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.

Chemical short-range-order induced multiscale strengthening in refractory medium entropy alloys

High/medium entropy alloys(H/MEAs)are generally possible to exhibit chemical short-range order(SRO).However,the complex role of SRO on mechanical properties from nano-scale to meso-scale is still challenging so far.Here,we study the strengthening mechanism and deformation behavior in a model body-centered-cubic HfNbTa MEA by using atomic-scale molecular dynamics,micro-scale dislocation dynamics,and meso-scale crystal plasticity finite element.The SRO inhibits dislocation nucleation at the atomic scale,improving the flow stress.The SRO-induced ultrastrong local stress fluctuation greatly improves the micro-scale dislocation-based strength by the significant dislocation forest strengthening.Moreover,the Ta-rich locally ordered structure leads to an obvious heterogeneous strain and stress partitioning,which forms a strong strain gradient in the adjacent grain interiors and contributes to the strong back-stress-induced strain hardening.

Second Order Parallel Tensors on Quasi-constant Curvature Manifolds

The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold there is no nonzero parallel 2_form. Unless the Ricci principal curvature corresponding to the generator of M is equal to zero.

The Inertial Manifolds for a Class of Higher-Order Coupled Kirchhoff-Type Equations

In this paper, we mainly deal with a class of higher-order coupled Kirch-hoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial manifolds are proved by using spectral gap condition. The main result we gained is that the inertial manifolds are established under the proper assumptions of M(s) and gi(u,v), i=1, 2.

The Inertial Manifold for a Class of Nonlinear Higher-Order Coupled Kirchhoff Equations with Strong Linear Damping

This paper considers the long-time behavior for a system of coupled wave equations of higher-order Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of the inertial manifold while such equations satisfy the spectral interval condition.

基于参数化降阶模型的非线性气动弹性高效分析

针对非线性气动弹性分析时需要在时域求解多个流场参数条件下结构运动方程而造成的计算消耗过大的问题,提出了一种适用于参数变化时非定常流场高效计算的参数化降阶模型,不仅可以应用于计算机翼等结构的总体气动力还可以得到每个时刻的结构表面的流场数据分布,并成功应用于典型机翼的跨声速颤振边界的计算,大大地提高了计算效率.结果显示,单流场条件时降阶模型的计算速度比直接使用时域分析方法提高了3倍;在计算多流场参数条件下,参数化降阶模型相比于使用单流场降阶模型计算速度提高了3.5倍,相较于时域分析方法提高了10倍.

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。

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.

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.

Lattice of Finite Group Actions on Prism Manifolds

The set of finite group actions (up to equivalence) which operate on a prism manifold M, preserve a Heegaard Klein bottle and have a fixed orbifold quotient type, form a partially ordered set. We describe the partial ordering of these actions by relating them to certain sets of ordered pairs of integers. There are seven possible orbifold quotient types, and for any fixed quotient type we show that the partially ordered set is isomorphic to a union of distributive lattices of a certain type. We give necessary and sufficent conditions, for these partially ordered sets to be isomorphic and to be a union of Boolean algebras.

基于改进局部保持投影算法的轴承故障特征提取

在局部保持投影算法中常采用欧氏距离来度量线性数据间的相似性,而在实际工程中欧氏距离并不能准确度量非线性数据间的相似性,从而使算法对高维数据的特征提取性能不佳。针对以上问题提出了基于相关性Rank-order度量的局部保持投影算法,首先应用相关系数计算样本间相关距离实现数据相似性的初步度量,在此基础上再计算Rank-order距离用于评估具有共享邻居的样本间相似性从而得到更有效的相似度矩阵并构建降维模型,最后通过在公开轴承故障数据集和实际采集的轴承数据集上的实验表明,与传统方法相比改进算法对非线性数据有较好的特征提取效果,证明了改进算法的有效性。