Empirical Electron Theory Of Solids Research Articles

Valence electron structures and thermal and magnetic properties of RCo5 (R=light rare earth) intermetallic compounds with medium- and high-entropy design at R site

RCo5-type (R=light rare earth) medium- and high-entropy intermetallic compounds, which are designed by random occupation of equiatomic multiple rare earth elements at the rare earth site, are prepared by arc melting and vacuum heat-treatment technologies, and their crystal structures and magnetic properties are studied by X-ray diffraction and magnetic measurements. The empirical electron theory of solids and molecules is used to investigate their valence electron structures, thermal and magnetic properties. The theoretical bond lengths and magnetic moments match the experimental ones well. The study reveals that the thermal and magnetic properties are strongly related to the valence electron structures modulated by medium- and high-entropy design at rare earth. The medium and high entropized designs induce the increase of the covalence electron numbers nc. It is helpful for stabilizing the crystal structure. The number of covalence electron pair of the strongest R-CoI bond affects the melting point. The magnetic moments of RCo5-type medium- and high-entropy intermetallic compounds, which mainly originate from the 3d magnetic electrons of Co atoms, are modulated by medium and high entropized rare earth due to their exchange interactions. The magnetic moment of Co at the 2c site is larger than that of Co at the 3g site, which is due to the electron transformations from magnetic to covalence electron for bonding with the rare earth at the 3g site. Curie temperatures raise with the increasing 3d magnetic electron numbers of Co atom.

Analysis of the formation mechanism of ceramic grains and mechanical properties of Mo2FeB2-based cermets by valence electron structure

The valence electron structures (VES) of Mo2FeB2-based cermets were constructed based on the empirical electron theory of solids and molecules (EET). The formation mechanism of grains and the influence of grain morphologies on the mechanical properties of the materials were explained in accordance with the calculated phase structure formation factors (S') and the interface electron structure (σN: the number of atom state groups, ∆ρ': electron density difference, and ρ': electron density), respectively. The results indicated that the morphologies of the Mo2FeB2 hard phase grains were reflected by the S' value of the distinct crystal planes. The progressive decrease in the Mo/B atomic ratio aggravated the differences between the S(210)' and S(001)' values and promoted the preferential growth of the hard phase grains along the [001] direction. This resulted in an increase in the (210)/(100) interface area, with the grains gradually forming an elongated structure. However, it was noticed that as the ratio of Mo to B increased, the value of |S(210)' − S(001)'| gradually tended toward 0, which allowed the elongated hard phase grains to transform into quasi-equiaxial grains. In addition, the maximum decrease in the σN value recorded was over 2500 when the Mo to B ratio increased continuously, indicating that the bonding strength at the (210)/(100) interface between the hard and binder phases was better at low Mo/B atomic ratios than at high Mo/B atomic ratios. This helped improve the fracture toughness and transverse rupture strength of the Mo2FeB2-based cermets.

Investigation on the Atomic Mechanism for Grain Refinement of Magnesium Alloys by Mg-Zr Master Alloy.

The valence electron structure, bond energy, and cohesive energy of Mg, Zr, and α-Mg containing Zr, and α-Zr containing Mg crystals were calculated using the empirical electron theory of solids and molecules (EET). The calculation results show that the bond and cohesive energies of Zr were much greater than those of Mg, so Zr particles could precipitate ahead of α-Mg in general magnesium alloy melts or insoluble Zr particles exist when the magnesium melt temperature is relatively low. The bond energy of α-Zr decreases with the increase in Mg content; therefore, at the end of the growth of Zr particles, the remaining Zr atoms in the melt exist in the form of Mg-Zr clusters. In order to reduce the surface energy of Zr particles, the outer surface of Zr particles tends to terminate with a Zr-Mg atomic layer, that is, a stable two-dimensional Zr-Mg atomic layer is formed first on the (0001) crystal surface of the outermost surface of Zr particles. Furthermore, on the basis of the calculated results, a complementary criterion to the edge-to-edge model of heterogeneous nucleation is also proposed. {ure and single Zr particles cannot become the heterogeneous nucleus of α-Mg, but when there is an atomic layer of two-dimensional Zr-Mg on its surface, the nucleation of particles can be activated. Mg atoms in the liquid phase preferentially attach to the Zr-Mg/Mg-Zr atomic layer on the surface of Zr particles to grow and form a stable ordered structure, which lastly transforms Zr particles into efficient heterogeneous cores.

Strong Dependence of Thermal and Magnetic Properties on Valence Electron Structures in R2Co17 (R = Rare Earth) Intermetallics.

The valence electron structures (VESs) and thermal and magnetic properties of R2Co17 intermetallics with rhombohedral (R = Ce, Pr, Nd, Sm, Gd, and Tb) and hexagonal (R = Y, Dy, Ho, and Er) structures are studied systematically with the empirical electron theory of solids and molecules (EET). The calculated values, which cover the bond length, cohesive energy, melting point, magnetic moment, and Curie temperature, fit the experimental ones well. The study reveals that the thermal and magnetic properties of R2Co17 are strongly related to their VESs. It shows that the properties of R2Co17 can be modulated by covalence electron number nc/atom for cohesive energy and melting point, the 3d magnetic electrons of various Co sublattices for magnetic moment, the electron transformation from covalence electrons to 3d magnetic electrons for the moments of various Co sublattices, and molecular moment for Curie temperature. The structural stability of R2Co17 depends upon the distribution probability of covalence electrons on various bonds. The pseudobinary La-Co 2:17 phase can be stabilized by doping a transition metal into La2Co17 by modulating the covalence electron number per Co atom to be very close to the stable nc/Co range of rhombohedral LR2Co17 (LR=light rare earth).

Study on properties of single-phase high entropy alloys with FCC structure based on the empirical electron theory

The valence electron structures, thermal properties, hardness and magnetic moments of single-phase high entropy alloys with the face-centered cubic structure have been first investigated with the empirical electron theory of solids and molecules. The theoretical bond lengths agree with the experimental ones well. The calculated melting points of CrFeCoNi, CrMnFeCoNi and CrFeCoNiCu alloys are consistent with their differential thermal analysis (DTA) measured ones. The calculated magnetic moments of ferromagnetic FeCoNi and FeCoNiX0.25 (XAl or Si) alloys agree with the observed ones well. The physical properties of these alloys are strongly associated with their valence electron structures. It is suggested that the melting point, cohesive energy, hardness and magnetic moments of the face-centered cubic high entropy alloys are mainly modulated by bonding factor f, covalent electrons per atom nc/atom, covalence electron pair nA and 3d magnetic electron, respectively.

Theoretical Calculation and Analysis of Coherent Interfacial Energy between B1-Type Carbides and FCC Iron Matrix

The valence electron structures (VES) of unit cells of the FCC iron matrix (γ) and B1-type carbides (ξ) in γ-Fe-M-C alloy systems (M=Nb, Ti, and V) were calculated using the empirical electron theory of solids and molecules (EET). Based on the results, the coherent interfacial energy between B1-type carbides and FCC iron matrix in γ-Fe-M-C alloy system was calculated and analyzed by combining EET and the discrete lattice plane-nearest neighbor broken bond (DLP-NNBB) method with covalent bond energy. The results showed that the solid solution strengthening effect was produced by the solute phase boundary segregation of the alloy elements at the γ/ξ interface, which enhanced the covalent bond network. The Nb alloy system had the largest segregation effect in γ-Fe-M-C alloy system. Moreover, the γ/ξ interfacial energy varies with different alloy elements over the range of 0.4-1.3 J/m2, and the γ-Fe-Nb-C alloy system has the largest coherent interfacial energy.The proposed theoretical method is consistent with the theoretical values calculated using other models, as well as empirical values. This indicates that the method proposed in this work is feasible for providing theoretical analysis and guidance.

Theoretical calculation of elastic properties and electronic structure of B2 iron aluminides and ternary iron—aluminum alloys

The mechanical properties of FeAl and ternary Fe–X–Al (X = Cr, Mo) alloys are investigated using first-principles density functional theory (DFT), with the valence electron structures also being determined using the empirical electron theory of solids and molecules. The structural attributes of FeAl are fitted using an E–V curve, and the stable structures of the ternary alloys are systematically predicted along with their respective elastic constants and phonon frequencies. The bonding nature in FeAl is partly defined by covalence with orbital hybridization, which explains its intrinsic brittleness. The micro-mechanism by which the ductility of FeAl is improved by Cr or Mo addition is as follows: Cr or Mo addition increases the cohesive capacity of the bonds in FeAl; s, p, and d orbital electrons of the alloying element are mainly involved in the hybridization of FeAl; and the alloying elements increase the electron density of Fe and Al atomic bonding.

The study on order behavior and electronic structure of flaky FeSiAl powder

In this paper, the grain growth, lattice strain, order behavior and electronic structure of FeSiAl powder were studied. Only the disorder bcc α-Fe peaks were exhibited after milling, and as the ball milling time increases, the internal strain rose and the grain size decreased. When the anneal temperature reached 773 K, we could see the obvious DO3 superlattice peak at (1 1 1), (2 0 0) and (3 1 1) plane. At the same time, the internal strain decreased and the grain size rose with the increment of annealing temperature. Annealing at temperatures above 773 K results in a long-range order (LRO) parameter about 0.67–0.76. This high LRO parameter further supports the observation of the formation of order DO3 structures. Furthermore, we found that the interaction between Fe and Si, Al atoms can decrease magnetic moment of the Fe atom. By the calculation of the empirical electron theory of solids and molecules, we confirmed that grinding process could change the electronic structure and the bond length difference ΔD of powder milled for 20 h had the smallest values.

Studies on Formation Mechanism of In Situ Particles During Laser Direct Deposition of Fe-Based Composite Coatings with Valence Electron Structure Parameters

In this study, the formation regularity of C-Cr, C-Fe, and C-Fe-Cr in situ particles during the laser direct deposition of Fe-based composite coatings was theoretically investigated using the phase stability (PS) and phase formation ability (PFA) calculated based on the empirical electron theory of solids and molecules (EET). The calculation results showed that Cr7C3, Cr3C2, and Fe3C are more likely to appear during the laser direct deposition of Fe-based composite coatings because they have ideal PS and PFA values in comparison with Cr3C, Cr23C6, Fe7C3, Fe23C6, and Fe4C compounds. The addition of Cr is beneficial for the formation of (Fe, Cr)3C compounds when the Cr substitution ratio of Fe atoms is within 33.3 pct, whereas it is easier for the (Cr, Fe)7C3 and Cr7C3 compounds to appear in the alloy coatings when the Cr substitution ratio of Fe atoms is greater than 57.1 pct. These investigation results will provide theoretical guidance for the composition design and performance optimization of in situ particle-reinforced Fe-based composite coatings.

Analysis of Transition Mechanism of Cubic Boron Nitride Single Crystals under High Pressure-High Temperature with Valence Electron Structure Calculation**Supported by the National Natural Science Foundation of China under Grant No 51272139.

The possibilities of hexagonal boron nitride (hBN) and lithium boron nitride (Li3BN2) transition into cubic boron nitride (cBN) under synthetic pressure 5.0 GPa and synthetic temperature 1700 K are analyzed with the use of the empirical electron theory of solids and molecules. The relative differences in electron density are calculated for dozens of bi-phase interfaces hBN/cBN, Li3BN2/cBN. These relative differences of hBN/cBN are in good agreement with the first order of approximation (), while those of Li3BN2/cBN are much greater than 10%. This analysis suggests that Li3BN2 is impossible to be intermediate phase but is a catalyst and cBN should be directly transformed by hBN.

Strength design of Zr(x)Ti(x)Hf(x)Nb(x)Mo(x) alloys based on empirical electron theory of solids and molecules

In this paper, the valence electron structure parameters of Zr(x)Ti(x)Hf(x)Nb(x)Mo(x) alloys were calculated based on the empirical electron theory of solids and molecules (EET), and their performance through these parameters were predicted. Subsequently, the alloys with special valence electron structure parameters were prepared byarc melting. The hardness and high-temperature mechanical properties were analyzed to verify the prediction. Research shows that the influence of shared electron number nA on the strongest bond determines the strength of these alloys and the experiments are consistent with the theoretical prediction.

A novel model to account for the heterogeneous nucleation mechanism of α-Mg refined with Al4C3 in Mg-Al alloy

To explore the heterogeneous nucleation mechanism of Mg-Al alloy refined by Al4C3, the valence electron structure and cohesive energy of Al4C3 crystal were calculated using the empirical electron theory of solids and molecules. A novel model to account for heterogeneous nucleation process of α-Mg on Al4C3 is described. The weak bonds exist in the surface of Al4C3 might leads to the replacement of atoms in Al4C3 surface by Mg atoms in melt, which ultimately result in easily stacking of Mg atoms on the newly formed surface of Al4C3. This model also indicates that Mg-Al atom cluster preferentially occupies the atom vacancies on Al4C3 surface in comparison to Mg-Mg atom cluster, which can decrease the refining efficiency of Al4C3 in high Al containing magnesium alloys.

Valence electron structure model of spall strength in middle carbon steel

A phenomenological theory to model spall strength in middle carbon steel was proposed by using empirical electron theory of solids and molecules (EET). Under plate impact load (strain rate, 105–106 s−1), valence electron structure (VES) of α-Fe, α-Fe-C, and ε-Fe3C phases have obvious change than quasi-static load (strain rate, 10−3–10−2 s−1). Theoretical spall strength of ASTM1045 were calculated at plate impact pressure range of 5.37–8.17 GPa. Experimental spall strength were experimented by using 57 mm-diameter, 12.5 m-long single-stage gas gun and velocity interferometer system for any reflector (VISAR). The relative error of theoretical and experimental spall strength is less than 7.6%.

Effect of the new type metal electrode on the properties of ferroelectric ceramic

ABSTRACTBased on the empirical electron theory of solids and molecules, the valence-electron structures (VES) and the surface energy of the Ni‒Cu electrode of Pb(Ti, Zr)O3 piezoelectric ceramics were calculated by using the empirical electron surface model. The relationship between VES and the wettability of electrode materials was determined firstly. The results indicate that the increase of wettability results from the reduction of the surface energy when the Cu content of Ni1−xCux gradually increases. The Pb(Ti, Zr)O3 ceramics brazed with metal electrode were fabricated, and the experimental results show that the trend of the wettability is in agreement with the calculation results.

Correlation between valence electronic structure and magnetic properties in RCo5 (R = rare earth) intermetallic compound**Project supported by the National Natural Science Foundation of China (Grant No. 11274110).

The magnetisms of RCo5 (R = rare earth) intermetallics are systematically studied with the empirical electron theory of solids and molecules (EET). The theoretical moments and Curie temperatures agree well with experimental ones. The calculated results show strong correlations between the valence electronic structure and the magnetic properties in RCo5 intermetallic compounds. The moments of RCo5 intermetallics originate mainly from the 3d electrons of Co atoms and 4f electrons of rare earth, and the s electrons also affect the magnetic moments by the hybridization of d and s electrons. It is found that moment of Co atom at 2c site is higher than that at 3g site due to the fact that the bonding effect between R and Co is associated with an electron transformation from 3d electrons into covalence electrons. In the heavy rare-earth-based RCo5 intermetallics, the contribution to magnetic moment originates from the 3d and 4f electrons. The covalence electrons and lattice electrons also affect the Curie temperature, which is proportional to the average moment along the various bonds.

Study based on the analysis of valence electron structure for adiabatic shear sensitivity of 30CrMnMo and C45E4 steel in process of high‐speed penetration

AbstractIn this paper, the influence of valence electron structure parameters on the adiabatic shearing sensitivity has been studied for two grade steels (30CrMnMo and C45E4) as a function of covalent pair number and lattice electron number by empirical electron theory of solids and molecules in high‐speed penetration process. The research shows that the adiabatic shearing sensitivity increases with the increase of the covalent electron pair number nA, decreases with the increase of the lattice electron number nl. The nA of each structure unit in 30CrMnMo steel is larger than that in C45E4steel, the nl of each structure unit in 30CrMnMo steel is smaller than that in C45E4steel. Therefore, the adiabatic shearing sensitivity is higher for 30CrMnMo targets damaged by adiabatic shear failure, and yet C45E4 targets were damaged by ductile fracture without any adiabatic shear band. The basis can be provided for appropriately selecting and designing materials with different adiabatic shearing sensitivity by studying the specific alloy elements on the influence of adiabatic shearing sensitivity in valence electron structure level.

Effect of Rare Earth Elements on Isothermal Transformation Kinetics in Si-Mn-Mo Bainite Steels

Isothermal heat treatments to Si-Mn-Mo steel specimens were performed, and time-temperature-transformation curves (C-curves) were plotted by DIL805A/D differential dilatometer. The effect of rare earth (RE) elements on bainite transformation kinetics was systematically studied by adopting the empirical electron theory of solids and molecules, Johnson-Mehl-Avrami equation calculation, dilatometry, and metallography. Experimental results show that the addition of RE in Si-Mn-Mo bainite steels leads to the C-curves moving to bottom right and prolongs incubation period of bainite transformation. Moreover, RE addition increases the values of phase structure factors (n A, F C D ) and activation energy of bainite transformation, inhibits the formation of granular bainite, and refines microstructures of bainitic ferrite and substructures. During the bainite transformation process, bainite transformation is delayed due to the drag effect, which is induced by the segregation of RE at the ferrite interphase and the retardation of Fe-C-RE (segregation units) on carbon diffusion.

Electronic theoretical model of static and dynamic strength of steels

Valence electron structure has an intrinsical influence on the physical properties of material. On the basis of empirical electron theory of solids and molecules, combining with dynamic mechanical process of calculating steel, we constructe a new model for calculating static and dynamic strengths of steel. The static (dynamic) strengths of multi-composition steel, predicted by the proposed model, accord well with the experimental values. It is the first time to introduce the valence electron structure into the model for predicting dynamic properties.

Research of Cr1-xMxN's (M=Al,V,Ti,etc.,x=0.5) Coating Valence Electron Structure Calculation and Wear-Resisting Performance

Based on empirical electron theory of solid and molecule (EET, Empirical Electron Theory of Solids and Molecules) ,this paper calculated the Cr1 – xMxN molecular coating’s valence electron structure of the phase space and the valence electron structure of coating matrix phase out of phase interface. By analysing microscopic valence electron structure, we discussed the alloy elements’ influence on this series of coatings’ resistance. And we found that V elements can significantly increase the metal chromium nitride’s were resistance , element Ti takes the second place, element Al also has some effect.

Theoretical Calculation of Electronic Structure and Mechanical Properties of Quenched Carbon Structural Steel

To investigate the fatigue property of carbon structural steel in theory, the microstructure and properties of quenched martensite must be studied in detail. In this paper, the electronic structure and mechanical properties of carbon structural steel in quenched state were calculated by the empirical electron theory of solids and molecules (EET). The relationship between electronic structure parameters and mechanical properties of martensite was investigated. The mechanical properties of quenched carbon structural steel were calculated theoretically, and the result of theoretical calculation is consistent with the experiment result.