Generalization properties of restricted Boltzmann machine for short-range order

A biased sampling algorithm for the restricted Boltzmann machine(RBM) is proposed, which allows generating configurations with a conserved quantity. To validate the method, a study of the short-range order in binary alloys with positive and negative exchange interactions is carried out. The network is trained on the data collected by Monte–Carlo simulations for a simple Ising-like binary alloy model and used to calculate the Warren–Cowley short-range order parameter and other thermodynamic properties. We demonstrate that the proposed method allows us not only to correctly reproduce the order parameters for the alloy concentration at which the network was trained, but can also predict them for any other concentrations.

Characterization of local chemical ordering and deformation behavior in high entropy alloys by transmission electron microscopy

Short-range ordering(SRO)is one of the most important structural features of high entropy alloys(HEAs).However,the chemical and structural analyses of SROs are very difficult due to their small size,complexed compositions,and varied locations.Transmission electron microscopy(TEM)as well as its aberration correction techniques are powerful for characterizing SROs in these compositionally complex alloys.In this short communication,we summarized recent progresses regarding characterization of SROs using TEM in the field of HEAs.By using advanced TEM techniques,not only the existence of SROs was confirmed,but also the effect of SROs on the deformation mechanism was clarified.Moreover,the perspective related to application of TEM techniques in HEAs are also discussed.

SHORT-RANGE ORDER STRUCTURES OF Fe-Ge AMORPHOUS THIN FILMS

The short-range order structures of Fe_xGe_(1-x) amorphous thin films,(x=8.7,19.1 and 28.5%)have been studied by means of X-ray absorption spectrum.The nearest neighbors around a Ge or an Fe atom are constituted by two coordinate sub-shells with a very short dis- tance,In two films with lower Fe content,structural parameters of the nearest neighbors around a Ge atom are very near to that in amorphous germanium,and the positions of Fe at- oms are randomly substitutional.But when x=28.5%,some great changes occur on the short-range order structure of a-Fe_xGe_(1-x) film:its structure deviates from continuous ran- dora network and tends toward dense random packing of atoms.Meanwhile,there is a strong- er interaction between near neighboring Fe-Ge atoms in a-Fe_xGe_(1-x) films.

Electrical Resistivity due to Short-range Order in Ni_2Cr

Residual electrical resistivity of Ni2Cr alloy due to short-range order (SRO) has been calculated at a temperature which is above the transition temperature, Tc, from long-range order to shortrange order. The atomic form factors for Ni and Cr are calculated in the pseudopotential formalism. We discuss the result of our calculations indicating a decrease in the value of residual electrical resistivity due to SRO in the light of experimental resistivity studies done on Ni72.5Cr27.5 and Ni65Cr35.

Observation and computer simulation of multicomponent chemical short-range order (MCSRO) for the bulk metallic glasses

The atomic configuration of chemical short-range order (CSRO) for the Zr-base metallic glasses was investigated by using nano-diffraction and high resolution transmission electronic microscopy (HRTEM) technology with a beam size of 0.5 nm. It is il- lustrated that the pattern of atomic configuration of CSRO might have various compound counterparts because of the chemical inter- action of bonding atoms. Some atomic configuration of MCSRO is similar to the icosahedral structure with 10-fold symmetry of very weak spots. In deed, the nano-beam technology could clearly detect the evolution of atomic configuration in nanometer scale during the transformation from the metallic melt to the primary crystallization. The local atomic configuration of CSRO is also investigated by molecular dynamics simulation (MD) for the Zr2Ni compound in a wider temperature range. The CSRO in the melt could be pic- torially demonstrated as distorted coordination polyhedron of the compound structure and/or the structure similar to cubo-octahedron analogs. The MD simulation illustrates that the atomic packing of long-range order disappears just above the melting point, but the chemical interaction of bonding atoms still exists that leads to form the various CSRO with the atomic configuration similar to stable or metastable unit cell of Zr2Ni compound. The icosahedral polyhedron became more abundance as the overheating temperature was raised.

Prediction of chemical short-range order in high-/medium-entropy alloys

Chemical short-range orders(CSROs),as the built-in sub-nanoscale entities in a high-/medium-entropy alloy(H/MEA),have aroused an ever-increasing interest.With multi-principal elements in an H/MEA to form a complex concentrated solution,a variety of sub-systems of species exist to induce the metastable ordered compounds as candidates for ultimate CSROs.The issues remain pending on the origin of CSROs as to how to judge if CSRO will form in an H/MEA and particularly,what kind of CSROs would be stably produced if there were multiple possibilities.Here,the first-principles method,along with the proposed local formation energy calculation in allusion to the atomic-scale chemical heterogeneities,is used to predict the CSRO formation based on the mechanical stability,thermodynamic formation energy,and electronic characteristics.The simulations are detailed in an equiatomic ternary VCoNi MEA with three kinds of potential compounds,i.e.,L1_(1),L1_(2),and B2,in the face-centered cubic matrix.It turns out that L1_(1)is stable but hard to grow up so as to become the final CSRO.L1_(1)is further predicted as CSROs in CrCoNi,but unable to form in FeCoNi and CrMnFeCoNi alloys.These predictions are consistent with the experimental observations.Our findings shed light on understanding the formation of CSROs.This method is applicable to other H/MEAs to design and tailor CSROs by tuning chemical species/contents and thermal processing for high performance.

Structure and dynamical properties during solidification of liquid aluminum induced by cooling and compression

The structural transformation from a liquid into a crystalline solid is an important subject in condensed matter physics and materials science. In the present study, first-principles molecular dynamics calculations are performed to investigate the structure and properties of aluminum during the solidification which is induced by cooling and compression. In the cooling process and compression process, it is found that the icosahedral short-range order is initially enhanced and then begin to decay, the face-centered cubic short-range order eventually becomes dominant before it transforms into a crystalline solid.

Anomalies in the short-range local environment and atomic diffusion in single crystalline equiatomic CrMnFeCoNi highentropy alloy

Multi-edge extended X-ray absorption fine structure(EXAFS)spectroscopy combined with reverse Monte Carlo(RMC)simulations was used to probe the details of element-specific local coordinations and component-dependent structure relaxations in single crystalline equiatomic CrMnFeCoNi high-entropy alloy as a function of the annealing temperature.Two representative states,namely a high-temperature state,created by annealing at 1373 K,and a low-temperature state,produced by long-term annealing at 993 K,were compared in detail.Specific features identified in atomic configurations of particular principal components indicate variations in the local environment distortions connected to different degrees of compositional disorder at the chosen representative temperatures.The detected changes provide new atomistic insights and correlate with the existence of kinks previously observed in the Arrhenius dependencies of component diffusion rates in the CrMnFeCoNi high-entropy alloy.

Chemical short-range orders in high-/medium-entropy alloys

High(or medium)-entropy alloys(H/MEAs)are complex concentrated solid solutions prone to develop the chemical short-range orders(CSROs),as an indispensable structural constituent to make H/MEAs essentially different from the traditional alloys.The CSROs are predicted to play roles in dislocation behaviors and mechanical properties.So far,the image of CSROs is built up by the theoretical modeling and computational simulations in terms of the conventional concept,i.e.,the preference/avoidance of elemental species to satisfy the short-ranged ordering in the first and the next couple of nearest-neighbor atomic shells.In these simulated CSROs,however,the structural image is missing on the atomic scale,even though the lattice periodicity does not exist in the CSROs.Further,it is pending as to the issues if and what kind of CSRO may be formed in a specific H/MEA.All these are ascribed to the challenge of experimentally seeing the CSROs.Until recently,the breakthrough does not appear to convincingly identify the CSROs in the H/MEAs by using the state-of-the-art transmission electron microscope.To be specific,the electron diffractions provide solid evidence to doubtlessly ascertain CSROs.The structure motif of CSROs is then constructed,showing both the lattice structure and species ordering occupation,along with the stereoscopic topography of the CSRO.It is suggested that the CSROs,as the first landscape along the path of development of the local chemical ordering,offer one more route to substantially develop the ordered structure on the atomic scale in the H/MEAs,parallel to the existing grain-leveled microstructure.The findings of CSROs make a step forward to understand the CSROs-oriented relationship between the microstructure and mechanical properties.This review focuses on the recent progress mainly in the experimental aspects of the identification,structure motif,and mechanical stability in CSROs,along with the chemical medium-range orders as the growing CSROs。

Effect of short-range order on the high-temperature plastic deformation behavior of Ni-Cr-W,Ni-W,and Ni-Re single crystals

The development of a Ni-based superalloy that consists of only theγ-solid-solution phase is highly desired for some applications such as high-temperature gas-cooled reactors in power plants.In this study,the temperature dependence of the plastic deformation behavior of Ni-22Cr-8W(at%)alloy was examined for the first time by using a single crystal,focusing on the influence of the short-range order(SRO),especially upon high-temperature deformation behavior.The critical resolved shear stress(CRSS)for(111)[10¯1]slip exhibited a rapid decrease as the temperature increased at low temperatures but an almost constant value of∼45 MPa between 500 and 900℃.In addition,a slight yield stress anomaly(YSA)was observed,reaching a maximum value at 1000℃.To clarify the influence of the SRO on the YSA behavior,the mechanical properties of Ni-8W and Ni-5Re single crystals were also examined.Similar temperature dependence for the CRSS,including the occurrence of slight YSA,was observed for Ni-8W,in which SRO developed.In the Ni-5Re single crystal in which SRO did not significantly develop,however,the CRSS monotonically decreased as the temperature increased.The results suggest that the presence of SRO in a Ni-Cr-W alloy contributes to the strengthening of the alloy not only at low temperatures but also at high temperatures up to∼1000℃.The results strongly suggested that the pseudo-PLC effect is related to the origin of YSA appearing in Ni-basedγ-solid-solution alloys at high temperatures.

Effect of Cerium on Chemical Short Range Order of Al-Fe-Ce Amorphous Alloy

The chemical short-range order of Al-Fe-Ce amorphous alloy was studied by means of X-ray diffraction (XRD) and differential scanning calorimetry (DSC). It is found that the prepeak position in X-ray diffraction intensity curve shifts to higher angles as the content of Fe increases, but it shifts to smaller angles as the content of Ce increases. The crystallization character of the amorphous alloy changes with the variation of the content of Fe and Ce. Ce can improve the interaction between atoms and the capacity of compound formation, so it is favorable to Al-based glass formability.

Dilute long period stacking/order(LPSO)-variant phases along the composition gradient in a Mg-Ho-Cu alloy

We have systematically investigated the microstructures of as-cast Mg_(97.49)Ho_(1.99)Cu_(0.43)Zr_(0.09)alloy by atomic resolution high-angle annular dark field scanning transmission electron microscopy(HAADF-STEM), revealing the coexistence of 18R, 14H and 24R long period stacking/order(LPSO) phases with fully coherent interfaces along step-like composition gradient in a blocky intermetallic compound distributed at grain boundary. The short-range order(SRO) L1_(2)-type Cu_(6)Ho_(8)clusters embedded across AB’C’A-stacking fault layers are directly revealed at atomic scale. Importantly, the order degree of SRO clusters in the present dilute alloy is significant lower than previous 6M and 7M in-plane order reported in ternary Mg-TM(transition metal)-RE(rare earth) alloys, which can be well matched by 9M in-plane order. This directly demonstrates that SRO in-plane L1_(2)-type clusters can be expanded into more dilute composition regions bounded along the definite TM/RE ratio of 3/4. In addition, the estimated chemical compositions of solute enriched stacking fault(SESF) in all LPSO variants are almost identical with the ideal SESF composition of 9M in-plane order, regardless of the type of LPSO phases. The results further support the viewpoint that robust L1_(2)-type TM_(6)RE_(8)clusters play an important role in governing LPSO phase formation.

Cooling Rate Dependence of Structural Order and Energy Landscape in Zr_(55)Cu_(35)Al_(10) Glass

Classical molecular dynamics simulation has been widely used to study the rapid cooling process of preparing amorphous alloys.However,the simulated cooling rate is several orders of magnitude higher than the experimental cooling rate.In this paper,Zr_(55)Cu_(35)Al_(10)alloy was taken as an example.It is found that adding isothermal annealing at a temperature slightly lower than Tand prolonging isothermal annealing time could effectively reduce the cooling rate.The glassy sample prepared in this way demonstrates significant energetic stability and well-developed short-range and medium-range order.

Short-range ordering and its effects on mechanical properties of high-entropy alloys

In this letter,we briefly summarize experimental and theoretical findings of fo rmation and characterization of short-range orderings(SROs)as well as their effects on the defo rmation behavior of high-entropy alloys(HEAs).We show that existence of SROs is a common yet key structural feature of HEAs,and tuning the degree of SROs is an effective way for optimizing mechanical properties of HEAs.In additional,the challenges concerning about formation mechanism and characterization of SROs in HEAs are discussed,and future research activities in this regard are also proposed.

Chemical short-range order domain in bulk amorphous alloy and the prediction of glass forming ability

Short-range order domains of face central cubic Zr2Ni (F-Zr2Ni) and tetragonal Zr2Ni (T-Zr2Ni) type structure with a size about 1—3 nanometers were observed in bulk amorphous Zr52.5Cu17.9Ni14.6Al10Ti5 alloy by using HREM and nano-beam electron diffraction technique. A new thermodynamic model was formulated based on the concept of chemical short-range order (SCRO). The molar fractions of CSRO and thermodynamic properties in Ni-Zr, Cu-Zr, Al-Zr, Al-Ni, Zr-Ni-Al and Zr-Ni-Cu were calculated. According to the principle of maximum CSRO,GDthe opti-mum glass forming ability (GFA) compositions were predicted in binary and ternary alloys. These results were proved to be valid by the experimental data of crystallizing activation energy, DTx and XRD patterns. The TTT curves of Zr-Ni-Cu alloys calculated based on CSRO model shows that the lowest critical cooling rate GFA is in the order of 100 K/s, which is close to the practical cooling rate for the preparation of Zr-based BMG alloys.

Effect of Short-Range Ordering on the Strength-Ductility Synergy of Fine-Grained Cu–Mn Alloys at Different Temperatures

Uniaxial tensile tests were carried out at room temperature(RT)and 250℃,respectively,to investigate the effect of shortrange ordering(SRO)on the mechanical properties and deformation micromechanism of fine-grained(FG)Cu–Mn alloys with high stacking fault energy.The results show that at RT,with the increase in SRO degree,the strength of FG Cu–Mn alloys is improved without a loss of ductility,and corresponding deformation micromechanism is mainly manifested by a decrease in the size of dislocation cells.In contrast,at a high temperature of 250℃,the SRO degree becomes violently enhanced with increasing Mn content,and the deformation microstructures thus transform from dislocation cells to planar slip bands and even to deformation twins,significantly enhancing the work hardening capacity of the alloys and thus achieving a better strength-ductility synergy of FG Cu–Mn alloys.

Al-Fe-Ce非晶合金中的二十面体短程序

采用X射线衍射(XRD)和高分辨透射电镜(HRTEM)对Al-Fe-Ce非晶合金的局域结构进行了研究,分析了二十面体短程序对非晶合金的形成及热稳定性的影响。Al-Fe-Ce非晶合金中的二十面体短程序均匀弥散分布在非晶基体中,Al颗粒被二十面体化学短程序紧紧包围,二十面体化学短程序阻碍了Al颗粒的长大,面心立方铝(fcc-Al)的形核需要二十面体结构的分解及溶于其中的元素的扩散。二十面体结构单元的存在和均匀分布有利于增强非晶合金的玻璃形成能力和非晶相的热稳定性。

Effect of the repeated melting of mother ingot on the stability of icosahedral phase precipitated from Zr-Al-Ni-Cu-Ag glass

Differential scanning calorimetry (DSC) shows that repeated melting of mother ingot improves the stability of icosahedral phase (I-phase) precipitated from Zr65Al7.5Ni10Cu12.5Ag5 glass. The Kissinger analysis of crystallization implies that the effective activation energies for the pre-cipitation of I-phase and its decomposition considerably increases due to the repeated melting of mother ingot. Repeated melting of mother ingot refines ingot microstructure. Because of structure heredity, the size of the short-range orders (SROs) in the glassy alloy produced from the mother ingot with finer microstructure becomes smaller, which makes the rearrangement of atoms more difficult, and the I-phase more stable.

New insights into the properties of high-manganese steel

In the Collaborative Research Centre 761’s“Steel ab initio-quantum mechanics guided design of new Fe based materials,”scientists and engineers from RWTH Aachen University and the Max Planck Institute for Iron Research conducted research on mechanism-controlled material development with a particular focus on high-manganese alloyed steels.From 2007 to 2019,a total of 55 partial projects and four transfer projects with industrial participation(some running until 2021)have studied material and process design as well as material characterization.The basic idea of the Collaborative Research Centre was to develop a new methodological approach to the design of structural materials.This paper focuses on selected results with respect to the mechanical properties of high-manganese steels,their underlying physical phenomena,and the specific characterization and modeling tools used for this new class of materials.These steels have microstructures that require characterization by the use of modern methods at the nm-scale.Along the process routes,the generation of segregations must be taken into account.Finally,the mechanical properties show a characteristic temperature dependence and peculiarities in their fracture behavior.The mechanical properties and especially bake hardening are affected by short-range ordering phenomena.The strain hardening can be adjusted in a never-before-possible range,which makes these steels attractive for demanding sheet-steel applications.

玻璃形成液体其内在结构中的二十面体

采用分子动力学模拟(molecular dynamics简称MD)的方法,并利用势能曲面(potential energy landscape简称PEL)理论对玻璃形成液体进行研究.在模拟中,键角分布序参数(An)被首先应用于描述二元玻璃形成液体其内在结构(Inherent Structure简称IS)中的结构序.通过计算An,得出了一般液体和IS液体中六面体、八面体和二十面体结构随温度的变化情况.在IS液体中二十面体序所占比例明显多于一般液体.在IS液体中,六面体、八面体的结构随温度的变化不是很明显,而二十面体结构随着温度的变化呈现出一定的规律.得出了二十面体是IS的主要变化的结构.玻璃转变是一般液体接近IS的过程,同时也是二十面体增多的过程.