Theoretical Phase Diagram Research Articles

Validity of Effective Potentials in Crowded Solutions of Linear and Ring Polymers with Reversible Bonds.

We perform simulations to compute the effective potential between the centers-of-mass of two polymers with reversible bonds. We investigate the influence of the topology on the potential by employing linear and ring backbones for the precursor (unbonded) polymer, finding that it leads to qualitatively different effective potentials. In the linear and ring cases the potentials can be described by Gaussians and generalized exponentials, respectively. The interactions are more repulsive for the ring topology, in analogy with known results in the absence of bonding. We also investigate the effect of the specific sequence of the reactive groups along the backbone (periodic or with different degrees of randomness), establishing that it has a significant impact on the effective potentials. When the reactive sites of both polymers are chemically orthogonal so that only intramolecular bonds are possible, the interactions become more repulsive the closer to periodic the sequence is. The opposite effect is found if both polymers have the same types of reactive sites and intermolecular bonds can be formed. We test the validity of the effective potentials in solution, in a broad range of concentrations from high dilution to far above the overlap concentration. For this purpose, we compare simulations of the effective fluid and test particle route calculations with simulations of the real all-monomer system. Very good agreement is found for the reversible linear polymers, indicating that unlike in their nonbonding counterparts many-body effects are minor even far above the overlap concentration. The agreement for the reversible rings is less satisfactory, and at high concentration the real system does not show the clustering behavior predicted by the effective potential. Results similar to the former ones are found for the partial self-correlations in ring/linear mixtures. Finally, we investigate the possibility of creating, at high concentrations, a gel of two interpenetrated reversible networks. For this purpose we simulate a 50/50 two-component mixture of reversible polymers with orthogonal chemistry for the reactive sites, so that intermolecular bonds are only formed between polymers of the same component. As predicted by both the theoretical phase diagram and the simulations of the effective fluid, the two networks in the all-monomer mixture do not interpenetrate, and phase separation (demixing) is observed instead.

Reversible potassium-ion alloying storage in crystalline silicene

Silicon has been recognized as one of the most appealing alloying anode materials for lithium/sodium-ion storage. However, the K-Si alloying reaction is still missing in potassium-ion batteries produced so far, even though the theoretical phase diagram allows the existence of corresponding products. Herein, we synthesize crystalline silicene from Zintl phase CaSi2 and demonstrate that potassium-ions can be inserted/extracted efficiently in it with enhanced cycle stability (without capacity fading over 3000 cycles in silicene//K battery with Coulombic efficiency remains above 99.4 %). Contrary to established perceptions of “inert silicon”, the reversible kinetics-controlled K-Si phase transition occurring in silicene is illustrated by in situ synchrotron X-ray diffraction, and enables the formation of KSi as the dominant discharged product realizing a reliable reversible potassiation storage capacity of 180.1 mA h g−1. The versatile alloying electrochemistry of silicon observed here is expected to spur the development of durable potassium-ion batteries.

Competing magnetic phases in the frustrated spin-1/2 chain compound β−TeVO4 probed by NMR

In frustrated spin-1/2 chains the competition between the nearest- and next-nearest-neighbor exchange interactions leads to a rich phase diagram that becomes even richer in the presence of perturbations in their material realizations. These effects are still largely unexplored, so that new insight into static and dynamic magnetism, in particular by sensitive local probes, is highly desired. Here we present a comprehensive $^{17}$O nuclear magnetic resonance study of $\beta$-TeVO$_4$, where the anisotropy of the main exchange interactions and additional weak interchain exchange interactions complement the theoretical phase diagram. Our results confirm the dynamical nature of the intriguing spin-stripe phase that has been reported in previous studies. In addition, we find that the magnetic order in the high-field phase, which develops just below the magnetization saturation, is consistent with an unusual type of spin-density-wave (SDW) order with different alignments of the magnetic moments on the neighboring chains. This is reminiscent of the ordering in the SDW phase, realized in the absence of the magnetic field, and is thus most likely stabilized by magnetic anisotropy.

Magnetism of two-dimensional honeycomb layered Na2Ni2TeO6 driven by intermediate Na-layer crystal structure

The microscopic spin-spin correlations in the 2D layered spin-1 honeycomb lattice compound Na2Ni2TeO6 have been investigated by neutron diffraction and inelastic neutron scattering. The honeycomb lattice of spin-1 Ni2+ ions, within the crystallographic ab planes, are well separated along the c axis by an intermediate Na layer whose crystal structure contains chiral nuclear density distributions of Na ions. The chirality of the alternating Na layers is opposite. Such alternating chirality of the Na layer dictates the magnetic periodicity along the c axis where an up-up-down-down spin arrangement of the in-plane zigzag AFM structure is found. Besides, the above described commensurate (CM) zigzag AFM order state is found to coexist with an incommensurate (ICM) AFM state below the TN ~ 27.5 K. The ICM state is found to appear at much higher temperature ~ 50 K and persists down to lowest measured temperature of 1.7 K. Our reverse Monte Carlo (RMC) analysis divulges a two dimensional (2D) magnetic correlations (within the ab plane) of the ICM AFM state over the entire temperature range 1.7-50 K. Further, the spin-Hamiltonian has been determined by carrying out inelastic neutron scattering experiments and subsequent linear spin-wave theory analysis which reveals the presence of competing inplane exchange interactions up to 3 rd nearest neighbours consistent with the zigzag AFM ground state, and weak interplanar interaction as well as a weak single-ion-anisotropy. The values of the exchange constants yield that Na2Ni2TeO6 is situated well inside the zigzag AFM phase (spans over a wide ranges of J2/J1 and J3/J1 values) in the theoretical phase diagram. The present study, thus, provides a detailed microscopic understanding of the magnetic correlations and divulges the intertwining magneto-structural correlations.

The influence of polymer concentration on the morphology and mechanical properties of asymmetric polyvinyl alcohol (PVA) membrane for O2/N2 separation

The polymeric based membrane technology has been an attractive alternative option among other gas separation technologies due to its ease of operation, good efficiency and low operational cost. However, a few concerns have been expressed about the polymeric based membrane technology for GS applications, such as the permeability-selectivity trade-off, mechanical stability and its environmental impacts. Therefore, the main objective of this research is to investigate the effects of polymer concentration on a biopolymer-PVA asymmetric membrane morphology, its mechanical properties and gas transport behaviour in order to optimize it for O2/N2 separation using the non-solvent induced phase separation (NIPS) technique. For this purpose, initially, a theoretical solubility model and cloud point phase diagram analysis were conducted to study the solubility and demixing behaviour of the PVA/Water/THF ternary system. Afterwards, these membranes were prepared at different polymeric concentrations from 10 to 14 weight percent (wt.%) and then characterized using scanning electron microscopy (SEM), porosity measurement test, universal testing machine (UTM) and gas permeation test to analyse their physical structure, mechanical properties and GS performance. The analysis results showed that a lower polymer concentration of 10 wt.% facilitated larger pore sizes of 2.486 ± 1.2 μm with a higher porosity of 77.73 ± 15.26% having higher O2 permeance but lower O2/N2 selectivity and mechanical properties. Whereas, a higher polymer concentration of 12 wt.% promoted smaller pore sizes of 2.096 ± 0.5 μm with a porosity of 56.31 ± 3.6%, having better O2/N2 separation performance and higher mechanical properties. However, increasing the polymeric concentration to 14 wt.% resulted in a densified membrane structure having voids and small pore sizes of 1.447 ± 0.9 μm, with a porosity of 31.35 ± 11.98%, and lower elasticity causing membrane rigidified, making it unsuitable for GS applications. Therefore, the intermediate concentration of 12 wt.% PVA asymmetric membrane represents the most optimum morphology and mechanical properties for better O2/N2 separation.

Interfacial self-assembly of SiO2-PNIPAM core-shell particles with varied crosslinking density.

Spherical particles confined to liquid interfaces generally self-assemble into hexagonal patterns. It was theoretically predicted by Jagla two decades ago that such particles interacting via a soft repulsive potential are able to form complex, anisotropic assembly phases. Depending on the shape and range of the potential, the predicted minimum energy configurations include chains, rhomboid and square phases. We recently demonstrated that deformable core-shell particles consisting of a hard silica core and a soft poly(N-isopropylacrylamide) shell adsorbed at an air/water interface can form chain phases if the crosslinker is primarily incorporated around the silica core. Here, we systematically investigate the interfacial self-assembly behavior of such SiO2-PNIPAM core-shell particles as a function of crosslinker content and core size. We observe chain networks predominantly at low crosslinking densities and smaller core sizes, whereas higher crosslinking densities lead to the formation of rhomboid packing. We correlate these results with the interfacial morphologies of the different particle systems, where the ability to expand at the interface and form a thin corona at the periphery depends on the degree of crosslinking close to the core. We perform minimum energy calculations based on Jagla-type pair potentials with different shapes of the soft repulsive shoulder. We compare the theoretical phase diagram with experimental findings to infer to which extent the interfacial interactions of the experimental system may be captured by Jagla pair-wise interaction potentials.

Magnetic properties of the quasi two-dimensional centered honeycomb antiferromagnet GdInO3

The crystal structure and magnetic property of the single crystalline hexagonal rare-earth indium oxides ${\mathrm{GdInO}}_{3}$ have been studied by combing experiments and model calculations. The two inequivalent ${\mathrm{Gd}}^{3+}$ ions form the centered honeycomb lattice, which consists of honeycomb and triangular sublattices. The dc magnetic susceptibility and specific heat measurements suggest two antiferromagnetic phase transitions at ${T}_{\text{N1}}=2.3\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and ${T}_{\text{N2}}=1.02\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. An inflection point is observed in the isothermal magnetization curve, which can be an indication of an up-up-down phase with a 1/3 magnetization plateau, further supported by our theoretical calculation. We also observe a large magnetic entropy change originated from the magnetic frustration in ${\mathrm{GdInO}}_{3}$. By considering a classical spin Hamiltonian, we establish the ground state phase diagram, which suggests that ${\mathrm{GdInO}}_{3}$ has a weak easy-axis anisotropy and is close to the equilateral triangular-lattice system. The theoretical ground-state phase diagram may be used as a reference in NMR, ESR, or $\ensuremath{\mu}\mathrm{SR}$ experiments in future.

Stripe phases in WSe2/WS2 moiré superlattices.

Stripe phases, in which the rotational symmetry of charge density is spontaneously broken, occur in many strongly correlated systems with competing interactions1-11. However, identifying and studying such stripe phases remains challenging. Here we uncover stripe phases in WSe2/WS2 moiré superlattices by combining optical anisotropy and electronic compressibility measurements. We find strong electronic anisotropy over a large doping range peaked at 1/2 filling of the moiré superlattice. The 1/2 state is incompressible and assigned to an insulating stripe crystal phase. Wide-field imaging reveals domain configurations with a preferential alignment along the high-symmetry axes of the moiré superlattice. Away from 1/2 filling, we observe additional stripe crystals at commensurate filling 1/4, 2/5 and 3/5, and compressible electronic liquid crystal states at incommensurate fillings. Our results demonstrate that two-dimensional semiconductor moiré superlattices are a highly tunable platform from which to study the stripe phases and their interplay with other symmetry breaking ground states.

Competition between fractional quantum Hall liquid and Wigner solid at small fillings: Role of layer thickness and Landau level mixing

What is the fate of the ground state of a two-dimensional electron system (2DES) at very low Landau level filling factors ($\nu$) where interaction reigns supreme? An ordered array of electrons, the so-called Wigner crystal, has long been believed to be the answer. It was in fact the search for the elusive Wigner crystal that led to the discovery of an unexpected, incompressible liquid state, namely the fractional quantum Hall state at $\nu=1/3$. Understanding the competition between the liquid and solid ground states has since remained an active field of fundamental research. Here we report experimental data for a new two-dimensional system where the electrons are confined to an AlAs quantum well. The exceptionally high quality of the samples and the large electron effective mass allow us to determine the liquid-solid phase diagram for the two-dimensional electrons in a large range of filling factors near $\simeq 1/3$ and $\simeq 1/5$. The data and their comparison with an available theoretical phase diagram reveal the crucial role of Landau level mixing and finite electron layer thickness in determining the prevailing ground states.

Electric-Field-Driven Assembly of Dipolar Spheres Asymmetrically Confined between Two Electrodes.

Externally applied electric fields have previously been utilized to direct the assembly of colloidal particles confined at a surface into a large variety of colloidal oligomers and nonclose-packed honeycomb lattices (J. Am. Chem. Soc. 2013, 135, 7839-7842). The colloids under such confinement and fields are observed to spontaneously organize into bilayers near the electrode. To extend and better understand how particles can come together to form quasi-two-dimensional materials, we have performed Monte Carlo simulations and complementary experiments of colloids that are strongly confined between two electrodes under an applied alternating current electric field, controlling field strength and particle area fraction. Of particular importance, we control the fraction of particles in the upper vs lower plane, which we describe as asymmetric confinement, and which effectively modulates the coordination number of particles in each plane. We model the particle-particle interactions using a Stockmayer potential to capture the dipolar interactions induced by the electric field. Phase diagrams are then delineated as a function of the control parameters, and a theoretical model is developed in which the energies of several idealized lattices are calculated and compared. We find that the resulting theoretical phase diagrams agree well with simulation. We have not only reproduced the structures observed in experiments using parameters that are close to experimental conditions but also found several previously unobserved phases in the simulations, including a network of rectangular bands, zig zags, and a sigma lattice, which we were then able to confirm in experiment. We further propose a simple way to precisely control the number ratio of particles between different planes, that is, superimposing a direct current electric field with the alternating current electric field, which can be implemented conveniently in experiments. Our work demonstrates that a diverse collection of materials can be assembled from relatively simple ingredients, which can be analyzed effectively through comparison of simulation, theory, and experiment. Our model further explains possible pathways between different phases and provides a platform for examining phases that have yet to be observed in experiments.

Electron Theory Calculation of Thermodynamic Properties of Steels and Its Application to Theoretical Phase Diagram of the Fe-Mo-B Ternary System

Electron Theory Calculation of Thermodynamic Properties of Steels and Its Application to Theoretical Phase Diagram of the Fe-Mo-B Ternary System

Electron Theory Calculation of Thermodynamic Properties of Steels and Its Application to Theoretical Phase Diagram of the Fe–Mo–B Ternary System

Electron Theory Calculation of Thermodynamic Properties of Steels and Its Application to Theoretical Phase Diagram of the Fe–Mo–B Ternary System

Stability of in-plane and out-of-plane chiral skyrmions in epitaxial MnSi(111)/Si(111) thin films: Surface twists versus easy-plane anisotropy

The revisited theoretical phase diagrams for thin films of cubic helimagnets with the easy-plane anisotropy are shown to have different topology as previously reported [Phys. Rev. B 85, 094429 (2012)]. For both in-plane and out-of-plane directions of an applied magnetic field, the phase diagrams exhibit extensive areas of stable skyrmions, which overlap for a wide range of anisotropy parameters. Although the existence of the out-of-plane skyrmions was contradicted within the previous theoretical models, we prove that additional surface twists lead to their stability, while the moderate easy-plane anisotropy increases the stability range of in-plane skyrmions. Moreover, the interplay between the anisotropy and the surface twists gives rise to a stable spiral state canted with respect to the surfaces. Being absent in bulk helimagnets, this oblique spiral occupies vast areas at the phase diagrams in thin-film nanosystems and serves as a connecting-link between cones and helicoids. Our theory gives clear directions for renewed experimental studies of in-plane and out-of-plane skyrmions in epitaxial MnSi(111)/Si(111) thin films.

Origin of Magnetic Ordering in a Structurally Perfect Quantum Kagome Antiferromagnet.

The ground state of the simple Heisenberg nearest-neighbor quantum kagome antiferromagnetic model is a magnetically disordered spin liquid, yet various perturbations may lead to fundamentally different states. Here we disclose the origin of magnetic ordering in the structurally perfect kagome material YCu_{3}(OH)_{6}Cl_{3}, which is free of the widespread impurity problem. Abinitio calculations and modeling of its magnetic susceptibility reveal that, similar to the archetypal case of herbertsmithite, the nearest-neighbor exchange is by far the dominant isotropic interaction. Dzyaloshinskii-Moriya (DM) anisotropy deduced from electron spin resonance, susceptibility, and specific-heat data is, however, significantly larger than in herbertsmithite. By enhancing spin correlations within kagome planes, this anisotropy is essential for magnetic ordering. Our study isolates the effect of DM anisotropy from other perturbations and unambiguously confirms the predicted phase diagram.

Quantum transitions of nematic phases in a spin-1 bilinear-biquadratic model and their implications for FeSe

Since its discovery, iron-based superconductivity has been known to develop near an antiferromagnetic order, but this paradigm fails in the iron chalcogenide FeSe, whose single-layer version holds the record for the highest superconducting transition temperature in the iron-based superconductors. The striking puzzle that FeSe displays nematic order (spontaneously broken lattice rotational symmetry) while being non-magnetic, has led to several competing proposals for its origin in terms of either the $3d$-electron's orbital degrees of freedom or spin physics in the form of frustrated magnetism. Here we argue that the phase diagram of FeSe under pressure could be qualitatively described by a quantum spin model with highly frustrated interactions. We implement both the site-factorized wave-function analysis and the large-scale density matrix renormalization group (DMRG) in cylinders to study the spin-$1$ bilinear-biquadratic model on the square lattice, and identify quantum transitions from the well-known $(\pi,0)$ antiferromagnetic state to an exotic $(\pi,0)$ antiferroquadrupolar order, either directly or through a $(\pi/2,\pi)$ antiferromagnetic state. These many phases, while distinct, are all nematic. We also discuss our theoretical ground-state phase diagram for the understanding of the experimental low-temperature phase diagram obtained by the NMR [P. S. Wang {\it et al.}, Phys. Rev. Lett. 117, 237001 (2016)] and X-ray scattering [K. Kothapalli {\it et al.}, Nature Communications 7, 12728 (2016)] measurements in pressurized FeSe. Our results suggest that superconductivity in a wide range of iron-based materials has a common origin in the antiferromagnetic correlations of strongly correlated electrons.

Phenomenological theory of phase transitions in the MPB region of (1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 single crystals

ABSTRACTA higher-order Landau–Ginzburg–Devonshire theory is proposed to describe phenomenologically the complex phase transitions in the MPB region of the relaxor ferroelectric (1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3(PMN-PT) single crystals. Using the singularity theory, a structurally stable 10th-order potential with four varying expansion coefficients (a1, a11, a2 and a12) depending on temperature and composition is found out. By studying on two- and three-dimensional sections of a four-dimensional phase diagram a1-a11-a2-a12 in the space of phenomenological parameters, the range of coefficient parameters by which the structural stability of the potential model can be guaranteed is determined. The theoretical temperature-composition phase diagram is constructed and it is shown that this is in good agreement with both recent experimental data and first-principle calculation for the symmetry change. Moreover, temperature dependence of dielectric constants for various compositions is studied.

Theoretical phase diagram of two-component composite fermions in double-layer graphene

Theory predicts that double layer systems realize "two-component composite fermions," which are formed when electrons capture both intra- and inter-layer vortices, to produce a wide variety of new strongly correlated liquid and crystal states as a function of the layer separation. Recent experiments in double layer graphene have revealed a large number of layer-correlated fractional quantum Hall states in the lowest Landau level, many of which have not been studied quantitatively in previous theoretical works. We consider the competition between various liquid and crystal states at several of these filling factors (specifically, the states at total filling factors $\nu=3/7$, $4/9$, $6/11$, $4/7$, $3/5$, $2/3$, and $4/5$) to determine the theoretical phase diagram as a function of the layer separation. We compare our results with experiments and identify various observed states. In particular, we show that at small layer separations the states at total fillings $\nu=3/7$ and $\nu=3/5$ are partially pseudospin polarized, where pseudospin refers to the layer index. For certain fractions, such as $\nu=3/7$, interlayer correlations are predicted to survive to surprisingly large interlayer separations.

A theoretical phase diagram for an active nematic on a spherical surface.

Systems combining rod-shaped objects with self-generated motion such as suspensions of microtubules or growing bacterial colonies are commonly modeled as active nematics - nematic liquid crystals with an additional active stress term. Confining a 2D active nematic to the surface of a sphere generates novel behaviour as the four +1/2 nematic defects which are produced by the spherical geometry move round each other in an intricate dance. Here, these defects are modeled as point particles experiencing elastic forces from defect position and orientation, and self-propulsion due to activity. This model exhibits four qualitatively distinct types of trajectory state: two which are consistent with previous experimental and simulated trajectories; and two others, which are apparently novel and in regions of parameter space that may not yet have been explored. This work also explains a discrepancy between some previous point-particle models and the trajectories seen in experiments and simulations: this was due to a failure to fully account for the spherical geometry in the point-particle models.

Theoretical phase diagram of unconventional alkali-doped fullerides

By constructing an effective model based on recently calculated \emph{ab }initio bare interaction parameters, we study the phase diagram of alkali doped fullerides as a function of temperature and internal pressure. We use a slave-rotor mean-field approach at the weak and intermediate coupling limits and a variational mean-field approach at the strong coupling limit, and find a good agreement with experimental phase diagram. We explain the unified description of the phase diagram including the proximity of s-wave superconducting state and the Mott-insulating state, and the existence of Jahn-Teller distorted metallic state using orbital selective physics. We ague that the double electronic occupation of two degenerate orbitals triggers both s-wave superconductivity and Jahn-Teller distortion. While the orbital ordering of two electrons causes the distortion, the remaining single electron in the third orbital causes the metal-insulator transition.

Chemomechanics of transfer printing of thin films in a liquid environment

The liquid-assisted transfer printing is emerging as a competitive manufacturing technique in the delivery and assembly of thin film-layered functional materials and structures. In essence, this technique is underpinned by the detachment of thin films under a synergistic effect of external mechanical loading and interior chemical reaction at interfaces in a liquid environment. Here, we have developed a comprehensive chemomechanics theory for the transfer printing of thin films from as-fabricated SiO2/Si wafer substrate in a liquid water environment. The kinetic chemical reaction at the interface of liquid molecules and interfacial solid bonds is incorporated into the interface energy release rate of thin film detachment, and a rate dependent interfacial debonding process is obtained. We further couple it with mechanical deformation of thin films by taking into account various peeling conditions including peeling rate, peeling angle and thin film thickness to theoretically predicate the steady-state peeling force. Besides, we implement this chemomechanics theory into a finite element model with all atomic information informed and present a reactive atomistic-continuum multiscale model to simulate the detachment of thin films at the continuum scale. In parallel, we have conducted the peeling experiments of three different separation layers on wafer substrates in both dry air and water conditions. Quantitative comparisons among theoretical predictions, simulation results, and experimental measurements are performed and good agreement is obtained. The competition between interfacial delamination and mechanical deformation of thin films during peeling is also analyzed, and a theoretical phase diagram is given to provide an immediate guidance for transfer printing of silicon nanomembranes in the fabrication of functional structures and electronic devices. In addition, the capillary force due to surface wettability of materials is discussed and compared with chemical reaction-induced driving force for transfer printing on a wide range of thin film/substrate systems. The chemomechanics theory and reactive atomistic-continuum simulation model established are expected to lay a foundation for quantitative understanding and descriptions of transfer printing of thin films in a liquid environment.