Supercluster-coupled crystal growth in metallic glass forming liquids

While common growth models assume a structure-less liquid composed of atomic flow units, structural ordering has been shown in liquid metals. Here, we conduct in situ transmission electron microscopy crystallization experiments on metallic glass nanorods, and show that structural ordering strongly affects crystal growth and is controlled by nanorod thermal history. Direct visualization reveals structural ordering as densely populated small clusters in a nanorod heated from the glass state, and similar behavior is found in molecular dynamics simulations of model metallic glasses. At the same growth temperature, the asymmetry in growth rate for rods that are heated versus cooled decreases with nanorod diameter and vanishes for very small rods. We hypothesize that structural ordering enhances crystal growth, in contrast to assumptions from common growth models. The asymmetric growth rate is attributed to the difference in the degree of the structural ordering, which is pronounced in the heated glass but sparse in the cooled liquid.


Supplementary Note 1: Quantification of a crystal growth front using intensity profiles of Fourier filtered atomic resolution TEM images
Supplementary Fig. 2 shows a step-by-step procedure for obtaining a Fourier filtered TEM image, which was used to determine the growth front position and growth rate. Supplementary Fig. 2a shows indicates the presence of a crystalline phase. We apply an annular mask to the FFT pattern, in which the inner radius of the mask excludes the center spot while the outer radius of the mask covers most of the main spots ( Supplementary Fig. 2d). We constructed a Fourier filtered image by inverse fast Fourier transforming the data in Supplementary Fig. 2d, as shown in Supplementary   Fig. 2e. To quantify the growth front, an intensity profile from the dashed area in cyan was generated along the direction perpendicular to the (200) crystallographic plane ( Supplementary   Fig. 2f). The position of the growth front was determined as the location at which the intensity envelope was below 10 % of the maximum.

Supplementary Note 2: Determination of the growth rate during isothermal crystallization experiments
The crystal growth rate is strongly affected by the crystallographic orientation of a grain. We first tracked the grain growth in two orientations. For example, for isothermal crystallization of a 65 nm nanorod from the liquid melt state, the average growth rates were measured to be ~ 0.3 nm s -1 and ~ 6 nm s -1 along d200 and d110 directions respectively. The growth rate along the densely packed direction is ~ 20 times faster than the growth rate perpendicular to the largest inter-planar spacing plane. For the growth rate comparison as a function of the nanorod diameter and thermal history ( Fig. 3c and 3d of the main text), we only use the growth rate perpendicular to the (200) plane for the following reasons: i) a larger inter-planar spacing generates a larger change in contrast, making quantitative analysis more accurate, and ii) a slower growth rate allows us to average more frames for a better signal-to-noise ratio while ensuring that the time resolution after averaging is still high enough to track the crystallization process.

Thermal quenching protocol for preparing glasses
We investigated isothermal growth kinetics of a crystal invading an amorphous sample using molecular dynamics (MD) simulations of binary Lennard-Jones atoms. We first initialized the sample in a FCC crystal structure. We then fixed the positions of the atoms in the central region of the sample (~ 5 layers) and equilibrated the system at high temperature above the melting temperature T0 > 2.6 (in units of ε/kb, where ε is the depth of the Lennard-Jones potential and kb is Boltzmann's constant). In Supplementary Fig. 3, we show that the total potential energy per atom, U/N, increases rapidly near T ≈ 2.6, which indicates the melting transition. We then cooled the system using a linear ramp, = # − • , with cooling rate, , to a final temperature T = 0.01, much below the glass transition temperature Tg ≈ 0.38 1,2 . We studied cooling rates higher than the critical cooling rate so that edges of the sample were initially amorphous at T = 0.01 with the fixed FCC crystal in the central region. The critical cooling rate was determined to be ~ 0.02 (in units where σ is the diameter and m is the mass of the smaller atom) at which the probability of crystallization is 0.5 for the system (Supplementary Fig. 4). After the quench to T = 0.01, we heat the system in the fast heating rate limit to T = 0.1 and run the simulations at fixed temperature for times t = 100 (in units of ( *, -) ), which is comparable to the structural relaxation time near Tg. During the isothermal simulations at T = 0.1, the crystal region in the center of the sample expands into the amorphous regions.

Crystal growth rate measurements in MD simulations
We now describe our method to quantify the crystallization kinetics during the isothermal simulations at temperature T = 0.1. We identify crystal-like atoms that reside in structurally ordered local environments. We detect FCC crystalline order using the Voronoi surface areaweighted bond orientational order parameter for each particle, as shown in equation (1) .
For HI > 0.7, we consider that the bond orientational order of particles and is large and correlated. If particle has more than 6 highly correlated neighbors, we define it to be a "crystallike" particle. Otherwise, the particle is considered "liquid-like". Using this technique, for each snapshot of the system, we can determine the fraction of crystal-and liquid-like particles.
In initially rapidly heated to 900°C for less than 5 sec, then quenched to room temperature to erase any thermal history. After the melt-quench step, the rods were brought up to the isothermal crystallization temperature rapidly and held at the temperature for the entire in situ experiment.
Growth fronts of crystalline grains were tracked during the isothermal crystallization. b.
Isothermal crystallization quenched from the melt state. The rods were initially rapidly heated to 900°C for less than 5 sec, then cooled to the isothermal crystallization temperature rapidly and held at the temperature for the entire in situ experiment. Growth fronts of crystalline grains were tracked during the isothermal crystallization. The particles are colored pink and green to represent the A and B type atoms, respectively. When the system is heated to T = 2.0 and 2.5, which is below the melting temperature, the two regions on the ends that were free to relax during simulation remained largely crystalline. At T = 2.9

Supplementary
(marked as a dashed line in (a)), the two regions on the ends melt, while the central region remains a FCC crystal. Based on these results, for studies of crystallization upon heating, the system was prepared by first bringing it to equilibrium in the liquid state at T = 2.9, followed by rapid cooling to low temperature T = 0.01. Growth of the middle crystalline region into the glass phase was monitored by heating the system to T = 0.1.