulation Methods
a. Ab initio molecular dynamics simulations. The ab initio molecular dynamics (AIMD) simulations were carried out using the DFT as implemented in the Vienna ab initio simulation package [1]. Projected augmented plane waves [2] (PAWs) with the Perdew-Wang exchange-correlation potentials have been adopted. The valence state of each element has been defined previously in the provided PAW potentials and the planewave cutoff is 245 eV. All the dynamical simulations were carried out in the canonical ensemble by means of a Nosé thermostat to control temperature. Newton's equations of motion were integrated using the Verlet algorithm in the velocity form with a time step of 1 fs. Only the Γ-point was considered to sample the supercell Brillouin zone. The simulations procedures are described below.
b. Classical molecular dynamics simulations. Classical molecular dynamics simulation were performed using interatomic interactions built within the Modified Embedded-Atom Model (MEAM) designed for the Au-Si system [3,4].
The MEAM formalism is well documented in the literature therefore we refer the reader to Refs. [5][6][7][8] for a detailed description. Here we recall only the main feature for a comprehensive purpose. In the MEAM formalism, the potential energy functional can be expressed as where ) ( i i F  is the embedding energy function depending on the background represents the pair potential interaction as a function of interatomic distance rij between atoms i and j, and ij S is a screening factor. Briefly, the electron density is calculated first for each atomic site from an analytic expression taking into account the length and directionality in bonding of the neighbors. Then, from a specific form of the embedding function and the total energy, estimated using the equation of state of Rose at 0 K for a given reference structure, the pair potential is determined as a function of the interatomic distance using Eq. (1).
For Au-Si alloys we consider the model of Ryu and Cai [9,10] based on the fitting of the experimental Au-Si phase diagram and a refinement of existing MEAM potentials for the pure elements Au and Si. Here we use a further refinement of this potential done in [3,4], leading to a good agreement with AIMD simulations.
With this MEAM potential we have performed molecular dynamics simulations using the LAMMPS code [11] to investigate the structural and dynamic properties of the of Si(001)/ AuSi and Si(111)-(6×6)/ AuSi interfaces as described below. As for the AIMD simulations, the classical molecular dynamics (MD) simulations were done using the Verlet algorithm in the velocity form with a time step of 1 fs. The simulation were conducted in the canonical ensemble (NVT ensemble) using a Nose thermostat. Figure S1: Schematic view of the interface design. The axis orientations of the simulation boxes are given by the red (x-axis), green (y-axis) and blue (z-axis) thick arrows. Si atoms are in yellow color, and Au atoms are in pink color.

Design of the solid/liquid interfaces and simulation procedures
The design of the solid/liquid interface is described schematically in Figure S1, which was done either by AIMD and classical MD. The liquid and crystalline part of the system are simulated independently by molecular dynamics simulation à T = 700 K, with the same size in x and y directions so that equilibrium configurations can be directly assembled. The number of atoms of the eutectic Au-Si liquid was chosen to match the composition and experimental density [12]. An appropriate length in the z-direction is also chosen. The specific size of each simulation box is described below. A simulation length of 20 ps (AIMD and MD) were sufficient to equilibrate the liquid and the crystalline systems.
After equilibration, the liquid and crystalline parts were assembled, as shown in Figure S1, with an initial separation distance between the two parts chosen to correspond to the Au-Si distance found in the liquid alloy [3,4]. The solid/liquid interface is then equilibrated again during a few ps. For the simulations at T = 600 K and below, the equilibrated solid/liquid interface obtained at T = 700 K was cooled down with a cooling rate of 10 12 K/s, by a linear temperature ramp.
The total simulation time after equilibration for all temperature is 110 ps for AIMD runs and 30 ns for classical MD. At each temperature, the box size Lz of the solid/liquid interface is slightly reduced to maintain the experimental density in the liquid slab. The self-diffusion coefficient is obtained by standard techniques [13] from the slope at long times of the mean-square displacement (MSD)

Calculation of the self-diffusion coefficients
0 z zi zi+1 bin n where ri(t) denotes the position of atom i at time t. Of interest here is the determination of the self-diffusion coefficients as a function of the distance from the interface to study its influence. Figure S2 shows a schematic representation of the solid liquid interface in which the liquid part is divided in bins of 10 Å width, placed each 5 Å (as can be seen there is an overlap of adjacent bins).