Correlation of work function and stacking fault energy through Kelvin probe force microscopy and nanohardness in diluteα-magnesium

Electronic interactions of the Group 2A elements with magnesium have been studied through the dilute solid solutions in binary Mg-Ca,Mg-Sr and Mg-Ba systems.This investigation incorporated the difference in the‘Work Function'(ΔWF)measured via Kelvin Probe Force Microscopy(KPFM),as a property directly affected by interatomic bond types,i.e.the electronic structure,nanoindentation measurements,and Stacking Fault Energy values reported in the literature.It was shown that the nano-hardness of the solid-solutionα-Mg phase changed in the order of Mg-Ca>Mg-Sr>Mg-Ba.Thus,it was shown,by also considering the nano-hardness levels,that SFE of a solid-solution is closely correlated with its‘Work Function'level.Nano-hardness measurements on the eutectics andΔWF difference between eutectic phases enabled an assessment of the relative bond strength and the pertinent electronic structures of the eutectics in the three alloys.Correlation withΔWF and at least qualitative verification of those computed SFE values with some experimental measurement techniques were considered important as those computational methods are based on zero Kelvin degree,relatively simple atomic models and a number of assumptions.As asserted by this investigation,if the results of measurement techniques can be qualitatively correlated with those of the computational methods,it can be possible to evaluate the electronic structures in alloys,starting from binary systems,going to ternary and then multi-elemental systems.Our investigation has shown that such a qualitative correlation is possible.After all,the SFE values are not treated as absolute values but rather become essential in comparative investigations when assessing the influences of alloying elements at a fundamental level,that is,free electron density distributions.Our study indicated that the principles of‘electronic metallurgy'in developing multi-elemental alloy systems can be followed via practical experimental methods,i.e.ΔWF measurements using KPFM and nanoindentation.

Effect of stacking fault energy on mechanical properties of ultrafine-grain Cu and Cu-Al alloy processed by cold-rolling

Cu,Cu-2.2%Al and Cu-4.5%Al with stacking fault energies（SFE） of 78,35 and 7 mJ/m2 respectively were processed by cold-rolling（CR） at liquid nitrogen temperature（77 K） after hot-rolling.X-ray diffraction measurements indicate that a decrease in SFE leads to a decrease in crystallite size but increase in microstrain,dislocation and twin densities of the CR processed samples.Tensile tests at room temperature indicate that as the stacking fault energy decreases,the strength and ductility increase.The results indicate that decreasing stacking fault energy is an optimum method to improve the ductility without loss of strength.

Stacking fault energy and electronic structure of molybdenum under solid solution softening/hardening

Ab initio calculations are used to understand the fundamental mechanism of the solid solution softening/hardening of the Mo-binary system.The results reveal that the Mo-Ti,Mo-Ta,Mo-Nb,and Mo-W interactions are primarily attractive with negative heats of formation,while the interactions of Mo-Re,and Mo-Zr would be mainly repulsive with positive heats of formation.It is also shown that the addition of Re and Zr would cause the solid solution softening of Mo by the decrease of the unstable stacking fault energy and the increase of ductility.On the contrary,the elements of W,Ta,Ti,and Nb could bring about the solid-solution hardening of Mo through the impediment of the slip of the dislocation and the decrease of ductility.Electronic structures indicate that the weaker/stronger chemical bonding due to the alloying elements should fundamentally induce the solid solution softening/hardening of Mo.The results are discussed and compared with available evidence in literatures,which could deepen the fundamental understanding of the solid solution softening/hardening of the binary metallic system.

Stacking fault energy,yield stress anomaly, and twinnability of Ni_3Al:A first principles study

Using first principles calculations combined with the quasiharmonic approach, we study the effects of temperature on the elastic constants, generalized stacking fault energies, and generalized planar fault energies of Ni3Al. The antiphase boundary energies, complex stacking fault energies, superlattice intrinsic stacking fault energies, and twinning energies decrease slightly with temperature. Temperature dependent anomalous yield stress of Ni3Al is predicted by the energybased criterion based on elastic anisotropy and antiphase boundary energies. It is found that p increases with temperature and this can give a more accurate description of the anomalous yield stress in Ni3Al. Furthermore, the predicted twinnablity of Ni3Al is also decreasing with temperature.

EFFECT OF Cr AND Al CONTENT ON THE STACKING FAULT ENERGY IN r-Fe-Mn ALLOYS

The effects of Cr and Al content were investigated on the stacking fault energy in austenitic Fe-31Mn-(0-7.26)Cr-0.96C and Fe-31Mn-(0-8.68)Al-0.85C alloys by the thermodynamic analysis. The results show that the additions of chromium or aluminum increase the non-magnetic component of the stacking fault energy in the γ-Fe-Mn alloys, and the effect of aluminum is larger than that of chromium. The change in the magnetic entropy caused in the antiferromagnetic transition increases the free energy difference between the γ and s phases in the γr-Fe-Mn alloys. The effects of chromium and aluminum on the magnetic component were discussed on the basis of the influence of both upon the antiferromagnetic transition in the γ-Fe-Mn alloys.

Variation in Creep Rupture of γ′ Strengthened Superalloys with Stacking Fault Energy of Matrices

The correlation between the creep rupture behaviour and the stacking fault energy of matrices of γ′strengthened superalloys has been studied dur- ing constant load creep.At high temperature and intermediate stress,the creep rupture time and strain strongly depend on the stacking fault energy of matrices rather than the creep friction stress,but at higher stress,the role of grain boundary carbides becomes more obvious. However,in the considerably extensive stress range investigated here,the mean creep rate is a power function of the stacking fault energy of matrices and the power index decreases with in- creasing initial applied stress.Particularly,at inter- mediate stresses the product of this index and the initial applied stress compensated by the shear modulus is same for two series of superalloys. Hence,this product may be a criterion predicting that the matrix deformation controls high tempera- ture creep rupture.

Stacking fault probability and stacking fault energy in CoNi alloys

The stacking fault probability of CoNi alloys with different contents of Ni was measured by X ray diffraction methods. The results show that the stacking fault decreases with increasing Ni content and with increasing temperature. The thermodynamical calculation has found an equation that can express the stacking fault energy γ of CoNi at temperature T . The phase equilibrium temperature depends on the composition of the certain alloy. The relationship between stacking fault energy γ and stacking fault probability P sf is determined.

An efficient scheme for accelerating the calculation of stacking fault energy in multi-principal element alloys

We present the High-Throughput Computing and Statistical Analysis(HCSA)scheme,which efficiently and accurately predicts the stacking fault energies(SFEs)of multi-principal element alloys(MPEAs).Our approach estimates the SFE of a single complex supercell by averaging numerous SFEs from small supercells,resulting in superior accuracy compared to traditional density functional theory(DFT)calculations.To validate our scheme,we applied it to NiFe and Ni_(10)Co_(60)Cr_(25)W_(5)alloys,achieving an SFE error of only 11%,in contrast to the 45%error obtained from traditional DFT calculations for NiFe.We observed a strong correlation between the average SFEs of samples with the same valence electron concentration as that of the experimental data.Our scheme provides an efficient and reliable tool for predicting SFEs in MPEAs and holds the potential to significantly accelerate materials design and discovery processes.

Predicting the variation of stacking fault energy for binary Cu alloys by first-principles calculations

The variation of stacking fault energy(SFE)in a number of binary Cu alloys is predicted through considering the Suzuki segregation by the full potential linearly augmented plane wave(FPLAPW)method.The calculated results show that some solute atoms(Mg,Al,Si,Zn,Ga,Ge,Cd,Sn,and Pb),which prefer to form the Suzuki segregation,may decrease the value of SFE;while the others(Ti,Mn,Fe,Ni,Zr,Ag,and Au),which do not cause the Suzuki segregation may not decrease the SFE.Furthermore,it is interesting to find that the former alloying elements are located on the right of Cu group while the latter on the left of Cu group in the periodic table of elements.The intrinsic reasons for the new findings can be traced down to the valences electronic structure of solute and Cu atoms,i.e.,the similarity of valence electronic structure between solute and Cu atoms increases the value of SFE,while the difference decreases the value of SFE.

Evolution of microstructure and texture of cold-drawn polycrystalline Ag with low stacking fault energy

The evolution of microstructure and texture for drawn polycrystalline Ag was investigated by transmission electron microscopy and electron backscattering diffraction.The results show that there are deformation twins and some un-tangled discrete dislocations at low strains.When the strain is increased to 0.58,a lot of high density dislocation walls and microbands come into being.At the same time,some twins lose the twinning relationship of 60°<111>.At a strain of 0.94,both dislocation boundaries and twin boundaries will rotate to the axis direction of wires and the shear bands start to appear.When the strain is higher than 1.96,most of the boundaries are parallel to the drawn direction.Texture analysis indicates that with the strain increasing,the volume fraction of complex texture component decreases,but<111>and<100>texture components increase.However,the variation in the volume fraction of each texture component as strains is not evident when the strains are higher than 0.58.For polycrystalline Ag with low stacking fault energy,complex texture components are easily formed.

Texture and Microstructure Evolution During Tensile Testing of TWIP Steels with Diverse Stacking Fault Energy

Texture and microstructure evolution in two kinds of the twinning induced plasticity （TWIP） steels （Fe-Mn- Si-AI and Fe-Mn-C） with diverse stacking fault energies during tensile testing were investigated by interrupted testing. The strain-hardening rate curves of the two steels were quite similar, but the texture characterization curves （maximum of pole density measured by X-ray diffraction） were varied. According to the curvature of max pole density curves, the evolution of the texture and the microstructure can be divided into three stages： low strain stage, medium stage and high stage. In low strain stage the difference of the microstructure came from the intensity of dislocation, which was much smaller in Fe-Mn-Si-AI. The main difference of the microstructure in medium and high strain stages originated from the numbers of activated twin systems. There were more than one twin systems activated in Fe-Mn-C, while only a single twin system activated in Fe-Mn-Si-AI. Texture showed various differences in the whole tensile process because it was affected by their micromechanism, such as concentration of the dislocation and the activation of twin systems. Texture in low strain stage was connected with annealing twin; the evolution ofthe texture was mainly induced by deformation twin generation. More than one activated twin systems in medium and high stages may counteract each other in the view of concentration of the grain orientations.

Influence of Temperature on Stacking Fault Energy and Creep Mechanism of a Single Crystal Nickel-based Superalloy

The influence of temperatures on the stacking fault energies and deformation mechanism of a Re- containing single crystal nickel-based superalloy during creep at elevated temperatures was investigated by means of calculating the stacking fault energy of alloy, measuring creep properties and performing contrast analysis of dislocation configuration. The results show that the alloy at 760 ℃ possesses lower stacking fault energy, and the stacking fault of alloy increases with increasing temperature. The defor- mation mechanism of alloy during creep at 760 ℃ is 7＇ phase sheared by 〈110〉 super-dislocations, which may be decomposed to form the configuration of Shockley partials plus super-lattice intrinsic stacking fault, while the deformation mechanism of alloy during creep at 1070 ℃ is the screw or edge super- dislocations shearing into the rafted 7＇ phase. But during creep at 7（50 and 980 ℃, some super- dislocations shearing into 7＇ phase may cross-slip from the {111} to {100} planes to form the K-W locks with non-plane core structure, which may restrain the dislocations slipping to enhance the creep resis- tance of alloy at high temperature. The interaction between the Re and other elements may decrease the diffusion rate of atoms to improve the microstructure stability, which is thought to be the main reason why the K-W locks are to be kept in the Re-containing superalloy during creep at 980 ℃.

Effect of Carbon Content on Stacking Fault Energy of Fe-20Mn-3Cu TWIP Steel

The influence of carbon content on the stacking fault energy （SFE） of Fe-20Mn-3Cu twinning-induced plasticity （TWIP） steel was investigated by means of X-ray diffraction peak-shift method and thermodynamic modeling. The experimental result indicated that the stacking fault probability decreases with increasing carbon addition, the SFE increases linearly when the carbon content in mass percent is between 0.23 M and 1.41%. The thermody namic calculation results showed that the SFE varied from 22.40 to 29.64 mJ ~ m 2 when the carbon content in mass percent changes from 0.23 % to 1.41%. The XRD analysis revealed that all steels were fully austenitic before and after deformation, which suggested that TWIP effect is the predominant mechanism during the tensile deformation process of Fe-20Mn-3Cu-XC steels.

On the stacking fault forming probability and stacking fault energy in carbon-doped 17 at%Mn steels via transmission electron microscopy and atom probe tomography

Assessing the stacking fault forming probability(P_(sf)) and stacking fault energy(SFE)in medium-or highMn base structural materials can anticipate and elucidate the microstructural evolution before and after deformation.Typically,these two parameters have been determined from theoretical calculations and empirical results.However,the estimation of SFE values in Fe–Mn–C ternary systems is a longstanding debate due to the complicated nature of carbon:that is,whether the carbon doping indeed plays an important role in the formation of stacking faults;and how the amount of carbon atoms exist at grain boundaries or at internal grains with respect to the nominal carbon doping contents.Herein,the use of atom probe tomography and transmission electron microscopy(TEM)unveils the influence of carbondoping contents on the structural properties of dual-phase Fe–17 Mn–x C(x=0–1.56 at%)steels,such as carbon segregation free energy at grain boundaries,carbon concentration in grain interior,interplanar D-spacings,and mean width of intrinsic stacking faults,which are essential for SFE estimation.We next determined the Psfvalues by two different methods,viz.,reciprocal-space electron diffraction measurements and stacking fault width measurements in real-space TEM images.Then,SFEs in the Fe–17 Mn–x C systems were calculated on the basis of the generally-known SFE equations.We found that the high amount of carbon doping gives rise to the increased SFE from 8.6 to 13.5 m J/m^(2)with non-linear variation.This SFE trend varies inversely with the mean width of localized stacking faults,which pass through both other stacking faults and pre-existingε-martensite plates without much difficulty at their intersecting zones.The high amount of carbon doping acts twofold,through increasing the segregation free energy(due to more carbon at grain boundaries)and large lattice expansion(due to increased soluble carbon at internal grains).The experimental data obtained here strengthens the composition-dependent SFE maps for predicting the deformation structure and mechanical response of other carbon-doped high-Mn alloy compositions.

Effective Stacking Fault Energy in Face-Centered Cubic Metals

As a typical configuration in plastic deformations, dislocation arrays possess a large variation of the separation of the partial dislocation pairs in face-centered cubic（fcc） metals. This can be manifested conveniently by an effective stacking fault energy（SFE）. The effective SFE of dislocation arrays is described within the elastic theory of dislocations and verified by atomistic simulations. The atomistic modeling results reveal that the general formulae of the effective SFE can give a reasonably satisfactory prediction for all dislocation types, especially for edge dislocation arrays. Furthermore, the predicted variation of the effective SFE is consistent with several previous experiments, in which the measured SFE is not definite, changing with dislocation density. Our approach could provide better understandings of cross-slip and the competition between slip and twinning during plastic deformations in fcc metals.

Counter-balancing effects of Si on C partitioning and stacking fault energy of austenite in 10Mn quenching and partitioning steel

Silicon is an essential alloying element in quenching and partitioning(Q&P)steels,because it is known to suppress carbide precipitation during partitioning step and promote carbon partitioning to stabilize austenite.When 2 wt%Si was added to 10Mn-2Al-0.2C steel,the size and fraction of the carbides formed during partitioning became smaller than in the Si-free counterpart.Moreover,the suppression of carbide formation promoted C partitioning into austenite as expected.However,austenite stability was always lower with Si under the equivalent partitioning condition because Si effectively decreased the stacking fault energy of austenite.As partitioning progressed,the both yield and tensile strengths of the Si-added steel exceeded that of the Si-free steel with the similar ductility level.This was because Si was an effective solid solution strengthener,and the austenite in the Si-added steel exhibited the appropriate stability to gradually transform into martensite throughout the deformation.The resulting strengthening effect compensated for the softening caused by martensite recovery.Consequently,strain hardening rate decreased continuously throughout deformation,which resulted in high tensile strength and ductility.

The influence of temperature on stacking fault energy in Fe-based alloys

Temperature has great influence on the stacking fault energy (SFE). Both SFE and dγ 0/dT for Fe-based alloys containing substitutional or interstitial atoms increase with increasing temperature. Based on the thermodynamic model of SFE, the equation $\frac{{d\gamma _0 }}{{dT}} = \frac{{d\gamma ^{ch} }}{{dT}} + \frac{{d\gamma ^{se\user1{g}} }}{{dT}} + \frac{{d\gamma ^{MG} }}{{dT}}$ and those expressions for three items involved are established. The calculatedγ 0/dT is generally consistent with the experimental. The influence of chemical free energy on the temperature dependence of SFE is almost constant, and is obviously stronger than that of magnetic and segregation contributions. The magnetic transition and the segregation of alloying elements at stacking faults cause a decrease in SFE of the alloys when temperature increases; that is, dγ MG/dT<0 and dγ seg/dT<0. Meanwhile, such an influence decreases with increasing temperature, except for the dγ seg/dT} of Fe?Mn?Si alloys. With these results, the experimental phenomena that the SFE of Fe-based alloys is not zero at the thermo-dynamically equilibrated temperature (T 0) of the λ and ε phases and they are positive both atT>T 0 andT<T 0 can be reasonably explained.

Determination of stacking fault energies in a high-Nb TiAl alloy at 298 K and 1273 K

The stacking fault energies of Ti-46Al-8.5Nb-0.2W alloy at 298 K and 1273 K were determined. The principle for the determination of the stacking fault energies is based on the fact that the stacking fault energy and the elastic interaction energy acting on the dissociated partial dislocations are equal. After the compress deformations with the strain of 0.2% at 298 K and 1273 K, and water quench to maintain the dislocation structures deformed at 1273 K, the dissociation distances between two partial dislocations were determined by weak beam transmission electron microscopy (WBTEM) technique. Based on these dissociation distances and the corresponding calculation method, the stacking fault energies were determined to be 77-81 mJ/m2 at 298 K and to be 57-60mJ/m2 at 1273 K respectively.

First-principles study of the effects of selected interstitial atoms on the generalized stacking fault energies, strength, and ductility of Ni

We analyze the influences of interstitial atoms on the generalized stacking fault energy （GSFE）, strength, and ductility of Ni by first-principles calculations. Surface energies and GSFE curves are calculated for the （112） （111） and / 101） （ 1 1 1） systems. Because of the anisotropy of the single crystal, the addition of interstitials tends to promote the strength of Ni by slipping along the （10T） direction while facilitating plastic deformation by slipping along the （115） direction. There is a different impact on the mechanical behavior of Ni when the interstitials are located in the slip plane. The evaluation of the Rice criterion reveals that the addition of the interstitials H and O increases the brittleness in Ni and promotes the probability of cleavage fracture, while the addition of S and N tends to increase the ductility. Besides, P, H, and S have a negligible effect on the deformation tendency in Ni, while the tendency of partial dislocation is more prominent with the addition of N and O. The addition of interstitial atoms tends to increase the high-energy barrier γmax, thereby the second partial resulting from the dislocation tends to reside and move on to the next layer.

Determination of stacking fault energies in a high-Nb TiAl alloy at 298 K and 1273 K

The stacking fault energies of Ti-46Al-8.5Nb-0.2W alloy at 298 K and 1273 Kwere determined. The principle for the determination of the stacking fault energies is based on thefact that the stacking fault energy and the elastic interaction energy acting on the dissociatedpartial dislocations are equal. After the compress deformations with the strain of 0.2% at 298 K and1273 K, and water quench to maintain the dislocation structures deformed at 1273 K, thedissociation distances between two partial dislocations were determined by weak beam transmissionelectron microscopy (WBTEM) technique. Based on these dissociation distances and the correspondingcalculation method, the stacking fault energies were determined to be 77-81 mJ/m^2 at 298 K and tobe 57-60mJ/m^2 at 1273 K respectively.