Observing growth of metallic crystals inside liquid metal solvents

Domain: physics
Published: 2025-11-24
Editorial outcome: major_revision

Abstract
Liquid metals are promising unconventional solvents for dissolving metals and growing their crystals. However, how the crystals grow within these metallic solvents cannot be observed easily due to the opacity of liquid metals. Using X-ray micro-computed tomography, the three-dimensional formations of crystals inside liquid metal solvents, under different conditions, are presented. In this work, we explore the use of different liquid metals solvents for growing metallic crystals, while imaging the crystals shape and sizes inside liquid metals. We use gallium-based solvents and platinum, as the solutes and demonstrate the use of liquid metals for forming metallic crystals through modulating environmental boundary effects, controlled cooling rates, and solvent selection. It is observed that the cooling rate and composition of the reaction media will influence crystals morphologies and intermetallic phases. As a proof-of-concept, we perform hydrogen evolution reaction using metallic crystals extracted from the solvents, showcasing the potential of liquid metal-based synthesis in tailoring metallic crystals properties for enhancing catalytic activity demonstrating a strategy for engineering metallic crystals in liquid metal solvents.

Introduction
Liquid metals neither resemble solid metals nor typical liquids. Liquid metals possess relatively high density and a shimmering surface, while also displaying a perplexing fluidity. They maintain many of the metallic and physicochemical properties of solid metals, while offering liquid-like characteristics. Liquid metals embody some core qualities from its constituent metallic solid and liquid phases, while exhibiting strong interactions with solid metals when in direct contact with them when kept at the right temperatures. Such conditions are innately favorable for dissolution, interdiffusion, and intermetallic formation of metals inside liquid metals. Therefore, liquid metals present promising possibilities as reaction media for dissolving metallic elements and synthesizing a wide variety of metallic crystals.

Gallium-based alloys, characterized by their low melting points, are amongst the most extensively researched liquid metals. Gallium (Ga), as a p-block post-transition metal, is able to form covalent bonds with other elements, and exhibits a low melting point due to the relatively weak intermolecular forces. Liquid Ga forms intermetallic phases with many metals, particularly post-transition and zinc group metals, at or near room temperature. Additionally, considering the evidence of local structuring within liquid Ga at low temperatures, liquid Ga offers the potential to direct the growth of solute metal structures by favoring particular symmetries and or orientations during crystal growth, post-nucleation.

While liquid metals offer promising potential as the growth media for metallic solutes, crystal growth observation within liquid metal solvents has remained a challenge. One reason for this is that liquid metals are non-transparent to low- and mid-energy electromagnetic waves, and even high energy electron beams struggle to penetrate them, leading to a tendency to overlook phenomena that cannot be directly observed. Investigating crystal growth within bulk liquid metals provides fundamental insights into the growth mechanisms, elucidating the underlying principles governing solidification kinetics and phase transformations inside liquid metal systems. The possible access to observe inside liquid metal solvents allows for the more precise control of crystal morphology, size, and distribution, leading to the exploration of novel pathways for fabricating crystalline structures. It also enables more accurate predictions of material behavior under diverse conditions for the synthesis and processing of advanced materials using this category of solvents.

Altogether, controlling the dimensions and facets of the formed crystals requires real-time observational access during synthesis. Furthermore, no information on the location or growth direction within the liquid metal solvent has been reported so far, due to the limitations of existing observational tools, which rely on low-energy waves that cannot penetrate the bulk of the metallic solvents. This means, how the environmental conditions alter the crystal growth and morphologies, during the growth of crystals inside a liquid metal solvent, could not be determined. Hence, there is a need to introduce the use of instrumental techniques and procedures for realizing the elaborate growth mechanisms inside liquid metals.

In this study, X-ray micro-computed tomography (XCT) analysis was employed as the primary technique to observe the synthesized crystals within the liquid metal under different conditions. While the XCT technique has been used in metal additive manufacturing during development processes and certification in various sectors, such as aerospace, tooling, and biomedical applications, their utilization in the analysis of liquid metal–based materials remain rare. XCT analysis offers distinct advantages over other visualization techniques, including the ability to focus on the evaluation of internal structures, orientation, size, and distribution, without the need for sample preparation. Additionally, the sample can be fully recovered once the analysis is complete. The XCT technique provides a comprehensive three-dimensional (3D) representation, enabling detailed visualization of internal features that are otherwise unobservable.

The novelty of this research lies in the ability to observe crystal growth and morphologies inside liquid metal using XCT. This method allows crystal growth to be visualized without disrupting the surrounding environment or the boundary (i.e., the liquid metal as a solvent). To the best of the authors’ knowledge, there is no existing literature discusses the direct observation of crystals forming inside liquid metal.

Here, platinum (Pt) is dissolved as a solute metal in liquid Ga and liquid eutectic Ga-indium (EGaIn), which serves as the solvents, representing our model systems. This process leads to the formation of intermetallic compounds comprising two or more metals with an ordered crystal structure and defined stoichiometry. We demonstrate that the morphology and crystal formation processes of compounds inside liquid metals can be tailored under different growing conditions applied to the metallic solvents. The influence of the rate of cooling and reaction media type on this system are specifically investigated. Liquid metals, such as Ga and EGaIn, have low melting points (29.6 °C and 15 °C, respectively), allowing them to remain liquid at low temperatures, making them accessible and easy to handle in laboratory settings. Post-transition elements, in such liquid metals, exhibit covalent characteristics and also directional bonding, enabling their use as solvents for metallic solutes. Particularly, a recent study by Liu et al. have investigated the crystallization of liquid Ga, showing the presence of two different crystalline phases (α-Ga and β-Ga), distinguished by directional bonding. In particular, directional bonding has been predicted at the surface of Ga-based liquid metals. The low viscosity of Ga-based liquid metal facilitates manipulation and processing, such as extraction. Additionally, liquid metals function as electronic liquids with intrinsic conductivity, distinguishing them from conventional solvents. Unlike highly reactive low-melting-point metals like alkali metals, post-transition liquid metals are stable in air and moisture, enhancing their practicality.

Pt is chosen since it results in a high X-ray contrast with respect to Ga and Indium (In). XCT analysis is utilized to provide observations of the spatial arrangement of formed crystals inside the liquid metal droplets in a non-destructive manner. By voltage-based zeroing of the surface tension of the liquid metals, the synthesized metallic crystals are extracted and characterized as complementary investigations to XCT. The binding energy calculations and ab initio molecular dynamic (AIMD) simulations are also performed to support the data analysis. Finally, as a proof-of-concept application, we utilize the crystals extracted from inside the liquid metal droplets as electrocatalysts in a hydrogen evolution reaction (HER) study, demonstrating the viability of using the method for creating functional metallic crystals.

Results
Growth of crystals within liquid metal droplets
In this study, the changes to the crystallinity, microstructure, and spatial arrangement of intermetallic crystals within liquid metal droplets, due to the influence of environmental boundaries and solvent contents, were explored. Various metallic crystals inside the liquid metal bulk were grown at different conditions which will be discussed subsequently.

Two different solvent systems, Ga and EGaIn, were used in a liquid state to serve as the reaction media. The solute element of 2 weight percentage (wt%) of Pt, was thermally dissolved into these two different solvent systems. Pt (density of 21,450 kg/m3) was used as it provides a stark contrast with Ga (density of 5905 kg/m3) and In (density of 7290 kg/m3) for X-ray imaging, owing to their significantly different densities and X-ray attenuation profiles. The higher X-ray attenuation behavior of Pt maximizes the likelihood of observing the formed crystals inside the liquid metal systems.

After homogeneous liquid alloys were produced, these alloy systems were subjected to two different cooling rates: (a) fast-cooling, and (b) slow-cooling. The cooling allowed the solute metals to become oversaturated and precipitate inside the liquid metal solvents in crystalline forms. Fast-cooling is defined as leaving the liquid metal droplet to cool naturally from 500 °C to ambient temperature, after ~5 min, during which the temperature remained nearly constant. This results in an approximate average cooling rate of ~95 °C/min. Moderate-cooling is defined as a controlled temperature reduction from 500 °C to 20 °C at an intermediate rate of 10 °C/min, between the fast- and slow-cooling conditions, and is achieved over 48 min. In contrast, slow-cooling is defined as a controlled temperature reduction from 500 °C to 20 °C, achieved in over 480 min, at a rate of 1 °C/min. EGaIn is naturally in liquid format room temperature. In our experiments, bulk Ga also remained in its liquid state owing to the supercooling effect. By tuning the growth conditions, the choice of liquid metal solvent, and the rate of cooling, diverse crystal morphologies were produced.

Figure 1a depicts a schematic of the synthesized process for growing metallic crystals with distinct crystalline shapes using Ga or EGaIn liquid metals as the reaction media. These liquid metal droplets were then analyzed using XCT to observe the crystals formed within the bulk of liquid metals in their original state as illustrated in Fig. 1b. Afterward, the crystal extraction process from the liquid metal droplets (Fig. 1c) was carried out to examine their physical dimensions and crystalline structure in detail.

3D XCT observation of crystallites inside liquid metals
Supplementary Fig. 1 shows a photo of the XCT instrument used in this experiment, with the sample holder, a brass pin mounted on a rotational stage, positioned between the source (left) and the detector with filter wheel (right). The liquid metal droplet was drop-cast onto a silica wafer, mounted on the sample holder, as shown in the zoomed-in photo in Supplementary Fig. 1b (left). Our XCT collected a series of X-ray projection images through a sample rotating around a central vertical axis. These projections were then reconstructed to produce a stack of cross-sectional images that could be visualized in 3D. The intensity of each pixel in a cross-sectional image indicated the beam’s attenuation at that point within the sample. When two-dimensional (2D) image stacks, as illustrated in Supplementary Fig. 1c, were reconstructed into 3D volumes, the pixels were represented as voxels (volume elements).

A schematic diagram of the experimental design showing the overall crystal formation process, cooling duration, and cooling rate under different cooling conditions, is presented in Fig. 2a–c. Additionally, the photo of the sample, illustrating the opacity and surface reflectivity of a liquid metal droplet, is shown in Supplementary Fig. 1b (right). By utilizing XCT analysis, the crystal inside liquid metal droplet can be observed, while preserving their original environment, as presented in Fig. 2d–i. The XCT images for Pt-Ga droplets are shown in Fig. 2d, f, h, while the observations for Pt-EGaIn systems are presented in Fig. 2e, g, i, under different rates of cooling (fast-, moderate-, and slow-cooling). Based on many observations, most crystals grew near the interface of droplets that likely acted as a substrate for seeding. The crystals formed in the liquid Ga system (Fig. 2d, f, h) were predominantly rod-shaped, whereas those grown in the liquid EGaIn medium (Fig. 2e, g, i) were mainly polyhedral. A decrease in cooling rate, from fast- to slow-cooling, resulted in progressively larger crystals. Under fast-cooling conditions (Fig. 2d, e), small crystals were obtained. At a moderate-cooling (Fig. 2f, g), the crystals exhibited dimensions that were intermediate between those formed under fast- and slow-cooling conditions. Under the slow-cooling conditions (Fig. 2h, i), much larger crystals were observed. Specifically, crystals formed in Ga-based solvents, fast-cooling (Fig. 2d) produced small crystal, while moderate- (Fig. 2f) and slow-cooling (Fig. 2h), led to the progressive development of elongated crystal, rod-like morphologies. In contrast, crystals formed in EGaIn-based solvents tended to be more equiaxed, with sizes increasing from small crystals under fast-cooling (Fig. 2e) to progressively larger, polyhedral-shaped crystals formed under moderate- (Fig. 2g) and slow-cooling (Fig. 2i). Other supporting observations can be seen in Supplementary Videos 1–6 and Supplementary Figs. 4–7.

The size distribution of metallic crystals analyzed by XCT is depicted in Fig. 3a–f. The crystals formed under fast-cooling conditions tend to have a smaller size distribution, with dimensions ranging from 0 to 650 µm (median of 85 µm) and from 0 to 500 µm (median of 73 µm) for Ga and EGaIn solvent-based crystals, respectively. Under moderate-cooling condition, the size distribution of crystals grown in Ga-based solvents ranges up to 860 µm (rod-shaped crystals with a median size of 290 µm), while for those grown in EGaIn-based solvents, the distribution reaches up to 560 µm (polyhedral-shaped crystals with a median size of 130 µm). In contrast, crystals obtained under slow-cooling conditions resulted in broader size distributions, with Ga solvent-based crystals measuring up to 2800 µm (long rod shaped crystals-median of 664 µm for the length of rods only) while EGaIn solvent-based crystals ranged in size up to 1100 µm (polyhedron - median 459 µm), respectively.

The crystal growth speed varies depending on the chemical composition of the liquid metal solvent and the cooling rate, as illustrated in Fig. 3g–i. Crystals formed in Ga-based liquid metal solvents exhibit faster growth compared to those in EGaIn-based solvents. Regarding cooling rates, the fast-cooling conditions results in the fastest crystal growth relative to the moderate- and slow-cooling conditions. The crystal growth speed distribution in Ga-based solvents ranges from 13 to 120 µm/min, with a median of 17 µm/min under fast-cooling; from 3 to 18 µm/min, with a median of 6 µm/min under moderate-cooling; and from 0.5 to 5.7 µm/min, with a median of 1.4 µm/min under slow-cooling conditions. For crystals formed in EGaIn-based solvents, the growth speed distribution ranges from 8.3 to 90.5 µm/min with a median of 14.6 µm/min; from 1.5 to 11.6 µm/min with a median of 2.8 µm/min; and from 0.3 to 2.2 µm/min with a median of 0.95 µm/min under fast-, moderate-, and slow-cooling respectively.

For a more comprehensive comparison, we have also conducted additional experiments to observe crystal growth in other liquid metal solvent systems, specifically eutectic Ga-tin (EGaSn) and the eutectic alloy of Ga, In, and Sn (EGaInSn), as illustrated in Supplementary Figs. 2, 3, and Supplementary Note 1. In short, crystals formed in Ga-based solvent exhibit the greatest length and the fastest growth rate. The addition of other components, In and Sn, reduces both the crystal length and growth rate. Among the cooling conditions, the fast-cooling condition lead to the shortest crystal length and the fastest crystal growth rate.

Altogether, we illustrated that XCT offers a reliable way to overcome the challenge of observing crystal growth within the bulk of liquid metal, an opaque material that is impossible to penetrate with light and electrons. The combination of using Ga, as the liquid metal solvent, with fast-cooling provides the highest crystal growth rate among all conditions. Under fast-cooling conditions, the temperature decreases rapidly (95 °C/ min), creating a strong driving force for crystallization to begin. Crystal growth kinetics change, limiting the time for crystal growth and leading to the formation of many nucleation sites for small crystals to emerge. By contrast, under slow-cooling conditions, the temperature decreases gradually (1 °C/min), allowing the growth environment to remain in saturated condition for Pt for a longer time. This provides the system with sufficient time for the formation of fewer but larger crystals. The broader size distributions observed under slow-cooling conditions can also be attributed to the longer time available for crystal growth. The phenomenon is similar to conventional crystal growth.

Crystals extraction and characterization
To further investigate the detailed properties of the crystals formed within the liquid metal droplet, both the bulk sample containing the crystals and the extracted crystals were examined to characterize their physical dimensions and crystalline structure. The characterization of the bulk sample aims to explore the crystal properties in their original environment, while the post-extraction analysis focuses on examining the extracted crystals without interference from the background (solvent). To extract the crystal from the liquid metal droplet, the extraction process was carried out by removing the liquid metal solvent, starting with the filtration of the metallic colloidal solvents while applying voltage and a vacuum-driven force to the liquid metal droplets. (Fig. 1c and Supplementary Note 2)

Crystallographic structures of the bulk sample and the formed intermetallic crystals were assessed using X-ray diffraction (XRD) to distinguish various phases in the crystals generated at from different conditions. As can be seen, the impact of compositions of the reaction media and boundaries led to the formation of different intermetallic phases. XRD analysis revealed that Pt dissolved in the liquid Ga system resulted mostly in Ga2Pt intermetallic phase (Fig. 4a, c), while Pt dissolved in the liquid EGaIn resulted in the predominance of Ga7Pt3 (Fig. 4b, c). Additionally, some InPt73 phases were also found in crystals from the EGaIn solvent. Additional peaks corresponding to Ga and In are observed in the XRD of the bulk sample, confirming the presence of the solvents used as the growth medium (Supplementary Fig. 9a, b).

The pre- and post-extraction XRD results are consistent, suggesting that the extraction process does not alter the characteristics of the formed intermetallic crystals. The crystallographic parameters of the formed crystals in two different liquid metal solvents are summarized in Supplementary Table 1. The phase diagrams governing the formation of crystals are presented in Supplementary Fig. 8.

The surface morphology and the surface elemental mapping of the intermetallic crystals, both within the bulk sample and extracted from the liquid droplet Ga vs EGaIn systems, were also observed using scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). The schematic of crystal growth preferences is illustrated in Fig. 4d. Altogether, the crystals exhibited various morphologies and dimensions, as shown by SEM-EDS imaging in Fig. 4e–j. When Pt was dissolved in liquid Ga as the reaction medium, rod-shaped crystals were predominant (Fig. 4e–g), whereas polyhedral crystals were more frequent in liquid EGaIn reaction medium (Fig. 4h–j). The SEM observations of the surface of the bulk samples reveal similar morphologies to those observed in the extracted crystals at the surface boundaries, with the crystals still surrounded by their solvent (Ga or EGaIn), as shown in Supplementary Fig. 9c–f. In the fast-cooling process, the crystals tend to reside at the interface of the droplets, emerging from their solvent. In contrast, in the slow-cooling samples, crystals tend to be located beneath the interface, likely due to their larger size. Overall, these SEM observations align with the results obtained from the XCT analysis.

Table 1 summarizes the intermetallic crystals formed under different liquid metal solvent systems and growth conditions, highlighting the key aspects where the solvent composition influences the resulting crystal morphology and phase composition of the formed crystals. Crystals grown in Ga-based solvent generally exhibit a rod-like morphology, predominantly forming the Ga2Pt intermetallic phase. In contrast, crystals formed in EGaIn-based solvent systems present a polyhedral crystal morphology, with the majority composition corresponding to the Ga7Pt3 intermetallic phase.

Measurements of dimensions from the SEM observations also suggest that the slow-cooling process induced more intense growth around a few seeds, promoting the formation of larger crystal structures (Fig. 4g, j) ranging from 0 to 1400 µm (median 206 µm for rods) for Ga solvent-based crystals (length of rods) and 0 to 850 µm (median 115 µm for clusters) for EGaIn solvent-based polyhedral crystals (Supplementary Figs. 10c, f). Crystals obtained under moderate-cooling conditions exhibit sizes intermediate between those formed under slow- and fast-cooling (Fig. 4f, i), ranging from 0 to 650 µm, with median sizes ~70 µm and 50 µm for crystals formed in Pt-Ga and Pt-EGaIn solvent, respectively (Supplementary Fig. 10b, e). In comparison, fast-cooling, results in smaller crystals (Fig. 4e, h) observed to range between 0 to 200 µm (median 52 µm) and 0 to 160 µm (median 32 µm) for Ga and EGaIn solvent-based crystals, respectively (Supplementary Fig. 10a, d). These size distributions are similar above approximately a 25 µm threshold (XCT imaging limit in our work) to those presented in Fig. 3. The imaging rate of our XCT instrument is a limitation and more advanced XCT instruments can result in a much better matching of the median value.

The larger crystal sizes formed during the slow-cooling process result from the increased time available for solute molecules to arrange into the growing crystal lattice. Besides, the slow-cooling condition provides more time for the Ostwald ripening process to occur where the smaller crystals dissolve, allowing the solute to redistribute, and contribute to the growth of larger crystals. Different parameters of the environmental boundaries, the cooling rates, and the chemical compositions of solvent are crucial factors governing material formation and properties, thereby shaping the growth behavior of crystals. How the addition of other parameters, such as magnetic field, can influence crystals characteristics remain as interesting topics for future studies.

DFT and AIMD simulations for defining crystals growth
The effect of intermetallic Pt crystals on the liquid metal properties was determined using ab initio molecular dynamics simulations. The first model system (Fig. 5a–e), the Pt particles were represented using a Pt(001) surface, interfacing with liquid metal (Ga, EGaIn, and In) to provide insight into the fundamental atomic distribution and interaction between the growing Pt crystals and liquid metals (Ga, EGaIn, and In). The second model system of Pt dopant in 6-layer Ga matrix was intended to examine the availability of Pt at the liquid metal interface, in order to better understand possible growth mechanisms.

The simulations represent fast-cooling (Fig. 5) and slow-cooling (Supplementary Fig. 12) conditions. The analysis of system pressure during the AIMD simulations is provided in the Supplementary Note 3. The radial distribution functions (RDFs) for the three systems (Fig. 5b) show that the main interaction between the Ga and Pt atoms is at a distance of ca. 2.5 Å in the Ga(l)/Pt system, while the dominant peak between In and Pt is at a greater distance of ca. 3.0 Å in the In(l)/Pt system. The dominant peak in the RDF between Ga and Pt is higher in intensity than that between In and Pt, suggesting that the interaction between Ga and Pt is stronger than that between In and Pt. In the EGaIn(l)/Pt system, the intensity of the first-shell peak at 2.5 Å, corresponding to a Ga-Pt interaction increases in intensity compared to the pure Ga system, while the peak at 3.0 Å, corresponding to an In-Pt interaction, decreases. This indicates that the addition of In to liquid Ga enhances the interaction between Ga and Pt and weakens the interaction between In and Pt. The RDFs for the liquid metals themselves (Fig. 5c) indicate that they retain their liquid properties, as evidenced by the absence of distinct peaks representing long-range ordering.

The density profiles of Ga and In along the z-axis (starting from the outermost Pt surface layer at ca. 9.3 Å) for the simulation representing fast-cooling (Fig. 5d, e) show distinct patterns. In the Ga(1)/Pt system, Ga reaches its highest peak at ca. 9.8 Å, with multiple lower-intensity peaks at greater distances. In contrast, for the In(l)/Pt system, the In is mostly located a bit further from the Pt surface, at a distance of ca. 10.1 Å. In the EGaIn system, the main Ga peak is again at ca. 9.7 Å, however, the In is more evenly distributed throughout the system as shown by peaks of more uniform intensities. Also, the first peak for In shifts to ca. 10.8 Å. This also indicates that the solid Pt has a less pronounced effect on the distribution of In, consistent with the weaker interactions between In and Pt as also indicated by the RDFs.

The mean squared displacement (MSD) analysis (Fig. 5f) shows that the liquid metals maintain their diffusive behavior, under these conditions. Notably, Ga in the Ga(l)/Pt system exhibits a higher diffusion rate than In in the In(l)/Pt system. However, the addition of In to Ga significantly impacts the mobility of Ga, resulting in a lower diffusion rate in the EGaIn(l)/Pt system. Hu et al. have conducted an extended theoretical investigation of classical nucleation possibilities, highlighting the roles of interfacial pre-ordering and interfacial energy in influencing crystallization. A high degree of geometric structuring is apparent within 8.5 Å of liquid Ga interfaces (surface of liquid metal) and can be engineered by the addition of oxide layers or other elements. The preferential mobility of Pt atoms toward the bulk liquid Ga, combined with the strong Ga-Pt interaction, limits Pt’s diffusion and affects their interfacial behavior. The observation of different intermetallic compositions depending on cooling rate and solvent suggests a kinetic explanation for the change of composition, based on the relative availability of the Pt dopant as the crystal forms in solution.

DFT calculations of the mobility of individual Pt atoms were performed for slabs of liquid Ga or EGaIn, 6 atomic layers thick, at 500 K. This temperature was chosen to ensure the surface in the simulations remained liquid, as the melting point of a finite slab of Ga is well-understood to be higher than that of bulk Ga in experiment and maximizes the chance of migration of the dopant being observed. This offset in temperature can be thought of as a systematic shift made to ensure that the liquid Ga in the simulations maintains a similar mobility to experimentally observed Ga.

Pt was doped into the cell in place of a Ga atom at approximately the mid-point of the model. The duration of the simulation was 100 ps with a 2 fs timestep (Supplementary Note 3). The average MSD of the dopant atom in the z-direction – i.e. towards the surface of the slab – are pictured in Fig. 5g. Notably, the MSD for the Pt atom in Ga is significantly higher than in EGaIn, reflecting a higher mobility of the dopant. This will be reflected in a higher availability of Pt as the intermetallic crystal phase grows and thus provides an explanation for the higher proportion of the Pt-deficient Ga7Pt3 intermetallic phase in the EGaIn solvent.

Proof-of-concept HER performance
To demonstrate a utilization of the findings, a proof-of-concept HER study of the synthesized materials, using different metal solvent systems and cooling, was evaluated in both acidic (0.5 M H2SO4) and alkaline (0.1 M KOH) media. In this study, the synthesized crystals were first loaded onto a polished glassy carbon electrode (GCE) with a surface area of 0.196 cm2, which served as the working electrode. A graphite rod and a saturated calomel electrode (Hg/Hg2Cl2, SCE) were used as the counter and reference electrodes, respectively. The schematic illustrations of HER samples preparation and experimental setup are shown in Fig. 6a, b. The potential was applied to the system and calculated according to the Nernst equation (Supplementary Eq. (2a, b)), and the Tafel plots were derived from the polarization curves using the Tafel equation (Supplementary Eq. (3a, b)).

The variation in HER performance among the samples can be attributed to the solvent used, the extracted solid crystals, their phase, and their surface porosity. A detailed discussion of these differences is presented as follows and illustrated in Fig. 6. Based on linear sweep voltammograms-LSV (Fig. 6c, d) and Tafel analysis (Supplementary Fig. 14), crystals obtained from the liquid Ga system showed superior HER activity compared to those from the liquid EGaIn system across both media, regardless of cooling rate during synthesis.

Among all samples, the electrode containing crystals from the liquid Ga system formed during fast-cooling exhibited the highest HER catalytic activity (Fig. 6c, d). The Pt-Ga crystals produced under fast-cooling conditions were primarily composed of Ga2Pt, which contained smaller crystals than those synthesised during slow-cooling. These crystals displayed high HER performance, achieving a low overpotential of −102 mV vs RHE at a current density of −10 mA/cm² in acidic medium (Fig. 6c). In alkaline medium (0.1 M KOH), the same crystals required a slightly more negative potential of −171 mV vs RHE at −10 mA/cm² (Fig. 6d). Supplementary Fig. 13 illustrates the LSV of Pt/C serves as the benchmark. Since Ga is much cheaper than Pt, achieving good HER performance with less Pt represents a technological advancement.

Figure 6c, d and Supplementary Fig. 14 demonstrate that the catalytic activity for all of the systems are better in the acidic environment compared to alkaline conditions. In alkaline electrolytes, it is known that HER activity depends on the speed of water dissociation. The additional energy barrier introduced by water dissociation determines the rate of alkaline HER. This is the reason the benchmark of Pt displays sluggish alkaline HER. Crystals extracted from a liquid Ga-based solvent formed Ga2Pt intermetallic crystals, and it is well known that Pt plays the catalytic role in HER. It is worth mentioning that the usage of Ga in this system also proved advantageous, as we have previously shown that each Pt atom can be covered by several Ga atoms, with Ga atoms exhibiting activation comparable to that of Pt atoms.

Something also important is the strong performance of Ga2Pt, regardless of the crystal size dimensions. This phenomenon may stem from small pores on the surface of Ga2Pt crystals, formed as Ga was etched away during extraction, as shown in our SEM images (Fig. 7a–d). The extraction process produced porous surfaces with varying porosity due to crystal orientation and surface properties under different growth solvents and cooling conditions. The crystals obtained after fast- and slow-cooling have different surface properties, which result in varying pore sizes after initial NaOH washing. Specific phases of the Ga-Pt alloys have a higher tendency to form porous structures due to their crystal orientation and surface properties. It appears that the nano- and meso-porous surface of samples, obtained through fast-cooling, leads to a more porous surface, enhance a higher surface area, contributing to better HER performance compared to the slow-cooling samples, where only sparce etched areas are present, resulting in a less porous surface.

The pore size distribution is illustrated in Fig. 7e–h. The pore size distributions of crystal obtained from Ga- and EGaIn-based solvents, under fast-cooling condition, generally show comparable pore sizes, ranging from 10 to 300 nm. Under slow-cooling conditions, the pore sizes are typically larger than those formed under fast-cooling conditions. It ranges from 15 to 500 nm for Ga-based crystals, and 40 to 1020 nm for EGaIn-based crystals. In addition, regarding the porous morphology (Fig. 7a–d), the porous structure that emerged from Ga-based solvent crystals tend to be more elongated, whereas those from EGaIn-based solvent crystals are generally more circular.

The crystals obtained from EGaIn solvent systems, exhibited inferior HER activity compared to those obtained from Ga solvent samples. The inclusion of In in liquid metal solvents, EGaIn(l), led to the presence of In on the surface of and within crystals (Fig. 4h–j). The presence of In could potentially hamper the active catalytic sites of Pt (Supplementary Note 4). In addition, it is also seen that pores in In-containing samples are not as widespread across the surface of crystals (Fig. 7c, d). This may either be due to the presence of surface In or the effect of crystal orientation that hampered the production of surface pores.

Overall, we showed that In inclusion and surface structural changes affect the catalytic performance of the extracted crystals for HER activity. Altogether, the solvents’ properties and cooling rates contributed to the modulation of crystal phases, their interfaces, and subsequently altered catalytic performance of the materials extracted from solvents. Fast-cooling of Ga leads to the highest HER activity of the extracted crystals, compared to those extracted from EGaIn and the slow-cooling.

Methods
Materials and liquid metal droplet preparation
Gallium (Ga shots, 99.999%, Indium Corporation, USA), Indium (In shots, 99.999%, Indium Corporation, USA), and Platinum (Pt beads, ≤3 mm, 99.999%, Indium Corporation, USA) were used as received for alloy preparation. Sodium hydroxide (NaOH pellets, Chem-Supply, Pty., Ltd) were used in extraction experiments. To prepare the liquid metal droplets, pre-weighed liquid metal solvents (Ga and In) were first melted and mixed in a glass vial on a hot plate at 300 °C for 2 h to create a homogeneous solvent. Pt beads (2% by wt) were dissolved into the liquid metal solvents on a hot plate at 500 °C for 6 h to ensure successful alloying was accomplished and homogeneous liquid alloys were obtained. The liquid metal droplets were prepared by drop-casting the liquid melts onto a silicon wafer. For fast-cooling process, the liquid metal droplets were left as is. For slow-cooling, the liquid metal droplet was placed into a LINKAM stage (LINKAM HFS600E-PB4) programmed to pre-condition at 500 °C for 1 h, followed by cooling from 500 °C to 20 °C at a rate of 1 °C per minute. All of the experiments were conducted in an ambient environment.

X-ray micro-CT scanning for liquid metal droplet
The Bruker X-ray Micro-CT Skyscan 2214 (micro-XCT) scanner was used for scanning the liquid metal droplet sample for analyzing the microstructure and spatial arrangement of the formed crystal within liquid metal bulk. The X-ray source was set to a beam energy of 140 kV with a current of 65 μA. A Cu 0.5 mm filter was used to minimize the effects of beam hardening. The samples were rotated over 180° during collection of the projections. The projections were then reconstructed with NRecon software (Version 2.2.0.6). CTVox (from the Bruker 3D.Suite, Version 3.3.1) software was utilized for visualizing the 3D reconstructed dataset, while the Avizo (ThermoFisher Scientific, Version 2022.2) software was employed to analyze the size distribution of the formed crystals, which can be used for measuring the 3D length of the crystals by determining the maximum Feret diameter of each object. The samples were scanned at the practical limit of resolution for our XCT, given the dimensions of the droplets. As a result, the minimum resolvable feature was determined to be 25 µm or greater.

Extracting and washing the formed crystals
The extraction process utilized a 20 µm pore size nylon membrane filter (Merck Millipore), placed in a funnel assembled with a vacuum system to accelerate the filtration process and allow the liquid metal to diffuse through the membrane. The liquid metal alloy droplet was then deposited on the surface of the membrane and immersed in an excess of 1.0 M sodium hydroxide solution as an electrolyte. A positive gold electrode was connected to the liquid alloy, while the negative gold electrode was immersed in the electrolyte surrounding the liquid metal droplet. A DC voltage of +5 V was applied to the system using a programmable linear power supply (Singlet SPD 3303x) to reduce the surface tension of liquid metal alloy to near zero. The liquid metal passed through the membrane, leaving behind the unfiltered portion containing crystal formed on top of the membrane. The crystals were obtained for further washing process. The formed crystals from the extraction process were washed with 15 mL of 0.50 M NaOH to remove the excess Ga/EGaIn inclusions. Subsequently, the product was washed with Milli-Q water to remove excess NaOH. Finally, the crystals were collected for further characterization and utilization.

Theoretical calculations
DFT calculations were carried out using the Vienna ab initio simulation package (VASP, Version 6.4.2). The core electrons were treated utilizing the projector augmented wave method (PAW) method and the Perdew−Burke−Ernzerhof (PBE) exchange correlation functional was used. The kinetic energy cutoff value for the wavefunctions was set to 550 eV.

Three systems were created to represent the different solvents used experimentally and to investigate their interaction with the Pt particles. In each cell, a layer of amorphous Ga, GaIn or In were placed on the top of a 4-layer Pt(001)-[4×4] slab. A (001) plane of Pt crystal was chosen to represent the Pt particles. The Pt(001) surface was cleaved from bulk Pt and expanded to a 4×4 supercell with optimized lattice parameters of 11.1×11.1 Å2. The upper amorphous Ga and In layers, each comprising 72 atoms, were generated using the Amorphous Cell module in Materials Studio 2022 and placed on the top of the Pt(001) surface. Similarly, the amorphous EGaIn system was constructed with 54 Ga atoms and 18 In atoms (atomic ratio of Ga/In = 3:1). A vacuum region greater than 15 Å in the direction perpendicular to the slabs was implemented to eliminate interactions between periodic cells. The three models, Ga(l)/Pt, EGaIn(l)/Pt and In(l)/Pt all had the same supercell dimensions of 11.1×11.1×40.0 Å3. All systems were sampled with 1×1×1 k-points in consideration of the efficiency, given the large number of electrons in Pt atoms and the dynamics of liquid metals. All atoms in the systems were relaxed until the Helman-Feynman force on each relaxed atom reached less than 0.03 eV Å−1 and the total energy was converged to 1×10−4 eV.

To simulate a fast-cooling process, an ab initio molecular dynamics simulation (as implemented in VASP) was performed for a simulation time of 10 ps (using a 2 fs timestep and a total of 5000 steps) using an NVT ensemble, and a Nose-Hoover thermostat to control the temperature, decreasing from 773 K to 293 K. A slow-cooling process was simulated by performing an AIMD simulation for 15 ps (using a 2 fs timestep for 7500 steps) and the same NVT ensemble and temperature control algorithm. The density profile analysis was obtained by extracting the distribution of Ga atoms along the z-axis from the last 500 frames of the AIMD trajectories. The MSD analysis was obtained from the last 800 frames of the AIMD trajectories.

Materials characterizations
The morphology and elemental distribution of the extracted crystals were characterized using a SEM/EDX instrument (JEOL InTouchScope, JSM-IT500HR, paired with a JEOL, Ex-74600U4L2Q model, EDX detector). ImageJ 1.8.0 software was used to quantify the pore size distribution in single crystal. The crystallographic structures and different phases of samples were characterized using the X’pert Multipurpose X-ray diffraction system (PANalytical, λ=1.5418 Å, Cu-Kα radiation) with the acquisition parameters for voltage of 45 kV, current of 40 mA, and a step size of 0.02°.

Hydrogen evolution reaction studies
Sulfuric acid (H2SO4, 98% solution, Sigma-Aldrich), potassium hydroxide (KOH pellets, Chem-Supply, Pty., Ltd), a commercially available Pt/C catalyst (10 wt% Pt loading, Fuel Cell Store, USA), and Nafion solution (99.99%, Sigma-Aldrich) were used in electrochemical studies. Electrochemical measurements were carried out with a CHI760E workstation (CH Instruments Inc., USA) integrated with a rotating ring disk electrode apparatus (PINE Research, USA) coupled to a three-electrode cell. A glassy carbon electrode (GCE, 5 mm in diameter with a surface area of 0.1963 cm2) loaded with different catalysts was used as the working electrode. A graphite rod was used as the counter-electrode throughout the measurements, and a saturated calomel electrode (SCE) electrode was used as the reference electrode. Prior to the sample deposition, the GCE was finely polished with 0.05 m alumina oxide particles on a cloth and rinsed with Milli-Q water. To prepare the catalyst ink, the catalyst powder was uniformly dispersed in a mixture of 450 µL ethanol and 50 µL Nafion (0.5% wt.%). The suspension was sonicated for 30 min to achieve a homogenous catalyst ink. Subsequently, 10 µL of the catalyst ink was deposited onto a polished working electrode and dried at room temperature before testing. In this study, the catalyst powder for the sample consisted of 1 mg crystals, containing ~0.008 mg of Ga and 0.011 mg of Pt, while the control utilized 10 mg of 10% Pt/C, corresponding to 0.02 mg of Pt. Polarization (LSV) curves were carried out in 0.5 M H2SO4 (giving an electrolyte pH of 0) and 0.1 M KOH (giving an electrolyte pH of 13) which was degassed with nitrogen gas for 10 min prior to any measurement, at 5.0 mV/s. All polarization curves were automatically corrected for the iR contribution from the cell. The working electrode was rotated at a speed of 1600 rpm to alleviate the accumulation of evolved hydrogen bubbles on the GCE surface. The recorded potential was converted to a RHE according to the Nernst equation. The electrochemical measurements were performed in a controlled laboratory environment of 25 °C average room temperature.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In the manuscript entitled \"Tailoring the Growth of Metallic Crystals Inside Liquid Metal Solvents\", the authors investigated the three-dimensional formations of the metallic crystals inside liquid metal solvents using X-ray micro-computed tomography, which reveal that the cooling rate and composition of the reaction media influence crystal morphology and intermetallic phases. And this liquid metal-based synthesis showed potential in tailoring their properties for enhancing catalytic activity.\nI think the work can be considered by “Nature Communications” after the following points are suitably addressed:\n1. In lines 154-156, the (Figs. 2a, b) and (Figs. 2c, d) in the sentence should be changed to (Figs. 2a, c) and (Figs. 2b, d), respectively.\n2. For the crystals obtained under slow cooling conditions (Figs. 2b, d), which exhibit irregular three-dimensional structures, how did the author measure the crystal size? The detailed analysis method should be included in the manuscript.\n3. The conclusion in line 248 regarding the reduced Ga-Ga interaction in liquid EGaIn alloy does not align with the data presented in Fig. 4c.\n4. Generally, smaller nanoparticles possess more surface atoms and unique electronic structures, which maybe exhibit superior catalytic performance. However, the nanoparticle size is very large in this work. What advantages can these large alloy particles provide in the catalytic reactions.\n5. In introduction, the authors mentioned \"Additionally, once extracted, the spatial arrangement of the formed crystals within the solvent may be disrupted\". However, in the section of \"Crystals Extraction and Characterization\", the authors also extracted the crystal to further investigate the fundamental process behind the crystals' dimensional changes. Can these characterization results reflect the real properties of the crystals?\n6. In the HER experiments, the overpotential comparison among these different catalysts was conducted at a current density of -10 mA/cm². Please provide experimental details, such as catalyst loading, pretreatment procedures of catalyst or others.", "reviewer_2": "The work by Widjajana et al. studied the synthesis of metallic crystals in the solution of liquid metals like Ga and EGaIn. They observed the different properties of the formed metallic crystals, assisted by different cooling rates. The physical mechanism was investigated by computational modeling. Finally, the function of metallic crystals was tested from hydrogen evolution reaction to assess its potential usage. The work follows a typical framework of materials science research and made trials on new materials fabrication procedures. However, I cannot see the critical scientific question that was discussed and answered in this work. The novelty from technical and scientific is not convincing enough. Therefore I cannot recommend its publication in Nature Communications, while providing the following suggestions/comments for the authors to consider.\nThe introduction part gives some information on many different aspects, what are the main focus and motivation/question/literature for the current study? Why the research topic is important to be published in the journal? How can the authors control the morphology, composition, and crystal structure of the metallic crystals formed inside of the solvents? What are their differences from other circumstances? Why are the solvents critical?\nThe crystal property analysis to me is too abstract. There are much more to be discussed and analyzed.\nWhy the crystal size observation is consistent with the classical nucleation theory (CNT)? More details are needed for clarification. CNT assumes random fluctuation for nucleation and depends on the chemical potential difference under the condition of a spherical nucleus. What are the connections and differences from the current experiments? What are the quantitative variables here related to CNT?\nWhat is “fast” versus “slow” cooling? How to quantitatively define them in the experiments? If cooled faster, will a glassy state be reached?\nThe DFT and AIMD calculations are performed under different conditions from the solvent environments in experiments. How can one close this gap to make convincing conclusion? More evidence and discussion are helpful.\nThe current discussion on the HER activity lacks a comparison test to highlight the better performance of metallic crystals made by the current method. I cannot see why the liquid metal solvents are important to control the properties of these crystals. Are these functions inherently from the materials themselves, irrespective of how they are made?"}, "author_response": "Response the review comments:\nReviewer #1 (Remarks to the Author):\nIn the manuscript entitled \"Tailoring the Growth of Metallic Crystals Inside Liquid Metal\nSolvents\", the authors investigated the three-dimensional formations of the metallic crystals\ninside liquid metal solvents using X-ray micro-computed tomography, which reveal that the\ncooling rate and composition of the reaction media influence crystal morphology and\nintermetallic phases. And this liquid metal-based synthesis showed potential in tailoring their\nproperties for enhancing catalytic activity.\nI think the work can be considered by “Nature Communications” after the following points are\nsuitably addressed:\nResponse: We sincerely thank you for your constructive comments and for considering our\nmanuscript for publication in “Nature Communications”. We have carefully addressed the\ndetailed points raised and revised the manuscript to incorporate each of the suggestions.\n1. In lines 154-156, the (Figs. 2a, b) and (Figs. 2c, d) in the sentence should be changed to (Figs.\n2a, c) and (Figs. 2b, d), respectively.\nResponse: Thanks for the suggestions. We have improved the figure, revised the sentences,\nand included the correct link to Fig. 2. The caption and related text have been modified\naccordingly.\n(Page 8): “Under fast-cooling conditions, smaller crystals were obtained as depicted in Figs.\n2a, c. These crystals were dispersed at the interface of the liquid metal droplet. Conversely,\nunder the slow-cooling condition, much larger crystals were obtained as per Figs. 2b, d. The\ncrystals formed in the liquid Ga system (Figs. 2a, b) were mostly rod-shaped, while\npolyhedron-shaped tended to be observed in the liquid EGaIn medium (Figs. 2c and d).”\nFig. 2 | 3D observation of grown crystals within a liquid metal droplet through XCT\nscanning. a,b, Formation of crystals inside Ga liquid metal droplet under (a) fast-cooling, and\n(b) slow-cooling condition. c,d, Formation of crystals inside EGaIn liquid metal droplet under\n(c) fast-cooling, and (d) slow-cooling condition. e,f,g,h, Size distributions of the crystals under\ndifferent experimental conditions in (a) to (d).\n2. For the crystals obtained under slow cooling conditions (Figs. 2b, d), which exhibit irregular\nthree-dimensional structures, how did the author measure the crystal size? The detailed analysis\nmethod should be included in the manuscript.\nResponse: Thanks for your suggestion. To address it, the following text has been added to the\npaper on page 8: “All data were obtained using the image processing software Avizo (Thermo\nFisher Scientific), which can be used for measuring the 3D length of the crystals by determining\nthe maximum Feret diameter of each object.”\n3. The conclusion in line 248 regarding the reduced Ga-Ga interaction in liquid EGaIn alloy\ndoes not align with the data presented in Fig. 4c.\nResponse: We appreciate your thoughtful insight. To improve clarity, we have removed the\nfollowing sentence on page 13: “It is also noted that both the Ga-Ga and In-In interactions\ndecrease due to the presence of the Ga-In interaction in the liquid EGaIn alloy.” which was\nredundant. In short, the simulation results conclude that there is a stronger interaction between\nGa and Pt compared to In and Pt. Additionally, the introduction of In could potentially reduce\nor inhibit the Ga-Pt growth. They have been explained in the paper.\n4. Generally, smaller nanoparticles possess more surface atoms and unique electronic structures,\nwhich maybe exhibit superior catalytic performance. However, the nanoparticle size is very\nlarge in this work. What advantages can these large alloy particles provide in the catalytic\nreactions.\nResponse: Thank for your excellent comment. We agree with your feedback that the smaller\nnanoparticles (crystal formed under the fast-cooling process) have more surface atoms and\nexhibit better HER activity than those formed under the slow-cooling method as shown in Figs.\n5a, b. The larger crystal system was fabricated to facilitate the observation in our micro-XCT\nanalysis, and this limitation can be addressed by utilizing nano-XCT. To highlight the influence\nof crystal size on HER performance and their nanoporous surface obtained after washing, we\nhave revised Fig. 5 in the paper (Page 18).\nFig. 5 | HER activity of the extracted crystals obtained under different experimental\nconditions. a,b, Polarization (LSV) curves for the formed crystals performed in (a) an acidic\nelectrolyte, and (b) an alkaline electrolyte. c,d, SEM images showing porosity of typical\ncrystals formed in EGaIn liquid metal solvents under (c) slow-cooling, and (d) fast-cooling\nmethod. e,f, SEM images showing porosity of typical crystals formed in Ga liquid metal\nsolvents under (e) slow-cooling, and (f) fast-cooling method.\n5. In introduction, the authors mentioned \"Additionally, once extracted, the spatial arrangement\nof the formed crystals within the solvent may be disrupted\". However, in the section of\n\"Crystals Extraction and Characterization\", the authors also extracted the crystal to further\ninvestigate the fundamental process behind the crystals' dimensional changes. Can these\ncharacterization results reflect the real properties of the crystals?\nResponse: We appreciate your thoughtful insight. Once the crystals are extracted from the\nsolvent (liquid metal droplet), we can no longer track their spatial arrangement (how the\ncrystals are positioned) within their growth environment in the liquid metal droplet.\nAdditionally, extraction process terminates their growth. The purpose of XCT analysis is to\nprovide in-process control while preserving the pristine condition of the sample. In short, post-\nextraction characterization still reflects the intrinsic properties of the crystals. The choice of\nanalysis depends on the intended application of the material.\nTo address this comment, we performed pre-extraction analyses, and the results align with the\npost-extraction characterizations, as shown in the new Supplementary Fig. 5 (SI, page S10). To\nimprove clarity, we revised the text in the paper.\n(Page 9): “To further investigate the detailed properties of the crystals formed within the liquid\nmetal droplet, both the bulk sample containing the crystals and the extracted crystals were\nexamined to characterize their physical dimensions and crystalline structure. The\ncharacterization of the bulk sample aims to explore the crystal properties in their original\nenvironment, while the post-extraction analysis focuses on examining the extracted crystals\nwithout interference from the background (solvent).”\n(Page 10): “Additional peaks corresponding to Ga and In are observed in the XRD of the bulk\nsample, confirming the presence of the solvents used as the growth medium (Supplementary\nFigs. 5a, b). The pre- and post-extraction XRD results are consistent, suggesting that the\nextraction process does not alter the characteristics of the formed intermetallic crystals.”\n(Page 10): “The SEM observations of the surface of the bulk samples reveal similar\nmorphologies to those observed in the extracted crystals at the surface boundaries, with the\ncrystals still surrounded by their solvent (Ga or EGaIn), as shown in Supplementary Figs. 5c-\nf. In the fast-cooling process, the crystals tend to reside at the interface of the droplets,\nemerging from their solvent. In contrast, in the slow-cooling samples, the crystals tend to be\nlocated beneath the interface, likely due to their larger size.”\nSupplementary Fig. 5 | Characterization of bulk liquid metal samples containing the\nformed crystals. a, b, XRD patterns of bulk samples from (a) Ga liquid metal solvent and (b)\nEGaIn liquid metal solvent under fast- and slow-cooling conditions. c, d, SEM images of bulk\nGa liquid metal samples under (c) fast- and (d) slow-cooling conditions. e, f, SEM images of\nbulk EGaIn liquid metal samples under (e) fast- and (f) slow-cooling conditions.\n6. In the HER experiments, the overpotential comparison among these different catalysts was\nconducted at a current density of -10 mA/cm². Please provide experimental details, such as\ncatalyst loading, pretreatment procedures of catalyst or others.\nResponse: Thank you for your suggestions. We have revised the text to include the following\nsentences.\n(Page 16): “In this study, the synthesized crystals were first loaded onto a polished glassy\ncarbon electrode (GCE) with a surface area of 0.196 cm2, which served as the working\nelectrode. A graphite rod and a saturated calomel electrode (Hg/Hg Cl , SCE) were used as the\n2 2\ncounter and reference electrodes, respectively.”\n(Page 22): “To prepare the catalyst ink, the catalyst powder was uniformly dispersed in a\nmixture of 450 µL ethanol and 50 µL Nafion (0.5% wt.%). The suspension was sonicated for\n30 min to achieve a homogenous catalyst ink. Subsequently, 10 μL of the catalyst ink was\ndeposited onto a polished working electrode and dried at room temperature before testing. In\nthis study, the catalyst powder for the sample consisted of 1 mg crystals, containing\napproximately 0.008 mg of Ga and 0.011 mg of Pt, while the control utilized 10 mg of 10%\nPt/C, corresponding to 0.02 mg of Pt.”\nReviewer #2 (Remarks to the Author):\nThe work by Widjajana et al. studied the synthesis of metallic crystals in the solution of liquid\nmetals like Ga and EGaIn. They observed the different properties of the formed metallic\ncrystals, assisted by different cooling rates. The physical mechanism was investigated by\ncomputational modeling. Finally, the function of metallic crystals was tested from hydrogen\nevolution reaction to assess its potential usage.\nThe work follows a typical framework of materials science research and made trials on new\nmaterials fabrication procedures. However, I cannot see the critical scientific question that was\ndiscussed and answered in this work. The novelty from technical and scientific is not\nconvincing enough. Therefore, I cannot recommend its publication in Nature Communications,\nwhile providing the following suggestions/comments for the authors to consider.\nResponse: We appreciate your valuable comments and the time taken for reviewing our\nmanuscript. We understand the concerns about the scientific novelty and critical questions\nregarding our work. After careful reconsideration, we have made the following revisions and\nclarifications, as outlined below.\nIn addition, we included additional materials to further highlight the novelty of our work,\nincluding expanding discussions, explaining the scientific gap that the work covers, adding\nthree new figures and two tables, and significantly improved all existing figures.\n1. The introduction part gives some information on many different aspects, what are the main\nfocus and motivation/question/literature for the current study? Why the research topic is\nimportant to be published in the journal?\nResponse: Thank you for your comments. We address the questions as follows:\nThe main focus of this study is to provide direct (in situ) observation of crystal growth inside\nliquid metal using X-ray micro computed tomography (XCT), without disrupting the growth\nprocess itself. This is something that has not been shown previously.\nThe opaque nature of liquid metal makes it non-transparent to low- and mid- energy\nelectromagnetic waves, and even high-energy electron beams struggle to penetrate them1.\nTherefore, the motivation of this study is to (1) determine whether crystals successfully grow\ninside liquid metals without disrupting their environment, and (2) observe the spatial location\nof the crystal growth within liquid metals.\nWe add more explanation to the paper to illustrate the current challenge in this field, propose a\nsolution to address this issue, and draw your attention to the following:\n(Original text, page 3): “While liquid metals offer promising potential as the growth media for\nmetallic solutes2, crystal growth observation within liquid metal solvents has remained a\nchallenge3. One reason for this is that liquid metals are non-transparent to low- and mid- energy\nelectromagnetic waves, and even high energy electron beams struggle to penetrate them,\nleading to a tendency to overlook phenomena that cannot be directly observed1. Investigating\ncrystal growth within bulk liquid metals provides fundamental insights into the nucleation and\ngrowth mechanisms, elucidating the underlying principles governing solidification kinetics and\nphase transformations inside liquid metal systems.”\n(Original text, page 7): “By utilizing XCT analysis, the crystal inside liquid metal droplet can\nbe observed, while preserving their original environment, as presented in Figs. 2a-d.”\nThis research topic is important because direct observation of crystal growth inside liquid metal\ncan serve as a preliminary quality control, to determine whether the crystals have formed\nsuccessfully, as per the demand of the application. In this work, for the first time, we show that\nXCT can function as an in-process control (IPC) during crystal fabrication. This observation\nmethod offers an innovative approach for controlling the quality of liquid metal-based crystals\nduring fabrication. The following text has been added to the paper in response to the second\nquestion:\n(Page 4): “The novelty of this research lies in the ability to observe crystal growth and\nmorphologies inside liquid metal using XCT. This method allows crystal growth to be\nvisualized without disrupting the surrounding environment or the boundary (i.e., the liquid\nmetal as a solvent). To the best of the authors’ knowledge, there is no existing literature\ndiscusses the direct observation of crystals forming inside liquid metal.”\nAdditionally, we have significantly revised Fig. 1 (page 7), which shows the schematic of our\nstudy, and added Supplementary Fig. 1 (SI, page S6), which includes a real photo of the XCT\nused in this study, a photograph of the sample showing the opacity of the liquid metal droplet,\nand a schematic illustration of the cross-sectional CT 2D image slices. We have also added the\nfollowing sentences to the paper.\n(Page 6): “Afterward, the crystal extraction process from the liquid metal droplets (Fig. 1c)\nwas carried out to examine their physical dimensions and crystalline structure in detail.”\n(Page 7): “Supplementary Fig. 1 shows a photo of the XCT instrument used in this experiment,\nwith the sample holder, a brass pin mounted on a rotational stage, positioned between the\nsource (left) and the detector with filter wheel (right). The liquid metal droplet was drop-cast\nonto a silica wafer, mounted onto the sample holder, as shown in the zoomed-in photo in\nSupplementary Fig. 1b (left).”\n(Page 7): “When two-dimensional (2D) image stacks, as illustrated in Supplementary Fig. 1c,\nwere reconstructed into 3D volumes, the pixels were represented as voxels (volume elements)4.”\n(Page 7): “The photo of the sample, illustrating the opacity and surface reflectivity of a liquid\nmetal droplet, is shown in Supplementary Fig. 1b (right).”\nFig. 1 | Schematic illustration of growing crystals inside liquid metal bulk and the XCT\nanalysis. a, Alloying procedure for growing metal crystals inside a droplet of liquid metal\nsolvent. b, Experimental setup for XCT scanning of liquid metal droplets. c, Extraction process\nof crystals from inside liquid metals electrochemically aided by a vacuum-driven force.\nSupplementary Fig. 1 | Photos of instrument and sample. a, XCT instrument. b, liquid metal\ndroplet mounted onto XCT sample holder (left) and top view of liquid metal droplet as a sample\n(right). c, Schematic illustration of the cross-sectional CT 2D image slices.\n2. How can the authors control the morphology, composition, and crystal structure of the\nmetallic crystals formed inside of the solvents? What are their differences from other\ncircumstances? Why are the solvents critical?\nResponse: Thank you for your comments. We answer each question as follows and summarize\nthe responses in the provided table.\nRegarding your first question, the authors control the morphology, composition, and crystal\nstructure of the metallic crystals formed inside the liquid metals solvents by (1) adjusting the\ncomposition (%) of the solvents (in this case Ga and EGaIn) and the solutes (Pt) (2) regulating\nthe heating duration during the fabrication process, and (3) controlling the cooling rate of the\nfabrication process.\nRegarding your second question, the main difference between the crystal fabrication process\nbased on liquid metal and other circumstances, such as ceramic, arc melting, and high-\nfrequency induction heating, is primarily due to the absence of a need for high temperatures in\nthe fabrication process5.\nRegarding your third question, the reason why using liquid metals as solvents is critical in\ncrystal fabrication can be describes as follows: (1) Liquid metals (Ga and EGaIn) have a low\nmelting points, 29.6 ˚C and 15 ˚C, respectively and they remain in a liquid state at low\ntemperatures, making them practically accessible and easy to handle in a safe laboratory\nenvironments6, (2) Liquid metals are post-transition elements, they are more prone to\ncovalency and exhibit directional bonding effects, making them suitable for metallic bonding,\nas a result, they can be used as solvents (reaction media) for metallic solutes7, (3) Compared to\nother metals, liquid metals have low viscosity8, making them feasible to manipulate and\nenabling further processing, such as extraction, as demonstrated in this study, (4) Metals are\nelectronic liquids with electron conductivity which are in essence different conventional\nsolvents, and (5) Finally, unlike other low-melting-point metals, such as alkali metals, which\nare highly reactive in the presence of air and moisture, post-transition liquid metals eliminate\nsuch problems.\nTo improve the clarity of the text, the following text has been added to the paper:\n(Page 4): “Liquid metals, such as Ga and EGaIn, have low melting points (29.6 ˚C and 15 ˚C,\nrespectively), allowing them to remain liquid at low temperatures, making them accessible and\neasy to handle in laboratory settings6. As post-transition elements, they exhibit covalent\ncharacteristics and directional bonding, enabling their use as solvents for metallic solutes7.\nTheir low viscosity8 facilitates manipulation and processing, such as extraction. Additionally,\nliquid metals function as electronic liquids with intrinsic conductivity, distinguishing them\nfrom conventional solvents. Unlike highly reactive low-melting-point metals like alkali metals,\npost-transition liquid metals are stable in air and moisture, enhancing their practicality.”\nIn addition, we have added Supplementary Table 2 to highlight the key points showing how\nsolvents (liquid metals) critically influence the morphology and composition of the formed\ncrystals.\n(Page 11): “Supplementary Table 2 summarizes the intermetallic crystals formed in different\nliquid metal solvent systems and growth conditions, highlighting the critical points where\nliquid metals influence the morphology and composition of the formed crystals.”\n(SI, page S17): Supplementary Table 2 | Summary of crystal properties formed from\ndifferent liquid metal solvents under varying cooling rates.\nCooling rate Solvent composition Major morphologies Crystal composition\n- Ga Pt (tetragonal)\n- Ga Pt (cubic)\n- Ga Pt (tetragonal)\n2\n- Ga Pt (cubic)\n- Ga Pt (cubic)\n7 3\n- In Pt (cubic)\n7 3\n- Ga Pt (tetragonal)\n- Ga Pt (cubic)\n- Ga Pt (cubic)\n7 3\n- In Pt (cubic)\n7 3\n3. The crystal property analysis to me is too abstract. There are much more to be discussed\nand analyzed.\nResponse: Thank you for your suggestions. To address your comment, we have added the\ncrystallographic parameters of the formed crystals, as listed in Supplementary Table 1.\n(Page 10): “The crystallographic parameters of the formed crystals in two different liquid metal\nsolvents are summarized in Supplementary Table 1.”\n(SI, page S16): Supplementary Table 1 | Crystallographic parameters of the formed\ncrystals in two different liquid metal solvents\nLiquid\nChemical Crystal Space Interaxial angles of\nmetal Unit cell (Å)\nformula system group a unit cell (˚)\nsolvent\na = b = 8.5540; c\nGa Pt9 Tetragonal I41/ acc α = β = γ = 90\n2\n= 21.5740\nGa (l)\na = b = c =\nGa Pt10 Cubic Fm-3m α = β = γ = 90\n2\n5.9110\na = b = c =\nGa Pt 11 Cubic Im-3m α = β = γ = 90\n7 3\n8.7990\nEGaIn (l)\na = b = c =\nIn Pt 12 Cubic Im-3m α = β = γ = 90\n7 3\n9.4160\nWe further performed XRD measurements of the droplets before extracting particles and SEM\nimaging on the surface of droplets also before the crystal extraction process. In these cases, the\ncrystals remained inside or near the surface of the liquid metal solvent droplets, allowing us to\nbetter present the properties of the pristine system (in its natural state), as depicted in the new\nSupplementary Fig. 5 (SI, page S10). The following text has been added to the revised\nmanuscript.\n(Page 10): “Additional peaks corresponding to Ga and In are observed in the XRD of the bulk\nsamples, confirming the presence of the solvents used as the growth medium (Supplementary\nFigs. 5a, b). The pre- and post-extraction XRD results are consistent, suggesting that the\nextraction process does not alter the characteristics of the formed intermetallic crystals.”\n(Page 10): “The SEM observations of the surface of the bulk samples reveal similar\nmorphologies to those observed in the extracted crystals at the surface boundaries, with the\ncrystals still surrounded by their solvent (Ga or EGaIn), as shown in Supplementary Figs. 5c-\nf. In the fast-cooling process, the crystals tend to reside at the interface of the droplets,\nemerging from their solvent. In contrast, in the slow-cooling samples, the crystals tend to be\nlocated beneath the interface, likely due to their larger size.”\nSupplementary Fig. 5 | Characterization of bulk liquid metal samples containing the\nformed crystals. a, b, XRD patterns of bulk samples from (a) Ga liquid metal solvent and (b)\nEGaIn liquid metal solvent under fast- and slow-cooling conditions. c, d, SEM images of bulk\nGa liquid metal samples under (c) fast- and (d) slow-cooling conditions. e, f, SEM images of\nbulk EGaIn liquid metal samples under (e) fast- and (f) slow-cooling conditions.\nWe also revised Fig. 3 (page 12) to include a schematic of crystal growth preferences (Fig. 3d)\nand the following text was added to the paper.\n(Page 10): “The schematic of crystal growth preferences is illustrated in Fig. 3d. Altogether,\nthe crystals exhibited various morphologies and dimensions, as shown by SEM-EDS imaging\nin Figs. 3e-h and Supplementary Figs. 5c-f.”\nFig. 3 | Characterizations of crystals extracted from the liquid metal droplets. a,b, XRD\npatterns of the extracted crystals from (a) Ga liquid metal droplets, and (b) EGaIn liquid metal\ndroplets under the fast- and slow-cooling conditions. c, The ratios of extracted intermetallic\ncrystal phases formed inside the liquid metal droplets. d, Growth preferences for rod-shaped\ncrystal, with the inset illustrating the tetragonal Ga Pt unit cell (top), and polyhedral-shaped\n2\ncrystal, with the inset showing the cubic Ga Pt unit cell (bottom). Ga atoms are shown in green,\n7 3\nand Pt atoms in blue. e,f, SEM images of typical crystals inside Ga liquid metal droplets under\n(e) fast-cooling and (f) slow-cooling conditions. g,h, SEM images of typical crystals inside\nEGaIn liquid metal droplets under (g) fast-cooling and (h) slow-cooling conditions.\n4. Why the crystal size observation is consistent with the classical nucleation theory (CNT)?\nMore details are needed for clarification. CNT assumes random fluctuation for nucleation and\ndepends on the chemical potential difference under the condition of a spherical nucleus. What\nare the connections and differences from the current experiments? What are the quantitative\nvariables here related to CNT?\nResponse: Thank you for your thoughtful comment. We agree that it is important to distinguish\nthe nucleation phase of crystal formation from the growth phase. The simulations conducted in\nthis work are aimed at probing only the diffusion-limited growth phase of the crystals and serve\nto indicate why the growth of a crystal of a particular stoichiometry might be favored. Many\nmodels of crystal formation, including CNT, make this separation between nucleation and\ngrowth processes. Indeed, the two processes often compete for crystal substrate. The main\nquantitative variable related to CNT is the nucleation rate (J), which at certain stages (due to\ncompetition with crystal growth), the nucleation rate tends to be inversely related to the crystal\nsize. In summary, the simulations show that diffusion-limited growth can explain the difference\nin intermetallic phase, due to different rates of dopant diffusion, while the experimental\nvariation of cooling rates shows that nucleation rate differences explain the much larger crystal\nsize under slow-cooling conditions. Accordingly, we have revised the following text in the\nSupplementary note.\n(SI, page S1): “The observed crystal size results from the competing processes of nucleation\nand growth, with the nucleation process can be explained with the classical nucleation theory\n(CNT). In this equation, the rate of nucleation (J in m-3∙s-1) decreases exponentially with\nincreasing energy barrier (∆G∗ in Joule mol-1) and with increasing temperature of the system\n(T in Kelvin). The ∆𝐺∗ is related to the undercooling (∆𝑇) (i.e., fast- and slow-cooling), such\nthat ∆𝐺∗ ∝ ∆𝑇 -2 13. This indicates that higher cooling rates (fast-cooling) result in higher\nsupersaturation in the system, leading to a lower critical energy barrier and a higher nucleation\nrate. In contrast, in the slow-cooling method, the temperature decreases gradually, resulting in\na smaller (∆𝑇), leading to an energy barrier of nucleation (∆G) must be overcome for nucleation\nto occur, resulting to a lower nucleation rate (J). The CNT equation is provided in\nSupplementary Eq. 114.\n−∆G∗ (Eq. S1)\nJ = J ∙exp( )\n0 𝑘 ∙T\nB\nin which 𝐽 is the initial nucleation rate in m-3 s-1, and 𝑘 is the Boltzmann constant. Here, ∆𝐺∗\n0 𝐵\nbarrier must be overcome to form a crystal. Therefore, the observation of crystal formed under\ndifferent cooling rates, fast- and slow-cooling methods, varying the energetic interactions\nbetween solute and solvent, leads to differences patterns, as observed through XCT analysis in\nFig. 2. In summary, the nucleation rate differences due to different cooling rates explain the\nmuch larger crystal size under slow-cooling conditions.”\n5. What is “fast” versus “slow” cooling? How to quantitatively define them in the experiments?\nIf cooled faster, will a glassy state be reached?\nResponse: Thank you for your insightful comments. Regarding the first question, we have\nrevised the following text in the paper.\n(Page 6): “Fast-cooling is defined as leaving the liquid metal droplet to cool naturally from\n500 °C to ambient temperature, after approximately 5 minutes, during which the temperature\nremained nearly constant. This results in at an approximate average cooling rate of ~95 °C/min.\nIn contrast, slow-cooling is defined as a controlled temperature reduction from 500 °C to 20°C,\nachieved in over 480 minutes, at a rate of 1 °C/min.”\nRegarding the second question, the glassy state is not reached during the fast-cooling as the\nnew XRD analysis of the bulk show sharp peaks that correspond to the regular periodic\narrangement of atoms in the crystal lattice. Please see the new Supplementary Figs. 5a, b in\nresponse to Reviewer#2 Question 3.\n6. The DFT and AIMD calculations are performed under different conditions from the solvent\nenvironments in experiments. How can one close this gap to make convincing conclusion?\nMore evidence and discussion are helpful.\nResponse: We appreciate the reviewer's interest in our selection of two different model systems\nto represent features of the experimental liquid metal system. To address the comments, the\nfollowing discussions have been added to the text:\n(Page 13): “The first model system (Figs. 4a-e), the Pt particles were represented using a Pt(001)\nsurface, interfacing with liquid metal (Ga, EGaIn, and In) to provide insight into the\nfundamental atomic distribution and interaction between the growing Pt crystals and liquid\nmetals (Ga, EGaIn, and In).” While this does not represent the nucleation phase of crystal\nformation, it does provide information into what factors might be important in the growth phase,\nand under this environment once a crystal surface already exists.\n(Page 13): “The second model system of Pt dopant in 6-layer Ga matrix was intended to\nexamine the availability of Pt at the liquid metal interface, in order to better understand possible\ngrowth mechanisms.” This model system is consistent with other examples in the literature15.\nWhile the small system is somewhat limited in fully representing a bulk material, it is still able\nto provide useful information about energetic interactions and dopant behaviors16, 17.\nTo address your comments regarding the simulations performed under different conditions\nfrom the solvent environments in experiments, we discuss and draw your attention to the\nfollowing:\n- In the first simulation experiment, the DFT and AIMD calculations are performed under\nthe same solvent environments and cooling rates as in the practical experiments. Regarding\nthe cooling systems (fast- and slow-cooling), the authors stated in the main manuscript\n(Original text, page 13): “The simulations represent fast-cooling (Fig. 4) and slow-cooling\n(Supplementary Fig. 8) conditions.” and the details of the experimental method can be\nfound in the Methods (Original text, page 21): “To simulate a fast-cooling process, an ab\ninitio molecular dynamics simulation (as implemented in VASP) was performed for a\nsimulation time of 10 ps (using a 2 fs timestep and a total of 5000 steps) using an NVT\nensemble, and a Nose-Hoover thermostat18 to control the temperature, decreasing from\nfor 15 ps (using a 2 fs timestep for 7500 steps) and the same NVT ensemble and\ntemperature control algorithm.”\n- In addition, regarding the solvent environment, the Radial Distribution Functions (RDFs)\nand density profile were analyzed under the same solvent environment as the practical\nexperimental, illustrating the interaction between solute atoms (Pt) and solvent atoms (Ga\nor Ga/In), as well as between solvent atoms (Ga or Ga/In), as shown below in Fig. 4 (page\n15) and Supplementary Fig. 8 (SI, page S13), for fast- and slow-cooling, respectively.\nAltogether, these simulations are performed under conditions that align with the cooling\nrate and solvent used in the laboratory experiment.\n- In the second model simulation systems, we note that the temperature selected from these\nsimulations (500 K) differed from that in experiment (773 K to 293 K). We stated in the\noriginal Supplementary note, page S2: “The temperature was selected to ensure that the\natomically thin Ga-based systems remained liquid for the duration of the simulation, and\nthis value is above previous estimates of the melting point for 6-layer Ga and GaIn15.” To\nimprove the clarity of the text, the following text is added to the paper. (Page 14): “This\ntemperature was chosen to ensure that the surface in the simulations remained liquid, as\nthe melting point of a finite slab of Ga is well-understood to be higher than that of bulk Ga\nin experiment19 and maximizes the chance of migration of the dopant being observed. This\noffset in temperature can be thought of as a systematic shift made to ensure that the liquid\nGa in the simulations maintains a similar mobility to experimentally observed Ga.”\nIn short, these two simulation models complement each other and are performed under\nconditions that align with the practical experiments. There is a stronger interaction between Ga\nand Pt compared to In and Pt. The introduction of In could potentially reduce or inhibit the Ga-\nPt growth, possibly leading to the formation of a Pt-deficient intermetallic phase.\nFig. 4 | AIMD simulations of the liquid metals’ solvents with solid Pt under fast-cooling\nconditions. a, Snapshots of the Ga(l) (upper), EGaIn(l) (middle) and In(l) (lower) on the Pt(001)\nsurface structures after a 10 ps simulation time. b, RDFs between the liquid metal (Ga and In)\nand Pt atoms. c, RDFs between the liquid metal atoms. d,e Density profile analysis of the liquid\nmetal atoms: (d) Ga and (e) In. f, MSD of the liquid metal atoms. g, MSD of Pt atoms\nperpendicular to the surface in a Ga or EGaIn liquid metal matrix.\nSupplementary Fig. 8 | AIMD simulations of the liquid metal solvents with solid Pt under\nslow-cooling conditions. a, Snapshots of the Ga(l) (upper), EGaIn(l) (middle), and In(l) (lower)\non the Pt(001) surface structures after a 15 ps simulation time. b, RDFs between the liquid\nmetal (Ga and In) and Pt atoms. c, RDFs between the liquid metal atoms. d, Density profile\nanalysis of the liquid metal atoms. e, MSD of the liquid metal atoms.\n7. The current discussion on the HER activity lacks a comparison test to highlight the better\nperformance of metallic crystals made by the current method. I cannot see why the liquid metal\nsolvents are important to control the properties of these crystals. Are these functions inherently\nfrom the materials themselves, irrespective of how they are made?\nResponse: Thank you for your comments. In this work, HER is only intended to demonstrate\na potential implication of the findings as a proof-of-concept. We want to show that the crystal\nformed from liquid metal-based materials exhibits different HER performance based on the\ncrystal phase that are governed by the condition and type of the liquid metal solvents. To\naddress your comments, we modified the text and the figure to more clearly highlight the\nmission of this section.\n(Page 16): “To demonstrate a utilization of the findings, a proof-of-concept HER study of the\nsynthesized materials, using different metal solvent systems and cooling, was evaluated in both\nacidic (0.5 M H₂SO₄) and alkaline (0.1 M KOH) media.”\nOur results show that the variations in HER activity in our materials arise from the different\ncrystal properties formed due to variations in the growth environment and conditions.\n(Page 16): “The variation in HER performance among the samples can be attributed to the\nsolvent used, the extracted solid crystals, their phase, and their surface porosity. A detailed\ndiscussion of these differences is presented as follows and illustrated in Fig. 5.”\nWe discussed in the paper that our crystals possess porous structures, so we added new\nsubfigures and insets to Fig. 5, to highlight the points mentioned above, as well as to include\nSEM images showing the porosity in the formed crystals fabricated using liquid metal solvents.\nWe showed that during extra washing with 0.5 M NaOH, more Ga content can be etched away,\nforming nanoporous structures on the surface of the crystals. The porosity increases their\nsurface area, thereby leading to better performance compared to non-porous crystals. The\nfollowing text is now added to the paper:\n(Page 17): “The extraction process produced porous surfaces with varying porosity due to\ncrystal orientation and surface properties under different growth solvents and cooling\nconditions. The crystals obtained after fast- and slow-cooling have different surface properties,\nwhich result in varying pore sizes after initial NaOH washing. This manifests itself in Figs.\n5c-f. Specific phases of the Ga-Pt alloys have a higher tendency to form porous structures due\nto their crystal orientation and surface properties. It appears that the mesoporous surface of\nsamples, obtained through fast-cooling, leads to a higher surface area and contributes to better\nHER performance compared to the slow-cooling samples, where only sparce etched areas are\npresent, resulting in a less porous surface.”\n(Page 17): “This may either be due to presence of surface In or the effect of crystal orientation\nthat hampered the formation of surface pores.”\nIn addition to the HER performance of overpotential at a given current density curve in Fig. 5\n(page 18), the Tafel plot and exchange current density are shown in Supplementary Fig. 10 (SI,\npage S15), illustrating the HER kinetics and the intrinsic catalytic activity of the materials. It\ncan be observed that crystals formed from a liquid Ga solvent under the fast-cooling method\nexhibit HER activity comparable to that of Pt/C for standard benchmarking. The following text\nhas been added to the paper.\n(Page 16): “Supplementary Fig. 9 illustrates the linear sweep voltammograms of Pt/C serves\nas the benchmark. Since Ga is much cheaper than Pt, achieving good HER performance with\nless Pt represents a technological advancement.”\nFinally, the conclusion of the work is that the fabrication method influences the HER activity\nof the formed crystals. As shown in Fig. 5, under the same solvent composition but with\ndifferent cooling rates, the crystals exhibit varying HER activity. We added following text to\nthe paper.\n(Page 17): “Altogether, the solvents’ properties and cooling rates contributed to the modulation\nof crystal phases, their interfaces, and subsequently altered catalytic performance of the\nmaterials extracted from solvents. Fast-cooling of Ga leads to the highest HER activity of the\nextracted crystals, compared to those extracted from EGaIn and the slow-cooling.”\nFig. 5 | HER activity of the extracted crystals obtained under different experimental\nconditions. a,b, Polarization (LSV) curves for the formed crystals performed in (a) an acidic\nelectrolyte, and (b) an alkaline electrolyte. c,d, SEM images showing porosity of typical\ncrystals formed in EGaIn liquid metal solvents under (c) slow-cooling, and (d) fast-cooling\nmethod. e,f, SEM images showing porosity of typical crystals formed in Ga liquid metal\nsolvents under (e) slow-cooling, and (f) fast-cooling method.\nSupplementary Fig. 9 | HER activity of the Pt/C as benchmark under different\nexperimental conditions. (a) acidic electrolyte, and (b) alkaline electrolyte.\nSupplementary Fig. 10 | HER activity of the extracted crystals under different\nexperimental conditions. a,b, Tafel plots derived from the polarization curves in (a) acidic\nelectrolyte, and (b) alkaline electrolyte. c,d, Exchange current density value in (c) acidic\nelectrolyte, and (d) alkaline electrolyte."}, {"round": 2, "reviewer_comments": {"reviewer_1": "After the revision, this work can be recommended for the publication in \"Nature Communications\".", "reviewer_2": "The authors made great efforts to address my previous concerns and the manuscript has been much improved. I agree that this work is helpful to elucidate the underlying principles governing solidification kinetics and phase transformations with detailed study, especially in the growth stage, but not in the nucleation stage, as the authors actually cannot capture the nuclei. So generally I will suggest to remove discuss regarding to nucleation, but only focus on growth discussion, with clear explanation.\nIt will add a lot of value by measuring the growth speed for rod-shaped and polyhedral-shaped crystals in two solvents. This direct measurement will help support the above aim of the current study. However, at this moment, this kind of discussion in obscure.\nHow the shape of the crystal changes during growth? From figure 1a, the liquid state has much different shape than the precipitate. A further suggestion is more precise shape control by adding magnetic field during crystal growth.\nThe authors discussed the directional bonding effect but not with much details. The role of this bond in droplet crystallization has been discussed by 10.1002/smll.202305798.\nSupplementary table 2 conveys interesting information, which, I think, should be an important component with necessary discussion in the main text.\nIn the response to point (4), the conjecture with the classical nucleation theory is not well supported. More theoretical discussion on the classical nucleation theory has been extended in https://doi.org/10.1038/s41467-022-32241-z.\nWhen the HER performance is compared to Pt/C, what is the sample state, comparable to rod or polyhedron? If the porous structure is important, what is the significance of crystallization from the solvent, backing to my previous concern?"}, "author_response": "Response to the Reviewer comments:\nReviewer #1 (Remarks to the Author):\nAfter the revision, this work can be recommended for the publication in \"Nature\nCommunications\".\nResponse: We sincerely thank you for your supportive feedback and recommendation for\npublication in “Nature Communications”. We appreciate your comments and constructive\nsuggestions, which have helped us enhance the overall quality and clarity of our manuscript.\nReviewer #2 (Remarks to the Author):\nThe authors made great efforts to address my previous concerns and the manuscript has been\nmuch improved. I agree that this work is helpful to elucidate the underlying principles\ngoverning solidification kinetics and phase transformations with detailed study, especially in\nthe growth stage, but not in the nucleation stage, as the authors actually cannot capture the\nnuclei. So generally I will suggest to remove discuss regarding to nucleation, but only focus on\ngrowth discussion, with clear explanation.\nResponse: We sincerely thank you for acknowledging the improvements made to our\nmanuscript. We understand your concern regarding the nucleation stage and have accordingly\nremoved the related discussion and instead focused on crystal growth with clearer and more\ndetailed explanation. Furthermore, we have included additional measurements to address the\ndetailed points raised below, introduced two new figures to more clearly address each comment,\nand thoroughly revised the manuscript to incorporate all suggestions.\n1. It will add a lot of value by measuring the growth speed for rod-shaped and polyhedral-\nshaped crystals in two solvents. This direct measurement will help support the above aim of\nthe current study. However, at this moment, this kind of discussion in obscure.\nResponse: We appreciate your comments and agree with your feedback that measuring the\ncrystals growth speed adds significant value to our manuscript. Therefore, we conducted these\nmeasurements and added the following figure (Fig. 3, page 11) in the revised manuscript to\nillustrate how the crystal growth speed varies with different liquid metal solvent compositions\nand cooling rates. Accordingly, the following discussion has been incorporated into the revised\nmanuscript.\n(Page 10): “The crystal growth speed varies depending on the chemical composition of the\nliquid metal solvent and the cooling rate, as illustrated in Figs. 3g-i. Crystals formed in Ga-\nbased liquid metal solvents exhibit faster growth compared to those in EGaIn-based solvents.\nRegarding cooling rates, the fast-cooling conditions results in the fastest crystal growth relative\nto the moderate- and slow-cooling conditions. The crystal growth speed distribution in Ga-\nbased solvents ranges from 13 to 120 µm/min, with a median of 17 µm/min under fast-cooling;\nfrom 3 to 18 µm/min, with a median of 6 µm/min under moderate-cooling; and from 0.5 to 5.7\nµm/min, with a median of 1.4 µm/min under slow-cooling conditions. For crystals formed in\nEGaIn-based solvents, the growth speed distribution ranges from 8.3 to 90.5 µm/min with a\nmedian of 14.6 µm/min; from 1.5 to 11.6 µm/min with a median of 2.8 µm/min; and from 0.3\nto 2.2 µm/min with a median of 0.95 µm/min under fast-, moderate-, and slow-cooling\nrespectively.”\n(Page 10): “Altogether, we illustrated that XCT offers a reliable way to overcome the challenge\nof observing crystal growth within the bulk of liquid metal, an opaque material that is\nimpossible to penetrate with light and electrons6. The combination of using Ga, as the liquid\nmetal solvent, with fast-cooling rate provides the highest crystal growth rate among all\nconditions.”\nFig. 3 | Statistical distribution of crystal under different liquid metal compositions and\ncooling rates. a-c Size distribution of crystals formed in Ga-based liquid metal under (a) fast-\ncooling, (b) moderate-cooling, and (c) slow-cooling conditions. d-f Size distribution of crystals\nformed in EGaIn-based liquid metal under (d) fast-cooling, (e) moderate-cooling, and (f) slow-\ncooling conditions. g-i Crystal growth speed distribution under different liquid metal\ncompositions and cooling rates: (g) fast-cooling, (h) moderate-cooling, and (i) slow-cooling\nconditions.\n2. How the shape of the crystal changes during growth? From figure 1a, the liquid state has\nmuch different shape than the precipitate. A further suggestion is more precise shape control\nby adding magnetic field during crystal growth.\nResponse: Thank you for your insight. We have addressed the first question by adding a large\nnumber of experiments under intermediate conditions to define the shape changes more\nprecisely in the paper. For addressing the following comment, we modified Figure 1. We also\nsuggested magnetic field control in the text for future work.\nIn response to your question regarding how the shape of the crystal changes during growth,\nadditional experiments were conducted to observe the morphological evolution under an\nintermediate (moderate) cooling rate. The results of this study show comparable crystal\nmorphologies, with progressively longer (larger) crystal dimensions observed from the fast- to\nslow-cooling rates. The following discussion and corresponding figures (Fig. 2, page 9 and Fig.\n3, page 11 – depicted in previous comment), which illustrate these shape changes, have been\nadded to the revised manuscript.\n(Page 6): “Moderate-cooling rate is defined as a controlled temperature reduction from 500 ˚C\nto 20 ˚C at an intermediate rate of 10˚C/min, between the fast- and slow-cooling conditions,\nand is achieved over 48 min.”\n(Page 7): “A schematic diagram of the experimental design showing the overall crystal\nformation process, cooling duration, and cooling rate under different cooling conditions, is\npresented in Figs. 2a-c.”\n(Page 8): “The morphological evolution of crystals grown under the moderate-cooling rate, as\nshown in Figs. 2f, g, yields dimensions that are intermediate between those formed under fast-\nand slow-cooling conditions.”\n(Page 10): “Under moderate-cooling condition, the size distribution of crystals grown in Ga-\nbased solvents ranges up to 860 µm (rod-shaped crystals with a median size of 290 µm), while\nfor those grown in EGaIn-based solvents, the distribution reaches up to 560 µm (polyhedral-\nshaped crystals with a median size of 130 µm).”\nFig. 2 | Schematic plot of experimental design for the crystallization process and their\ncorresponding 3D observation of grown crystals within a liquid metal droplet using XCT\nscanning. a-c Diagram of the experimental design showing (a) overall crystal formation\nprocess, (b) cooling duration, and (c) cooling rate values under different cooling conditions. d,\ne Formation of crystals under fast-cooling rate within (d) Ga liquid metal droplet, and (e) EGaIn\nliquid metal droplet. f, g Formation of crystals under moderate-cooling rate within (f) Ga liquid\nmetal droplet, and (g) EGaIn liquid metal droplet. h, i Formation of crystals under slow-cooling\nrate within (h) Ga liquid metal droplet, and (i) EGaIn liquid metal droplet.\nRegarding your question related to Fig. 1a (page 7), we have improved the figure and added\ninset showing crystalline precipitates within liquid metal bulk to clearly illustrate the\ndifferences in resulting products between the heating and cooling processes. In addition, the\ncorresponding legend and related text have been modified accordingly.\nFig. 1 | Schematic illustration of growing crystals inside liquid metal bulk and the XCT\nanalysis. a Alloying procedure for growing metal crystals inside a droplet of liquid metal\nsolvent, with inset showing crystalline precipitates within liquid metal bulk formed during the\ncooling process b Experimental setup for XCT scanning of liquid metal droplets. c Extraction\nprocess of crystals from inside liquid metals electrochemically aided by a vacuum-driven force.\nRegarding the addition of a magnetic field during crystal growth, the scope of the current study\nfocuses on observing crystal growth within the bulk of liquid metal, with variations in chemical\ncomposition ratios and cooling rates as controlled variables. Therefore, at this stage, we have\nnot considered incorporating a magnetic field to control crystal growth. However, we agree\nthat in certain applications, applying a magnetic field could be beneficial. To explore this, our\npreliminary plan is to consider the type of magnetic field applied to the system, including its\nstrength and direction. Following your interesting suggestion to apply a magnetic field for more\nprecise shape control during crystal growth, the following sentence has been added to the\nrevised manuscript.\n(Page 13): “Different parameters of the environmental boundaries, the cooling rates, and the\nchemical compositions of solvent are crucial factors governing material formation and\nproperties, thereby shaping the growth behavior of crystals. How the addition of other\nparameters, such as magnetic field7, 8, can influence crystals characteristics remain as\ninteresting topics for future studies.”\n3. The authors discussed the directional bonding effect but not with much details. The role of\nthis bond in droplet crystallization has been discussed by 10.1002/smll.202305798.\nResponse: We appreciate your detailed insight into this manuscript. Thank you for directing\nus to this relevant work. We have cited this reference in the revised manuscript and added the\nfollowing text for a more detailed explanation, as follows.\n(Page 4): “Post-transition elements, in such liquid metals, exhibit covalent characteristics and\nalso directional bonding, enabling their use as solvents for metallic solutes1, 2. Particularly, a\nrecent study by Liu et al. have investigated the crystallization of liquid Ga, showing the\npresence of two different crystalline phases (α-Ga and β-Ga), distinguished by directional\nbonding3. In particular, directional bonding has been predicted at the surface of Ga-based liquid\nmetals4, 5.”\n4. Supplementary table 2 conveys interesting information, which, I think, should be an\nimportant component with necessary discussion in the main text.\nResponse: We appreciate your supportive comments. The following table (Table 1, page 13)\nhas been moved to the main text, and the corresponding discussion has been added,\naccordingly.\n(Page 12): “Table 1 summarizes the intermetallic crystals formed under different liquid metal\nsolvent systems and growth conditions, highlighting the key aspects where the solvent\ncomposition influences the resulting crystal morphology and phase composition of the formed\ncrystals. Crystals grown in Ga-based solvent generally exhibit a rod-like morphology,\npredominantly forming the Ga Pt intermetallic phase. In contrast, crystals formed in EGaIn-\n2\nbased solvent systems present a polyhedral crystal morphology, with the majority composition\ncorresponding to the Ga Pt intermetallic phase.”\n7 3\nTable 1 | Crystal properties extracted from different liquid metal solvents under various\ncooling rates\nSolvent composition Major morphologies Crystal composition Cooling rate\n- Ga Pt (tetragonal)\n- Ga Pt (cubic)\n2\n- Ga Pt (tetragonal)\n- Ga Pt (cubic)\n2\n- Ga Pt (tetragonal)\n2\n- Ga Pt (cubic)\n- Ga Pt (cubic)\n7 3\nEGaIn Polyhedral shape - In Pt (cubic)\n7 3\n- Ga Pt (tetragonal)\n2\n- Ga Pt (cubic) Slow-cooling\n7 3\n- In Pt (cubic)\n7 3\n5. In the response to point (4), the conjecture with the classical nucleation theory is not well\nsupported. More theoretical discussion on the classical nucleation theory has been extended in\nhttps://doi.org/10.1038/s41467-022-32241-z.\nResponse: Thank you for bringing this highly relevant work to our attention. We have\nincorporated insights from this referenced article into the revised manuscript. Following your\nsuggestions, an extended theoretical discussion on classical nucleation theory has been added\nto better support the conjecture.\n(Page 15): “Hu et al. 9 have conducted an extended theoretical investigation of classical\nnucleation possibilities, highlighting the roles of interfacial pre-ordering and interfacial energy\nin influencing crystallization. A high degree of geometric structuring is apparent within 8.5Å\nof liquid Ga interfaces (surface of liquid metal) and can be engineered by the addition of oxide\nlayers or other elements10. The preferential mobility of Pt atoms toward the bulk liquid Ga,\ncombined with the strong Ga-Pt interaction, limits Pt’s diffusion and affects their interfacial\nbehaviour11. The observation of different intermetallic compositions depending on cooling rate\nand solvent suggests a kinetic explanation for the change of composition, based on the relative\navailability of the Pt dopant as the crystal forms in solution.”\nIn response to your last suggestion, we also excluded the discussion on nucleation from the\nrevised manuscript and focused on crystal growth.\n6. When the HER performance is compared to Pt/C, what is the sample state, comparable to\nrod or polyhedron? If the porous structure is important, what is the significance of\ncrystallization from the solvent, backing to my previous concern?\nResponse: Thank you for your thoughtful comments. We have addressed each question as\nfollows.\nRegarding the sample state comparable to rod or polyhedron in HER performance, the catalyst\npowder, both Pt/C and the samples, are in solid state. The samples are crystalline precipitates\nobtained from extracted crystal, rod-shaped crystals from the Ga-based solvent and polyhedral-\nshaped crystals from the EGaIn-based solvent, both having almost comparable mass fraction\nratios of Pt (Ga Pt and Ga Pt ). This catalyst powder is weighed (1 mg of crystals each) and\n2 7 3\nsuspended to achieve a uniformly dispersed catalyst mixture. The detailed method can be found\nin the original manuscript.\n(Page 24): “To prepare the catalyst ink, the catalyst powder was uniformly dispersed in a\nmixture of 450 µL ethanol and 50 µL Nafion (0.5% wt.%). The suspension was sonicated for\n30 min to achieve a homogenous catalyst ink. Subsequently, 10 μL of the catalyst ink was\ndeposited onto a polished working electrode and dried at room temperature before testing. In\nthis study, the catalyst powder for the sample consisted of 1 mg crystals, containing\napproximately 0.008 mg of Ga and 0.011 mg of Pt, while the control utilized 10 mg of 10%\nPt/C, corresponding to 0.02 mg of Pt.\nTo enhance clarity, we have added new schematic figures (Fig. 6, page 19) to clearly illustrate\nthe catalyst powder preparation process (Fig. 6a) and the HER experimental setup (Fig. 6b).\n(Page 18): “The schematic illustrations of HER samples preparation and experimental setup\nare shown in Figs. 6a, b.”\nFig. 6 | Schematic illustration of HER experiments and corresponding results under\ndifferent experimental conditions. a Catalyst powder preparation process. b HER\nexperimental setup. c, d Polarization (LSV) curves for the formed crystals performed in (c) an\nacidic electrolyte, and (d) an alkaline electrolyte.\nRegarding the significance of crystallization from the solvent in forming porous structures, we\nhave added measurements of pore size distribution, to clearly highlight the differences between\nthe two different crystal-based liquid metal solvents (Ga and EGaIn), as illustrated in Fig. 7,\npage 21. The following text has been added to the revised manuscript to better elaborate on the\nsignificance of crystallization in different solvents for porous structure formation.\n(Page 20): “The pore size distribution is illustrated in Figs. 7e-h. The pore size distributions of\ncrystals obtained from Ga- and EGaIn-based solvents, under fast-cooling condition, generally\nshow comparable pore sizes, ranging from 10 to 300 nm. Under slow-cooling conditions, the\npore sizes are typically larger than those formed under fast-cooling conditions. It ranges from\n15 to 500 nm for Ga-based crystals, and 40 to 1020 nm for EGaIn-based crystals. In addition,\nregarding the porous morphology (Figs. 7a-d), the porous structure that emerged from Ga-\nbased solvent crystals tend to be more elongated, whereas those from EGaIn-based solvent\ncrystals are generally more circular.”\nFig. 7 | Porous characteristics of crystals formed under various experimental conditions.\na-d SEM images showing the porosity of typical crystals formed in Ga-based liquid metal\nsolvents under (a) fast-cooling, and (b) slow-cooling, and in EGaIn-based liquid metal solvents\nunder (c) fast-cooling, and (d) slow-cooling conditions. e-h Pore size distribution of typical\ncrystals formed in Ga-based liquid metal solvents under (e) fast-cooling, (f) slow-cooling,\nand those formed in EGaIn-based liquid metal solvents (g) fast-cooling, (h) slow-cooling\nconditions.\nReferences\n1. Brown TL. The Chemistry of Metallic Elements in the Ionosphere and Mesosphere. Chem.\nRev. 73, 645 (1973).\n2. Fatima SS, et al. Current state and future prospects of liquid metal catalysis. Nat. Catal. 6,\n1131-1139 (2023).\n3. Liu J, et al. Size Dependent Phase Transformation of Liquid Gallium. Small 20, e2305798\n(2024).\n4. Steenbergen KG, Lambie S, Gaston N. Discerning order from chaos: characterising the\nsurface structure of liquid gallium. Mater. Horiz. 12, 1314-1322 (2025).\n5. Lambie S, Steenbergen KG, Gaston N. Resolving decades of debate: the surprising role of\nhigh-temperature covalency in the structure of liquid gallium. Mater. Horiz. 11, 4201-4206\n(2024).\n6. Kalantar-Zadeh K, Daeneke T, Tang J. The atomic intelligence of liquid metals. Science\n385, 372-373 (2024).\n7. Wei J, et al. Growth of CdZnTe crystal under high magnetic field and its photon-counting\ndetector performance. J. Alloys Compd. 1011, 178390 (2025).\n8. Shen LQ, et al. Shear-band affected zone revealed by magnetic domains in a ferromagnetic\nmetallic glass. Nat. Commun. 9, 4414 (2018).\n9. Hu YC, Tanaka H. Revealing the role of liquid preordering in crystallisation of supercooled\nliquids. Nat. Commun. 13, 4519 (2022).\n10. Steenbergen KG, Lambie S, Ruffman C, Gaston N. Atomic-Scale Dynamics at the\nInterface of Doped Liquid Gallium: Contrasting Effects of Gallium Oxide and Vacuum.\nSmall Sci. 5, 2500153 (2025).\n11. Rahim MA, et al. Low-temperature liquid platinum catalyst. Nat. Chem. 14, 935-941\n(2022)."}, {"round": 3, "reviewer_comments": {"reviewer_2": "From the authors’ response to my first concern, it is a little bit confusing that fast-cooling gives rise to a larger crystal growth speed with a larger variance than slow cooling (see Fig. 3-i), because slower cooling gives longer time to structural relaxation and crystal growth. What is the reason behind this? When I look at the revised Fig. 2, the cooling rate will alter the shape of the crystal. This is an interesting feature, for which a shape correction factor may be included in the crystal growth speed analysis.\nAs the authors included new experiments with a moderate cooling rate, they should be added to Table I.\nThe other parts are looking good. After the above concerns are addressed, the work is punishable in nature communications."}, "author_response": "Response to the Reviewer comments:\nReviewer #2 (Remarks to the Author):\nThe other parts are looking good. After the concerns are addressed, the work is publishable in\n\"Nature Communications\".\nResponse: We thank you for your feedback and recommendation for publication. We have\ncarefully addressed the points raised and revised the manuscript accordingly.\n1. From the authors’ response to my first concern, it is a little bit confusing that fast-cooling\ngives rise to a larger crystal growth speed with a larger variance than slow cooling (see Fig. 3-\ni), because slower cooling gives longer time to structural relaxation and crystal growth. What\nis the reason behind this? When I look at the revised Fig. 2, the cooling rate will alter the shape\nof the crystal. This is an interesting feature, for which a shape correction factor may be included\nin the crystal growth speed analysis.\nResponse: Thank you for your final detailed insight into our manuscript. We have addressed\neach question as follows.\nResponding to the first comment regarding the reason for the variance in growth speed under\ndifferent cooling conditions, fast-cooling results in a higher crystal growth speed, as the rapid\ntemperature drop accelerates crystal formation (numerous and small). In contrast, slow-cooling\nallows more time for structural relaxation and crystal growth, where the gradual decrease in\ntemperature leads to slower crystals growth (fewer and larger). To strengthen the discussion,\nthe following text has been added to provide a more comprehensive explanation, as follows.\n(Page 10): “The combination of using Ga, as the liquid metal solvent, with fast-cooling\nprovides the highest crystal growth rate among all conditions. Under fast-cooling conditions,\nthe temperature decreases rapidly (95 ˚C/ min), creating a strong driving force for\ncrystallization to begin. Crystal growth kinetics change, limiting the time for crystal growth\nand leading to the formation of many nucleation sites for small crystals to emerge. By contrast,\nunder slow-cooling conditions, the temperature decreases gradually (1 ˚C/ min), allowing the\ngrowth environment to remain in saturated condition for Pt for a longer time. This provides the\nsystem with sufficient time for the formation of fewer but larger crystals. The broader size\ndistributions observed under slow-cooling conditions can also be attributed to the longer time\navailable for crystal growth. The phenomenon is similar to conventional crystal growth1, 2.”\nIn response to your question regarding Fig. 2 (page 9) on how the cooling rate alters crystal\nshape, the following text has been added to the revised manuscript to provide a clearer\nexplanation on the influence of the cooling rate on crystal morphologies.\n(Page 8): “The crystals formed in the liquid Ga system (Figs. 2d, f, h) were predominantly rod-\nshaped, whereas those grown in the liquid EGaIn medium (Figs. 2e, g, i) were mainly\npolyhedral. A decrease in cooling rate, from fast- to slow-cooling, resulted in progressively\nlarger crystals. Under fast-cooling conditions (Figs. 2d, e), small crystals were obtained. At a\nmoderate-cooling (Figs. 2f, g), the crystals exhibited dimensions that were intermediate\nbetween those formed under fast- and slow-cooling conditions. Under the slow-cooling\nconditions (Figs. 2h, i), much larger crystals were observed. Specifically, crystals formed in\nGa-based solvents, fast-cooling (Fig. 2d) produced small crystal, while moderate- (Fig. 2f) and\nslow-cooling (Fig. 2h), led to the progressive development of elongated crystal, rod-like\nmorphologies. In contrast, crystals formed in EGaIn-based solvents tended to be more equiaxed,\nwith sizes increasing from small crystals under fast-cooling (Fig. 2e) to progressively larger,\npolyhedral-shaped crystals formed under moderate- (Fig. 2g) and slow-cooling (Fig. 2i).”\nIn relation to your subsequent comments, we have also conducted additional experiments by\nextracting crystals from their solvent under moderate-cooling conditions, which confirmed the\nabove-described observations.\n(Page 14): “Crystals obtained under moderate-cooling conditions exhibit sizes intermediate\nbetween those formed under slow- and fast-cooling (Figs. 4f, i), ranging from 0 to 650 µm,\nwith median sizes approximately 70 µm and 50 µm for crystals formed in Pt-Ga and Pt-EGaIn\nsolvent, respectively (Supplementary Figs. 10b, e).”\n2. As the authors included new experiments with a moderate cooling rate, they should be added\nto Table I.\nResponse: To address your comment, we have conducted additional experiments, isolating\ncrystals under moderate-cooling conditions, and the results are included in Table 1 (page 13).\nThese findings show that logical crystal phases formed with in-between fast- and slow-cooling\nconditions crystal morphologies. To enhance clarity, Fig. 4 (page 15) and Supplementary Figs.\n10 (page S15) have been updated to clearly illustrate the crystal properties obtained under\ndifferent cooling conditions.\nTable 1 | Crystal properties extracted from different liquid metal solvents under various\ncooling rates\nSolvent composition Major morphologies Crystal composition Cooling rate\nRod shape - Ga Pt (tetragonal)\n(small size) - Ga Pt (cubic)\n(medium size) - Ga Pt (cubic)\n(large size) - Ga Pt (cubic)\n2\n- Ga Pt (tetragonal)\n(small size) - Ga Pt (cubic)\n7 3\n- In Pt (cubic)\n7 3\n- Ga Pt (tetragonal)\n(medium size) - Ga Pt (cubic)\n7 3\n- In Pt (cubic)\n7 3\n- Ga Pt (tetragonal)\n- Ga Pt (cubic) Slow\n7 3\n(large size)\n- In Pt (cubic)\n7 3\nFig. 4 | Characterizations of crystals extracted from the liquid metal droplets. a, b XRD\npatterns of the extracted crystals from (a) Ga liquid metal, and (b) EGaIn liquid metal under\nthe fast-, moderate-, and slow-cooling conditions. c The ratios of extracted intermetallic crystal\nphases formed inside the liquid metal. d Growth preferences for rod-shaped crystal, with the\ninset illustrating the tetragonal Ga Pt unit cell (top), and polyhedral-shaped crystal, with the\n2\ninset showing the cubic Ga Pt unit cell (bottom). Ga atoms are shown in green and Pt atoms\n7 3\nin blue. e, f, g SEM images of typical crystals inside Ga liquid metal under (e) fast-, (f)\nmoderate-, and (g) slow-cooling conditions. h, i, j SEM images of typical crystals inside EGaIn\nliquid metal under (h) fast-, (i) moderate-, and (j) slow-cooling conditions.\nSupplementary Fig. 10 | Size distribution comparison of the formed crystals under\ndifferent experimental conditions obtained from SEM images. a, b, c Pt-Ga under (a) fast-,\n(b) moderate-, and (c) slow-cooling conditions. d, e, f Pt-EGaIn under (d) fast-, (e) moderate-,\nand (f) slow-cooling conditions.\nReferences\n1. Galenko PK, Ankudinov V. Local non-equilibrium effect on the growth kinetics of crystals.\nActa Mater. 168, 203-209 (2019).\n2. Ma K, Zhao Y, Xu X, Hou H. The effect of undercooling on growth velocity and\nmicrostructure of Ni95Cu5 alloys. J. Cryst. Growth 513, 30-37 (2019)."}, {"round": 4, "reviewer_comments": {"reviewer_2": "the authors made necessary responses and revisions to address my concerns. the work looks good to publish"}, "author_response": ""}]

Decision letter