Supercooled liquid metal droplets with protective shells

Abstract

The droplets include a core including an alloy having a major amount of a first metallic element and a minor amount of a second element, the core being in a liquid state below the solidus temperature of the alloy. A shell is disposed surrounding the core and includes an outer surface including a major amount of the second element and a minor amount of the first metallic element, the shell being in a solid state below the solidus temperature of the alloy. The alloy can include a solder material that can be used to form a solder connection below the solidus temperature of the alloy.

Description

[Technical field]

[0001] (CROSS REFERENCE TO RELATED APPLICATIONS) This application claims priority to U.S. Nonprovisional Patent Application No. 17 / 383,150, entitled "UNDERCOOLED LIQUID METALLIC DROPLETS HAVING A PROTECTIVE SHELL," filed July 22, 2021, and claims the benefit of and priority to U.S. Provisional Patent Application No. 63 / 056,448, entitled "UNDERCOOLED LIQUID METALLIC DROPLETS HAVING A PROTECTIVE SHELL," filed July 24, 2020. The disclosures of each of the foregoing applications are incorporated herein by reference in their entirety. [Background technology]

[0002] Currently, there are various electronic devices that contain low temperature materials that are not suitable for forming soldered connections due to the high processing temperatures required for soldering. For electronic devices with low temperature materials, new low temperature soldering materials and processes are needed. Summary of the Invention

[0003] Some embodiments of the present disclosure relate to supercooled liquid metal droplets surrounded by a protective shell that maintains the core in a liquid state below the solidus temperature of the core material. The protective shell can be relatively free of nucleation sites and can incorporate a thermodynamic barrier that prevents the core from transforming to a solid below the solidus temperature of the core. The shell can include one or more layers arranged according to the reduction potential of each element. The shell can be coated in a fluid that protects the exterior of the shell from oxidation and degradation. In some embodiments, the liquid metal droplets can be used to solder materials at temperatures below the solidus temperature of the droplet.

[0004] In some embodiments, the droplet includes a core including a major amount of a first metallic element and a minor amount of a second element, the core being in a liquid state below the solidus temperature of the first metallic element. A shell is disposed around the core and includes an outer surface including a major amount of the second element and a minor amount of the first metallic element, the shell being in a solid state below the solidus temperature of the first metallic element. In various embodiments, the second element is a metal. In some embodiments, the second element is a metalloid. In various embodiments, the shell includes a concentration gradient transitioning from a first concentration of the second element at the inner surface of the shell to a second concentration at the outer surface, the first concentration being lower than the second concentration.

[0005] In some embodiments, the droplet further comprises a fluid disposed on the exterior surface. In various embodiments, the exterior of the shell comprises a third element having a lower concentration than the concentrations of the first metallic element and the second element. In some embodiments, the shell comprises a concentration gradient of at least the first metallic element and the second element that prevents the core from transitioning to a solid state. In various embodiments, the first metallic element and the second element at the exterior surface are an oxide of the first metallic element and an oxide of the second element. In some embodiments, the first metallic element has a lower E than the second element. o In various embodiments, the second element has a higher E than the first metallic element. o has.

[0006] In some embodiments, the droplet comprises a core comprising at least one metallic element in a liquid phase and a shell in a solid phase and disposed completely surrounding the core. The shell comprises a concentration gradient of the at least one metallic element that varies through a thickness of the shell, and the shell prevents the metallic element from transitioning to a solid phase at temperatures below the solidus temperature of the at least one metallic element. In various embodiments, the shell has at least two layered regions, each of the at least two layered regions being defined by a unique element having a predominant concentration within each layered region.

[0007] In some embodiments, the at least one metallic element is a first metallic element and the core includes a second metallic element having a lower concentration than the first metallic element. In various embodiments, the first metallic element forms a predominant proportion of an interior region of the shell and the second metallic element forms a predominant proportion of an exterior region of the shell. In some embodiments, the concentration of the first metallic element decreases from the interior region of the shell towards the exterior region of the shell and the concentration of the second metallic element increases from the interior region of the shell towards the exterior region of the shell.

[0008] In some embodiments, the change in concentration of the first and second metallic elements creates a thermodynamic shift in activation energy for the core to transition from a liquid phase to a solid phase. In various embodiments, the interior region of the shell comprises oxides and suboxides of the first metallic element, and the exterior region of the shell comprises oxides and suboxides of the second metallic element. In some embodiments, the second metallic element has a lower E than the first metallic element. o has.

[0009] In some embodiments, the droplet comprises a supercooled liquid core comprising a first element, a second element, and a third element, the first element being in a higher concentration than the second and third elements. A solid shell encompasses the liquid core and comprises a concentration gradient of the first, second, and third elements. In various embodiments, the first, second, and third elements are arranged in layers to form the shell.

[0010] In some embodiments, a method of forming a droplet includes forming a liquid core of the droplet from an alloy including a first element, a second element, and a third element, and forming a solid shell around the liquid core. The solid shell includes an innermost layer having a predominant concentration of one of the first, second, or third elements and an outermost layer having a predominant concentration of a different one of the first, second, or third elements. The method further includes cooling the liquid core and the solid shell below a solidus temperature of the alloy while maintaining the core in a liquid state.

[0011] In some embodiments, the solid shell includes three layers, an innermost layer having a predominant concentration of a first element, a middle layer having a predominant concentration of a second element, and an outermost layer having a predominant concentration of a third element. In various embodiments, the shell is formed in an oxidizing environment. In some embodiments, the oxidizing environment is controlled by varying the partial pressure of oxygen in the oxidizing environment. In various embodiments, the innermost layer has a greater E than the middle layer. o and the intermediate layer has a larger E than the outermost layer. o In some embodiments, the thickness of one or more of the three layers of the solid shell is determined by the time of exposure to an oxidizing environment.

[0012] In some embodiments, the shell is formed in a reducing environment. In various embodiments, the innermost layer has a lower E than the middle layer. o and the intermediate layer has a lower E o In some embodiments, the thickness of one or more of the three layers of the solid shell is determined by the exposure time to the reducing environment. In various embodiments, the method further includes exposing the solid shell to one or more chelating agents to remove at least a portion of the outermost layer. In various embodiments, the one or more chelating agents can be used to polish the outer surface of the shell, which can improve activation, droplet packing, and droplet flow, all of which are properties that can improve the performance of the droplets in the solder paste material (e.g., the droplet and flux combination). In some embodiments, the one or more chelating agents include at least one of a carboxylate, an amide, an alkoxide, an amine, a thiol, or a phosphate. In various embodiments, the method further includes an etching process to polish the inner layer of the solid shell.

[0013] Many advantages are achieved by the present invention over the prior art. For example, embodiments of the present invention provide the ability to solder materials at temperatures below the solidus temperature of the core element. [Brief description of the drawings]

[0014] [Figure 1] 1 depicts a simplified partial cross-sectional view of a droplet having a supercooled liquid metal core surrounded by a solid metal shell, according to an embodiment of the present disclosure. [Figure 2A] 1 illustrates a partial cross-sectional view of an example of a droplet having a bilayer shell formed in an oxidizing environment, according to an embodiment of the present disclosure. [Figure 2B] 2B illustrates a concentration gradient graph of an example of the relative concentration of each element and its oxide (eg, Sn and Bi) for a cross section of the droplet illustrated in FIG. 2A. [Figure 2C] 1 illustrates a partial cross-sectional view of an example of a droplet having a three-layer shell formed in an oxidizing environment, according to an embodiment of the present disclosure. [Figure 2D] 2D illustrates a concentration gradient graph of an example of the relative concentration of each element and its oxide (eg, Bi, Sn, and In) for a cross section of the droplet illustrated in FIG. 2C. [Diagram 3] 1 illustrates steps associated with a method of forming a supercooled droplet including a liquid metal core surrounded by a solid shell including at least two layers, according to an embodiment of the present disclosure. [Figure 4] 1 illustrates steps associated with a method of forming a supercooled droplet including a liquid metal core surrounded by a solid shell including an outer surface having a different composition than the liquid metal core, according to an embodiment of the present disclosure. [Figure 5A] 1 illustrates a partial cross-sectional view of an example of a droplet having a bilayer shell formed in a reducing environment, according to an embodiment of the present disclosure. [Figure 5B] 5B illustrates a concentration gradient graph of an example of the relative concentration of each element and its oxide (eg, Sn and Bi) for a cross section of the droplet illustrated in FIG. 5A. [Figure 5C] 1 illustrates a partial cross-sectional view of an example of a droplet having a three-layer shell formed in a reducing environment, according to an embodiment of the present disclosure. [Figure 5D] 5D illustrates a concentration gradient graph of an example of the relative concentration of each element and its oxide (eg, Bi, Sn, and In) for the cross section of the droplet illustrated in FIG. 5C. [Figure 6A]1 illustrates Darken-Gurry plots overlaid and compared with redox-indicating analogs, according to embodiments of the present disclosure. [Figure 6B] 6B is the plot of FIG. 6A with E° and vapor pressure introduced according to an embodiment of the present disclosure. [Figure 7A] FIG. 1 is a schematic diagram of surface-tunable impediment to the solidification of core-shell metal particles, according to an embodiment of the present disclosure. [Figure 7B] 1 is a high angle annular dark field scanning transmission electron microscope image of a shell according to an embodiment of the present disclosure. [Figure 8] 1 illustrates the stability of supercooled field metal particles according to an embodiment of the present disclosure. [Figure 9A] 1 illustrates a Sobel filtered HAADF STEM image of a metal particle highlighting the shell oxide thickness, according to an embodiment of the present disclosure. [Figure 9B] FIG. 9B illustrates an analysis of the oxide thickness of the shell of the metal particle shown in FIG. 9A. [Figure 9C] 9B illustrates an SEM image of the metal particle shown in FIG. 9A. [Figure 9D] 1 illustrates a chart showing change in subcooling versus number of heating cycles according to an embodiment of the present disclosure. [Figure 9E] 1 illustrates a chart showing the change in surface area to volume ratio with respect to subcooling, according to an embodiment of the present disclosure. [Figure 10] 1 shows a chart of change in ΔT versus change in yield for various alloys in accordance with an embodiment of the present disclosure. [Figure 11A] 1 shows a table of organic ligands of various properties that have been investigated, according to an embodiment of the present disclosure. [Figure 11B] 1 shows a table of oxide shell property variations according to embodiments of the present disclosure. [Figure 12A] 1 illustrates the correlation between composition change and subcooling according to an embodiment of the present disclosure. [Figure 12B] 1 illustrates the correlation between change in enthalpy and subcooling according to an embodiment of the present disclosure. [Figure 13]1 shows a table of various alloys that were evaluated and the results, according to an embodiment of the present disclosure. [Figure 14A] 1 shows a DSC trace of supercooled SAC305 particles according to an embodiment of the present disclosure. [Figure 14B] 1 illustrates theoretical surface work versus particle radius according to an embodiment of the present disclosure. [Figure 15] 1 shows the particle size distribution of as-synthesized particles according to an embodiment of the present disclosure. [Figure 16] 1 shows a table including constants for elements used in some embodiments, according to an embodiment of the present disclosure. [Figure 17] 1 shows a table tabulating undercooling levels and yields before and after reflow for various alloys according to some embodiments of the present disclosure. [Figure 18] FIG. 2 is a close-up view of a virtual surface oxide architecture of a field metal according to an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] The technology disclosed herein generally relates to supercooled liquid metal droplets surrounded by a solid shell. More specifically, the technology disclosed herein relates to droplets of metal that are in a stable liquid state below the solidus temperature and are enveloped in a shell having one or more solid metal and / or organic layers. In some embodiments, the shell can be designed to impede (e.g., prevent) the liquid-to-solid phase transition of the droplet, as described in more detail below. Various invention embodiments, including methods, processes, systems, configurations, and the like, are described herein.

[0016] For example, in some embodiments, droplets are formed surrounded by a shell having two or more layers, each layer including a concentration gradient and defined by a predominant element. In another example, droplets are formed surrounded by a shell having an outer composition that is predominantly different elements than the predominant element of the core. In some embodiments, the droplets may be formed in an oxidizing atmosphere to promote the formation of a particular outer layer or arrangement of layers, while in other embodiments, the droplets may be formed in a reducing atmosphere to promote the formation of a different particular outer layer or arrangement of layers.

[0017] To better understand the features and aspects of supercooled liquid metal droplets surrounded by a solid metal shell according to the present disclosure, further context of the present disclosure is provided in the following sections by discussing several specific configurations of supercooled metal droplets according to embodiments of the present disclosure. These embodiments are merely examples, and other embodiments can have other configurations using different elements, fluid materials, gases, layer mechanisms, etc.

[0018] FIG. 1 depicts a simplified partial cross-sectional view of a droplet 100 having a supercooled liquid metal core 105 surrounded by a solid metal shell 110, according to an embodiment of the present disclosure. In some embodiments, the shell 110 can prevent the supercooled liquid metal core 105 from transitioning to a solid when the droplet 100 is exposed to temperatures below the solidus temperature of the liquid metal core by providing an inner surface that does not contain nucleation sites and / or by creating a "thermodynamic tension" that increases the energy threshold at which liquid-to-solid phase transformation occurs, as described in more detail below. As depicted in FIG. 1, the shell 110 includes two layers 115, 120, each of which can have a different composition, as described in more detail below. In some embodiments, the shell 110 can be made of one, two, three, or more layers, each of which can be defined by a different predominant concentration of an element. In further embodiments, the shell 110 can be terminated with a ligand 125 or other liquid, as described in more detail below.

[0019] More specifically, as defined herein, a layer (e.g., 115, 125) is a region of the shell 110 having a predominant concentration of a particular element. The approximate boundaries of each layer (e.g., innermost beginning and outermost ending) are defined where that particular element is no longer predominant and another element has a predominant concentration. Thus, each layer may also be referred to as an enriched region, and each enriched region may be defined by the predominance of a particular element, and each enriched region may have a concentration gradient of two or more elements. In some embodiments, the concentration gradient may be designed to create thermodynamic tensions that impede phase transformation of the core, as described in more detail below.

[0020] In some embodiments having multiple layers, each layer has a reduction potential E of the predominant element in that layer relative to the reduction potential of the predominant element in the other layers. o More specifically, in some embodiments, the lowest E o (e.g., those with the greatest tendency to form oxides in an oxidizing environment) can form the outermost layer of the shell and have the highest E o An element having a lower tendency to form oxides (e.g., the lowest tendency to form oxides) may form the innermost layer of the shell. Conversely, if formed in reducing conditions, the opposite shell order may be formed. In further embodiments, the arrangement of each layer may depend on other factors, such as the tendency of each element to react with the gas or fluid in which the droplets are formed. In some embodiments, the shell 110 may be at least partially terminated in a fluid, which may be a ligand or other composition that improves the stability of the shell, as described in more detail below.

[0021] Two-layer shell in an oxidizing environment FIG. 2A illustrates a partial cross-sectional view of an example of a droplet having a two-layer shell formed in an oxidizing environment, according to an embodiment of the present disclosure. As shown in FIG. 2A, the liquid metal core 205 of the droplet 200 is predominantly the element bismuth (Bi) with the remainder being the element tin (Sn). In the embodiment depicted in FIG. 2A, the core 205 includes 58 weight percent Bi and 42 weight percent Sn, although in other embodiments, these elements can have any other suitable ratio. For example, in one embodiment, the core 205 includes 95 weight percent Bi and 5 weight percent Sn. In some embodiments, the liquid metal core 205 is a single metallic element, while in other embodiments, it can be an alloy of multiple metallic elements or a combination of metallic, metalloid, metalloid, and / or non-metallic elements, as described in more detail below. As further shown in FIG. 2A, the core 205 includes a shell 210 having two layers, with layer 1 (215) being the innermost layer and layer 2 (220) being the outermost layer. In the example shown in FIG. 2A, layer 1 (225) is predominantly bismuth oxide (Bi a O b , where a and b are any rational numbers), and layer 2 (220) is predominantly tin oxide (Sn c O d , where c and d are any rational numbers). In some embodiments, each layer 215, 220 can have a concentration gradient of multiple metal oxides and can be defined by a predominant metal oxide (e.g., layer 1 (215) is predominantly bismuth oxide and layer 2 (220) is predominantly tin oxide, as described in more detail below).

[0022] The inner surface 225 of layer 1 (215) can have a relatively smooth surface without nucleation sites, preventing nucleation and growth (i.e., phase transformation) of the liquid metal core 205 from transitioning to a solid at temperatures below the solidus temperature of the core (e.g., below 138° C. for eutectic 58Bi42Sn). In some embodiments, the concentration gradient within the shell 210 can create thermodynamic tensions that create an increased energy barrier for the liquid-to-solid phase transformation to occur, thereby increasing the stability of the liquid metal core 205 in a liquid state below its solidus temperature.

[0023] 2B illustrates an example concentration gradient graph of the relative concentration of each element and its oxide (e.g., Sn and Bi) for a cross-section of the droplet 200 illustrated in FIG. 2A. These concentration gradients are merely examples, and other embodiments may have different elements and / or different concentration gradients. As shown in the concentration graph 245 of FIG. 2B, starting from the left portion of the graph within the liquid core 205, the concentration of element Sn is relatively constant at around 42%, and the concentration of element Bi is also relatively constant at around 58%.

[0024] Proceeding first to layer 1 (215) (i.e., in the case of FIG. 2B, towards the right of the concentration graph 245), the elements Sn and Bi are converted into oxides (e.g., Bi a O b and Sn c O d ), and the concentrations of both elements (e.g., their oxides) change rapidly, with the bismuth oxide increasing to about 90% and the tin oxide decreasing to about 10% in the middle portion of layer 1 (215). Towards the right side of layer 1 (215), the concentration of bismuth oxide decreases and the concentration of tin oxide increases, such that at the interface between layer 1 (215) and layer 2 (220) the concentrations of tin oxide and bismuth oxide are equal. Thus, within layer 1, the concentration of Bi is greater than Sn, and layer 1 (215) can be identified as having a large amount of Bi and a small amount of Sn.

[0025] Now, proceeding to layer 2 (220), the composition of bismuth oxide continues to decrease to about 10% while the concentration of tin oxide reaches a maximum at about 90%. Thus, at the exterior surface 235 of the shell 210, tin oxide has a higher concentration than bismuth oxide. In some embodiments, during the formation of the shell 210, the environment may be a so-called "oxidizing environment" that includes one or more forms of oxygen that promote the formation of oxides (e.g., tin oxide and bismuth oxide). In some embodiments, the exterior surface 235 may be covered with a fluid 230 that stabilizes the exterior surface from oxidation and / or degradation, as described in more detail below.

[0026] The concentration gradient within the shell 210 can create a thermodynamic tension that prevents the phase transformation of the liquid core 205 to a solid. More specifically, the concentration gradient can generate a relatively large surface dipole that creates a relatively large Laplace pressure jump condition, suggesting that the core is at a relatively high pressure to support such a large pressure jump condition. In order to solidify, a critical nucleating agent size is required, which means that there is diffusion away from this tension, further increasing the free energy of the entire droplet 200. However, the free energy of the droplet 200 should be decreasing for this to be a spontaneous process. This situation increases the barrier to solidification. As evidence of this condition, when high melting point alloys cool, they form a glassy (e.g., amorphous) structure, as opposed to the crystalline structure that metals prefer under normal conditions. This change to an amorphous structure indicates that the liquid to solid transition is likely occurring from a hindered hypereutectic- or hypoeutectic composition.

[0027] In the example shown in FIGS. 2A and 2B, the liquid metal core 205 is predominantly the element Bi, and the shell 210 is predominantly an oxide of a metal different from the metal core at its outer surface (e.g., Sn c O d ). More specifically, the core 205 is composed predominantly of Bi, and the outer surface of the droplet is composed primarily of Sn.

[0028] In some embodiments, the core 205 may include a relatively small percentage of other elements, which may include, for example, elements that predominate at the outer surface. As described herein, a small percentage may be less than a comparable large percentage. In further embodiments, the outer surface may include a relatively small percentage (e.g., less than 50 percent, less than 10 percent, less than 1 percent) of other elements, which may include, for example, elements that predominate at the core.

[0029] In some embodiments, the shell 210 may have one layer where the predominant element of the outer surface of the shell is different from the predominant element of the core. For example, in one embodiment, the predominant element of the liquid metal core is tin and the predominant element of the shell is indium. That is, the core may be predominantly tin with a small amount of indium and the outer surface of the shell may be predominantly indium (e.g., indium oxide) with a small amount of tin (e.g., tin oxide).

[0030] As used herein, the term oxide (e.g., tin oxide) and chemical expressions (e.g., Sn c O d ) represents all possible oxides of tin where c and d are rational numbers. Furthermore, the particular oxide (e.g., rational numbers c and d) may vary throughout a particular droplet where one form of tin oxide may be present in layer 1 (215) and another form may be present in layer 2 (220).

[0031] In some embodiments, the fluid 230 can present a physical barrier to physico-chemisorption of the shell 210. In one embodiment, the fluid is a ligand or other solution, such as, but not limited to, a solution of ammonia groups, a solution of sulfur groups, carboxylic acids, any organic acid, any inorganic acid, phosphotungstic acid, hexafluorophosphoric acid, trichloroacetic acid, tribromoacetic acid, chloroacetic acid, zwitterionic species (e.g., glutamic acid, serine, etc.), dicarboxylic acids (e.g., glutaric acid, malonic acid, fumaric acid, oxalic acid, pimelic acid, etc.), anhydrides, dicarboxylates, acetals, ketals, hemiacetals, and other reactive species. Those skilled in the art having the benefit of this disclosure will understand that the above list of fluids is not exhaustive and other organic and non-organic fluids can be used and are within the scope of this disclosure. In a further embodiment, after formation, the exterior surface of the shell 210 can be contacted with a gas, such as, for example, nitrogen, to prevent oxidation and / or degradation of the shell 210. In still further embodiments, the exterior surface of the shell 210 may be terminated with a relatively inert metal such as, for example, gold, silver, nickel, or platinum. In one embodiment, the exterior surface may be stable to fluids, gases, or without terminations.

[0032] In some embodiments, during the formation of the shell 210, the process may be carried out in an oxidizing environment. In one embodiment, oxygen in one or more forms (e.g., O, O 2 , O 3) can be injected in gas form into the solution in which the droplets 200 are formed to promote rapid oxide formation and growth of the shell 210. In some embodiments, this change can be referred to as a change in the partial pressure of oxygen. Additionally, the oxidizing environment can promote the sequence of shell formation and shell layering, i.e., elements with the highest probability of oxide formation can dominate in the shell and form the outer surface of the shell. The exposure time and / or oxygen concentration to the oxidizing environment can change the thickness of one or more layers of the shell. Similarly, a change in the environment to a reducing atmosphere, where oxidation is prevented by the removal of oxygen and other oxidizing gases, can change the sequence of shell layers. A reducing atmosphere can be formed via reducing gases such as hydrogen, carbon monoxide, and gases such as hydrogen sulfide that are oxidized by the oxygen present.

[0033] Three-layer shell in an oxidizing environment FIG. 2C illustrates a partial cross-sectional view of an example of a droplet having a three-layer shell formed in an oxidizing environment, according to an embodiment of the present disclosure. As shown in FIG. 2C, the liquid metal core 255 of the droplet 250 is predominantly the element bismuth (Bi) with minor amounts of the elements indium (In) and tin (Sn). In the embodiment shown in FIG. 2C, the core 255 includes 57 weight percent Bi, 25 weight percent In, and 17 weight percent Sn, although in other embodiments, these elements can have any other suitable ratio. In some embodiments, the liquid metal core 255 is a single metallic element, while in other embodiments, it may be an alloy of multiple metallic elements or a combination of metallic, metalloid, metalloid, and / or non-metallic elements, as described in more detail below. As further shown in FIG. 2C, the core 255 includes a shell 260 having three layers, with layer 1 (265) being the innermost layer, layer 2 (270) being the middle layer, and layer 3 (275) being the outermost layer. In the example shown in FIG. 2C, layer 1 (265) is predominantly bismuth oxide (Bi a O b , where a and b are any rational numbers), and layer 2 (270) is composed predominantly of tin oxide (Sn c O d, where c and d are any rational numbers), and layer 3 (275) is predominantly indium oxide (In e O f , where e and f are any rational numbers). In some embodiments, each layer 265, 270, 275 can have a concentration gradient of multiple metal oxides and can be defined by a predominant metal oxide (e.g., layer 1 (265) is predominantly bismuth oxide, layer 2 (270) is predominantly tin oxide, and layer 3 (275) is predominantly indium oxide, as described in more detail below).

[0034] The inner surface 285 of layer 1 (265) can have a relatively smooth surface without nucleation sites, preventing nucleation and growth (i.e., phase transformation) of the liquid metal core 255 from transitioning to a solid at temperatures below the solidus temperature of the core (e.g., below 62° C. for 57Bi26In17Sn). In some embodiments, a concentration gradient within the shell 260 can create thermodynamic tensions that create an increased energy barrier for the liquid-to-solid phase transformation to occur, thereby increasing the stability of the liquid metal core 255 in a liquid state below its solidus temperature.

[0035] 2D illustrates an exemplary concentration gradient graph of the relative concentration of each element and its oxide (e.g., Bi, Sn, and In) for a cross-section of the droplet 250 illustrated in FIG. 2C. These concentration gradients are merely examples, and other embodiments may have different elements and / or different concentration gradients. As shown in the concentration graph 290 of FIG. 2D, starting from the left portion of the graph within the liquid core 285, the concentration of element Bi is also relatively constant at around 57%, the concentration of element In is also relatively constant at around 26%, and the concentration of element Sn is also relatively constant at around 17%.

[0036] Proceeding first to layer 1 (265) (i.e., toward the right of the concentration graph 290 for FIG. 2D), the elements Bi, Sn, and In form oxides (e.g., Bi a O b , Sn c O d and Ine O f ), and the concentration of each element (e.g., their oxides) varies with bismuth oxide increasing and becoming dominant, tin oxide increasing at a slower rate, and indium oxide decreasing. Towards the right side of layer 1 (265), the concentration of bismuth oxide is greater than the concentrations of tin oxide and indium oxide, and therefore layer 1 (265) can be identified as having a large amount of Bi.

[0037] Proceeding now to layer 2 (270), the composition of bismuth oxide decreases, while the concentration of tin oxide increases and dominates in layer 2. Thus, layer 2 (270) can be identified as having a high amount of tin. Now, proceeding to layer 3 (275), the composition of tin oxide and bismuth oxide decreases, while indium continues to increase and dominates in layer 3. Thus, layer 3 (275) can be identified as having a high amount of indium. Thus, at the exterior surface 293 of the shell 260, indium oxide has a higher concentration than bismuth oxide or tin oxide. In some embodiments, during the formation of the shell 210, the environment may be a so-called "oxidizing environment" that includes one or more forms of oxygen that promote the formation of oxides (e.g., indium oxide, tin oxide, and bismuth oxide). In some embodiments, the exterior surface 293 may be covered with a fluid 280 that stabilizes the exterior surface from oxidation and / or degradation, as described in more detail below.

[0038] The concentration gradient within the shell 260 can create thermodynamic tensions that prevent the phase transformation of the liquid core 255 to a solid. In the example shown in Figures 2C and 2D, the liquid metal core 255 is predominantly elemental Bi, the shell 260 includes three layers, and the outer surface 293 is predominantly composed of a metal oxide different from the metal core (e.g., In e O f ). More specifically, the core 255 is composed predominantly of Bi, while the outer surface of the droplet is composed primarily of In.

[0039] In some embodiments, the core 255 may include a relatively small percentage of other elements, which may include, for example, elements that predominate at the outer surface. As described herein, a small percentage may be less than a comparable large percentage. In further embodiments, the outer surface may include a relatively small percentage (e.g., less than 50 percent, less than 10 percent, less than 1 percent) of other elements, which may include, for example, elements that predominate at the core.

[0040] In some embodiments, the shell 260 may have an outer layer where the predominant element of the outer surface of the shell is different than the predominant element of the core. For example, in one embodiment, the predominant element of the liquid metal core is bismuth and the predominant element of the shell is indium. That is, in some embodiments, the core may be predominantly bismuth with a small amount of indium, and the outer surface of the shell may be predominantly indium (e.g., indium oxide) with a small amount of bismuth (e.g., bismuth oxide).

[0041] In some embodiments, as described in more detail below, the fluid 230 can present a physical barrier to physi- and chemi-adsorption of the shell 260. In yet another embodiment, the exterior surface 293 of the shell 260 can be terminated with a relatively inert metal, such as, for example, gold, silver, nickel, or platinum. In one embodiment, the exterior surface can be stable without fluids, gases, or terminations.

[0042] In some embodiments, during the formation of the shell 210, the process may be carried out in an oxidizing environment. In one embodiment, oxygen in one or more forms (e.g., O, O 2 , O 3) can be injected in gas form into the solution in which the droplets 250 are formed to promote rapid oxide formation and growth of the shell 260. Additionally, the oxidizing environment can promote the sequence of shell formation and shell layer sequence, i.e., elements with the highest probability of oxide formation can dominate in the shell and form the outer surface of the shell. Thus, changing the environment to a reducing atmosphere, where oxidation is prevented by removal of oxygen and other oxidizing gases, can change the sequence of shell layers. The reducing atmosphere can be formed via reducing gases such as hydrogen, carbon monoxide, and gases such as hydrogen sulfide that are oxidized by the oxygen present. Similarly, the thickness of one or more layers of the shell can be changed by changing the exposure time to the reducing gas and / or the concentration of the reducing gas in the environment. In further embodiments, the environment can be dynamically changed between reducing and oxidizing environments during the growth of the shell to promote the formation of specific shell layers in a specific sequence.

[0043] The relative concentrations of Sn, In, Bi and related oxides shown in Figures 2A-2D are for illustration only, and one of ordinary skill in the art having the benefit of this disclosure will understand that other embodiments may have different relative concentrations and / or different elements.

[0044] Manufacturing Process 3 illustrates steps associated with a method 300 of forming supercooled droplets including a liquid metal core surrounded by a solid shell including at least two layers, according to an embodiment of the present disclosure. As depicted in FIG. 3, in step 305, a molten solution is prepared that includes a major amount of element A and a minor amount of element B. In some embodiments, the molten solution can be formed by heating element A and adding element B. In other embodiments, element A and element B can be premixed, but simply exist as solids that can be heated to form a molten solution.

[0045] In step 310, the molten solution from step 305 is immersed in a fluid. In some embodiments, the fluid includes a conjugate acid-base pair, where the acid component is configured to polish the shell in situ and the base is configured to stabilize the shell against physisorption and chemisorption. More specifically, in one embodiment, the acid component smoothes the inner surface of the shell to minimize nucleation sites that may solidify the liquid metal core when cooled below the solidus temperature. In other embodiments, other types of fluids can be used. In further embodiments, one or more gases can be added to the fluid, such as, but not limited to, oxygen to promote oxide formation, or a reducing gas to retard oxide formation. Exemplary gases are described in detail herein and can be used to promote a particular sequence of formation of one or more layers of the shell.

[0046] In step 315, the molten solution can be separated into droplets while immersed in the fluid and / or gas. In some embodiments, the molten solution can be separated using a mechanical shearing device, such as a high-speed blade immersed in the fluid. During shearing, each droplet is surrounded by the fluid and / or gas, which can be introduced into the fluid. The fluid and / or gas can be selected and / or changed during the shearing process to engineer the shell properties and / or the sequence of shell layers as the droplets are formed. That is, the formation of the shell can be performed in a chemically dynamic (e.g., varying gas flow rate, gas composition, gas partial pressure, temperature, fluid composition) and mechanically dynamic (e.g., varying shear rate, shear stress, etc.) environment that can be optimized to form a specific shell composition.

[0047] In step 320, a shell may be formed around each droplet. In some embodiments, the shell may include two or more layers, each layer may be defined by a different predominant concentration of an element. During the formation of the shell, elements dispersed in the bulk may be stabilized on the surface of the core due to their potential to be oxidized and / or their stronger affinity for the fluid. Internal migration and diffusion of elements in the core brings them to the surface, and reaction and stabilization at the surface causes them to remain at the surface building the shell, as discussed in more detail below.

[0048] In one embodiment, the fluid and the one or more elements can be selected to have a higher tendency to bond than the one or more elements have to form an oxide. That is, the fluid and the elements can be designed to react preferentially. Thus, the elements with the highest tendency to react with the fluid form the outermost layer, the elements with the next highest tendency to react with the fluid form the middle layer, and the elements with the next highest tendency to react with the fluid form the innermost layer. In one example, an ammonia-based fluid can be selected to react preferentially with the transition metal. In another example, a sulfur-based fluid can be selected to react preferentially with gold, a carboxylate-based fluid can be selected to react preferentially with indium, and a phosphate can be selected to react preferentially with gallium.

[0049] In various embodiments, the solid shell can be exposed to one or more chelating agents to remove at least a portion of the outermost layer. In some embodiments, the one or more chelating agents include at least one of a carboxylate, an amide, an alkoxide, an amine, a thiol, or a phosphate, although other suitable chelating agents can be used.

[0050] In another embodiment, one or more elements can be selected that have a higher tendency to form oxides than the element's tendency to react with the fluid. Thus, each layer has a reduction potential E of the predominant element in that layer relative to the reduction potential of the predominant element in other layers. oMore specifically, the cohesive energy density and partial miscibility can be used to obtain a lower E o Elements can be "selected" and then pressed onto the surface of the core to form a shell during processing. This lower E o An element can be completely removed from the bulk of the core, substantially removed from the bulk of the core, or partially removed from the bulk of the core, depending on the desired final concentration of this element in the core and in the shell, which can be controlled by the selection of processing parameters such as fluid properties, oxidant concentration, partial pressure and / or temperature, time, etc.

[0051] In further embodiments, the shell is formed using a competition between the reduction potential of one or more elements and the reaction potential with the fluid, allowing one to design a multi-layer shell having a particular arrangement of shell layers and layer compositions. More specifically, the highest potential for reaction may be for element A to react with the fluid, the next highest reaction potential may be for element B to react with oxygen to form an oxide, the next highest reaction potential may be for element C to react with the fluid, etc. Thus, by selecting the appropriate elements, fluids and / or gases, one can design the mechanics and composition of the layers within the shell.

[0052] In some embodiments, a particular amount of an element (e.g., element B) can be included in the molten solution (e.g., where the molten solution includes element A and element B) to preferentially form a portion of the shell, leaving no or little element B in the liquid core of each droplet, where the core is substantially 100% element A. In some embodiments, the elements can be miscible (e.g., dissolve in each other), while in other embodiments, one or more of the elements can be immiscible and form interstitials that do not dissolve with the base metal. In embodiments with immiscible elements, removing all or nearly all of the immiscible element from the core (i.e., displacing it from the core to form the shell) can increase the amount of supercooling that causes the nucleation and subsequent solidification of the core in embodiments where certain elements may precipitate from solution into the core. To remove element B from the core to form the shell, the fluid and / or gas can be selected to have a high probability of reaction with element B and a low probability of reaction with element A, such that the shell is preferentially formed from element B. In further embodiments, the time and temperature can be adjusted during shell formation to diffuse most or all of element B into the shell. In further embodiments, some or substantially all of element B can be leached out of the bulk.

[0053] In some embodiments, miscibility and reduction potential are exploited to construct an alloy that allows the element with the highest oxidation / reduction potential to concentrate on the outer surface of the shell under these dynamic processing conditions. If this component is not highly soluble compared to other alloy components (e.g., In vs. Ge in Sn, or Bi vs. Ge in In), it may have an increased tendency to be present on the surface. In some embodiments, modified Darken-Gurry plots and / or Hume-Rothery rules can be used to predict solubility in the bulk and correct these solubility parameters by the probability of partitioning to the surface to predict the final alloy composition.

[0054] In further embodiments, the particular compound formed can be controlled by controlling the time and temperature during shell formation. For example, when forming tin oxide, using a relatively short time and / or low temperature will preferentially form 2+ tin oxide, while using a relatively long time and / or high temperature will preferentially form 4+ tin oxide.

[0055] In step 325, the droplets, each containing a shell, are cooled below the solidus temperature of the core material. That is, the composition of the core has a particular solidus temperature after the formation of the shell, and due to the lack of nucleation sites on the inner surface of the shell and / or the concentration gradient of the shell, the liquid metal core can be cooled below the solidus temperature without transitioning the core to a solid state. In some embodiments, the droplets are coated in a fluid that protects the shell from degradation. In various embodiments, the droplets are about 1 micron in diameter, while in other embodiments they are 0.5 microns to 10 microns in diameter, and in other embodiments they are 0.25 microns to 100 microns in diameter.

[0056] It will be understood that method 300 is illustrative and that variations and modifications are possible: steps described as sequential may be performed in parallel, the order of steps may be changed, and steps may be modified, combined, added, or omitted.

[0057] 4 illustrates steps associated with a method 400 of forming supercooled droplets including a liquid metal core surrounded by a solid shell including an outer surface having a different composition than the liquid metal core, according to an embodiment of the present disclosure. As depicted in FIG. 4, in step 405, a molten solution is prepared that includes a major amount of element A and a minor amount of element B. In some embodiments, the molten solution can be formed by heating element A and adding element B. In other embodiments, element A and element B can be premixed, but exist as solids that can simply be heated to form a molten solution.

[0058] In step 410, the molten solution from step 505 is immersed in a fluid. In some embodiments, the fluid includes a conjugate acid-base pair, where the acid component is configured to polish the shell in situ and the base is configured to stabilize the shell against physical and chemical adsorption. More specifically, in one embodiment, the acid component smoothes the inner surface of the shell to minimize nucleation sites that may solidify the liquid metal core when cooled below the solidus temperature. In other embodiments, other types of fluids can be used. In further embodiments, one or more gases, such as, but not limited to, oxygen, can be added to the fluid.

[0059] In step 415, the molten solution can be broken into droplets while immersed in the fluid and / or gas. In some embodiments, the molten solution can be broken up using a mechanical shearing device, such as a high speed blade immersed in the fluid. During shearing, each droplet is surrounded by fluid and / or gas. The fluid and / or gas can be selected to engineer the properties of the shell and / or droplets, as described in more detail below.

[0060] In step 420, a shell may be formed around each droplet. In some embodiments, the shell may include two or more layers, each defined by a different predominant concentration of an element. In some embodiments, the liquid metal core includes a majority of element A and a minor amount of element B, and the outer surface of the shell includes a majority of element B and a minor amount of element A. As discussed above in step 320, various methods may be used to selectively engineer the composition and arrangement of each layer.

[0061] In step 425, the droplets, each containing a shell, are cooled below the solidus temperature of the core material. That is, the composition of the core after formation of the shell has a particular solidus temperature due to the lack of nucleation sites on the inner surface of the shell and / or due to the concentration gradient of the shell, and the liquid metal core can be cooled below its solidus temperature without transitioning the core to a solid state. In some embodiments, the droplets are coated in a fluid that protects the shell from degradation. In various embodiments, the droplets are about 1 micron in diameter, while in other embodiments they are 0.5 microns to 10 microns in diameter, and in other embodiments they are 0.25 microns to 100 microns in diameter.

[0062] In one embodiment, a solder alloy known as SAC305, which includes tin, silver, and copper, is doped with germanium such that the core of the droplet is substantially SAC305 and the exterior shell is predominantly germanium, in another embodiment, an alloy of bismuth and tin is doped with germanium and the exterior shell is predominantly germanium.

[0063] In a further embodiment, after the droplets are formed, they can be subjected to a temperature to increase the amount of supercooling they can withstand, as described in more detail below.

[0064] It will be understood that method 400 is illustrative and that variations and modifications are possible: steps described as sequential may be performed in parallel, the order of steps may be changed, and steps may be modified, combined, added, or omitted.

[0065] Two-layer shell in reducing environment 5A illustrates a partial cross-sectional view of an example of a droplet having a two-layer shell formed in a reducing environment, according to an embodiment of the present disclosure. Droplet 500 in FIG. 5A is similar to droplet 200 in FIG. 2A in that the core contains the same constituent elements in similar concentrations, but because droplet 500 is formed in a reducing environment, instead of forming bismuth oxide on its outer surface as droplet 200 does, droplet 500 forms tin oxide on its outer surface.

[0066] As shown in FIG. 5A, the liquid metal core 505 of the droplet 500 is predominantly the element bismuth (Bi) with the remainder being the element tin (Sn). In the embodiment depicted in FIG. 5A, the core 505 includes 58 weight percent Bi and 42 weight percent Sn, although in other embodiments, these elements can have any other suitable ratio. For example, in one embodiment, the core 505 includes 95 weight percent Bi and 5 weight percent Sn. In some embodiments, the liquid metal core 505 is a single metallic element, while in other embodiments, it may be an alloy of multiple metallic elements or a combination of metal, metalloid, metalloid, and / or non-metallic elements, as described in more detail below. As further shown in FIG. 5A, the core 505 includes a shell 510 having two layers, with layer 1 (515) being the innermost layer and layer 2 (520) being the outermost layer. In the example shown in FIG. 5A, layer 1 (525) is predominantly tin oxide (Sn c O d , where c and d are any rational numbers), and layer 2 (220) is composed predominantly of bismuth oxide (Bi a Ob b , where a and b are any rational numbers). In some embodiments, each layer 515, 520 can have a concentration gradient of multiple metal oxides and can be defined by a predominant metal oxide (e.g., layer 1 (515) is predominantly tin oxide and layer 2 (520) is predominantly bismuth oxide, as described in more detail below).

[0067] The inner surface 525 of layer 1 (515) can have a relatively smooth surface without nucleation sites, preventing nucleation and growth (i.e., phase transformation) of the liquid metal core 505 from transitioning to a solid at temperatures below the solidus temperature of the core (e.g., below 138° C. for eutectic 58Bi42Sn). In some embodiments, the concentration gradient within the shell 510 creates thermodynamic tensions that create an increased energy barrier for the liquid-to-solid phase transformation to occur, thereby increasing the stability of the liquid metal core 505 in its liquid state even below its solidus temperature.

[0068] 5B illustrates an example concentration gradient graph of the relative concentration of each element and its oxide (e.g., Sn and Bi) for a cross-section of the droplet 500 illustrated in FIG. 5A. These concentration gradients are merely examples, and other embodiments may have different elements and / or different concentration gradients. As shown in concentration graph 545 of FIG. 5B, starting from the left portion of the graph within the liquid core 505, the concentration of element Sn is relatively constant at around 42%, and the concentration of element Bi is also relatively constant at around 58%.

[0069] Proceeding first to layer 1 (515) (i.e., toward the right of the concentration graph 545 in FIG. 5B), the elements Sn and Bi form oxides (e.g., Sn a O b and Bi c O d ), and the concentrations of both elements (e.g., their oxides) change rapidly in the middle portion of layer 1 (515) where the tin oxide increases to about 90% and the bismuth oxide decreases to about 10%. Thus, within layer 1 (515), the concentration of Sn is higher than Bi, and thus layer 1 can be identified as having a large amount of Sn and a small amount of Bi.

[0070] Now, proceeding to layer 2 (520), the composition of tin oxide continues to decrease to about 10% while the concentration of bismuth oxide reaches a maximum at about 90%. Thus, at the exterior surface 535 of the shell 510, bismuth oxide has a higher concentration than tin oxide. In some embodiments, during the formation of the shell 510, the environment may be a so-called "reducing environment" that promotes the formation of bismuth oxide on the exterior surface 535 and may include one or more forms of reducing gases such as, for example, hydrogen, carbon monoxide, and gases such as hydrogen sulfide that are oxidized by the oxygen present. In some embodiments, the exterior surface 535 may be covered with a fluid 530 that stabilizes the exterior surface from oxidation and / or degradation, as described in detail herein.

[0071] Concentration gradients within the shell 510 can create thermodynamic tensions that impede phase transformation of the liquid core 505 to a solid. In some embodiments, the core 505 can include relatively small percentages of other elements, which may include, for example, elements that predominate at the exterior surface. As described herein, a small percentage can be less than a comparable large percentage. In further embodiments, the exterior surface can include relatively small percentages (e.g., less than 50 percent, less than 10 percent, less than 1 percent) of other elements, which may include, for example, elements that predominate at the core.

[0072] In some embodiments, the fluid 530 can present a physical barrier to physical and chemical adsorption of the shell 510. In still further embodiments, the exterior surface of the shell 510 can be terminated with a relatively inert metal such as, for example, gold, silver, nickel, or platinum. In one embodiment, the exterior surface can be stable without fluids, gases, or terminations.

[0073] Three-layer shell in an oxidizing environment 5C illustrates a partial cross-sectional view of an example of a droplet having a three-layer shell formed in a reducing environment, according to an embodiment of the present disclosure. Droplet 550 in FIG. 5C is similar to droplet 250 in FIG. 2C in that the core contains the same constituent elements in similar concentrations, but because droplet 550 is formed in a reducing environment, instead of forming indium oxide on its outer surface as droplet 250 does, droplet 550 forms bismuth oxide on its outer surface.

[0074] As shown in FIG. 5C, the liquid metal core 555 of the droplet 550 is predominantly the element bismuth (Bi) with minor amounts of the elements indium (In) and tin (Sn). In the embodiment shown in FIG. 5C, the core 555 includes 57 weight percent Bi, 26 weight percent In, and 17 weight percent Sn, although in other embodiments, these elements can have any other suitable ratio. In some embodiments, the liquid metal core 555 is a single metal element, while in other embodiments, it can be an alloy of multiple metal elements, or a combination of metal, metalloid, metalloid, and / or non-metal elements, as described in more detail below. As further shown in FIG. 5C, the core 555 includes a shell 560 having three layers, with layer 1 (565) being the innermost layer, layer 2 (570) being the middle layer, and layer 3 (575) being the outermost layer. In the example shown in FIG. 5C, layer 1 (565) is predominantly indium oxide (In a O b , where a and b are any rational numbers), and layer 2 (570) is composed of predominantly tin oxide (Sn c O d , where c and d are any rational numbers), and layer 3 (575) is composed predominantly of bismuth oxide (Bi e O f , where e and f are any rational numbers). In some embodiments, each layer 565, 570, 575 can have a concentration gradient of multiple metal oxides and can be defined by a predominant metal oxide (e.g., layer 1 (565) is predominantly indium oxide, layer 2 (570) is predominantly tin oxide, and layer 3 (575) is predominantly bismuth oxide, as described in more detail below).

[0075] The inner surface 585 of layer 1 (565) can have a relatively smooth surface without nucleation sites, preventing nucleation and growth (i.e., phase transformation) of the liquid metal core 555 from transitioning to a solid at temperatures below the solidus temperature of the core (e.g., below 62° C. for 57Bi26In17Sn). In some embodiments, the concentration gradient within the shell 560 creates thermodynamic tensions that create an increased energy barrier for the liquid-to-solid phase transformation to occur, thereby increasing the stability of the liquid metal core 555 in its liquid state even below its solidus temperature.

[0076] 5D illustrates an example concentration gradient graph of the relative concentration of each element and its oxide (e.g., Bi, Sn, and In) for the cross section of the droplet 550 shown in FIG. 5C. These concentration gradients are merely examples, and other embodiments may have different elements and / or different concentration gradients. As shown in the concentration graph 590 of FIG. 5D, starting from the left portion of the graph within the liquid core 55, the concentration of the element Bi is relatively constant at around 57%, the concentration of the element In is relatively constant at around 26%, and the concentration of the element Sn is also relatively constant at around 17%.

[0077] Proceeding first to layer 1 (565) (i.e., in the case of FIG. 5D, towards the right of concentration graph 590), the elements Bi, Sn, and In are present as oxides (e.g., In a O b , Sn c O d and Bi e O f ), the concentration of each element (e.g., its oxide) changes with indium oxide increasing and becoming dominant, tin oxide increasing at a slower rate, and bismuth oxide decreasing. Towards the right of layer 1 (565), the concentration of indium oxide is greater than the concentrations of tin oxide and indium oxide, and therefore layer 1 (565) can be identified as having a large amount of In.

[0078] Proceeding now to layer 2 (570), the composition of indium oxide decreases, while the concentration of tin oxide increases and becomes predominant in layer 2. Thus, layer 2 (570) can be identified as having a large amount of tin. Now, proceeding to layer 3 (575), the composition of tin oxide and indium oxide decreases, while bismuth continues to increase and becomes predominant in layer 3. Thus, layer 3 (575) can be identified as having a large amount of bismuth. Thus, at the exterior surface 593 of the shell 560, bismuth oxide has a higher concentration than indium oxide or tin oxide. In some embodiments, during the formation of the shell 510, the environment can be a so-called "reducing environment" that promotes the formation of bismuth oxide on the exterior surface 593, and can include one or more forms of reducing gases, such as, for example, hydrogen, carbon monoxide, and gases such as hydrogen sulfide that are oxidized by any oxygen present. In some embodiments, the exterior surface 593 can be covered with a fluid 580 that stabilizes the exterior surface from oxidation and / or degradation, as described in detail herein.

[0079] Concentration gradients within shell 560 can create thermodynamic tensions that impede phase transformation of liquid core 555 to a solid. In some embodiments, core 555 can include relatively small percentages of other elements, which may include, for example, elements that predominate at the exterior surface. As described herein, a small percentage can be less than a comparable large percentage. In further embodiments, the exterior surface can include relatively small percentages (e.g., less than 50 percent, less than 10 percent, less than 1 percent) of other elements, which may include, for example, elements that predominate at the core.

[0080] In some embodiments, as described in more detail below, the fluid 580 can present a physical barrier to physical and chemical adsorption of the shell 560. In still further embodiments, the exterior surface 593 of the shell 560 can be terminated with a relatively inert metal such as, for example, gold, silver, nickel, or platinum. In one embodiment, the exterior surface can be stable without fluids, gases, or terminations.

[0081] The relative concentrations of Sn, In, Bi and related oxides shown in Figures 5A-5D are for illustration only, and one of ordinary skill in the art having the benefit of this disclosure will understand that other embodiments may have different relative concentrations and / or different elements.

[0082] Impediment to phase transitions due to surface asymmetry Surface speciation and autogenous speciation in metals can be influenced by miscibility, reactivity, and environment. Under non-reactive environments, surface speciation can be influenced by flux, cohesive energy density, and surface energy minimization. Under oxidizing (e.g. ambient) conditions, reduction potential, curvature, and surface plasticity play a role, influencing surface texture and stoichiometry. This speciation can modify the energy landscape of the material through surface work asymmetry. This complex surface architecture poses an activity platform based on asymmetry in surface structure and its induced effect on solubility that can be exploited to hinder the liquid-solid transition. The induced interface order makes Cahn-Hilliard type diffusion unfavorable, thus hindering homogeneous nucleation. The in situ formed surface passivating oxide, along with the concomitant size reduction, establishes a physical barrier against heterogeneous nucleating agents while trapping the molten metal in a "containerless" state (as the oxide is a continuum from the bulk). Engineering the distribution of components across the metal particle and its surface can affect the degree of undercooling and provide a generalized approach to hinder it.

[0083] Homogeneous material mixing can be understood from discipline-specific rules. In metals (entropy-dominant), solid solutions can be understood via the Hume-Rothery rule, which is often captured in a two-dimensional Darken-Gurry plot (Figure 6A). In metals, the focus on solid solutions can be driven by structural uses of these materials, but often a molten liquid phase is required to facilitate processing. This need is exacerbated by advances in flexible, wearable, and bioelectronics, as most substrates are not compatible with temperatures above 100 °C, even at low temperatures. Liquid-solid (LS) phase transitions can be considered in enabling new applications of metals, especially in hybrid / mixed material systems. However, this transition depends on the underlying kinetics and thermodynamics. Kinetics, diffusion can be important for nucleation and growth, and thus rapid cooling is often used to form metastable states such as glasses or supercooled liquids.

[0084] Thermodynamically, nucleating agents (extrinsic or homogeneous) lower the activation barrier that favors the LS phase transformation. If the nucleation barrier is high or Cahn-Hilliard type diffusion is unfavorable, the LS transition can be thermodynamically hindered. Heterogeneous (extrinsic source) nucleation can be eliminated through containerless approaches or through surface barriers such as passivating oxides. High entropy favors the liquid phase, significantly reducing the probability of homogeneous nucleation. High entropy can be achieved through composition or through di-mergence in the distribution of microstates occupied by the alloy components. For example, high surface area to volume ratio in nanoparticles can lead to limited homogeneous nucleation. Clever selection of dimensions coupled with surface organization and speciation over the passivating oxide can induce divergence in the density of energy states (microstates) that the alloy components can occupy. This divergence in energy states can lead to perturbations in the bulk energy landscape (similar to nanoparticles) and can therefore be used to tune diffusion and equilibrium conditions. Oxidation processes can be an essential component in understanding the miscibility and LS phase transitions of metal powders prepared at ambient temperatures.

[0085] Redefining the Darken-Gurry plot in an oxidizing environment means that the valence is expressed as the standard reduction potential (E 0 ) and cohesive energy density (CED). For illustrative purposes only, considering the example of Bi, In, Sn, the Darken-Gurry plot (Figure 6A) is overlaid and compared with the redox-dictated analog (Figure 6B). In Figure 6B, the introduction of E° and vapor pressure (instead of CED) allows the prediction of surface speciation. In the modified Darken-Gurry plot, the so-called preferential interaction parameter (PIP) is defined by the area in the 3D plot where the overlapping area implies solubility. E 0The component dominates at the surface. In one example, in the field metal (BiInSn), a predominantly In2O3 shell should form, but with significant incorporation of Sn suboxides, the interfacial Bi should segregate below the oxide shell. However, this segregated Bi occupies a trapped state because it would be energetically costly to dissolve in the bulk when the mixture is extruded from the eutectic. Immiscible but significantly lower E such as Te 0 Introducing elements leads to a TeO2 shell, likely with only a small perturbation to the eutectic composition, but with induced surface speciation (Figure 6A). This speciation leads to an increase in thermodynamic stress and is therefore more likely to hinder the LS phase transition.

[0086] In contrast, high E 0 The introduction of a component (Figure 6B) confines it in the bulk and increases the E 0 A large difference in is likely to result in the formation of intermetallic compounds that favor homogeneous nucleation and therefore insufficient undercooling. Surface-driven thermodynamic tuning of the LS transition can be achieved by i) establishing a smooth passivating oxide shell on the surface of the molten metal, ii) engineering this oxide shell through skillful selection of alloy composition, processing temperature (to control thickness), and surface ligands, and iii) achieving this organization while the metal is superheated and under mechanical stress, then rapidly cooling to near the melting point of the alloy, followed by ambient cooling. Skillful selection of processing conditions and management of the relaxation energy landscape can lead to hindered solidification. Similarly, the activation energy can be lowered to result in tunable solidification based on the divergence (asymmetry) of the surface microstate distribution.

[0087] FIG. 7A is a schematic diagram of surface-tunable hindrance of solidification of core-shell metal particles 700. FIG. 7B is a high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) Sobel filter analysis of the oxide thickness of the shell 710. Since the surface properties may not be dynamic, the metastable state created should be stable over long periods of time and resilient to various handling conditions if the oxide layer is not destroyed. FIG. 8 shows the stability of supercooled field metal particles (under about 2 years of storage and 50 thermal cycles) prepared by this approach. FIG. 8 illustrates differential scanning calorimetry (DSC) traces of field metal particles under different conditions.

[0088] background The supercooled liquid is a metastable phase due to a hindered liquid-solid transition. The free energy change during the LS phase transition can be defined by the following equation:

[0089]

number

[0090] In a droplet, the Laplace pressure jump condition (ΔP=2γ / r, where γ=surface tension and r=radius) can cause mechanical equilibrium but can also induce an asymmetry in the chemical potential below this oxide interface. By definition, the surface tension term (γ) is the product of the interfacial excess (Γ) and the difference in chemical potentials.

[0091]

number

[0092] However, liquid metals and associated oxides are non-volatile and therefore

[0093]

number

[0094]

number

[0095] As a result, as the complexity of surfaces and interfaces increases, so does their ability to impede homogeneous nucleation (e.g., high activation energies, ΔE a). Metastable interfaces can perturb the phase transition dynamics and may be the basis for the energy landscape inversion phase transition theory (LIPT). Here, a similar global energy landscape inversion is used to synthesize and stabilize metastable supercooled liquid metal droplets.

[0096] result Supercooled core-shell metal particles were synthesized using the SLICE (Shearing Liquid into Complex Particles) method. In the majority of this work, field metal (32.5% Bi, 16.5% Sn and 51% In, Tm≈335 K) and eutectic bismuth-tin (58% Bi, 42% Sn, Tm≈411 K) were used as the base alloys, but the method can be used for other alloys as well. Molten ingots were sheared in the presence of conjugate acid-base pairs to form supercooled core-shell particles with diameters of about 1 μm. The acid-base pair polishes (acid) and stabilizes (base) a thin oxide shell (about 4 nm, FIG. 9A, FIG. 9B) in situ. FIG. 9A illustrates a Sobel filtered HAADF STEM image of a metal particle highlighting the oxide thickness of the shell 910. FIG. 9B illustrates an analysis of the oxide thickness of the shell 910 of the metal particle shown in FIG. 9A. The as-synthesized particles were analyzed using DSC to analyze the degree of undercooling, yield, and purity. Other microscopy and spectroscopy techniques (e.g., SEM in FIG. 9C) were used to characterize the particles 900. For field metal, the yield of undercooled particles was (>98%), while the degree of undercooling was ΔT / Tm≈0.34 for the freshly made particles (FIG. 8).

[0097] To assess the stability of the synthesized supercooled particles, accelerated and ambient aging experiments were performed on the supercooled field metal particles. Samples (15 g) were stored in ethyl acetate under ambient conditions (benchtop) for >2 years, resulting in a total loss of supercooled particles of 43% at 8 months and 57% at 2 years. Figure 9D illustrates a chart showing the change in supercooling versus the number of heating cycles. Figure 9E illustrates a chart showing the change in surface area to volume ratio versus supercooling. ΔT / Tm changed from 0.34 to 0.14 over 2 years, with no loss in yield. The change in ΔT / Tm is likely due to continued growth of the oxide shell and / or loss of protective ligands. This data suggests that the supercooled metal particles are stable to accidental ambient perturbations over extended periods of time. To further complement this, a second sample was subjected to accelerated aging via weekly thermal cycling (200 K to 373 K) for 70 cycles. For accelerated aging samples, a significant change in ΔT / Tm is observed (Figure 9E). The freezing point of these supercooled particles gradually increases but approaches an asymptote at about 273 K with an exponential decay slope (maximum Δ(ΔT / Tm)=0.15, Figure 9E). Thermally driven growth in the oxide shell, loss of surface ligands, and associated changes in surface morphology due to repeated expansion and contraction contribute to the decrease in ΔT / Tm. Upon heating the particles to 473 K (where complete loss of supercooling is observed), a gradual increase in particle size from the original ∼1 μm was observed. This change also directly impacts ΔT / Tm. Powder X-ray diffraction confirms the change in overall crystallinity with temperature. The amorphous supercooled material transforms into a fully crystalline state after heating it to 473 K, manifesting solidification. This is further confirmed by coupled TGA-IR-MS, where a loss of surface ligands is observed between 475K and 573K, followed by a gradual increase in mass with increasing oxidation and sintering.

[0098] Preservation of the organic layer may be a key factor in maintaining the stability of these core-shell metal particles. The organic ligands may act as a physical barrier (limited physico- and chemisorption) for the thin surface oxide shell. Changes in surface morphology were observed after repeated heating cycles, while the control sample (maintained at ambient temperature) remained spherical and smooth. Surface defects may be precursors to further oxide growth, decreasing the interfacial chemical potential gradient per unit volume (Δμ tension) and ultimately decreasing ΔT / Tm. The slow oxygen diffusion process at lower temperatures justifies the slope of the freezing point change. The asymptote in ΔT / Tm (Figure 9D) occurs when the oxide reaches a critical thickness, and thus, significantly slower oxygen diffusion occurs. From this study, the surface of the particle may play a role in supercooling. Maintaining a smooth, ligand-stabilized surface may be a key factor for stable supercooling, but other factors may also play important roles. FIG. 10 shows a chart of the change in ΔT versus the change in yield for various alloys, however, this chart is intended as an example only and any of the listed alloys or other alloys may be suitable for making core-shell metal particles.

[0099] Interface-driven supercooling of various alloys From Eq. 1, interface-driven chemical potential changes can modify the kinetics of the LS phase transition. To delineate the role of the surface beyond the observed stabilization, the role of the chemical properties of the dominant surface components was investigated. First, organic ligands of various properties were investigated, both analogs of acetate and other (four in total) moieties with better binding to the passivating oxide (Figure 11). To understand the effect of the surface oxide, various lower and higher standard reduction potentials (E 0 ) components were introduced into BiSn-based alloys.

[0100] Effect of oxide shell and interface properties FIG. 12A shows the correlation between the change in composition and the undercooling, and FIG. 12B shows the correlation between the change in enthalpy and the undercooling. Further details for each alloy are shown in Table 1700 of FIG. 17. This data is described in more detail in the publication entitled "Stabilization of Undercooled Metals via Passivating Oxide Layers" Angew.Chem.Int.Ed. 2021, Vol. 60, pp. 5928-5935, and in the associated supplementary information entitled "Stabilization of Undercooled Metals via Passivating Oxide Layers" published in Angewandte Chemie by Andrew Martin et al., which are incorporated herein by reference in their entirety for all purposes. FIG. 13 shows a table listing the change in undercooling and yield for BiSn-based alloys with different additives that form eutectic (eut.) phases or are simply added in small amounts (imp.).

[0101] The field metal (eutectic BiInSn alloy) has significant undercooling (ΔT / Tm=0.34) and is dominated by the indium oxide surface (lowest E 0 ) to form an oxide shell. To evaluate the role of the oxide shell on supercooling, particles were prepared from eutectic BiSn (yield=89%, ΔT / Tm=0.36, Figs. 12A and 13). Binary BiSn gave slightly higher ΔT / Tm, albeit with a slightly lower yield of supercooled particles, compared to ternary BiInSn. The effect of additives to BiSn-based alloys (by forming 3-, 4-, or 5-component eutectic alloys or by adding small amounts of "impurities") was evaluated. First, other non-indium-containing ternary alloys were evaluated to ensure that the change in yield was not the result of a change in compositional entropy (based solely on the number of components making up the alloy). In (in the field metal) was replaced by Pb (E 0 When the ZnSnPbCd (Wood's metal, Cd E = -0.13 V, Rose's metal, BiSnPb) was used, the supercooling degree T / Tm = 0.30 decreased slightly, but a quantitative yield (100%) was obtained, Fig. 12B). 0=-0.4V), which led to a decrease in both the yield (95%) and the supercooling T / Tm = 0.21 (Fig. 13). 0 =-0.34V) led to the recovery of quantitative yield (100%), but with a concomitant loss in undercooling (T / Tm=0.13). Taken together, these data suggest that an increase in compositional entropy does not necessarily correlate with an increase in metastability (Figure 13). The alloys formed typically result in higher yields, but ΔT / Tm remains constant or decreases with increasing composition. Most of the added components that form these alloys have a low E compared to Sn. 0 (E 0 =-0.14V) (the dominant component in the oxide shell of the BiSn particles). Therefore, the lower E 0 The addition of elements likely plays a role in restructuring the surface architecture and modifying the supercooling behavior. To better understand this, we investigated the effect of gallium (E 0 =-0.51 V) containing homolog (BiSnGa) was quantitatively supercooled (yield=73.4%, ΔT / Tm=0.29, FIG. 13). The addition of Ga modifies both the surface and bulk behavior due to the strong Ga-Sn interaction, resulting in a significant shift in the thermal behavior (captured by the large broadening of the freezing and melting peaks in the thermogram).

[0102] The role of the dominant component in the oxide shell (E 0 in terms of the chemical potential gradient, Sn(E 0 =-0.14V) 0 Small amounts (e.g., ≦1%) of “impurities” having a lattice constant of 0.1% were introduced into the eutectic BiSn. Figure 13 summarizes the results based on DSC traces from each sample of the supercooled alloy. In general, the higher the E 0 The addition of impurities is accompanied by a perturbation of the surface suboxide and bulk cohesive energy density, but does not modify the dominant components in the oxide shell. The latter is more favorable, leading to a decrease in metastability due to a higher tendency to form important nucleating agents. The addition of Ge (E0 = 0.1 V, 1%) led to similar ΔT / Tm with slightly lower yields. Increasing the amount of Ge (about 15%) led to a decrease in ΔT / Tm. Lower E 0 As for impurities, the oxide shell is likely to be dominated by additives. A small amount of Sb(E 0 =-0.51V, 1%) and Te(E 0 =-0.90 V, 1%) led to ΔT / Tm=0.31 (63% yield) and ΔT / Tm=0.35 (81% yield), respectively. Both additives lead to a decrease in supercooling and yield, which is expected in this system since both modify the surface.

[0103] In addition to the change in surface oxide and cohesive energy density, the formation of nucleating agents can depend on the flux. The flux in a viscous medium or solid can be proportional to the atomic radius. Ho(E 0 =-2.33V) and Au(E 0 =1.83V) led to relatively significant changes in both ΔT / Tm (0.26 and 0.33) and yield (82.3% and 65.11%, respectively). From these data, ΔT / Tm decreases with either a change in the oxide shell structure or a change in the cohesive energy density. Certain preparation methods can lead to statistical enrichment of minor components in some particles, modifying the yield and degree of supercooling. Darken-Gurry and TC-YM plots show that even when the atomic sizes are comparable, solid solubility can be limited when the difference in Pauling electronegativity is >0.4.

[0104] Understanding Compositional Entropy To evaluate the cause of the discrepancy between yield and degree of undercooling, the correlation between the number of components, ΔT, and ΔT / Tm for all prepared homologs of BiSn was evaluated. It was observed that an increase in the number of components forming a eutectic alloy generally leads to a decrease in Tm and ΔT / Tm, although other additives may have different effects. Adding relatively large amounts of impurities (see Ge in Figure 13) leads to a similar decrease. It follows that an increase in the number and amount of components in the alloy may interfere with the ability to prevent solidification, which may result from the formation of intermetallic compounds upon cooling. The increase in favorable interactions can be correlated with the enthalpy of the system. Thus, the compositional entropy increases, but the increase in cohesive energy density reduces the entropic advantage of preventing solidification. The addition of Ga, for example, confirms this behavior. Theoretically, Ga becomes dominant in the oxide, but the strong interaction with Sn helps the bulk relaxation. The correlation between ΔHf and the transition point was evaluated to confirm this inference. The three parameters (Tm, ΔT, and ΔT / Tm) decrease with increasing enthalpy of fusion, albeit at different rates. Thus, alloys with stronger bulk interactions may be more difficult to supercool.

[0105] FIG. 14A shows the DSC trace of supercooled SAC305 particles. FIG. 14B shows the theoretical surface work versus particle radius. Similar to the Darken-Gurry plot, the intermediate sizes and E 0 Impurity elements with a difference of 0.01 to 0.25 tend to give the highest ΔT / Tm. To test this hypothesis, a ternary alloy (SAC305 solder) was undercooled, resulting in a ΔT / Tm of 0.3 (95.2% yield, FIG. 14B). SAC305 has a significantly higher ΔHf compared to either of the BiSn-based alloys, and therefore requires a large amount of surface work to achieve a comparable degree of undercooling.

[0106] Prediction, analysis and simplification of supercooling behavior In some embodiments, based on accumulated data for various alloys, maximum undercooling may be achievable in binary-ternary alloys with moderate ΔHf. The average minimum undercooling and ΔHf from each additive reveals a critical point in approximately ternary alloys. Comparing ΔHf and the number of components in the alloy with ΔT / Tm, a global surface map is generated. From the slope of this plot, in some embodiments, the maximum is found in the window of binary and ternary alloys with moderate ΔHf. This speaks to the fact that enthalpy-entropy balance may be important in achieving high undercooling levels by adjusting the surface work. Based on Eq. 1, when the enthalpy and entropy contributions in a system are balanced, the two terms are eliminated, leading to a simplified description of the associated free energies as follows:

[0107]

number

[0108] Equation 3 explicitly states that ΔG depends on the surface work when ΔHf≈0. Thus, the surface composition in liquid metal core-shell particles manifests the LS phase transition. This simplified equation also suggests that alloys with high ΔHf, such as SAC305, may require more work to reach the same undercooling as BiSn. The theoretical amount of surface work can be enhanced based on the curvature (increased Laplace pressure jump), and therefore, as expected, the degree of undercooling should increase with decreasing grain size. Because the grain size distribution is tunable using SLICE, the supercooling behavior of the synthesized particles can be predicted.

[0109] This work demonstrates a new method to hinder the LS phase transition by tuning the interfacial tension of metal core–shell particles. i. Supercooled particles can be stabilized using organic core-shell architectures. Organic ligands limit chemisorption and physisorption on smooth passivated oxides, improving stability. At ambient conditions, the majority of particles remain supercooled for >2 years of storage. ii. Judicious selection of alloying components enhances the enthalpy-compositional entropy balance, which can be important in maximizing surface work and therefore supercooling. Balancing the miscibility and partitioning between the surface and bulk allows for tunable supercooling and stability. iv. Solubility was redefined by introducing a preferential interaction parameter (PIP) that captures the tailored miscibility due to surface reactions. In addition to predicting solubility, this parameter predicts surface speciation and therefore the associated divergence in interfacial tension. Favorable liquid miscibility with simultaneous segregation of the less miscible component to the surface leads to the determination of improved supercooling (metastability).

[0110] Experimental Method Bismuth-tin alloying: Tin ingots were melted and then transferred to a crucible. The mass of tin in the crucible was recorded as 42% of the total alloy weight, and 58 weight percent bismuth shot was calculated based on the mass of tin to achieve the eutectic composition. Other metals of different compositional percentages were deposited into the molten tin pool and mixed until completely dissolved. Bismuth shot was then added to the mixture and mixed until completely dissolved.

[0111] Synthesis of BiSn-based alloy particles: Various supercooled metal particles with bismuth tin-based alloys were synthesized in the following manner. One gram of trichloroacetic acid was mixed into 200 mL of diethylene glycol in a beaker. Metal pellets weighing about 5 g were added to the solution and heated to 433 K on a hot plate with stirring. A high-speed rotating blade was used for the shearing process, variable heating tape was wrapped around the device, and an aramid blanket was used to seal the device to limit heat dissipation during the shearing process. The diethylene glycol solution was transferred to the device and then sheared at about 27,000 rpm for 4 minutes with the shear blades elevated on one side to create an angle of about 10°. Once complete, the solution was extracted and washed using ethanol and ethyl acetate while cooling at ambient conditions. The solution was filtered using a Buchner filter with a Whatman GF / F paper filter. The filtered particles were washed, collected, and stored in ethyl acetate.

[0112] Synthesis of SAC305 particles: 0.5 ml of paraffin oil, 0.2 g of trichloroacetic acid, 0.2 g of poly(acrylic acid) and 0.5 g of SAC305 alloy were placed in a 5 mL beaker heated in an oil bath. The solution was heated to 533 K and maintained at that temperature to keep the metal in liquid form. A rotating blade was used to shear the particles at about 27,000 rpm for 6 minutes. The particles were then extracted and quenched in an ethanol bath and then cooled to room temperature. Once at room temperature, the particles were decanted and washed using ethyl acetate to remove traces of oil content.

[0113] Differential Scanning Calorimetry (DSC) Analysis: A DSC (Model Q2000, TA Instruments) equipped with a liquid nitrogen cooling unit was employed to measure the level of supercooling. The particles stored in ethyl acetate solution were transferred to an aluminum pan and the ethyl acetate content was allowed to evaporate at ambient conditions, after which the sample was sealed with an aluminum lid. The samples were heated from a standby temperature of 313 K to 573 K (varied for different alloys) at a heating rate of 10 K / min and then cooled to 203 K at the same rate. Some alloys were cycled through heating and cooling cycles to demonstrate reflow and recyclability behavior. Data analysis was performed using TA TRIOS software.

[0114] Scanning Electron Microscopy (SEM) Characterization: Metal particles stored in ethyl acetate solution were transferred onto a silicon wafer using a pipette and then characterized by scanning electron microscopy (FEI Quanta 250 FEI-SEM). Samples were mounted on standard SEM mounts (Ted Pella Inc.) adhered with copper tape. The SEM was operated under high vacuum at a voltage of 10-15 kV, spot size 3, and working distance of 10 mm. Micrographs were taken at various magnifications using an Everhart-Thorley secondary electron detector and a backscatter detector.

[0115] High angle annular dark field scanning transmission electron microscopy (HAADF-STEM) characterization: The synthesized metal particles were drop cast onto a copper TEM grid (Ted Pella Inc.) and mounted on a double-tilt TEM sample holder. Images were acquired using an aberration-corrected FEI Titan Themis300 with a probe-corrected TEM operated at 200 kV. EDS analysis was performed on the same instrument using a Super-X EDX detector. Oxide shell thickness approximation was performed using the "Find edges" function within the J.Sobel filter, which allows pixel contrast intensity calculation along the drawn line, where higher intensity corresponds to lighter colors (white) and a drop in intensity corresponds to the oxide layer (black).

[0116] Thermogravimetric Analysis (TGA)-Infrared (IR)-Mass Spectrometry (MS) Analysis: A combined TGA-IR-MS instrument (Netzsch STA449F1) was used to analyze the mass changes and evolved gases released during the thermal treatment of the particles. Samples were deposited in alumina crucibles with matching reference crucibles and dried. Simulated dry air (80% oxygen 20% nitrogen) was used as purge gas. The samples were then loaded and passed through a heating ramp step at 10°C / min. The obtained data was analyzed using Proteus and Opus software.

[0117] Free Energy and Symmetry Gibbs free energy (G) is a thermodynamic potential that can be used as a tool to determine whether an event occurring is favorable given a constant temperature and pressure. A thermodynamic system undergoes a favorable transition if the change in G (ΔG) from one state to another results in a lower energy state (i.e., ΔG<0). The main component of the Gibbs free energy equation involves a balance between enthalpy (H) and entropy (S) and reads as follows: G=H-TS. Enthalpy is a state function into which the internal energy and PV work in the system enters (H=U+PV), where U is the internal energy of the system which can be further expanded as U=TdS-PdV+δw' (δw' is the non-pv or non-mechanical work on the system). When the G term is expanded into a more general derivative form, we end up with the familiar ΔG=ΔH-TΔS+δw'. In some calculations, δw' is ignored by assuming that there is no non-pv work done on the system. The equation then turns into a competition between whether the process is enthalpy dominated (increasing order) or entropy dominated (increasing symmetry), which can be depicted, for example, by the processes of freezing (low temperature, atomic ordering, exothermic, enthalpy dominated) or melting (high temperature, atomic disordering, endothermic, entropy dominated), respectively.

[0118] Landau's theory of phase transitions expresses the thermodynamic potential as a function of the order parameter (θ), giving an entirely new perspective on phase transition events. In Landau's theory, ordering events result in θ approaching 0, where nearest neighbor interactions force order in one direction, and thus U becomes dominant (same principle as enthalpy-dominated events or solidification, but ordering in this case deals with magnetic order, M). At the other end, disorder or large entropy results in θ approaching 1. Extending Landau, Ising theory introduces the J exchange constant (a parameter that deals directly with nearest neighbor interactions), the coordination number (q), and the Boltzmann constant (K B ) gives a better quantification parameter for the balance between the orders in the symmetry of the form. In Ising theory, the order-symmetry balance is given by

[0119]

number

[0120] The correlations between the thermodynamic potentials postulated by Gibbs, Landau and Ising provide a tool for controlling phase transitions, especially the liquid-solid phase transition that is important for supercooling.

[0121] nucleation Supercooling, also known as solidification or nucleation, is a process that occurs within the liquid-solid transition window. Solidification is an event initiated by nucleation that occurs due to the energy minimization of the system, when the free energy difference between the liquid and solid states becomes negative (ΔG ls<0). Different free energy terms can be used to describe this phenomenon, but the Gibbs free energy (ΔG), assuming constant temperature and pressure, can be used to describe this event. There are multiple nucleation initiation mechanisms, which can be categorized into two main classifications, homogeneous and heterogeneous. Homogeneous nucleation can be described as:

[0122]

number

[0123] where ΔG corresponds to the free energy of the particle / droplet. ΔG is determined by the volumetric and interfacial terms based on the radius (r), the volumetric free energy (Δg) and the interfacial energy (γ). Due to the ratio of these volumetric and interfacial terms, there is a division between cases where the interfacial terms dominate (low r) and cases where the volumetric terms dominate (high r). At a certain radius, the transition point between these two regions is the nucleus critical size (r * ) The activation energy for reaching this critical size can be used to define the onset of the solidification process, ΔG * =16πγ 3 / 3Δg 2 Thus, achieving high activation energy can be exploited to achieve high supercooling.

[0124] The definition of homogeneous nucleation is primarily governed by intrinsic processes and properties, whereas heterogeneous nucleation is an extrinsic process that relies on nucleation seeds existing within the boundaries of the system. The formation of heterogeneous nucleants can be described by using the interfacial tension equilibrium equation:

[0125]

number

[0126] In the formula γ ls, Gamma sv and γlv are the liquid-solid, solid-vapor and liquid-vapor interfacial tensions, respectively, and θ is the wetting angle. Considering this relationship, the heterogeneous nucleating agent is * The volume reached is much smaller than that for homogeneous nucleation and depends on the wetting angle. The rate of volume reduction can be described by the following equation: f(θ) = 1 / 4(2-3cosθ + cos 3 θ), where f(θ) is the ratio between the critical heterogeneous nucleation energy and the critical homogeneous nucleation energy

[0127]

number

[0128] supercooling thermodynamics The free energy of a thermodynamic system at constant temperature and pressure can be defined by the Gibbs free energy, which is commonly expressed as ΔG=ΔH-TΔS, where H and S are the enthalpy and entropy of the system, respectively. The free energy of the system depends on the balance of these two terms, and phase transitions can be driven by either enthalpic or entropic forces. If ΔG<0, then supercooling (liquid-solid transition) G S -G L <0, the process is considered favorable. The free energy term is the specific heat (C p ), where

[0129]

number

[0130]

number

[0131] ΔH f is the enthalpy of fusion, T m is the melting temperature, ΔT is the temperature difference between the melting point and the freezing point, and the term ΔT / T m is used to determine the degree of subcooling in the system. Under different assumptions that lead to an increase in ΔG, C p Various studies have been carried out to evaluate the increase in the . This change ultimately increases the degree of supercooling. Some models introduce what is known as the maximum supercooling limit. Studies of the liquid-solid transition have focused on the enthalpy and entropy terms (based on PV) and often ignore the presence of the interface and surface terms previously discussed in nucleation theory due to their often minor or negligible effect on the overall system. However, given different processing conditions that drive the high interfacial tension towards the bulk, the surface terms can become dominant in the bulk.

[0132] FIG. 15 shows the particle size distribution of the as-synthesized particles, which in this embodiment ranges from 0.1 to 1.5 microns, although other embodiments may have particle sizes in different ranges.

[0133] Undercooling of various BiSn-based alloys Figure 16 shows a table with constants for elements used in some embodiments. Figure 17 shows a table 1700 that lists undercooling levels and yields before and after reflow for various alloys according to some embodiments of the present disclosure. ΔT is T m From T f The yield was calculated by taking the ratio of the areas under the melting and freezing curves.

[0134]

number

[0135] ΔT and yield calculations were performed on the as-synthesized and reflowed samples, with the true yield reported from the reflowed sample since the reflow process removes any solidus content that appears during the synthesis process.

[0136] Influence of organic ligands ΔT / T when the inductive properties of the organic shell are opposite m A comparison of the ΔT / T of SAC305 particles shows the estimated surface chemical potential gradient across the change under positive or negative inductive surface moieties. This could be due to an inductive effect if the electron density across the binding moiety is perturbed, or it could be due to the nature of the ligand-oxide bond. Introducing this inductive effect into the SAC305 particle synthesis increases the ΔT / T of these particles. m from 0.21 to 0.3, pushing the freezing point to <100 °C. The stabilization of these particles due to the presence of organic ligands was also confirmed, as these particles were able to withstand multiple thermal cycles without experiencing a significant shift in supercooling.

[0137] FIG. 17 illustrates tabulated data showing the effect of different ligands on BiSn particle synthesis. The influence of organic ligands used to synthesize core-shell particles is explored by using various acids, thus modifying the inductive effect due to the change in electronegative character from the ligand. The most common experiments performed in this work are performed using trichloroacetic acid, which is highly electron-withdrawing (i.e., highly electronegative). This behavior induces a negative inductive effect on the surfaces to which these ligands attach, creating electronic tension (negative dipole moment) on the interface. When an acid with the opposite electronegative behavior (e.g., phosphotungstic acid) is used, a positive inductive effect is applied, thus creating electronic compression. Both negative and positive inductive effects can create a high degree of supercooling (e.g., >0.34), although with varying yields.

[0138] To investigate the effect of inductive effects, ligands with lower electronegativity are used (tribromoacetic acid and chloroacetic acid). Both acids used lead to lower supercooling and lower yields. This result further suggests that the effect of surface inductive effects from the organic shell itself plays a role in driving the supercooling behavior for core-shell particles.

[0139] liquid metal surface oxide This part of the disclosure describes an opportunity in passivating oxides of liquid metal particles. The complexity and order of the subsurface presents an opportunity to prevent homogeneous nucleation and allow enhanced supercooling. The plasticity of the underlying liquid metal surface presents an autonomously repairing subsurface, thus allowing the lowest E, unless stoichiometrically limited. o components become dominant at the surface. This plasticity offers the opportunity to synthesize organometallic polymers that self-assemble in situ into high aspect ratio nanomaterials. The induced surface speciation suggests that under appropriate oxidant tension, the oxide thickness and composition can be tuned, leading to temperature-dependent composition inversion and so-called chameleon metals.

[0140] Figure 18 is a close-up of a hypothetical surface oxide architecture of a field metal. In this case, the surface is assumed to have neither mass nor volume (e.g., Gibbs Dividing plane, GDP). In other cases, the surface constitutes a bulk continuum that differs only by the number density of the components occupying such regions (Gibbs-Duhem Interface, GDI). Thermodynamically, a surface can contain the mass, energy, and dissipation boundary plateau of any system. Thus, defining a surface by mass distribution alone may be insufficient. Considering the energy distribution, GDP requires duality in that the transition from one phase to the other constitutes a point in space where two values ​​of energy are feasible, and there is an instantaneous jump in energy. This scenario negates the analogy of equilibrium and is unlikely. On the other hand, GDI with a decreasing concentration gradient can describe low or high cohesive energy density (vapor pressure) material systems. In crystalline materials, the lattice planes are well defined, and it can therefore be argued that GDP is appropriate in such scenarios. Considering a flat crystalline metallic system (pressure jump = 0, vapor pressure ≈ 0) and taking into account the nature of metallic bonding, a "sea of ​​electrons" should occupy the surface. Taking into account electron duality and the uncertainty principle, defining the surface trajectory is a matter of cancelling the electron flow (velocity) at the surface and vice versa. Assuming an energy gradient (GDI) near the surface for an equilibrium mixed material, autonomous speciation is likely driven by curvature in the Lowengrub-Voigt model or thermal oxidation composition inversion.

[0141] In some embodiments, the following governance rules drive speciation: Preferential formation of bonds to reacting components can lead to order and organization over relatively short distances (1-2 nm), such as in hydrocarbon self-assembled monolayers. In more stochastic systems, redox-driven differentiation can occur over nanometers, such as the formation of passivating oxides on metal alloys. It therefore follows that the surface of a material can be a complex piece due to its size (nm), energy profile composition, structure, and reactivity.

[0142] Liquid metal particles: Most metals oxidize rapidly in air to form a thin layer of oxide. Although a thin passivating oxide layer constitutes the particle surface, the oxide is not a metal, but can be stated to be a thermodynamically distinct component. In this respect, defining a surface is a matter of looking for a set of components that are not part of the object under consideration. Although dissimilar, the passivating oxide and the energetically distinct interfacial metal layer constitute the surface.

[0143] Passivating oxides may not be similar to self-assembled monolayers (SAMs) on hard metals, and are distinctly different entities from organics and metals. Unlike monolayer systems with critical attachment points at, for example, Au-S bonds, passivating oxides are dynamic continuums emerging from the bulk, the result of equilibrium systems. This relationship leads to the tensor nature of surface tension, as opposed to the scalar nature of SAMs. The governing rules for its establishment can depend on the environment (temperature, reactants, pressure, etc.), the reactivity of the alloy's components, cohesive energy density (how similar the alloy components are to each other), diffusivity (and therefore atomic radius), and the thermodynamic state of the bulk. The high vapor pressures of both the metal and oxide can preclude the possibility of a concentration gradient, which in turn incorporates a duality of energy at the metal-oxide interface, suggesting the presence of an energy jump (GDP) across the surface. It follows that some gradient in composition or energy state can exist as the metal-oxide layer is approached from either the oxide or metal side of the interface. Thus, a surface, regardless of the definition adopted, is a metastable region of material whose energy state can only be averaged from the divergence of energy states across each point of the surface. At the periphery, a diffuse layer of speciated surface material (σ) reflects the energy gradient between the system and its surroundings, which may be dynamic and susceptible to small perturbations. Equilibrium conditions are established based on the standard reduction potentials of the underlying components, their tendency to flux, and their interactions with other alloy components. Figure 19 illustrates this behavior for BiInSn (field metal). Understanding this surface therefore depends on the observed length scale, time, and its complexity, among other properties. Passivating oxides are typically larger than most SAMs (e.g., eutectic gallium indium oxide ≈ 2 nm, while decanethiol SAMs ≈ 1 nm).

[0144] analogy SAMs are one particular example of thin (nanometer) layers on metal surfaces that significantly modify the properties of materials, including work function, tribology / wettability, electrical conductivity, and plasmonic activity, among others. SAMs can form through a thermodynamically driven self-assembly process, resulting in highly ordered structures. Thin layers of deposited materials raise great opportunities in more fundamental areas, most notably structure-property relationships and interface phenomena. SAM systems can be modeled as two interfaces around a bulk (often a hydrocarbon), where each of these three components can be investigated separately by tuning the basic building blocks, the molecules. Due to the small size of the molecules and their dependence on molecular orientation, small changes in the surface can modify the entire system. However, under well-controlled conditions, SAMs can be analyzed. Applications of SAMs can be divided into two types, with some applications directly exploiting the structure-property relationships of the SAM molecules. For example, the monomolecular nature of SAMs leads to their use in molecular electronics, as well as candidates in tunable hydrophobic coatings. On the other hand, the highly tunable nature of SAMs makes them a great candidate platform for constructing / anchoring other components onto metal surfaces.

[0145] Research on the passivating oxide layer of liquid metal particles has been very limited, due in part to challenges in characterization techniques. This difficulty arises primarily from the compositional complexity within the underlying metal-oxide interface over very short distances. However, this passivating oxide layer, when properly formed and / or engineered, offers various advantages to the material. In non-reactive droplets, the curved surfaces of micro- to nano-sized particles impart steep energy and compositional gradients that are largely captured by the interfacial excess, Γi, and Laplace pressure jump conditions (ΔP=2γ / r, where γ is the surface tension and r is the radius of the particle). By definition, this steep gradient serves the purpose of establishing both energy and mechanical equilibrium between the particle and the surroundings. However, in the case of metal droplets, exposure to ambient conditions leads to the rapid formation of a passivating oxide layer. In metal alloys, the difference in redox potentials and diffusivities is such that at time t=0 of exposure to air, competitive oxidation ensues and the most abundant and most diffusive components predominate at the surface of the formed oxide, resulting in the lowest standard reduction potential (E 0 However, over time, kinetically resolved self-sorting speciation and precipitation often occurs, resulting in the presentation of monometallic oxides on the surface of the metal alloy. This sorting / organization is known as E 0 The oxidation process is governed by, but not limited to, stoichiometry, atomic size, cohesive energy density, atomic flux, oxidant diffusivity, temperature and pressure. Once a certain thickness is reached, oxidation slows infinitely and equilibrium is established.

[0146] In an oxidizing environment, all elements in the alloy have an equal probability of oxidizing at t=0. This is perturbed only by their stoichiometry and tendency to occupy the surface. Kinetically, this becomes a competition with the most "favorable" element dominating at the outer surface of the oxide layer. In EGaIn, this element is gallium. Over time, as the oxidizer flux slowly decreases, the oxide reaches d_c^p, leading to the formation of underlying suboxides, originating from less reactive components that are kinetically limited to oxidize completely. In the case of eutectic, selective depletion of some of the alloy components produces energetically unfavorable hypoeutectic, which leads to enrichment of unreacted components at the metal-oxide interface that mirrors the one across the oxide shell. However, steep compositional gradients present interfaces with large chemical potential gradients (Δμ), and thus metastable surfaces. Δμ coupled to ΔP presents a divergence of stresses proportional to the size of the grain. Such gradients affect the grain properties.

[0147] Based on the asymmetric energy distribution across the surface oxide, it may be possible to induce relaxation by perturbing the bulk energy dissipation and tuning the surface stress. Considering that the molten metal has a high symmetry (i.e., no order as defined in the Landau phase transformation theory), the formation of the passivating oxide and the underlying concentration to maintain the equilibrium (e.g., eutectic composition) should introduce some pressure on the free diffusion. The growth of the nucleation should overcome the surface tension. Even after the nucleation seed is formed, a competition between growth (reduction of bulk energy) and shrinkage (increase of surface energy) ensues, with the process biased towards the former with increasing size. It can be stated that the magnitude of the nucleation rate is sensitive to the value of the interfacial energy, and a small percentage of σls (solid-liquid interfacial free energy) variation can modify the predicted rate by several orders of magnitude. It can also be stated that a second non-dynamic solid-liquid interface, as well as the associated order and free energy transformation, exists below the passivating oxide layer and leads to two solid-liquid interfacial free energy perturbations that must be overcome for successful nucleation growth: the nucleation interface and the oxide interface.

[0148] Unlike a dynamic nucleating-seed interface, where the shrinkage of the nucleating agent is overcome with growth, the structure of the passivating oxide is fixed and cannot be perturbed throughout growth. Thus, by designing the surface oxide with respect to the miscibility of the bulk (liquid) components, one can significantly influence the growth of the nucleating agent, especially for small (<10 μm) particles. Thus, the passivating oxide should lead to a significant hindrance of the liquid-solid phase transformation and thus enhance the supercooling. Traditionally, supercooling has been achieved by removing the heterogeneous nucleating agent, for example, through a containerless approach. However, the containerless approach does not remove the homogeneous nucleating agent, a process that arises from structural fluctuations in the liquid, and therefore does not exploit the non-dynamic surface-oxide interfacial tension.

[0149] The smaller the particle, the higher the chance of supercooling. This size effect is due to the large surface area to volume ratio that limits homogeneous nucleation. Considering that the Gibbs free energy (ΔG) is expressed as follows: ΔG = ΔH-TΔS + δw', where ΔH and ΔS are the enthalpy and entropy changes, respectively, T = temperature, and δw' = non-PV work. Under the correct enthalpy-entropy compensation conditions, the surface work (δw') can dominate in ΔG. While the aforementioned methods rely heavily on manipulating phase transitions by upsetting the balance between bulk enthalpy and entropy, it is often assumed that δw' and the surface contributions are negligible due to entropy limitations. However, by definition, curved surfaces are metastable and therefore a source of free energy stress that can modify the energy landscape of the entire material. Thus, by engineering surface oxides, these size dependencies (surface area to volume ratio) can be extended from the nanoscale to the microscale.

[0150] The surface work term captures the amount of energy required to maintain a surface per unit area, δŵ' = γdA. By definition, surface tension is the product of the interfacial excess and the chemical potential difference,

[0151]

number

[0152] In addition to the effect on free energy, the formation of a uniform, smooth, passivating oxide layer forms a physical barrier against inhomogeneous nucleation, thus enhancing the stability of the supercooled state. This understanding has enabled the synthesis of stable undercooled liquid metal core-shell (ULMCS) particles, enabling heat-free soldering and numerous other ambient or low-temperature metal processes. As the surface is the primary driving force for metastability, the destruction of the oxide shell results in instantaneous flow, coalescence, and solidification. Recent developments have allowed the supercooling of commercially available lead-free solder SAC305, enabling low-temperature surface mounting and electronic packaging. This low-temperature sintering has enabled the integration of conductive traces or circuits onto otherwise temperature-sensitive substrates (i.e., organics and polymers). Understanding surface oxides presents a Braess-type paradox. Surface speciation can induce reverse organization on liquid metals.

[0153] Although droplet 100 (see FIG. 1) is described and illustrated as one particular composition and structure, embodiments of the present disclosure are suitable for use with numerous compositions and structures. Any elements and combinations thereof can be used in the core and shell. The shell can have any number of layers that are inorganic and / or organic.

[0154] In the foregoing specification, the embodiments of the present disclosure have been described with reference to numerous specific details that may vary from implementation to implementation. Therefore, the specification and drawings should be regarded as illustrative rather than restrictive. The sole and exclusive indication of the scope of the present disclosure, and what the applicant intends to be the scope of the disclosure, is the literal equivalent scope of the set of claims issued from this application in the particular form in which such claims are issued, including any subsequent amendments. The specific details of the particular embodiments may be combined in any suitable manner without departing from the spirit and scope of the embodiments of the present disclosure.

[0155] Additionally, spatially relative terms such as "bottom" or "top" may be used to describe the relationship of an element and / or feature to another element and / or feature, for example, as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device during use and / or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, an element described as a "bottom" surface may then be oriented "on top" of the other element or feature. The device may be oriented differently (e.g., rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.

[0156] The terms "and," "or," and "one / or" as used herein may include a variety of meanings that are also expected to depend at least in part on the context in which such terms are used. Typically, "or," when used to associate a list, such as A, B, or C, is intended to mean A, B, and C, which are used herein in an inclusive sense, as well as A, B, or C, which are used herein in an exclusive sense. Additionally, the term "one or more" as used herein may be used to describe any feature, structure, or characteristic in the singular, or may be used to describe any combination of features, structures, or characteristics. However, it should be noted that this is merely an example, and claimed subject matter is not limited to this example. Additionally, the term "at least one of," when used to associate a list, such as A, B, or C, may be interpreted to mean any combination of A, B, and / or C, such as A, B, C, AB, AC, BC, AA, AAB, ABC, AABBCCC, etc.

[0157] References throughout this specification to "one example," "an example," "a particular example," or "an exemplary implementation" mean that a particular feature, structure, or characteristic described in connection with a feature and / or example may be included in at least one feature and / or example of the claimed subject matter. Thus, the appearances of the phrases "in one example," "an example," "in a particular example," "in a particular implementation," or other similar phrases in various places throughout this specification do not necessarily all refer to the same features, examples, and / or limitations. Furthermore, particular features, structures, or characteristics may be combined in one or more examples and / or characteristics.

[0158] In some implementations, operations or processing may involve physical manipulation of physical quantities. Typically, although not necessarily, such quantities may take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, or otherwise manipulated. It has proven convenient at times, primarily for reasons of common usage, to refer to such signals as bits, data, values, elements, symbols, characters, terms, numbers, numerals, or the like. It should be understood, however, that all of these or similar terms are to be associated with the appropriate physical quantities and are merely convenient labels. Unless otherwise stated, and as will be apparent from the description herein, descriptions utilizing terms such as "processing," "computing," "calculating," "determining," and the like throughout this specification should be understood to refer to operations or processes of a particular apparatus, such as a special purpose computer, a special purpose computing apparatus, or a similar special purpose electronic computing device. Thus, in the context of this specification, a special purpose computer or a similar special purpose electronic computing device can manipulate or transform signals that are typically represented as physical electronic or magnetic quantities in the memory, registers, or other information storage, transmission, or display devices of the special purpose computer or a similar special purpose electronic computing device.

[0159] In the foregoing detailed description, numerous specific details are set forth to provide a thorough understanding of the claimed subject matter. However, it will be understood by those skilled in the art that the claimed subject matter may be practiced without these specific details. In other instances, methods and apparatuses that would be known by those skilled in the art have not been described in detail so as not to obscure the claimed subject matter. Therefore, the claimed subject matter is not limited to the particular examples disclosed, and it is intended that such claimed subject matter also include all embodiments falling within the scope of the appended claims, and their equivalents.

Claims

1. A solder material comprising: a core including an alloy including a major amount of a first metallic element and a minor amount of a second element, the core being in a liquid state below the solidus temperature of the alloy; a shell completely surrounding the core and including an outer surface comprising a major amount of the second element and a minor amount of the first metallic element, the shell being in a solid state below the solidus temperature of the alloy.

2. The solder material of claim 1 , wherein the second element is a metal.

3. The solder material of claim 1 , wherein the second element is a metalloid.

4. 2. The solder material of claim 1, wherein the shell comprises an innermost layer having a predominant concentration of the first metallic element and an outermost layer having a predominant concentration of the second metallic element.

5. The solder material of claim 4 , wherein the innermost layer has a greater Eo than the outermost layer.

6. The solder material of claim 4 , wherein the innermost layer has a lower Eo than the outermost layer.

7. The solder material of claim 4 , wherein the innermost layer and the outermost layer comprise an oxide of the first metallic element and an oxide of the second element.

8. The solder material of claim 1 further comprising a ligand coating on said exterior surface.

9. A method of forming a solder material, comprising: forming a liquid core of the solder material from an alloy including a first element, a second element, and a third element; forming a solid shell around the liquid core completely surrounding the liquid core, the solid shell including an innermost layer having a predominant concentration of one of the first element, the second element, or the third element, and an outermost layer having a predominant concentration of a different one of the first element, the second element, or the third element; and cooling the liquid core and the solid shell below a solidus temperature of the alloy while maintaining the liquid core in a liquid state.

10. 10. The method of claim 9, wherein the solid shell comprises three layers, the innermost layer having a predominant concentration of the first element, a middle layer having a predominant concentration of the second element, and the outermost layer having a predominant concentration of the third element.

11. The method of claim 10 , wherein the solid shell is formed in an oxidizing environment.

12. The method of claim 11 , wherein the oxidizing environment is controlled by varying the partial pressure of oxygen in the oxidizing environment.

13. The method of claim 11 , wherein the innermost layer has a greater Eo than the middle layer, which has a greater Eo than the outermost layer.

14. The method of claim 11 , wherein a thickness of one or more of the three layers of the solid shell is determined by a time of exposure to the oxidizing environment.

15. The method of claim 10 , wherein the solid shell is formed in a reducing environment.

16. 16. The method of claim 15, wherein the innermost layer has a lower Eo than the middle layer, which has a lower Eo than the outermost layer.

17. 16. The method of claim 15, wherein a thickness of one or more of the three layers of the solid shell is determined by exposure time to the reducing environment.

18. The method of claim 10, further comprising exposing the solid shell to one or more chelating agents to remove at least a portion of the outermost layer.

19. 20. The method of claim 18, wherein the one or more chelating agents comprise at least one of a carboxylate, an amide, an alkoxide, an amine, a thiol, or a phosphate.

20. The method of claim 10 further comprising an etching process to polish away an inner layer of the solid shell.

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