Entropy Release Research Articles

Synthesis, crystal structure, and thermodynamic properties of two new selenate chlorides: M2Cu(SeO4)Cl2 with M = K and Rb

Two new selenate chlorides have been prepared for the first time by hydrothermal method. Their crystal structures have been determined. Both compounds are related to the chlorothionite mineral structure type but not isostructural to each other. K2Cu(SeO4)Cl2 crystallize in the orthorhombic system with the space group Pnma (#62) and unit cell parameters a = 7.7941(2)Å, b = 6.1297(2) Å, c = 16.6644(5) Å, V = 796.15(4) Å3, Z = 4 whereas Rb2Cu(SeO4)Cl2 crystallize in monoclinic system, P21/n (#14), and parameters a = 8.0701(3), b = 12.9474(5), c = 16.9354(7), β = 103.657(2)°, V = 1719.49(12) Å3, Z = 8. Potassium compound are isostructural to the related sulfate chloride, while rubidium selenate is differ from their sulfate analogue and from prototype compound K2Cu(SO4)Cl2. Both examined crystal structures feature copper ions in planar coordination CuO2Cl2 which form isolated magnetic chains along ⟨0 1 0⟩ direction in the structure. The study of M2Cu(SeO4)Cl2 was carried out in measurements of magnetic susceptibility χ(T) = M/B in the temperature range 2–350 K, magnetization M(B) at 2 K and specific heat Cp(T) in the range 2–120 K. At lowering temperature, the magnetic susceptibility exhibits no anomalies and follows by Curie law. An increase of the Cp(T) curve below 3 ÷ 8 K indicates the release of magnetic entropy. The study of thermodynamic properties unexpectedly shows that the investigated selenates M2Cu(SeO4)Cl2 (M = K and Rb) behave like paramagnets and the interaction between copper ions in the structural chains is negligible, opposite related sulfates demonstrating 1D magnetic behavior for Cu2+ magnetic ions.

J_{eff}=1/2 Hyperoctagon Lattice in Cobalt Oxalate Metal-Organic Framework.

We report the magnetic properties of a cobalt oxalate metal-organic framework featuring the hyperoctagon lattice. Our thermodynamic measurements reveal the J_{eff}=1/2 state of the high-spin Co^{2+} (3d^{7}) ion and the two successive magnetic transitions at zero field with two-stage entropy release. ^{13}C-NMR measurements reveal the absence of an internal magnetic field in the intermediate temperature phase. Multiple field-induced phases are observed before full saturation at around 40T. We argue the unique cobalt oxalate network gives rise to the Kitaev interaction and/or a bond frustration effect, providing an unconventional platform for frustrated magnetism on the hyperoctagon lattice.

A New Theory about Interfacial Proton Diffusion Revisited: The Commonly Accepted Laws of Electrostatics and Diffusion Prevail.

The high propensity of protons to stay at interfaces has attracted much attention over the decades. It enables long-range interfacial proton diffusion without relying on titratable residues or electrostatic attraction. As a result, various phenomena manifest themselves, ranging from spillover in material sciences to local proton circuits between proton pumps and ATP synthases in bioenergetics. In an attempt to replace all existing theoretical and experimental insight into the origin of protons' preference for interfaces, TELP, the "Transmembrane Electrostatically-Localized Protons" hypothesis, has been proposed. The TELP hypothesis envisions static H+ and OH- layers on opposite sides of interfaces that are up to 75 µm thick. Yet, the separation at which the electrostatic interaction between two elementary charges is comparable in magnitude to the thermal energy is more than two orders of magnitude smaller and, as a result, the H+ and OH- layers cannot mutually stabilize each other, rendering proton accumulation at the interface energetically unfavorable. We show that (i) the law of electroneutrality, (ii) Fick's law of diffusion, and (iii) Coulomb's law prevail. Using them does not hinder but helps to interpret previously published experimental results, and also helps us understand the high entropy release barrier enabling long-range proton diffusion along the membrane surface.

Crystal growth and magnetic properties of the coupled alternating S=1 spin chain Sr2Ni(SeO3)3

The structural, magnetic, and thermodynamic properties of a quasi-one-dimensional (1D) $S=1$ alternating spin chain compound ${\mathrm{Sr}}_{2}\mathrm{Ni}{(\mathrm{Se}{\mathrm{O}}_{3})}_{3}$ are investigated by using synchrotron x-ray powder diffraction, magnetic susceptibility $\ensuremath{\chi}(H,T)$, and heat capacity ${C}_{\mathrm{P}}(H,T)$ measurements together with density functional theory (DFT) calculations. The $\ensuremath{\chi}(H,T)$ and ${C}_{\mathrm{P}}(H,T)$ data reveal long-range antiferromagnetic order at ${T}_{\mathrm{N}}=3.4(3)$ K and short-range order at ${T}_{\mathrm{m}}\ensuremath{\approx}7.8\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The short-range magnetic order together with 95% of spin entropy release above ${T}_{\mathrm{N}}$ signifies the importance of 1D spin correlations persisting to $\ensuremath{\sim}8{T}_{\mathrm{N}}$. Theoretical DFT calculations with generalized gradient approximation determine leading exchange interactions, suggesting that interchain interactions are responsible for the observed long-range magnetic ordering. In addition, the temperature-field phase diagram of ${\mathrm{Sr}}_{2}\mathrm{Ni}{(\mathrm{Se}{\mathrm{O}}_{3})}_{3}$ is determined based on the $\ensuremath{\chi}(T,H)$ and ${C}_{\mathrm{P}}(T,H)$ data. Interestingly, a nonmonotonic phase boundary of ${T}_{\mathrm{m}}$ is found for an external field applied along a hard axis. Our results suggest that the ground state and magnetic behavior of ${\mathrm{Sr}}_{2}\mathrm{Ni}{(\mathrm{Se}{\mathrm{O}}_{3})}_{3}$ rely on the interplay of single-ion anisotropy, bond alternation, and interchain interactions.

Enhancement of the magnetocaloric effect in geometrically frustrated cluster spin glass systems

In this work, we theoretically demonstrate that a strong enhancement of the magnetocaloric effect is achieved in geometrically frustrated cluster spin-glass systems just above the freezing temperature. We consider a network of clusters interacting randomly which have triangular structure composed of Ising spins interacting antiferromagnetically. The intercluster disorder problem is treated using a cluster spin glass mean-field theory, which allows exact solution of the disordered problem. The intracluster part can be solved using exact enumeration. The coupling between the inter and intracluster problem incorporates the interplay between effects coming from geometric frustration and disorder. As a result, it is shown that there is the onset of cluster spin glass phase even with very weak disorder. Remarkably, it is exactly within a range of very weak disorder and small magnetic field that is observed the strongest isothermal release of entropy.

Open-Source Energy, Entropy, and Exergy 0D Heat Release Model for Internal Combustion Engines

Internal combustion engines face increased market, societal, and governmental pressures to improve performance, requiring researchers to utilize modeling tools capable of a thorough analysis of engine performance. Heat release is a critical aspect of internal combustion engine diagnostic analysis, but is prone to variability in modeling validity, particularly as engine operation is pushed further from conventional combustion regimes. To that end, this effort presents a comprehensive open-source, zero-dimensional equilibrium heat release model. This heat release analysis is based on a combined mass, energy, entropy, and exergy formulation that improves upon well-established efforts constructed around the ratio of specific heats. Furthermore, it incorporates combustion using an established chemical kinetics mechanism to endeavor to predict the global chemical species in the cylinder. Future efforts can augment and improve the chemical kinetics reactions for specific combustion conditions based on the radical pyrolysis of the fuel. In addition, the incorporation of theoretical calculations of energy and exergy based on the change in chemical species allows for cross-checking of combustion model validity.

Study of entropy production due to electroweak phase transition in Z2 symmetric extension of the Standard Model

In this work, we consider the simple ${Z}_{2}$ symmetric extension to the Standard Model (SM) and proceed to study the nature of electroweak phase transition (EWPT) in the early Universe. We show that the nature of the phase transition changes from a smooth crossover in the SM to a strong first order with this addition of the real scalar. Furthermore, we show that the entropy release in this scenario is higher than that of the SM. This can lead to a strong dilution of the energy density of gravitational waves, as we show in the latter part of the paper.

Possible quadrupole-order-driven commensurate-incommensurate phase transition in B20 CoGe

The B20-type cobalt germanide CoGe was investigated by measuring the specific heat, resistivity, and $^{59}$Co nuclear magnetic resonance (NMR). We observed a phase transition at $T_Q=13.7$ K, evidenced by a very narrow peak of the specific heat and sharp changes of the nuclear spin-spin ($T_2^{-1}$) and spin-lattice ($T_1^{-1}$) relaxation rates. The fact that the entropy release is extremely small and the Knight shift is almost independent of temperature down to low temperatures as anticipated in a paramagnetic metal indicates that the $T_Q$ transition is of non-magnetic origin. In addition, we detected a crossover scale $T_0\sim30$ K below which the resistivity and the NMR linewidth increase, and $T_1^{-1}$ is progressively distributed in space, that is, a static and dynamical spatial inhomogeneity develops. While the order parameter for the $T_Q$ transition remains an open question, a group-theoretical analysis suggests that the finite electric quadrupole density arising from the low local site symmetry at cobalt sites could drive the crystal symmetry lowering from the P2$_1$3 symmetry that is commensurate to the R3 symmetry with an incommensurate wavevector, which fairly well accounts for the $T_Q$ transition. The quadrupole-order-driven commensurate-incommensurate phase transition may be another remarkable phenomenon arising from the structural chirality inherent in the noncentrosymmetric B20 family.

Is the Second Law of Thermodynamics Able to Classify Drugs?

Specialization characterizes pharmacology, with the consequence of classifying the various treatments into unrelated categories. Treating a specific disease usually requires the design of a specific drug. The second law of thermodynamics is the driving force both for chemical reactions and for life. It applies to diseases and treatment. In most common diseases, there is a metabolic shift toward anabolism and anaerobic glycolysis, resulting in the release of entropy in the form of biomass. In accordance with the second principle of thermodynamics, treatment should aim at decreasing the entropy flux, which stays inside the body in the form of biomass. Most treatments aim at increasing the amount of entropy that is released by the cell in the form of thermal photons. As clinically different diseases often requires similar drugs, this calls for reinforcement in a quest for a single unified framework. For example, treatment of aggressive autoimmune diseases requires the same cytotoxic chemotherapy than for cancer. This strongly suggests that despite their apparent disparity, there is an underlying unity in the diseases and the treatments. The shift toward increased entropy release in the form of heat offers sound guidelines for the repurposing of drugs.

Particle Dark Matter Density and Entropy Production in the Early Universe

Dark Matter (DM) density is reduced if entropy production takes place after DM particles abundance is frozen out in the early universe. We study a possibility of such reduction due to entropy production in the electroweak phase transition (EWPT). We compare scenarios of entropy production in the standard model (SM) and its simplest extension, the two-Higgs doublet model (2HDM). Assuming the EWPT is of second order in the SM scenario and the first order in the 2HDM, we calculate the entropy release in these scenarios and the corresponding dilution of preexisting DM density in the early universe. We find the effect of dilution in EWPT significant for confrontation with observations of any form of possible DM (including primordial black holes (PBHs)), which is frozen out, decoupled, frozen in, or formed before EWPT.

Local strain-induced energy storage as driving force for autogenous scratch closure

In this work we rationalize the relationship between polymer architecture, energy stored during scratch damage, entropy release during healing and gap closure of scratches.

Physical properties of the quasi-two-dimensional square lattice antiferromagnet Ba2FeSi2O7

We report magnetization (\ensuremath{\chi}, $M$), magnetic specific heat (${C}_{\mathrm{M}}$), and neutron powder diffraction results on a quasi-two-dimensional (2D) $S=2$ square lattice antiferromagnet ${\mathrm{Ba}}_{2}{\mathrm{FeSi}}_{2}{\mathrm{O}}_{7}$ consisting of ${\mathrm{FeO}}_{4}$ tetrahedrons with highly compressive tetragonal distortion (27%). Despite of the quasi-2D lattice structure, both \ensuremath{\chi} and ${C}_{\mathrm{M}}$ present three-dimensional magnetic long-range ordering below the N\'eel temperature ${T}_{\mathrm{N}}=5.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Neutron diffraction data show a collinear ${\mathbit{Q}}_{\mathbit{m}}=$(1,0,1/2) antiferromagnetic (AFM) structure below ${T}_{\mathrm{N}}$ but the ordered moment aligned in the $ab$ plane is suppressed by 26% from the ionic spin $S=2$ value ($4{\ensuremath{\mu}}_{\mathrm{B}}$). Both the AFM structure and the suppressed moments are well explained by using Monte Carlo simulations with a large single-ion in-plane anisotropy $D=1$.4 meV and a rather small Heisenberg exchange ${J}_{\mathrm{intra}}=0$.15 meV in the plane. The characteristic 2D spin fluctuations are recognized in the magnetic entropy release and diffuse scattering above ${T}_{\mathrm{N}}$. This new quasi-2D magnetic system also displays unusual nonmonotonic dependence of ${T}_{\mathrm{N}}$ as a function of magnetic field $H$.

Metabolic Shifts as the Hallmark of Most Common Diseases: The Quest for the Underlying Unity.

A hyper-specialization characterizes modern medicine with the consequence of classifying the various diseases of the body into unrelated categories. Such a broad diversification of medicine goes in the opposite direction of physics, which eagerly looks for unification. We argue that unification should also apply to medicine. In accordance with the second principle of thermodynamics, the cell must release its entropy either in the form of heat (catabolism) or biomass (anabolism). There is a decreased flow of entropy outside the body due to an age-related reduction in mitochondrial entropy yield resulting in increased release of entropy in the form of biomass. This shift toward anabolism has been known in oncology as Warburg-effect. The shift toward anabolism has been reported in most diseases. This quest for a single framework is reinforced by the fact that inflammation (also called the immune response) is involved in nearly every disease. This strongly suggests that despite their apparent disparity, there is an underlying unity in the diseases. This also offers guidelines for the repurposing of old drugs.

Effect of structural disorder on the Kitaev magnet Ag3LiIr2O6

The search for an ideal Kitaev spin liquid candidate with anyonic excitations and long-range entanglement has motivated the synthesis of a new family of intercalated Kitaev magnets such as ${\mathrm{H}}_{3}\mathrm{Li}{\mathrm{Ir}}_{2}{\mathrm{O}}_{6}$, ${\mathrm{Cu}}_{2}\mathrm{Ir}{\mathrm{O}}_{3}$, and ${\mathrm{Ag}}_{3}\mathrm{Li}{\mathrm{Ir}}_{2}{\mathrm{O}}_{6}$. The absence of a susceptibility peak and a two-step release of the magnetic entropy in these materials have been proposed as evidence of proximity to the Kitaev spin liquid. Here we present a comparative study of the magnetic susceptibility, heat capacity, and muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) between two samples of ${\mathrm{Ag}}_{3}\mathrm{Li}{\mathrm{Ir}}_{2}{\mathrm{O}}_{6}$ in the clean and disordered limits. In the disordered limit, the absence of a peak in either susceptibility or heat capacity and the lack of zero-field muon precession in the $\ensuremath{\mu}\mathrm{SR}$ signal give the impression of a proximate spin liquid state. However, in the clean limit, peaks are resolved in both susceptibility and heat capacity, and spontaneous oscillations appear in the $\ensuremath{\mu}\mathrm{SR}$ signal, confirming long-range antiferromagnetic order in the ground state. The $\ensuremath{\mu}\mathrm{SR}$ oscillations fit to a Bessel function, characteristic of incommensurate order, as reported in the parent compound $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Li}}_{2}\mathrm{Ir}{\mathrm{O}}_{3}$. Our results clarify the role of structural disorder in the intercalated Kitaev magnets.

Ligand dependent magnetism of the = 3/2 Mott insulator Cs2 MX 6 (M = Ta, Nb, X = Br, Cl)

Magnetic and structural properties of double perovskite type bromides Cs2 MBr6 (M = Ta, Nb), where Ta4+ (5d 1) and Nb4+ (4d 1) ions form the face centered cubic lattice, are investigated and compared with chlorides Cs2 MCl6. Cs2TaBr6 exhibits the effective magnetic moment of 0.24 μ B, which is much smaller than the spin only value of a d 1 ion, 1.73 μ B, and comparable to 0.25 μ B in Cs2TaCl6. On the other hand, the effective magnetic moment of Cs2NbBr6 is 0.7 μ B and is substantially smaller than 1.0 μ B in Cs2NbCl6. On cooling, successive structural and magnetic phase transitions accompanying the release of electronic entropy approximately Rln 4 in total as expected for the J eff = 3/2 state are observed. The type of the ligand changes the temperature dependence of magnetic susceptibility at low temperature as well as its magnitude. The role of the ligands on the magnetism of J eff = 3/2 Mott insulators are discussed in the light of metal–ligand hybridization and the electron–lattice coupling.

Magnetic and magnetocaloric properties in GdZn2 synthesized by ball milling

In this study, we prepared GdZn2 by mechanical alloying method and measured its magnetization to reveal the magnetic and magnetocaloric properties. For a milling time (MT) ≥ 10 and 20 h, the GdZn2 phase was confirmed by X-ray diffraction measurements. For MT = 40 and 60 h, amorphous like patterns are observed. For MT = 10 and 20 h, magnetization (M) as a function of temperature below 80 K shows ferromagnetic-like increase. The observed values of M are 4.5 μB at 5 K for MT = 10 and 20 h, which is smaller than that of the theoretical expected value of 7 μB. For MT = 40 and 60 h, the long-range ferromagnetic order collapses because there is no spontaneous magnetization. The value of ΔT, where ΔT is the full width at half maximum of the magnetic entropy change (ΔSm (T)), increases significantly for MT ≤ 20 h because of the gradual release of magnetic entropy by the milling effect. Since M decreases with increasing MT, the maximum values of |ΔSm|, the relative cooling power, and the refrigerant capacity also decreases.

Strong magnetic anisotropy and unusual magnetic field reinforced phase in URhSn with a quasi-kagome structure

The physical properties of URhSn with quasi-kagome structure are studied using single-crystalline samples via electrical resistivity, magnetic susceptibility, heat capacity, thermal expansion, and high-field magnetization measurements. Remarkable magnetic anisotropy is found in the ferromagnetic (FM) state below ${T}_{\mathrm{C}}=16\phantom{\rule{4pt}{0ex}}\mathrm{K}$ as well as in the ordered state between ${T}_{\mathrm{C}}$ and ${T}_{\mathrm{O}}=54\phantom{\rule{4pt}{0ex}}\mathrm{K}$, where the easy and hard magnetization directions are the hexagonal [0001] and $[10\overline{1}0]$ axes. In the paramagnetic state, the magnetic susceptibility shows a Curie-Weiss behavior; the Weiss temperatures are positive and negative for [0001] and $[10\overline{1}0]$, respectively, indicating the presence of both FM and antiferromagnetic (AFM) correlations. The entropy release for $5f$ electrons is approximately $R\phantom{\rule{0.16em}{0ex}}\mathrm{ln}3$ at ${T}_{\mathrm{O}}$. The thermal expansion coefficient is strongly anisotropic around ${T}_{\mathrm{O}}$ between the hexagonal basal plane and the [0001] axis, indicating its remarkable anisotropic magnetoelastic response and uniaxial stress dependences. Interestingly, the magnetic field response of the higher-temperature ordered state is unusual: ${T}_{\mathrm{O}}(H)$ increases and the heat-capacity jump is enhanced with the magnetic field for $H\phantom{\rule{0.16em}{0ex}}||\phantom{\rule{4pt}{0ex}}[0001]$. Based on the established thermodynamic evidence for the second-order transition at ${T}_{\mathrm{O}}(H)$, a plausible scenario is the occurrence of a canted AFM ordering or a conical state under magnetic fields, which is stabilized when coupled with field-induced magnetic moments along the [0001] axis. Another possibility is the occurrence of quadrupole ordering at ${T}_{\mathrm{O}}(H)$.

Short Range Ordering (SRO) Reaction in Ni-base Alloy X-750

The short range ordering (SRO) reaction of the X-750 Ni-base alloy used as a garter spring material for CANDU reactors was systematically investigated through differential scanning calorimeter (DSC) analysis. Water quenching (WQ) after solution annealing (SA) and 20% cold rolled (CR) X-750 were prepared and these samples were subjected to ordering treatment at 475 <sup>o</sup>C for up to 2,160 hours. The WQ and CR specimens showed an exothermic reaction due to the release of entropy formed by the WQ and CR processes, respectively, whereas the ordered WQ and CR specimens exhibited endothermic reactions. The exothermic reaction from the WQ and CR specimens means the SRO reaction occurred. In the WQ specimen, two exothermic reactions at 577 <sup>o</sup>C and 671 <sup>o</sup>C were observed, which corresponds to SRO formation of Ni<sub>2</sub>Cr and CrFe, respectively. The critical temperature and thermal activation energy for these specimens were measured by varying the heating rate. The lattice variation with ordering time at 475 <sup>o</sup>C up to 2,160 hours was measured by XRD using CuKa X-ray. A 0.03-0.09% lattice contraction of the (200) plane occurred, depending on prior treatment condition. We discuss whether a lattice contraction due to SRO reaction may cause voids, providing formation sites for He bubbles in the X-750 garter spring exposed to the operating environment of the CANDU reactor.

Thermodynamic and transport properties in disordered Kitaev models

Effects of bond randomness and site dilution are systematically investigated for the Kitaev model describing a quantum spin liquid with fractional excitations of itinerant Majorana fermions and localized fluxes. We find that, in the high-temperature region where the itinerant Majorana fermions release their entropy, both types of disorders suppress the longitudinal thermal conductivity while keeping the specific heat almost unchanged. This suggests that both disorders reduce the mean-free path of the Majorana fermions. On the other hand, in the low-temperature region, the other specific heat peak associated with the entropy release from the localized fluxes is suppressed for both cases, but it is broadened and shifted to the lower-temperature side by the bond randomness, while the position and the width are almost unchanged against the site dilution. Contrasting behavior is also found in the thermal Hall effect under a magnetic field; the half quantization of the thermal Hall conductivity is fragile against the site dilution, while it remains for the bond randomness despite the reduced onset temperature. We discuss the contrasting behavior from the stability of the topological nature by calculating flux condensation and Majorana excitation gap.

Synthesis, Structure, and Anomalous Magnetic Ordering of the Spin-1/2 Coupled Square Tetramer System K(NbO)Cu4(PO4)4.

Quasi-zero-dimensional antiferromagnets with weakly coupled clusters of multiple spins can provide an excellent platform for exploring exotic quantum states of matter. Here, we report the synthesis and the characterization of a copper-based insulating antiferromagnet, K(NbO)Cu4(PO4)4. Single-crystal X-ray diffraction measurements reveal that the crystal structure belongs to the tetragonal space group P4/nmm, in which Cu2+ ions align to form a quasi-two-dimensional layer of spin-1/2 coupled square tetramers. The structure is quasi-isostructural to recently reported magnetoelectric antiferromagnets, A(TiO)Cu4(PO4)4 (A = Ba, Sr, and Pb) with the P4212 space group. Despite their structural similarities, whereas the antiferromagnetic transition in A(TiO)Cu4(PO4)4 produces conventional anomalies in magnetization and heat capacity, that in K(NbO)Cu4(PO4)4 has several unusual features such as an upturn in magnetic susceptibility and a very weak specific heat anomaly that corresponds to a spin entropy release as small as 3%. These results indicate that the magnetism of K(NbO)Cu4(PO4)4 is far different from that of A(TiO)Cu4(PO4)4 and suggest that the ground state is very close to a quantum nonmagnetic singlet state. The origin of the distinct magnetism in K(NbO)Cu4(PO4)4 is discussed in terms of structural modifications of a Cu4O12 unit forming a square tetramer. Our study demonstrates that the present material family, represented by an extended chemical formula A(BO)Cu4(PO4)4 (AB = KNb, BaTi, SrTi, and PbTi), has broad chemical controllability of their magnetism. This makes this system an attractive material platform to study the physics of quantum spin-1/2 coupled square tetramers.