Spontaneous Liquefaction of Solid Metal–Liquid Metal Interfaces in Colloidal Binary Alloys

Abstract Crystallization of alloys from a molten state is a fundamental process underpinning metallurgy. Here the direct imaging of an intermetallic precipitation reaction at equilibrium in a liquid‐metal environment is demonstrated. It is shown that the outer layers of a solidified intermetallic are surprisingly unstable to the depths of several nanometers, fluctuating between a crystalline and a liquid state. This effect, referred to herein as crystal interface liquefaction, is observed at remarkably low temperatures and results in highly unstable crystal interfaces at temperatures exceeding 200 K below the bulk melting point of the solid. In general, any liquefaction process would occur at or close to the formal melting point of a solid, thus differentiating the observed liquefaction phenomenon from other processes such as surface pre‐melting or conventional bulk melting. Crystal interface liquefaction is observed in a variety of binary alloy systems and as such, the findings may impact the understanding of crystallization and solidification processes in metallic systems and alloys more generally.


Supplementary Discussion 1: The melting point of Ga2Cu
Figure S1: Cu-Ga phase diagram where the x-axis denotes atomic ratio of Ga to Cu in atomic percent and the y-axis denotes temperature of the system in degrees Celsius.The purple shaded region labeled 'L' (position upper right) indicates temperature and composition conditions where the alloy is liquid.Areas below the liquidus line indicate conditions where the sample is either completely or partially solid.Several defined intermetallic phases are indicated, with the CuGa2 intermetallic being of particular significance for this work.The horizontal line labeled 259 indicates the maximum temperature for stable CuGa2.For high Ga concentrations the liquidus line can be considered as the temperature dependent solubility of Cu in Ga.Reproduced with permission from Springer Materials.The phase transition behavior of the CuGa2 intermetallic compound within the liquid Ga solvent was investigated using the differential scanning calorimetry (DSC).Both bulk and nanosized samples were investigated.During the heating scan for the bulk Cu-Ga sample (Figure S2) one distinct Ga melting peak is observed with onset at 32.1 °C while a subtle intermetallic melting peak is seen with onset at 256 °C.The slight increase of the Ga melting point from 29.8 to 32.1 °C reveals that the added Cu affects bonding structures within the bulk gallium sample resulting in a higher melting energy requirement.Upon cooling, the crystallization of both, the intermetallic compound and gallium occurred at temperatures lower than expected due to pronounced supercooling effects which are not uncommon in metallic systems. [1]Interestingly for nanocolloidal Cu-Ga (Figure S3), there were three distinct peaks with onsets at -36.7 °C, -17.2 °C, and 29.3 °C during the heating cycle.These peaks are likely caused by melting of various Ga phases.The peak at 29.3 °C can be associated with the melting of -Ga, while the peak at -17.2 °C is most likely associated with the melting of -Ga. Additionally, studies on gallium nanoparticles showed that several lower melting point phases can preferentially form for smaller sized particles.Since our nanodroplets are known to be a polydisperse system (size range 50 nm -1 µm), [4] it is thus expected that populations of particles will crystallize in different phases that then melt at different temperatures.These melting points are further augmented by general size dependent melting point depression effects.At high temperatures, the melting of the CuGa2 intermetallic can be observed at a peak onset of 256 °C, which corresponds to the peak observed in the bulk sample.While this melting transition is a minor feature in the DSC scan, it has been clearly identified and observed at that temperature during in-situ heating TEM experiments.The comparatively low intensity of the peak is the result of solid CuGa2 only making up a small fraction of the overall sample at that temperature due to the higher solubility of Cu up to ~250 °C.
During the cooling cycle, the observed cluster of peaks below -11.7 °C is likely caused by the freezing of individual liquid metal nanodroplets.Crystallization is a stochastic process and may occur in different particles at different times, hence causing the observed feature. [5]The crystallization of the intermetallic commences at an peak onset of 242 °C which is comparable to the observations made for the bulk sample.
[8][9] The intermetallic CuGa2 compound does not appear to be significantly impacted by size effects which may be in part due to the metallic nature of the surrounding medium.Melting point depreciation is usually caused by the increased impact of surface atoms, which lack the stabilizing effects of a complete network of neighbors, at the nanoscale.In a liquid metal environment, a delocalized metallic bond that spans across both the solvent and the intermetallic may counteract these effects.Since this work predominantly deals with the properties of intermetallics inside a liquid metal environment, bulk phase diagrams can still provide valuable guidance.A 9 at% Cu-Ga metal in metal colloid sample was heated in the TEM until the intermetallic fully dissolved, thus creating a homogeneous liquid mixture of Cu and Ga atoms.During the heating process, the system traverses along the solid-liquid boundary of the phase diagram which is equivalent to the solubility limit of Cu in Ga.The concentration of Cu in the liquid portion of the droplet can then be measured using electron dispersive X-ray spectroscopy, providing a direct measure of the dissolution process.

Supplementary Discussion 2: TEM beam heating effects
Since the used in-situ system is well calibrated by the manufacturer, the dissolution process of the solid intermetallic can then be used as an internal standard to estimate beam heating.If beam heating was considerable, the measured dissolution curve would be shifted from the expected values based on reported solubility curves.Figure S4A shows several dark field images measured at different temperatures.The top row shows the room temperature sample as well as an image taken at high temperatures where the intermetallic is fully dissolved.During heating, the solid fraction slowly reduces in size until it is fully dissolved.The temperature at which the entire intermetallic has become molten is in agreement with the DSC measurements discussed above and the phase diagram shown in Figure S1. Figure S4B shows three individually measured concentrations at specified temperatures (purple) superimposed onto the solubility limit of the Cu-Ga system (black), indicating that beam heating is negligible.
Here I is the incident beam current in C/s, ΔE is the average energy loss in J/C, t is the sample thickness in nm, λ is the electron mean free path in nm, k is the thermal conductivity of the sample in W/mK, d is the incident electron beam diameter in nm, R0 is the travelling distance of heating in nm, and T is the sample temperature in K.
Upon rearranging equation ( 1), we can get T as the subject which is the temperature of the sample after thermal equilibrium is achieved.
After utilizing equation ( 2) and applying either measured or literature values for the relevant variables, we arrive at an estimated temperature increase of 0.04 °C which confirms that beam heating is indeed negligible.
Aside from measuring the dissolution process, TEM based elemental mapping also indicates where the surface oxide layers reside.All synthesized nanodroplets contain an oxide layer that spontaneously forms in oxygen containing environments (i.e.Air).nder almost all circumstances the intermetallic compound was found to be preferentially positioned inside the droplet closely situated to the surface oxide.This could be caused by preferential nucleation at the interface or due to weak surface interactions (i.e.van der Waals forces).Throughout this work, the intermetallic compound has been carefully studied in areas where it is detached from the oxide in order to minimize any local impact of the interface.

Figure S6:
Crystal lattice of (A) AgGa [18] and (B) Bi [19] with an FFT showcasing the crystal structure which confirmed their planar orientation and thus the intermetallic or nonintermetallic compound.

Unaltered Figures
Each Figure that is listed here has been altered in the main manuscript to provide visual aid.This enhances the readers' experience if they lack access to the supplementary videos and makes it easier to follow the discussion.
Note, it is highly recommended to watch the supplementary videos since they provide a clearer picture as to what is happening.

Figure S2 :
Figure S2: Differential scanning calorimetry of a Cu-Ga liquid metal alloy bulk sample, showcasing a slight increase in the melting point of Ga (onset at 32.1 °C in comparison to 29.8 °C for pure Ga), and a very slight peak with onset at 256 °C indicating the complete dissolution of the CuGa2.

Figure S3 :
Figure S3: Differential scanning calorimetry of a Cu-Ga liquid metal alloy nanodroplet system showcasing three distinct Ga melting peaks indicating size effects.The dissolution of the intermetallic CuGa2 is still observed with onset at 256 °C.

Figure
Figure S4: (A) Cu-Ga nanodroplet whereby the Cu intermetallic dissolves as the temperature increases until complete dissolution is achieved.(B) 3-point temperature calibration curve showing the measured Cu concentrations determined at the red indicated points in Figure S3A (purple data points accompanied by measured values), overlaid over the solidliquid boundary manually extracted from the phase diagram shown in Figure S1, revealing that beam heating is negligible.

Figure S7 :
Figure S7: EDS spectrum data showcasing the atomic percentage and hence the compositional analysis of (A) Ag3Sn, (B) Cu5Sn4, (C) AgGa, and (D) Bi, whereby the percentages are similar to their stoichiometric ratios thus confirming intermetallic composition.

Figure S8 :
Figure S8: Mechanism for [01 ̅ 3] facet melting from AIMD simulations run at 100 °C.Specific atom movements are highlighted in orange.

Figure S9 :
Figure S9: AIMD simulations of the (A) [01 ̅ 3] and (B) [1 ̅ 00] facets of Ga2Cu at 100 °C.Snapshots of the (A) [01 ̅ 3] and (B) [1 ̅ 00] facets interfacing with liquid gallium after 200 ps (left).Copper is colored purple and gallium from Ga2Cu is colored light grey, while the liquid gallium is colored dark grey.Energies required to remove gallium atoms from their positions are highlighted in orange.Atomic pairwise probability distributions of gallium as a function of z position in the system are also shown (right).The z position within the system has been divided into defined layers which are indicated by the colored bars to the right of the visual AIMD snapshot.

Figure S10 :
Figure S10: Atomic density profiles for Ga and Cu atoms from the AIMD simulations, calculated over the final 2 ps of each simulation.In each case the first layer is defined as the bottom layer that is frozen in AIMD simulation.

Figure S11 :
Figure S11: (A) Material selection process showing the solute metals (top) and the liquid metal solvents (bottom), (B) Schematic of an intermetallic colloidal particle undergoing an

Figure S12 :
Figure S12: Dynamic movement investigated in (A) Ag-Sn, (B) Cu-Sn, (C) Ag-Ga, and (D) Bi-Ga.The left column shows dark field images of the studied droplets.The colored elemental map highlights the distribution of the respective added solute metal measured via electron dispersive X-ray spectroscopy.The composition of the solid colloidal particle has been determined via electron diffraction studies.The middle and right-hand columns show highresolution images of an outer facet exposed to the liquid metal liquor.