Thermodynamics around magnetic phase transitions in alternating double-chain spin systems

The thermodynamics and quantum phase transitions of two typically alternating double-chain systems are investigated by Green＇s function theory.（i） For the completely antiferromagnetic（AFM） alternating double-chain, the low-temperature antiferromagnetism with gapped behavior is observed, which is in accordance with the experimental result. In a magnetic field, we unveil the ground state phase diagram with zero plateau, 1/2 plateau, and polarized ferromagnetic（FM） phases,as a result of the intra-cluster spin-singlet competition. Furthermore, the Gr ¨uneisen ratio is an excellent tool to identify the quantum criticality and testify various quantum phases.（ii） For the antiferromagnetically coupled FM alternating chains,the 1/2 magnetization plateau and double-peak structure of specific heat appear, which are also observed experimentally.Nevertheless, the M–h curve shows an anomalous behavior in an ultra-low field, which is ascribed to the effectively weak Haldane-like state, demonstrated by the two-site entanglement entropy explicitly.

Investigations of phase transition, elastic and thermodynamic properties of GaP by using the density functional theory

The phase transition of gallium phosphide （GAP） from zinc-blende （ZB） to a rocksalt （RS） structure is investigated by the plane-wave pseudopotential density functional theory （DFT）. Lattice constant a0, elastic constants cij, bulk modulus B0 and the pressure derivative of bulk modulus B0 are calculated. The results are in good agreement with numerous experimental and theoretical data. From the usual condition of equal enthalpies, the phase transition from the ZB to the RS structure occurs at 21.9 GPa, which is close to the experimental value of 22.0 GPa. The elastic properties of GaP with the ZB structure in a pressure range from 0 GPa to 21.9 GPa and those of the RS structure in a pressure range of pressures from 21.9 GPa to 40 GPa are obtained. According to the quasi-harmonic Debye model, in which the phononic effects are considered, the normalized volume V/Vo, the Debye temperature 8, the heat capacity Cv and the thermal expansion coefficient a are also discussed in a pressure range from 0 CPa to 40 GPa and a temperature range from 0 K to 1500 K.

Thermodynamics and geometrothermodynamics of regular black hole with nonlinear electrodynamics

In this paper we investigate the phase transition and geometrothermodynamics of regular electrically charged black hole in nonlinear electrodynamics theory coupled to general relativity. We analyze the types of phase transition of the thermodynamic system by calculating its temperature, heat capacity, and free energy, etc. We find that there are secondorder phase transitions from the heat capacity for a large value of S. In addition, employing the geometrothermodynamics, we obtain a Legendre invariance metric and find the relationship between the thermodynamical phase transition and the singularity of the curvature scalar in the regular black hole with the nonlinear electrodynamics.

Crystal structure,phase transitions,and thermodynamic properties of magnesium metavanadate(MgV_(2)O_(6))

As a promising anode material for magnesium ion rechargeable batteries,magnesium metavanadate(MgV_(2)O_(6))has attracted considerable research interest in recent years.A MgV_(2)O_(6)sample was synthesized via a facile solid-state reaction by multistep-firing stoichiometric mixtures of MgO and V2O5 powder under an air atmosphere.The solid-state phase transition fromα-MgV_(2)O_(6)toβ-MgV_(2)O_(6)occurred at 841 K and the enthalpy change was 4.37±0.04 kJ/mol.The endothermic effect at 1014 K and the enthalpy change was 26.54±0.26 kJ/mol,which is related to the incongruent melting ofβ-MgV_(2)O_(6).In situ XRD was performed to investigate phase transition of the as-prepared MgV_(2)O_(6)at high temperatures.The cell parameters obtained by Rietveld refinement indicated that it crystallizes in a monoclinic system with the C2/m space group,and the lattice parameters of a=9.280 A°,b=3.501 A°,c=6.731 A°,β=111.76°.The solid-state phase transition fromα-MgV_(2)O_(6)toβ-MgV_(2)O_(6)was further studied by thermal kinetics,indicating that this process is controlled first by a fibril-like mechanism and then by a spherulitic-type mechanism with an increasing heating rate.Additionally,the enthalpy change of MgV_(2)O_(6)at high temperatures was measured utilizing the drop calorimetry,heat capacity was calculated and given as:Cp=208.3+0.03583T-4809000T^(−2)(298-923 K)(J mol^(−1)K^(−1)),the high-temperature heat capacity can be used to calculate Gibbs free energy of MgV_(2)O_(6)at high temperatures.

Phase transition and thermodynamic properties of TiO_2 from first-principles calculations

The pressure induced phase transitions of TiO2 from anatase to columbite structure and from rutile to columbite structure and the temperature induced phase transition from anatase to rutile structure and from columbite to rutile structure are investigated by ab initio plane-wave pseudopotential density functional theory method （DFT）, together with quasi-harmonic Debye model. It is found that the zero-temperature transition pressures from anatase to columbite and from rutile to columbite are 4.55 GPa and 19.92 GPa, respectively. The zero-pressure transition temperatures from anatase to rutile and from columbite to rutile are 950 K and 1500 K, respectively. Our results are consistent with the available experimental data and other theoretical results. Moreover, the dependence of the normalized primitive cell volume V/Vo on pressure and the dependences of thermal expansion coefficient α on temperature and pressure are also obtained successfully.

First-principles calculations for transition phase and thermodynamic properties of GaAs

The transition phase of GaAs from the zincblende （ZB） structure to the rocksalt （RS） structure is investigated by ab initio plane-wave pseudopotential density functional theory method, and the thermodynamic properties of the ZB and RS structures are obtained through the quasi-harmonic Debye model. It is found that the transition from the ZB structure to the RS structure occurs at the pressure of about 16.3 GPa, this fact is well consistent with the experimental data and other theoretical results. The dependences of the relative volume V/V0 on the pressure P, the Debye temperature Θ and specific heat Cv on the pressure P, as well as the specific heat CV on the temperature T are also obtained successfully.

Phase transition and thermodynamic properties of SrS via first-principles calculations

The phase transition of SrS from NaCl structure （B1） to CsCl structure （B2） is investigated by means of ab initio plane-wave pseudopotential density functional theory, and the thermodynamic properties of the B1 and the B2 structures are obtained through the quasi-harmonic Debye model. It is found that the transition phase from the B1 to the B2 structures occurs at 17.9 GPa, which is in good agreement with experimental data and other calculated results. Moreover, the thermodynamic properties （including specific heat capacity, the Debye temperature, thermal expansion and Griineisen parameter） have also been obtained successfully.

Phase transition and thermodynamic properties of BiFeO_3 from first-principles calculations

The first-principles projector-augmented wave method employing the quasi-harmonic Debye model,is applied to investigate the thermodynamic properties and the phase transition between the trigonal R3c structure and the orthorhombic Pnma structure.It is found that at ambient temperature,the phase transition from the trigonal R3c phase to the orthorhombic Pnma phase is a first-order antiferromagnetic-nonmagnetic and insulator-metal transition,and occurs at 10.56 GPa,which is in good agreement with experimental data.With increasing temperature,the transition pressure decreases almost linearly.Moreover,the thermodynamic properties including Grneisen parameter,heat capacity,entropy,and the dependences of thermal expansion coefficient on temperature and pressure are also obtained.

Phase transition and thermodynamic properties of ThO2： Quasi-harmonic approximation calculations and anharmonic effects

Formation control and obstacle avoidance for multi-agent systems have attracted more and more attention. In this paper, the problems of formation control and obstacle avoidance are investigated by means of a consensus algorithm. A novel distributed control model is proposed for the multi-agent system to form the anticipated formation as well as achieve obstacle avoidance. Based on the consensus algorithm, a distributed control function consisting of three terms(formation control term, velocity matching term, and obstacle avoidance term) is presented. By establishing a novel formation control matrix, a formation control term is constructed such that the agents can converge to consensus and reach the anticipated formation. A new obstacle avoidance function is developed by using the modified potential field approach to make sure that obstacle avoidance can be achieved whether the obstacle is in a dynamic state or a stationary state. A velocity matching term is also put forward to guarantee that the velocities of all agents converge to the same value. Furthermore, stability of the control model is proven. Simulation results are provided to demonstrate the effectiveness of the proposed control.

Phase transition,structural and thermodynamic properties of Mg_2 Si polymorphs

The plane-wave pseudo-potential method within the framework of first principles is used to investigate the structural and elastic properties of Mg2Si in its intermediate pressure （Pnma） and high pressure phases （P63/mrnc）. The lattice constants, the band structures. The bulk moduli of the Mg2Si polymorphs are presented and discussed. The phase transition from anti-cotunnite to Ni2In-type Mg2Si is successfully reproduced using a vibrational Debye-like model. The phase boundary can be described as P = 24.02994 ＋ 3.93 × 10^-3T -- 4.66816 × 10^-5T2 -- 2.2501 × 10^-9T3＋ 2.33786 × 10^-11T4. To complete the fundamental characteristics of these polymorphs we have analysed thermodynamic properties, such as thermal expansion and heat capacity, in a pressure range of 1-40 GPa and a temperature range of 0-1300 K. The obtained results tend to support the available experimental data and other theoretical results. Therefore, the present results indicate that the combination of first principles and a vibrational Debye-like model is an efficient scheme to simulate the high temperature behaviours of Mg2Si.

Phase transition, thermodynamic and elastic properties of ZrC

First principles calculation and quasi-harmonic Debye model were used to obtain more physical properties of zirconium carbide under high temperature and high pressure.The results show that the B1structure of ZrC is energetically more favorable with lower heat of formation than the B2structure,and that mechanical instability and positive heat of formation induce the inexistence of the B2structure at normal pressure.It is also found that the B1structure would transform to the B2structure under high pressure below the critical point of V/V0=0.570.In addition,various thermodynamic and elastic properties of ZrC are obtained within the temperature range of0-3000K and the pressure range of0-100GPa.The calculated results not only are discussed and understood in terms of electronic structures,but also agree well with corresponding experimental data in the literature.

Thermodynamic phase transition and winding number for the third-order Lovelock black hole

Phase transition is important for understanding the nature and evolution of the black hole thermodynamic system.In this study,we predicted the phase transition of the third-order Lovelock black hole using the winding numbers in complex analysis,and qualitatively validated this prediction by the generalized free energy.For the 7<d<12-dimensional black holes in hyperbolic topology and the 7-dimensional black hole in spherical topology,the winding number obtained is three,which indicates that the system undergoes first-order and second-order phase transitions.For the 7<d<12-dimensional black holes in spherical topology,the winding number is four,and two scenarios of phase transitions exist,one involving a purely second-order phase transition and the other involving simultaneous first-order and second-order phase transitions.This result further deepens the research on black hole phase transitions using the complex analysis.

Paraelectric-ferroelectric interface dynamics induced by latent heat transfer and irreversibility of ferroelectric phase transitions

The temperature gradients that arise in the paraelectric-ferroelectric interface dynamics induced by the latent heat transfer are studied from the point of view that a ferroelectric phase transition is a stationary, thermal-electric coupled transport process. The local entropy production is derived for a ferroelectric phase transition system from the Gibbs equation. Three types of regions in the system are described well by using the Onsager relations and the principle of minimum entropy production. The theoretical results coincides with the experimental ones.

Observing dynamic oscillatory behavior of triple points among black hole thermodynamic phase transitions

Understanding the dynamic process of black hole thermodynamic phase transitions at a triple point is a huge challenge. In this paper, we conduct the first investigation of dynamic phase behavior at a black hole triple point. By numerically solving the Smoluchowski equation near the triple point for a six-dimensional charged Gauss-Bonnet anti-de Sitter black hole, we report that initial small, intermediate, or large black holes can transit to the other two coexistent phases at the triple point, indicating that thermodynamic phase transitions can indeed occur dynamically. More significantly, we observe characteristic weak and strong oscillatory behavior in this dynamic process, which can be understood from an investigation of the rate of first passage from one phase to another. Our results further an understanding of the dynamic process of black hole thermodynamic phase transitions.

Thermodynamics and phase transition of topological dS black holes with a nonlinear source

We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in dS spacetime.Considering the correlation of the thermodynamic quantities respectively corresponding to the black hole horizon and cosmological horizon of dS spacetime and taking the region between the two horizons as a thermodynamic system,we derive effective thermodynamic quantities of the system according to the first law of thermodynamics,and investigate the thermodynamic properties of the system under the influence of nonlinearity parameter α.It is shown that nonlinearity parameter α influences the position of the black hole horizon and the critical state of the system,and along with electric charge has an effect on the phase structure of the system,which is obvious,especially as the effective temperature is below the critical temperature.The critical phase transition is proved to be second-order equilibrium phase transition by using the Gibbs free energy criterion and Ehrenfest equations.

Thermodynamic quantities and phase transitions of five-dimensional de Sitter hairy spacetime

In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters satisfy the first law of thermodynamics,the equivalent thermodynamic quantities of spacetime and the Smarr relation of five-dimensional de Sitter hairy spacetime are obtained.Then,we study the thermodynamic characteristics of the spacetime described by these equivalent thermodynamic quantities and find that de Sitter hairy spacetime has a phase transition and critical phenomena similar to those of van de Waals systems or charged AdS black holes.It is shown that the phase transition point of de Sitter hairy spacetime is determined by the ratio of two event horizon positions and the cosmic event horizon position.We discuss the influence of the hair parameter and electric charge on the critical point.We also find that the isochoric heat capacity of the spacetime is not zero,which is consistent with the ordinary thermodynamic system but differs from the isochoric heat capacity of AdS black holes,which is zero.Using the Ehrenfest equations,we prove that the critical phase transition is a second order equilibrium phase transition.Research on the thermodynamic properties of five-dimensional de Sitter hairy spacetime lays a foundation for finding a universal de Sitter spacetime thermodynamic system and studying its thermodynamic properties.Our universe is an asymptotically dS spacetime,and the thermodynamic characteristics of de Sitter hairy spacetime will help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of the accelerated expansion of the universe.

Alternative approach to thermodynamic phase transitions

One of the major open problems in theoretical physics is the lack of a consistent quantum gravity theory.Recent developments in our knowledge on thermodynamic phase transitions of black holes and their van der Waalslike behavior may provide an interesting quantum interpretation of classical gravity.Studying different methods of investigating phase transitions can extend our understanding of the nature of quantum gravity.In this paper,we present an alternative theoretical approach for finding thermodynamic phase transitions in the extended phase space.Unlike the standard methods based on the usual equation of state involving temperature,our approach uses a new quasiequation constructed from the slope of temperature versus entropy.This approach addresses some of the shortcomings of the other methods and provides a simple and powerful way of studying the critical behavior of a thermodynamical system.Among the applications of this approach,we emphasize the analytical demonstration of possible phase transition points and the identification of the non-physical range of horizon radii for black holes.

Low Temperature Heat Capacities and Thermodynamic Properties of Zinc L-Threonate Zn(C_4H_7O_5)_2(s) by Adiabatic Calorimetry

Low-temperature heat capacities of the solid compound Zn（C4H7O5）2（s） were measured in a temperature range from 78 to 374 K, with an automated adiabatic calorimeter. A solid-to-solid phase transition occurred in the temperature range of 295？322 K. The peak temperature, the enthalpy, and entropy of the phase transition were determined to be （316.269±1.039） K, （11.194±0.335） kJ？mol-1, and （35.391±0.654） J？K-1？mol-1, respectively. The experimental values of the molar heat capacities in the temperature regions of 78？295 K and 322？374 K were fitted to two polynomial equations of heat capacities（Cp,m） with reduced temperatures（X） and [X = f（T）], with the help of the least squares method, respectively. The smoothed molar heat capacities and thermodynamic functions of the compound, relative to that of the standard reference temperature 293.15 K, were calculated on the basis of the fitted polynomials and tabulated with an interval of 5 K. In addition, the possible mechanism of thermal decomposition of the compound was inferred by the result of TG-DTG analysis.

Thermodynamic re-assessment of Fe-Ti binary system

The Fe-Ti binary system was re-assessed using the CALPHAD method in order to improve the capability of being extrapolated to a ternary or higher-order system. Compared with previous assessments, the main focus was put on the thermodynamic description of the two intermetallic compounds Fe2Ti and FeTi. The C14_Laves phase Fe2Ti was described by the two-sublattice model, which is widely used at present. By checking the homogeneity range on the boundary of the ternary systems involving the binary, the phase boundary of this compound was further confirmed. The FeTi phase with a BCC_B2 crystal structure was treated as the ordered phase of the BCC_A2 phase and a unified Gibbs energy function was used to describe both the ordered and disordered phases. Reproduction of the specific heat capacities of these compounds was another aspect paid particular attention to. Comprehensive comparisons of the calculated and experimental results regarding the phase diagram and thermodynamic properties show a good agreement between them and prove the validity of the present thermodynamic description.

Macroscopic Self-Organized Electrochemical Patterns in Excitable Tissue and Irreversible Thermodynamics

In this paper we make the assertion that the key to understand the emergent properties of excitable tissue (brain and heart) lies in the application of irreversible thermodynamics. We support this assertion by pointing out where symmetry break, phase transitions both in structure of membranes as well as in the dynamic of interactions between membranes occur in excitable tissue and how they create emergent low dimensional electrochemical patterns. These patterns are expressed as physiological or physiopathological concomitants of the organ or organism behavior. We propose that a set of beliefs about the nature of biological membranes and their interactions are hampering progress in the physiology of excitable tissue. We will argue that while there is no direct evidence to justify the belief that quantum mechanics has anything to do with macroscopic patterns expressed in excitable tissue, there is plenty of evidence in favor of irreversible thermodynamics. Some key predictions have been fulfilled long time ago and they have been ignored by the mainstream literature. Dissipative structures and phase transitions appear to be a better conceptual context to discuss biological self-organization. The central role of time as a global coupling agent is emphasized in the interpretation of the presented results.