First-order Liquid-liquid Phase Transition Research Articles

Polyamorphism gets a magnetic boost

Four decades since the concept of polyamorphism was introduced by [L. S. Palatnik (1909–1994), Fiz. Nizk. Temp. 25, 400 (1909)], numerous investigations proved its presence in a broad variety of nonmagnetic short-range ordered materials, like structural, metallic, a-metallic, inorganic molecule, orientational, electron glasses, water, ice, carbons, and others. It was manifested by phase transitions between amorphous states as a function of the quench condition and under compression, mediated by long-wave fluctuations of an order parameter. There has been much recent discussion given to the phenomenon of polyamorphism where distinct, different states of amorphous liquids and solids are observed as a function of density. The outstanding contribution of the recently late [A. Sella, et al. (1956–2022), Nat. Mater. 21, 490 (2022)],2 in the field should be recognized here. Underlying this phenomenon is the possibility of a first-order liquid-liquid phase transition driven by the density and entropy differences between the two amorphous phases. Magnetic boost of multilayer graphene under pressure was also recently discovered. Their famous spin counterparts, such as spin liquid, spin ice, and spin glass have been less studied at this end despite numerous similarities, registered so far. Taking that in mind, for further polyamorphism platform development, we demonstrate the signatures of phase transition in spin glass, driven by a magnetic field, and eventually, a novel type of polyamorphism, the spin-glass one.

First-order liquid-liquid phase transition in nitrogen-oxygen mixtures

The first-order liquid-liquid phase transition (LLPT) describes the counterintuitive nature between two distinct liquids in a single system. However, the physical understanding of LLPT in simple liquid mixtures has remained elusive. Here, a first-order LLPT for nitrogen-oxygen (N-O) mixtures is investigated via extensive ab initio molecular dynamics simulations. The first-order LLPT is characterized by discontinuities of a short-range order and transport properties, occurring at the transition pressures identified by looking at isotherms. The LLPT in N-O mixtures is dominated primarily by the molecular-to-polymeric transformation. The resulting phase boundaries and further structural analysis show the crucial influence of oxygen on weakening the LLPT of N-O mixtures by promoting chemical reactions with nitrogen and crippling polymerizations. Furthermore, noncovalent interactions of short- to long-range van der Waals have evident impacts on the LLPT boundary. The introduction of the strongly constrained and appropriately normed functional with revised Vydrov--van Voorhis nonlocal correlation (SCAN-$r\mathrm{VV}10$) functional to describe the phase-transition behaviors improves the agreement with experimental data. The results highlight the characteristic features of the complex interplay in binary mixtures and revisit the first-order phase transition of dense nitrogen.

First-order liquid-liquid phase transition in compressed hydrogen and critical point.

One of the fundamental problems relating to the properties of hydrogen is that of insulator-metal transition. Recent theoretical and experimental studies show that the metallization in liquid hydrogen could be a first-order phase transition and involve molecular to atomic transition. However, the location of the critical point is still an unresolved question. Earlier studies reported the critical point at a temperature of 1500-2000 K, but recent experimental observations on diamond-anvil cells show that the discontinuous transition still persists at temperatures well above 2000 K. We have carried out a detailed study on the liquid-liquid phase transition in dense hydrogen by uisng ab initio molecular dynamics simulations and found new evidence for the abrupt metallization between weakly dissociated and strongly dissociated fluid phases at temperatures as high as 3000 and 4000 K. Also, the predicted phase boundary is in excellent agreement with the recent experiments. Our results suggest that this first-order transition in liquid hydrogen likely ends in a critical point around 4000 K, which is significantly higher than the previous theoretical predictions.

Hydrogen bond correlated percolation in a supercooled water monolayer as a hallmark of the critical region

Numerical simulations for a number of water models have supported the possibility of a metastable liquid-liquid critical point (LLCP) in the deep supercooled region. Here we consider a theoretical model for a supercooled liquid water monolayer and its mathematical mapping onto a percolation problem. The mapping allows us to identify the finite-size clusters at any state-point, and the infinite cluster at the critical point, with the regions of correlated hydrogen bonds (HBs). We show that the percolation line coincides with the first-order liquid-liquid phase transition ending at the LLCP. At pressures below the LLCP, the percolation line corresponds to the strong maxima of the thermodynamic response functions and to the locus of maximum correlation length (Widom line). At higher pressures, we find a percolation transition with a positive slope and we discuss its possible relation with the thermodynamics.

Direct imaging of a first-order liquid-liquid phase transition in undercooled molten Pd[sbnd]Ni[sbnd]P alloys and its thermodynamic implications

Polyamorphic transition is the transition between two amorphous states or two liquid states (LLT) at a fixed composition of a substance. Experience in LLT is limited. Besides, its nature remains largely unknown as it occurs under the experimental conditions of high pressure/temperature (P/T) or high undercooling. In this study, we found that some undercooled PdNiP melts undergo a LLT. Contrary to all earlier studies, PdNiP specimens that contain the structural changes that occur at different stages of the LLT can be prepared for electron microscopy. HRTEM (high resolution transmission electron microscope) establishes that it is a first-order phase transition. From thermodynamics, a first-order phase change is accompanied by a latent heat. Here it was measured by a DSC (differential scanning calorimeter). A first-order LLT has important thermodynamic implications. First, it reconfirms that a liquid has different kinds of short-range-orders (SROs). Second, the first-order LLT implies that the SROs of a liquid are divided into distinct groups, each containing either a SRO or a number of different SROs, but not all. Physically, each group represents a real liquid. Third, the SRO(s) in a group can be assigned an independent Gibbs free energy, GSRO(P, T, c=composition) and the thermodynamics of the liquids can be described in terms of these GSRO.

Nature of the first-order liquid-liquid phase transition in supercooled silicon.

The first-order liquid-liquid phase transition in supercooled Si is revisited by long-time first-principle molecular dynamics simulations. As the focus of the present paper, its nature is revealed by analyzing the inherent structures of low-density liquid (LDL) and high-density liquid (HDL). Our results show that it is a transition between a sp(3)-hybridization LDL and a white-tin-like HDL. This uncovers the origin of the semimetal-metal transition accompanying it and also proves that HDL is the metastable extension of high temperature equilibrium liquid into the supercooled regime. The pressure-temperature diagram of supercooled Si thus can be regarded in some respects as shifted reflection of its crystalline phase diagram.

Pressure-induced transformations in computer simulations of glassy water

Glassy water occurs in at least two broad categories: low-density amorphous (LDA) and high-density amorphous (HDA) solid water. We perform out-of-equilibrium molecular dynamics simulations to study the transformations of glassy water using the ST2 model. Specifically, we study the known (i) compression-induced LDA-to-HDA, (ii) decompression-induced HDA-to-LDA, and (iii) compression-induced hexagonal ice-to-HDA transformations. We study each transformation for a broad range of compression/decompression temperatures, enabling us to construct a "P-T phase diagram" for glassy water. The resulting phase diagram shows the same qualitative features reported from experiments. While many simulations have probed the liquid-state phase behavior, comparatively little work has examined the transitions of glassy water. We examine how the glass transformations relate to the (first-order) liquid-liquid phase transition previously reported for this model. Specifically, our results support the hypothesis that the liquid-liquid spinodal lines, between a low-density and high-density liquid, are extensions of the LDA-HDA transformation lines in the limit of slow compression. Extending decompression runs to negative pressures, we locate the sublimation lines for both LDA and hyperquenched glassy water (HGW), and find that HGW is relatively more stable to the vapor. Additionally, we observe spontaneous crystallization of HDA at high pressure to ice VII. Experiments have also seen crystallization of HDA, but to ice XII. Finally, we contrast the structure of LDA and HDA for the ST2 model with experiments. We find that while the radial distribution functions (RDFs) of LDA are similar to those observed in experiments, considerable differences exist between the HDA RDFs of ST2 water and experiment. The differences in HDA structure, as well as the formation of ice VII (a tetrahedral crystal), are a consequence of ST2 overemphasizing the tetrahedral character of water.

Stability of dense liquid carbon dioxide.

We present ab initio calculations of the phase diagram of liquid CO(2) and its melting curve over a wide range of pressure and temperature conditions, including those relevant to the Earth. Several distinct liquid phases are predicted up to 200GPa and 10,000K based on their structural and electronic characteristics. We provide evidence for a first-order liquid-liquid phase transition with a critical point near 48GPa and 3,200K that intersects the mantle geotherm; a liquid-liquid-solid triple point is predicted near 45GPa and 1,850K. Unlike known first-order transitions between thermodynamically stable liquids, the coexistence of molecular and polymeric CO(2) phases predicted here is not accompanied by metallization. The absence of an electrical anomaly would be unique among known liquid-liquid transitions. Furthermore, the previously suggested phase separation of CO(2) into its constituent elements at lower mantle conditions is examined by evaluating their Gibbs free energies. We find that liquid CO(2) does not decompose into carbon and oxygen up to at least 200GPa and 10,000K.

Interplay of the Glass Transition and the Liquid-Liquid Phase Transition in Water

Water has multiple glassy states, often called amorphous ices. Low-density (LDA) and high-density (HDA) amorphous ice are separated by a dramatic, first-order like phase transition. It has been argued that the LDA-HDA transformation connects to a first-order liquid-liquid phase transition (LLPT) above the glass transition temperature Tg. Direct experimental evidence of the LLPT is challenging to obtain, since the LLPT occurs at conditions where water rapidly crystallizes. In this work, we explore the implications of a LLPT on the pressure dependence of Tg(P) for LDA and HDA by performing computer simulations of two water models – one with a LLPT, and one without. In the absence of a LLPT, Tg(P) for all glasses nearly coincide. When there is a LLPT, different glasses exhibit dramatically different Tg(P) which are directly linked with the LLPT. Available experimental data for Tg(P) are only consistent with the scenario including a LLPT.

Phase-field model of solid-liquid phase transition with density difference and latent heat in velocity and elastic fields

We present a phase-field model of solid-liquid transitions with inhomogeneous temperature in one-component systems, including hydrodynamics and elasticity. Our model can describe plastic deformations at large elastic strains. We use it to investigate the melting of a solid domain, accounting for the latent heat effect, where there appears a velocity field in liquid and an elastic field in solid. We present simulation results in two dimensions for three cases of melting. First, a solid domain is placed on a heated wall, which melts mostly near the solid-liquid-wall contact region. Second, a solid domain is suspended in a warmer liquid under shear flow, which rotates as a whole because of elasticity and melts gradually. Cooling of the surrounding liquid is accelerated by convection. Third, a solid rod is under high compression in liquid, where slips appear from the solid-liquid interface, leading to a plastic deformation. Subsequently, melting starts in the plastically deformed areas, eventually resulting in the fracture of the rod into pieces. In these phase-transition processes, the interface temperature is kept nearly equal to the coexisting temperature T(cs)(p) away from the heated wall, but this local equilibrium is not attained near the the contact region. We also examine a first-order liquid-liquid phase transition under heating from a boundary in one-component liquids.

First-order liquid-liquid phase transition in dense hydrogen

We use ab initio molecular-dynamics simulations to study the nonmetal-to-metal transition in dense liquid hydrogen. By calculating the equation of state of hydrogen at high pressures up to several megabars and temperatures above the melting line up to 1500 K we confirm the first-order nature of this transition at these temperatures. We characterize both phases based on equation of state data, the electrical conductivity, and the pair-correlation functions, which are all derived self-consistently from these simulations. We locate the respective transition line in the phase diagram and give an estimate for its critical point. We compare with available experimental data and other theoretical predictions.

Theoretical evidence for a first-order liquid-liquid phase transition in gallium

We report on theoretical results that lend support to recent experimental observations suggesting the existence of a first-order liquid-liquid phase transformation (LLPT) in gallium. Using molecular dynamics simulation based on a modified embedded-atom model, we observe a transition from a high-density to a low-density liquid in the supercooled regime. The first-order character of the transition is established through the detection of the release of latent heat and our findings suggest that the LLPT terminates in a critical point that is located in the tensile-strained domain of the metastable phase diagram.

First-Order Liquid-Liquid Phase Transition in Compressed Nitrogen

We report results of first-principles molecular dynamics simulations, which predict a first-order phase transition from molecular to polymeric liquid nitrogen. The liquid-liquid phase boundary is near 88 GPa along the 2000 K isotherm and has a critical point between 4000 and 5000 K and 50 to 75 GPa. At higher temperatures, molecular nitrogen undergoes temperature-driven dissociation to an atomic liquid. The nature of the liquid-liquid transition and the structure of the new polymeric phase are characterized, and ways to experimentally confirm our findings are proposed.

Molecular Dynamics Simulations of Liquid Phosphorus at High Temperature and Pressure

By performing ab initio molecular dynamics simulations, we have investigated the microstructure, dynamical and electronic properties of liquid phosphorus (P) under high temperature and pressure. In our simulations, the calculated coordination number (CN) changes discontinuously with density, and seems to increase rapidly after liquid P is compressed to 2.5 g/cm3. Under compression, liquid P shows the first-order liquid-liquid phase transition from the molecular liquid composed of the tetrahedral P4 molecules to complex polymeric form with three-dimensional network structure, accompanied by the nonmetal to metal transition of the electronic structure. The order parameters Q6 and Q4 are sensitive to the microstructural change of liquid P. By calculating diffusion coefficients, we show the dynamical anomaly of liquid P by compression. At lower temperatures, a maximum exists at the diffusion coefficients as a function of density; at higher temperatures, the anomalous behavior is weakened. The excess entropy shows the same phenomena as the diffusion coefficients. By analysis of the angle distribution functions and angular limited triplet correlation functions, we can clearly find that the Peierls distortion in polymeric form of liquid P is reduced by further compression.

First-Principles Simulations on the Nature of the Melting Line of Sodium

We report a first-principles molecular dynamics study of the reentering behavior that has been recently observed experimentally in the melting line of bcc sodium [Gregoryanz et al., Phys. Rev. Lett. 94, 185502 (2005)10.1103/PhysRevLett.94.185502]. Our results show the liquid phase to be more compressible than the solid phase, and to remain so at high pressures, eventually becoming denser than the solid phase and hence causing the change of slope in the melting line from positive to negative. The maximum of the melting line thus occurs without any accompanying first-order liquid-liquid phase transition.

Quantum Monte Carlo Simulation of the High-Pressure Molecular-Atomic Crossover in Fluid Hydrogen

A first-order liquid-liquid phase transition in high-pressure hydrogen between molecular and atomic fluid phases has been predicted in computer simulations using ab initio molecular dynamics approaches. However, experiments indicate that molecular dissociation may occur through a continuous crossover rather than a first-order transition. Here we study the nature of molecular dissociation in fluid hydrogen using an alternative simulation technique in which electronic correlation is computed within quantum Monte Carlo methods, the so-called coupled electron-ion Monte Carlo method. We find no evidence for a first-order liquid-liquid phase transition.

On the role of frustration on the glass transition and polyamorphism of mesoscopically heterophase liquids

The model of heterophase fluctuations is developed accounting frustration of the mesoscopic solidlike fluctuons. Within the framework of this model, the glass transition and polyamorphous transformations are considered. It is shown that the frustration increases the temperature range in which the heterophase liquid state exists. the upper and lower boundaries of this temperature range are determined. These boundaries separate different phase states-amorphous solid, heterophase liquid, and fluid phases. Polyamorphous liquid-liquid transitions in the liquid are investigated. Frustration can call forth continuous fluid-solid phase transformation avoiding the first- or second-order phase transition. Conditions under which the first-order phase transition fraction takes place are formulated. Two scenarios of the first-order liquid-liquid polyamorphous transformation are described. As an example the glacial phase formation and the first-order liquid-liquid phase transition in triphenyl phosphate are considered and discussed. Impact of frustration on the liquid crystallization and crystallinity of the glassy state is studied.

Liquid-liquid phase transition in Pb-Sn melts

A first-order liquid-liquid (LL) phase transition as a function of temperature in Pb-Sn melts is suggested by internal friction experiments and verified by differential thermal analysis with an entropy-driven order-disorder mechanism. It differs remarkably with other already found LL phase transitions in some aspects. The findings may throw light on the nature of viscous liquids in condensed state physics and be of significance in materials science. The present work makes a beneficial attempt at exploring internal friction as an experimental method for studying liquids.

Explicit Gibbs free energy equation of state applied to the carbon phase diagram

We provide a simple explicit form for the Gibbs free energy $G(P,T)$ of diamond, graphite, and liquid carbon. The Gibbs free energy function is shown to reproduce the known equation of state properties of carbon up to pressures of 600 GPa (6 MBar) and temperatures of 15 000 K. Recent experiments on graphite melting suggest the presence of a first-order liquid-liquid phase transition at roughly 6 GPa. We show that such a transition is consistent with shock compression data at higher pressures. We reanalyze experiments on the diamond-liquid melting line with our equation of state. Our analysis suggests that the diamond-liquid melting line may have a more positive slope as a function of pressure than previously estimated. A maximum in the diamond melting line is predicted by the model, in agreement with recent ab initio simulations.

A first-order liquid–liquid phase transition in phosphorus

First-order structural phase transitions are common in crystalline solids, whereas first-order liquid-liquid phase transitions (that is, transitions between two distinct liquid forms with different density and entropy) are exceedingly rare in pure substances. But recent theoretical and experimental studies have shown evidence for such a transition in several materials, including supercooled water and liquid carbon. Here we report an in situ X-ray diffraction observation of a liquid-liquid transition in phosphorus, involving an abrupt, pressure-induced structural change between two distinct liquid forms. In addition to a known form of liquid phosphorus--a molecular liquid comprising tetrahedral P4 molecules--we have found a polymeric form at pressures above 1 GPa. Changing the pressure results in a reversible transformation from the low-pressure molecular form into the high-pressure polymeric form. The transformation is sharp and rapid, occurring within a few minutes over a pressure range of less than 0.02 GPa. During the transformation, the two forms of liquid coexist. These features are strongly suggestive of a first-order liquid-liquid phase transition.