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.

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.

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.

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 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 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 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.

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.

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.

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.

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.

Magnetic properties and magnetocaloric effects in NaZn_(13)-type La(Fe,Al)(13)-based compounds

In this article, our recent progress concerning the effects of atomic substitution, magnetic field, and temperature on the magnetic and magnetocaloric properties of the LaFe13-xAlx compounds are reviewed. With an increase of the aluminum content, the compounds exhibit successively an antiferromagnetic （AFM） state, a ferromagnetic （FM） state, and a mictomagnetic state. Furthermore, the AFM coupling of LaFe13 -xAlx can be converted to an FM one by substituting Si for A1, Co for Fe, and magnetic rare-earth R for La, or introducing interstitial C or H atoms. However, low doping levels lead to FM clusters embedded in an AFM matrix, and the resultant compounds can undergo, under appropriate applied fields, first an AFM-FM and then an FM-AFM phase transition while heated, with significant magnetic relaxation in the vicinity of the transition temperature. The Curie temperature of LaFe13-xAlx can be shifted to room temperature by choosing appropriate contents of Co, C, or H, and a strong magnetocaloric effect can be obtained around the transition temperature. For example, for the LaFel 1.5All.5Co.2Hl.o compound, the maximal entropy change reaches 13.8 J.kg-1.K-1 for a field change of 0-5 T, occurring around room temperature. It is 42% higher than that of Gd, and therefore, this compound is a promising room-temperature magnetic refrigerant.

Giant magnetocaloric effect in the Gd_5 Ge_(2.025)Si_(1.925)In_(0.05) compound

The magnetocaloric properties of the GdsGe2.025Si1.925In0.05 compound have been studied by x-ray diffraction, magnetic and heat capacity measurements. Powder x-ray diffraction measurement shows that the compound has a dominant phase of monoclinic Cd5Ge2Si2-type structure and a small quantity of Gds（Ge,Si）3-type phase at room temperature. At about 270 K, this compound shows a first order phase transition. The isothermal magnetic entropy change （△SM） is calculated from the temperature and magnetic field dependences of the magnetization and the temperature dependence of MCE in terms of adiabatic temperature change （△Tad） is calculated from the isothermal magnetic entropy change and the temperature variation in zero-field heat-capacity data. The maximum △SM is -13.6 J·kg^-1.K^- 1 and maximum ATad is 13 K for the magnetic field change of 0 5 T. The Debye temperature （θD） of this compound is 149 K and the value of DOS at the Fermi level is 1.6 states/eV.atom from the low temperature zero-field heat-capacity data. A considerable isothermal magnetic entropy change and adiabatic temperature change under a field change of 0-5 T jointly make the Gd5Ge2.025Si1.925In0.05 compound an attractive candidate for a magnetic refrigerant.

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.

The magnetic properties and magnetocaloric effects in binary R-T(R = Pr,Gd,Tb,Dy,Ho,Er,Tm;T = Ga,Ni,Co,Cu)intermetallic compounds

In this paper, we review the magnetic properties and magnetocaloric effects（MCE） of binary R–T（R = Pr, Gd, Tb,Dy, Ho, Er, Tm; T = Ga, Ni, Co, Cu） intermetallic compounds（including RGa series, RNi series, R_（12）Co_7 series, R_3 Co series and RCu_2series）, which have been investigated in detail in the past several years. The R–T compounds are studied by means of magnetic measurements, heat capacity measurements, magnetoresistance measurements and neutron powder diffraction measurements. The R–T compounds show complex magnetic transitions and interesting magnetic properties.The types of magnetic transitions are investigated and confirmed in detail by multiple approaches. Especially, most of the R–T compounds undergo more than one magnetic transition, which has significant impact on the magnetocaloric effect of R–T compounds. The MCE of R–T compounds are calculated by different ways and the special shapes of MCE peaks for different compounds are investigated and discussed in detail. To improve the MCE performance of R–T compounds,atoms with large spin（S） and atoms with large total angular momentum（J） are introduced to substitute the related rare earth atoms. With the atom substitution, the maximum of magnetic entropy change（？SM）, refrigerant temperature width（Twidth）or refrigerant capacity（RC） is enlarged for some R–T compounds. In the low temperature range, binary R–T（R = Pr, Gd,Tb, Dy, Ho, Er, Tm; T = Ga, Ni, Co, Cu） intermetallic compounds（including RGa series, RNi series,R_（12）Co_7 series, R_3 Co series and RCu_2series） show excellent performance of MCE, indicating the potential application for gas liquefaction in the future.

Magnetocaloric Effect in Colossal Magnetoresistance Material (La_(0.6)Dy_(0.1))Sr_(0.3)MnO_3

The magnetocaloric effect in the A-site doping colossal magnetoresistance material (La_(0.6)Dy_(0.1))Sr_(0.3)MnO_3 was studied. From the measurement and calculation of isothermal magnetization (M-H) curves under various temperatures, a large magnetocaloric effect with ferromagnetic-paramagnetic transition, additional magnetism exchange action introduces additional magnetic entropy change was discovered. This result suggests that (La_(0.6)Dy_(0.1))Sr_(0.3)MnO_3 is a suitable candidate as working substance at room temperature in magnetic refrigeration technology.

Magnetocaloric effect of (Gd_(1-x)Nd_x)Co_2 alloys in low magnetic field

The phases and magnetocaloric effect in the alloys （Gd1-xNdx）Co2 with x = 0, 0.1, 0.2, 0.3, and 0.4 were investigated by X-ray diffraction analysis and magnetization measurement. The samples are single phase with a cubic MgCu2-type structure. The To decreases obviously with increasing Nd content from 404 K of the alloy with x = 0 to 272 K of the alloy with x = 0.4; forx = 0.3, the To is 296 K, which is near room temperature. In the samples （Gd1-xNdx）Co2 with x = 0.0, 0.1, 0.2, 0.3, and 0.4, the maximum magnetic entropy change is 1.471, 1.228, 1.280, 1.381 and 1.610 J·kg^-1·K^-1, respectively, in the applied field range of 0-2.0 T. The results of Arrott plots confirmed that the transition type were second order magnetic transition forx = 0, 0.3, and 0.4.