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In the past few years, there has been a rapid development of liquid metal alloys for the fabrication of nano-/meso-sized porous and composite structures with ultra-large interfaces for various materials. However, this approach currently has two important limitations. First, it generates bicontinuous structures with a high-order topology for a limited range of alloy compositions. Secondly, the structure has a larger size of the binder due to significant enlargement during high-temperature separation. Here, we demonstrate computationally and experimentally that these limitations can be overcome by adding an element to metal melts that promotes high-order topology by limiting the leakage of immiscible elements during decoupling. Next, we explain this finding by showing that the bulk diffusion transfer of immiscible elements in liquid melts strongly influences the evolution of the solid fraction and the topology of structures during flaking. The results reveal fundamental differences between liquid metals and electrochemical impurity removal, and also establish a new method for obtaining structures from liquid metals with given dimensions and topology.
Delegation has evolved into a powerful and versatile technology for the fabrication of nano-/meso-sized open pores and composite structures with ultra-high interfacial surface for various functional and structural materials such as catalysts1,2, fuel cells3,4, electrolytic capacitors5,6, materials resistant to radiation damage 7, high-capacity battery materials with increased mechanical stability 8, 9 or composite materials with excellent mechanical properties 10, 11. In various forms, delegation involves the selective dissolution of one element of an initially unstructured “precursor alloy” in the external environment, which leads to the reorganization of undissolved alloying elements with a non-trivial topology, different from the topology of the original alloy. , Composition of ingredients. Although conventional electrochemical delegation (ECD) using electrolytes as the environment is the most studied to date, this method limits the delegating systems (such as Ag-Au or Ni-Pt) to those containing relatively noble elements (Au, Pt) and have a sufficiently large difference in reduction potential to provide porosity. An important step towards overcoming this limitation has been the recent rediscovery of the liquid metal alloying method13,14 (LMD), which uses alloys of liquid metals (e.g., Cu, Ni, Bi, Mg, etc.) with other elements in the environment. (e.g. TaTi, NbTi, FeCrNi, SiMg, etc.)6,8,10,11,14,15,16,17,18,19. LMD and its hard metal alloy removal (SMD) variant operate at lower temperatures when the base metal is hard20,21 resulting in a composite of two or more interpenetrating phases after chemical etching of one phase. These phases can transform into open pores. structures. Delegation methods have been further improved by the recent introduction of vapor phase delegation (VPD), which exploits differences in vapor pressure of solid elements to form open nanoporous structures through selective evaporation of a single element22,23.
At a qualitative level, all of these impurity removal methods share two important common features of a self-organized impurity removal process. Firstly, this is the selective dissolution of the aforementioned alloying elements (such as B in the simplest alloy AXB1-X) in the external environment. The second, first noted in the pioneering experimental and theoretical studies on the ECD24, is the diffusion of the undissolved element A along the interface between the alloy and the environment during the removal of impurities. Diffusion is able to form atomic-rich regions through a process similar to spinodal decay in bulk alloys, albeit limited by the interface. Despite this similarity, different alloy removal methods may produce different morphologies for unclear reasons18. While ECD can generate topologically related high-order structures for atomic fractions (X) of undissolved elements (such as Au in AgAu) as low as 5%25, computational and experimental studies of LMD show that this seemingly similar method only generates topologically related structures. For example, for much larger X, the associated bicontinuous structure is about 20% in the case of TaTi alloys decoupled by Cu melts (see Fig. 2 in ref. 18 for a side-by-side comparison with various ECD and LMD form X). This discrepancy is theoretically explained by a diffusion-coupled growth mechanism distinct from interfacial spinodal decomposition and very similar to eutectic-coupled growth26. In an impurity removal environment, diffusion-coupled growth allows A-rich filaments (or flakes in 2D) and B-rich liquid channels to co-grow by diffusion during impurity removal15. Pair growth leads to an aligned topologically unbound structure in the middle part of X and is suppressed in the lower part of X, where only unbound islands rich in A phase can form. At larger X, bonded growth becomes unstable, favoring the formation of perfectly bonded 3D structures that maintain structural integrity even after single-phase etching. Interestingly, the orientational structure produced by LMD17 or SMD20 (Fe80Cr20)XNi1-X alloys has been observed experimentally for X up to 0.5, suggesting that diffusion-coupled growth is a ubiquitous mechanism for LMD and SMD rather than the commonly resulting porous ECD does not have a preferred alignment structure.
To elucidate the reason for this difference between ECD and NMD morphology, we performed phase field simulations and experimental studies of NMD of TaXTi1-X alloys, in which the dissolution kinetics were modified by adding dissolved elements to liquid copper. We concluded that although both ECD and LMD are regulated by selective dissolution and interfacial diffusion, these two processes also have important differences that may lead to morphological differences18. First, the peel kinetics in the ECD is controlled by the interface with a constant peel front velocity V12 as a function of the applied voltage. This is true even when a small fraction of refractory particles (eg Pt in Ag-Au) are added to the parent alloy, which retards interfacial fluidity, cleans and stabilizes the unalloyed material, but otherwise retains the same morphology 27 . Topologically coupled structures are obtained only at low X at low V, and the retention of miscible elements 25 is large to maintain a solid volume fraction large enough to prevent fragmentation of the structure. This suggests that the rate of dissolution with respect to interfacial diffusion may play an important role in morphological selection. In contrast, the alloy removal kinetics in an LMD is diffusion controlled15,16 and the rate decreases relatively faster with time \(V \sim \sqrt{{D}_{l}/t}\), where Dl is the miscibility element for the fluid diffusion coefficient . .
Secondly, during ECD, the solubility of immiscible elements in the electrolyte is extremely low, so they can only diffuse along the alloy-electrolyte interface. In contrast, in LMD, the “immiscible” elements (A) of AXB1-X precursor alloys typically have little, though limited, melt solubility. This slight solubility can be inferred from analysis of the ternary phase diagram of the CuTaTi ternary system shown in Supplementary Figure 1. Solubility can be quantified by plotting a liquidus line versus equilibrium concentrations of Ta and Ti on the liquid side of the interface (\({c}_{ {{{{{{\rm{Ta))))))}}}} ^{l}\ ) and \({c}_{{{{({\rm{Ti}}}}}} }^ {l}\), respectively, at the delegation temperature (Supplementary Fig. 1b) solid-liquid interface Local thermodynamic equilibrium is maintained during alloying, }}}}}}^{l}\) is approximately constant and its value is related to X. Supplementary Figure 1b shows that \({c}_{{{{{{{\rm{Ta}}}}} ))}^{l}\) falls in the range 10-3 − 10 ^{l}\) are equal to 15.16. This “leakage” of immiscible elements in the alloy can affect both the formation of an interfacial structure at the delamination front, in its turn, which can contribute to the dissolution and coarsening of the structure due to volume diffusion.
In order to separately evaluate the contribution of (i) the reduced rate of removal of alloy V and (ii) the reduced rate of infiltration of immiscible elements into the melt, we proceeded in two steps. First, thanks to \(V \sim \sqrt{{D}_{l}/t}\), by studying the morphological evolution of the structure of the bundle front, it was possible to study the effect of decreasing V sufficiently. big time. Therefore, we investigated this effect by running phase field simulations over longer time periods than previous studies, which revealed the presence of topologically uncoupled alignment structures formed by the diffusion-coupled growth of the X15 intermediate. Second, in order to investigate the effect of immiscible elements on reducing the leakage rate, we added Ti and Ag to the copper melt to increase and decrease the leakage rate, respectively, and studied the resulting morphology, segregation kinetics, and concentration distribution in the melt. delegated Cu melt through calculations and experiments inside the alloy structure. We have added Ti additions ranging from 10% to 30% to the media to remove the Cu melt. The addition of Ti increases the Ti concentration at the edge of the delegated layer, which reduces the Ti concentration gradient within this layer and reduces the dissolution rate. It also increases Ta’s leakage rate by increasing \({c}_{{{({\rm{Ti}}}}}}}}^{l}\), so \({c}_{{{{ { {\rm{Ta}}}}}}}}^{l}\) (Supplementary Fig. 1b). The amount of silver we add varies from 10% to 30%. Since the main effect of adding Ag is to reduce the solubility of alloying elements in the melt, we have modeled the CuAgTaTi quaternary system as an efficient (CuAg)TaTi ternary system in which the solubility of Ti and Ta depends on the concentration of Ag in the CuAg melt (see Note) 2 and Supplementary Figs. . 2–4). The addition of Ag does not increase the concentration of Ti at the edge of the delegated structure. However, since the solubility of Ti in Ag is lower than that of Cu, this reduces \({c}_{{{{{\rm{Ta}}}}}}}}^{l}\) (Supplementary Fig. 1 ) 4b) and leakage rate Ta.
The results of phase field simulations show that coupled growth becomes unstable over a sufficiently long time to promote the formation of topologically coupled structures at the decay front. We experimentally confirm this conclusion by showing that the underlying layer of the Ta15T85 alloy, which forms near the delamination front at a later stage of delamination, remains topologically bonded after etching of the copper-rich phase. Our results also suggest that the leakage rate has a profound effect on morphological evolution due to bulk diffusive transport of immiscible elements in liquid melts. It is shown here that this effect, which is absent in ECD, strongly affects the concentration profiles of various elements in the delegated layer, the fraction of the solid phase, and the topology of the LMD structure.
In this section, we first present the results of our study by phase field simulation of the effect of adding Ti or Ag to Cu melts resulting in different morphologies. On fig. Figure 1 presents the results of three-dimensional modeling of the phase field of TaXTi1-X alloys obtained from Cu70Ti30, Cu70Ag30 and pure copper melts with a low atomic content of immiscible elements from 5 to 15%. The first two rows show that the addition of both Ti and Ag promotes the formation of topologically bonded structures compared to the unbound structure of pure Cu (third row). However, the addition of Ti, as expected, increased Ta leakage, thereby preventing delamination of low X alloys (Ta5Ti95 and Ta10Ti90) and causing massive dissolution of the exfoliated porous layer during Ta15Ti85 delamination. On the contrary, the addition of Ag (second row) contributes to the formation of a topologically related structure of all components of the base alloy with a slight dissolution of the delegated layer. The formation of a bicontinuous structure is additionally illustrated in Figs. 1b, which shows images of the delegated structure with increasing depth of delamination from left to right and an image of the solid-liquid interface at maximum depth (far right image).
3D phase field simulation (128 × 128 × 128 nm3) showing the dramatic effect of adding a solute to a liquid melt on the final morphology of the delegated alloy. The upper mark indicates the composition of the parent alloy (TaXTi1-X) and the vertical mark indicates the melt composition of the Cu-based softening medium. Areas with a high Ta concentration in the structure without impurities are shown in brown, and the solid-liquid interface is shown in blue. b Three-dimensional simulation of the phase field of the undoped Ta15Ti85 precursor alloy in the Cu70Ag30 melt (190 × 190 × 190 nm3). The first 3 frames show the solid region of the delegated structure at different delegation depths, and the last frame shows only the solid-liquid interface at the maximum depth. The movie corresponding to (b) is shown in Supplementary Movie 1.
The effect of solute addition was further explored with 2D phase field simulations, which provided additional information on interfacial mode formation at the delamination front and allowed access to greater lengths and time scales than 3D simulations to quantify the delamination kinetics. On fig. Figure 2 shows images of the simulation of the removal of the Ta15Ti85 precursor alloy through Cu70Ti30 and Cu70Ag30 melts. In both cases, diffusion-coupled growth is very unstable. Instead of penetrating vertically into the alloy, the tips of the fluid channels move chaotically left and right in very complex trajectories during a stable growth process that promotes aligned structures that promote the formation of topologically related structures in 3D space (Fig. 1). However, there is an important difference between Ti and Ag additives. For the Cu70Ti30 melt (Fig. 2a), the collision of two liquid channels leads to the merging of the solid-liquid interface, which leads to the extrusion of the solid binders captured by the two channels from the structure and, ultimately, to dissolution. On the contrary, for the Cu70Ag30 melt (Fig. 2b), Ta enrichment at the interface between the solid and liquid phases prevents coalescence due to a decrease in Ta leakage into the melt. As a result, compression of the bond at the delamination front is suppressed, thereby promoting the formation of connective structures. Interestingly, the chaotic oscillatory motion of the liquid channel creates a two-dimensional structure with a certain degree of alignment when the cutoff is suppressed (Fig. 2b). However, this alignment is not the result of a stable growth of the bond. In 3D, unstable penetration creates a non-coaxial connected bicontinuous structure (Fig. 1b).
Snapshots of 2D phase field simulations of Cu70Ti30 (a) and Cu70Ag30 (b) melts remelted to Ta15Ti85 alloy illustrating unstable diffusion-coupled growth. Pictures showing different impurity removal depths measured from the initial position of the flat solid/liquid interface. The insets show different regimes of liquid channel collisions, leading to the detachment of solid binders and the preservation of Cu70Ti30 and Cu70Ag30 melts, respectively. The domain width of Cu70Ti30 is 1024 nm, Cu70Ag30 is 384 nm. The colored band indicates the Ta concentration, and the different colors distinguish between the liquid region (dark blue), the base alloy (light blue), and the unalloyed structure (almost red). Movies of these simulations are featured in Supplemental Movies 2 and 3, which highlight the complex pathways that penetrate liquid channels during unstable diffusion-coupled growth.
Other results of 2D phase field simulation are shown in Fig.3. Graph of delamination depth versus time (slope equal to V) in fig. 3a shows that the addition of Ti or Ag to the Cu melt slows down the separation kinetics, as expected. On fig. 3b shows that this slowdown is caused by a decrease in the Ti concentration gradient in the liquid within the delegated layer. It also shows that the addition of Ti(Ag) increases (decreases) the concentration of Ti on the liquid side of the interface (\({c}_{{{{{{{\rm{Ti))))))))) ^{l \) ), which leads to leakage of Ta, measured by the fraction of Ta dissolved in the melt as a function of time (Fig. 3c), which increases (decreases) with the addition of Ti(Ag). Figure 3d shows that for both solutes, the volume fraction of solids remains above the threshold for the formation of bicontinuous topologically related structures28,29,30. While adding Ti to the melt increases the leakage of Ta, it also increases the retention of Ti in the solid binder due to phase equilibrium, thereby increasing the volume fraction to maintain the cohesiveness of the structure without impurities. Our calculations generally agree with experimental measurements of the volume fraction of the delamination front.
The phase field simulation of the Ta15Ti85 alloy quantifies the different effects of Ti and Ag additions to the Cu melt on the alloy removal kinetics measured from the alloy removal depth as a function of time (a), the Ti concentration profile in the liquid at an alloy removal depth of 400 nm (negative depth widens into the melt outside the alloy structure (alloy front on the left) b Ta leakage versus time (c) and solid fraction in the unalloyed structure versus melt composition (d) The concentration of additional elements in the melt is plotted along the abscissa (d). (Ti – green line, Ag – purple line and experiment).
Since the speed of the delamination front decreases with time, the evolution of the morphology during delamination shows the effect of reducing the delamination speed. In a previous phase field study, we observed eutectic-like coupled growth resulting in aligned topologically unbound structures during removal of the Ta15Ti85 precursor alloy by pure copper melts15. However, long runs of the same phase field simulation show (see Supplementary Movie 4) that when the decomposition front speed becomes small enough, the coupled growth becomes unstable. The instability manifests itself in the lateral rocking of the flakes, which prevents their alignment and, thus, promotes the formation of topologically connected structures. The transition from stable bound growth to unstable rocking growth occurs near xi = 250 nm at a rate of 4.7 mm/s. On the contrary, the corresponding delamination depth xi of the Cu70Ti30 melt is about 40 nm at the same rate. Therefore, we could not observe such a transformation when removing the alloy with the Cu70Ti30 melt (see Supplementary Movie 3), because adding 30% Ti to the melt significantly reduces the alloy removal kinetics. Finally, although diffusion-coupled growth is unstable due to slower delamination kinetics, the distance λ0 of hard bonds at the delamination front roughly obeys the \({\lambda }_{0}^{2}V=C\) law of stationary growth15,31 where C is a constant.
To test the predictions of the phase field simulation, alloy removal experiments were performed with larger samples and longer alloy removal times. Figure 4a is a schematic diagram showing the key parameters of the delegated structure. The total depth of delamination is equal to xi, the distance from the initial boundary of the solid and liquid phases to the delamination front. hL is the distance from the initial solid-liquid interface to the edge of the delegated structure before etching. A large hL indicates a strong Ta leakage. From the SEM image of the delegated sample, we can measure the size hD of the delegated structure before etching. However, since the melt also solidifies at room temperature, it is possible to retain a delegated structure without bonds. Therefore, we etched the melt (copper rich phase) to obtain the transition structure and used hC to quantify the thickness of the transition structure.
a Schematic diagram of the evolution of morphology during the removal of impurities and the determination of geometric parameters: leakage layer thickness Ta hL, thickness of the delaminated structure hD, thickness of the connecting structure hC. (b), (c) Experimental validation of phase field simulation results comparing SEM cross sections and 3D etched morphology of Ta15Ti85 alloy prepared from pure Cu(b) and Cu70Ag30 melts, yielding topological bonds with uniform bond size Structure (c), scale bar 10 µm.
The cross sections of the delegated structures shown in fig. 4b,c confirm the main predicted effects of adding Ti and Ag to Cu melts on the morphology and kinetics of the delegated alloy. On fig. Figure 4b shows the lower region of the SEM cut (on the left) of the Ta15T85 alloy alloyed by immersion in pure copper for 10 s to a depth of xi ~ 270 μm. On a measurable experimental time scale, which is several orders of magnitude larger than in phase field simulations, the decoupling front velocity is well below the aforementioned threshold velocity of 4.7 mm/s, below which stable eutectic bond growth becomes unstable. Therefore, the structure above the peel front is expected to be topologically fully connected. Before etching, a thin layer of the base alloy was completely dissolved (hL = 20 μm), which was associated with Ta leakage (Table 1). After chemical etching of the copper-rich phase (right), only a thin layer of delegated alloy (hC = 42 µm) remains, indicating that much of the delegated structure lost structural integrity during etching and was not, as expected, topologically bonded (Fig. 1a). , the rightmost image in the third row). On fig. 4c shows the full SEM cross section and 3D images of the etching of the Ta15Ti85 alloy removed by immersion in the Cu70Ag30 melt for 10 s to a depth of about 200 µm. Since the peel depth is theoretically predicted to increase with \({x}_{i}(t)=\sqrt{4p{D}_{l}t}\) diffusion controlled kinetics (see Supplementary Note 4) 15 16, With the addition of 30% Ag to the Cu melt, a decrease in the depth of separation from 270 μm to 220 μm corresponds to a decrease in the Peclet number p by a factor of 1.5. After chemical etching of the Cu/Ag rich phase (right), the entire delegated structure retains structural integrity (hC = 200 µm), demonstrating that it is basically a predicted topologically coupled bicontinuous structure (Figure 1, rightmost image) second row and entire bottom row ). All measurements of the delegated base alloy Ta15T85 in various melts are summarized in Table. 1. We also present results for unalloyed Ta10Ti90 base alloys in various melts, confirming our conclusions. Measurements of the leakage layer thickness Ta showed that the structure dissolved in the Cu70Ag30 melt (hL = 0 μm) is smaller than that in the pure Cu melt (hL = 20 μm). On the contrary, the addition of Ti to the melt dissolves more weakly alloyed structures (hL = 190 μm). The decrease in the dissolution of the delegated structure between the pure Cu melt (hL = 250 μm) and the Cu70Ag30 melt (hL = 150 μm) is more pronounced in the delegated alloys based on Ta10Ti90.
To understand the effect of different melts, we performed an additional quantitative analysis of the experimental results in Fig. 5 (see also Supplementary Data 1). On fig. Figures 5a–b show measured concentration distributions of different elements along the direction of exfoliation in exfoliation experiments in pure Cu melt (Fig. 5a) and Cu70Ag30 melt (Fig. 5b). The concentrations of various elements are plotted against the distance d from the delamination front to the edge of the delamination layer in the solid binder and the phase that was liquid (enriched in Cu or CuAg) at the time of delamination. Unlike ECD, where the retention of miscible elements is determined by the rate of separation, in LMD, the concentration in a solid binder is determined by the local thermodynamic equilibrium between the solid and liquid phases and, thus, the coexistence properties of the solid and liquid phases. Alloy State Diagrams. Due to the dissolution of Ti from the base alloy, the Ti concentration decreases with increasing d from the delamination front to the edge of the delamination layer. As a result, the Ta concentration increased with increasing d along the bundle, which was consistent with the phase field simulation (Supplementary Fig. 5). The Ti concentration in the Cu70Ag30 melt falls more shallowly than in the pure Cu melt, which is consistent with the slower alloy removal rate. The measured concentration profiles in Figs. 5b also show that the ratio of the concentrations of Ag and Cu in the liquid is not exactly constant along the layer of the delegated alloy, while in the simulation of the phase field this ratio was assumed to be constant in the simulation of the melt as a pseudo-element Cu70Ag30. Despite this quantitative difference, the phase field model captures the predominant qualitative effect of adding Ag on suppressing Ta leakage. Fully quantitative modeling of the concentration gradients of all four elements in solid binders and liquids requires a more accurate four-component model of the TaTiCuAg phase diagram, which is beyond the scope of this work.
Measured concentration profiles depending on the distance d from the delamination front of the Ta15Ti85 alloy in (a) pure Cu melt and (b) Cu70Ag30 melt. Comparison of the measured volume fraction of solids ρ(d) of the delegated structure (solid line) with the theoretical prediction corresponding to the equation without leakage Ta (dashed line). (1) (c) Inflate equation prediction. (1) Equation corrected at the delamination front. (2) That is, Ta leakage is considered. Measure the average bond width λw and distance λs (d). Error bars represent the standard deviation.
On fig. 5c compares the measured volume fraction of solids ρ(d) (solid line) for pure delegated Cu and Cu70Ag30 structures from the melt with the theoretical prediction (dashed line) obtained from mass conservation using the measured Ta concentration in the solid binder \({ c }_ {Ta}^{s}(d)\) (Fig. 5a,b) and ignore the leakage of Ta and the transport of Ta between bonds with different depths of separation. If Ta changes from solid to liquid, all of the Ta contained in the base alloy must be redistributed into a solid binder. Thus, in any layer of the remote structure perpendicular to the direction of removal of the alloy, the conservation of mass means that \({c}_{Ta}^{s}(d){S}_{s}(d)={c}_ {Ta}^{0}(d){S}_{t}\), where \({c}_{Ta}^{s}(d)\) and \({c}_{Ta }^ {0}\) are the Ta concentrations at position d in the binder and matrix alloy, respectively, and Ss(d) and St are the cross-sectional areas of the hard binder and the entire remote region, respectively. This predicts the volume fraction of solids in the remote layer.
This can be easily applied to the structure of delegated pure Cu and Cu70Ag30 melts using the corresponding \({c}_{Ta}^{s}(d)\) curves corresponding to the blue line. These predictions are superimposed on Fig. 5c showing that ignoring Ta leakage is a poor predictor of the volume fraction distribution. Leak-free mass conservation predicts a monotonic decrease in the volume fraction with increasing d, which is qualitatively observed in pure Cu melts, but not in Cu70Ag30 melts, where ρ(d) has a minimum. In addition, this leads to a significant overestimation of the volume fractions at the separation front for both melts. For the smallest measurable d ≈ 10 µm, the predicted ρ values ​​for both melts exceed 0.5, while the measured ρ values ​​for the Cu and Cu70Ag30 melts are slightly higher than 0.3 and 0.4, respectively.
To emphasize the main role of the Ta leakage, we then show that the quantitative discrepancy between the measured and predicted ρ values ​​near the decomposition front can be eliminated by refining our theoretical predictions to include this leakage. To this end, let us calculate the total number of Ta atoms flowing from a solid into a liquid when the decay front moves over a distance Δxi = vΔt in the time interval Δt Δxi = vΔt, where \(v={\dot{x)) _{i }( t )\) – delamination rate, depth and time can be derived from the known relationship \({x}_{i}(t)=\sqrt{4p{D}_{l}t} \) deaeration. The local law of conservation of mass at the separation front (d ≈ 0) is such that ΔN = DlglΔtSl/va, where gl is the concentration gradient of Ta atoms in the liquid, va is the atomic volume corresponding to the concentration defined as an atomic fraction, and Sl = St − Ss is the cross-sectional area of ​​the liquid channel at the delamination front. The concentration gradient gl can be calculated by assuming that the concentration of Ta atoms has a constant value \({c}_{Ta}^{l}\) at the interface and is very small in the melt outside the exfoliated layer, which gives \( {g}_ {l}={c}_{Ta}^{l}/{x}_{i}\) So, \({{\Delta}}N=({{\Delta} { x}_{i} {S}_{l}/{v}_{a}){c}_{Ta}^{l}/(2p)\). When the front moves to a distance Δxi, the solid fraction is equal to the total number of Ta atoms removed from the base alloy, \({{\Delta}}{x}_{i}{S}_{t} {c }_{Ta}^ { 0}/{v}_{a}\), to the sum of the number of Ta atoms leaking into the liquid, ΔN, and included in the solid binder\({{ \Delta}} {x}_{i}{S}_{s }{c}_{Ta}^{s}/{v}_{a}\). This equation, together with the above expression for ΔN and the relations St = Ss + Sl and phases at the delamination front.
In the limit of zero solubility of Ta atoms, which reduces to an early prediction of the absence of leaks, \(\rho ={c}_{Ta}^{0}/{c}_{Ta}^{s}\)liquid ( \({c }_{Ta}^{l}=0\)). Using the values ​​\({c}_{Ta}^{l}\about 0.03\) from experimental measurements (not shown in Fig. 5a, b) and Peclet numbers p ≈ 0.26 and p ≈ 0.17 and solids concentrations \( {c}_{Ta}^{s}\approximately 0.3\) and \({c}_{Ta}^{s}\approximately 0.25\) for Cu and Cu70Ag30 melts, respectively , we obtain the predicted value of the melt, ρ ≈ 0.38 and ρ ≈ 0.39. These predictions are quantitatively in fairly good agreement with the measurements. The rest of the differences (predicted 0.38 vs. measured 0.32 for pure Cu melt and 0.39 predicted vs. measured 0.43 for Cu70Ag30 melt) can be explained by greater measurement uncertainty for very low Ta concentrations in liquids (\( {c }_{Ta }^ {l}\approximately 0.03\)), which is expected to be slightly larger in pure copper melt.
Although the present experiments were performed on specific base alloys and melt elements, we expect that the results of the analysis of these experiments will help to derive the equations. (2) Wide applicability to other LMD doping systems and other related methods such as Solid State Impurity Removal (SSD). Until now, the influence of the leakage of immiscible elements on the LMD structure has been completely ignored. This is mainly due to the fact that this effect is not significant in ECDD, and so far it has been naively assumed that NMD is similar to REC. However, the key difference between ECD and LMD is that in LMD the solubility of immiscible elements in liquids is greatly increased due to the high concentration of miscible elements on the liquid side of the interface (\({c}_{Ti} ^{ l}\)), which in turn increases the concentration of immiscible elements (\({c}_{Ta}^{l}\)) on the liquid side of the interface and decreases the volume fraction predicted by the solid state equation. (2) This improvement is due to the fact that the solid-liquid interface during LMD is in local thermodynamic equilibrium, so high \({c}_{Ti}^{l}\) helps to improve \({c} _ {Ta} ^{l}\ Similarly, high \({c}_{Ti}^{s}\) allows Cu to be incorporated into hard binders, and the concentration of solid Cu in these binders varies from about 10% gradually decreases to values ​​are negligible at the edge of the small delegated layer (Supplementary Fig. 6).In contrast, the electrochemical removal of Ag from AgAu alloys by ECD is a non-equilibrium reaction that does not increase the solubility of Au in the electrolyte.In addition to LMD, we also hope that our results are applicable to solid state drives, where the solid boundary is expected to maintain local thermodynamic equilibrium during alloy removal.This expectation is supported by the fact that a change in the volume fraction of solids in the delegated layer of the SSD structure was observed, implying I, that during the delegation there is a dissolution of the solid ligament, associated with the leakage of immiscible elements.
And the equation. (2) In order to predict a significant decrease in the solid fraction at the alloy removal front due to Ta leakage, it is also necessary to take into account Ta transport in the alloy removal region in order to understand the solid fraction distribution in the entire alloy removal layer, which is consistent with pure copper and Cu70Ag30 melt. For the Cu70Ag30 melt (red line in Fig. 5c), ρ(d) has a minimum of about half of the delegated layer. This minimum is due to the fact that the total amount of Ta contained in the hard binder near the edge of the delegated layer is greater than in the base alloy. That is, for d ≈ 230 μm \({S}_{s}(d){c}_{Ta}^{s}(d)\, > \,{S}_{t}{c} _ { Ta}^{0}\), or completely equivalent, the measured ρ(d) = Ss(d)/St ≈ 0.35 is much larger than the equation predicts. (1) No leakage\({c}_{Ta}^{0}/{c}_{Ta}^{s}(d)\approx. 0.2\). This means that part of the escaping Ta is transported from the separation front to a region remote from this front, diffusing in the liquid and along the solid-liquid interface, where it is redeposited.
This redeposition has the opposite effect of Ta leakage to enrich Ta hard binders, and the hard fraction distribution can be qualitatively explained as a balance of Ta leakage and redeposition. For the Cu70Ag30 melt, the Ag concentration in the liquid increases with increasing d (brown dotted line in Fig. 5b) to reduce Ta leakage by decreasing Ta solubility, which leads to an increase in ρ(d) with increasing d after reaching a minimum. This maintains a solid portion large enough to prevent fragmentation due to detachment of the hard bond, which explains why structures delegated in Cu70Ag30 melts retain structural integrity after etching. In contrast, for pure copper melts, leakage and redeposition almost cancel each other out, resulting in a slow reduction in solids below the fragmentation threshold for most of the delegated layer, leaving only a very thin layer that retains structural integrity near the boundary of the delegated layer. (Fig. 4b, Table 1).
So far, our analyzes have mainly focused on explaining the strong influence of the leakage of miscible elements in a dislocating medium on the solid fraction and the topology of delegated structures. Let us now turn to the effect of this leakage on the coarsening of the bicontinuum structure within the delegated layer, which usually occurs during LMD due to high processing temperatures. This is different from ECD where coarsening is virtually non-existent during removal of the alloy, but can be caused by annealing at higher temperatures after removal of the alloy. So far, coarsening during LMD has been modeled under the assumption that it occurs due to diffusion of immiscible elements along the solid-liquid interface, similar to the surface diffusion-mediated coarsening of annealed nanoporous ECD structures. Thus, the bond size has been modeled using standard scaling laws capillary enlargement.
where tc is the coarsening time, defined as the time elapsed after the passage of the delamination front at depth xi within the delamination layer (where λ has an initial value of λ00) until the end of the delamination experiment, and the scaling index n = 4 diffuses the surface. Eq should be used with caution. (3) Interpret the measurements of λ and distance d for the final structure without impurities at the end of the experiment. This is due to the fact that the region near the edge of the delegated layer takes longer to enlarge than the region near the front. This can be done with additional equations. (3) Communication with tc and d. This relation can be easily obtained by predicting the depth of removal of the alloy as a function of time, \({x}_{i}(t)=\sqrt{4p{D}_{l}t}\), which gives tc( d ) = te − tf(d), where te is the duration of the entire experiment, \({t}_{f}(d)={(\sqrt{4p{D}_{l}{t}_{ e } }-d)}^{2}/(4p{D}_{l})\) is the time for the delamination front to reach a depth equal to the final delamination depth minus d. Plug this expression for tc(d) into the equation. (3) Predict λ(d) (see additional note 5).
To test this prediction, we performed measurements of the width and distance between the bundles on full cross sections of the delegated structures shown in Supplementary Figure 9 for pure Cu and Cu70Ag30 melts. From line scans perpendicular to the delamination direction at different distances d from the delamination front, we obtained the average width λw(d) of Ta-rich bundles and the average distance λs(d) between bundles. These measurements are shown in fig. 5d and compared with the predictions of the equation. (3) in Supplementary Fig. 10 for different values ​​of n. The comparison shows that a surface diffusion index of n = 4 gives poor predictions. This prediction is not significantly improved by choosing n = 3 for bulk diffusion-mediated capillary coarsening, which one might naively expect to provide a better fit due to Ta leakage into the liquid.
This quantitative discrepancy between theory and experiment is not surprising, since Eq. (3) describes capillary coarsening at a constant volume fraction ρ, while at LMD the solids fraction ρ is not constant. ρ changes spatially within the removed layer at the end of the alloy removal, as shown in fig. 5c. ρ also changes with time during removal of impurities at a fixed removal depth, from the value of the removal front (which is approximately constant in time and thus independent of tf and d) to the measured value of ρ(d) shown in Fig. 5c corresponding to the last time. From fig. 3d, it can be estimated that the decay front values ​​are about 0.4 and 0.35 for the AgCu and pure Cu melts, respectively, which in all cases is higher than the final value of ρ at time te. It is important to note that the decrease in ρ with time at a fixed d is a direct consequence of the presence of a concentration gradient of the miscible element (Ti) in the liquid. Since the concentration of Ti in liquids decreases with increasing d, the equilibrium concentration of Ti in solids is also a decreasing function of d, which leads to the dissolution of Ti from solid binders and a decrease in the solid fraction over time. The temporal change in ρ is also affected by leakage and redeposition of Ta. Thus, due to the additional effects of dissolution and reprecipitation, we expect that coarsening during LMD will, as a rule, occur at non-constant volume fractions, which will lead to structural evolution in addition to capillary coarsening, but also due to diffusion in liquids and not only along the boundary solid-liquid.
Equation facts. (3) Bond width and spacing measurements for 3 ≤ n ≤ 4 are not quantified (Supplementary Fig. 10), suggesting that dissolution and redeposition not due to interface reduction play a dominant role in the present experiment. For capillary coarsening, λw and λs are expected to have the same dependence on d, while Fig. 5d shows that λs increases with d much faster than λw for pure Cu and Cu70Ag30 melts. While a coarsening theory that takes into account dissolution and redeposition must be considered to explain these measurements quantitatively, this difference is expected qualitatively, since the complete dissolution of small bonds contributes to an increase in the distance between the bonds. In addition, the λs of the Cu70Ag30 melt reaches its maximum value at edge of the layer without alloy, but the fact that λs of the pure copper melt continues to increase monotonically can be explained by the increase in the Ag concentration in the liquid, where d is used to explain ρ(d) in Fig. 5c nonmonotonic behavior. Increasing the Ag concentration with increasing d suppresses Ta leakage and binder dissolution, which leads to a decrease in λs after reaching the maximum value.
Finally, note that computer studies of capillary coarsening at constant volume fraction show that when the volume fraction falls below a threshold of approximately 0.329.30, the structure fragments during coarsening. In practice, this threshold may be slightly lower because fragmentation and concomitant genus reduction occur on a time scale comparable to or greater than the total alloy removal time in this experiment. The fact that the delegated structures in Cu70Ag30 melts retain their structural integrity even though ρ(d) is slightly below 0.3 in the average range of d indicates that fragmentation, if any, occurs only partially. The volume fraction threshold for fragmentation may also depend on dissolution and reprecipitation.
This study draws two main conclusions. First, and more practically, the topology of the delegated structures produced by LMD can be controlled by selecting the melt. By choosing a melt to reduce the solubility of the immiscible element A of the AXB1-X base alloy in the melt, although limited, a highly delegated structure can be created that retains its cohesiveness even at low concentrations of the floor element X and structural integrity. It was previously known that this was possible for ECD25, but not for LMD. The second conclusion, which is more fundamental, is why in LMD the structural integrity can be preserved by modifying the delegating medium, which is interesting in itself and could explain the observations of our TaTi alloy in pure Cu and CuAg melts in , but also in more generally to clarify important, previously underestimated differences between ECD and LMD.
In ECD, the cohesiveness of the structure is maintained by keeping the impurity removal rate at a low level X, which remains constant over time for a fixed driving force, small enough to keep enough miscible element B in the solid binder during impurity removal to maintain solids volume. the ρ fraction is large enough to prevent fragmentation25. In LMD, the alloy removal rate \(d{x}_{i}(t)/dt=\sqrt{p{D}_{l}/t}\) decreases with time due to diffusion limited kinetics. Thus, regardless of the type of melt composition that affects only the Peclet number p, the delamination rate quickly reaches a value small enough to retain a sufficient amount of B in the solid binder, which is directly reflected in the fact that ρ at the delamination front remains approximately constant with time. Fact and above the fragmentation threshold. As shown by the phase field simulation, the peel rate also quickly reaches a value small enough to destabilize the growth of the eutectic bond, thereby facilitating the formation of topologically bonded structures due to the lateral rocking motion of the lamellae. Thus, the main fundamental difference between ECD and LMD lies in the evolution of the delamination front through the internal structure of the layer after splitting and ρ, rather than the delamination rate.
In ECD, ρ and connectivity remain constant throughout the remote layer. In LMD, in contrast, both vary within a layer, which is clearly shown in this study, which maps the atomic concentration and distribution of ρ throughout the depth of the delegated structures created by the LMD. There are two reasons for this change. First, even at a zero solubility limit A, the concentration gradient B in the liquid, which is absent in the DZE, induces a concentration gradient A in the solid binder, which is in chemical equilibrium with the liquid. The gradient A, in turn, induces a gradient ρ inside the layer without impurities. Second, the leakage of A into the liquid due to non-zero solubility further modulates the spatial variation of ρ within this layer, with the reduced solubility helping to keep ρ higher and more spatially uniform to maintain connectivity.
Finally, the evolution of the bond size and connectivity within the delegated layer during LMD is much more complex than the surface diffusion-limited capillary coarsening at a constant volume fraction, as previously thought by analogy with the coarsening of annealed nanoporous ECD structures. As shown here, coarsening in LMD occurs in a spatiotemporally varying solid fraction and is typically influenced by diffusional transfer of A and B in the liquid state from the delamination front to the edge of the disjointed layer. The scaling laws for capillary coarsening limited by surface or bulk diffusion cannot quantify changes in the width and distance between bundles within a delegated layer, assuming that A and B transport associated with fluid concentration gradients play equal or identical roles. More important than reducing the area of ​​the interface. The development of a theory that takes into account these various influences is an important prospect for the future.
Titanium-tantalum binary alloys were purchased from Arcast, Inc (Oxford, Maine) using a 45 kW Ambrell Ekoheat ES induction power supply and a water-cooled copper crucible. After several heats, each alloy was annealed for 8 hours at a temperature within 200° C. of the melting point to achieve homogenization and grain growth. Samples cut from this master ingot were spot-welded to Ta wires and suspended from a robotic arm. Metal baths were prepared by heating a mixture of 40 g Cu (McMaster Carr, 99.99%) with Ag (Kurt J. Lesker, 99.95%) or Ti particles at high power using a 4 kW Ameritherm Easyheat induction heating system until complete dissolution. baths. fully heated melt. Reduce the power and let the bath stir and equilibrate for half an hour at a reaction temperature of 1240°C. Then the robotic arm is lowered, the sample is immersed in the bath for a predetermined time and removed for cooling. All heating of the alloy billet and LMD was carried out in an atmosphere of high purity argon (99.999%). After removing the alloy, the cross sections of the samples were polished and examined using optical microscopy and scanning electron microscopy (SEM, JEOL JSM-6700F). Elemental analysis was performed by energy dispersive X-ray spectroscopy (EDS) in SEM. The three-dimensional microstructure of the delegated samples was observed by dissolving the solidified copper-rich phase in a 35% nitric acid solution (analytical grade, Fluka).
The simulation was carried out using the previously developed model of the field of the decoupling phase of the ternary alloy15. The model relates the evolution of the phase field ϕ, which distinguishes between the solid and liquid phases, to the concentration field ci of alloying elements. The total free energy of the system is expressed as
where f(φ) is the double barrier potential with minima at φ = 1 and φ = 0 corresponding to solids and liquids, respectively, and fc(φ, c1, c2, c3) is the chemical contribution to volume freedom describing the energy density of thermodynamic properties alloy. To simulate the remelting of pure Cu or CuTi melts into TaTi alloys, we use the same form fc(φ, c1, c2, c3) and parameters as in the reference. 15. To remove TaTi alloys with CuAg melts, we have simplified the quaternary system (CuAg)TaTi to an effective ternary system with different parameters depending on the Ag concentration, as described in Supplementary Note 2. The evolution equations for the phase field and the concentration field were obtained in the variant form in the form
Where \({M}_{ij}={M}_{l}(1-\phi){c}_{i}\left({\delta}_{ij}-{c}_{j} \right)\) is the atomic mobility matrix, and Lϕ governs the kinetics of atomic attachment at the solid-liquid interface.
Experimental data supporting the results of this study can be found in the supplementary data file. Simulation parameters are given in the additional information. All data are also available from the respective authors upon request.
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