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Phase diagrams for two-phase solids and eutectic, monotectic, peritectic, and syntectic reactions in low gravity applications to processes and products are considered.
The eutectic is one of only three solidification classes that exist. The others are isostructural and peritectic-class reactions, respectively. Simplistically, in a binaryeutectic phase diagram, a single liquid phase isothermally decomposes to two solid phases in a cooperative manner. The melting point minimum at the eutectic composition, isothermal solidification temperature, near-isocompositional solidification and refined solidification microstructure lend themselves naturally to such applications as brazing and soldering; industries that eutectic alloys dominate. Interest in direct process control of microstructures has led, more recently, to in-situ eutectic directional solidification with applications in electro-magnetics and electro-optics. In these cases, controlled structural refinement and the high aspect ratio and regularity of the distributed eutectic phases is highly significant to the fabrication and application of these in-situ natural composites. The natural pattern formation and scaling of the dispersed phase on a sub-micron scale has enormous potential application, since fabricating bulk materials on this scale mechanically has proven to be particularly difficult. It is thus of obvious importance to understand the solidification of eutectic materials since they are of great commercial significance. The dominant theory that describes eutectic solidification was derived for diffusion-controlled growth of alloys where both solid eutectic phases solidify metallically, i.e. without faceting at the solidification interface. Both high volume fraction (lamellar) and low volume fraction (rod-like) regular metallic arrays are treated by this theory. Many of the useful solders and brazements, however, and most of the regular in-situ composites are characterized by solidification reactions that are faceted/non-faceted in nature, rather than doubly non-faceted (metallic). Further, diffusion-controlled growth conditions are atypical terrestrially since gravitationally-driven convection is pervasive. As a consequence, it is important to determine whether these faceted/non-faceted composites behave in the same manner as their doubly non-faceted counterparts, particularly in the presence of convection. Prior analytical convective sensitivity testing of this theory predicted insensitivity. Prior experimental testing of this theory offered broad-based agreement between theory and experiment, though most results were for high volume fraction lamellar eutectics that solidified without faceting at the solidification interface. Directional solidification experiments of low volume fraction rod eutectics under damped (microgravity or magnetic field) conditions, however, have demonstrated significant sensitivity, challenging this fundamental theory. More recent theories have been proposed which introduce kinetic undercooling, faceting, fluid shear of the solute redistribution zone and the possibility that the interface composition is not the same as the bulk liquid composition. This program tests the established and proposed analytical theories and addresses the origins of discrepancies between the experimental and analytical results.
Qubit regularization provides a rich framework to explore quantum field theories. The freedom to choose how the important symmetries of the theory are embedded in the qubit regularization scheme allows us to construct new lattice models with rich phase diagrams. Some of the phases can contain topological terms which lead to critical phases. In this work we introduce and study the SU(3)-F qubit regularization scheme to embed the SO(3) spin-symmetry. We argue that qubit models in this regularization scheme contain several phases including a critical phase which describes the k = 1 Wess-Zumino-Witten (WZW) conformal field theory (CFT) at long distances, and two massive phases one of which is trvially gapped and the other which breaks the lattice translation symmetry. We construct a simple space-time Euclidean lattice model with a single coupling U and study it using the Monte Carlo method. We show the model has a critical phase at small U and a trivially massive phase at large U with a first order transition separating the two. Another feature of our model is that it is symmetric under space-time rotations, which means the temporal and spatial lattice spacing are connected to each other. The unitary time evolution operator obtained by a Wick rotation of the transfer matrix of our model can help us compute the physics of the k = 1 WZW CFT in real time without the need for tuning the temporal lattice spacing to zero. We use this idea to introduce the concept of a relativistic quantum circuit on a discrete space-time lattice.
We present a detailed study of the magnetic and electronic properties of U 2 Rh 3 Si 5 , a material that has been demonstrated to exhibit a first-order antiferromagnetic phase transition. From a high-magnetic-field study, together with extensive experiments in moderate fields, we establish the magnetic phase diagrams for all crystallographic directions. The possibility of an electronic phase in a narrow interval above the Néel temperature as a precursor of a magnetic phase is discussed.
Lattice ℤ 3 theories with complex actions share many key features with finite- density QCD including a sign problem and $\mathcal{CK}$ symmetry. Complex ℤ 3 spin and gauge models exhibit a generalized Kramers-Wannier duality mapping them onto chiral ℤ 3 spin and gauge models, which are simulatable with standard lattice methods in large regions of parameter space. The Migdal-Kadanoff real-space renormalization group (RG) preserves this duality, and we use it to compute the approximate phase diagram of both spin and gauge ℤ 3 models in dimensions one through four. Chiral ℤ 3 spin models are known to exhibit a Devil’s Flower phase structure, with inhomogeneous phases that can be thought of as ℤ 3 analogues of chiral spirals. Out of the large class of models we study, we find that only chiral spin models and their duals have a Devil’s Flower structure with an infinite set of inhomogeneous phases, a result we attribute to Elitzur’s theorem. We also find that different forms of the Migdal-Kadanoff RG produce different numbers of phases, a violation of the expectation for universal behavior from a real-space RG. We discuss extensions of our work to ℤ N models, SU(N) models and nonzero temperature.
Transitions between phases and states of crystallographic order in films, noting conditions for preferential nucleation and analogies between two- and three-dimensional phase diagrams
The magnetic phase diagram of a spin-$\frac{1}{2}$ chain antiferromagnet Sr 2 CuO 3 is studied by an ultrasound phase-sensitive detection technique. The system is in the extreme proximity of the Luttinger-liquid quantum-critical point and we observe an unusually strong effect of magnetic field, which is very weak compared to the in-chain interaction, on the Néel ordering temperature. Inside the ordered phase, we detect an unexpected, field-induced continuous phase transition. The transition is accompanied by softening of magnetic excitation observed by electron-spin resonance, which in previous work [E. G. Sergeicheva et al., Phys. Rev. B 95, 020411(R) (2017)] was associated with a longitudinal (amplitude) mode of the order parameter. These results suggest a transition from a transverse collinear antiferromagnet to an amplitude-modulated spin-density-wave phase in a very weak magnetic field, which is unexpected for a system of weakly coupled Heisenberg spin-$\frac{1}{2}$ chains.
Metal hydrides are important across diverse applications, such as hydrogen storage, batteries, gas sensors, nuclear reactions, and high-temperature superconductivity. Previous computational studies of metal hydrides under extreme pressures, e.g., 𝑂(10 2 ) GPa, usually treat them as stoichiometric compounds without considering interstitial lattice disorder. As pressures become more moderate in the 𝑂(10 0 ) GPa and below range, hydrogen disorder at interstitial lattice sites becomes prominent, e.g., in the N-doped Lu hydride that was recently claimed superconducting near 1 GPa. Further adding compositional complexity from alloying and/or multielement interstitial occupation makes elucidating pressure- and temperature-dependent observables intractable by first-principles calculations alone. We therefore propose a lattice graph neural-network surrogate modeling approach to predict configuration- and pressure-dependent equation-of-state properties. Their efficiency permits Monte Carlo simulations to calculate Gibbs energies and pressure-dependent phase diagrams, thereby revealing insights into the synthesis conditions required for achieving desired phase equilibria. We demonstrate this concept for the compositionally complex cubic Lu(H,N,Va) 3 system where three constituents (hydrogen, nitrogen and vacancy) have disordered multielement interstitial occupancies and insights into pressure-dependent phase equilibria are critically needed, e.g., N-doping levels can significantly lower dehydrogenation temperatures and provide a new strategy to optimize hydrogen-storage alloys. This work can improve the thermodynamic understanding of the Lu-H-N system and help rational synthesis of N-doped Lu hydrides, but more generally demonstrates an efficient approach to model pressure-dependent thermodynamics of multicomponent solid solutions.
This work reports a ternary structure in the P-Pt-Rh system, which has a composition not reported in the literature. The structure formed in the Pt-6 wt.% Rh alloy which was partially melted in a P-enriched CO environment near 1000 °C isothermally and non-isothermally as part of the type B thermocouple assembly. A composition and a crystal structure of this phase were investigated by utilizing SEM, EPMA, XRD and TEM techniques to discuss the potential of this structure being a true ternary phase. The EPMA indicated chemistries of the ternary structure from both isothermal and non-isothermal samples were about 23P-52Pt-25Rh (at.%) and, 22P-54Pt-24Rh (at.%) respectively. TEM diffraction patterns identified this ternary structure to be crystalline with a complex non-cubic structure, and confirmed it was not amorphous. Finally, by superimposing the compositions in the ternary phase diagram, it was concluded this phase was not extensions of any binary phases known in the respective binary systems.
The energy and transportation industries demand materials that retain their mechanical property at high temperatures. Refractory complex concentrated alloys (RCCAs) with a BCC + B2 microstructure offer a potential solution, where maintaining the high temperature mechanical properties can be achieved by precipitation strengthening. This depends on the B2 phase in RCCAs being thermodynamically stable with a high solvus temperature. Recently, we predicted the high temperature stability of the B2 structure in the Ta-Re binary system, using density functional theory. Here, in this study, we provide experimental evidence for the existence of this phase for the first time, using a Ta 65 Re 35 alloy. Despite Ta-Re binary phase diagrams predicting a single-phase BCC microstructure for Ta 65 Re 35 , we show that a high Z nanoscale secondary phase appears after heat treatment at 1550 °C and 1100 °C. Scanning transmission electron microscopy (STEM) revealed that this phase has a cubic structure and is equiatomic TaRe though B2 superlattice reflections were absent in fast Fourier transforms (FFT) and diffraction patterns (DPs). DP simulations indicate that the B2 TaRe superlattice reflections are up to two orders of magnitude weaker than their fundamental reflections, making their detection challenging via electron microscopy. Neutron diffraction confirmed the second phase had a B2 structure. This study identified a previously unobserved high temperature stable B2 phase in the Ta-Re system, enabling the development of new high temperature BCC + B2 RCCAs.
High-throughput methods enable accelerated discovery of novel materials in complex systems such as high-entropy alloys, which exhibit intricate phase stability across vast compositional spaces. Computational approaches, including Density Functional Theory (DFT) and calculation of phase diagrams (CALPHAD), facilitate screening of phase formability as a function of composition and temperature. However, the integration of computational predictions with experimental validation remains challenging in high-throughput studies. In this work, we introduce a quantitative confidence metric to assess the agreement between predictions and experimental observations, providing a quantitative measure of the confidence of machine learning models trained on either DFT or CALPHAD input in accounting for experimental evidence. The experimental dataset was generated via high-throughput in-situ synchrotron X-ray diffraction on compositionally varied FeNiMnCr alloy libraries, heated from room temperature to ~1000 °C. Agreement between the observed and predicted phases was evaluated using either temperature-independent phase classification or a model that incorporates a temperature-dependent probability of phase formation. This integrated approach demonstrates where strong overall agreement between computation and experiment exists, while also identifying key discrepancies, particularly in FCC/BCC predictions at Mn-rich regions to inform future model refinement.
Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable, when interacting with its surroundings. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium, thus commonly termed as equilibrium or Gibbs thermodynamics. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system in the later 1800's and early 1900's. With the quantum mechanics (QM) developed in 1920's, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau in the 1940's. In 1960's the development of density functional theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager in 1930's and Prigogine and co-workers in the 1950's. In 1960's to 1970's the digitization of thermodynamics was developed by Kaufman in the framework of the CALculation of PHAse Diagrams (CALPHAD) modeling of individual phases with internal degrees of freedom. CALPHAD modeling of thermodynamics and atomic transport properties has enabled computational design of complex materials in the last 50 years. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. The zentropy theory is capable of accurately predicting the free energy of individual phases, transition temperatures and properties of magnetic and ferroelectric materials with free energies of individual configurations solely from DFT-based calculations and without fitting parameters, and is being tested for other phenomena including superconductivity, quantum criticality, and black holes. Those predictions include the singularity at critical points with divergence of physical properties, negative thermal expansion, and the strongly correlated physics. Furthermore, those individual configurations may thus be considered as the genomic building blocks of individual phases in the spirit of the materials genome®. This has the potential to shift the paradigm of CALPHAD modeling from being heavily dependent on experimental inputs to becoming fully predictive with inputs solely from DFT-based calculations and machine learning models built on those calculations and existing experimental data through newly developed and future open-source tools. Furthermore, through the combined law of thermodynamics including the internal entropy production, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena that the phenomenological Onsager flux and reciprocal relationships are due to the dependence of the conjugate potential of a molar quantity on nonconjugate molar quantities and other potentials, which can be predicted by the zentropy theory and CALPHAD modeling.
Inverse design methods are powerful computational approaches for creating colloidal systems which self-assemble into a target morphology by reverse engineering the Hamiltonian of the system. Despite this, these optimization procedures tend to yield Hamiltonians which are too complex to be experimentally realized. An alternative route to complex structures involves the use of several different components, however, conventional inverse design methods do not explicitly account for the possibility of phase separation into compositionally distinct structures. We present an inverse design scheme for multicomponent colloidal systems by combining active learning with a method to directly compute their ground state phase diagrams. This explicitly accounts for phase separation and can locate stable regions of Hamiltonian parameter space which grid-based surveys are prone to miss. Using this we design low-density, binary structures with Lennard-Jones-like pairwise interactions that are simpler than in the single component case and potentially realizable in an experimental setting. This reinforces the concept that ground states of simple, multicomponent systems might be rich with previously unappreciated diversity, enabling the assembly of non-trivial structures with only few simple components instead of a single complex one.
Epitaxial cobaltites have emerged as exemplary materials for electrochemical gating, in large part due to their topotactic perovskite (P) ↔ brownmillerite (BM) transformations. SrCoO 3-δ , for example, can be cycled between metallic ferromagnetic P SrCoO 3 and insulating BM SrCoO 2.5 , realizing exceptional modulation of electronic, thermal, and optical properties. It is often presumed that such cycling also generates ferromagnetic–antiferromagnetic (F-AF) modulation due to the G-type AF order in bulk SrCoO 2.5 . Little is understood about magnetism in thin-film BM SrCoO 2.5 , however, meaning that the true magnetic property modulation is unclear. We address this here through a neutron diffraction study of BM La 1-x Sr x CoO 2.5 films at x = 0.5 and 1.0. Lightly compressively strained SrCoO 2.5 films are shown to retain G-type AF order, albeit with suppressed Néel temperature (~340 K). Of high interest for AF spintronics, room-temperature F–AF cycling is thus possible across the SrCoO 3-δ P ↔ BM transformation. At x = 0.5, however, BM La 0.5 Sr 0.5 CoO 2.5 films are found to exhibit no detectable G-type AF order but instead weak F order (Curie temperature ~115 K), unveiling a La 0.5 Sr 0.5 CoO 3-δ phase diagram with two distinct F phases. These results thus uncover new, unanticipated magnetic phase behavior in these materials, in addition to being directly relevant to cobaltite-based magnetoionics.
We study the Kitaev-Heisenberg model with spin-1 local degree of freedom on a honeycomb lattice numerically by the infinite density matrix renormalization group method on a cylinder geometry. By tuning the relative value of the Kitaev and Heisenberg exchange couplings, we obtain the phase diagram with two spin liquid phases and four symmetry-broken phases. Here, we identify that the spin liquid phases are gapless by calculating the central charge at the pure Kitaev points without the Heisenberg interactions. Comparing to its spin-1/2 counterpart, the position and number of gapless modes of the spin-1 case are quite different. Due to the approximate Z 2 local conservations, the expectation value of the Wilson loop operator measuring the flux of each plaquette stays near to 1, and the static spin-spin correlations remain short range in the entire spin liquid phases.
We study the ground-state properties of a spin-1 Heisenberg model on a square lattice with the first- and second-nearest-neighbor antiferromagnetic couplings $J_1$ and $J_2$ and a three-spin scalar chirality term $J_\chi$. Using the density matrix renormalization group calculation, we map out a global phase diagram including various magnetic order phases and an emergent quantum spin liquid phase. The nature of the spin liquid is identified as a bosonic non-Abelian Moore-Read state from the fingerprint of the entanglement spectra and identification of a full set of topological sectors. We further unveil a stripe magnetic order coexisting with this spin liquid. Furthermore, our results not only establish a rare example of non-Abelian spin liquids in simple spin systems but also demonstrate the coexistence of fractionalized excitations and magnetic order beyond mean-field descriptions.
Here we investigate quantum order by disorder in a frustrated spin nanotube formed by wrapping a J1–J2 Heisenberg model at 45° around a cylinder. Using Schwinger boson theory and density matrix renormalization group (DMRG), we have computed the ground-state phase diagram to reveal a Z2 phase in which collinear spin stripes form a right- or left-handed helix around the nanotube. We have derived an analytic estimate for the critical η c = J 1 /2J 2 of the Z 2 -helical phase transition, which is in agreement with the DMRG results. By evaluating the entanglement spectrum and nonlocal string order parameters we discuss the topology of the Z 2 -helical phase.
Helical conductors with spin-momentum locking are promising platforms for Majorana fermions. Here we report observation of two topologically distinct phases supporting helical edge states in charge neutral Bernal-stacked tetralayer graphene in Hall bar and Corbino geometries. As the magnetic field B ⊥ and out-of-plane displacement field D are varied, we observe a phase diagram consisting of an insulating phase and two metallic phases, with 0, 1, and 2 helical edge states, respectively. These phases are accounted for by a theoretical model that relates their conductance to spin-polarization plateaus. Transitions between them arise from a competition among interlayer hopping, electrostatic and exchange interaction energies. Finally, our work highlights the complex competing symmetries and the rich quantum phases in few-layer graphene.