Introduction

Monitoring of the phase transformation process of materials is crucial for both basic research and practical applications1,2,3. Phase-change materials not only exhibit ultrafast switching capabilities on the picosecond scale2 but also possess long-term data retention capabilities4,5. Moreover, they can be seamlessly integrated into nanoscale-integrated chips6. Among these materials, gallium (Ga) has garnered significant attention in the scientific community due to its exceptional properties7. Ga demonstrates low-energy transitions and rapid response speeds during phase transitions, enabling it to function as a storage medium in nanophotonic devices6. Ga nanoparticles have been utilized to achieve binary all-optical memory and higher-logic all-optical memory8. Extensive investigations9,10,11,12 have been conducted on the dielectric function13,14, refractive index15, and resistivity16 of Ga during phase transitions. Furthermore, the expansion of Ga and its alloys upon freezing has been employed to create thermally switchable electronics17. However, there have been limited studies on the kinetics of Ga’s phase transition process using optical devices. Some researchers have employed commercial X-ray diffraction (XRD) to detect the phase transition of Ga, focusing primarily on the coexistence and transition behavior of Ga particles between the solid and liquid phases at the phase transition point11,12,18.

Whispering gallery mode (WGM) microcavities are widely employed in various fields such as nonlinear optics19,20,21, high-sensitivity sensors22,23,24,25,26,27,28, integrated devices29,30,31, and microlasers32,33,34,35,36. These microcavities offer advantages such as high quality (Q) factor, small mode volume, and long photon lifetime37,38,39. Researchers have explored the use of optical microcavities for monitoring phase-change processes in materials. For instance, microbubble resonators have been utilized to characterize the operando monitoring of phase transition processes in hydrogels40,41 and responsive polymers42. By filling phase transition materials into the inherent microfluidic channels of microbubble resonators, phase transition behaviors can be effectively studied. Liquid crystals, as typical phase transition materials, have been incorporated into microcavities43,44, exhibiting exceptional thermal sensitivity. Additionally, the introduction of liquid metal into the microbubble cavities of optical microfluidics has enabled broadband thermal tuning of optical and mechanical modes45. Preliminary investigations of phase transitions in liquid metal alloys have been conducted in microbubble cavities, leveraging the sensitivity change of the modes to determine the occurrence of phase transitions46.

In this paper, we combine phase-change materials with optical microfluidic microbubble cavities, allowing us to study the properties of phase-change materials optically. Thanks to the low-melting point of Ga47, we can quickly realize the solid-liquid phase transition of Ga in the microcavity using a thermoelectric controller (TEC). The surface plasmon polaritons (SPPs) localized on the surface of Ga can be coupled with the optical WGM to form a hybrid plasmonic-photonic mode under specific wall thicknesses48, and its Q is as high as 105. By in situ monitoring this high-Q hybrid mode, the phase transition process of Ga with very clear evidence has been demonstrated. A hysteresis loop between the solid-to-liquid and liquid-to-solid transitions, as well as nonreciprocal wavelength change, were presented. The thermal expansion coefficients of Ga in different states (0.41 × 10−5 K−1 for solid, −0.75 × 10−5 K−1 for liquid) were measured. We also obtained the phase transition kinetics of Ga and a metastability state during the melting process. We further studied the supercooling properties of Ga. Finally, we also monitored the solid-liquid phase transition of Ga simultaneously through optomechanical resonance. This provides an additional dimension for monitoring the physical properties of materials with microcavities, thus expanding the sensing applications of microcavities.

Results

Simulation and characterization

In this study, the combination of phase-change materials with optical microfluidic microbubble cavities leads to intriguing phenomena. Figure 1a shows a schematic diagram of a Ga-core optical microfluidic microbubble resonator (MBR), with the inset displaying a photograph of the sample. The sample has a radius of 110 μm and a wall thickness of 6 μm. The MBR fabrication process is described in the Methods and in Fig. S1 of the Supplementary Information. The eigenfrequencies and field distributions of transverse electric (TE) and transverse magnetic (TM) modes were calculated using the finite element method (COMSOL Multiphysics)48. The permittivity of Ga in its solid and liquid phase states was determined by fitting the measured date from the literature14. Figure 1b, c depict the dependence of Q factor on different wall thicknesses. As the wall thickness of the MBR increases, the field distribution of the hybrid mode in the shell becomes larger, resulting in a higher Q. The SPPs is TM-polarized, thus the Q factor of the TM hybrid plasmonic/photonics mode is lower than that of the TE photonic mode48. The Q factors of both the TE and TM hybrid modes gradually stabilize when the thickness exceeds 8 μm. The Q of the TM and TE modes in liquid-phase Ga is higher than that in solid phase Ga at the same wall thickness of the MBR. This difference is attributed to the variation in permittivity of Ga between its solid and liquid phases.

Fig. 1: Schematic diagram and mode characteristics.
figure 1

a Schematic diagram of the metal Ga-core optofluidic MBR. Inset, a photograph of liquid metal MBR coupled to a tapered fiber. Variation of Q with wall thickness for b TE mode and c TM mode in liquid and solid phase Ga. Insets in b, c are the electric field distributions of TE and TM modes, respectively. d Transmission spectra of Ga at 22.2 °C (solid, pink line) and 27.8 °C (liquid, purple line). e The phase transition of Ga was monitored by tracking the wavelength drift and Q of WGM.

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Before conducting the phase transition measurement, we performed characterizations of the transmissions and Q factors of the sample. We injected low-melting point Ga into the optofluidic MBR using a microfluidic pump. A tapered fiber with a diameter of ~2 μm was employed to couple the modes (see Fig. S2 in the Supplementary Information for an experimental setup diagram). For stable coupling, the tapered fiber is contacted with the microcavity throughout the measurement. For the subsequent analysis, we focused solely on the hybrid modes, as they contain more information about the liquid core. The methods used to distinguish between the two polarization modes are presented in Fig. S3 of the Supplementary Information. To distinguish with the optomechanical mode below, the hybrid mode is denoted as an optical mode in the following.

The TM-polarized transmission spectra are shown in Fig. 1d, where the pink line represents the transmission spectrum of solid Ga at 22.2 °C, and the purple line represents the transmission spectrum of liquid Ga at 27.8 °C. By fitting the resonance dips using a Lorentz function (black lines), Q factors are determined as Qs = 3.75 × 105 for solid Ga-core MBR and Ql = 5.79 × 105 for liquid Ga-core MBR, respectively. It is noteworthy that the liquid Ga-core MBR exhibits a higher Q factor compared to the solid Ga-core MBR, consistent with the numerical simulation results presented in Fig. 1c. Additionally, the resonance transmission depth for the liquid phase is deeper than that for the solid phase (Fig. 1d). The coupling condition is under-coupled due to the high loss of the optical mode and the change of the transmission depth is caused by the change in cavity loss. Importantly, Fig. 1e illustrates that the phase transition dynamics of Ga can be continuously monitored by tracking the wavelength shift and linewidth broadening of the resonant mode in real time. During the phase transition, as the melting point is reached, the WGM exhibits a blue shift and linewidth compression. Conversely, as the freezing point is reached, the resonance displays a redshift and linewidth broadening throughout the phase transition process.

Phase transition measurement with optical modes

To enhance the reliability and stability of the measurements, the fiber taper was attached to the surface of the Ga-core optofluidic MBR during the experiment. Initially, the MBR was heated by the TEC. Figure 2a illustrates the wavelength change of the optical mode with increasing temperature. As the temperature rises from 21.5 to 25.28 °C, the resonance wavelength continuously redshifts. However, at 25.35 °C, we observed a sudden jump in the optical mode, resulting in a blueshift of the resonance wavelength. This behavior corresponds to the initial phase transition stage, where the Ga exists as a stable solid-liquid mixture. Further increasing the temperature by 0.07 to 25.42 °C leads to a continued blueshift of the resonance wavelength by a larger step. Figure 2c presents the overall wavelength change of the optical mode during the entire heating process. Remarkably, Ga exhibits two wavelength blueshifts during the conversion from the solid phase to the liquid phase. This phenomenon can be attributed to the volume changes and sudden variations in the permittivity of Ga. When Ga melts, it undergoes volume contraction, causing a blueshift in the wavelength. Conversely, upon solidification, the volume expands, resulting in a redshift7. The total wavelength change during the complete transition from the solid phase to the liquid phase is 26.4 pm (blueshift). Each data point in Fig. 2c was recorded after achieving full stabilization at each temperature. The transmission spectrum was then recorded following a 30-s wait period. Since the temperature change during the phase transition is only 0.14 °C, the influence of the thermo-optical coefficient on the wavelength change was ignored.

Fig. 2: Phase transition measurement with optical modes.
figure 2

Transmission spectrum of the optical mode for a heating and b cooling in the temperature range 21.5–27.8 °C. Wavelength variation with temperature. c Heating up and d cooling down. e Hysteresis loop for wavelength shifts. f Q value variations in two reversible processes.

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The total change for phase transition can be written as: \(\Delta {\lambda }_{1}=i\uparrow +{ii}\downarrow\), where i represents the change dominated by permittivity and ii represents change dominated by the volume. The symbols “↑”, “↓” indicate the wavelength redshift and blueshift, respectively. It is worth noting that the melting point of Ga in this study is relatively lower than the reported bulk Ga melting point49 due to the microstructure of the cavity. This finding is consistent with previous reports on the melting point inhibition of Ga in microstructured opals50.

Following the monitoring of the solid-to-liquid phase transition process, the inverse liquid-to-solid phase transition was conducted by gradually decreasing the temperature from 27.8 °C. As shown in Fig. 2b, a sudden redshift of the center wavelength was observed at the freezing temperature of 23.67 °C. Unlike the solid-to-liquid phase transition, the solidification of Ga occurs instantaneously7. The resonance wavelength of each steady state during cooling is presented in Fig. 2d.

Interestingly, we observed a hysteresis-like phenomenon40 in the phase transition, where the transition points between heating and cooling temperatures were not the same. This behavior is illustrated in Fig. 2e. Near the phase transition point, the total wavelength change ∆λ2 = i ↓ +ii↑ for liquid-to-solid phase transition was found to be 5.03 pm (redshift). It is important to note that ∆λ1 was not equal to ∆λ2. At the melting (freezing) point, the change in the permittivity of Ga dominates wavelength shifts, denoted by i = ±5.39 pm. The permittivity-dominated wavelength shifts i is reciprocal. This is confirmed by the reversibility of the Q (determined by the imaginary part of permittivity) change for the melting and freezing points (see Fig. 2f). The two stems of the MBR were sealed by solid-liquid metal, so the expansion and contraction of the liquid metal induce internal pressure changes within the microcavity. These internal pressure changes, in turn, lead to changes in the microcavity radius. However, the expansion and contraction coefficients are temperature-dependent51,52. Hence, we concluded that the volume-dominated change ii was nonreciprocal, and ii ↑ =10.42 pm, ii ↓ =31.79 pm. The resonance condition is written as:

$${2\pi n}_{{eff}}R=m\lambda ,$$
(1)

where R is the radius of the microcavity, \(\lambda\) is the WGM resonant wavelength, m is the angular momentum term, and neff is the effective refractive index. The variations in the radius of the microcavity R caused by Ga at the melting point and freezing point were calculated to be 2.27 nm (contraction) and 0.74 nm (expansion) using Eq. 1, respectively. Correspondingly, the volume changes of MBR at the melting point and freezing point were calculated to be 344.99 and 112.46 μm3, respectively.

The observed optical modes in solid Ga-core and liquid Ga-core MBR exhibit distinct thermal sensitivities. As shown in Fig. 2c, d, the thermal sensitivity in the solid Ga-core MBR is ~20 pm/°C, whereas in the liquid Ga-core MBR, it ranges from 1.54 to 2.65 pm/°C (this variation is induced by fitting error, 2 pm/°C is used for the following calculations). Comparing the thermal sensitivity of the solid Ga-core MBR to that of silica (10.82 pm/°C53), we find that the thermal sensitivity in the solid Ga-core MBR is greater. On the other hand, the thermal sensitivity in the liquid Ga-core MBR is significantly smaller than that of silica. The thermal sensitivities of WGM microcavity can be expressed as:

$$\frac{\Delta \lambda }{\Delta T}=\lambda \left({{\rm{\alpha }}}_{{\rm{Ga}}}+{{\rm{\alpha }}}_{{{\rm{SiO}}}_{2}}+\frac{{\partial \text{n}}_{\text{eff}}}{\partial \text{T}}\frac{1}{{\text{n}}_{\text{eff}}}\right),$$
(2)

where the \(\Delta\)λ is the resonant wavelength shift, α is the linear thermal expansion coefficient, \(\Delta T\) is the change of temperature and \({\partial n}_{\text{eff}}/\partial T\) is thermo-optic coefficient. For silica, \({\alpha }_{{\text{SiO}}_{2}}\) = 0.55 × 10−6 K−1 and \({\partial n}_{\text{eff}}/\partial T\) = 1.2 × 10−5 K−1. The thermo-optical coefficient of Ga is neglected in Eq. 2 due to that the field distribution of the hybrid mode is mostly confined in silica. The linear thermal expansion coefficient of solid Ga and liquid Ga were calculated to be \({\alpha }_{\text{Ga},\text{s}}=0.41\times {10}^{-5}{{\rm{K}}}^{-1}\) and \({\alpha }_{\text{Ga},\text{l}}\) = −0.75 × 10−5 K−1, respectively, which agree well with the previous measured data49,54,55,56.

Next, the phase transition kinetics of Ga were measured by fast switching the TEC temperature. The transmission spectra were recorded using a data acquisition card at intervals of 0.1 s. After stabilizing the mode at 25 °C (region I), the temperature was rapidly raised to 27.1 °C (region III) to induce the solid-to-liquid phase transition (region II). The wavelength change of Ga during heating from the solid phase to the liquid phase is presented in Fig. 3a. Initially, the wavelength redshifted during the initial phase transition phase and then continued to decrease until it briefly remained stable. Subsequently, the wavelength decreased slowly, followed by a rapid decrease. Finally, the wavelength slowly redshifted by a small amplitude until it stabilized. The phase transition process lasted for 74.6 s, during which the wavelength changed by 471 pm. Similarly, the phase transition kinetics of Ga during freezing (region II) were obtained by rapidly decreasing the temperature from 24.3 °C (region I) to 23.6 °C (region III), as shown in Fig. 3b. The phase transition kinetics lasted for 95.3 s, and the wavelength changed by 288.8 pm. It is important to note that the phase transition kinetics depicted in Fig. 3a, b also involve the absorption and release of heat, which cannot be quantitatively analyzed at present. The response time of wavelength when switching the temperature is 0.9 s (see section S3 in the Supplementary Information), indicating the fast response speed of the MBR. Consequently, we can disregard the lagged effect of MBR wall thickness on the resonant wavelength drift.

Fig. 3: Phase transition kinetics measurement.
figure 3

a Real-time monitoring of solid-to-liquid phase transition kinetics during Ga melting. b Real-time monitoring of liquid- to-solid phase transition kinetics during Ga cooling. c Solid-to-liquid phase transition by increasing the temperature in 0.07 °C steps. d Liquid-to-solid phase transition by decreasing the temperature in 0.07 °C steps.

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To further investigate the phase transition of Ga, we conducted a study where we finely controlled the temperature near the melting and freezing points. The temperature was increased from 25.28 °C (region I) with a step of 0.07 °C. During this process, the wavelength suddenly blueshifted and remained stable at a particular temperature, as shown in Fig. 3c. The inset in the figure demonstrates the stability of the wavelength at this temperature (region II). This observation indicates the presence of metastability during the melting of Ga, which has also been mentioned in previous literature12,57. As the temperature continued to increase, the wavelength further decreased (region III) until it eventually stabilized (region IV). After reaching this stable state, the wavelength did not decrease any further but instead began to increase with a certain sensitivity (region V). This behavior suggests that the phase transition of Ga had been completed. These findings highlight the complex dynamics and metastable states involved in the phase transition of Ga near its melting and freezing points.

In a similar manner, we also studied the phase transition of Ga near the freezing point. After stabilizing the mode at 24.23 °C (region I), the temperature was decreased in steps of 0.07 °C. During this cooling process, we observed a blueshift of 0.38 pm in the wavelength due to the temperature reduction (region II). As the temperature was continued to cool down (region III), we observed that the liquid-solid phase transition was completed (region IV), and the wavelength shift resulted from the decrease in temperature (region V). Unlike the melting phase transition, no metastability phenomenon was observed during the liquid-solid phase transition near the freezing point. These observations indicate that the phase transition behavior of Ga can exhibit different characteristics depending on whether it is undergoing melting or freezing, with the presence of metastability observed during melting but not during freezing. In the above experiments, we conducted multiple replicates of the sample. The solid-liquid phase transition of Ga was monitored many times, and the phase transition temperature point of Ga remained consistent. Consequently, our experiments are reproducible.

Supercooling property measurement of Ga

In this section of the study, the supercooling properties of Ga were investigated using an MBR with a radius of 107 µm and a wall thickness of 8 µm. The experiment involved continuously heating the Ga at temperatures exceeding its melting point for 5 min, resulting in the liquid-phase Ga having different initial temperatures. Subsequently, the temperature was reduced at a step of 0.07 °C every 30 s. During this process, transmission spectra of the liquid/solid phase transition of Ga were obtained at different initial temperatures, as shown in Section S4 of the Supplementary Information. From these spectra, the freezing points of Ga at different initial temperatures were extracted, as depicted in Fig. 4a. It is observed that the freezing temperature decreases as the initial temperature increases, which is consistent with the supercooling properties of Ga reported in previous references14,58. The measured data aligns with the previously reported data, as shown in Fig. 4a. This indicates that the experimental results obtained in this study agree with the existing reported data regarding the supercooling properties of Ga.

Fig. 4: Supercooling effect measurement.
figure 4

a Freezing temperature decreases with increasing initial temperature. Previously reported data from refs. 14,58 are displayed for comparison. b Melting points at different initial temperatures.

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In addition to studying the freezing points, the melting points of solid Ga were also measured at different initial temperatures. The transmission spectra of the solid-to-liquid phase transition process of Ga at different initial temperatures can be seen in Fig. S6, the Supplementary Information. Interestingly, it was observed that the melting temperature of solid Ga remained constant at 25.91 °C, regardless of the different initial temperatures, as shown in Fig. 4b, which is consistent with previous studies59,60,61.

The supercooling property of Ga enables us to access the plasma properties of liquid Ga at temperatures significantly below its melting point. This finding has important implications for the development of flexible wearable technology, as it allows for the utilization of liquid Ga at lower temperatures, expanding the potential applications and benefits in this field47. In this section, we have conducted several replicate experiments on this sample, and the results have been consistently favorable, further confirming the robust reproducibility of our method.

Phase transition measurement with OM modes

The frequency of the RBM in the optofluidic MBR is influenced by factors such as the sound velocity and density of the liquid metal, as well as the density, Young’s modulus, and Poisson’s ratio of the silica material62,63,64,65. In this section, the phase transition process was monitored using optomechanical (OM) mode sensing of velocity and density in the MBR. To facilitate the excitation of OM modes, a relatively thick-walled MBR with a wall thickness of 16 µm was fabricated to minimize light absorption by Ga. For optomechanical mode measurement, relatively larger pump laser power was launched into a fundamental optical mode and the pump laser wavelength was manually tuned to the blue side of the optical mode. The pump laser power can be coupled to the microcavity stably by thermal self-stability. As a result of the optomechanical effect, the output power detected by the photoelectric detector exhibited oscillations. The mechanical oscillation spectrum was then obtained using a real-time spectrum analyzer (Keysight 9020B) to identify the frequency of the radial breathing mechanical mode.

The mechanical spectrum of the radial breathing mode (RBM) was characterized in different phase states, as shown in Fig. 5a. The RBM linewidth of the solid Ga-core MBR (∆ωs = 77756.86 Hz) was found to be 2.97 times larger than that of the liquid Ga-core MBR (∆ωl = 26219.39 Hz). The mechanical quality factors (Qm) were determined to be Qm,s = 257.40 for the solid phase and Qm,l = 517.02 for the liquid phase. The Qm is mainly influenced by material damping, which differs significantly between liquid and solid materials. For the phase transition measurement, the focus was primarily on the OM mode frequencies. The monitoring of the phase transition process using the mechanical frequency of the RBM is shown in Fig. 5b. The mechanical spectra at different temperatures can be seen in Section S5 of the Supplementary Information. The hysteresis phenomenon is also observed, with the mechanical frequency changes at the melting and freezing points being reciprocal, unlike the optical mode measurement shown in Fig. 2e.

Fig. 5: Phase transition measurement with OM modes.
figure 5

a The mechanical spectrum of RBM in different Ga phase states. b Mechanical frequency variations with temperature heating up and cooling down. The inset shows the three-dimensional displacement field of the RBM.

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By monitoring the OM mode, it becomes possible to precisely measure the physical parameters of the liquid metal during the phase transition process, such as sound velocity and density. However, it is necessary to develop new measurement technologies to separate and analyze all the parameters involved in this complex process.

Discussion

In discussion, this study investigated the phase transition properties of Ga in an optofluidic MBR by monitoring both the optical mode and OM mode. The observed wavelength (frequency) changes of the optical mode (OM mode) exhibited hysteresis loops during the solid-to-liquid and liquid-to-solid transitions. The solid Ga-core and liquid Ga-core MBR showed different thermal sensitivities of the optical mode (approximately 20 pm/°C for solid and about 2 pm/°C for liquid), attributed to the change in the linear thermal expansion coefficient of Ga. The calculated linear thermal expansion coefficients were 0.41 × 10−5 K−1 for solid Ga and −0.75 × 10−5 K−1 for liquid Ga. The phase transition kinetics of Ga were also investigated, revealing the presence of a metastable state during the solid-to-liquid transition. Furthermore, the supercooling properties of Ga were explored, demonstrating that the solidification temperature decreases with increasing initial temperature, while the melting point remains unaffected by the initial temperature.

The optofluidic MBR proved to be an excellent platform for in situ monitoring of the phase transition of liquid metal and precise measurement of physical parameters during the phase transition. For instance, the precise measurement of the linear thermal expansion coefficients using this technique offers a cost-effective and easily operable alternative to XRD and HRTEM measurements12,18. The findings of this study hold potential applications in guiding the synthesis of new liquid metal alloys, such as GaInSn, as well as the design of phase-change memory devices66,67. While the wavelength shift was observed during the phase transition kinetics, the extraction of endothermic and exothermic heat release data is currently not possible. Future studies should focus on establishing a theoretical interpretation to separate the thermal contributions from other influencing factors in the wavelength shift.

Methods

The fabrication process of MBR

The fabrication process of the MBR is briefly described as follows (see Fig. S1 of the Supplementary Information). Quartz capillary tubes with an ultra-low absorption loss and a diameter of 125 μm were selected for the preparation of the MBR. (1) One end of the capillary tube was connected to a 10 mL syringe for inflation and pressurization, while the other end was sealed using a fusion splicer and cleaned with lens paper soaked in alcohol. (2) The capillary tube was heated using a hydrogen-oxygen flame to remove the coating, then placed in the fusion splicer, and subjected to the appropriate fusion program. During this process, the quartz at the electrode probe was melted by discharge, while air was injected into the tube through the syringe, forming a bubble-like microcavity at the discharge point. (3) The fabricated MBR was positioned on a glass stand, secured with UV glue, the sealed end was cut off, and both ends were fitted with Teflon tubing, which were then fixed in place with UV glue. A layer of epoxy resin glue was applied to fully cover the interface, ensuring a reliable seal. With these steps completed, the sample preparation was finished.

Wall thickness control

The control of MBR wall thickness relies on the initial thickness and a gradual expansion method. The initial thickness of the capillaries, plays a crucial role in determining the wall thickness of the MBR. To regulate the wall thickness, capillaries underwent an etching process prior to fabrication, serving as a preliminary control mechanism. Additionally, to achieve MBRs with varying radii and wall thicknesses using a capillary of a specific thickness, a combination of relatively low pressure and multiple heating and compression steps was employed. This approach enabled a gradual increase in the MBR’s radius while simultaneously reducing the wall thickness. Consequently, by incrementally adjusting the radius to an appropriate value, the desired wall thickness of the MBR could be attained.