Liquid–liquid transition in supercooled gallium alloys under nanoconfinement

Structural transformations in liquids pose severe challenges to condensed matter physics. Conclusive theoretical and experimental evidences of a phase transition between different structures in liquids (liquid–liquid phase transition (LLPT)) were obtained for water [1–3] and few other liquids [4–8]. However, the nature of LLPT is poorly understood and even its occurrence in many substances is in doubt. LLPT can occur when temperature or pressure changes. Alterations in the liquid structure are associated with a sharp change in the density [8]. It was suggested that LLPT at ambient pressure takes place under strong supercooling [9]. Therefore, LLPT in bulk is disguised by crystallization or vitrification processes. In contrast, liquids confined to nanoporous matrices are easy to supercool to temperatures much lower than the melting temperatures [10]. This raises expectations that LLPT can be found in liquids under nanoconfinement.

Generally, they tried to reveal LLPT using various experimental techniques. Among them, neutron scattering and x-ray diffraction provided the most convincing evidences due to their sensitivity to the short-range order [8]. However, solidification often masks the alterations in neutron and x-ray patterns induced by LLPT. For metallic substances NMR acts as another experimental technique which gives valuable information about the internal structure of liquids and solids through measurements of the shift in the resonance frequency, the Knight shift, caused by coupling with conduction electrons [11]. Studies of the Knight shift were already applied to reveal some striking phenomena in low-dimensional metals such as enhanced polymorphism in sodium nanoparticles [12], continuous melting in the sodium-potassium alloy nanoparticles [13], and reduction of electron susceptibility in metals embedded into mesoporous matrices ([14] and references therein). The Knight shift measurements also showed the transformations in the nanostructured liquid gallium [15].

In the present paper we use NMR measurements of the Knight shift to study new features of phase diagrams of the nanostructured Ga–In–Sn and Ga–In alloys, namely LLPT in the supercooled state and the associated anomalous behavior upon melting and freezing. Both these alloys are the most perspective liquid metallic materials for soft robotics [16]. It should be emphasized that LLPT in metallic alloys at ambient pressure were not reported until now and there are only few publications about a reduction of the solidus temperatures and changes of component solubility in eutectic alloys induced by reduced dimensionality [17, 18]. Recently possible LLPTs were reported for some metallic alloys under high pressure [19, 20].

The nanostructured ternary Ga–In–Sn and binary Ga–In alloys were obtained by embedding the liquid alloys into opal matrices under pressure up to 10 kbar. The opal matrices (photonic crystals) consist of close-packed amorphous silica spheres with the mean diameter 260 nm according to AFM. There are interconnected octahedral and tetrahedral pores between silica spheres in the cubic close packing. The total pore volume in the ideal close packing of rigid spheres is 26%. The size of silica spheres is to those of octahedral and tetrahedral pores as 1:0.441:0.225. However, sintering the opals reduces somewhat the pore sizes. The composition of the Ga–In alloy was 94 at.% Ga and 6 at.% In. According to the phase diagram of the bulk gallium–indium alloy [21] the frozen alloy segregates into two phases: an In-rich solid solution with a structure of crystalline indium and a phase with a structure of α- or β-Ga which has very low amount of dissolved indium. The solidus temperature for the phase with the α-Ga structure is 288.5 K and the eutectic point corresponds to the alloy composition 14.2 at.% In, while the solidus temperature for β-Ga is 244.4 K and the eutectic point corresponds to 6.2 at.% In. Therefore, the composition of the alloy studied here is close to the eutectic point for β-Ga. The composition of the Ga–In–Sn ternary alloy is close to the eutectic one: 77.2 at.% Ga, 14.4 at.% In, and 8.4 at.% Sn [22]. The melting temperature of the eutectic composition of the ternary alloy is 283.7 K [22]. The filling of the opals with the alloys was about 80% as was estimated by weighing the empty and loaded opal matrices. From loaded opals the samples for NMR studies were cut in the shape of parallelepipeds 3  ×  3  ×  6 mm.

Studies were carried out using NMR Bruker Avance 400, Avance 500, and Avance 750 pulse spectrometers at magnetic fields 9.4, 11.7, and 17.6 T, respectively, within a temperature range from 150 K to room temperature. Some measurements were conducted up to 327 K. We observed the variations with temperature of the Knight shift and integral intensity of the NMR lines for the isotopes ⁶⁹Ga, ⁷¹Ga, and ¹¹⁵In in the liquid alloys. The NMR spectra were obtained as Fourier transforms of free-induction decays after 90° pulses. At each target temperature the samples were stabilized for about 20 min. The rate of changing temperature did not excide 0.5 K min⁻¹ to prevent the temperature overshoots. Signals from the gallium isotopes in a GaAs single crystal were used as references for the Knight shift of relevant isotopes in the samples. For the indium isotope the Knight shift was evaluated relative to a signal from the molar solution of the indium nitrate In(NO₃)₃ salt. Note that at room temperature the confined alloys were totally in the liquid state in agreement with their phase diagrams and the general reduction of the melting temperatures under nanoconfinement [10].

At room temperature and at higher temperatures the NMR spectra for both gallium isotopes in opals loaded with Ga–In and Ga–In–Sn alloys consisted of a single quite narrow Lorentzian line, which corresponds to the confined melts. An example of the ⁷¹Ga line at 290 K is shown in figure 1 for the ternary alloy. Note that the signals from solid alloys were not observed because of strong broadening the NMR lines due to the Knight shift anisotropy and quadrupole coupling. The Knight shift for both isotopes did not depend on magnetic field as in bulk metals and alloys [23].

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Upon cooling the lines first moved to high frequency and then split into two signals at lower temperatures. Upon further cooling only the signal with higher frequency (larger Knight shift) survived. The evolution of the NMR spectra for the ⁷¹Ga isotope observed at cooling from room temperature is illustrated in figures 1 and 2. The split lines were deconvolved into two signals as it is also shown in figures 1 and 2. From the NMR spectra the Knight shift dependences on temperature were found. The variations of the Knight shift during the full thermal cycles down to complete freezing of confined alloys and back can be seen in figure 3 for the ternary and binary alloys. At temperatures where the spectra consisted of two signals figure 3 exhibits the Knight shift for both of them.

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Figure 4 shows the temperature dependences of the integral intensity of NMR signals from the ⁷¹Ga and ¹¹⁵In isotopes in the liquid ternary and binary confined alloys for full thermal cycles. The intensity is proportional to the total amount of gallium or indium in the unfrozen fraction of alloys. The ⁷¹Ga NMR signal for the liquid ternary alloy disappeared completely upon cooling just below 180 K. Upon warming a weak signal appeared at about 205 K when the melting process started (figure 4(a)). The Knight shift at this temperature was very similar to that for the high-frequency signal observed upon cooling (figure 3(a)). At further warming the Knight shift followed the temperature behavior of the high-frequency signal seen at cooling. Then it continued to approach the Knight shift of the single lines obtained upon cooling. The curves found upon cooling and warming merged each other at about 275 K. A somewhat different scenario was seen for the binary alloy. The complete freezing associated with the disappearance of the ⁷¹Ga high-frequency signal occurred below 155 K (figure 4(b)). The ⁷¹Ga NMR signal appeared once more upon warming only at 247 K. At this and higher temperatures the Knight shift found upon warming coincided with that seen upon cooling. Note, that the signal from liquid indium remained a single line down to indium freezing.

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The integral intensity of the ¹¹⁵In NMR signals reduces to zero upon cooling at higher temperatures compared to that for gallium for both the ternary and binary alloys. Similarly, a signal from liquid indium in the ternary alloy upon warming appears at higher temperatures compared to the gallium signal. This evidences that from 220 K down to the end of freezing of the ternary alloy and from 165 K down to the complete freezing of the binary alloy the liquid fraction consists mainly of gallium. The same is valid for the range between the onset of melting of the ternary alloy and about 250 K. However, the melting of major parts of indium and gallium in the ternary alloy (relevant to the high-temperature hysteresis loop in figure 4(a) and of the total indium and gallium in the binary alloy occurs simultaneously. Note that freezing of the major part of indium in the ternary alloy also occurs at higher temperature compared to freezing of the major part of gallium (see figure 4(a)). To facilitate the comparison of the indium NMR signal intensity upon cooling and warming with variations of the gallium Knight shift and line splitting, we inserted vertical bars in figure 3 which show the temperature ranges of indium freezing and melting.

The melting and freezing of the ternary alloy occur in two steps which are associated with two loops of the thermal hysteresis. These two steps are related to different crystalline modifications of the gallium-rich phase in the frozen eutectic alloy [24, 25]. According to the observed temperatures of freezing and melting in the confined ternary alloy one can suggest that these two modifications have structures of α- and β-Ga [21]. The freezing and melting of the binary alloy under nanoconfinement are associated to the single thermal hysteresis loop which is related to the emergence of a single crystalline modification.

Within the temperature ranges of the coexistence of two ⁷¹Ga NMR signals we can evaluate the relative intensities of these signals. The insets to figure 4 show them for the ternary and binary alloys. One can see that the low-frequency signal gradually transforms into the high-frequency one upon cooling.

The emergence of a second ⁷¹Ga NMR signals in both alloys and the coexistence of two signals within some temperature ranges prove unambiguously the appearance of a new liquid state at supercooling and segregation of liquid alloys into two parts. This phenomenon can be caused by LLPT in the alloys or by changes in the composition of the melts confined to different pores due to freezing of indium. Two following factors evidence in favor of the first suggestion. First, no noticeable changes in the even temperature dependence of the ⁷¹Ga Knight shift was detected upon cooling for the ternary alloy within a range from 270 to 260 K (figure 3(a)) where the major part of indium was frozen and the composition of the liquid alloy was strongly altered (figure 4(a)). In addition, a splitting of the NMR line upon cooling was observed recently in pure liquid metallic gallium embedded into an opal matrix [15] and this splitting was treated as LLPT in accordance with later theoretical simulations [26, 27].

For both alloys the splitting of the ⁷¹Ga NMR line correlated to the indium freezing. In the binary alloy the splitting started with the onset of freezing indium roughly at 175 K and the high-frequency signal only was seen below 165 K where indium was completely frozen (figures 3(b) and 4(b)). For the ternary alloy the ⁷¹Ga line started splitting near 245 K where a part of indium associated to the low-temperature loop of thermal hysteresis started freezing. Only one ⁷¹Ga signal survived below 225 K where this part of indium froze (figures 3(a) and 4(a)). Therefore, we can suggest that LLPT occurs in the supercooled alloys.

Important information on LLPT can be obtained from studies of the Knight shift during partial thermal cycles which lowest temperature corresponds to incomplete freezing. Figure 5 shows variations of the Knight shift for the ternary and binary alloys upon cooling from room temperature down to temperatures at which the low-frequency signals disappeared and only the high-frequency signals could be observed and upon subsequent warming. Then, the ⁷¹Ga NMR spectra consisted of a single line at warming up to room temperature for both alloys. The Knight shifts first follow closely the shift variations of the high-frequency signals seen at cooling. At further warming the Knight shifts approach gradually the line positions observed upon cooling. The convergence temperature is about 275 K for the triple alloy and 225 K for the binary alloy. The approaching process is smooth and does not correlate with the melting of indium. This additionally proves that the line splitting upon cooling is not a direct result of changes in the alloy composition but is caused by LLPT.

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Figures 3 and 5 show that the phase transition is characterized by a large thermal hysteresis. The transition upon cooling is associated with the step-like change in the Knight shift which corresponds to the step-like changes in the structure of confined liquid. While at warming the phase transition is continuous in agreement with gradual changes in the Knight shift. This thermal asymmetry can arise in the case when the upper limit of the hysteresis loop coincides to the critical point of the boundary line between two liquid phases [9]. The Knight shift commonly increases with increasing the electron density [11]. Therefore, we can suggest that the low-temperature liquid is denser that the high-temperature one.

The most significant finding of the present studies is the LLPT detection in two gallium alloys under nanoconfinement. Nevertheless, we would like to mention briefly other changes in the phase diagrams of the confined ternary and binary alloys. Figure 4 shows remarkable reduction of the solidus temperatures. This reduction is caused partially by the increased surface-to-volume ratio under nanoconfinement and by formation of structures different from the α-Ga one [21, 24]. In addition, figure 4 demonstrates shifts of the eutectic points in the supercooled alloys to the gallium-rich compositions as the indium NMR signals vanish upon cooling at higher temperatures compared to the gallium signals. These effects will be discussed in details elsewhere. Note, that the phenomenon of the impact of size reduction on the eutectic compositions in metallic alloys was studied until now only for individual nanoparticles of some binary alloys [17]. No studies of the changes in the eutectic composition were carried out for a network of particles confined to mesoporous matrices.

NMR studies revealed a step-like splitting of the gallium resonance line upon cooling in the Ga–In–Sn and Ga–In supercooled alloys embedded into silica opal matrices. At further cooling only one signal survived. The findings demonstrate heterogeneity and transformations in confined melts. The detailed measurements of the Knight shift and intensity of the ⁷¹Ga and ¹¹⁵In NMR signals proved that the line splitting was not caused by changes in the liquid alloy composition but it occurs due to LLPT under nanoconfinement. At warming the gradual change of the Knight shift was observed which could happen when the confined alloys pass over the critical point of the LLPT line on the phase diagram.

We acknowledge the financial support from RFBR (Russia), grant 19-07-00028.