Solid-liquid Phase Transition Research Articles

Trimodal thermal energy storage material for renewable energy applications.

The global aim to move away from fossil fuels requires efficient, inexpensive and sustainable energy storage to fully use renewable energy sources. Thermal energy storage materials1,2 in combination with a Carnot battery3-5 could revolutionize the energy storage sector. However, a lack of stable, inexpensive and energy-dense thermal energy storage materials impedes the advancement of this technology. Here we report the first, to our knowledge, 'trimodal' material that synergistically stores large amounts of thermal energy by integrating three distinct energy storage modes-latent, thermochemical and sensible. The eutectic mixture of boric and succinic acids undergoes a transition at around 150 °C, with a record high reversible thermal energy uptake of 394 ± 5% J g-1. We show that the transition involves melting of the boric acid component, which simultaneously undergoes dehydration into metaboric acid and water that dissolve into the liquid. Being retained in the liquid state allows the metaboric acid to readily rehydrate to re-form boric acid on cooling. Thermal stability is demonstrated over 1,000 heating-cooling cycles. The material is very low cost, environmentally friendly and sustainable. This combination of a solid-liquid phase transition and a chemical reaction demonstrated here opens new pathways in the development of high energy capacity materials.

Multi-gradient energy-saving smart windows with thermo-response and multimodal thermal energy storage.

Buildings, especially installed windows, account for a large proportion of global energy consumption. The research trend of smart windows leans towards multi-functional integration, concurrently achieving solar modulation and thermal management. However, sometimes a one-time performance switch cannot meet demands, making the design of multi-gradient adjustable smart windows particularly important. The combination of the temperature-responsive optical properties of hydroxypropyl cellulose (HPC), the high specific heat capability of water (sensible heat storage) and the solid-liquid phase transition of κ-carrageenan (latent heat storage) is proposed first and can be used to prepare the thermo-responsive hydrogel and multi-gradient energy-saving smart window with thermo-response and multimodal thermal energy storage (MGES smart window) quickly without long-term polymerization. The MGES smart window has excellent solar modulation capability (ΔTlum = 82.72% and ΔTsol = 68.65%) together with outstanding specific heat absorption ability (c = 4.2 kJ kg-1 K-1) and phase transition heat (ΔH = 1.23 kJ kg-1), showing superior energy saving and conserving performance. In demonstrations, the MGES smart windows can reduce the surface and indoor temperature by more than 15 °C and 10.6 °C compared with normal windows. Simulations suggest that they can cut off 45.1% of building energy consumption. To sum up, the MGES smart windows realize multi-aspect adjustment of energy, opening up a new avenue for green buildings.

Temperature-sensitive intelligent gel to prevent coal spontaneous combustion: Large-scale simulation fire extinguishing experimental study

Coal spontaneous combustion seriously endangers mine safety production. In this study, a temperature-sensitive intelligent gel was synthesised from methylcellulose (MC), polyethene glycol (PEG) and sodium chloride (NaCl). The flow characteristics of temperature-sensitive intelligent gel (abbreviated as TSIG) under different conditions were analyzed by viscosity test. An infrared spectrometer also analyzed the microscopic flame retardant mechanism of temperature-sensitive intelligent gel. A large-scale simulation fire extinguishing test bench was designed at the coal mine site to analyze the flame retardant effect of the temperature-sensitive intelligent gel on coal oxidation reaction at different injection temperatures. The results show that the temperature-sensitive intelligent gel undergoes a liquid–solid phase transition at a temperature higher than 60 °C. When MC: PEG: NaCl = 1: 6: 5, the temperature-sensitive intelligent gel showed the best flow characteristics. The large-scale simulation fire extinguishing experiments show that the CO concentration is significantly reduced after the temperature-sensitive intelligent gel is injected at the coal temperature of 300–900 ℃, and both show excellent fire extinguishing effects. The addition of temperature-sensitive intelligent gel can inhibit the number of free radicals in the process of coal oxidation, block the chain reaction of coal spontaneous combustion, and comprehensively inhibit the process of coal spontaneous combustion. The research results provided theoretical support for the application of temperature-sensitive intelligent gel in coal spontaneous combustion areas. Additionally, they guided the design of temperature-sensitive intelligent gel to prevent coal spontaneous combustion technology.

Reduction of the residual warpage of fused deposition modeling by negative thermal expansion filler

We investigated the suppression of residual warpage using a negative thermal expansion (NTE) material filler, Zn1.6Mg0.4P2O7. To focus on the effect of thermal expansion on residual warpage, we used acrylonitrile-butadiene-styrene, which is an amorphous polymer with a small volume change around the liquid–solid phase transition, as the matrix. Composite pellets were prepared using a kneader, and filaments were produced for fused deposition modeling (FDM) using an extruder. We fabricated a bar-like test piece using a standard FDM machine and measured the warpage deformation using 3D scanning. The experimental results were supported by the finite element method. We also compared similarly sized SiO2 powders to discuss the advantages of NTE over conventional fillers. The warpage of a 100 mm x 5 mm x 2 mm bar-like test piece was reduced by approximately 75% by introducing Zn1.6Mg0.4P2O7 at 40 vol%. The effect of Zn1.6Mg0.4P2O7 at 30 vol% is similar to that of a conventional SiO2 filler at 40 vol%. Reducing the residual deformation through fillers would reduce energy consumption and simplify the device by avoiding build stage and chamber heating.

Dulcitol/Starch Systems as Shape-Stabilized Phase Change Materials for Long-Term Thermal Energy Storage.

In recent years, there has been an increasing interest in phase change materials (PCM) based on dulcitol and other sugar alcohols. These materials have almost twice as large latent heat of fusion as other organic materials. Sugar alcohols are relatively cheap, and they can undergo cold crystallization, which is crucial for long-term thermal energy storage. The disadvantage of dulcitol and other sugar alcohols is the solid-liquid phase transition. As a result, the state of matter of the material and its volume change, and in the case of materials modified with microparticles or nanoparticles, sedimentation of additives in liquid PCM can occur. In this study, we obtained shape-stable phase change materials (SSPCM) by co-gelation of starch and dulcitol. To characterize the samples obtained, differential scanning calorimetry (DSC), step-mode DSC, thermogravimetric analysis (TGA), Fourier transform infrared spectroscopy (FTIR), and scanning electron microscopy (SEM) were used, and they were also used to test for shape stabilization. The results show that the obtained systems have great potential as shape-stabilized phase change materials. The sample dulcitol/starch with a 50:50 ratio exhibited the highest heat of cold crystallization, up to 52.90 J/g, while the heat of melting was 126.16 J/g under typical DSC measuring conditions. However, depending on the applied heating program, the heat of cold crystallization can even reach 125 J/g. The thermal stability of all compositions was higher than the phase change temperature, with only 1% mass loss occurring at temperatures above 200 °C, while the phase change occurred at a maximum of 190 °C.

Improving the solid–liquid phase transition of low energy-consuming biphasic solvent through the introduction of H2O

Non-aqueous biphasic absorbents have excellent energy-saving features in capturing CO2. However, the high hygroscopicity of chemical absorbents and the moisture content in flue gas can alter the moisture content of absorbents, thereby affecting their carbon capture performance and stability. In this research, an absorbent for solid–liquid phase transition composed of N-Aminoethylpiperazine (AEP) and dimethyl sulfoxide (DMSO) was developed. The influence of H2O content on CO2 capture capacity and phase transition behavior was explored. The introduction of H2O could not only reduce the viscosity to achieve fast CO2 capture and large CO2 absorption capacity (1.05 mol·mol−1) but also generate dispersed solid particles, allowing for quick sedimentation of the solids, thus enhancing the rate of phase separation. The desorption efficiency of this biphasic solvent was maintained above 83 % after four cycles. It could be desorbed in the middle stage of absorption without waiting for absorption saturation, greatly saving time and cost. Finally, the principle of the CO2 absorption process in this system and the regulatory effect of H2O on the solid–liquid phase were studied through characterization and quantum calculation.

Phase change thermal interface materials with interface adaptability and self-healing properties

Thermal stress resulting from excessive temperatures is a major cause of electronic device failure. In this work, with easy installation and good interface adaptability, Phase Change Thermal Interface Materials (PCTIMs) which possess high thermal conductivity were prepared. By incorporating phase change material stearic acid (SA) into the thermal interface material, the instantaneous heat absorption during the solid-liquid phase transition of SA effectively alleviates the problem of instantaneous high heat flux impacting electronic devices. Additionally, the solid-liquid transition reduces the modulus of TIMs, thereby minimizing the contact thermal resistance between the heat source and the heat sink during mechanical installation. To further enhance performance, the thermal interface material utilizes a dynamically cross-linked polyolefin elastomer (POE) with borate bonds, which effectively restricts the flow of SA even at its phase change point due to the three-dimensional cross-linked framework. By constructing a thermal conductive network using carbon fibers and aluminum nitride of different dimensions, the thermal conductivity of the thermal interface material reached 1.82 W∙m−1K−1 with a filler content of only 30 vol % . At 70 °C, with a force of 50 N applied to a sample area of 400 mm², the contact thermal resistance was only 2.39×10−4 K∙m2W−1. Furthermore, the PCTIMs exhibits excellent self-healing ability under thermal conditions, assuring the permanent encapsulation of small electronic devices.

Cyclodextrin Metal-Organic Framework Functionalized Carbon Materials with Optimized Interface Electronics and Selective Supramolecular Channels for High-Performance Lithium-Sulfur Batteries.

During the reaction process in lithium-sulfur batteries, Lewis acidic lithium polysulfides (LiPSs) affect ion distribution and overall electrolyte stability, degrading battery performance and product distribution (e.g., Li2S). Here, a microenvironment regulation strategy with optimized interface electronics and selective supramolecular channels, is proposed to enhance LiPS reaction kinetics through Lewis basic γ-cyclodextrin metal-organic framework (γ-CDMOF). To validate this concept, γ-CDMOF is rapidly synthesized on 3D graphene foam (GF) via a microwave-assisted method, resulting in a γ-CDMOF/GF cathode for high-performance Li-S batteries. A range of analytical techniques combined with density functional theory (DFT) calculations confirm that introducing a Lewis basic supramolecular microenvironment mitigates the LiPSs shuttle effect, enhances polysulfide capture, and improves sulfur redox conversion. Additionally, COMSOL simulations reveal that the γ-CDMOF framework and oxygen sites significantly reduce volumetric expansion stress during the LiPS solid-liquid phase transition. Impressively, the γ-CDMOF/GF cathode exhibits exceptional performance, including a high specific capacity (1253.01 mAh g⁻¹ at 0.1C), excellent rate performance (589.68 mAh g⁻¹ at 5C), and long cycle life (over 1200 cycles). This study introduces a new concept of supramolecular microenvironment regulation and interfacial interaction strategy, offering a unique approach for the development of multifunctional electrode materials.

Investigating zero-point vibrations of solid hydrogen via statistical moment method

Zero-point vibrations of solid hydrogen are investigated by analyzing the molecular mean-squared displacement (MSD) and mean-squared relative displacement functions within the statistical moment method approach in statistical mechanics. Numerical computations of these thermodynamic properties were conducted for solid hydrogen from 0 K to its phase transition temperature using the Wigner-Kirkwood mean-field potential derived from the Buckingham exp-6 potential. We have shown that the quantum-mechanical zero-point vibrations play an important role at low temperature. And these thermodynamic quantities increase with temperature, suggesting that both thermal and quantum effects play a significant role near the liquid-solid phase transition. The favorable consistency between our findings and the recent experimental inelastic neutron scattering measurements of MSD attests to the potential of SMM as a novel approach for determining the atomic vibrations of solid hydrogen. This approach allows us to study these effects including the anharmonicity of lattice vibrations.

Comparative Study on the Effect of External Magnetic Field on Aluminum Alloy 6061 and 7075 Resistance Spot-Welding Joints

This study investigates the effects of the external magnetic field on the microstructure and mechanical property aluminum alloy 6061-T6 and 7075-T651 resistance spot welding joints. The melting behavior of 6061 and 7075 was analyzed via the calculation of the phase diagram (CALPHAD) technique. The CALPHAD results indicate that, for the 6061 aluminum alloy, the liquid fraction shows a minimal increase at the beginning stage during the solid–liquid phase transition process but with a sharp rise at the ending stage (near the liquidus). In contrast, for the 7075 aluminum alloy, the liquid fraction gradually increases throughout the entire solid–liquid phase transition process. The differences in melting behavior between the 6061 and 7075 alloys lead to different liquation crack morphologies in their spot-welded joints. In the 6061 alloy, the cracks tend to be “eyebrow-shaped”, allowing the liquid metal in the nugget to feed the gaps, and this does not significantly compromise the mechanical properties of the joint. In contrast, the 7075 alloy develops slender cracks that extend through the partially melted zone (PMZ), making it difficult for the liquid metal to feed these gaps, thereby significantly deteriorating the joint’s mechanical strength. Compared to conventional resistance spot-welding joints, the heat exchange between the nugget and the workpiece is enhanced under the external magnetic field, leading to a wider PMZ. This exacerbates the detrimental effects of liquation cracks on the mechanical properties of the 7075 joints. Lap-shear tests indicate that the mechanical properties of the 6061 aluminum alloy joints are improved under electromagnetic stirring. For 7075 aluminum alloy joints, the mechanical properties improve when the welding current is below 34 kA. However, when the welding current exceeds 34 kA, because the widening of the PMZ increases the tendency for liquation cracks, the joint’s mechanical property is deteriorated.

Phase transition heat storage and self-healing mechanism of spinel-calcium aluminate composite aggregate in corundum castable

Corundum-spinel castable is a vital refractory material used in steel ladle linings. Conventional approaches for assessing the thermal shock resistance of corundum-spinel refractory are not entirely representative of the actual application scenarios. This study investigates the influence of spinel-calcium aluminate composite aggregate on the thermal shock resistance of corundum castable using supersonic frequency induction heating technology. The research uncovers how CMA aggregate enhances the thermal shock resistance of corundum castable by cyclic thermal shock tests under varying operational conditions. Results reveal that the incorporation of CMA aggregate led to significant improvements in cold crushing strength and strength retention ratio following thermal shocks. The observed enhancement predominantly stems from the presence of CA/CA2 phase within the CMA aggregate, which undergoes a solid-liquid phase transition at high temperatures, enabling the absorption and retention of substantial heat and aiding in the repair of microcracks within the materials and at the interfacial regions.

Thermal experiment study on the self-luminous properties of metallic iron during solid–liquid phase transition

According to the thermal experiment study of the self-luminescence spectrum of industrially pure iron (DT8) at a heating and cooling rate of 5 °C/min, at the moment of 0 (800 °C), DT8 had no significant self-luminescence characteristics in the wavelength range of 200–1100 nm. At the same time, the first-order differentiation of the spectral intensity versus time was equal to zero at the beginning and end moments of the solid-liquid phase transition. When the solid-liquid melt temperatures are equal (i.e. 1531 °C), there are two sharp peaks at wavelengths of 589.1 nm and 766.7 nm of the self-luminous spectrum in the pure liquid state compared to the self-luminous spectrum in the pure solid state. The intensity of the spectrum decreases significantly as the metallic iron changes from the pure solid phase to the pure liquid phase, with a reduction rate greater than 20%. The appearance of the fitted peaks at 589.1 nm and 769 nm was found by XPS fitting analysis to be a significant feature of the difference in the auto-luminescence spectra of pure solid phase and pure liquid phase metallic iron at a constant melt pool temperature. After the transformation of pure solid phase into pure liquid phase, the decay rate of the self-luminous spectrum in the long-wave direction at wavelengths greater than 762 nm is greater than that in the short-wave direction at wavelengths less than 625 nm.

A Novel Paraffin Wax/Expanded Graphite/Bacterial Cellulose Powder Phase Change Materials for the Dependable Battery Safety Management

Although phase change materials (PCMs) exhibit effective performance in the thermal management of lithium-ion batteries (LIBs), their development is limited by low thermal conductivity and susceptibility to leakage during the solid–liquid phase transition. To address these challenges and enhance thermal management capabilities, this study introduces a novel composite phase change material (CPCM) synthesized by physically mixing paraffin (PA), expanded graphite (EG), and bacterial cellulose (BC). The thermal performance of CPCMs with varying BC proportions is evaluated, and their impact on temperature control in battery thermal management systems (BTMS) is assessed. The results show that the addition of EG and BC significantly improves the thermal conductivity of the CPCM, reaching a value of 1.39 W·m−1·K−1. This also enhances the uniformity of temperature distribution within the battery module and reduces CPCM leakage. By comparing temperature variations within the battery module under different operating conditions, it was found that the intricate network structure of the CPCM promotes uniform temperature distribution, effectively mitigating temperature rise. Consequently, the maximum temperature and maximum temperature difference within the battery module were maintained below 47 °C and 4 °C, respectively. Compared to a system without phase change material at a 3C discharge rate, the maximum cell temperature, maximum module temperature, and maximum temperature difference were reduced by 32.38%, 26.92%, and 34.94%, respectively. These findings provide valuable insights for the design and optimization of BTMS.

Experimental performance of avocado seed oil as a bio-based phase change material for refrigeration applications

Bio-based phase change materials (BPCMs) derived from agro-industrial residues represent an ecofriendly alternative for refrigeration applications. In this work, a BPCM was obtained by steam extraction from avocado seed and studied as a suitable cold thermal energy storage system. First, differential scanning calorimetry was used to determine that the solid-liquid phase transition occurred from -27°C to 15°C. This temperature range is of interest for the conservation different food products. The study aimed to determine the best distribution of the material, which was stored in plastic packaging bags, and placed in an insulated polystyrene thermal container. Two configurations were evaluated: (i) four bags of 75 mL, (ii) two bags of 75 mL and one of 150 mL. The temperatures of the avocado seed oil, and of the air inside the container, were measured during 6 to 8 h. It was concluded that, despite working with the same amount of avocado seed oil (300 mL) in different experiments, there was a better performance when the same volume of material was distributed in each wall. Furthermore, the utilization of avocado seed oil allowed to maintain low temperatures, suitable for food preservation during two additional hours. In the same way, in a yogurt storage experimentation of 8 h, the utilization of the avocado oil enhanced the temperature preservation by 6°C on the phase change range from 4°C to 14°C. While compared to water, the temperature difference was evaluated showing a good performance of the BPCM and an important stability on the temperature heating rate.

Impact of Encapsulated Phase Change Material Additives for Improved Thermal Performance of Silicone Gel Insulation

Abstract Passive cooling through phase change materials (PCM) creates beneficial complimentary cooling techniques aimed at providing thermal gradient mitigation during device operation without additional power requirements. These have been well studied but are difficult to implement due to complications concerning effective enclosure of the liquid phase. Encapsulated PCM particles can be embedded in other materials to form composites with form stable solid–liquid phase transitions. This study characterizes a new composite of silicone gel and encapsulated phase change materials (ePCMs) for use as an encapsulant. The ePCMs contain a paraffin core and titania shell resulting in a self-contained solid–liquid phase transition producing an average of 132.9 J/g of latent heat capacity. The gel composites gain latent heat capacity as a linear function of ePCM concentration by weight. The 30% ePCM sample contains 41.0 J/g of latent heat capacity, approximately 30% of ePCM control samples. The specific heat capacity of the silicone gel without ePCMs is 1.539 J/g-° C and 2.825 J/g-° C for the ePCM particles. As the ePCM concentration increases, the specific heat capacity is increased toward the highest value of the pure ePCMs across all temperature ranges. The coefficient of thermal expansion of the composites is increased with ePCM concentration up to a maximum of 96% in the 20% ePCM concentration. The elastic modulus remains relatively constant across ePCM concentrations and temperatures. In the needle–needle breakdown voltage testing the 20% sample has a 6 kV/mm reduction in dielectric strength and higher than 20% ePCM samples show increased variability in strength due to the dispersed particles. Overall, the results from these material characterizations demonstrate the promise of dielectric composites containing ePCM particles to add passive cooling capability into electronics devices without complex structures.

Self-assembly and energy storage potentials of biphasic phase change azobenzene liquid crystalline block copolymers

Flexible polymeric materials with potentials in energy storage have attracted extensive attention in today's sustainable society. Here, we reported a series of crystalline-liquid crystalline biphasic phase change block copolymers, poly(ethylene oxide)-b-poly(11-(4-(4-cyanophenylazo)phenoxy)undecane methacrylate) (PEO-b-PMAAzo), and studied the UV and Li+ ions coordination-mediated self-assembly for the potentials in phase change energy storage and solid electrolytes. The PEO-b-PMAAzo BCPs possess both the solid-liquid phase transition of PEO and the photo-chemical-thermal energy transition of PMAAzo block. Meanwhile, PEO has the capability to coordinate with the Li+ for the ionic conductivity. We explored the binary phase change behaviors and thermal energy density of the BCPs with different lithium ion concentrations before and after UV irradiation. The addition of LiTFSI salts increases the interaction parameters (χ) of the BCPs leading to phase transition of the self-assembled nanostructures. The phase diagram covering LAM, HEX, GYR, Fddd and HPL nanostructures facilitating ion transport was demonstrated. The PMAAzo block enabled the solid feature of the BCPs and ensured the high energy density and high conductivity. This work demonstrates that the combination of the functional polymers in one BCP not only provides multiple morphology tunabilities but also enables multiple functionalities from energy conversation and storage to ionic conductive electrolytes.

Phase diagram of ruthenium characterized In Situ by synchrotron X-ray diffraction and Ab Initio simulations

In this work, an in situ characterization of the high-pressure and high-temperature phase diagram of ruthenium was carried out. This experiment was performed using a combination of laser-heated diamond anvil cell (LH-DAC) and X-ray diffraction (XRD) techniques at the beamline ID27 of the European Synchrotron Radiation Facility (ESRF). XRD patterns were collected in the range of 15 GPa to 110 GPa and from ambient temperature up to 6600 K. While the hcp-fcc transition, predicted to occur at elevated temperatures was not observed, this study has produced the first experimental observation of a solid–liquid phase transition of Ru at HP conditions. A P-V-T equation of state valid up to 100 GPa and 3000 K is reported.

Experimental investigation on effect of cooling rate on carbide precipitation during solidification of high manganese steel

In order to elucidate the effect of cooling rate on the carbide formation during the solidification process of high manganese steel Mn13, the solidification process is artificially divided into two stages, namely the liquid-solid phase transition stage and solid-state cooling stage. The final Mn13 samples with different cooling rates are used to the analysis of solidification structure and carbides by high-temperature confocal microscopy (HTCLSM), optical microscopy (OM), electron backscatter diffraction (EBSD), and scanning electron microscopy (SEM). The result shows that the change of cooling rate at the liquid-solid phase transition stage has a great influence on the solidification structure and carbide precipitation. At this stage, with the increase of cooling rate from 0.2 °C/s to 5.0 °C/s, the dendrite structure is obviously refined, and the secondary dendrite arm spacing and cooling rate are satisfied with the relationship: λΠ=54.14×v−0.33. Also, the average grain size in the Mn13 sample decreases from 549 μm to 346 μm, and the aspect ratio of gains in the Mn13 sample increases from 1.7 to 2.0. Moreover, the distribution of carbide in the interdendritic regions and grain boundaries increases, and the morphology of carbide at the grain boundary change from block to dendrite. But it seems that the change of cooling rate from 1 °C/s to 5.0 °C/s at the solid-state cooling stage has a slight effect on the secondary dendrite arm spacing, the average size and aspect ratio of the grain structure and the amount and morphology of carbide precipitation at the grain boundary.

Multiscale mushy layer model for Arctic marginal ice zone dynamics

Perhaps the most dynamic component of the Arctic sea ice cover is the marginal ice zone (MIZ), the transitional region between dense pack ice to the north and open ocean to the south. It widens by a factor of four while seasonally migrating more than 1600 km poleward in the Bering–Chukchi Sea sector, impacting climate dynamics, ecological processes, and human accessibility to the Arctic. Here we showcase a transformative mathematical modeling approach to understanding changes in MIZ location and width, focusing on their seasonal cycles as observed by satellites. We view the MIZ as a liquid-solid phase transition region, or mushy zone, on the scale of the Arctic Ocean. Invoking the physics of phase changes, the MIZ is modeled as a dynamic, multiscale composite material layer; this model captures 96% of the annual cycle of MIZ location and 78% of the annual cycle of MIZ width. Temperature in the upper ocean is described by a nonlinear heat equation with effective parameters obtained using homogenization theory for a random medium of ice floes in a sea water host. Observations and simulations together indicate that MIZ location closely tracks the below-ice 273 K isotherm while the width of the MIZ follows vertical heat flux convergence, but with a three-week lag.

Thermodynamics and simulation of 3D crystals and phase transitions under external fields.

A field-supported multiphase kinetic Monte Carlo method previously applied to self-assembled trimesic acid molecular layers [Ustinov et al., Phys. Chem. Chem. Phys. 24, 26111 (2022)] was generalized to three-dimensional gas-liquid and gas-solid systems. This method allows us to calculate the thermodynamic potentials of the liquid and solid phases and then determine the parameters of the liquid-solid phase transition. In this study, the requirement that the gas phase be ideal was introduced as an additional condition. It was shown that in a two-phase system, the sum of the analytical expression for the chemical potential of an ideal gas and the external potential imposed on the gas phase exactly equals the chemical potential of the equilibrium crystal or liquid phase. For example, the coexistence of crystalline/liquid krypton and ideal gas has been considered. A comparison with previously published data has shown that the proposed approach provides the most accurate results for determining the parameters of phase transitions and fully satisfies the Gibbs-Duhem equation. This method does not impose any restrictions on the complexity or hardness of dense phases.