Thermodynamic theory of flotation for a complex multiphase solid -liquid system and high-entropy flotation

The flotation of complex solid–liquid multiphase systems involve interactions among multiple components,the core problem facing flotation theory.Meanwhile,the combined use of multicomponent flotation reagents to improve mineral flotation has become an important issue in studies on the efficient use of refractory mineral resources.However,studying the flotation of complex solid–liquid systems is extremely difficult,and no systematic theory has been developed to date.In addition,the physical mechanism associated with combining reagents to improve the flotation effect has not been unified,which limits the development of flotation theory and the progress of flotation technology.In this study,we applied theoretical thermodynamics to a solid–liquid flotation system and used changes in the entropy and Gibbs free energy of the reagents adsorbed on the mineral surface to establish thermodynamic equilibrium equations that de-scribe interactions among various material components while also introducing adsorption equilibrium constants for the flotation reagents adsorbed on the mineral surface.The homogenization effect on the mineral surface in pulp solution was determined using the chemical potentials of the material components of the various mineral surfaces required to maintain balance.The flotation effect can be improved through synergy among multicomponent flotation reagents;its physical essence is the thermodynamic law that as the number of compon-ents of flotation reagents on the mineral surface increases,the surface adsorption entropy change increases,and the Gibbs free energy change of adsorption decreases.According to the results obtained using flotation thermodynamics theory,we established high-entropy flotation theory and a technical method in which increasing the types of flotation reagents adsorbed on the mineral surface,increasing the adsorption entropy change of the flotation reagents,decreasing the Gibbs free energy change,and improving the adsorption efficiency and stability of the flotation reagents improves refractory mineral flotation.

Magnetic properties and magnetic entropy changes of La1-xPrxFe11.5Si1.5 compounds with 0 ≤ x ≤ 0.5

Magnetic properties and magnetic entropy changes in LaFe11.5Si1.5 have been investigated by partially substituting Pr by La. It is found that La1-xPrxFe11.5Si1.5 compounds remain cubic NaZn13-type structures even when the Pr content is increased to 0.5, i.e. x = 0.5. Substitution of Pr for La leads to a reduction in both the crystal constant and the Curie temperature. A stepwise magnetic behaviour in the isothermal magnetization curves is observed, indicating that the characteristic of the itinerant electron metamagnetic （IEM） transition above Tc becomes more prominent with the Pr content increasing. As a result, the magnetic entropy change is remarkably enhanced from 23.0 to 29.4 J/kg·K as the field changes from 0 to 5T, with the value of x increasing from 0 to 0.5. It is more attractive that the magnetic entropy changes for all samples are shaped into high plateaus in a wide range of temperature, which is highly favourable for Ericsson-type magnetic refrigeration.

Magnetic entropy change and magnetic phase transition of LaFe11.4Al1.6Cx （x=0-0.8） compounds

The unit cell volume and phase transition temperature of LaFe11.4Al1.6Cx compounds have been studied. The magnetic entropy change, refrigerant capacity and the type of magnetic phase transition are investigated in detail for LaFe11.4Al1.6Cx with x=0.1, All the LaFe11.4Al1.6Cx （x=0-0.8） compounds have the cubic NaZn13-type structure. The addition of carbon atoms brings about a considerable increase in the lattice parameter. The bulk expansion results in the change of phase transition temperature （Tc）, Tc increases from 187K to 269 K with x varying from 0.1 to 0.8, Meanwhile an increase in the lattice parameter can also cause a change of the magnetic ground state from antiferromagnetic to ferromagnetic. Large magnetic entropy change IASI is found over a large temperature range around Tc and the refrigerant capacity is about 322J/kg for LaFe11.4Al1.6C0.1. The magnetic phase transition belongs in weakly first-order one for x=0.1.

Magnetic entropy change involving martensitic transition in NiMn-based Heusler alloys

Our recent progress on magnetic entropy change（S） involving martensitic transition in both conventional and metamagnetic NiMn-based Heusler alloys is reviewed.For the conventional alloys,where both martensite and austenite exhibit ferromagnetic（FM） behavior but show different magnetic anisotropies,a positive S as large as 4.1 J·kg^-1·K^-1 under a field change of 0-0.9 T was first observed at martensitic transition temperature T M～197 K.Through adjusting the Ni：Mn：Ga ratio to affect valence electron concentration e/a,T M was successfully tuned to room temperature,and a large negative S was observed in a single crystal.The △S attained 18.0 J·kg^-1·K^-1 under a field change of 0-5 T.We also focused on the metamagnetic alloys that show mechanisms different from the conventional ones.It was found that post-annealing in suitable conditions or introducing interstitial H atoms can shift the T M across a wide temperature range while retaining the strong metamagnetic behavior,and hence,retaining large magnetocaloric effect（MCE） and magnetoresistance（MR）.The melt-spun technique can disorder atoms and make the ribbons display a B2 structure,but the metamagnetic behavior,as well as the MCE,becomes weak due to the enhanced saturated magnetization of martensites.We also studied the effect of Fe/Co co-doping in Ni 45（Co1-xFex）5 Mn36.6In13.4 metamagnetic alloys.Introduction of Fe atoms can assist the conversion of the Mn-Mn coupling from antiferromagnetic to ferromagnetic,thus maintaining the strong metamagnetic behavior and large MCE and MR.Furthermore,a small thermal hysteresis but significant magnetic hysteresis was observed around TM in Ni51Mn49-xInx metamagnetic systems,which must be related to different nucleation mechanisms of structural transition under different external perturbations.

Magnetoresistances and magnetic entropy changes associated with negative lattice expansions in NaZn13-type compounds LaFeCoSi

Magnetoresistances and magnetic entropy changes in NaZn13-type compounds La（Fel-xCox）11.9Si1.1 （x=0.04, 0.06, and 0.08） with Curie temperatures of 243 K, 274 K, and 301 K, respectively, are studied. The ferromagnetic ordering is accompanied by a negative lattice expansion. Large magnetic entropy changes in a wide temperature range from ～230 K to ～320 K are achieved. Raising Co content increases the Curie temperature but weakens the magnetovolume effect, thereby causing a decrease in magnetic entropy change. These materials exhibit a metallic character below Tc, whereas the electrical resistance decreases abruptly and then recovers the metal-like behaviour above Tc. Application of a magnetic field retains the transitions via increasing the ferromagnetic ordering temperature. An isothermal increase in magnetic field leads to an increase in electrical resistance at temperatures near but above Tc, which is a consequence of the field-induced metamagnetic transition from a paramagnetic state to a ferromagnetic state.

Relationship Between Magnetic Field-Induced Entropy Change and Magnetic Field

The ingots with the composition oi LaFe13-x Six （ 1.2 〈 x 〈 2.2） were prepared by arc-melting, and subsequently homogenized by annealing for a long time. The sample was mainly composed of a single NaZn13-type phase. The dependence of magnetization on the magnetic field was measured at different temperatures for LaFe13- xSix （ 1.2 ≤ x ≤ 2.2） compound, and the entropy change （△S） was calculated using Maxwell relation. The variation of AS with H was discussed according to both the Landau second-order phase transition theory and the scaling law under mean-field approximation. The results show that the relation of △S ∝ H^2/3 is satisfied for the LaFe13-x Six compounds. The parameters obtained by the simulation of peak value of entropy change can be used to determine the degree of first-order magnetic phase transition. The present work may be useful for the research of the magnetic refrigeration.

Martensitic transformation and giant magnetic entropy change in Ni_(42.8)Mn_(40.3)Co_(5.7)Sn_(11.2) alloy

The crystal structure, phase transition, and magnetocaloric effect in Ni42.8Mn40.3Co5.7Sn11.2 alloy are investigated by structure analysis and magnetic measurements. A large magnetic entropy change of 45.6 J/kg.K is obtained at 215 K under a magnetic field of 30 kOe （1 Oe = 79.5775 A.m-1）. The effective refrigerant capacity of Ni42.8Mn40.3Co5.7Sn11.2 alloy reaches 72.1 J/kg under an applied field changing from 0 to 30 kOe. The external magnetic field shifts the martensitic transition temperature about 3-4 K/10 kOe towards low temperature, indicating that magnetic field can retard the phase transition to a certain extent. The origin of large magnetic entropy change is discussed in the paper.

Magnetic Transition and Magnetic Entropy Change of Gd_5Si_(1.75)Ge_(1.75)Sn_(0.5)

Gd5Si1.75 Ge1.75 Sn0.5 was prepared by arc melting method. The crystal structure and magnetic properties were investigated by XRD and VSM, respectively. The magnetization of the Gd5Si1.75 Ge1.75 Sn0.5 alloy changes abruptly near its corresponding Curie temperature 269 K, possesses a typical first which means that the alloy order phase transition. The Gd5Si1.75Ge1.75 Sn0.5 adopts in Gd5Si2Ge2-type monoclinic structure at room temperature, the maximal magnetic entropy change at a magnetic field change of 1.8 T is as large as 16.7 J·kg^-1·K^-1, exceeding that of Gd about two times and is a little larger than that of Gd5Si2Ge2.

Magnetic Entropy Change of (Gd_(1-x)RE_x)_5Si_4(RE=Dy, Ho) Alloys

The magnetic properties, including Curie points, magnetic phases transition and magnetic entropy changes, of （Gd1-xREx）5Sin（RE = Dy, Ho） alloys were systematically studied. The results show that the alloys keep the Sm5Ge4 orthorhombic structures as Gd5Si4, and the Curie points of the alloys almost linearly decrease with increasing content of x, so that the Curie points can be adjusted by adding different concentrations of Dv or Ho in the alloys. The magnetic properties of these alloys obey second order transition. The costs of these alloys are cheaper than that of Gd- Si-Ge alloys because there is not expensive element such as Ge. The large magnetic entropy change at low fields （ 〈 2 T） and wide temperature ranges of these alloys suggest that they are suitable to be the gradient function materials and candidates of magnetic refrigerants at room temperature with low fields.

Magnetic Field Induced Entropy Change for La-Fe Based NaZn_(13)-Typed Compounds

Magnetic field induced entropy change was investigated for La-Fe based NaZn13-type compounds with magnetic first-order phase transition. In view of magnetic refrigeration at room temperature, the developing of the materials and the understanding of the entropy change were., reviewed. For La-Fe-Si compounds, the entropy change about 29 J·kg^- 1·K^-1 was obtained at 190 K under the magnetic field of 5 T.While a large entropy change of about 15 J·kg^-1·K^-1 near room temperature under 5 T can be obtained by the substitution of Co for Fe in the compounds. It is found that the entropy change is mainly composed of that contributed from magnetic ordering and crystal lattice. The large entropy change consumed by lattice contribution is mainly due to the magnetic ordering one.

Coexistence of positive and negative magnetic entropy changes in CeMn_2(Si_(1-x)Ge_x)_2 compounds

A series of CeMn2（Si1-xGex）2（x = 0.2, 0.4, 0.6, 0.8） compounds are prepared by the arc-melting method. All the samples primarily crystallize in the Th Cr2Si2-type structure. The temperature dependences of zero-field-cooled（ZFC） and FC magnetization measurements show a transition from antiferromagnetic（AFM） state to ferromagnetic（FM） state at room temperature with the increase of the Ge concentration. For x = 0.4, the sample exhibits two kinds of phase transitions with increasing temperature： from AFM to FM and from FM to paramagnetic（PM） at around TN-197 K and T C-300 K,respectively. The corresponding Arrott curves indicate that the AFM–FM transition is of first-order character and the FM–PM transition is of second-order character. Meanwhile, the coexistence of positive and negative magnetic entropy changes can be observed, which are corresponding to the AFM–FM and FM–PM transitions, respectively.

Study on structure and magnetic entropy changes of Ce_(2-x)Pr_xFe_(16.5)Co_(0.5) alloys

A series of Ce2-xPrxFe16.5Co0.5 alloys were prepared by arc melting under purified argon atmosphere. The structure and magnetic entropy changes in Ce2-xPrxFe16.5Co0.5 alloys were investigated by means of X-ray diffraction pattern and MPMS XL-7 magnetometer. The experimental results show that the crystal structure of Ce2-xPrxFe16.5Co0.5 alloys keeps in Th2Zn17-type rhombohedral, and the Curie temperature of Ce2-xPrxFe16.5Co0.5 alloys can be shifted to room temperature around by a composition adjustment. The magnetic entropy changes (-ΔSM) in Ce2-xPrxFe16.5Co0.5 alloys are relatively large, and a platform of magnetic entropy changes appears near the temperature TC. Ce2-xPrxFe16.5Co0.5 alloys are the potential working media for magnetic refrigeration with their stable chemical properties and especially low price.

Magnetic Phase Transition and Magnetic Entropy Change in La_(0.8)Pr_(0.2)Fe_(11.4)Si_(1.6) Compound

The magnetic properties and the phase transformation of the partial substitution of Pr for La in LaFe11.4Si1.6 have been investigated by the means of X-ray diffraction (XRD) and vibrating sample magnetic (VSM). The results indicated that the single phase NaZn13-type cubic structure is stabilized for the compound La0.8Pr0.2Fe11.4Si1.6 and large values of the isothermal magnetic entropy change SM around the curie temperature TC～194 K in relative low magnetic fields. The maximum value︱SM︱max～37.07 J/kg·K-1 under a field of 1.5 T. Such large MCEs are attributed to the sharp change of the magnetization at the Curie temperature, the field-induced IEM transition and a strong temperature dependence of the critical field BC.

Study of Magnetic Entropy Changes in Gd1-x Tx ( T = Ti, Cr, Fe and Cu) Alloys

Magnetic refrigeration techniques based on the magnetocaloric effect (MCE) were demonstrated as a promising alternative to conventional vapour-cycle refrigeration.Recently, scientists focused their research on room temperature magnetic refrigeration.The rare earth Gd metal is regarded as a prototype for room temperature magnetic refrigerant.Considering the various requirements in application, it is necessary to search for the magnetic refrigerant possessing qualities as good as Gd but having different Tc above or below room temperature.In this article, we report the magnetic entropy changes in Gd1 -xTx(T = Ti, Cr, Fe and Cu) alloys.With a small quantity of T atoms introduced in Gd, the Curie temperature increases.The values of magnetic entropy change in these alloys are almost the same as or a little less than that of Gd.But the refrigerant capacities of these alloys are obviously larger than that of Gd.All these facts suggest that Gd1-xTx(T = Ti, Cr, Fe and Cu) alloys may be good refrigerants for room temperature magnetic refrigeration.

Entropy and heat generation of lithium cells/batteries

The methods and techniques commonly used in investigating the change of entropy and heat generation in Li cells/batteries are introduced, as are the measurements, calculations and purposes. The changes of entropy and heat generation are concomitant with the use of Li ceUs/batteries. In order to improve the management and the application of Li cells/batteries, especially for large scale power batteries, the quantitative investigations of the change of entropy and heat generating are necessary.

Entropy change-induced elastic softening of lithiated materials

To understand the ＂elastic softening＂ of Li-Si alloys for the development of Li-ion batteries, the effect of stress-induced change of entropy on the mechanical properties of lithiated materials is examined within the theories of thermodynamics and linear elasticity, An approach is presented whereby the change of Gibbs free energy is governed by the change of the mixture entropy due to stress-induced migration of mobile atoms, from which the contribution of the change of the mixture entropy to the apparent elastic modulus of lithiated materials is determined. The reciprocal of the apparent elastic modulus of a lithiated material is a linear function of the concentration of mobile Li-atoms at a stress-free state and the square of the mismatch strain per unit mole fraction of mobile Li-atoms.

Giant reversible barocaloric effects with high thermal cycle stability in epoxybonded(MnCoGe)_(0.96)(CuCoSn)_(0.04) composite

Hexagonal MnMX-based(M=Co or Ni,X=Si or Ge)alloys exhibit giant reversible barocaloric effects.However,giant volume expansion would result in the as-cast MnMX ingots fragmenting into powders,and inevitably bring the deterioration of mechanical properties and formability.Grain fragmentation can bring degradation of structural transformation entropy change during cyclic application and removal of pressure.In this paper,giant reversible barocaloric effects with high thermal cycle stability can be achieved in the epoxy bonded(MnCoGe)0.96(CuCoSn)0.04 composite.Giant reversible isothermal entropy change of 43.0 J·kg^(−1)·K^(−1) and adiabatic temperature change from barocaloric effects(ΔT_(BCE))of 15.6 K can be obtained within a wide temperature span of 30 K at 360 MPa,which is mainly attributed to the integration of the change in the transition temperature driven by pressure of−101 K·GPa^(−1) and suitable thermal hysteresis of 11.1 K.Further,the variation of reversibleΔ_(TBCE) against the applied hydrostatic pressure reaches up to 43 K·GPa^(−1),which is at the highest level among the other reported giant barocaloric compounds.More importantly,after 60 thermal cycles,the composite does not break and the calorimetric curves coincide well,demonstrating good thermal cycle stability.

Control of interfacial reaction and defect formation in Gd/Bi_(2)Te_(2.7)Se_(0.3) composites with excellent thermoelectric and magnetocaloric properties

The method to combine thermoelectric(TE)and magnetocaloric(MC)cooling techniques lies in developing a new material that simultaneously possesses a large TE and good MC cooling performance.In this work,using n-type Bi_(2)Te_(2.7)Se_(0.3)(BTS)as the TE base material and Gd as the second-phase MC material,Gd/BTS composites were prepared by the spark plasma sintering method.In the composites,interfacial reaction between Gd and BTS was identified,resulting in the formation of Gd Te,which has a large impact on the electron concentration through the adjustment of defect concentration.The MC/TE composite containing 2.5 wt%Gd exhibited a ZT value of 0.6 at 300 K,essentially retaining the original TE performance,while all the composites largely maintained the excellent MC performance of Gd.This work provides a potential pathway to achieving high performance in MC/TE composites.

Kinetic Implication from Temperature Effect on Hydrogen Evolution Reaction at Ag Electrode

Hydrogen evolution reaction （HER） at polycrystalline silver electrode in 0.1 mol/L HClO4 solution is investigated by cyclic voltammetry in the temperature range of 278-333 K. We found that at electrode potential φa,app decreases with φ, while pre-exponential factor A remains nearly unchanged,which conforms well the prediction from Butler-Volmer equation. In contrast, with φ nega-tive shifts from the onset potential for HER to the potential of zero charge （PZC≈-0.4 V）, both Ea,app and A for HER increase （e.g., Ea,app increases from 24 kJ/mol to 32 kJ/mol）. The increase in Ea,app and A with negative shift in φ from -0.25 V to PZC is explained by the increases of both internal energy change and entropy change from reactants to the transition states, which is correlated with the change in the hydrogen bond network during HER. The positive entropy effects overcompensate the adverse effect from the increase in the activation energy, which leads to a net increase in HER current with the activation energy negative shift from the onset potential of HER to PZC. It is pointed out that entropy change may contribute greatly to the kinetics for electrode reaction which involves the transfer of electron and proton, such as HER.

Magnetocaloric effects in RT X intermetallic compounds(R = Gd–Tm, T = Fe–Cu and Pd, X = Al and Si)

The magnetocaloric effect（MCE） of RT Si and RT Al systems with R = Gd–Tm, T = Fe–Cu and Pd, which have been widely investigated in recent years, is reviewed. It is found that these RT X compounds exhibit various crystal structures and magnetic properties, which then result in different MCE. Large MCE has been observed not only in the typical ferromagnetic materials but also in the antiferromagnetic materials. The magnetic properties have been studied in detail to discuss the physical mechanism of large MCE in RT X compounds. Particularly, some RT X compounds such as Er Fe Si,Ho Cu Si, Ho Cu Al exhibit large reversible MCE under low magnetic field change, which suggests that these compounds could be promising materials for magnetic refrigeration in a low temperature range.