Nanoscale size effects in crystallization of metallic glass nanorods

Atomistic understanding of crystallization in solids is incomplete due to the lack of appropriate materials and direct experimental tools. Metallic glasses possess simple metallic bonds and slow crystallization kinetics, making them suitable to study crystallization. Here, we investigate crystallization of metallic glass-forming liquids by in-situ heating metallic glass nanorods inside a transmission electron microscope. We unveil that the crystallization kinetics is affected by the nanorod diameter. With decreasing diameters, crystallization temperature decreases initially, exhibiting a minimum at a certain diameter, and then rapidly increases below that. This unusual crystallization kinetics is a consequence of multiple competing factors: increase in apparent viscosity, reduced nucleation probability and enhanced heterogeneous nucleation. The first two are verified by slowed grain growth and scatter in crystallization temperature with decreasing diameters. Our findings provide insight into relevant length scales in crystallization of supercooled metallic glasses, thus offering accurate processing conditions for predictable metallic glass nanomolding.


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The distribution of T c 's is within +/-2 o C . In addition, after 50 + cycles, the onset temperature from a different nanorod with the same diameter (~120 nm), was measured and the temperature difference was  TEM image (left) shows crystallized regions, which are marked with arrows. Chemical maps were acquired from the yellow boxed region and shown on the right. We observe a Cu-rich (and simultaneously Ni-poor) phase in the crystallized region, marked by the white dotted lines. Based on previous reports 1 , the Cu-rich/Ni-poor phase is likely to be CuP 2 . From the BF TEM image, we also observe a sharp line that is of lighter intensity. This may be a P 2 Pt 5 phase, based on the previous report 1 . Due to overlapping peaks in the EDX spectra (Phosphorous, P and Platinum, Pt, for example), the EDX analysis is not accurate enough to completely rule out any chemical effects on the crystallization kinetics. We perform repeated crystallization experiments (over 50 heating and cooling cycles) on the same nanorod to confirm the reliability of our in-situ heating experiments inside TEM. A large nanorod with a diameter of 120 nm was selected for cyclic heating experiments, so that the stochastic nature of reduced probability of nucleation does not play a role. The experiment procedure consists of a cyclic heating and cooling process on the nanorod with four steps; (1) heating from room temperature to 500 o C with a heating ramp rate of 0.67 o C sec -1 , (2) heating from 500 o C to 900 o C with a heating ramp rate of 10 6 o C sec -1 , (3) holding at 900 o C for less than 3 seconds and (4) cooling down from 900 o C to room temperature with a cooling rate of 10 6 o C sec -1 . We repeated the temperature cycle over 50 times and measured T c from the 1st to 15th and the 36th cycle using SAED TEM movies. Supplementary Figure 3a   7 shows the deviations in T c (ΔT) from the data set, which is the difference between the onset temperature of a particular cycle (T c ) and the average onset temperature (T average ). The standard deviation has been calculated using the "corrected sample standard deviation". The equation is as follows;

Supplementary
where N is the number of experiments (or cycles). The standard deviation of the cyclic experiment is only 1.52 o C, showing that T c can be reliably measured. In addition, after 50 + cycles, T c from a different nanorod, which has the same diameter (~120 nm), was measured. Its

Supplementary Note 3: Direct verification of slowed grain growth with decreasing nanorod diameter
The diameter-dependent apparent viscosity should affect the grain growth rate in glassy nanorods, which can be directly measured during in-situ heating inside TEM. Supplementary   Figure 4a, b show the snapshot DF TEM images that track grain growth in nanorods of two different diameters in the same temperature window. The grain growth rate is estimated by measuring the lateral dimension of the areas with bright intensity in the images. Grains grow ~5 times faster in the thicker (~53 nm) nanorod over the thinner (~21 nm) one. Supplementary   Figure 4c shows snapshot DF TEM images of a grain growth in a ~6 nm nanorod under an isothermal condition at 350 o C. The measured growth rate is ~0.1 nm sec -1 , which is over two orders of magnitude smaller than those observed in Supplementary Figure 4a, b. Figure 4d shows the grain growth rate for the nanorods of various diameters, which confirm the suppressed grain growth (thus, enhanced apparent viscosity) for thinner nanorods. In addition, we note that no grain growth occurs in extremely thin nanorods below ~5 nm ( Supplementary Figure 4c and Fig. 2d in the main text), which may suggest the critical nucleation size. This critical size is 9 determined by thermodynamic energy barriers 2,3 , while the critical size (~25 nm) at which a minimum T c occurs reflects a kinetic phenomenon.

Supplementary Note 4: Discussion of the growth mechanism
Our in-situ data also present an opportunity to study growth modes. We observe that for larger nanorods, multiple crystalline phases come out with chemical heterogeneity. Supplementary Figure 5 shows a partially crystallized, 80 nm nanorod. The rod was heated in-situ at a 0.67 o C sec -1 heating rate, and was quickly quenched back to room temperature when we observed partial crystallization. The EDX chemical mapping shows a Cu-rich/Ni-poor crystalline grain, which suggests a crystalline phase with a composition different from the glass composition. We think that this Cu-rich region may be a CuP 2 phase. We also observe a needle-like phase, which we think is P 2 Pt 5 phase based on Legg et al 1 . The two phases are not next to each other and they do not appear to grow cooperatively. Thus, it is unlikely that the crystallization mode is eutectic. It is unclear if this is primary crystallization because of limited temporal resolution of the in situ TEM data.

Supplementary Note 5: Single vs. poly-crystallization
The reduced probability of nucleation in small rods suggests that a single nucleation event could cause a complete crystallization in small rods. We have indeed observed singlecrystalline-like grain growth in thinner nanorods, typically below ~30 nm in diameter A large number of nanorods with a diameter of 10 ± 1 nm, 20 ± 1 nm, 50 ± 2 nm and 120 ± 3 nm were heated from room temperature to 500 o C with a constant ramp rate of 0.67 o C sec -1 . The onset temperatures (T c ) of each experiment were collected from non-tapered nanorods of uniform diameters, using dark field (DF) or selected area electron diffraction pattern (SAED) TEM movies, during heating. Figure 5a shows the temperature scatter, the deviation (ΔT), which is the difference between the onset temperatures (T c ) and the average onset temperature (T average ). We observe that the scatter becomes smaller as the size of nanorods increases. To see the scatter more clearly, the standard deviation has been calculated using the corrected sample standard deviation. The calculated standard deviations of 10 nm, 20nm, 50nm and 120 nm samples are 25.5 o C, 14.6 o C, 5.5 o C and 1.5 o C, respectively, as shown in Fig. 5b in the main text. The obtained values strongly suggest the stochastic phenomenon can be seen in smaller sized samples.
Thus, we can consider the nucleation event in a small nanorod (below ~30 nm) suggests the critical role that the reduced probability of nucleation plays on crystallization kinetics. We note that even in the presence of the temperature scatter, the non-monotonic behavior of T c still holds. studies suggest that it may be explained by considering the particle as a cluster of atoms. As the cluster decreases in size, surface atoms are bound to the 'bulk' more loosely due to the decreasing number of bulk atoms. Consequently, the melting temperature will deviate from the 1/D curve 5 . The change in the ratio of the surface-to-bulk energy may also lead to a structural transition 5,6 and a reduction in surface tension 7,8 .