Second-order Transition Research Articles

Algebraic-diagrammatic construction scheme for the polarization propagator including ground-state coupled-cluster amplitudes. II. Static polarizabilities.

The modification of the algebraic-diagrammatic construction (ADC) scheme for the polarization propagator using ground-state coupled-cluster (CC) instead of Møller-Plesset (MP) amplitudes, referred to as CC-ADC, is extended to the calculation of molecular properties, in particular, dipole polarizabilities. Furthermore, in addition to CC with double excitations (CCD), CC with single and double excitations (CCSD) amplitudes can be used, also in the second-order transition moments of the ADC(3/2) method. In the second-order CC-ADC(2) variants, the MP correlation coefficients occurring in ADC are replaced by either CCD or CCSD amplitudes, while in the F/CC-ADC(2) and F/CC-ADC(3/2) variants, they are replaced only in the second-order modified transition moments. These newly implemented variants are used to calculate the static dipole polarizability of several small- to medium-sized molecules, and the results are compared to the ones obtained by full configuration interaction or experiment. It is shown that the results are consistently improved by the use of CC amplitudes, in particular, for aromatic systems such as benzene or pyridine, which have proven to be difficult cases for standard ADC approaches. In this case, the second-order CC-ADC(2) and F/CC-ADC(2) variants yield significantly better results than the standard third-order ADC(3/2) method, at a computational cost amounting to only about 1% of the latter.

Analysis of the magnetic transition and magnetocaloric effect in Mn5Ge2.9Ag0.1 compound

Here we investigate analytical models to understand magnetic and magnetocaloric properties of Mn5Ge2.9Ag0.1 compound prepared by arc-melting method. The Mn5Ge2.9Ag0.1 alloy, undergoing a second-order transition, shows a maximum magnetic entropy change of about 6.86 J/kgK and the relative cooling power (RCP) value of 386 J/kg at 298 K under a field change of 5T. Based on a phenomenological model, the magnetocaloric properties obtained from temperature-dependent magnetization data are in good agreement with the experimental results. To give a better understanding of magnetic transition and the effective magnetic entropy change, we quantify the coupling of lattice energy and electronic energy contribution to the effective magnetic entropy change from a Landau theory plus Bean-Rodbell model. Interestingly, the coupling of lattice energy and electronic energy presents a positive value of up to 4.5% of the effective magnetic entropy change, producing a deleterious impact on the effective magnetic entropy change. The results suggest that the Mn5Ge2.9Ag0.1 system could be a very attractive material for room-temperature magnetic refrigeration applications.

Critical Properties of Perovskite Manganese Oxides Pr1−xBaxMnO3

The critical properties of polycrystalline Pr1−xBaxMnO3 (x = 0.13 and 0.23) samples prepared by using a standard ceramic fabrication method were investigated. Pr1−xBaxMnO3 exhibited a second-order magnetic transition. As per the modified Arrott plot method and double logarithmic M-μ0H curve, the critical exponents (CE) were calculated as β = 0.459 ± 0.03, γ = 1.346 ± 0.02, δ = 4.32 ± 0.04, and TC ≈ 130 K, for x = 0.13, and β = 0.424 ± 0.03, γ = 1.362 ± 0.02, δ = 4.19. ± 0.03, and TC ≈ 163 K, for x = 0.23. To confirm the reliability of such CE values, the M (H) data of Pr1−xBaxMnO3 were checked by the scaling equation M(H, t) = |t|βf±(H/|t|β + γ), where $$ t=\frac{T}{T_C}-1 $$ refers to the reduced temperature, f± is the scaling function above (+)/below (−) TC. The β values for Pr1−xBaxMnO3 (x = 0.13 and 0.23) are between β = 0.365 (3D Heisenberg exponent) and β = 0.5 (mean-field exponent), whereas γ values are fairly close to γ = 1.386. This reveals long- and short-range order coexisting in Pr1−xBaxMnO3.

Two-dimensional Wigner crystals of classical Lennard-Jones particles

The ground-state of two-dimensional (2D) systems of classical particles interacting pairwisely by the generalized Lennard-Jones potential is studied. Taking the surface area per particle A as a free parameter and restricting oneself to periodic Bravais lattices with one particle per unit cell, Bétermin (2018 Nonlinearity 31 3973) proved that the hexagonal, rhombic, square and rectangular structures minimize successively the interaction energy per particle as A increases. We show here that the second-order transitions between the rhombic/square and square/rectangular phases are of mean-field type. The aim of this paper is to extend Bétermin’s analysis to periodic 2D lattices with more than one particle per elementary cell. Being motivated by previous works dealing with other kinds of models, we propose as the ground-state the extensions of the 2D rectangular (one-chain) lattice, namely the ‘zig-zag’ (two-chain), three-chain, four-chain, etc structures possessing 2, 3, 4, etc particles per unit cell, respectively. By using a recent technique of lattice summation we find for the standard Lennard-Jones potential that their ground-state energy per particle approaches systematically as the number of particles per unit cell increases to the one of a phase separated state (the optimal hexagonal lattice). We analyze analytically the low-density limit and the limiting hard-core case of the generalized Lennard-Jones potential.

Zn and P Alloying Effect in Sub-Rapidly Solidified LaFe11.6Si1.4 Magnetocaloric Plates

The occupation mechanism and magnetic transition behavior of trace Zn and P alloying in the sub-rapidly solidified LaFe11.6Si1.4 magnetocaloric plates were investigated. The LaFe11.6Si1.4, LaFe11.6Si1.4Zn0.03, and LaFe11.6Si1.4P0.03 plates were fabricated using the centrifugal casting method in the present work. Experimental results showed that both Zn and P elements were distributed in the La5Si3 and LaFeSi phases during sub-rapid solidification. After annealed at 1373 K for 72 h, the LaFe11.6Si1.4 plate underwent a second-order magnetic transition, while both the LaFe11.6Si1.4Zn0.03 and LaFe11.6Si1.4P0.03 plates underwent a first-order transition. In combination with X-ray diffraction results, it was proposed that both Zn and P atoms prefer to enter the 96i site substituting for FeII/Si atoms according to the density-functional reconstruction of crystallographic structure. The Zn addition led to a slight decrease in magnetic entropy change from 7.0 to 5.9 J/(kg⋅K), while the P addition strikingly enhanced this property to 31.4 J/(kg⋅K) under a magnetic field change of 3 T. The effective refrigeration capacity of the annealed LaFe11.6Si1.4P0.03 plate reached 189.9 J/kg.

Ultrafast Structural Dynamics along the β-γ Phase Transition Path in MnAs.

We investigate the orthorhombic distortion and the structural dynamics of epitaxial MnAs layers on GaAs(001) using static and time-resolved x-ray diffraction. Laser-induced intensity oscillations of Bragg reflections allow us to identify the optical phonon associated with orthorhombic distortion and to follow its softening along the path towards an undistorted phase of hexagonal symmetry. The frequency of this mode falls in the THz range, in agreement with recent calculations. Incomplete softening suggests that the β-γ transformation deviates from a purely second-order displacive transition.

Frustrated diamond lattice antiferromagnet

We use series expansion methods to investigate the phase diagram of a spin-1/2 Heisenberg antiferromagnet on a diamond lattice with first- and second-neighbor interactions. Using series expansions at $T=0$, we find an apparent second-order transition from collinear N\'eel order to an incommensurate spiral with wave vector $(k,k,0)$ at ${J}_{2}/{J}_{1}\ensuremath{\sim}0.18$, considerably higher than the classical value $\frac{1}{8}$. We extend the calculation to the case of tetragonal distortion, as occurs in the material ${\mathrm{CuRh}}_{2}{\mathrm{O}}_{4}$. Here we find a clear second-order transition from N\'eel order to a $(0,0,k)$ spiral.

Fragility and anomalous susceptibility of weakly interacting networks.

Percolation is a fundamental concept that has brought new understanding of the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much fewer interlinks than the connections within each layer. For these kinds of structures, both continuous and abrupt phase transitions are observed in the size of the giant component. The continuous (second-order) transition corresponds to the formation of a giant cluster inside one layer and has a well-defined percolation threshold. The abrupt transition instead corresponds to the merger of coexisting giant clusters among different layers and is characterized by a remarkable uncertainty in the percolation threshold, which in turns causes an anomalous behavior of the observed susceptibility. We develop a simple mathematical model able to describe this phenomenon, using a susceptibility measure that defines the range where the abrupt transition is more likely to occur. Finite-size scaling analysis in the abrupt region supports the hypothesis of a genuine first-order phase transition.

Clustering and Bellerophon state in Kuramoto model with second-order coupling.

In this paper, clustering in the Kuramoto model with second-order coupling is investigated under the bimodal Lorentzian frequency distribution. By linear stability analysis and the Ott-Antonsen ansatz treatment, the critical coupling strength for the synchronization transition is obtained. The theoretical results are further verified by numerical simulations. It has been revealed that various synchronization paths, including the first- and second-order transitions as well as the multiple bifurcations, exist in this system with different parameters of frequency distribution. In certain parameter regimes, the Bellerophon states are observed and their dynamical features are fully characterized.

Magnetic transition and magnetocaloric effect of Gd4Sb3-xRx (R=Si, Ge, Sn, 0 ≤ x ≤ 0.75) compounds

The magnetic properties and magnetocaloric effect (MCE) of Gd4Sb3-xRx (R = Si, Ge, Sn, x = 0, 0.25, 0.5, 0.75) compounds have been studied systematically. The Curie temperature (Tc) of these compounds can be tuned from 270 K to 305 K depending on the substitution amount. All the compounds undergo a second-order magnetic transition from ferromagnetic (FM) state to paramagnetic (PM) state and exhibit considerable reversible MCE near room temperature. The maximum of magnetic entropy change (ΔSMmax) for a magnetic field change of 7 T can reach 4.25 Jkg-1K-1 in Gd4Sb3 phase and independent on Si substitution amount. By Ge and Sn substitution, reduced ΔSMmax of 3.5 and 4.25 Jkg-1K-1 can be obtained in Gd4Sb2.75Ge0.25 and Gd4Sb2.75Sn0.25 alloys respectively. The considerable MCE with no hysteresis and working temperature near room temperature suggests that these materials could be promising candidates as ambient magnetocaloric materials.

Phase Diagram of Superfluid 3He in a Nematic Aerogel in a Strong Magnetic Field

The simultaneous effect of a nematic aerogel and a strong magnetic field on the phase diagram of superfluid 3He is considered. Using the Ginzburg–Landau theory, the domains of existence of new phases, viz., β phase (P1), distorted β phase (P2), distorted A phase ( $$A_{4}^{{({\text{I}})}}$$ ), and distorted planar phase ( $$A_{4}^{{{\text{(II)}}}}$$ ), are determined. It is shown that order parameter components of the β phase have the maximal transition temperature. The conditions for the existence of the second-order transition from the distorted β phase to the distorted planar phase is formulated.

Comparative Assessment of Wind Speed Predictive Capability of First-and Second-order Markov Chain at Different Time Horizons for Wind Power Application

In this article, comparison between the first-and the second-order Markov chain in the prediction of wind speed of different time horizons (i.e., very-short-term, short-term, medium-term and long-term) are performed using the wind speed data of Alexander Bay, South Africa. The prediction capability of the first-and second-order Markov chains are tested by comparing the predicted values to the measured value using standard statistical tests. Furthermore, the values of the predicted wind speeds are used to forecast wind power for each of the time horizons using ENERCON-E53 wind turbine power curve. Some of the key results reveal that both first-and second-order Markov chains present good forecast of wind speeds on very-short-time horizon and as prediction times increase, they lose their precision. Hence, they work best with very short prediction time. The result also shows that second-order Markov chains, which are based on the second-order transition matrices, have better performance compared to first-order Markov chains.

Structural, Magnetic and Magnetocaloric Effect of Gd6(Mn1−xFex)23 Compounds

The influences of Mn/Fe ratio on the structural, magnetic and magnetocaloric properties of Gd6(Mn1−xFex)23 (x = 0.0–0.5) compounds have been investigated by means of X-ray diffraction (XRD) and magnetic measurements. The XRD results show the compounds crystallize in the cubic Th6Mn23-type structure, and the lattice size decreases with the decrease in Mn/Fe ratio. Magnetic measurements show that the samples exhibit a second-order magnetic transition from TC = 99 K for x = 0.3 down to TC = 89 K for x = 0.4 and increase to 293 K for x = 0.5. The magnetization measured at 10 K decreases from 119 emu/g for x = 0.0 to 82 emu/g for x = 0.4, but the magnetization is 105 emu/g at x = 0.5. For an applied field from 0 to 5 T, the maximum values of magnetic entropy change (− ΔSM) for Gd6(Mn1−xFex)23 compounds with x = 0.3, 0.4 and 0.5 are 3.56 J/kg K, 3.77 J/kg K and 1.79 J/kg K, respectively. The properties of Gd6(Mn1−xFex)23 compounds help to understand the exceptional physical characteristics and provide the information for seeking giant magnetocaloric materials.

Magnetic properties and magnetic entropy change of perovskite manganites La0.9–xEuxSr0.1MnO3 (x=0.000, 0.075) by experimental method and numerical fitting

Polycrystalline samples La0.9-xEuxSr0.1MnO3 (x = 0.000, 0.075) were prepared by the standard solid-state reaction method. The results show that the samples preform a characteristic of clusters spin-glass state at low temperature. The samples show a characteristic of ferromagnetism (FM) characteristic in the temperature range of 15–125 K and 15–150 K respectively; the samples show preformed clusters in the temperature range of 125–343 K and 150–325 K, respectively, the samples show paramagnetism (PM) characteristic above 343 and 325 K, respectively. The second-order transitions are found at 118 and 135 K for undoped and doped sample, respectively. When the applied magnetic field is 7 T, the maximum magnetic entropy change |ΔSM| value of the samples is near the Curie temperature (TC), and the value of |ΔSM| reaches 2.76 and 3.03 J/(K·kg), respectively. In addition, the relative cooling power (RCP) is found to be 425.28 and 443.53 J/kg. The numerical fitting data fit well with experimental data. These results indicate that both the samples have the potential to realize magnetic refrigeration in the high temperature region (T > 77 K).

Super-Resolution Imaging of the Brain Extracellular Space Deep within Intact Live Tissue using Carbon Nanotubes

The brain is a dynamic structure with the extracellular space (ECS) taking up almost a quarter of its volume. Signalling molecules, neurotransmitters and nutrients transit via the ECS, which constitutes a key microenvironment for cellular communication and the clearance of toxic metabolites. The spatial organization of the ECS varies during sleep, development and aging and is probably altered in neuropsychiatric and degenerative diseases, as inferred from electron microscopy and macroscopic biophysical investigations. Here we show an approach to directly observe the local ECS structures and rheology in brain tissue using super-resolution imaging. We first compare the luminescence efficiencies of single (6,5) single-walled carbon nanotubes excited by continuous-wave lasers at their second-order excitonic transition, at their K-momentum exciton-phonon sideband, or through upconversion (N Danné & AG Godin et al ACS Photonics 2018 5, 359). The effects of tissue scattering, absorption, autofluorescence, and temperature increase induced by excitation light are systematically examined. We inject single-walled carbon nanotubes into rat cerebroventricles and follow the near-infrared emission of individual nanotubes as they diffuse inside the ECS for tens of minutes in acute slices. Because of the interplay between the nanotube geometry and the ECS local environment, we can extract information about the dimensions and local viscosity of the ECS. We find a striking diversity of ECS dimensions down to 40 nm, and as well as of local viscosity values (AG Godin et al Nat Nanotechnol 2017 12 (3) 238). Moreover, by chemically altering the extracellular matrix of the brains of live animals before nanotube injection, we reveal that the rheological properties of the ECS are affected, but these alterations are local and inhomogeneous at the nanoscale.

Dynamical vertex approximation for the attractive Hubbard model

In this work, we adapt the formalism of the dynamical vertex approximation (D$\Gamma$A), a diagrammatic approach including many-body correlations beyond the dynamical mean-field theory, to the case of attractive onsite interactions. We start by exploiting the ladder approximation of the D$\Gamma$A scheme, in order to derive the corresponding equations for the non-local self-energy and vertex functions of the attractive Hubbard model. Second, we prove the validity of our derivation by showing that the results obtained in the particle-hole symmetric case fully preserve the exact mapping between the attractive and the repulsive models. It will be shown, how this property can be related to the structure of the ladders, which makes our derivation applicable for any approximation scheme based on ladder diagrams. Finally, we apply our D$\Gamma$A algorithm to the attractive Hubbard model in three dimensions, for different fillings and interaction values. Specifically, we focus on the parameters region in the proximity of the second-order transition to the superconducting and charge-density wave phases, respectively, and calculate (i) their phase-diagrams, (ii) their critical behavior, as well as (iii) the effects of the strong non-local correlations on the single-particle properties.

Monte Carlo study of the interfacial adsorption of the Blume-Capel model.

We investigate the scaling of the interfacial adsorption of the two-dimensional Blume-Capel model using Monte Carlo simulations. In particular, we study the finite-size scaling behavior of the interfacial adsorption of the pure model at both its first- and second-order transition regimes, as well as at the vicinity of the tricritical point. Our analysis benefits from the currently existing quite accurate estimates of the relevant (tri)critical-point locations. In all studied cases, the numerical results verify to a level of high accuracy the expected scenarios derived from analytic free-energy scaling arguments. We also investigate the size dependence of the interfacial adsorption under the presence of quenched bond randomness at the originally first-order transition regime (disorder-induced continuous transition) and the relevant self-averaging properties of the system. For this ex-first-order regime, where strong transient effects are shown to be present, our findings support the scenario of a non-divergent scaling, similar to that found in the original second-order transition regime of the pure model.

Equation of state and structural characterization of Cu4I4{PPh2(CH2CH = CH2)}4 under pressure

ABSTRACTCombined high pressure single crystal X-ray diffraction experiments and ab initio simulations based on the density functional theory have been performed on a copper(I) iodide cluster formulated [Cu4I4{PPh2(CH2CH = CH2)}4] under high pressure up to 5 GPa. An exhaustive study of compressibility has been done by means of determination of isothermal equations of state and structural changes with pressure at 298 K taking advantage of the single crystal is more precise than powder X-ray diffraction for this type of experiments. It allows us to report the evidence of the existence of an isostructural phase transition of second order at 2.3 GPa not detected so far.

Phase transitions in Rb2KLuF6 crystal

The Raman spectra of Rb2KLuF6 elpasolite crystal have been studied in a wide temperature range, including two phase transitions: from the cubic phase to the tetragonal phase and then to the monoclinic phase. The results of an analysis of the temperature dependences of the parameters of spectral lines are in good agreement with the thermodynamic data on the phase transitions. The analysis of Raman spectra shows that the transition from cubic to tetragonal phase is a second-order transition and the transition from the tetragonal to the monoclinic phase is a weak first-order transition.

Potassium octahydridotriborate: diverse polymorphism in a potential hydrogen storage material and potassium ion conductor.

Octahydridoborate, i.e. [B3H8]- containing compounds, have recently attracted interest for hydrogen storage. In the present study, the structural, hydrogen storage, and ion conductivity properties of KB3H8 have been systematically investigated. Two distinct polymorphic transitions are identified for KB3H8 from a monoclinic (α) to an orthorhombic (α') structure at 15 °C via a second-order transition and eventually to a cubic (β) structure at 30 °C by a first-order transition. The β-polymorph of KB3H8 displays a high degree of disorder of the [B3H8]- anion, which facilitates increased cation mobility, reaching a K+ conductivity of ∼10-7 S cm-1 above 100 °C. β-KB3H8 starts to release hydrogen at ∼160 °C, simultaneously with the release of B5H9 and trace amounts of B2H6. KBH4 and K3(BH4)(B12H12) are identified as crystalline decomposition products above 200 °C, and the formation of a KBH4 deficient structure of K3-x(BH4)1-x(B12H12) is observed at elevated temperature. The hydrogen-uptake properties of a KB3H8-2KH composite have been examined under 380 bar H2, resulting in the formation of KBH4 at T≥ 150 °C along with higher metal hydridoborates, i.e. K2B9H9, K2B10H10, and K2B12H12.