Thermodynamic Maxwell Relation Research Articles

Investigation of dynamic scaling behavior, electrocaloric performance, and pyroelectric energy storage of Ba0.85Ca0.15Ti0.9Zr0.1O3 ceramic

In this current study, comprehensive investigations were carried out to examine the pyroelectric energy storage, electrocaloric performance, and temperature-sensitive scaling behavior of Ba0.85Ca0.15Zr0.10Ti0.9O3 ceramics synthesized by mixed oxide route. Tetragonal and orthorhombic symmetries were concurrently present with the presence of a single perovskite material under ambient conditions, according to X-ray diffraction (XRD) and Rietveld refinement investigations. The scanning electron micrograph reveals distinct, pore-free grain structures. The dielectric performance shows a temperature-dependent characteristic with a diffuse phase transition. The temperature-sensitive behavior of ferroelectric hysteresis was analyzed with a variety of applied electric fields. The pyroelectric energy storage capabilities were assessed using the Olsen cycle for calculation. Furthermore, figures of merit (FoMs) for pyroelectric properties, including responsivity (Fv), current responsivity (Fi), energy harvesting (Fe), new energy harvesting (Fe*), and detectivity (Fd), were computed. An indirect method based on the thermodynamic Maxwell's relation was employed to analyze the changes in adiabatic temperature, isothermal entropy, and electrocaloric strength. The scaling relationships for ferroelectric hysteresis, specifically about the coercive field (EC), remnant polarization (Pr), and hysteresis area (<A>), were methodically explored across varying temperatures (T). The power-law temperature exponents were found for all the associated hysteresis parameters.

Parameters of State in the Global Thermodynamics of Binary Ideal Gas Mixtures in a Stationary Heat Flow.

In this paper, we formulate the first law of global thermodynamics for stationary states of the binary ideal gas mixture subjected to heat flow. We map the non-uniform system onto the uniform one and show that the internal energy U(S*,V,N1,N2,f1*,f2*) is the function of the following parameters of state: a non-equilibrium entropy S*, volume V, number of particles of the first component, N1, number of particles of the second component N2 and the renormalized degrees of freedom. The parameters f1*,f2*, N1,N2 satisfy the relation (N1/(N1+N2))f1*/f1+(N2/(N1+N2))f2*/f2=1 (f1 and f2 are the degrees of freedom for each component respectively). Thus, only 5 parameters of state describe the non-equilibrium state of the binary mixture in the heat flow. We calculate the non-equilibrium entropy S* and new thermodynamic parameters of state f1*,f2* explicitly. The latter are responsible for heat generation due to the concentration gradients. The theory reduces to equilibrium thermodynamics, when the heat flux goes to zero. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.

Fundamental Relation for Gas of Interacting Particles in a Heat Flow.

There is a long-standing question of whether it is possible to extend the formalism of equilibrium thermodynamics to the case of nonequilibrium systems in steady-states. We have made such an extension for an ideal gas in a heat flow. Here, we investigated whether such a description exists for the system with interactions: the van der Waals gas in a heat flow. We introduced a steady-state fundamental relation and the parameters of state, each associated with a single way of changing energy. The first law of nonequilibrium thermodynamics follows from these parameters. The internal energy U for the nonequilibrium states has the same form as in equilibrium thermodynamics. For the van der Waals gas, U(S*,V,N,a*,b*) is a function of only five parameters of state (irrespective of the number of parameters characterizing the boundary conditions): the effective entropy S*, volume V, number of particles N, and rescaled van der Waals parameters a*, b*. The state parameters, a*, b*, together with S*, determine the net heat exchange with the environment. The net heat differential does not have an integrating factor. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.

Large magnetocaloric effect and magnetic properties of EuRhO3

We report on the structural, magnetic, and magnetocaloric properties of EuRhO3 powders. The oxidation states of Eu and Rh ions were studied using X-ray photoelectron spectroscopy (XPS). It is found that the Eu ions are mainly in the divalent oxidation state while the Rh ions have +4 state. EuRhO3 powders are found to be antiferromagnetic with a second order magnetic transition at Néel temperature (TN = 2.9 K). Analysis of the magnetic susceptibility versus temperature data in terms of the Curie–Weiss law: (χ = C/(T–θW)) for T > TN, yields θW = −3.1 K and effective magnetic moment μeffexp = 7.72 μB, which is close to the theoretical value μefftheo = 7.94 μB. The magnetic entropy change (–ΔSM), was determined by employing the thermodynamic Maxwell's relation. At μ0H = 5 T and near TN, (–ΔSMMax) and relative cooling power (RCP) exhibit large values of 33.7 J/(kg⋅K) and 238 J/kg, respectively. The large magnitude of –ΔSM and RCP show that the EuRhO3 compound could be a potential candidate to be used in cryogenic magnetic refrigeration.

The Mental Maxwell Relations: A Thermodynamic Allegory for Higher Brain Functions.

The theoretical framework of classical thermodynamics unifies vastly diverse natural phenomena and captures once-elusive effects in concrete terms. Neuroscience confronts equally varied, equally ineffable phenomena in the mental realm, but has yet to unite or to apprehend them rigorously, perhaps due to an insufficient theoretical framework. The terms for mental phenomena, the mental variables, typically used in neuroscience are overly numerous and imprecise. Unlike in thermodynamics or other branches of physics, in neuroscience, there are no core mental variables from which all others formally derive and it is unclear which variables are distinct and which overlap. This may be due to the nature of mental variables themselves. Unlike the variables of physics, perhaps they cannot be interpreted as composites of a small number of axioms. However, it is well worth exploring if they can, as that would allow more parsimonious theories of higher brain function. Here we offer a theoretical exercise in the spirit of the National Institutes of Health Research Domain Criteria (NIH RDoC) Initiative and the Cognitive Atlas Project, which aim to remedy this state of affairs. Imitating classical thermodynamics, we construct a formal framework for mental variables, an extended analogy – an allegory – between mental and thermodynamic quantities. Starting with mental correlates of the physical indefinables length, time, mass or force, and charge, we pursue the allegory up to mental versions of the thermodynamic Maxwell Relations. The Maxwell Relations interrelate the thermodynamic quantities volume, pressure, temperature, and entropy and were chosen since they are easy to derive, yet capable of generating nontrivial, nonobvious predictions. Our “Mental Maxwell Relations” interlink the mental variables consciousness, salience, arousal, and distraction and make nontrivial, nonobvious statements about mental phenomena. The mental system thus constructed is internally consistent, in harmony with introspection, and respects the RDoC criteria of employing only psychologically valid constructs with some evidence of a brain basis. We briefly apply these concepts to the problem of decision-making and sketch how some of them might be tested empirically.

Metamagnetic Transition in Heavy Fermion Superconductor UTe2

We have studied the magnetization of the recently discovered heavy fermion superconductor UTe$_2$ up to 56 T in pulsed-magnetic fields. A first-order metamagnetic transition has been clearly observed at $H_{\rm m}$ =34.9 T when the magnetic field $H$ is applied along the orthorhombic hard-magnetization $b$-axis. The transition has a critical end point at $\sim$11 K and 34.8 T, where the first order transition terminates and changes into a crossover regime. Using the thermodynamic Maxwell relation, we have evaluated the field dependence of the Sommerfeld coefficient of the specific heat directly related to the superconducting pairing. From the analysis, we found a significant enhancement of the effective mass centered at $H_{\rm m}$, which is reminiscent of the field-reentrant superconductivity of the ferromagnet URhGe in transverse fields. We discuss the origin of their field-robust superconductivity.

Magnetocaloric Effect Caused by Paramagnetic Austenite–Ferromagnetic Martensite Phase Transformation

In the present work, the magnetization of Ni50Mn17.5Ga25Cu7.5 alloy undergoing the first-order phase transition from paramagnetic austenite to ferromagnetic martensite was measured to evaluate the magnetic-field-induced entropy change (MFIEC) and refrigerant capacity (RC) of the alloy. A standard method (SM) of evaluation of MFIEC is based on thermodynamic Maxwell relation. In view of the criticism of SM expressed by some scientists, the alternative method (AM), which is based on thermodynamic relationships for free energy, was proposed recently for the determination of MFIEC. We developed this method and computed MFIEC in two ways—by AM and SM. The values of MFIEC obtained for Ni50Mn17.5Ga25Cu7.5 alloy by these methods appeared to be large but very different from each other. Moreover, AM reveals the possibility of both normal and inverse magnetocaloric effects in the adjoining temperature ranges, while SM results only in the normal magnetocaloric effect.

Effect of composition changes on the structural, magnetic and thermodynamic properties in Tb1-xDyxNi2 intermetallic compounds

The crystal structure, magnetic and thermodynamic properties of polycrystalline Tb1-xDyxNi2 intermetallic compounds with x = 0.25, 0.5 and 0.75 have been investigated. Experimental data on thermodynamic properties, i.e. the isothermal entropy change ΔSmag, are compared with results of theoretical calculations which were performed considering a model Hamiltonian that includes the crystalline electric field effects and exchange magnetic interaction.High-field isothermal magnetic entropy change was calculated according to magnetic measurements using thermodynamic Maxwell's relation. A large entropy change has been observed for all Dy concentrations. The maximum relative cooling power (RCP) of studied compounds reaches fairly high values, which are close to those reported for other magnetic refrigerants operating at temperatures below 40 K. The obtained results show that studied compounds can be considered as cooling agents in magnetic refrigerators performing an Ericsson cycle in the temperature range 20–40 K.

Influence of replacement of Mn by Cr on magnetocaloric properties of quenched NiMn1–xCrxGe alloys

In this paper, the crystallographic, magnetic, thermomagnetic, and magnetocaloric properties of the quenched NiMn1−xCrxGe (x = 0.04, 0.18, and 0.25) half-Heusler alloys have been studied by x-ray diffraction, differential scanning calorimetry and magnetization measurements. An influence of partial substitution of Cr for Mn and quenching of the samples on the character of structural and magnetic phase transitions is presented. Quenching of the alloys results in the formation of two phase (orthorhombic and hexagonal) crystal structure. The magnetic properties were investigated by means of magnetization measurements over a wide temperature (5–400 K) and magnetic field (up to 60 kOe) ranges. The experimental data indicate that at quenching and with increasing Cr content the magnetic order changes from antiferromagnetic to ferromagnetic. Hardened compounds exhibit a thermal hysteresis in the vicinity of the magnetic phase transition, what is characteristic for a first-order magnetic phase transition. The magnetic phase transition temperatures are decreased as a result of quenching of the samples. The magnetic entropy changes were calculated using the field dependences of isothermal magnetization in terms of the thermodynamic Maxwell relation. The magnetic entropy changes, |ΔSMmax|, obtained for the hardened alloys with x = 0.25 have the maximum value equal to 23 J/(kg·K) near the magnetic phase transition for a field change of ΔH = 0–60 kOe.

First indirect experimental evidence and theoretical discussion of giant refrigeration capacity through the reversible pressure induced spin-crossover phase transition

We report on the giant barocaloric effect and refrigerant capacity in the [Fe(pzt)6](PF6)2 (pzt = 1-propyltetrazole) spin-crossover material. The refrigerant capacity in [Fe(pzt)6](PF6)2 is RC = 1380 J kg−1, 5 times higher than the big value reported in (NH4)2SO4, upon pressure variation ΔP = 1 kbar. This huge caloric effect is ascribed to the coupling interactions between the crystal lattice (phonons) and the order parameter (γHS) that describes the molar fraction of high spin molecules (Fe+2N6)-(t2g4eg2) in [Fe(pzt)6](PF6)2. Our theoretical entropy includes the lattice, electronic and configurational coupled-contributions and was obtained from a microscopic model. A new methodology to obtain the barocaloric effect potentials is presented using a proper thermodynamic Maxwell relation for spin-crossover systems. The experimental results, for the isothermal entropy change, were calculated from the pressure dependence of γHS data. Besides, the determination of molecular volume change between high and low spin states through caloric measurements was discussed.

Magnetic and magnetocaloric properties of the La0.9−xAgxMn1.1O3 compounds

The influence of Ag+ ions and Mn non-stoichiometry on the magnetic properties and magnetocaloric effect in the La0.9–xAgxMn1.1O3 compounds has been studied. The Ag+ ions content substituting for trivalent lanthanum ions was varied from x = 0.05 to 0.3. Magnetic measurements have been performed over a wide temperature (350–5 K) and magnetic field (up to 5 T) ranges. All the manganites studied show the ferromagnetic-like ordering with a first order magnetic phase transition. The magnetic entropy changes were evaluated from the isothermal curves of magnetization versus an applied magnetic field using both the thermodynamic Maxwell relation (MR) and calculation based on the Landau theory of phase transitions. The largest values of the magnetocaloric effect as well as the relative cooling power among the studied manganites are equal to 5.76 J/(kg K) and 185 J/kg, respectively, for La0.7Ag0.2Mn1.1O3 in the magnetic field change of 5 T near the Curie temperature of TC = 271 K. A good correlation between the magnetization, colossal magnetoresistance and magnetic entropy changes as a function of Ag concentration in the La0.9–xAgxMn1.1O3 manganites was established.

Thermodynamic framework for compact q-Gaussian distributions

Recent works have associated systems of particles, characterized by short-range repulsive interactions and evolving under overdamped motion, to a nonlinear Fokker–Planck equation within the class of nonextensive statistical mechanics, with a nonlinear diffusion contribution whose exponent is given by ν=2−q. The particular case ν=2 applies to interacting vortices in type-II superconductors, whereas ν>2 covers systems of particles characterized by short-range power-law interactions, where correlations among particles are taken into account. In the former case, several studies presented a consistent thermodynamic framework based on the definition of an effective temperature θ (presenting experimental values much higher than typical room temperatures T, so that thermal noise could be neglected), conjugated to a generalized entropy sν (with ν=2). Herein, the whole thermodynamic scheme is revisited and extended to systems of particles interacting repulsively, through short-ranged potentials, described by an entropy sν, with ν>1, covering the ν=2 (vortices in type-II superconductors) and ν>2 (short-range power-law interactions) physical examples. One basic requirement concerns a cutoff in the equilibrium distribution Peq(x), approached due to a confining external harmonic potential, ϕ(x)=αx2∕2 (α>0). The main results achieved are: (a) The definition of an effective temperature θ conjugated to the entropy sν; (b) The construction of a Carnot cycle, whose efficiency is shown to be η=1−(θ2∕θ1), where θ1 and θ2 are the effective temperatures associated with two isothermal transformations, with θ1>θ2; (c) Thermodynamic potentials, Maxwell relations, and response functions. The present thermodynamic framework, for a system of interacting particles under the above-mentioned conditions, and associated to an entropy sν, with ν>1, certainly enlarges the possibility of experimental verifications.

Generalized Maxwell Relations in Thermodynamics with Metric Derivatives

In this contribution, we develop the Maxwell generalized thermodynamical relations via the metric derivative model upon the mapping to a continuous fractal space. This study also introduces the total q-derivative expressions depending on two variables, to describe nonextensive statistical mechanics and also the α -total differentiation with conformable derivatives. Some results in the literature are re-obtained, such as the physical temperature defined by Sumiyoshi Abe.

Magnetic properties and magnetocaloric effect in La0.7Sr0.3−xBixMnO3 manganites

Structural properties, magnetization and magnetocaloric effect measurements in the compounds based on lanthanum–strontium–bismuth manganites La0.7Sr0.3−xBixMnO3 (LSBiMO) with 0.05⩽x⩽0.30 have been performed. The valence states of elements entering into the composition of investigated LSBiMO samples were analyzed for x=0.15 and 0.3 using the HR XPS spectra of Bi 4f, La 3d, Mn 3s and Sr 3d. According to X-ray powder diffraction data the crystalline structure of the samples is perovskite-like with a small rhombohedral distortion. The a and c lattice parameters and unit cell volume V are established to increase with increasing Bi content. All the manganites show ferromagnetic-like ordering with second order phase transition to paramagnetic state. The Curie temperature and magnetization decrease at substitution of Sr2+ for Bi3+ ions. The magnetic entropy changes were calculated using the field dependence of isothermal magnetization in the terms of the thermodynamic Maxwell relation. The maximum magnetic entropy change value was shown to be 0.94Jkg−1K−1 for x=0.05 for a field change of 1T.

Theoretical problems in solid electrocapillarity

The main problem in electrocapillarity of solid electrodes is the lack of clarity in determining the surface stress and basic equations. Within the framework of the Gibbs concept of geometrical dividing surface, the “surface stress” cannot be defined because methods of continuum mechanics can be applied to a physical surface layer (of finite thickness), but not to a mathematical surface. Gibbs never used the concept of surface stress, introducing only “surface tension” for a liquid electrode and “closely related quantity” for a solid electrode. Revisiting the derivation of the Gibbs adsorption equation, we prove its applicability to solid surfaces without the limiting requirement of constant state of strain, which was undeservedly interpreted by Eriksson as a shortcoming of the Gibbs theory caused to look for other approaches to surface stress problem. A critical analysis shows that the attempts (Shuttleworth, Eriksson, Couchman, Gokhstein, Weissmuller, etc.) to create a thermodynamic definition of the surface stress (as well as the formulation of fundamental thermodynamic equations and Maxwell relations operating with surface stresses) contain mathematical defects. It is shown that confusing interpretations of some Gibbs’ concepts encountered in the literature have led to “modifications” of the Lippmann equation based on the critical error in the Gibbs–Duhem relation due to the occurrence of an extensive variable, which is inadmissible. The famous Lippmann equation should not be modified, and it remains a unique electrocapillary relation applicable to liquid and solid electrodes.

Comparison of magnetocaloric properties of the Mn2−xFexP0.5As0.5 (x = 1.0 and 0.7) compounds

The Mn2−xFexP0.5As0.5 compounds (x = 0.7 and 1.0) studied exhibit the magnetic phase transitions, which are accompanied by a magnetic entropy change. For x = 1 the PM–FM transition is of the first order one with a weak (2–3 K) thermal hysteresis in the vicinity of TC = 275 K. The Mn1.3Fe0.7P0.5As0.5 compound possesses two magnetic transitions: the second-order PM–FM transition at TC = 190 K, followed by the FM–AFM transition at TN = 90 K, leading to normal and inverse magnetocaloric effects, respectively. The maximum values of magnetic entropy change are equal to 17 J kg−1 K−1 in MnFeP0.5As0.5 and 5 J kg−1 K−1 in Mn1.3Fe0.7P0.5As0.5 for a field change of 5 T. The magnetic entropy changes were calculated using both the isofield magnetization curves versus temperature and the isothermal magnetization curves versus applied magnetic field. The magnetocaloric effect in MnFeAs0.5P0.5 is discussed in the terms of both the thermodynamic Maxwell relation and the Clausius–Clapeyron equation.

Giant magnetic entropy change in manganese perovskite La0.67Sr0.16Ca0.17MnO3 near room temperature

Structural, magnetic and magnetocaloric properties of La0.67Sr0.16Ca0.17MnO3 perovskite have been studied. A solid state reaction method was used in the preparation phase. X-ray diffraction analysis using Rietveld refinement revealed that this sample crystallizes in the distorted rhombohedral system with R3‾c space group. The variation of magnetization (M) vs. temperature (T), under an applied magnetic field of 0.05T, revealed a transition from a ferromagnetic (FM) to paramagnetic (PM) phase at around Curie temperature (TC=336K). Using Arrott plots, it was found that the transition is of a second-order. Isothermal measurements of magnetization allow us, through thermodynamic Maxwell relations, to determine the magnetic entropy change (ΔSM). A large ΔSM deduced from isothermal magnetization curves, has been observed in our sample with a peak centered around its respective TC. The maximum of the magnetic entropy change ΔSMmax in a magnetic field change of 5T is found to be 5.51Jkg−1K−1 at 335K. In addition, the compound showed a large relative cooling power (RCP) value of about 234J/kg while the maximum refrigerant capacity of 174J/kg was attained at the applied field of 5T. As a result, the studied sample can be considered as a potential material for magnetic refrigeration.

Effect of partial Gd substitution on the magnetic and magnetocaloric properties in Dy-Ho-Gd-Co multicomponent compounds

The magnetic and magnetocaloric properties of polycrystalline (Dy0.9Ho0.1)1−xGdxCo2 (0.0 ≤ x ≤ 0.15) solid solutions were investigated experimentally using magnetic measurements; the Landau theory was also applied to clarify peculiarities of the magnetic phase transition in the compounds. X-ray diffraction patterns taken at room temperature exhibit the existence of the C15 cubic Laves phase structure for all samples under study. The lattice parameter increased from 0.7186 for x = 0.0 to 0.7194 nm for x = 0.15 and the Curie temperature TC increases from 130 to 183 K as the Gd content increases to x = 0.15. The isothermal entropy change ΔSmag was calculated according to magnetic measurements using the thermodynamic Maxwell's relation. A decrease in entropy change with the increase of Gd content has been observed. Under an external field change of from 0 to 3 T, the maximum entropy change decreased from 8.1 for x = 0.0 to 4.3 J kg−1 K−1 for x = 0.15. The effect of increasing the Gd amount in the (Dy0.9Ho0.1)1−xGdxCo2 solid solutions on their magnetic and magnetocaloric properties is discussed.

Magnetocaloric effect of an Fe-based metallic glass compared to benchmark gadolinium

We report on the magnetocaloric effect in an Fe-based metallic glass (Fe80B12Nb8) as compared to the benchmark material gadolinium. From temperature-dependent magnetization measurements, the magnetic entropy change was calculated using the thermodynamic Maxwell relations. The adiabatic temperature change was directly measured for both materials using a dedicated setup. An analysis of the magnetic transition in amorphous Fe80B12Nb8 and crystalline gadolinium using a mean field and a phenomenological model was carried out. It was shown that both materials, in particular crystalline gadolinium, which does not possess structural disorder but merely a fluctuation of the exchange integral, can be described using the Handrich model for the magnetic transition of disordered materials. Furthermore, the Landau theory of second-order phase transitions quantitatively describes the magnetic entropy change and its dependence on the applied field very well for both materials with different definitions of disorder.

The influence of Er substitution on magnetic and magnetocaloric properties of Ho1−xErxCo2 solid solution

In this work we report on the structural, magnetic and magnetocaloric properties of polycrystalline Ho1−xErxCo2 solid solutions (0.1 ≤ x ≤ 0.5). Powder X-ray diffraction study at room temperature showed that the compounds crystallize in the C15 cubic Laves phase structure (MgCu2 type). The magnetization behavior and magnetic transitions are analyzed in terms of Landau theory. Curie temperatures (TC) of Ho1−xErxCo2 decrease from 72 K in Ho0.9Er0.1Co2 to 50 K in Ho0.5Er0.5Co2. The magnetic measurements show that the compounds undergo a first-order phase transition from paramagnetic to a ferrimagnetic state at TC. A large isothermal entropy change ΔS is calculated from the magnetization curves using the thermodynamic Maxwell's relations observed for Ho1−xErxCo2 with all Er concentrations under study. The maximum effect of ∼5.4 J mol−1 K−1 is found in Ho0.6Er0.4Co2 (TC = 56 K) as the field changes from 0 to 3 T.