Configurational entropy-induced phase transition in spinel LiMn_(2)O_(4)

The spinel-type LiMn_(2)O_(4) is a promising candidate as cathode material for rechargeable Li-ion batteries due to its good thermal stability and safety.Experimentally,it is observed that in this compound there occur the structural phase transitions from cubic(Fd3m)to tetragonal(I4_(1)/amd)phase at slightly below room temperature.To understand the phase transition mechanism,we compare the Gibbs free energy between cubic phase and tetragonal phase by including the configurational entropy.Our results show that the configurational entropy contributes substantially to the stability of the cubic phase at room temperature due to the disordered Mn^(3+)/Mn^(4+)distribution as well as the orientation of the Jahn-Teller elongation of the Mn^(3+)O_(6) octahedron in the the spinel phase.Meanwhile,the phase transition temperature is predicted to be 267.8 K,which is comparable to the experimentally observed temperature.These results serve as a good complement to the experimental study,and are beneficial to the improving of the electrochemical performance of LiMn_(2)O_(4) cathode.

Thermoelectric performance of(AgBiTe_(2))_(1-x)(SnTe)_(x) with stable cubic enabled by enhanced configurational entropy

ABX_(2)(A=Ag,Na,Cu;B=Sb,Bi;X=S,Se,Te)(GroupsⅠ-Ⅴ-Ⅵ_(2))compounds,which are all characterized by the ultralow lattice thermal conductivity because of their strong lattice anharmonicity caused by lone-pair electrons,have aroused wide attention in thermoelectric community.The practical application of thermoelectric devices usually requires both the compatible n-type and p-type materials simultaneously.However,most ofⅠ-Ⅴ-Ⅵ_(2)compounds are intrinsic p-type semiconductors,lacking their n-type counterparts for thermoelectrics.Herein,in this work,we increase the configuration entropy of AgBiTe_(2)by alloying SnTe,in order to stabilize the cubic phase at room temperature.With further optimization of thermal and electrical performance,the thermoelectric performance could be improved simultaneously in both n-and p-type(AgBiTe_(2))_(1-x)(SnTe)_(x)(x=0.3,0.4)solid solutions.Finally,p-type compound with the nominal composition of(AgBi_(0.99)Cd_(0.01)Te_(2))_(0.6)(SnTe)_(0.4)and n-type of(AgBiTe_(2))_(0.7)(SnTe)_(0.3)~Br 6%show the maximum zT of~0.33 and~0.21,at 381 and 423 K,respectively.

Determination of neutron-skin thickness using configurational information entropy

Configurational information entropy(CIE)theory was employed to determine the neutron-skin thickness of neutron-rich calcium isotopes.The nuclear density distributions and fragment cross sections in 350 MeV/u ^(40-60)Ca+^(9)Be projectile fragmentation reactions were calculated using a modified statistical abrasion-ablation model.CIE quantities were determined from the nuclear density,isotopic,mass,and charge distributions.The linear correlations between the CIE determined using the isotopic,mass,and charge distributions and the neutron-skin thickness of the projectile nucleus show that CIE provides new methods to extract the neutron-skin thickness of neutron-rich nuclei.

Configurational information entropy analysis of fragment mass cross distributions to determine the neutron skin thickness of projectile nuclei

Configurational information entropy(CIE)analysis has been shown to be applicable for determining the neutron skin thickness(δnp)of neutron-rich nuclei from fragment production in projectile fragmentation reactions.The BNN+FRACS machine learning model was adopted to predict the fragment mass cross-sections(σ_(A))of the projectile fragmentation reactions induced by calcium isotopes from ^(36)Ca to ^(56)Ca on a ^(9)Be target at 140MeV/u.The fast Fourier transform was adopted to decompose the possible information compositions inσA distributions and determine the quantity of CIE(S_(A)[f]).It was found that the range of fragments significantly influences the quantity of S_(A)[f],which results in different trends of S_(A)[f]~δnp correlation.The linear S_(A)[f]~δnp correlation in a previous study[Nucl.Sci.Tech.33,6(2022)]could be reproduced using fragments with relatively large mass fragments,which verifies that S_(A)[f]determined from fragmentσAis sensitive to the neutron skin thickness of neutron-rich isotopes.

Suppressing interfacial polarization via entropy increase strategy for superior energy-storage performance of Na_(0.5)Bi_(0.5)TiO_(3)-based ceramics

High entropy engineering has emerged as a new strategy to improve the energy storage density and efficiency of dielectric capacitors due to its unique design concept.However,the recyclable energy storage density(Wrec)reported so far has never exceeded 2 J/cm^(3) for the type of high-entropy ceramics with equimolar elements occupying A or B site.In order to improve this type high-entropy ceramics.Na_(0.5)Bi_(0.5)TiO_(3)(NBT)was used as the matrix,equimolar Sr^(2+),La^(3+),K^(+)and Ba^(2+)were gradually introduced into at the A-site of the matrix lattice to increase configurational entropy.The results show that the relaxor degree,band gap width,interfacial polarization,and breakdown field strength are effectively improved with increasing entropy.Among them,suppressing interfacial polarization is an important factor to increase the breakdown field strength and thus enhance the energy storage performance.The(Na1/6Bi1/6Sr1/6La1/6K1/6Ba1/6)TiO_(3)(NBSLKBT)sample with the highest configurational entropy shows an ultra-high Wrec of 9.8 J/cm^(3) and the energy storage efficiency(η=86.5%).This work demonstrates that entropy strategy for superior energy-storage performance still works on the above type high-entropy ceramics and opens up a new way of modulating interface polarization by entropy increase strategy.

A Novel Approach to Probability

When P indistinguishable balls are randomly distributed among L distinguishable boxes, and considering the dense system , our natural intuition tells us that the box with the average number of balls P/L has the highest probability and that none of boxes are empty;however in reality, the probability of the empty box is always the highest. This fact is with contradistinction to sparse system (i.e. energy distribution in gas) in which the average value has the highest probability. Here we show that when we postulate the requirement that all possible configurations of balls in the boxes have equal probabilities, a realistic “long tail” distribution is obtained. This formalism when applied for sparse systems converges to distributions in which the average is preferred. We calculate some of the distributions resulted from this postulate and obtain most of the known distributions in nature, namely: Zipf’s law, Benford’s law, particles energy distributions, and more. Further generalization of this novel approach yields not only much better predictions for elections, polls, market share distribution among competing companies and so forth, but also a compelling probabilistic explanation for Planck’s famous empirical finding that the energy of a photon is hv.

Regulating local chemistry in ZrCo-based orthorhombic hydrides via increasing atomic interference for ultra-stable hydrogen isotopes storage

Developing a universal and reliable strategy for the modulation of composition and structure of energy storage materials with stable cycling performance is vital for hydrogen and its isotopes storage advanced system,yet still challenging.Herein,an ultra-stable lattice structure is designed and verified to increase atomic chaos and interference for effectively inhibiting disproportionation reaction and improving cycling stability in ZrCo-based hydrogen isotopes storage alloy.After screening in terms of configuration entropy calculation,we construct Zr_(1-2)Nb_(x)Co_(1-2x)Cu_(x)Ni_(x)(x=0.15,0.2,0.25) alloys with increased atomic chaos,and successfully achieve stable isostructural de-/hydrogenation during 100 cycles,whose cycling capacity retentions are above 99%,much higher than 22.4%of pristine ZrCo alloy.Both theoretical analysis and experimental evidences indicate the high thermo-stability of orthorhombic lattice in Zr_(0.8)Nb_(0.2)Co_(0.6)Cu_(0.2)Ni_(0.2) alloy.Notably,the increased atomic chaos and interference in Zr_(0.8)Nb_(0.2)Co_(0.6)Cu_(0.2)Ni_(0.2) alloy causes regulation in hydrogen local chemical neighborhood,thereby confusing the hydrogen release order,which effectively eliminates lattice distortion and unlocks an ultrastable lattice structure.This study provides a new and comprehensive inspiration for hydrogen atoms transport behaviors and intrinsic reason of stable orthorhombic transformation,which can contribute to paving the way for other energy storage materials modulation.

Influence of high configuration entropy on damping behaviors of Ti-Zr-Hf-Ni-Co-Cu high entropy alloys

TiNi-based shape memory alloys(SMAs)have been used as damping materials to eliminate noise and mechanical vibration.However,their application is limited by low working temperatures and damping capacity.In this work,two novel Ti-Zr-Hf-Ni-Co-Cu high entropy shape memory alloys(HESMAs)with different transformation temperatures and damping properties were investigated.The results show that Ti_(25)Zr_(8)Hf_(17)Ni_(30)Co_(5)Cu_(15) has superior damping performance arising from martensitic transformation,shape memory effect(thermal cycle at constant load)as well as superelasticity.Compared to traditional TiNi-based SMAs,the as-cast HESMAs exhibit a much higher ultrahigh yield strength(∼2 GPa)and storage modulus(∼50 GPa).The high configuration entropy of the HESMAs with high uneven internal stress and severe lattice distortion is revealed as the underlying mechanisms governing distinctive damping performance.The effects of high configuration entropy and microheterogeneity on the martensitic transforma-tion behavior and damping performance of HESMAs are clarified in this work,which provides a basis for designing alloys with superior damping properties.

Stabilizing n-type cubic AgBiSe_(2) thermoelectric materials through alloying with PbS

Phase transition generates rapid changes of transport parameters and poor mechanical property,and thus restricts the application of thermoelectric materials.AgBiSe_(2) exhibits cubic phase at above 580 K with high-symmetry structure and low lattice thermal conductivity,indicating the potentiality of high thermoelectric performances.In this work,the cubic structure of AgBiSe_(2) was achieved at ambient conditions by alloying with PbS,enhancing the configurational entropy at both cationic and anionic sites.The cubic structure was rather stable after several measurement cycles.Nb substitution at cationic sites effectively reduced band gap,and increased both carrier concentration and effective mass.All samples exhibited relatively low lattice thermal conductivity(0.68-0.34 W/(m·K))in the temperature range of 300-773 K,due to the nanoscale inhomogeneity and the random distribution of multiple species at some atomic sites.A maximum zT of 0.65 at 773 K was obtained for(Ag_(0.99)Nb_(0.01)BiSe_(2))_(0.8)(PbS)_(0.2) sample.The entropy-driven structural stabilization is a promising strategy to achieve stable structure for practical thermoelectric applications.

Novel P2-type layered medium-entropy ceramics oxide as cathode material for sodium-ion batteries

High-entropy oxides(HEOs)and medium-entropy oxides(MEOs)are new types of single-phase solid solution materials.MEOs have rarely been reported as positive electrode material for sodium-ion batteries(SIBs).In this study,we first proposed the concept of the application of MEOs in SIBs.P2-type 3-cation oxide Na_(2/3)Ni_(1/3)Mn_(1/3)Fe_(1/3)O_(2)(NaNMF)and 4-cation oxide Na_(2/3)Ni_(1/3)Mn_(1/3)Fe_(1/3-x)Al_(x)O_(2)(NaNMFA)were prepared using the solid-state method,rather than the doping technology.In addition,the importance of the concept of entropy stabilization in material performance and battery cycling was demonstrated by testing 3-cation(NaNMF)and 4-cation(NaNMFA)oxides in the same system.Thus,NaNMFA can provide a reversible capacity of about 125.6 mAh-g”1 in the voltage range of 2-4.2 V,and has enhanced cycle stability.The capacity and decay law of the MEO batteries indicate that the configurational entropy(1.28 R(NaNMFA)>1.10 R(NaNMF))of the cationic system,is the main factor affecting the structural and cycle stability of the electrode material.This work emphasizes that the rational design of MEOs with novel structures and different electrochemically active elements may be the strategy for exploring high-performance SIB cathode materials in next-generation energy storage devices.

Entropy versus enthalpy in hexagonal-close-packed highentropy alloys

The addition of hexagonal-close-packed(hcp)non-rare-earth elements Zr,Ti and Co,to the 10-component hep rare-earth-based high-entropy alloys(HEAs)with a composition of ScYLaNdGdTbDyHoErLuX(X=Zr,Co and Ti)was investigated.The enthalpy of mixing between elements was found to have a significant effect on the formation of phases.The addition of Co combines with elements that had a strong chemical affinity to form intermetallic compounds by the effect of enthalpy.Ti was added with all elements with poor chemical affinity and exhibited rejection to form a phase alone.These were the two terminal manifestations of the role of enthalpy over entropy.Part of Zr was soluble in the matrix under the action of entropy,while the other part had a greater affinity for Sc than the other elements to form a precipitate under the action of enthalpy.This was the result of the local balance between the effect of enthalpy and entropy.The solid solution of the elements had different degrees of strengthening effect,among which Zr had the most excellent strengthening effect from 185 to 355 MPa,so the solid solution strengthening model and precipitation strengthening model were proposed to predict the strength of the alloy with the addition of Zr effectively.