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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.
Sapphire (Al 2 O 3 ), known for its remarkable incompressibility at ambient conditions, plays a pivotal role in both static and dynamic compression research. Accurately characterizing its equation of state (EoS) is essential for these applications. Here, we present a complete Hugoniot of Al 2 O 3 as locus of experimentally assessed, high-precision, pressure, density and temperature states up to 14 Mbar and 43 kK. The Hugoniot is established with single shock experiments using magnetically launched hyper velocity flyers on the Z Accelerator at Sandia National Laboratories. We explore principal Hugoniot states at very high shock 𝑇 and 𝑝 in the solid phase, tracking the solid-liquid boundary and culminating at 2.4-fold compression, where data provides a direct constraint on the liquid phase. Corresponding shock release data probe thermodynamic states complementary to the Hugoniot and place additional constraints on tabular EoS models. Our findings indicate a significant deviation from existing tabular EoS models for Al 2 O 3 dictating a comprehensive overhaul. We develop two advanced EoSs for Al 2 O 3 the SESAME 97412 model, featuring an extensive phase diagram that includes three solid phases and the liquid phase, and the updated LEOS 2200m2 model. EoS development is assisted with Quantum Molecular Dynamics simulations. Our experimental data allows for stringent testing of our EoSs. Both models accurately capture the Hugoniot of Al 2 O 3 up to the highest pressures and temperatures. Rigorous experimental determination of extreme pressures and temperatures, paired with sophisticated models, advances the frontier of EoS development beyond 1 terapascal.
By analogy with the Landau-Ginzburg theory of ordinary zero-form symmetries, we introduce and develop a Landau-Ginzburg theory of one-form global symmetries, which we call mean string field theory. The basic dynamical variable is a string field – defined on the space of closed loops – that can be used to describe the creation, annihilation, and condensation of effective strings. Like its zero-form cousin, the mean string field theory provides a useful picture of the phase diagram of broken and unbroken phases. We provide a transparent derivation of the area law for charged line operators in the unbroken phase and describe the dynamics of gapless Goldstone modes in the broken phase. The framework also provides a theory of topological defects of the broken phase and a description of the phase transition that should be valid above an upper critical dimension, which we discuss. We also discuss general consequences of emergent one-form symmetries at zero and finite temperature.
Resistivity measurements as a function of temperature were performed on alloys of the binary material system In sub(1-x) Bi sub x for x varying between 0 and 1. It was found that for all single-phase alloys (the pure elements, alpha-In, and the three intermetallic compounds) at temperatures sufficiently above the Debye-temperature, the resistivity p can be expressed as p = a sub o T(n), where a sub o and n are composition-dependent constants. The same exponential relationship can also be applied for the sub-system In-In2Bi, when the two phases are in compositional equilibrium. Superconductivity measurements on single and two-phase alloys can be explained with respect to the phase diagram. There occur three superconducting phases (alpha-In, In2Bi, and In5Bi3) with different transition temperatures in the alloying system. The magnitude of the transition temperatures for the various intermetallic phases of In-Bi is such that the disappearance or occurrence of a phase in two component alloys can be demonstrated easily by means of superconductivity measurements.
The results are described of studies of a random-anisotropy Blume-Emery-Griffiths spin-1 Ising model using mean-field theory, transfer-matrix calculations, and position-space renormalization-group calculations. The interplay between the quenched randomness of the anisotropy and the annealed disorder introduced by the spin-1 model leads to a rich phase diagram with a variety of phase transitions and reentrant behavior. The results may be relevant to the study of the phase separation of He-3 - He-4 mixtures in porous media in the vicinity of the superfluid transition.
Concentration gradients in meteoritic kamacite predicted from Fe-Ni phase diagram and diffusion analysis